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isl_pw_multi_aff_from_map: detect easy floors directly from constraints
[isl.git] / isl_test.c
bloba76e32cc99d52780ab6803209a94d45406dabc87
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
26 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
27
28 static char *srcdir;
29
30 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
31 char *filename;
32 int length;
33 char *pattern = "%s/test_inputs/%s.%s";
34
35 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
36 + strlen(suffix) + 1;
37 filename = isl_alloc_array(ctx, char, length);
38
39 if (!filename)
40 return NULL;
41
42 sprintf(filename, pattern, srcdir, name, suffix);
43
44 return filename;
45 }
46
47 void test_parse_map(isl_ctx *ctx, const char *str)
48 {
49 isl_map *map;
50
51 map = isl_map_read_from_str(ctx, str);
52 assert(map);
53 isl_map_free(map);
54 }
55
56 int test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
57 {
58 isl_map *map, *map2;
59 int equal;
60
61 map = isl_map_read_from_str(ctx, str);
62 map2 = isl_map_read_from_str(ctx, str2);
63 equal = isl_map_is_equal(map, map2);
64 isl_map_free(map);
65 isl_map_free(map2);
66
67 if (equal < 0)
68 return -1;
69 if (!equal)
70 isl_die(ctx, isl_error_unknown, "maps not equal",
71 return -1);
72
73 return 0;
74 }
75
76 void test_parse_pwqp(isl_ctx *ctx, const char *str)
77 {
78 isl_pw_qpolynomial *pwqp;
79
80 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
81 assert(pwqp);
82 isl_pw_qpolynomial_free(pwqp);
83 }
84
85 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
86 {
87 isl_pw_aff *pwaff;
88
89 pwaff = isl_pw_aff_read_from_str(ctx, str);
90 assert(pwaff);
91 isl_pw_aff_free(pwaff);
92 }
93
94 int test_parse(struct isl_ctx *ctx)
95 {
96 isl_map *map, *map2;
97 const char *str, *str2;
98
99 str = "{ [i] -> [-i] }";
100 map = isl_map_read_from_str(ctx, str);
101 assert(map);
102 isl_map_free(map);
103
104 str = "{ A[i] -> L[([i/3])] }";
105 map = isl_map_read_from_str(ctx, str);
106 assert(map);
107 isl_map_free(map);
108
109 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
110 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
111 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
112
113 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
114 str2 = "{ [x, y] : 2y >= 6 - x }";
115 if (test_parse_map_equal(ctx, str, str2) < 0)
116 return -1;
117
118 if (test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
119 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
120 return -1;
121 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
122 if (test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }",
123 str) < 0)
124 return -1;
125
126 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
127 map = isl_map_read_from_str(ctx, str);
128 str = "{ [new, old] -> [o0, o1] : "
129 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
130 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
131 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
132 map2 = isl_map_read_from_str(ctx, str);
133 assert(isl_map_is_equal(map, map2));
134 isl_map_free(map);
135 isl_map_free(map2);
136
137 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
138 map = isl_map_read_from_str(ctx, str);
139 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
140 map2 = isl_map_read_from_str(ctx, str);
141 assert(isl_map_is_equal(map, map2));
142 isl_map_free(map);
143 isl_map_free(map2);
144
145 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
146 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
147 if (test_parse_map_equal(ctx, str, str2) < 0)
148 return -1;
149
150 str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
151 str2 = "{ [i,j] -> [min(i,j)] }";
152 if (test_parse_map_equal(ctx, str, str2) < 0)
153 return -1;
154
155 str = "{ [i,j] : i != j }";
156 str2 = "{ [i,j] : i < j or i > j }";
157 if (test_parse_map_equal(ctx, str, str2) < 0)
158 return -1;
159
160 str = "{ [i,j] : (i+1)*2 >= j }";
161 str2 = "{ [i, j] : j <= 2 + 2i }";
162 if (test_parse_map_equal(ctx, str, str2) < 0)
163 return -1;
164
165 str = "{ [i] -> [i > 0 ? 4 : 5] }";
166 str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
167 if (test_parse_map_equal(ctx, str, str2) < 0)
168 return -1;
169
170 str = "[N=2,M] -> { [i=[(M+N)/4]] }";
171 str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
172 if (test_parse_map_equal(ctx, str, str2) < 0)
173 return -1;
174
175 str = "{ [x] : x >= 0 }";
176 str2 = "{ [x] : x-0 >= 0 }";
177 if (test_parse_map_equal(ctx, str, str2) < 0)
178 return -1;
179
180 str = "{ [i] : ((i > 10)) }";
181 str2 = "{ [i] : i >= 11 }";
182 if (test_parse_map_equal(ctx, str, str2) < 0)
183 return -1;
184
185 str = "{ [i] -> [0] }";
186 str2 = "{ [i] -> [0 * i] }";
187 if (test_parse_map_equal(ctx, str, str2) < 0)
188 return -1;
189
190 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
191 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
192 test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
193 test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
194
195 if (test_parse_map_equal(ctx, "{ [a] -> [b] : (not false) }",
196 "{ [a] -> [b] : true }") < 0)
197 return -1;
198
199 if (test_parse_map_equal(ctx, "{ [i] : i/2 <= 5 }",
200 "{ [i] : i <= 10 }") < 0)
201 return -1;
202
203 if (test_parse_map_equal(ctx, "{Sym=[n] [i] : i <= n }",
204 "[n] -> { [i] : i <= n }") < 0)
205 return -1;
206
207 return 0;
208 }
209
210 void test_read(struct isl_ctx *ctx)
211 {
212 char *filename;
213 FILE *input;
214 struct isl_basic_set *bset1, *bset2;
215 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
216
217 filename = get_filename(ctx, "set", "omega");
218 assert(filename);
219 input = fopen(filename, "r");
220 assert(input);
221
222 bset1 = isl_basic_set_read_from_file(ctx, input);
223 bset2 = isl_basic_set_read_from_str(ctx, str);
224
225 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
226
227 isl_basic_set_free(bset1);
228 isl_basic_set_free(bset2);
229 free(filename);
230
231 fclose(input);
232 }
233
234 void test_bounded(struct isl_ctx *ctx)
235 {
236 isl_set *set;
237 int bounded;
238
239 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
240 bounded = isl_set_is_bounded(set);
241 assert(bounded);
242 isl_set_free(set);
243
244 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
245 bounded = isl_set_is_bounded(set);
246 assert(!bounded);
247 isl_set_free(set);
248
249 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
250 bounded = isl_set_is_bounded(set);
251 assert(!bounded);
252 isl_set_free(set);
253 }
254
255 /* Construct the basic set { [i] : 5 <= i <= N } */
256 void test_construction(struct isl_ctx *ctx)
257 {
258 isl_int v;
259 isl_space *dim;
260 isl_local_space *ls;
261 struct isl_basic_set *bset;
262 struct isl_constraint *c;
263
264 isl_int_init(v);
265
266 dim = isl_space_set_alloc(ctx, 1, 1);
267 bset = isl_basic_set_universe(isl_space_copy(dim));
268 ls = isl_local_space_from_space(dim);
269
270 c = isl_inequality_alloc(isl_local_space_copy(ls));
271 isl_int_set_si(v, -1);
272 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
273 isl_int_set_si(v, 1);
274 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
275 bset = isl_basic_set_add_constraint(bset, c);
276
277 c = isl_inequality_alloc(isl_local_space_copy(ls));
278 isl_int_set_si(v, 1);
279 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
280 isl_int_set_si(v, -5);
281 isl_constraint_set_constant(c, v);
282 bset = isl_basic_set_add_constraint(bset, c);
283
284 isl_local_space_free(ls);
285 isl_basic_set_free(bset);
286
287 isl_int_clear(v);
288 }
289
290 void test_dim(struct isl_ctx *ctx)
291 {
292 const char *str;
293 isl_map *map1, *map2;
294
295 map1 = isl_map_read_from_str(ctx,
296 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
297 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
298 map2 = isl_map_read_from_str(ctx,
299 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
300 assert(isl_map_is_equal(map1, map2));
301 isl_map_free(map2);
302
303 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
304 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
305 assert(isl_map_is_equal(map1, map2));
306
307 isl_map_free(map1);
308 isl_map_free(map2);
309
310 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
311 map1 = isl_map_read_from_str(ctx, str);
312 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
313 map2 = isl_map_read_from_str(ctx, str);
314 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
315 assert(isl_map_is_equal(map1, map2));
316
317 isl_map_free(map1);
318 isl_map_free(map2);
319 }
320
321 static int test_div(isl_ctx *ctx)
322 {
323 unsigned n;
324 const char *str;
325 int empty;
326 isl_int v;
327 isl_space *dim;
328 isl_set *set;
329 isl_local_space *ls;
330 struct isl_basic_set *bset;
331 struct isl_constraint *c;
332
333 isl_int_init(v);
334
335 /* test 1 */
336 dim = isl_space_set_alloc(ctx, 0, 3);
337 bset = isl_basic_set_universe(isl_space_copy(dim));
338 ls = isl_local_space_from_space(dim);
339
340 c = isl_equality_alloc(isl_local_space_copy(ls));
341 isl_int_set_si(v, -1);
342 isl_constraint_set_constant(c, v);
343 isl_int_set_si(v, 1);
344 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
345 isl_int_set_si(v, 3);
346 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
347 bset = isl_basic_set_add_constraint(bset, c);
348
349 c = isl_equality_alloc(isl_local_space_copy(ls));
350 isl_int_set_si(v, 1);
351 isl_constraint_set_constant(c, v);
352 isl_int_set_si(v, -1);
353 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
354 isl_int_set_si(v, 3);
355 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
356 bset = isl_basic_set_add_constraint(bset, c);
357
358 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
359
360 assert(bset && bset->n_div == 1);
361 isl_local_space_free(ls);
362 isl_basic_set_free(bset);
363
364 /* test 2 */
365 dim = isl_space_set_alloc(ctx, 0, 3);
366 bset = isl_basic_set_universe(isl_space_copy(dim));
367 ls = isl_local_space_from_space(dim);
368
369 c = isl_equality_alloc(isl_local_space_copy(ls));
370 isl_int_set_si(v, 1);
371 isl_constraint_set_constant(c, v);
372 isl_int_set_si(v, -1);
373 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
374 isl_int_set_si(v, 3);
375 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
376 bset = isl_basic_set_add_constraint(bset, c);
377
378 c = isl_equality_alloc(isl_local_space_copy(ls));
379 isl_int_set_si(v, -1);
380 isl_constraint_set_constant(c, v);
381 isl_int_set_si(v, 1);
382 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
383 isl_int_set_si(v, 3);
384 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
385 bset = isl_basic_set_add_constraint(bset, c);
386
387 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
388
389 assert(bset && bset->n_div == 1);
390 isl_local_space_free(ls);
391 isl_basic_set_free(bset);
392
393 /* test 3 */
394 dim = isl_space_set_alloc(ctx, 0, 3);
395 bset = isl_basic_set_universe(isl_space_copy(dim));
396 ls = isl_local_space_from_space(dim);
397
398 c = isl_equality_alloc(isl_local_space_copy(ls));
399 isl_int_set_si(v, 1);
400 isl_constraint_set_constant(c, v);
401 isl_int_set_si(v, -1);
402 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
403 isl_int_set_si(v, 3);
404 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
405 bset = isl_basic_set_add_constraint(bset, c);
406
407 c = isl_equality_alloc(isl_local_space_copy(ls));
408 isl_int_set_si(v, -3);
409 isl_constraint_set_constant(c, v);
410 isl_int_set_si(v, 1);
411 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
412 isl_int_set_si(v, 4);
413 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
414 bset = isl_basic_set_add_constraint(bset, c);
415
416 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
417
418 assert(bset && bset->n_div == 1);
419 isl_local_space_free(ls);
420 isl_basic_set_free(bset);
421
422 /* test 4 */
423 dim = isl_space_set_alloc(ctx, 0, 3);
424 bset = isl_basic_set_universe(isl_space_copy(dim));
425 ls = isl_local_space_from_space(dim);
426
427 c = isl_equality_alloc(isl_local_space_copy(ls));
428 isl_int_set_si(v, 2);
429 isl_constraint_set_constant(c, v);
430 isl_int_set_si(v, -1);
431 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
432 isl_int_set_si(v, 3);
433 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
434 bset = isl_basic_set_add_constraint(bset, c);
435
436 c = isl_equality_alloc(isl_local_space_copy(ls));
437 isl_int_set_si(v, -1);
438 isl_constraint_set_constant(c, v);
439 isl_int_set_si(v, 1);
440 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
441 isl_int_set_si(v, 6);
442 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
443 bset = isl_basic_set_add_constraint(bset, c);
444
445 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
446
447 assert(isl_basic_set_is_empty(bset));
448 isl_local_space_free(ls);
449 isl_basic_set_free(bset);
450
451 /* test 5 */
452 dim = isl_space_set_alloc(ctx, 0, 3);
453 bset = isl_basic_set_universe(isl_space_copy(dim));
454 ls = isl_local_space_from_space(dim);
455
456 c = isl_equality_alloc(isl_local_space_copy(ls));
457 isl_int_set_si(v, -1);
458 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
459 isl_int_set_si(v, 3);
460 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
461 bset = isl_basic_set_add_constraint(bset, c);
462
463 c = isl_equality_alloc(isl_local_space_copy(ls));
464 isl_int_set_si(v, 1);
465 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
466 isl_int_set_si(v, -3);
467 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
468 bset = isl_basic_set_add_constraint(bset, c);
469
470 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
471
472 assert(bset && bset->n_div == 0);
473 isl_basic_set_free(bset);
474 isl_local_space_free(ls);
475
476 /* test 6 */
477 dim = isl_space_set_alloc(ctx, 0, 3);
478 bset = isl_basic_set_universe(isl_space_copy(dim));
479 ls = isl_local_space_from_space(dim);
480
481 c = isl_equality_alloc(isl_local_space_copy(ls));
482 isl_int_set_si(v, -1);
483 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
484 isl_int_set_si(v, 6);
485 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
486 bset = isl_basic_set_add_constraint(bset, c);
487
488 c = isl_equality_alloc(isl_local_space_copy(ls));
489 isl_int_set_si(v, 1);
490 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
491 isl_int_set_si(v, -3);
492 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
493 bset = isl_basic_set_add_constraint(bset, c);
494
495 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
496
497 assert(bset && bset->n_div == 1);
498 isl_basic_set_free(bset);
499 isl_local_space_free(ls);
500
501 /* test 7 */
502 /* This test is a bit tricky. We set up an equality
503 * a + 3b + 3c = 6 e0
504 * Normalization of divs creates _two_ divs
505 * a = 3 e0
506 * c - b - e0 = 2 e1
507 * Afterwards e0 is removed again because it has coefficient -1
508 * and we end up with the original equality and div again.
509 * Perhaps we can avoid the introduction of this temporary div.
510 */
511 dim = isl_space_set_alloc(ctx, 0, 4);
512 bset = isl_basic_set_universe(isl_space_copy(dim));
513 ls = isl_local_space_from_space(dim);
514
515 c = isl_equality_alloc(isl_local_space_copy(ls));
516 isl_int_set_si(v, -1);
517 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
518 isl_int_set_si(v, -3);
519 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
520 isl_int_set_si(v, -3);
521 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
522 isl_int_set_si(v, 6);
523 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
524 bset = isl_basic_set_add_constraint(bset, c);
525
526 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
527
528 /* Test disabled for now */
529 /*
530 assert(bset && bset->n_div == 1);
531 */
532 isl_local_space_free(ls);
533 isl_basic_set_free(bset);
534
535 /* test 8 */
536 dim = isl_space_set_alloc(ctx, 0, 5);
537 bset = isl_basic_set_universe(isl_space_copy(dim));
538 ls = isl_local_space_from_space(dim);
539
540 c = isl_equality_alloc(isl_local_space_copy(ls));
541 isl_int_set_si(v, -1);
542 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
543 isl_int_set_si(v, -3);
544 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
545 isl_int_set_si(v, -3);
546 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
547 isl_int_set_si(v, 6);
548 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
549 bset = isl_basic_set_add_constraint(bset, c);
550
551 c = isl_equality_alloc(isl_local_space_copy(ls));
552 isl_int_set_si(v, -1);
553 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
554 isl_int_set_si(v, 1);
555 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
556 isl_int_set_si(v, 1);
557 isl_constraint_set_constant(c, v);
558 bset = isl_basic_set_add_constraint(bset, c);
559
560 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
561
562 /* Test disabled for now */
563 /*
564 assert(bset && bset->n_div == 1);
565 */
566 isl_local_space_free(ls);
567 isl_basic_set_free(bset);
568
569 /* test 9 */
570 dim = isl_space_set_alloc(ctx, 0, 4);
571 bset = isl_basic_set_universe(isl_space_copy(dim));
572 ls = isl_local_space_from_space(dim);
573
574 c = isl_equality_alloc(isl_local_space_copy(ls));
575 isl_int_set_si(v, 1);
576 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
577 isl_int_set_si(v, -1);
578 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
579 isl_int_set_si(v, -2);
580 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
581 bset = isl_basic_set_add_constraint(bset, c);
582
583 c = isl_equality_alloc(isl_local_space_copy(ls));
584 isl_int_set_si(v, -1);
585 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
586 isl_int_set_si(v, 3);
587 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
588 isl_int_set_si(v, 2);
589 isl_constraint_set_constant(c, v);
590 bset = isl_basic_set_add_constraint(bset, c);
591
592 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
593
594 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
595
596 assert(!isl_basic_set_is_empty(bset));
597
598 isl_local_space_free(ls);
599 isl_basic_set_free(bset);
600
601 /* test 10 */
602 dim = isl_space_set_alloc(ctx, 0, 3);
603 bset = isl_basic_set_universe(isl_space_copy(dim));
604 ls = isl_local_space_from_space(dim);
605
606 c = isl_equality_alloc(isl_local_space_copy(ls));
607 isl_int_set_si(v, 1);
608 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
609 isl_int_set_si(v, -2);
610 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
611 bset = isl_basic_set_add_constraint(bset, c);
612
613 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
614
615 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
616
617 isl_local_space_free(ls);
618 isl_basic_set_free(bset);
619
620 isl_int_clear(v);
621
622 str = "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
623 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
624 set = isl_set_read_from_str(ctx, str);
625 set = isl_set_compute_divs(set);
626 isl_set_free(set);
627 if (!set)
628 return -1;
629
630 str = "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
631 bset = isl_basic_set_read_from_str(ctx, str);
632 n = isl_basic_set_dim(bset, isl_dim_div);
633 isl_basic_set_free(bset);
634 if (!bset)
635 return -1;
636 if (n != 0)
637 isl_die(ctx, isl_error_unknown,
638 "expecting no existentials", return -1);
639
640 str = "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
641 set = isl_set_read_from_str(ctx, str);
642 set = isl_set_remove_divs_involving_dims(set, isl_dim_set, 0, 2);
643 set = isl_set_fix_si(set, isl_dim_set, 2, -3);
644 empty = isl_set_is_empty(set);
645 isl_set_free(set);
646 if (empty < 0)
647 return -1;
648 if (!empty)
649 isl_die(ctx, isl_error_unknown,
650 "result not as accurate as expected", return -1);
651
652 return 0;
653 }
654
655 void test_application_case(struct isl_ctx *ctx, const char *name)
656 {
657 char *filename;
658 FILE *input;
659 struct isl_basic_set *bset1, *bset2;
660 struct isl_basic_map *bmap;
661
662 filename = get_filename(ctx, name, "omega");
663 assert(filename);
664 input = fopen(filename, "r");
665 assert(input);
666
667 bset1 = isl_basic_set_read_from_file(ctx, input);
668 bmap = isl_basic_map_read_from_file(ctx, input);
669
670 bset1 = isl_basic_set_apply(bset1, bmap);
671
672 bset2 = isl_basic_set_read_from_file(ctx, input);
673
674 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
675
676 isl_basic_set_free(bset1);
677 isl_basic_set_free(bset2);
678 free(filename);
679
680 fclose(input);
681 }
682
683 void test_application(struct isl_ctx *ctx)
684 {
685 test_application_case(ctx, "application");
686 test_application_case(ctx, "application2");
687 }
688
689 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
690 {
691 char *filename;
692 FILE *input;
693 struct isl_basic_set *bset1, *bset2;
694
695 filename = get_filename(ctx, name, "polylib");
696 assert(filename);
697 input = fopen(filename, "r");
698 assert(input);
699
700 bset1 = isl_basic_set_read_from_file(ctx, input);
701 bset2 = isl_basic_set_read_from_file(ctx, input);
702
703 bset1 = isl_basic_set_affine_hull(bset1);
704
705 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
706
707 isl_basic_set_free(bset1);
708 isl_basic_set_free(bset2);
709 free(filename);
710
711 fclose(input);
712 }
713
714 int test_affine_hull(struct isl_ctx *ctx)
715 {
716 const char *str;
717 isl_set *set;
718 isl_basic_set *bset;
719 int n;
720
721 test_affine_hull_case(ctx, "affine2");
722 test_affine_hull_case(ctx, "affine");
723 test_affine_hull_case(ctx, "affine3");
724
725 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
726 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
727 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
728 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
729 set = isl_set_read_from_str(ctx, str);
730 bset = isl_set_affine_hull(set);
731 n = isl_basic_set_dim(bset, isl_dim_div);
732 isl_basic_set_free(bset);
733 if (n != 0)
734 isl_die(ctx, isl_error_unknown, "not expecting any divs",
735 return -1);
736
737 return 0;
738 }
739
740 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
741 {
742 char *filename;
743 FILE *input;
744 struct isl_basic_set *bset1, *bset2;
745 struct isl_set *set;
746
747 filename = get_filename(ctx, name, "polylib");
748 assert(filename);
749 input = fopen(filename, "r");
750 assert(input);
751
752 bset1 = isl_basic_set_read_from_file(ctx, input);
753 bset2 = isl_basic_set_read_from_file(ctx, input);
754
755 set = isl_basic_set_union(bset1, bset2);
756 bset1 = isl_set_convex_hull(set);
757
758 bset2 = isl_basic_set_read_from_file(ctx, input);
759
760 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
761
762 isl_basic_set_free(bset1);
763 isl_basic_set_free(bset2);
764 free(filename);
765
766 fclose(input);
767 }
768
769 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
770 {
771 const char *str1, *str2;
772 isl_set *set1, *set2;
773 int orig_convex = ctx->opt->convex;
774 ctx->opt->convex = convex;
775
776 test_convex_hull_case(ctx, "convex0");
777 test_convex_hull_case(ctx, "convex1");
778 test_convex_hull_case(ctx, "convex2");
779 test_convex_hull_case(ctx, "convex3");
780 test_convex_hull_case(ctx, "convex4");
781 test_convex_hull_case(ctx, "convex5");
782 test_convex_hull_case(ctx, "convex6");
783 test_convex_hull_case(ctx, "convex7");
784 test_convex_hull_case(ctx, "convex8");
785 test_convex_hull_case(ctx, "convex9");
786 test_convex_hull_case(ctx, "convex10");
787 test_convex_hull_case(ctx, "convex11");
788 test_convex_hull_case(ctx, "convex12");
789 test_convex_hull_case(ctx, "convex13");
790 test_convex_hull_case(ctx, "convex14");
791 test_convex_hull_case(ctx, "convex15");
792
793 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
794 "(i0 = 1 and i1 = 0 and i2 = 1) or "
795 "(i0 = 0 and i1 = 0 and i2 = 0) }";
796 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
797 set1 = isl_set_read_from_str(ctx, str1);
798 set2 = isl_set_read_from_str(ctx, str2);
799 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
800 assert(isl_set_is_equal(set1, set2));
801 isl_set_free(set1);
802 isl_set_free(set2);
803
804 ctx->opt->convex = orig_convex;
805 }
806
807 void test_convex_hull(struct isl_ctx *ctx)
808 {
809 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
810 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
811 }
812
813 void test_gist_case(struct isl_ctx *ctx, const char *name)
814 {
815 char *filename;
816 FILE *input;
817 struct isl_basic_set *bset1, *bset2;
818
819 filename = get_filename(ctx, name, "polylib");
820 assert(filename);
821 input = fopen(filename, "r");
822 assert(input);
823
824 bset1 = isl_basic_set_read_from_file(ctx, input);
825 bset2 = isl_basic_set_read_from_file(ctx, input);
826
827 bset1 = isl_basic_set_gist(bset1, bset2);
828
829 bset2 = isl_basic_set_read_from_file(ctx, input);
830
831 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
832
833 isl_basic_set_free(bset1);
834 isl_basic_set_free(bset2);
835 free(filename);
836
837 fclose(input);
838 }
839
840 void test_gist(struct isl_ctx *ctx)
841 {
842 const char *str;
843 isl_basic_set *bset1, *bset2;
844
845 test_gist_case(ctx, "gist1");
846
847 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
848 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
849 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
850 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
851 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
852 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
853 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
854 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
855 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
856 bset1 = isl_basic_set_read_from_str(ctx, str);
857 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
858 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
859 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
860 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
861 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
862 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
863 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
864 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
865 bset2 = isl_basic_set_read_from_str(ctx, str);
866 bset1 = isl_basic_set_gist(bset1, bset2);
867 assert(bset1 && bset1->n_div == 0);
868 isl_basic_set_free(bset1);
869 }
870
871 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
872 {
873 isl_set *set, *set2;
874 int equal;
875 int one;
876
877 set = isl_set_read_from_str(ctx, str);
878 set = isl_set_coalesce(set);
879 set2 = isl_set_read_from_str(ctx, str);
880 equal = isl_set_is_equal(set, set2);
881 one = set && set->n == 1;
882 isl_set_free(set);
883 isl_set_free(set2);
884
885 if (equal < 0)
886 return -1;
887 if (!equal)
888 isl_die(ctx, isl_error_unknown,
889 "coalesced set not equal to input", return -1);
890 if (check_one && !one)
891 isl_die(ctx, isl_error_unknown,
892 "coalesced set should not be a union", return -1);
893
894 return 0;
895 }
896
897 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
898 {
899 int r = 0;
900 int bounded;
901
902 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
903 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
904
905 if (test_coalesce_set(ctx,
906 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
907 "-x - y + 1 >= 0 and -3 <= z <= 3;"
908 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
909 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
910 "-10 <= y <= 0}", 1) < 0)
911 goto error;
912 if (test_coalesce_set(ctx,
913 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
914 goto error;
915 if (test_coalesce_set(ctx,
916 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
917 goto error;
918
919 if (0) {
920 error:
921 r = -1;
922 }
923
924 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
925
926 return r;
927 }
928
929 int test_coalesce(struct isl_ctx *ctx)
930 {
931 const char *str;
932 struct isl_set *set, *set2;
933 struct isl_map *map, *map2;
934
935 set = isl_set_read_from_str(ctx,
936 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
937 "y >= x & x >= 2 & 5 >= y }");
938 set = isl_set_coalesce(set);
939 assert(set && set->n == 1);
940 isl_set_free(set);
941
942 set = isl_set_read_from_str(ctx,
943 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
944 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}");
945 set = isl_set_coalesce(set);
946 assert(set && set->n == 1);
947 isl_set_free(set);
948
949 set = isl_set_read_from_str(ctx,
950 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
951 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}");
952 set = isl_set_coalesce(set);
953 assert(set && set->n == 2);
954 isl_set_free(set);
955
956 set = isl_set_read_from_str(ctx,
957 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
958 "y >= 0 & x >= 6 & x <= 10 & y <= x}");
959 set = isl_set_coalesce(set);
960 assert(set && set->n == 1);
961 isl_set_free(set);
962
963 set = isl_set_read_from_str(ctx,
964 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
965 "y >= 0 & x >= 7 & x <= 10 & y <= x}");
966 set = isl_set_coalesce(set);
967 assert(set && set->n == 2);
968 isl_set_free(set);
969
970 set = isl_set_read_from_str(ctx,
971 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
972 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}");
973 set = isl_set_coalesce(set);
974 assert(set && set->n == 2);
975 isl_set_free(set);
976
977 set = isl_set_read_from_str(ctx,
978 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
979 "y >= 0 & x = 6 & y <= 6}");
980 set = isl_set_coalesce(set);
981 assert(set && set->n == 1);
982 isl_set_free(set);
983
984 set = isl_set_read_from_str(ctx,
985 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
986 "y >= 0 & x = 7 & y <= 6}");
987 set = isl_set_coalesce(set);
988 assert(set && set->n == 2);
989 isl_set_free(set);
990
991 set = isl_set_read_from_str(ctx,
992 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
993 "y >= 0 & x = 6 & y <= 5}");
994 set = isl_set_coalesce(set);
995 assert(set && set->n == 1);
996 set2 = isl_set_read_from_str(ctx,
997 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
998 "y >= 0 & x = 6 & y <= 5}");
999 assert(isl_set_is_equal(set, set2));
1000 isl_set_free(set);
1001 isl_set_free(set2);
1002
1003 set = isl_set_read_from_str(ctx,
1004 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1005 "y >= 0 & x = 6 & y <= 7}");
1006 set = isl_set_coalesce(set);
1007 assert(set && set->n == 2);
1008 isl_set_free(set);
1009
1010 set = isl_set_read_from_str(ctx,
1011 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
1012 set = isl_set_coalesce(set);
1013 assert(set && set->n == 1);
1014 set2 = isl_set_read_from_str(ctx,
1015 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }");
1016 assert(isl_set_is_equal(set, set2));
1017 isl_set_free(set);
1018 isl_set_free(set2);
1019
1020 set = isl_set_read_from_str(ctx,
1021 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
1022 set = isl_set_coalesce(set);
1023 set2 = isl_set_read_from_str(ctx,
1024 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}");
1025 assert(isl_set_is_equal(set, set2));
1026 isl_set_free(set);
1027 isl_set_free(set2);
1028
1029 set = isl_set_read_from_str(ctx,
1030 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1031 "2 <= i and i <= n }");
1032 set = isl_set_coalesce(set);
1033 assert(set && set->n == 1);
1034 set2 = isl_set_read_from_str(ctx,
1035 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
1036 "2 <= i and i <= n }");
1037 assert(isl_set_is_equal(set, set2));
1038 isl_set_free(set);
1039 isl_set_free(set2);
1040
1041 map = isl_map_read_from_str(ctx,
1042 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1043 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1044 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1045 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1046 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1047 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1048 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1049 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1050 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1051 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1052 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1053 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1054 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1055 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1056 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1057 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1058 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1059 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1060 map = isl_map_coalesce(map);
1061 map2 = isl_map_read_from_str(ctx,
1062 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1063 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1064 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1065 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1066 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1067 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1068 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1069 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1070 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1071 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1072 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1073 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1074 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1075 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1076 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1077 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1078 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1079 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }");
1080 assert(isl_map_is_equal(map, map2));
1081 isl_map_free(map);
1082 isl_map_free(map2);
1083
1084 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1085 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1086 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1087 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
1088 map = isl_map_read_from_str(ctx, str);
1089 map = isl_map_coalesce(map);
1090 map2 = isl_map_read_from_str(ctx, str);
1091 assert(isl_map_is_equal(map, map2));
1092 isl_map_free(map);
1093 isl_map_free(map2);
1094
1095 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
1096 "[o0, o1, o2, o3, o4, o5, o6] : "
1097 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1098 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1099 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1100 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1101 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1102 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1103 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1104 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1105 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1106 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1107 "o6 >= i3 + i6 - o3 and M >= 0 and "
1108 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1109 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
1110 map = isl_map_read_from_str(ctx, str);
1111 map = isl_map_coalesce(map);
1112 map2 = isl_map_read_from_str(ctx, str);
1113 assert(isl_map_is_equal(map, map2));
1114 isl_map_free(map);
1115 isl_map_free(map2);
1116
1117 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1118 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1119 "(o0 = 0 and M >= 2 and N >= 3) or "
1120 "(M = 0 and o0 = 0 and N >= 3) }";
1121 map = isl_map_read_from_str(ctx, str);
1122 map = isl_map_coalesce(map);
1123 map2 = isl_map_read_from_str(ctx, str);
1124 assert(isl_map_is_equal(map, map2));
1125 isl_map_free(map);
1126 isl_map_free(map2);
1127
1128 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1129 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1130 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1131 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
1132 map = isl_map_read_from_str(ctx, str);
1133 map = isl_map_coalesce(map);
1134 map2 = isl_map_read_from_str(ctx, str);
1135 assert(isl_map_is_equal(map, map2));
1136 isl_map_free(map);
1137 isl_map_free(map2);
1138
1139 test_coalesce_set(ctx,
1140 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
1141 "(i1 = M and M >= 1) }", 0);
1142 test_coalesce_set(ctx,
1143 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
1144 test_coalesce_set(ctx,
1145 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1146 "(y = 3 and x = 1) }", 1);
1147 test_coalesce_set(ctx,
1148 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1149 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1150 "i1 <= M and i3 <= M and i4 <= M) or "
1151 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1152 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1153 "i4 <= -1 + M) }", 1);
1154 test_coalesce_set(ctx,
1155 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1156 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
1157 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1158 return -1;
1159 if (test_coalesce_set(ctx, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0) < 0)
1160 return -1;
1161 if (test_coalesce_set(ctx, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1) < 0)
1162 return -1;
1163 if (test_coalesce_set(ctx, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1) < 0)
1164 return -1;
1165 if (test_coalesce_set(ctx, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0) < 0)
1166 return -1;
1167 if (test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1) < 0)
1168 return -1;
1169 if (test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0) < 0)
1170 return -1;
1171 if (test_coalesce_set(ctx, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1172 return -1;
1173 if (test_coalesce_set(ctx, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0) < 0)
1174 return -1;
1175 if (test_coalesce_set(ctx, "{ [a, b] : exists e : 2e = a and "
1176 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }", 0) < 0)
1177 return -1;
1178 if (test_coalesce_set(ctx,
1179 "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1180 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1181 "j >= 1 and j' <= i + j - i' and i >= 1; "
1182 "[1, 1, 1, 1] }", 0) < 0)
1183 return -1;
1184 if (test_coalesce_set(ctx, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1185 "[i,j] : exists a : j = 3a }", 1) < 0)
1186 return -1;
1187 return 0;
1188 }
1189
1190 void test_closure(struct isl_ctx *ctx)
1191 {
1192 const char *str;
1193 isl_set *dom;
1194 isl_map *up, *right;
1195 isl_map *map, *map2;
1196 int exact;
1197
1198 /* COCOA example 1 */
1199 map = isl_map_read_from_str(ctx,
1200 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1201 "1 <= i and i < n and 1 <= j and j < n or "
1202 "i2 = i + 1 and j2 = j - 1 and "
1203 "1 <= i and i < n and 2 <= j and j <= n }");
1204 map = isl_map_power(map, &exact);
1205 assert(exact);
1206 isl_map_free(map);
1207
1208 /* COCOA example 1 */
1209 map = isl_map_read_from_str(ctx,
1210 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1211 "1 <= i and i < n and 1 <= j and j < n or "
1212 "i2 = i + 1 and j2 = j - 1 and "
1213 "1 <= i and i < n and 2 <= j and j <= n }");
1214 map = isl_map_transitive_closure(map, &exact);
1215 assert(exact);
1216 map2 = isl_map_read_from_str(ctx,
1217 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1218 "1 <= i and i < n and 1 <= j and j <= n and "
1219 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1220 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1221 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1222 assert(isl_map_is_equal(map, map2));
1223 isl_map_free(map2);
1224 isl_map_free(map);
1225
1226 map = isl_map_read_from_str(ctx,
1227 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1228 " 0 <= y and y <= n }");
1229 map = isl_map_transitive_closure(map, &exact);
1230 map2 = isl_map_read_from_str(ctx,
1231 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1232 " 0 <= y and y <= n }");
1233 assert(isl_map_is_equal(map, map2));
1234 isl_map_free(map2);
1235 isl_map_free(map);
1236
1237 /* COCOA example 2 */
1238 map = isl_map_read_from_str(ctx,
1239 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1240 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1241 "i2 = i + 2 and j2 = j - 2 and "
1242 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1243 map = isl_map_transitive_closure(map, &exact);
1244 assert(exact);
1245 map2 = isl_map_read_from_str(ctx,
1246 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1247 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1248 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1249 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1250 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1251 assert(isl_map_is_equal(map, map2));
1252 isl_map_free(map);
1253 isl_map_free(map2);
1254
1255 /* COCOA Fig.2 left */
1256 map = isl_map_read_from_str(ctx,
1257 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1258 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1259 "j <= n or "
1260 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1261 "j <= 2 i - 3 and j <= n - 2 or "
1262 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1263 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1264 map = isl_map_transitive_closure(map, &exact);
1265 assert(exact);
1266 isl_map_free(map);
1267
1268 /* COCOA Fig.2 right */
1269 map = isl_map_read_from_str(ctx,
1270 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1271 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1272 "j <= n or "
1273 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1274 "j <= 2 i - 4 and j <= n - 3 or "
1275 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1276 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1277 map = isl_map_power(map, &exact);
1278 assert(exact);
1279 isl_map_free(map);
1280
1281 /* COCOA Fig.2 right */
1282 map = isl_map_read_from_str(ctx,
1283 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1284 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1285 "j <= n or "
1286 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1287 "j <= 2 i - 4 and j <= n - 3 or "
1288 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1289 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1290 map = isl_map_transitive_closure(map, &exact);
1291 assert(exact);
1292 map2 = isl_map_read_from_str(ctx,
1293 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1294 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1295 "j <= n and 3 + i + 2 j <= 3 n and "
1296 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1297 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1298 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1299 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1300 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1301 assert(isl_map_is_equal(map, map2));
1302 isl_map_free(map2);
1303 isl_map_free(map);
1304
1305 /* COCOA Fig.1 right */
1306 dom = isl_set_read_from_str(ctx,
1307 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1308 "2 x - 3 y + 3 >= 0 }");
1309 right = isl_map_read_from_str(ctx,
1310 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1311 up = isl_map_read_from_str(ctx,
1312 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1313 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1314 right = isl_map_intersect_range(right, isl_set_copy(dom));
1315 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1316 up = isl_map_intersect_range(up, dom);
1317 map = isl_map_union(up, right);
1318 map = isl_map_transitive_closure(map, &exact);
1319 assert(exact);
1320 map2 = isl_map_read_from_str(ctx,
1321 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1322 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1323 assert(isl_map_is_equal(map, map2));
1324 isl_map_free(map2);
1325 isl_map_free(map);
1326
1327 /* COCOA Theorem 1 counter example */
1328 map = isl_map_read_from_str(ctx,
1329 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1330 "i2 = 1 and j2 = j or "
1331 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1332 map = isl_map_transitive_closure(map, &exact);
1333 assert(exact);
1334 isl_map_free(map);
1335
1336 map = isl_map_read_from_str(ctx,
1337 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1338 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1339 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1340 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1341 map = isl_map_transitive_closure(map, &exact);
1342 assert(exact);
1343 isl_map_free(map);
1344
1345 /* Kelly et al 1996, fig 12 */
1346 map = isl_map_read_from_str(ctx,
1347 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1348 "1 <= i,j,j+1 <= n or "
1349 "j = n and j2 = 1 and i2 = i + 1 and "
1350 "1 <= i,i+1 <= n }");
1351 map = isl_map_transitive_closure(map, &exact);
1352 assert(exact);
1353 map2 = isl_map_read_from_str(ctx,
1354 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1355 "1 <= i <= n and i = i2 or "
1356 "1 <= i < i2 <= n and 1 <= j <= n and "
1357 "1 <= j2 <= n }");
1358 assert(isl_map_is_equal(map, map2));
1359 isl_map_free(map2);
1360 isl_map_free(map);
1361
1362 /* Omega's closure4 */
1363 map = isl_map_read_from_str(ctx,
1364 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1365 "1 <= x,y <= 10 or "
1366 "x2 = x + 1 and y2 = y and "
1367 "1 <= x <= 20 && 5 <= y <= 15 }");
1368 map = isl_map_transitive_closure(map, &exact);
1369 assert(exact);
1370 isl_map_free(map);
1371
1372 map = isl_map_read_from_str(ctx,
1373 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1374 map = isl_map_transitive_closure(map, &exact);
1375 assert(!exact);
1376 map2 = isl_map_read_from_str(ctx,
1377 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1378 assert(isl_map_is_equal(map, map2));
1379 isl_map_free(map);
1380 isl_map_free(map2);
1381
1382 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1383 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1384 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1385 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1386 map = isl_map_read_from_str(ctx, str);
1387 map = isl_map_transitive_closure(map, &exact);
1388 assert(exact);
1389 map2 = isl_map_read_from_str(ctx, str);
1390 assert(isl_map_is_equal(map, map2));
1391 isl_map_free(map);
1392 isl_map_free(map2);
1393
1394 str = "{[0] -> [1]; [2] -> [3]}";
1395 map = isl_map_read_from_str(ctx, str);
1396 map = isl_map_transitive_closure(map, &exact);
1397 assert(exact);
1398 map2 = isl_map_read_from_str(ctx, str);
1399 assert(isl_map_is_equal(map, map2));
1400 isl_map_free(map);
1401 isl_map_free(map2);
1402
1403 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1404 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1405 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1406 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1407 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1408 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1409 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1410 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1411 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1412 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1413 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1414 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1415 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1416 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1417 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1418 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1419 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1420 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1421 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1422 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1423 map = isl_map_read_from_str(ctx, str);
1424 map = isl_map_transitive_closure(map, NULL);
1425 assert(map);
1426 isl_map_free(map);
1427 }
1428
1429 void test_lex(struct isl_ctx *ctx)
1430 {
1431 isl_space *dim;
1432 isl_map *map;
1433
1434 dim = isl_space_set_alloc(ctx, 0, 0);
1435 map = isl_map_lex_le(dim);
1436 assert(!isl_map_is_empty(map));
1437 isl_map_free(map);
1438 }
1439
1440 void test_lexmin(struct isl_ctx *ctx)
1441 {
1442 const char *str;
1443 isl_basic_map *bmap;
1444 isl_map *map, *map2;
1445 isl_set *set;
1446 isl_set *set2;
1447 isl_pw_multi_aff *pma;
1448
1449 str = "[p0, p1] -> { [] -> [] : "
1450 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1451 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1452 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1453 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1454 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1455 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1456 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1457 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1458 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1459 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1460 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1461 map = isl_map_read_from_str(ctx, str);
1462 map = isl_map_lexmin(map);
1463 isl_map_free(map);
1464
1465 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1466 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1467 set = isl_set_read_from_str(ctx, str);
1468 set = isl_set_lexmax(set);
1469 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1470 set2 = isl_set_read_from_str(ctx, str);
1471 set = isl_set_intersect(set, set2);
1472 assert(!isl_set_is_empty(set));
1473 isl_set_free(set);
1474
1475 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1476 map = isl_map_read_from_str(ctx, str);
1477 map = isl_map_lexmin(map);
1478 str = "{ [x] -> [5] : 6 <= x <= 8; "
1479 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1480 map2 = isl_map_read_from_str(ctx, str);
1481 assert(isl_map_is_equal(map, map2));
1482 isl_map_free(map);
1483 isl_map_free(map2);
1484
1485 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1486 map = isl_map_read_from_str(ctx, str);
1487 map2 = isl_map_copy(map);
1488 map = isl_map_lexmin(map);
1489 assert(isl_map_is_equal(map, map2));
1490 isl_map_free(map);
1491 isl_map_free(map2);
1492
1493 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1494 map = isl_map_read_from_str(ctx, str);
1495 map = isl_map_lexmin(map);
1496 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1497 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1498 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1499 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1500 map2 = isl_map_read_from_str(ctx, str);
1501 assert(isl_map_is_equal(map, map2));
1502 isl_map_free(map);
1503 isl_map_free(map2);
1504
1505 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1506 " 8i' <= i and 8i' >= -7 + i }";
1507 bmap = isl_basic_map_read_from_str(ctx, str);
1508 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1509 map2 = isl_map_from_pw_multi_aff(pma);
1510 map = isl_map_from_basic_map(bmap);
1511 assert(isl_map_is_equal(map, map2));
1512 isl_map_free(map);
1513 isl_map_free(map2);
1514
1515 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1516 map = isl_map_read_from_str(ctx, str);
1517 map = isl_map_lexmin(map);
1518 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1519 map2 = isl_map_read_from_str(ctx, str);
1520 assert(isl_map_is_equal(map, map2));
1521 isl_map_free(map);
1522 isl_map_free(map2);
1523 }
1524
1525 struct must_may {
1526 isl_map *must;
1527 isl_map *may;
1528 };
1529
1530 static int collect_must_may(__isl_take isl_map *dep, int must,
1531 void *dep_user, void *user)
1532 {
1533 struct must_may *mm = (struct must_may *)user;
1534
1535 if (must)
1536 mm->must = isl_map_union(mm->must, dep);
1537 else
1538 mm->may = isl_map_union(mm->may, dep);
1539
1540 return 0;
1541 }
1542
1543 static int common_space(void *first, void *second)
1544 {
1545 int depth = *(int *)first;
1546 return 2 * depth;
1547 }
1548
1549 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1550 {
1551 isl_map *map2;
1552 int equal;
1553
1554 if (!map)
1555 return -1;
1556
1557 map2 = isl_map_read_from_str(map->ctx, str);
1558 equal = isl_map_is_equal(map, map2);
1559 isl_map_free(map2);
1560
1561 return equal;
1562 }
1563
1564 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1565 {
1566 int equal;
1567
1568 equal = map_is_equal(map, str);
1569 if (equal < 0)
1570 return -1;
1571 if (!equal)
1572 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1573 "result not as expected", return -1);
1574 return 0;
1575 }
1576
1577 void test_dep(struct isl_ctx *ctx)
1578 {
1579 const char *str;
1580 isl_space *dim;
1581 isl_map *map;
1582 isl_access_info *ai;
1583 isl_flow *flow;
1584 int depth;
1585 struct must_may mm;
1586
1587 depth = 3;
1588
1589 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1590 map = isl_map_read_from_str(ctx, str);
1591 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1592
1593 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1594 map = isl_map_read_from_str(ctx, str);
1595 ai = isl_access_info_add_source(ai, map, 1, &depth);
1596
1597 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1598 map = isl_map_read_from_str(ctx, str);
1599 ai = isl_access_info_add_source(ai, map, 1, &depth);
1600
1601 flow = isl_access_info_compute_flow(ai);
1602 dim = isl_space_alloc(ctx, 0, 3, 3);
1603 mm.must = isl_map_empty(isl_space_copy(dim));
1604 mm.may = isl_map_empty(dim);
1605
1606 isl_flow_foreach(flow, collect_must_may, &mm);
1607
1608 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1609 " [1,10,0] -> [2,5,0] }";
1610 assert(map_is_equal(mm.must, str));
1611 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1612 assert(map_is_equal(mm.may, str));
1613
1614 isl_map_free(mm.must);
1615 isl_map_free(mm.may);
1616 isl_flow_free(flow);
1617
1618
1619 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1620 map = isl_map_read_from_str(ctx, str);
1621 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1622
1623 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1624 map = isl_map_read_from_str(ctx, str);
1625 ai = isl_access_info_add_source(ai, map, 1, &depth);
1626
1627 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1628 map = isl_map_read_from_str(ctx, str);
1629 ai = isl_access_info_add_source(ai, map, 0, &depth);
1630
1631 flow = isl_access_info_compute_flow(ai);
1632 dim = isl_space_alloc(ctx, 0, 3, 3);
1633 mm.must = isl_map_empty(isl_space_copy(dim));
1634 mm.may = isl_map_empty(dim);
1635
1636 isl_flow_foreach(flow, collect_must_may, &mm);
1637
1638 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1639 assert(map_is_equal(mm.must, str));
1640 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1641 assert(map_is_equal(mm.may, str));
1642
1643 isl_map_free(mm.must);
1644 isl_map_free(mm.may);
1645 isl_flow_free(flow);
1646
1647
1648 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1649 map = isl_map_read_from_str(ctx, str);
1650 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1651
1652 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1653 map = isl_map_read_from_str(ctx, str);
1654 ai = isl_access_info_add_source(ai, map, 0, &depth);
1655
1656 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1657 map = isl_map_read_from_str(ctx, str);
1658 ai = isl_access_info_add_source(ai, map, 0, &depth);
1659
1660 flow = isl_access_info_compute_flow(ai);
1661 dim = isl_space_alloc(ctx, 0, 3, 3);
1662 mm.must = isl_map_empty(isl_space_copy(dim));
1663 mm.may = isl_map_empty(dim);
1664
1665 isl_flow_foreach(flow, collect_must_may, &mm);
1666
1667 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1668 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1669 assert(map_is_equal(mm.may, str));
1670 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1671 assert(map_is_equal(mm.must, str));
1672
1673 isl_map_free(mm.must);
1674 isl_map_free(mm.may);
1675 isl_flow_free(flow);
1676
1677
1678 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1679 map = isl_map_read_from_str(ctx, str);
1680 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1681
1682 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1683 map = isl_map_read_from_str(ctx, str);
1684 ai = isl_access_info_add_source(ai, map, 0, &depth);
1685
1686 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1687 map = isl_map_read_from_str(ctx, str);
1688 ai = isl_access_info_add_source(ai, map, 0, &depth);
1689
1690 flow = isl_access_info_compute_flow(ai);
1691 dim = isl_space_alloc(ctx, 0, 3, 3);
1692 mm.must = isl_map_empty(isl_space_copy(dim));
1693 mm.may = isl_map_empty(dim);
1694
1695 isl_flow_foreach(flow, collect_must_may, &mm);
1696
1697 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1698 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1699 assert(map_is_equal(mm.may, str));
1700 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1701 assert(map_is_equal(mm.must, str));
1702
1703 isl_map_free(mm.must);
1704 isl_map_free(mm.may);
1705 isl_flow_free(flow);
1706
1707
1708 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1709 map = isl_map_read_from_str(ctx, str);
1710 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1711
1712 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1713 map = isl_map_read_from_str(ctx, str);
1714 ai = isl_access_info_add_source(ai, map, 0, &depth);
1715
1716 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1717 map = isl_map_read_from_str(ctx, str);
1718 ai = isl_access_info_add_source(ai, map, 0, &depth);
1719
1720 flow = isl_access_info_compute_flow(ai);
1721 dim = isl_space_alloc(ctx, 0, 3, 3);
1722 mm.must = isl_map_empty(isl_space_copy(dim));
1723 mm.may = isl_map_empty(dim);
1724
1725 isl_flow_foreach(flow, collect_must_may, &mm);
1726
1727 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1728 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1729 assert(map_is_equal(mm.may, str));
1730 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1731 assert(map_is_equal(mm.must, str));
1732
1733 isl_map_free(mm.must);
1734 isl_map_free(mm.may);
1735 isl_flow_free(flow);
1736
1737
1738 depth = 5;
1739
1740 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1741 map = isl_map_read_from_str(ctx, str);
1742 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1743
1744 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1745 map = isl_map_read_from_str(ctx, str);
1746 ai = isl_access_info_add_source(ai, map, 1, &depth);
1747
1748 flow = isl_access_info_compute_flow(ai);
1749 dim = isl_space_alloc(ctx, 0, 5, 5);
1750 mm.must = isl_map_empty(isl_space_copy(dim));
1751 mm.may = isl_map_empty(dim);
1752
1753 isl_flow_foreach(flow, collect_must_may, &mm);
1754
1755 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1756 assert(map_is_equal(mm.must, str));
1757 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1758 assert(map_is_equal(mm.may, str));
1759
1760 isl_map_free(mm.must);
1761 isl_map_free(mm.may);
1762 isl_flow_free(flow);
1763 }
1764
1765 int test_sv(isl_ctx *ctx)
1766 {
1767 const char *str;
1768 isl_map *map;
1769 isl_union_map *umap;
1770 int sv;
1771
1772 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1773 map = isl_map_read_from_str(ctx, str);
1774 sv = isl_map_is_single_valued(map);
1775 isl_map_free(map);
1776 if (sv < 0)
1777 return -1;
1778 if (!sv)
1779 isl_die(ctx, isl_error_internal,
1780 "map not detected as single valued", return -1);
1781
1782 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1783 map = isl_map_read_from_str(ctx, str);
1784 sv = isl_map_is_single_valued(map);
1785 isl_map_free(map);
1786 if (sv < 0)
1787 return -1;
1788 if (sv)
1789 isl_die(ctx, isl_error_internal,
1790 "map detected as single valued", return -1);
1791
1792 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1793 umap = isl_union_map_read_from_str(ctx, str);
1794 sv = isl_union_map_is_single_valued(umap);
1795 isl_union_map_free(umap);
1796 if (sv < 0)
1797 return -1;
1798 if (!sv)
1799 isl_die(ctx, isl_error_internal,
1800 "map not detected as single valued", return -1);
1801
1802 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1803 umap = isl_union_map_read_from_str(ctx, str);
1804 sv = isl_union_map_is_single_valued(umap);
1805 isl_union_map_free(umap);
1806 if (sv < 0)
1807 return -1;
1808 if (sv)
1809 isl_die(ctx, isl_error_internal,
1810 "map detected as single valued", return -1);
1811
1812 return 0;
1813 }
1814
1815 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1816 {
1817 isl_map *map;
1818
1819 map = isl_map_read_from_str(ctx, str);
1820 if (bijective)
1821 assert(isl_map_is_bijective(map));
1822 else
1823 assert(!isl_map_is_bijective(map));
1824 isl_map_free(map);
1825 }
1826
1827 void test_bijective(struct isl_ctx *ctx)
1828 {
1829 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1830 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1831 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1832 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1833 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1834 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1835 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1836 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1837 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1838 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1839 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1840 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1841 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1842 }
1843
1844 void test_pwqp(struct isl_ctx *ctx)
1845 {
1846 const char *str;
1847 isl_set *set;
1848 isl_pw_qpolynomial *pwqp1, *pwqp2;
1849
1850 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1851 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1852
1853 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1854 isl_dim_in, 1, 1);
1855
1856 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1857 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1858
1859 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1860
1861 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1862
1863 isl_pw_qpolynomial_free(pwqp1);
1864
1865 str = "{ [i] -> i }";
1866 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1867 str = "{ [k] : exists a : k = 2a }";
1868 set = isl_set_read_from_str(ctx, str);
1869 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1870 str = "{ [i] -> i }";
1871 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1872
1873 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1874
1875 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1876
1877 isl_pw_qpolynomial_free(pwqp1);
1878
1879 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
1880 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1881 str = "{ [10] }";
1882 set = isl_set_read_from_str(ctx, str);
1883 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1884 str = "{ [i] -> 16 }";
1885 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1886
1887 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1888
1889 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1890
1891 isl_pw_qpolynomial_free(pwqp1);
1892
1893 str = "{ [i] -> ([(i)/2]) }";
1894 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1895 str = "{ [k] : exists a : k = 2a+1 }";
1896 set = isl_set_read_from_str(ctx, str);
1897 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1898 str = "{ [i] -> -1/2 + 1/2 * i }";
1899 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1900
1901 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1902
1903 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1904
1905 isl_pw_qpolynomial_free(pwqp1);
1906
1907 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1908 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1909 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1910 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1911
1912 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1913
1914 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1915
1916 isl_pw_qpolynomial_free(pwqp1);
1917
1918 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1919 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1920 str = "{ [x] -> x }";
1921 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1922
1923 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1924
1925 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1926
1927 isl_pw_qpolynomial_free(pwqp1);
1928
1929 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
1930 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1931 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1932 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
1933 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1934 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1935 isl_pw_qpolynomial_free(pwqp1);
1936 }
1937
1938 void test_split_periods(isl_ctx *ctx)
1939 {
1940 const char *str;
1941 isl_pw_qpolynomial *pwqp;
1942
1943 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1944 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1945 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1946 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1947
1948 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1949 assert(pwqp);
1950
1951 isl_pw_qpolynomial_free(pwqp);
1952 }
1953
1954 void test_union(isl_ctx *ctx)
1955 {
1956 const char *str;
1957 isl_union_set *uset1, *uset2;
1958 isl_union_map *umap1, *umap2;
1959
1960 str = "{ [i] : 0 <= i <= 1 }";
1961 uset1 = isl_union_set_read_from_str(ctx, str);
1962 str = "{ [1] -> [0] }";
1963 umap1 = isl_union_map_read_from_str(ctx, str);
1964
1965 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1966 assert(isl_union_map_is_equal(umap1, umap2));
1967
1968 isl_union_map_free(umap1);
1969 isl_union_map_free(umap2);
1970
1971 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1972 umap1 = isl_union_map_read_from_str(ctx, str);
1973 str = "{ A[i]; B[i] }";
1974 uset1 = isl_union_set_read_from_str(ctx, str);
1975
1976 uset2 = isl_union_map_domain(umap1);
1977
1978 assert(isl_union_set_is_equal(uset1, uset2));
1979
1980 isl_union_set_free(uset1);
1981 isl_union_set_free(uset2);
1982 }
1983
1984 void test_bound(isl_ctx *ctx)
1985 {
1986 const char *str;
1987 isl_pw_qpolynomial *pwqp;
1988 isl_pw_qpolynomial_fold *pwf;
1989
1990 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
1991 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1992 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1993 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
1994 isl_pw_qpolynomial_fold_free(pwf);
1995
1996 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1997 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1998 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1999 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
2000 isl_pw_qpolynomial_fold_free(pwf);
2001 }
2002
2003 void test_lift(isl_ctx *ctx)
2004 {
2005 const char *str;
2006 isl_basic_map *bmap;
2007 isl_basic_set *bset;
2008
2009 str = "{ [i0] : exists e0 : i0 = 4e0 }";
2010 bset = isl_basic_set_read_from_str(ctx, str);
2011 bset = isl_basic_set_lift(bset);
2012 bmap = isl_basic_map_from_range(bset);
2013 bset = isl_basic_map_domain(bmap);
2014 isl_basic_set_free(bset);
2015 }
2016
2017 struct {
2018 const char *set1;
2019 const char *set2;
2020 int subset;
2021 } subset_tests[] = {
2022 { "{ [112, 0] }",
2023 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2024 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2025 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2026 { "{ [65] }",
2027 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2028 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2029 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2030 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2031 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2032 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2033 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2034 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2035 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2036 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2037 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2038 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2039 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2040 };
2041
2042 static int test_subset(isl_ctx *ctx)
2043 {
2044 int i;
2045 isl_set *set1, *set2;
2046 int subset;
2047
2048 for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
2049 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
2050 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
2051 subset = isl_set_is_subset(set1, set2);
2052 isl_set_free(set1);
2053 isl_set_free(set2);
2054 if (subset < 0)
2055 return -1;
2056 if (subset != subset_tests[i].subset)
2057 isl_die(ctx, isl_error_unknown,
2058 "incorrect subset result", return -1);
2059 }
2060
2061 return 0;
2062 }
2063
2064 struct {
2065 const char *minuend;
2066 const char *subtrahend;
2067 const char *difference;
2068 } subtract_domain_tests[] = {
2069 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2070 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2071 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2072 };
2073
2074 static int test_subtract(isl_ctx *ctx)
2075 {
2076 int i;
2077 isl_union_map *umap1, *umap2;
2078 isl_union_set *uset;
2079 int equal;
2080
2081 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2082 umap1 = isl_union_map_read_from_str(ctx,
2083 subtract_domain_tests[i].minuend);
2084 uset = isl_union_set_read_from_str(ctx,
2085 subtract_domain_tests[i].subtrahend);
2086 umap2 = isl_union_map_read_from_str(ctx,
2087 subtract_domain_tests[i].difference);
2088 umap1 = isl_union_map_subtract_domain(umap1, uset);
2089 equal = isl_union_map_is_equal(umap1, umap2);
2090 isl_union_map_free(umap1);
2091 isl_union_map_free(umap2);
2092 if (equal < 0)
2093 return -1;
2094 if (!equal)
2095 isl_die(ctx, isl_error_unknown,
2096 "incorrect subtract domain result", return -1);
2097 }
2098
2099 return 0;
2100 }
2101
2102 int test_factorize(isl_ctx *ctx)
2103 {
2104 const char *str;
2105 isl_basic_set *bset;
2106 isl_factorizer *f;
2107
2108 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2109 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2110 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2111 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2112 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2113 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2114 "3i5 >= -2i0 - i2 + 3i4 }";
2115 bset = isl_basic_set_read_from_str(ctx, str);
2116 f = isl_basic_set_factorizer(bset);
2117 isl_basic_set_free(bset);
2118 isl_factorizer_free(f);
2119 if (!f)
2120 isl_die(ctx, isl_error_unknown,
2121 "failed to construct factorizer", return -1);
2122
2123 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2124 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2125 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2126 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2127 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2128 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2129 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2130 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2131 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2132 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2133 bset = isl_basic_set_read_from_str(ctx, str);
2134 f = isl_basic_set_factorizer(bset);
2135 isl_basic_set_free(bset);
2136 isl_factorizer_free(f);
2137 if (!f)
2138 isl_die(ctx, isl_error_unknown,
2139 "failed to construct factorizer", return -1);
2140
2141 return 0;
2142 }
2143
2144 static int check_injective(__isl_take isl_map *map, void *user)
2145 {
2146 int *injective = user;
2147
2148 *injective = isl_map_is_injective(map);
2149 isl_map_free(map);
2150
2151 if (*injective < 0 || !*injective)
2152 return -1;
2153
2154 return 0;
2155 }
2156
2157 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2158 const char *r, const char *s, int tilable, int parallel)
2159 {
2160 int i;
2161 isl_union_set *D;
2162 isl_union_map *W, *R, *S;
2163 isl_union_map *empty;
2164 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2165 isl_union_map *validity, *proximity;
2166 isl_union_map *schedule;
2167 isl_union_map *test;
2168 isl_union_set *delta;
2169 isl_union_set *domain;
2170 isl_set *delta_set;
2171 isl_set *slice;
2172 isl_set *origin;
2173 isl_schedule *sched;
2174 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2175
2176 D = isl_union_set_read_from_str(ctx, d);
2177 W = isl_union_map_read_from_str(ctx, w);
2178 R = isl_union_map_read_from_str(ctx, r);
2179 S = isl_union_map_read_from_str(ctx, s);
2180
2181 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2182 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2183
2184 empty = isl_union_map_empty(isl_union_map_get_space(S));
2185 isl_union_map_compute_flow(isl_union_map_copy(R),
2186 isl_union_map_copy(W), empty,
2187 isl_union_map_copy(S),
2188 &dep_raw, NULL, NULL, NULL);
2189 isl_union_map_compute_flow(isl_union_map_copy(W),
2190 isl_union_map_copy(W),
2191 isl_union_map_copy(R),
2192 isl_union_map_copy(S),
2193 &dep_waw, &dep_war, NULL, NULL);
2194
2195 dep = isl_union_map_union(dep_waw, dep_war);
2196 dep = isl_union_map_union(dep, dep_raw);
2197 validity = isl_union_map_copy(dep);
2198 proximity = isl_union_map_copy(dep);
2199
2200 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
2201 validity, proximity);
2202 schedule = isl_schedule_get_map(sched);
2203 isl_schedule_free(sched);
2204 isl_union_map_free(W);
2205 isl_union_map_free(R);
2206 isl_union_map_free(S);
2207
2208 is_injection = 1;
2209 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2210
2211 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2212 is_complete = isl_union_set_is_subset(D, domain);
2213 isl_union_set_free(D);
2214 isl_union_set_free(domain);
2215
2216 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2217 test = isl_union_map_apply_range(test, dep);
2218 test = isl_union_map_apply_range(test, schedule);
2219
2220 delta = isl_union_map_deltas(test);
2221 if (isl_union_set_n_set(delta) == 0) {
2222 is_tilable = 1;
2223 is_parallel = 1;
2224 is_nonneg = 1;
2225 isl_union_set_free(delta);
2226 } else {
2227 delta_set = isl_set_from_union_set(delta);
2228
2229 slice = isl_set_universe(isl_set_get_space(delta_set));
2230 for (i = 0; i < tilable; ++i)
2231 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2232 is_tilable = isl_set_is_subset(delta_set, slice);
2233 isl_set_free(slice);
2234
2235 slice = isl_set_universe(isl_set_get_space(delta_set));
2236 for (i = 0; i < parallel; ++i)
2237 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2238 is_parallel = isl_set_is_subset(delta_set, slice);
2239 isl_set_free(slice);
2240
2241 origin = isl_set_universe(isl_set_get_space(delta_set));
2242 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2243 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2244
2245 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2246 delta_set = isl_set_lexmin(delta_set);
2247
2248 is_nonneg = isl_set_is_equal(delta_set, origin);
2249
2250 isl_set_free(origin);
2251 isl_set_free(delta_set);
2252 }
2253
2254 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2255 is_injection < 0 || is_complete < 0)
2256 return -1;
2257 if (!is_complete)
2258 isl_die(ctx, isl_error_unknown,
2259 "generated schedule incomplete", return -1);
2260 if (!is_injection)
2261 isl_die(ctx, isl_error_unknown,
2262 "generated schedule not injective on each statement",
2263 return -1);
2264 if (!is_nonneg)
2265 isl_die(ctx, isl_error_unknown,
2266 "negative dependences in generated schedule",
2267 return -1);
2268 if (!is_tilable)
2269 isl_die(ctx, isl_error_unknown,
2270 "generated schedule not as tilable as expected",
2271 return -1);
2272 if (!is_parallel)
2273 isl_die(ctx, isl_error_unknown,
2274 "generated schedule not as parallel as expected",
2275 return -1);
2276
2277 return 0;
2278 }
2279
2280 int test_special_schedule(isl_ctx *ctx, const char *domain,
2281 const char *validity, const char *proximity, const char *expected_sched)
2282 {
2283 isl_union_set *dom;
2284 isl_union_map *dep;
2285 isl_union_map *prox;
2286 isl_union_map *sched1, *sched2;
2287 isl_schedule *schedule;
2288 int equal;
2289
2290 dom = isl_union_set_read_from_str(ctx, domain);
2291 dep = isl_union_map_read_from_str(ctx, validity);
2292 prox = isl_union_map_read_from_str(ctx, proximity);
2293 schedule = isl_union_set_compute_schedule(dom, dep, prox);
2294 sched1 = isl_schedule_get_map(schedule);
2295 isl_schedule_free(schedule);
2296
2297 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2298
2299 equal = isl_union_map_is_equal(sched1, sched2);
2300 isl_union_map_free(sched1);
2301 isl_union_map_free(sched2);
2302
2303 if (equal < 0)
2304 return -1;
2305 if (!equal)
2306 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2307 return -1);
2308
2309 return 0;
2310 }
2311
2312 int test_schedule(isl_ctx *ctx)
2313 {
2314 const char *D, *W, *R, *V, *P, *S;
2315
2316 /* Jacobi */
2317 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2318 W = "{ S1[t,i] -> a[t,i] }";
2319 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2320 "S1[t,i] -> a[t-1,i+1] }";
2321 S = "{ S1[t,i] -> [t,i] }";
2322 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2323 return -1;
2324
2325 /* Fig. 5 of CC2008 */
2326 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2327 "j <= -1 + N }";
2328 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2329 "j >= 2 and j <= -1 + N }";
2330 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2331 "j >= 2 and j <= -1 + N; "
2332 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2333 "j >= 2 and j <= -1 + N }";
2334 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2335 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2336 return -1;
2337
2338 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2339 W = "{ S1[i] -> a[i] }";
2340 R = "{ S2[i] -> a[i+1] }";
2341 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2342 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2343 return -1;
2344
2345 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2346 W = "{ S1[i] -> a[i] }";
2347 R = "{ S2[i] -> a[9-i] }";
2348 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2349 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2350 return -1;
2351
2352 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2353 W = "{ S1[i] -> a[i] }";
2354 R = "[N] -> { S2[i] -> a[N-1-i] }";
2355 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2356 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2357 return -1;
2358
2359 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2360 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2361 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2362 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2363 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2364 return -1;
2365
2366 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2367 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2368 R = "{ S2[i,j] -> a[i-1,j] }";
2369 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2370 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2371 return -1;
2372
2373 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2374 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2375 R = "{ S2[i,j] -> a[i,j-1] }";
2376 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2377 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2378 return -1;
2379
2380 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2381 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2382 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2383 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2384 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2385 "S_0[] -> [0, 0, 0] }";
2386 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2387 return -1;
2388 ctx->opt->schedule_parametric = 0;
2389 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2390 return -1;
2391 ctx->opt->schedule_parametric = 1;
2392
2393 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2394 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2395 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2396 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2397 "S4[i] -> a[i,N] }";
2398 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2399 "S4[i] -> [4,i,0] }";
2400 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2401 return -1;
2402
2403 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2404 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2405 "j <= N }";
2406 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2407 "j <= N; "
2408 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2409 "j <= N }";
2410 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2411 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2412 return -1;
2413
2414 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2415 " S_2[t] : t >= 0 and t <= -1 + N; "
2416 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2417 "i <= -1 + N }";
2418 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2419 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2420 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2421 "i >= 0 and i <= -1 + N }";
2422 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2423 "i >= 0 and i <= -1 + N; "
2424 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2425 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2426 " S_0[t] -> [0, t, 0] }";
2427
2428 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2429 return -1;
2430 ctx->opt->schedule_parametric = 0;
2431 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2432 return -1;
2433 ctx->opt->schedule_parametric = 1;
2434
2435 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2436 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2437 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2438 return -1;
2439
2440 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2441 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2442 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2443 "j >= 0 and j <= -1 + N; "
2444 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2445 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2446 "j >= 0 and j <= -1 + N; "
2447 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2448 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2449 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2450 return -1;
2451
2452 D = "{ S_0[i] : i >= 0 }";
2453 W = "{ S_0[i] -> a[i] : i >= 0 }";
2454 R = "{ S_0[i] -> a[0] : i >= 0 }";
2455 S = "{ S_0[i] -> [0, i, 0] }";
2456 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2457 return -1;
2458
2459 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2460 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2461 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2462 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2463 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2464 return -1;
2465
2466 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2467 "k <= -1 + n and k >= 0 }";
2468 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2469 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2470 "k <= -1 + n and k >= 0; "
2471 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2472 "k <= -1 + n and k >= 0; "
2473 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2474 "k <= -1 + n and k >= 0 }";
2475 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
2476 ctx->opt->schedule_outer_zero_distance = 1;
2477 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2478 return -1;
2479 ctx->opt->schedule_outer_zero_distance = 0;
2480
2481 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
2482 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2483 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2484 "Stmt_for_body24[i0, i1, 1, 0]:"
2485 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2486 "Stmt_for_body7[i0, i1, i2]:"
2487 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2488 "i2 <= 7 }";
2489
2490 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
2491 "Stmt_for_body24[1, i1, i2, i3]:"
2492 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2493 "i2 >= 1;"
2494 "Stmt_for_body24[0, i1, i2, i3] -> "
2495 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2496 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2497 "i3 >= 0;"
2498 "Stmt_for_body24[0, i1, i2, i3] ->"
2499 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2500 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2501 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2502 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2503 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2504 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2505 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2506 "i1 <= 6 and i1 >= 0;"
2507 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2508 "Stmt_for_body7[i0, i1, i2] -> "
2509 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2510 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2511 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2512 "Stmt_for_body7[i0, i1, i2] -> "
2513 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2514 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2515 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2516 P = V;
2517 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2518 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2519 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2520
2521 if (test_special_schedule(ctx, D, V, P, S) < 0)
2522 return -1;
2523
2524 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2525 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2526 "j >= 1 and j <= 7;"
2527 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2528 "j >= 1 and j <= 8 }";
2529 P = "{ }";
2530 S = "{ S_0[i, j] -> [i + j, j] }";
2531 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2532 if (test_special_schedule(ctx, D, V, P, S) < 0)
2533 return -1;
2534 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2535
2536 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2537 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2538 "j >= 0 and j <= -1 + i }";
2539 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2540 "i <= -1 + N and j >= 0;"
2541 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2542 "i <= -2 + N }";
2543 P = "{ }";
2544 S = "{ S_0[i, j] -> [i, j] }";
2545 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2546 if (test_special_schedule(ctx, D, V, P, S) < 0)
2547 return -1;
2548 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2549
2550 /* Test both algorithms on a case with only proximity dependences. */
2551 D = "{ S[i,j] : 0 <= i <= 10 }";
2552 V = "{ }";
2553 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2554 S = "{ S[i, j] -> [j, i] }";
2555 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2556 if (test_special_schedule(ctx, D, V, P, S) < 0)
2557 return -1;
2558 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2559 return test_special_schedule(ctx, D, V, P, S);
2560 }
2561
2562 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2563 {
2564 isl_union_map *umap;
2565 int test;
2566
2567 umap = isl_union_map_read_from_str(ctx, str);
2568 test = isl_union_map_plain_is_injective(umap);
2569 isl_union_map_free(umap);
2570 if (test < 0)
2571 return -1;
2572 if (test == injective)
2573 return 0;
2574 if (injective)
2575 isl_die(ctx, isl_error_unknown,
2576 "map not detected as injective", return -1);
2577 else
2578 isl_die(ctx, isl_error_unknown,
2579 "map detected as injective", return -1);
2580 }
2581
2582 int test_injective(isl_ctx *ctx)
2583 {
2584 const char *str;
2585
2586 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2587 return -1;
2588 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2589 return -1;
2590 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2591 return -1;
2592 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2593 return -1;
2594 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2595 return -1;
2596 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2597 return -1;
2598 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2599 return -1;
2600 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2601 return -1;
2602
2603 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2604 if (test_plain_injective(ctx, str, 1))
2605 return -1;
2606 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2607 if (test_plain_injective(ctx, str, 0))
2608 return -1;
2609
2610 return 0;
2611 }
2612
2613 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
2614 {
2615 isl_aff *aff2;
2616 int equal;
2617
2618 if (!aff)
2619 return -1;
2620
2621 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
2622 equal = isl_aff_plain_is_equal(aff, aff2);
2623 isl_aff_free(aff2);
2624
2625 return equal;
2626 }
2627
2628 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
2629 {
2630 int equal;
2631
2632 equal = aff_plain_is_equal(aff, str);
2633 if (equal < 0)
2634 return -1;
2635 if (!equal)
2636 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
2637 "result not as expected", return -1);
2638 return 0;
2639 }
2640
2641 int test_aff(isl_ctx *ctx)
2642 {
2643 const char *str;
2644 isl_set *set;
2645 isl_space *space;
2646 isl_local_space *ls;
2647 isl_aff *aff;
2648 int zero, equal;
2649
2650 space = isl_space_set_alloc(ctx, 0, 1);
2651 ls = isl_local_space_from_space(space);
2652 aff = isl_aff_zero_on_domain(ls);
2653
2654 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2655 aff = isl_aff_scale_down_ui(aff, 3);
2656 aff = isl_aff_floor(aff);
2657 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2658 aff = isl_aff_scale_down_ui(aff, 2);
2659 aff = isl_aff_floor(aff);
2660 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2661
2662 str = "{ [10] }";
2663 set = isl_set_read_from_str(ctx, str);
2664 aff = isl_aff_gist(aff, set);
2665
2666 aff = isl_aff_add_constant_si(aff, -16);
2667 zero = isl_aff_plain_is_zero(aff);
2668 isl_aff_free(aff);
2669
2670 if (zero < 0)
2671 return -1;
2672 if (!zero)
2673 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2674
2675 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
2676 aff = isl_aff_scale_down_ui(aff, 64);
2677 aff = isl_aff_floor(aff);
2678 equal = aff_check_plain_equal(aff, "{ [-1] }");
2679 isl_aff_free(aff);
2680 if (equal < 0)
2681 return -1;
2682
2683 return 0;
2684 }
2685
2686 int test_dim_max(isl_ctx *ctx)
2687 {
2688 int equal;
2689 const char *str;
2690 isl_set *set1, *set2;
2691 isl_set *set;
2692 isl_map *map;
2693 isl_pw_aff *pwaff;
2694
2695 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
2696 set = isl_set_read_from_str(ctx, str);
2697 pwaff = isl_set_dim_max(set, 0);
2698 set1 = isl_set_from_pw_aff(pwaff);
2699 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
2700 set2 = isl_set_read_from_str(ctx, str);
2701 equal = isl_set_is_equal(set1, set2);
2702 isl_set_free(set1);
2703 isl_set_free(set2);
2704 if (equal < 0)
2705 return -1;
2706 if (!equal)
2707 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2708
2709 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
2710 set = isl_set_read_from_str(ctx, str);
2711 pwaff = isl_set_dim_max(set, 0);
2712 set1 = isl_set_from_pw_aff(pwaff);
2713 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2714 set2 = isl_set_read_from_str(ctx, str);
2715 equal = isl_set_is_equal(set1, set2);
2716 isl_set_free(set1);
2717 isl_set_free(set2);
2718 if (equal < 0)
2719 return -1;
2720 if (!equal)
2721 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2722
2723 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
2724 set = isl_set_read_from_str(ctx, str);
2725 pwaff = isl_set_dim_max(set, 0);
2726 set1 = isl_set_from_pw_aff(pwaff);
2727 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
2728 set2 = isl_set_read_from_str(ctx, str);
2729 equal = isl_set_is_equal(set1, set2);
2730 isl_set_free(set1);
2731 isl_set_free(set2);
2732 if (equal < 0)
2733 return -1;
2734 if (!equal)
2735 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2736
2737 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
2738 "0 <= i < N and 0 <= j < M }";
2739 map = isl_map_read_from_str(ctx, str);
2740 set = isl_map_range(map);
2741
2742 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
2743 set1 = isl_set_from_pw_aff(pwaff);
2744 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
2745 set2 = isl_set_read_from_str(ctx, str);
2746 equal = isl_set_is_equal(set1, set2);
2747 isl_set_free(set1);
2748 isl_set_free(set2);
2749
2750 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
2751 set1 = isl_set_from_pw_aff(pwaff);
2752 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
2753 set2 = isl_set_read_from_str(ctx, str);
2754 if (equal >= 0 && equal)
2755 equal = isl_set_is_equal(set1, set2);
2756 isl_set_free(set1);
2757 isl_set_free(set2);
2758
2759 isl_set_free(set);
2760
2761 if (equal < 0)
2762 return -1;
2763 if (!equal)
2764 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2765
2766 return 0;
2767 }
2768
2769 int test_product(isl_ctx *ctx)
2770 {
2771 const char *str;
2772 isl_set *set;
2773 isl_union_set *uset1, *uset2;
2774 int ok;
2775
2776 str = "{ A[i] }";
2777 set = isl_set_read_from_str(ctx, str);
2778 set = isl_set_product(set, isl_set_copy(set));
2779 ok = isl_set_is_wrapping(set);
2780 isl_set_free(set);
2781 if (ok < 0)
2782 return -1;
2783 if (!ok)
2784 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2785
2786 str = "{ [] }";
2787 uset1 = isl_union_set_read_from_str(ctx, str);
2788 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
2789 str = "{ [[] -> []] }";
2790 uset2 = isl_union_set_read_from_str(ctx, str);
2791 ok = isl_union_set_is_equal(uset1, uset2);
2792 isl_union_set_free(uset1);
2793 isl_union_set_free(uset2);
2794 if (ok < 0)
2795 return -1;
2796 if (!ok)
2797 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2798
2799 return 0;
2800 }
2801
2802 int test_equal(isl_ctx *ctx)
2803 {
2804 const char *str;
2805 isl_set *set, *set2;
2806 int equal;
2807
2808 str = "{ S_6[i] }";
2809 set = isl_set_read_from_str(ctx, str);
2810 str = "{ S_7[i] }";
2811 set2 = isl_set_read_from_str(ctx, str);
2812 equal = isl_set_is_equal(set, set2);
2813 isl_set_free(set);
2814 isl_set_free(set2);
2815 if (equal < 0)
2816 return -1;
2817 if (equal)
2818 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2819
2820 return 0;
2821 }
2822
2823 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
2824 enum isl_dim_type type, unsigned pos, int fixed)
2825 {
2826 int test;
2827
2828 test = isl_map_plain_is_fixed(map, type, pos, NULL);
2829 isl_map_free(map);
2830 if (test < 0)
2831 return -1;
2832 if (test == fixed)
2833 return 0;
2834 if (fixed)
2835 isl_die(ctx, isl_error_unknown,
2836 "map not detected as fixed", return -1);
2837 else
2838 isl_die(ctx, isl_error_unknown,
2839 "map detected as fixed", return -1);
2840 }
2841
2842 int test_fixed(isl_ctx *ctx)
2843 {
2844 const char *str;
2845 isl_map *map;
2846
2847 str = "{ [i] -> [i] }";
2848 map = isl_map_read_from_str(ctx, str);
2849 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
2850 return -1;
2851 str = "{ [i] -> [1] }";
2852 map = isl_map_read_from_str(ctx, str);
2853 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2854 return -1;
2855 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
2856 map = isl_map_read_from_str(ctx, str);
2857 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2858 return -1;
2859 map = isl_map_read_from_str(ctx, str);
2860 map = isl_map_neg(map);
2861 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
2862 return -1;
2863
2864 return 0;
2865 }
2866
2867 int test_vertices(isl_ctx *ctx)
2868 {
2869 const char *str;
2870 isl_basic_set *bset;
2871 isl_vertices *vertices;
2872
2873 str = "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
2874 bset = isl_basic_set_read_from_str(ctx, str);
2875 vertices = isl_basic_set_compute_vertices(bset);
2876 isl_basic_set_free(bset);
2877 isl_vertices_free(vertices);
2878 if (!vertices)
2879 return -1;
2880
2881 str = "{ A[t, i] : t = 14 and i = 1 }";
2882 bset = isl_basic_set_read_from_str(ctx, str);
2883 vertices = isl_basic_set_compute_vertices(bset);
2884 isl_basic_set_free(bset);
2885 isl_vertices_free(vertices);
2886 if (!vertices)
2887 return -1;
2888
2889 return 0;
2890 }
2891
2892 int test_union_pw(isl_ctx *ctx)
2893 {
2894 int equal;
2895 const char *str;
2896 isl_union_set *uset;
2897 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
2898
2899 str = "{ [x] -> x^2 }";
2900 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
2901 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
2902 uset = isl_union_pw_qpolynomial_domain(upwqp1);
2903 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
2904 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
2905 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
2906 isl_union_pw_qpolynomial_free(upwqp1);
2907 isl_union_pw_qpolynomial_free(upwqp2);
2908 if (equal < 0)
2909 return -1;
2910 if (!equal)
2911 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2912
2913 return 0;
2914 }
2915
2916 int test_output(isl_ctx *ctx)
2917 {
2918 char *s;
2919 const char *str;
2920 isl_pw_aff *pa;
2921 isl_printer *p;
2922 int equal;
2923
2924 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
2925 pa = isl_pw_aff_read_from_str(ctx, str);
2926
2927 p = isl_printer_to_str(ctx);
2928 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
2929 p = isl_printer_print_pw_aff(p, pa);
2930 s = isl_printer_get_str(p);
2931 isl_printer_free(p);
2932 isl_pw_aff_free(pa);
2933 equal = !strcmp(s, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
2934 free(s);
2935 if (equal < 0)
2936 return -1;
2937 if (!equal)
2938 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2939
2940 return 0;
2941 }
2942
2943 int test_sample(isl_ctx *ctx)
2944 {
2945 const char *str;
2946 isl_basic_set *bset1, *bset2;
2947 int empty, subset;
2948
2949 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
2950 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
2951 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
2952 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
2953 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
2954 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
2955 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
2956 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
2957 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
2958 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
2959 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
2960 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
2961 "d - 1073741821e and "
2962 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
2963 "3j >= 1 - a + b + 2e and "
2964 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
2965 "3i <= 4 - a + 4b - e and "
2966 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
2967 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
2968 "c <= -1 + a and 3i >= -2 - a + 3e and "
2969 "1073741822e <= 1073741823 - a + 1073741822b + c and "
2970 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
2971 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
2972 "1073741823e >= 1 + 1073741823b - d and "
2973 "3i >= 1073741823b + c - 1073741823e - f and "
2974 "3i >= 1 + 2b + e + 3g }";
2975 bset1 = isl_basic_set_read_from_str(ctx, str);
2976 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
2977 empty = isl_basic_set_is_empty(bset2);
2978 subset = isl_basic_set_is_subset(bset2, bset1);
2979 isl_basic_set_free(bset1);
2980 isl_basic_set_free(bset2);
2981 if (empty)
2982 isl_die(ctx, isl_error_unknown, "point not found", return -1);
2983 if (!subset)
2984 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
2985
2986 return 0;
2987 }
2988
2989 int test_fixed_power(isl_ctx *ctx)
2990 {
2991 const char *str;
2992 isl_map *map;
2993 isl_int exp;
2994 int equal;
2995
2996 isl_int_init(exp);
2997 str = "{ [i] -> [i + 1] }";
2998 map = isl_map_read_from_str(ctx, str);
2999 isl_int_set_si(exp, 23);
3000 map = isl_map_fixed_power(map, exp);
3001 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
3002 isl_int_clear(exp);
3003 isl_map_free(map);
3004 if (equal < 0)
3005 return -1;
3006
3007 return 0;
3008 }
3009
3010 int test_slice(isl_ctx *ctx)
3011 {
3012 const char *str;
3013 isl_map *map;
3014 int equal;
3015
3016 str = "{ [i] -> [j] }";
3017 map = isl_map_read_from_str(ctx, str);
3018 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
3019 equal = map_check_equal(map, "{ [i] -> [i] }");
3020 isl_map_free(map);
3021 if (equal < 0)
3022 return -1;
3023
3024 str = "{ [i] -> [j] }";
3025 map = isl_map_read_from_str(ctx, str);
3026 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
3027 equal = map_check_equal(map, "{ [i] -> [j] }");
3028 isl_map_free(map);
3029 if (equal < 0)
3030 return -1;
3031
3032 str = "{ [i] -> [j] }";
3033 map = isl_map_read_from_str(ctx, str);
3034 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
3035 equal = map_check_equal(map, "{ [i] -> [-i] }");
3036 isl_map_free(map);
3037 if (equal < 0)
3038 return -1;
3039
3040 str = "{ [i] -> [j] }";
3041 map = isl_map_read_from_str(ctx, str);
3042 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
3043 equal = map_check_equal(map, "{ [0] -> [j] }");
3044 isl_map_free(map);
3045 if (equal < 0)
3046 return -1;
3047
3048 str = "{ [i] -> [j] }";
3049 map = isl_map_read_from_str(ctx, str);
3050 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
3051 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
3052 isl_map_free(map);
3053 if (equal < 0)
3054 return -1;
3055
3056 str = "{ [i] -> [j] }";
3057 map = isl_map_read_from_str(ctx, str);
3058 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
3059 equal = map_check_equal(map, "{ [i] -> [j] : false }");
3060 isl_map_free(map);
3061 if (equal < 0)
3062 return -1;
3063
3064 return 0;
3065 }
3066
3067 int test_eliminate(isl_ctx *ctx)
3068 {
3069 const char *str;
3070 isl_map *map;
3071 int equal;
3072
3073 str = "{ [i] -> [j] : i = 2j }";
3074 map = isl_map_read_from_str(ctx, str);
3075 map = isl_map_eliminate(map, isl_dim_out, 0, 1);
3076 equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
3077 isl_map_free(map);
3078 if (equal < 0)
3079 return -1;
3080
3081 return 0;
3082 }
3083
3084 /* Check that isl_set_dim_residue_class detects that the values of j
3085 * in the set below are all odd and that it does not detect any spurious
3086 * strides.
3087 */
3088 static int test_residue_class(isl_ctx *ctx)
3089 {
3090 const char *str;
3091 isl_set *set;
3092 isl_int m, r;
3093 int res;
3094
3095 str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3096 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3097 set = isl_set_read_from_str(ctx, str);
3098 isl_int_init(m);
3099 isl_int_init(r);
3100 res = isl_set_dim_residue_class(set, 1, &m, &r);
3101 if (res >= 0 &&
3102 (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
3103 isl_die(ctx, isl_error_unknown, "incorrect residue class",
3104 res = -1);
3105 isl_int_clear(r);
3106 isl_int_clear(m);
3107 isl_set_free(set);
3108
3109 return res;
3110 }
3111
3112 int test_align_parameters(isl_ctx *ctx)
3113 {
3114 const char *str;
3115 isl_space *space;
3116 isl_multi_aff *ma1, *ma2;
3117 int equal;
3118
3119 str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3120 ma1 = isl_multi_aff_read_from_str(ctx, str);
3121
3122 space = isl_space_params_alloc(ctx, 1);
3123 space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
3124 ma1 = isl_multi_aff_align_params(ma1, space);
3125
3126 str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3127 ma2 = isl_multi_aff_read_from_str(ctx, str);
3128
3129 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3130
3131 isl_multi_aff_free(ma1);
3132 isl_multi_aff_free(ma2);
3133
3134 if (equal < 0)
3135 return -1;
3136 if (!equal)
3137 isl_die(ctx, isl_error_unknown,
3138 "result not as expected", return -1);
3139
3140 return 0;
3141 }
3142
3143 static int test_list(isl_ctx *ctx)
3144 {
3145 isl_id *a, *b, *c, *d, *id;
3146 isl_id_list *list;
3147 int ok;
3148
3149 a = isl_id_alloc(ctx, "a", NULL);
3150 b = isl_id_alloc(ctx, "b", NULL);
3151 c = isl_id_alloc(ctx, "c", NULL);
3152 d = isl_id_alloc(ctx, "d", NULL);
3153
3154 list = isl_id_list_alloc(ctx, 4);
3155 list = isl_id_list_add(list, a);
3156 list = isl_id_list_add(list, b);
3157 list = isl_id_list_add(list, c);
3158 list = isl_id_list_add(list, d);
3159 list = isl_id_list_drop(list, 1, 1);
3160
3161 if (isl_id_list_n_id(list) != 3) {
3162 isl_id_list_free(list);
3163 isl_die(ctx, isl_error_unknown,
3164 "unexpected number of elements in list", return -1);
3165 }
3166
3167 id = isl_id_list_get_id(list, 0);
3168 ok = id == a;
3169 isl_id_free(id);
3170 id = isl_id_list_get_id(list, 1);
3171 ok = ok && id == c;
3172 isl_id_free(id);
3173 id = isl_id_list_get_id(list, 2);
3174 ok = ok && id == d;
3175 isl_id_free(id);
3176
3177 isl_id_list_free(list);
3178
3179 if (!ok)
3180 isl_die(ctx, isl_error_unknown,
3181 "unexpected elements in list", return -1);
3182
3183 return 0;
3184 }
3185
3186 const char *set_conversion_tests[] = {
3187 "[N] -> { [i] : N - 1 <= 2 i <= N }",
3188 };
3189
3190 /* Check that converting from isl_set to isl_pw_multi_aff and back
3191 * to isl_set produces the original isl_set.
3192 */
3193 static int test_conversion(isl_ctx *ctx)
3194 {
3195 int i;
3196 const char *str;
3197 isl_set *set1, *set2;
3198 isl_pw_multi_aff *pma;
3199 int equal;
3200
3201 for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
3202 str = set_conversion_tests[i];
3203 set1 = isl_set_read_from_str(ctx, str);
3204 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
3205 set2 = isl_set_from_pw_multi_aff(pma);
3206 equal = isl_set_is_equal(set1, set2);
3207 isl_set_free(set1);
3208 isl_set_free(set2);
3209
3210 if (equal < 0)
3211 return -1;
3212 if (!equal)
3213 isl_die(ctx, isl_error_unknown, "bad conversion",
3214 return -1);
3215 }
3216
3217 return 0;
3218 }
3219
3220 struct {
3221 const char *set;
3222 const char *ma;
3223 const char *res;
3224 } preimage_tests[] = {
3225 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
3226 "{ A[j,i] -> B[i,j] }",
3227 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
3228 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3229 "{ A[a,b] -> B[a/2,b/6] }",
3230 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
3231 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3232 "{ A[a,b] -> B[a/2,b/6] }",
3233 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
3234 "exists i,j : a = 2 i and b = 6 j }" },
3235 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
3236 "[n] -> { : 0 <= n <= 100 }" },
3237 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3238 "{ A[a] -> B[2a] }",
3239 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
3240 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3241 "{ A[a] -> B[([a/2])] }",
3242 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
3243 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
3244 "{ A[a] -> B[a,a,a/3] }",
3245 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
3246 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
3247 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
3248 };
3249
3250 int test_preimage(isl_ctx *ctx)
3251 {
3252 int i;
3253 isl_basic_set *bset1, *bset2;
3254 isl_multi_aff *ma;
3255 int equal;
3256
3257 for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
3258 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
3259 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
3260 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
3261 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
3262 equal = isl_basic_set_is_equal(bset1, bset2);
3263 isl_basic_set_free(bset1);
3264 isl_basic_set_free(bset2);
3265 if (equal < 0)
3266 return -1;
3267 if (!equal)
3268 isl_die(ctx, isl_error_unknown, "bad preimage",
3269 return -1);
3270 }
3271
3272 return 0;
3273 }
3274
3275 struct {
3276 const char *ma1;
3277 const char *ma;
3278 const char *res;
3279 } pullback_tests[] = {
3280 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
3281 "{ A[a,b] -> C[b + 2a] }" },
3282 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
3283 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
3284 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
3285 "{ A[a] -> C[(a)/6] }" },
3286 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
3287 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
3288 "{ A[a] -> C[(2a)/3] }" },
3289 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
3290 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
3291 "{ A[i,j] -> C[i + j, i + j] }"},
3292 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
3293 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
3294 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
3295 };
3296
3297 static int test_pullback(isl_ctx *ctx)
3298 {
3299 int i;
3300 isl_multi_aff *ma1, *ma2;
3301 isl_multi_aff *ma;
3302 int equal;
3303
3304 for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
3305 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
3306 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
3307 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
3308 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
3309 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3310 isl_multi_aff_free(ma1);
3311 isl_multi_aff_free(ma2);
3312 if (equal < 0)
3313 return -1;
3314 if (!equal)
3315 isl_die(ctx, isl_error_unknown, "bad pullback",
3316 return -1);
3317 }
3318
3319 return 0;
3320 }
3321
3322 struct {
3323 const char *name;
3324 int (*fn)(isl_ctx *ctx);
3325 } tests [] = {
3326 { "conversion", &test_conversion },
3327 { "list", &test_list },
3328 { "align parameters", &test_align_parameters },
3329 { "preimage", &test_preimage },
3330 { "pullback", &test_pullback },
3331 { "eliminate", &test_eliminate },
3332 { "reisdue class", &test_residue_class },
3333 { "div", &test_div },
3334 { "slice", &test_slice },
3335 { "fixed power", &test_fixed_power },
3336 { "sample", &test_sample },
3337 { "output", &test_output },
3338 { "vertices", &test_vertices },
3339 { "fixed", &test_fixed },
3340 { "equal", &test_equal },
3341 { "product", &test_product },
3342 { "dim_max", &test_dim_max },
3343 { "affine", &test_aff },
3344 { "injective", &test_injective },
3345 { "schedule", &test_schedule },
3346 { "union_pw", &test_union_pw },
3347 { "parse", &test_parse },
3348 { "single-valued", &test_sv },
3349 { "affine hull", &test_affine_hull },
3350 { "coalesce", &test_coalesce },
3351 { "factorize", &test_factorize },
3352 { "subset", &test_subset },
3353 { "subtract", &test_subtract },
3354 };
3355
3356 int main()
3357 {
3358 int i;
3359 struct isl_ctx *ctx;
3360
3361 srcdir = getenv("srcdir");
3362 assert(srcdir);
3363
3364 ctx = isl_ctx_alloc();
3365 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
3366 printf("%s\n", tests[i].name);
3367 if (tests[i].fn(ctx) < 0)
3368 goto error;
3369 }
3370 test_lift(ctx);
3371 test_bound(ctx);
3372 test_union(ctx);
3373 test_split_periods(ctx);
3374 test_pwqp(ctx);
3375 test_lex(ctx);
3376 test_bijective(ctx);
3377 test_dep(ctx);
3378 test_read(ctx);
3379 test_bounded(ctx);
3380 test_construction(ctx);
3381 test_dim(ctx);
3382 test_application(ctx);
3383 test_convex_hull(ctx);
3384 test_gist(ctx);
3385 test_closure(ctx);
3386 test_lexmin(ctx);
3387 isl_ctx_free(ctx);
3388 return 0;
3389 error:
3390 isl_ctx_free(ctx);
3391 return -1;
3392 }
Integer set library