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add isl_union_map_flat_range_product
[isl.git] / isl_test.c
blob55a50d54957aba48be427f8572fc7a6d831b60ea
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
9
10 #include <assert.h>
11 #include <stdio.h>
12 #include <limits.h>
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl/set.h>
16 #include <isl/flow.h>
17 #include <isl/constraint.h>
18 #include <isl/polynomial.h>
19 #include <isl/union_map.h>
20 #include <isl_factorization.h>
21 #include <isl/schedule.h>
22
23 static char *srcdir;
24
25 void test_parse_map(isl_ctx *ctx, const char *str)
26 {
27 isl_map *map;
28
29 map = isl_map_read_from_str(ctx, str, -1);
30 assert(map);
31 isl_map_free(map);
32 }
33
34 void test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
35 {
36 isl_map *map, *map2;
37
38 map = isl_map_read_from_str(ctx, str, -1);
39 map2 = isl_map_read_from_str(ctx, str2, -1);
40 assert(map && map2 && isl_map_is_equal(map, map2));
41 isl_map_free(map);
42 isl_map_free(map2);
43 }
44
45 void test_parse_pwqp(isl_ctx *ctx, const char *str)
46 {
47 isl_pw_qpolynomial *pwqp;
48
49 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
50 assert(pwqp);
51 isl_pw_qpolynomial_free(pwqp);
52 }
53
54 void test_parse(struct isl_ctx *ctx)
55 {
56 isl_map *map, *map2;
57 const char *str, *str2;
58
59 str = "{ [i] -> [-i] }";
60 map = isl_map_read_from_str(ctx, str, -1);
61 assert(map);
62 isl_map_free(map);
63
64 str = "{ A[i] -> L[([i/3])] }";
65 map = isl_map_read_from_str(ctx, str, -1);
66 assert(map);
67 isl_map_free(map);
68
69 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
70 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
71 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
72
73 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
74 str2 = "{ [x, y] : 2y >= 6 - x }";
75 test_parse_map_equal(ctx, str, str2);
76
77 test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
78 "{ [x,y] : x <= y, 2*y + 3 }");
79 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
80 test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }", str);
81
82 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
83 map = isl_map_read_from_str(ctx, str, -1);
84 str = "{ [new, old] -> [o0, o1] : "
85 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
86 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
87 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
88 map2 = isl_map_read_from_str(ctx, str, -1);
89 assert(isl_map_is_equal(map, map2));
90 isl_map_free(map);
91 isl_map_free(map2);
92
93 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
94 map = isl_map_read_from_str(ctx, str, -1);
95 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
96 map2 = isl_map_read_from_str(ctx, str, -1);
97 assert(isl_map_is_equal(map, map2));
98 isl_map_free(map);
99 isl_map_free(map2);
100
101 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
102 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
103 test_parse_map_equal(ctx, str, str2);
104
105 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
106 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
107 }
108
109 void test_read(struct isl_ctx *ctx)
110 {
111 char filename[PATH_MAX];
112 FILE *input;
113 int n;
114 struct isl_basic_set *bset1, *bset2;
115 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
116
117 n = snprintf(filename, sizeof(filename),
118 "%s/test_inputs/set.omega", srcdir);
119 assert(n < sizeof(filename));
120 input = fopen(filename, "r");
121 assert(input);
122
123 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
124 bset2 = isl_basic_set_read_from_str(ctx, str, 0);
125
126 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
127
128 isl_basic_set_free(bset1);
129 isl_basic_set_free(bset2);
130
131 fclose(input);
132 }
133
134 void test_bounded(struct isl_ctx *ctx)
135 {
136 isl_set *set;
137 int bounded;
138
139 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }", -1);
140 bounded = isl_set_is_bounded(set);
141 assert(bounded);
142 isl_set_free(set);
143
144 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }", -1);
145 bounded = isl_set_is_bounded(set);
146 assert(!bounded);
147 isl_set_free(set);
148
149 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }", -1);
150 bounded = isl_set_is_bounded(set);
151 assert(!bounded);
152 isl_set_free(set);
153 }
154
155 /* Construct the basic set { [i] : 5 <= i <= N } */
156 void test_construction(struct isl_ctx *ctx)
157 {
158 isl_int v;
159 struct isl_dim *dim;
160 struct isl_basic_set *bset;
161 struct isl_constraint *c;
162
163 isl_int_init(v);
164
165 dim = isl_dim_set_alloc(ctx, 1, 1);
166 bset = isl_basic_set_universe(dim);
167
168 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
169 isl_int_set_si(v, -1);
170 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
171 isl_int_set_si(v, 1);
172 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
173 bset = isl_basic_set_add_constraint(bset, c);
174
175 c = isl_inequality_alloc(isl_basic_set_get_dim(bset));
176 isl_int_set_si(v, 1);
177 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
178 isl_int_set_si(v, -5);
179 isl_constraint_set_constant(c, v);
180 bset = isl_basic_set_add_constraint(bset, c);
181
182 isl_basic_set_free(bset);
183
184 isl_int_clear(v);
185 }
186
187 void test_dim(struct isl_ctx *ctx)
188 {
189 const char *str;
190 isl_map *map1, *map2;
191
192 map1 = isl_map_read_from_str(ctx,
193 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
194 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
195 map2 = isl_map_read_from_str(ctx,
196 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }", -1);
197 assert(isl_map_is_equal(map1, map2));
198 isl_map_free(map2);
199
200 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
201 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }", -1);
202 assert(isl_map_is_equal(map1, map2));
203
204 isl_map_free(map1);
205 isl_map_free(map2);
206
207 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
208 map1 = isl_map_read_from_str(ctx, str, -1);
209 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
210 map2 = isl_map_read_from_str(ctx, str, -1);
211 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
212 assert(isl_map_is_equal(map1, map2));
213
214 isl_map_free(map1);
215 isl_map_free(map2);
216 }
217
218 void test_div(struct isl_ctx *ctx)
219 {
220 isl_int v;
221 int pos;
222 struct isl_dim *dim;
223 struct isl_div *div;
224 struct isl_basic_set *bset;
225 struct isl_constraint *c;
226
227 isl_int_init(v);
228
229 /* test 1 */
230 dim = isl_dim_set_alloc(ctx, 0, 1);
231 bset = isl_basic_set_universe(dim);
232
233 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
234 isl_int_set_si(v, -1);
235 isl_constraint_set_constant(c, v);
236 isl_int_set_si(v, 1);
237 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
238 div = isl_div_alloc(isl_basic_set_get_dim(bset));
239 c = isl_constraint_add_div(c, div, &pos);
240 isl_int_set_si(v, 3);
241 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
242 bset = isl_basic_set_add_constraint(bset, c);
243
244 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
245 isl_int_set_si(v, 1);
246 isl_constraint_set_constant(c, v);
247 isl_int_set_si(v, -1);
248 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
249 div = isl_div_alloc(isl_basic_set_get_dim(bset));
250 c = isl_constraint_add_div(c, div, &pos);
251 isl_int_set_si(v, 3);
252 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
253 bset = isl_basic_set_add_constraint(bset, c);
254
255 assert(bset && bset->n_div == 1);
256 isl_basic_set_free(bset);
257
258 /* test 2 */
259 dim = isl_dim_set_alloc(ctx, 0, 1);
260 bset = isl_basic_set_universe(dim);
261
262 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
263 isl_int_set_si(v, 1);
264 isl_constraint_set_constant(c, v);
265 isl_int_set_si(v, -1);
266 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
267 div = isl_div_alloc(isl_basic_set_get_dim(bset));
268 c = isl_constraint_add_div(c, div, &pos);
269 isl_int_set_si(v, 3);
270 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
271 bset = isl_basic_set_add_constraint(bset, c);
272
273 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
274 isl_int_set_si(v, -1);
275 isl_constraint_set_constant(c, v);
276 isl_int_set_si(v, 1);
277 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
278 div = isl_div_alloc(isl_basic_set_get_dim(bset));
279 c = isl_constraint_add_div(c, div, &pos);
280 isl_int_set_si(v, 3);
281 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
282 bset = isl_basic_set_add_constraint(bset, c);
283
284 assert(bset && bset->n_div == 1);
285 isl_basic_set_free(bset);
286
287 /* test 3 */
288 dim = isl_dim_set_alloc(ctx, 0, 1);
289 bset = isl_basic_set_universe(dim);
290
291 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
292 isl_int_set_si(v, 1);
293 isl_constraint_set_constant(c, v);
294 isl_int_set_si(v, -1);
295 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
296 div = isl_div_alloc(isl_basic_set_get_dim(bset));
297 c = isl_constraint_add_div(c, div, &pos);
298 isl_int_set_si(v, 3);
299 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
300 bset = isl_basic_set_add_constraint(bset, c);
301
302 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
303 isl_int_set_si(v, -3);
304 isl_constraint_set_constant(c, v);
305 isl_int_set_si(v, 1);
306 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
307 div = isl_div_alloc(isl_basic_set_get_dim(bset));
308 c = isl_constraint_add_div(c, div, &pos);
309 isl_int_set_si(v, 4);
310 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
311 bset = isl_basic_set_add_constraint(bset, c);
312
313 assert(bset && bset->n_div == 1);
314 isl_basic_set_free(bset);
315
316 /* test 4 */
317 dim = isl_dim_set_alloc(ctx, 0, 1);
318 bset = isl_basic_set_universe(dim);
319
320 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
321 isl_int_set_si(v, 2);
322 isl_constraint_set_constant(c, v);
323 isl_int_set_si(v, -1);
324 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
325 div = isl_div_alloc(isl_basic_set_get_dim(bset));
326 c = isl_constraint_add_div(c, div, &pos);
327 isl_int_set_si(v, 3);
328 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
329 bset = isl_basic_set_add_constraint(bset, c);
330
331 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
332 isl_int_set_si(v, -1);
333 isl_constraint_set_constant(c, v);
334 isl_int_set_si(v, 1);
335 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
336 div = isl_div_alloc(isl_basic_set_get_dim(bset));
337 c = isl_constraint_add_div(c, div, &pos);
338 isl_int_set_si(v, 6);
339 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
340 bset = isl_basic_set_add_constraint(bset, c);
341
342 assert(isl_basic_set_is_empty(bset));
343 isl_basic_set_free(bset);
344
345 /* test 5 */
346 dim = isl_dim_set_alloc(ctx, 0, 2);
347 bset = isl_basic_set_universe(dim);
348
349 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
350 isl_int_set_si(v, -1);
351 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
352 div = isl_div_alloc(isl_basic_set_get_dim(bset));
353 c = isl_constraint_add_div(c, div, &pos);
354 isl_int_set_si(v, 3);
355 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
356 bset = isl_basic_set_add_constraint(bset, c);
357
358 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
359 isl_int_set_si(v, 1);
360 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
361 isl_int_set_si(v, -3);
362 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
363 bset = isl_basic_set_add_constraint(bset, c);
364
365 assert(bset && bset->n_div == 0);
366 isl_basic_set_free(bset);
367
368 /* test 6 */
369 dim = isl_dim_set_alloc(ctx, 0, 2);
370 bset = isl_basic_set_universe(dim);
371
372 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
373 isl_int_set_si(v, -1);
374 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
375 div = isl_div_alloc(isl_basic_set_get_dim(bset));
376 c = isl_constraint_add_div(c, div, &pos);
377 isl_int_set_si(v, 6);
378 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
379 bset = isl_basic_set_add_constraint(bset, c);
380
381 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
382 isl_int_set_si(v, 1);
383 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
384 isl_int_set_si(v, -3);
385 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
386 bset = isl_basic_set_add_constraint(bset, c);
387
388 assert(bset && bset->n_div == 1);
389 isl_basic_set_free(bset);
390
391 /* test 7 */
392 /* This test is a bit tricky. We set up an equality
393 * a + 3b + 3c = 6 e0
394 * Normalization of divs creates _two_ divs
395 * a = 3 e0
396 * c - b - e0 = 2 e1
397 * Afterwards e0 is removed again because it has coefficient -1
398 * and we end up with the original equality and div again.
399 * Perhaps we can avoid the introduction of this temporary div.
400 */
401 dim = isl_dim_set_alloc(ctx, 0, 3);
402 bset = isl_basic_set_universe(dim);
403
404 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
405 isl_int_set_si(v, -1);
406 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
407 isl_int_set_si(v, -3);
408 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
409 isl_int_set_si(v, -3);
410 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
411 div = isl_div_alloc(isl_basic_set_get_dim(bset));
412 c = isl_constraint_add_div(c, div, &pos);
413 isl_int_set_si(v, 6);
414 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
415 bset = isl_basic_set_add_constraint(bset, c);
416
417 /* Test disabled for now */
418 /*
419 assert(bset && bset->n_div == 1);
420 */
421 isl_basic_set_free(bset);
422
423 /* test 8 */
424 dim = isl_dim_set_alloc(ctx, 0, 4);
425 bset = isl_basic_set_universe(dim);
426
427 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
428 isl_int_set_si(v, -1);
429 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
430 isl_int_set_si(v, -3);
431 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
432 isl_int_set_si(v, -3);
433 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
434 div = isl_div_alloc(isl_basic_set_get_dim(bset));
435 c = isl_constraint_add_div(c, div, &pos);
436 isl_int_set_si(v, 6);
437 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
438 bset = isl_basic_set_add_constraint(bset, c);
439
440 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
441 isl_int_set_si(v, -1);
442 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
443 isl_int_set_si(v, 1);
444 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
445 isl_int_set_si(v, 1);
446 isl_constraint_set_constant(c, v);
447 bset = isl_basic_set_add_constraint(bset, c);
448
449 /* Test disabled for now */
450 /*
451 assert(bset && bset->n_div == 1);
452 */
453 isl_basic_set_free(bset);
454
455 /* test 9 */
456 dim = isl_dim_set_alloc(ctx, 0, 2);
457 bset = isl_basic_set_universe(dim);
458
459 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
460 isl_int_set_si(v, 1);
461 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
462 isl_int_set_si(v, -1);
463 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
464 div = isl_div_alloc(isl_basic_set_get_dim(bset));
465 c = isl_constraint_add_div(c, div, &pos);
466 isl_int_set_si(v, -2);
467 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
468 bset = isl_basic_set_add_constraint(bset, c);
469
470 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
471 isl_int_set_si(v, -1);
472 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
473 div = isl_div_alloc(isl_basic_set_get_dim(bset));
474 c = isl_constraint_add_div(c, div, &pos);
475 isl_int_set_si(v, 3);
476 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
477 isl_int_set_si(v, 2);
478 isl_constraint_set_constant(c, v);
479 bset = isl_basic_set_add_constraint(bset, c);
480
481 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
482
483 assert(!isl_basic_set_is_empty(bset));
484
485 isl_basic_set_free(bset);
486
487 /* test 10 */
488 dim = isl_dim_set_alloc(ctx, 0, 2);
489 bset = isl_basic_set_universe(dim);
490
491 c = isl_equality_alloc(isl_basic_set_get_dim(bset));
492 isl_int_set_si(v, 1);
493 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
494 div = isl_div_alloc(isl_basic_set_get_dim(bset));
495 c = isl_constraint_add_div(c, div, &pos);
496 isl_int_set_si(v, -2);
497 isl_constraint_set_coefficient(c, isl_dim_div, pos, v);
498 bset = isl_basic_set_add_constraint(bset, c);
499
500 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
501
502 isl_basic_set_free(bset);
503
504 isl_int_clear(v);
505 }
506
507 void test_application_case(struct isl_ctx *ctx, const char *name)
508 {
509 char filename[PATH_MAX];
510 FILE *input;
511 int n;
512 struct isl_basic_set *bset1, *bset2;
513 struct isl_basic_map *bmap;
514
515 n = snprintf(filename, sizeof(filename),
516 "%s/test_inputs/%s.omega", srcdir, name);
517 assert(n < sizeof(filename));
518 input = fopen(filename, "r");
519 assert(input);
520
521 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
522 bmap = isl_basic_map_read_from_file(ctx, input, 0);
523
524 bset1 = isl_basic_set_apply(bset1, bmap);
525
526 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
527
528 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
529
530 isl_basic_set_free(bset1);
531 isl_basic_set_free(bset2);
532
533 fclose(input);
534 }
535
536 void test_application(struct isl_ctx *ctx)
537 {
538 test_application_case(ctx, "application");
539 test_application_case(ctx, "application2");
540 }
541
542 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
543 {
544 char filename[PATH_MAX];
545 FILE *input;
546 int n;
547 struct isl_basic_set *bset1, *bset2;
548
549 n = snprintf(filename, sizeof(filename),
550 "%s/test_inputs/%s.polylib", srcdir, name);
551 assert(n < sizeof(filename));
552 input = fopen(filename, "r");
553 assert(input);
554
555 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
556 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
557
558 bset1 = isl_basic_set_affine_hull(bset1);
559
560 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
561
562 isl_basic_set_free(bset1);
563 isl_basic_set_free(bset2);
564
565 fclose(input);
566 }
567
568 void test_affine_hull(struct isl_ctx *ctx)
569 {
570 test_affine_hull_case(ctx, "affine2");
571 test_affine_hull_case(ctx, "affine");
572 test_affine_hull_case(ctx, "affine3");
573 }
574
575 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
576 {
577 char filename[PATH_MAX];
578 FILE *input;
579 int n;
580 struct isl_basic_set *bset1, *bset2;
581 struct isl_set *set;
582
583 n = snprintf(filename, sizeof(filename),
584 "%s/test_inputs/%s.polylib", srcdir, name);
585 assert(n < sizeof(filename));
586 input = fopen(filename, "r");
587 assert(input);
588
589 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
590 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
591
592 set = isl_basic_set_union(bset1, bset2);
593 bset1 = isl_set_convex_hull(set);
594
595 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
596
597 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
598
599 isl_basic_set_free(bset1);
600 isl_basic_set_free(bset2);
601
602 fclose(input);
603 }
604
605 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
606 {
607 const char *str1, *str2;
608 isl_set *set1, *set2;
609 int orig_convex = ctx->opt->convex;
610 ctx->opt->convex = convex;
611
612 test_convex_hull_case(ctx, "convex0");
613 test_convex_hull_case(ctx, "convex1");
614 test_convex_hull_case(ctx, "convex2");
615 test_convex_hull_case(ctx, "convex3");
616 test_convex_hull_case(ctx, "convex4");
617 test_convex_hull_case(ctx, "convex5");
618 test_convex_hull_case(ctx, "convex6");
619 test_convex_hull_case(ctx, "convex7");
620 test_convex_hull_case(ctx, "convex8");
621 test_convex_hull_case(ctx, "convex9");
622 test_convex_hull_case(ctx, "convex10");
623 test_convex_hull_case(ctx, "convex11");
624 test_convex_hull_case(ctx, "convex12");
625 test_convex_hull_case(ctx, "convex13");
626 test_convex_hull_case(ctx, "convex14");
627 test_convex_hull_case(ctx, "convex15");
628
629 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
630 "(i0 = 1 and i1 = 0 and i2 = 1) or "
631 "(i0 = 0 and i1 = 0 and i2 = 0) }";
632 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
633 set1 = isl_set_read_from_str(ctx, str1, -1);
634 set2 = isl_set_read_from_str(ctx, str2, -1);
635 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
636 assert(isl_set_is_equal(set1, set2));
637 isl_set_free(set1);
638 isl_set_free(set2);
639
640 ctx->opt->convex = orig_convex;
641 }
642
643 void test_convex_hull(struct isl_ctx *ctx)
644 {
645 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
646 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
647 }
648
649 void test_gist_case(struct isl_ctx *ctx, const char *name)
650 {
651 char filename[PATH_MAX];
652 FILE *input;
653 int n;
654 struct isl_basic_set *bset1, *bset2;
655
656 n = snprintf(filename, sizeof(filename),
657 "%s/test_inputs/%s.polylib", srcdir, name);
658 assert(n < sizeof(filename));
659 input = fopen(filename, "r");
660 assert(input);
661
662 bset1 = isl_basic_set_read_from_file(ctx, input, 0);
663 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
664
665 bset1 = isl_basic_set_gist(bset1, bset2);
666
667 bset2 = isl_basic_set_read_from_file(ctx, input, 0);
668
669 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
670
671 isl_basic_set_free(bset1);
672 isl_basic_set_free(bset2);
673
674 fclose(input);
675 }
676
677 void test_gist(struct isl_ctx *ctx)
678 {
679 const char *str;
680 isl_basic_set *bset1, *bset2;
681
682 test_gist_case(ctx, "gist1");
683
684 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
685 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
686 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
687 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
688 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
689 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
690 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
691 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
692 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
693 bset1 = isl_basic_set_read_from_str(ctx, str, -1);
694 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
695 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
696 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
697 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
698 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
699 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
700 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
701 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
702 bset2 = isl_basic_set_read_from_str(ctx, str, -1);
703 bset1 = isl_basic_set_gist(bset1, bset2);
704 assert(bset1 && bset1->n_div == 0);
705 isl_basic_set_free(bset1);
706 }
707
708 void test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
709 {
710 isl_set *set, *set2;
711
712 set = isl_set_read_from_str(ctx, str, -1);
713 set = isl_set_coalesce(set);
714 set2 = isl_set_read_from_str(ctx, str, -1);
715 assert(isl_set_is_equal(set, set2));
716 if (check_one)
717 assert(set && set->n == 1);
718 isl_set_free(set);
719 isl_set_free(set2);
720 }
721
722 void test_coalesce(struct isl_ctx *ctx)
723 {
724 const char *str;
725 struct isl_set *set, *set2;
726 struct isl_map *map, *map2;
727
728 set = isl_set_read_from_str(ctx,
729 "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
730 "y >= x & x >= 2 & 5 >= y }", -1);
731 set = isl_set_coalesce(set);
732 assert(set && set->n == 1);
733 isl_set_free(set);
734
735 set = isl_set_read_from_str(ctx,
736 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
737 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}", -1);
738 set = isl_set_coalesce(set);
739 assert(set && set->n == 1);
740 isl_set_free(set);
741
742 set = isl_set_read_from_str(ctx,
743 "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
744 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}", -1);
745 set = isl_set_coalesce(set);
746 assert(set && set->n == 2);
747 isl_set_free(set);
748
749 set = isl_set_read_from_str(ctx,
750 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
751 "y >= 0 & x >= 6 & x <= 10 & y <= x}", -1);
752 set = isl_set_coalesce(set);
753 assert(set && set->n == 1);
754 isl_set_free(set);
755
756 set = isl_set_read_from_str(ctx,
757 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
758 "y >= 0 & x >= 7 & x <= 10 & y <= x}", -1);
759 set = isl_set_coalesce(set);
760 assert(set && set->n == 2);
761 isl_set_free(set);
762
763 set = isl_set_read_from_str(ctx,
764 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
765 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}", -1);
766 set = isl_set_coalesce(set);
767 assert(set && set->n == 2);
768 isl_set_free(set);
769
770 set = isl_set_read_from_str(ctx,
771 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
772 "y >= 0 & x = 6 & y <= 6}", -1);
773 set = isl_set_coalesce(set);
774 assert(set && set->n == 1);
775 isl_set_free(set);
776
777 set = isl_set_read_from_str(ctx,
778 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
779 "y >= 0 & x = 7 & y <= 6}", -1);
780 set = isl_set_coalesce(set);
781 assert(set && set->n == 2);
782 isl_set_free(set);
783
784 set = isl_set_read_from_str(ctx,
785 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
786 "y >= 0 & x = 6 & y <= 5}", -1);
787 set = isl_set_coalesce(set);
788 assert(set && set->n == 1);
789 set2 = isl_set_read_from_str(ctx,
790 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
791 "y >= 0 & x = 6 & y <= 5}", -1);
792 assert(isl_set_is_equal(set, set2));
793 isl_set_free(set);
794 isl_set_free(set2);
795
796 set = isl_set_read_from_str(ctx,
797 "{[x,y]: y >= 0 & x <= 5 & y <= x or "
798 "y >= 0 & x = 6 & y <= 7}", -1);
799 set = isl_set_coalesce(set);
800 assert(set && set->n == 2);
801 isl_set_free(set);
802
803 set = isl_set_read_from_str(ctx,
804 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
805 set = isl_set_coalesce(set);
806 assert(set && set->n == 1);
807 set2 = isl_set_read_from_str(ctx,
808 "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }", -1);
809 assert(isl_set_is_equal(set, set2));
810 isl_set_free(set);
811 isl_set_free(set2);
812
813 set = isl_set_read_from_str(ctx,
814 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
815 set = isl_set_coalesce(set);
816 set2 = isl_set_read_from_str(ctx,
817 "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}", -1);
818 assert(isl_set_is_equal(set, set2));
819 isl_set_free(set);
820 isl_set_free(set2);
821
822 set = isl_set_read_from_str(ctx,
823 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
824 "2 <= i and i <= n }", -1);
825 set = isl_set_coalesce(set);
826 assert(set && set->n == 1);
827 set2 = isl_set_read_from_str(ctx,
828 "[n] -> { [i] : 1 <= i and i <= n - 1 or "
829 "2 <= i and i <= n }", -1);
830 assert(isl_set_is_equal(set, set2));
831 isl_set_free(set);
832 isl_set_free(set2);
833
834 map = isl_map_read_from_str(ctx,
835 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
836 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
837 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
838 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
839 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
840 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
841 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
842 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
843 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
844 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
845 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
846 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
847 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
848 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
849 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
850 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
851 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
852 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
853 map = isl_map_coalesce(map);
854 map2 = isl_map_read_from_str(ctx,
855 "[n] -> { [i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
856 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
857 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
858 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
859 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
860 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
861 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
862 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
863 "[i0] -> [o0] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
864 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
865 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
866 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
867 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
868 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
869 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
870 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
871 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
872 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }", -1);
873 assert(isl_map_is_equal(map, map2));
874 isl_map_free(map);
875 isl_map_free(map2);
876
877 str = "[n, m] -> { [] -> [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
878 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
879 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
880 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }";
881 map = isl_map_read_from_str(ctx, str, -1);
882 map = isl_map_coalesce(map);
883 map2 = isl_map_read_from_str(ctx, str, -1);
884 assert(isl_map_is_equal(map, map2));
885 isl_map_free(map);
886 isl_map_free(map2);
887
888 str = "[M, N] -> { [i0, i1, i2, i3, i4, i5, i6] -> "
889 "[o0, o1, o2, o3, o4, o5, o6] : "
890 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
891 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
892 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
893 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
894 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
895 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
896 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
897 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
898 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
899 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
900 "o6 >= i3 + i6 - o3 and M >= 0 and "
901 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
902 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }";
903 map = isl_map_read_from_str(ctx, str, -1);
904 map = isl_map_coalesce(map);
905 map2 = isl_map_read_from_str(ctx, str, -1);
906 assert(isl_map_is_equal(map, map2));
907 isl_map_free(map);
908 isl_map_free(map2);
909
910 str = "[M, N] -> { [] -> [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
911 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
912 "(o0 = 0 and M >= 2 and N >= 3) or "
913 "(M = 0 and o0 = 0 and N >= 3) }";
914 map = isl_map_read_from_str(ctx, str, -1);
915 map = isl_map_coalesce(map);
916 map2 = isl_map_read_from_str(ctx, str, -1);
917 assert(isl_map_is_equal(map, map2));
918 isl_map_free(map);
919 isl_map_free(map2);
920
921 str = "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
922 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
923 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
924 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }";
925 map = isl_map_read_from_str(ctx, str, -1);
926 map = isl_map_coalesce(map);
927 map2 = isl_map_read_from_str(ctx, str, -1);
928 assert(isl_map_is_equal(map, map2));
929 isl_map_free(map);
930 isl_map_free(map2);
931
932 test_coalesce_set(ctx,
933 "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or "
934 "(i1 = M and M >= 1) }", 0);
935 test_coalesce_set(ctx,
936 "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }", 0);
937 test_coalesce_set(ctx,
938 "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
939 "(y = 3 and x = 1) }", 1);
940 test_coalesce_set(ctx,
941 "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
942 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
943 "i1 <= M and i3 <= M and i4 <= M) or "
944 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
945 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
946 "i4 <= -1 + M) }", 1);
947 test_coalesce_set(ctx,
948 "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
949 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }", 1);
950 test_coalesce_set(ctx,
951 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
952 "-x - y + 1 >= 0 and -3 <= z <= 3;"
953 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
954 "x-z + 20 >= 0 and x+z + 20 >= 0 and -10 <= y <= 0}", 1);
955 test_coalesce_set(ctx,
956 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1);
957 test_coalesce_set(ctx, "{[x,0] : x >= 0; [x,1] : x <= 20}", 0);
958 test_coalesce_set(ctx,
959 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1);
960 test_coalesce_set(ctx, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }", 1);
961 test_coalesce_set(ctx, "{ [0,0]; [i,i] : 1 <= i <= 10 }", 1);
962 test_coalesce_set(ctx, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }", 0);
963 test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 1 <= i <= 10 }", 1);
964 test_coalesce_set(ctx, "{ [0,0]; [i,2i] : 2 <= i <= 10 }", 0);
965 test_coalesce_set(ctx, "{ [1,0]; [i,2i] : 1 <= i <= 10 }", 0);
966 test_coalesce_set(ctx, "{ [0,1]; [i,2i] : 1 <= i <= 10 }", 0);
967 }
968
969 void test_closure(struct isl_ctx *ctx)
970 {
971 const char *str;
972 isl_set *dom;
973 isl_map *up, *right;
974 isl_map *map, *map2;
975 int exact;
976
977 /* COCOA example 1 */
978 map = isl_map_read_from_str(ctx,
979 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
980 "1 <= i and i < n and 1 <= j and j < n or "
981 "i2 = i + 1 and j2 = j - 1 and "
982 "1 <= i and i < n and 2 <= j and j <= n }", -1);
983 map = isl_map_power(map, &exact);
984 assert(exact);
985 isl_map_free(map);
986
987 /* COCOA example 1 */
988 map = isl_map_read_from_str(ctx,
989 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
990 "1 <= i and i < n and 1 <= j and j < n or "
991 "i2 = i + 1 and j2 = j - 1 and "
992 "1 <= i and i < n and 2 <= j and j <= n }", -1);
993 map = isl_map_transitive_closure(map, &exact);
994 assert(exact);
995 map2 = isl_map_read_from_str(ctx,
996 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
997 "1 <= i and i < n and 1 <= j and j <= n and "
998 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
999 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1000 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}", -1);
1001 assert(isl_map_is_equal(map, map2));
1002 isl_map_free(map2);
1003 isl_map_free(map);
1004
1005 map = isl_map_read_from_str(ctx,
1006 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1007 " 0 <= y and y <= n }", -1);
1008 map = isl_map_transitive_closure(map, &exact);
1009 map2 = isl_map_read_from_str(ctx,
1010 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1011 " 0 <= y and y <= n }", -1);
1012 assert(isl_map_is_equal(map, map2));
1013 isl_map_free(map2);
1014 isl_map_free(map);
1015
1016 /* COCOA example 2 */
1017 map = isl_map_read_from_str(ctx,
1018 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1019 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1020 "i2 = i + 2 and j2 = j - 2 and "
1021 "1 <= i and i < n - 1 and 3 <= j and j <= n }", -1);
1022 map = isl_map_transitive_closure(map, &exact);
1023 assert(exact);
1024 map2 = isl_map_read_from_str(ctx,
1025 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1026 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1027 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1028 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1029 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }", -1);
1030 assert(isl_map_is_equal(map, map2));
1031 isl_map_free(map);
1032 isl_map_free(map2);
1033
1034 /* COCOA Fig.2 left */
1035 map = isl_map_read_from_str(ctx,
1036 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1037 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1038 "j <= n or "
1039 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1040 "j <= 2 i - 3 and j <= n - 2 or "
1041 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1042 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1043 map = isl_map_transitive_closure(map, &exact);
1044 assert(exact);
1045 isl_map_free(map);
1046
1047 /* COCOA Fig.2 right */
1048 map = isl_map_read_from_str(ctx,
1049 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1050 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1051 "j <= n or "
1052 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1053 "j <= 2 i - 4 and j <= n - 3 or "
1054 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1055 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1056 map = isl_map_power(map, &exact);
1057 assert(exact);
1058 isl_map_free(map);
1059
1060 /* COCOA Fig.2 right */
1061 map = isl_map_read_from_str(ctx,
1062 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1063 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1064 "j <= n or "
1065 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1066 "j <= 2 i - 4 and j <= n - 3 or "
1067 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1068 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }", -1);
1069 map = isl_map_transitive_closure(map, &exact);
1070 assert(exact);
1071 map2 = isl_map_read_from_str(ctx,
1072 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1073 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1074 "j <= n and 3 + i + 2 j <= 3 n and "
1075 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1076 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1077 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1078 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1079 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }", -1);
1080 assert(isl_map_is_equal(map, map2));
1081 isl_map_free(map2);
1082 isl_map_free(map);
1083
1084 /* COCOA Fig.1 right */
1085 dom = isl_set_read_from_str(ctx,
1086 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1087 "2 x - 3 y + 3 >= 0 }", -1);
1088 right = isl_map_read_from_str(ctx,
1089 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }", -1);
1090 up = isl_map_read_from_str(ctx,
1091 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }", -1);
1092 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1093 right = isl_map_intersect_range(right, isl_set_copy(dom));
1094 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1095 up = isl_map_intersect_range(up, dom);
1096 map = isl_map_union(up, right);
1097 map = isl_map_transitive_closure(map, &exact);
1098 assert(exact);
1099 map2 = isl_map_read_from_str(ctx,
1100 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1101 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }", -1);
1102 assert(isl_map_is_equal(map, map2));
1103 isl_map_free(map2);
1104 isl_map_free(map);
1105
1106 /* COCOA Theorem 1 counter example */
1107 map = isl_map_read_from_str(ctx,
1108 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1109 "i2 = 1 and j2 = j or "
1110 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }", -1);
1111 map = isl_map_transitive_closure(map, &exact);
1112 assert(exact);
1113 isl_map_free(map);
1114
1115 map = isl_map_read_from_str(ctx,
1116 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1117 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1118 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1119 "1 <= i,i2 <= n and 1 <= j,j2 <= m }", -1);
1120 map = isl_map_transitive_closure(map, &exact);
1121 assert(exact);
1122 isl_map_free(map);
1123
1124 /* Kelly et al 1996, fig 12 */
1125 map = isl_map_read_from_str(ctx,
1126 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1127 "1 <= i,j,j+1 <= n or "
1128 "j = n and j2 = 1 and i2 = i + 1 and "
1129 "1 <= i,i+1 <= n }", -1);
1130 map = isl_map_transitive_closure(map, &exact);
1131 assert(exact);
1132 map2 = isl_map_read_from_str(ctx,
1133 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1134 "1 <= i <= n and i = i2 or "
1135 "1 <= i < i2 <= n and 1 <= j <= n and "
1136 "1 <= j2 <= n }", -1);
1137 assert(isl_map_is_equal(map, map2));
1138 isl_map_free(map2);
1139 isl_map_free(map);
1140
1141 /* Omega's closure4 */
1142 map = isl_map_read_from_str(ctx,
1143 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1144 "1 <= x,y <= 10 or "
1145 "x2 = x + 1 and y2 = y and "
1146 "1 <= x <= 20 && 5 <= y <= 15 }", -1);
1147 map = isl_map_transitive_closure(map, &exact);
1148 assert(exact);
1149 isl_map_free(map);
1150
1151 map = isl_map_read_from_str(ctx,
1152 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }", -1);
1153 map = isl_map_transitive_closure(map, &exact);
1154 assert(!exact);
1155 map2 = isl_map_read_from_str(ctx,
1156 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }", -1);
1157 assert(isl_map_is_equal(map, map2));
1158 isl_map_free(map);
1159 isl_map_free(map2);
1160
1161 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1162 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1163 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1164 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1165 map = isl_map_read_from_str(ctx, str, -1);
1166 map = isl_map_transitive_closure(map, &exact);
1167 assert(exact);
1168 map2 = isl_map_read_from_str(ctx, str, -1);
1169 assert(isl_map_is_equal(map, map2));
1170 isl_map_free(map);
1171 isl_map_free(map2);
1172
1173 str = "{[0] -> [1]; [2] -> [3]}";
1174 map = isl_map_read_from_str(ctx, str, -1);
1175 map = isl_map_transitive_closure(map, &exact);
1176 assert(exact);
1177 map2 = isl_map_read_from_str(ctx, str, -1);
1178 assert(isl_map_is_equal(map, map2));
1179 isl_map_free(map);
1180 isl_map_free(map2);
1181
1182 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1183 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1184 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1185 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1186 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1187 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1188 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1189 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1190 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1191 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1192 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1193 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1194 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1195 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1196 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1197 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1198 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1199 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1200 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1201 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1202 map = isl_map_read_from_str(ctx, str, -1);
1203 map = isl_map_transitive_closure(map, NULL);
1204 assert(map);
1205 isl_map_free(map);
1206 }
1207
1208 void test_lex(struct isl_ctx *ctx)
1209 {
1210 isl_dim *dim;
1211 isl_map *map;
1212
1213 dim = isl_dim_alloc(ctx, 0, 0, 0);
1214 map = isl_map_lex_le(dim);
1215 assert(!isl_map_is_empty(map));
1216 isl_map_free(map);
1217 }
1218
1219 void test_lexmin(struct isl_ctx *ctx)
1220 {
1221 const char *str;
1222 isl_map *map, *map2;
1223 isl_set *set;
1224 isl_set *set2;
1225
1226 str = "[p0, p1] -> { [] -> [] : "
1227 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1228 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1229 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1230 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1231 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1232 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1233 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1234 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1235 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1236 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1237 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1238 map = isl_map_read_from_str(ctx, str, -1);
1239 map = isl_map_lexmin(map);
1240 isl_map_free(map);
1241
1242 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1243 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1244 set = isl_set_read_from_str(ctx, str, -1);
1245 set = isl_set_lexmax(set);
1246 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1247 set2 = isl_set_read_from_str(ctx, str, -1);
1248 set = isl_set_intersect(set, set2);
1249 assert(!isl_set_is_empty(set));
1250 isl_set_free(set);
1251
1252 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1253 map = isl_map_read_from_str(ctx, str, -1);
1254 map = isl_map_lexmin(map);
1255 str = "{ [x] -> [5] : 6 <= x <= 8; "
1256 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1257 map2 = isl_map_read_from_str(ctx, str, -1);
1258 assert(isl_map_is_equal(map, map2));
1259 isl_map_free(map);
1260 isl_map_free(map2);
1261
1262 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1263 map = isl_map_read_from_str(ctx, str, -1);
1264 map2 = isl_map_copy(map);
1265 map = isl_map_lexmin(map);
1266 assert(isl_map_is_equal(map, map2));
1267 isl_map_free(map);
1268 isl_map_free(map2);
1269
1270 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1271 map = isl_map_read_from_str(ctx, str, -1);
1272 map = isl_map_lexmin(map);
1273 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1274 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1275 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1276 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1277 map2 = isl_map_read_from_str(ctx, str, -1);
1278 assert(isl_map_is_equal(map, map2));
1279 isl_map_free(map);
1280 isl_map_free(map2);
1281 }
1282
1283 struct must_may {
1284 isl_map *must;
1285 isl_map *may;
1286 };
1287
1288 static int collect_must_may(__isl_take isl_map *dep, int must,
1289 void *dep_user, void *user)
1290 {
1291 struct must_may *mm = (struct must_may *)user;
1292
1293 if (must)
1294 mm->must = isl_map_union(mm->must, dep);
1295 else
1296 mm->may = isl_map_union(mm->may, dep);
1297
1298 return 0;
1299 }
1300
1301 static int common_space(void *first, void *second)
1302 {
1303 int depth = *(int *)first;
1304 return 2 * depth;
1305 }
1306
1307 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1308 {
1309 isl_map *map2;
1310 int equal;
1311
1312 if (!map)
1313 return -1;
1314
1315 map2 = isl_map_read_from_str(map->ctx, str, -1);
1316 equal = isl_map_is_equal(map, map2);
1317 isl_map_free(map2);
1318
1319 return equal;
1320 }
1321
1322 void test_dep(struct isl_ctx *ctx)
1323 {
1324 const char *str;
1325 isl_dim *dim;
1326 isl_map *map;
1327 isl_access_info *ai;
1328 isl_flow *flow;
1329 int depth;
1330 struct must_may mm;
1331
1332 depth = 3;
1333
1334 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1335 map = isl_map_read_from_str(ctx, str, -1);
1336 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1337
1338 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1339 map = isl_map_read_from_str(ctx, str, -1);
1340 ai = isl_access_info_add_source(ai, map, 1, &depth);
1341
1342 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1343 map = isl_map_read_from_str(ctx, str, -1);
1344 ai = isl_access_info_add_source(ai, map, 1, &depth);
1345
1346 flow = isl_access_info_compute_flow(ai);
1347 dim = isl_dim_alloc(ctx, 0, 3, 3);
1348 mm.must = isl_map_empty(isl_dim_copy(dim));
1349 mm.may = isl_map_empty(dim);
1350
1351 isl_flow_foreach(flow, collect_must_may, &mm);
1352
1353 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1354 " [1,10,0] -> [2,5,0] }";
1355 assert(map_is_equal(mm.must, str));
1356 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1357 assert(map_is_equal(mm.may, str));
1358
1359 isl_map_free(mm.must);
1360 isl_map_free(mm.may);
1361 isl_flow_free(flow);
1362
1363
1364 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1365 map = isl_map_read_from_str(ctx, str, -1);
1366 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1367
1368 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1369 map = isl_map_read_from_str(ctx, str, -1);
1370 ai = isl_access_info_add_source(ai, map, 1, &depth);
1371
1372 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1373 map = isl_map_read_from_str(ctx, str, -1);
1374 ai = isl_access_info_add_source(ai, map, 0, &depth);
1375
1376 flow = isl_access_info_compute_flow(ai);
1377 dim = isl_dim_alloc(ctx, 0, 3, 3);
1378 mm.must = isl_map_empty(isl_dim_copy(dim));
1379 mm.may = isl_map_empty(dim);
1380
1381 isl_flow_foreach(flow, collect_must_may, &mm);
1382
1383 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1384 assert(map_is_equal(mm.must, str));
1385 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1386 assert(map_is_equal(mm.may, str));
1387
1388 isl_map_free(mm.must);
1389 isl_map_free(mm.may);
1390 isl_flow_free(flow);
1391
1392
1393 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1394 map = isl_map_read_from_str(ctx, str, -1);
1395 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1396
1397 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1398 map = isl_map_read_from_str(ctx, str, -1);
1399 ai = isl_access_info_add_source(ai, map, 0, &depth);
1400
1401 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1402 map = isl_map_read_from_str(ctx, str, -1);
1403 ai = isl_access_info_add_source(ai, map, 0, &depth);
1404
1405 flow = isl_access_info_compute_flow(ai);
1406 dim = isl_dim_alloc(ctx, 0, 3, 3);
1407 mm.must = isl_map_empty(isl_dim_copy(dim));
1408 mm.may = isl_map_empty(dim);
1409
1410 isl_flow_foreach(flow, collect_must_may, &mm);
1411
1412 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1413 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1414 assert(map_is_equal(mm.may, str));
1415 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1416 assert(map_is_equal(mm.must, str));
1417
1418 isl_map_free(mm.must);
1419 isl_map_free(mm.may);
1420 isl_flow_free(flow);
1421
1422
1423 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1424 map = isl_map_read_from_str(ctx, str, -1);
1425 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1426
1427 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1428 map = isl_map_read_from_str(ctx, str, -1);
1429 ai = isl_access_info_add_source(ai, map, 0, &depth);
1430
1431 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1432 map = isl_map_read_from_str(ctx, str, -1);
1433 ai = isl_access_info_add_source(ai, map, 0, &depth);
1434
1435 flow = isl_access_info_compute_flow(ai);
1436 dim = isl_dim_alloc(ctx, 0, 3, 3);
1437 mm.must = isl_map_empty(isl_dim_copy(dim));
1438 mm.may = isl_map_empty(dim);
1439
1440 isl_flow_foreach(flow, collect_must_may, &mm);
1441
1442 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1443 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1444 assert(map_is_equal(mm.may, str));
1445 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1446 assert(map_is_equal(mm.must, str));
1447
1448 isl_map_free(mm.must);
1449 isl_map_free(mm.may);
1450 isl_flow_free(flow);
1451
1452
1453 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1454 map = isl_map_read_from_str(ctx, str, -1);
1455 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1456
1457 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1458 map = isl_map_read_from_str(ctx, str, -1);
1459 ai = isl_access_info_add_source(ai, map, 0, &depth);
1460
1461 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1462 map = isl_map_read_from_str(ctx, str, -1);
1463 ai = isl_access_info_add_source(ai, map, 0, &depth);
1464
1465 flow = isl_access_info_compute_flow(ai);
1466 dim = isl_dim_alloc(ctx, 0, 3, 3);
1467 mm.must = isl_map_empty(isl_dim_copy(dim));
1468 mm.may = isl_map_empty(dim);
1469
1470 isl_flow_foreach(flow, collect_must_may, &mm);
1471
1472 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1473 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1474 assert(map_is_equal(mm.may, str));
1475 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1476 assert(map_is_equal(mm.must, str));
1477
1478 isl_map_free(mm.must);
1479 isl_map_free(mm.may);
1480 isl_flow_free(flow);
1481
1482
1483 depth = 5;
1484
1485 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1486 map = isl_map_read_from_str(ctx, str, -1);
1487 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1488
1489 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1490 map = isl_map_read_from_str(ctx, str, -1);
1491 ai = isl_access_info_add_source(ai, map, 1, &depth);
1492
1493 flow = isl_access_info_compute_flow(ai);
1494 dim = isl_dim_alloc(ctx, 0, 5, 5);
1495 mm.must = isl_map_empty(isl_dim_copy(dim));
1496 mm.may = isl_map_empty(dim);
1497
1498 isl_flow_foreach(flow, collect_must_may, &mm);
1499
1500 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1501 assert(map_is_equal(mm.must, str));
1502 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1503 assert(map_is_equal(mm.may, str));
1504
1505 isl_map_free(mm.must);
1506 isl_map_free(mm.may);
1507 isl_flow_free(flow);
1508 }
1509
1510 int test_sv(isl_ctx *ctx)
1511 {
1512 const char *str;
1513 isl_map *map;
1514 isl_union_map *umap;
1515 int sv;
1516
1517 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1518 map = isl_map_read_from_str(ctx, str, -1);
1519 sv = isl_map_is_single_valued(map);
1520 isl_map_free(map);
1521 if (sv < 0)
1522 return -1;
1523 if (!sv)
1524 isl_die(ctx, isl_error_internal,
1525 "map not detected as single valued", return -1);
1526
1527 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1528 map = isl_map_read_from_str(ctx, str, -1);
1529 sv = isl_map_is_single_valued(map);
1530 isl_map_free(map);
1531 if (sv < 0)
1532 return -1;
1533 if (sv)
1534 isl_die(ctx, isl_error_internal,
1535 "map detected as single valued", return -1);
1536
1537 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1538 umap = isl_union_map_read_from_str(ctx, str);
1539 sv = isl_union_map_is_single_valued(umap);
1540 isl_union_map_free(umap);
1541 if (sv < 0)
1542 return -1;
1543 if (!sv)
1544 isl_die(ctx, isl_error_internal,
1545 "map not detected as single valued", return -1);
1546
1547 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
1548 umap = isl_union_map_read_from_str(ctx, str);
1549 sv = isl_union_map_is_single_valued(umap);
1550 isl_union_map_free(umap);
1551 if (sv < 0)
1552 return -1;
1553 if (sv)
1554 isl_die(ctx, isl_error_internal,
1555 "map detected as single valued", return -1);
1556
1557 return 0;
1558 }
1559
1560 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
1561 {
1562 isl_map *map;
1563
1564 map = isl_map_read_from_str(ctx, str, -1);
1565 if (bijective)
1566 assert(isl_map_is_bijective(map));
1567 else
1568 assert(!isl_map_is_bijective(map));
1569 isl_map_free(map);
1570 }
1571
1572 void test_bijective(struct isl_ctx *ctx)
1573 {
1574 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
1575 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
1576 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
1577 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
1578 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
1579 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
1580 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
1581 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
1582 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
1583 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
1584 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
1585 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
1586 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
1587 }
1588
1589 void test_pwqp(struct isl_ctx *ctx)
1590 {
1591 const char *str;
1592 isl_set *set;
1593 isl_pw_qpolynomial *pwqp1, *pwqp2;
1594
1595 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1596 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1597
1598 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
1599 isl_dim_set, 1, 1);
1600
1601 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
1602 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1603
1604 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1605
1606 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1607
1608 isl_pw_qpolynomial_free(pwqp1);
1609
1610 str = "{ [i] -> i }";
1611 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1612 str = "{ [k] : exists a : k = 2a }";
1613 set = isl_set_read_from_str(ctx, str, 0);
1614 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1615 str = "{ [i] -> i }";
1616 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1617
1618 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1619
1620 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1621
1622 isl_pw_qpolynomial_free(pwqp1);
1623
1624 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
1625 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1626 str = "{ [10] }";
1627 set = isl_set_read_from_str(ctx, str, 0);
1628 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1629 str = "{ [i] -> 16 }";
1630 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1631
1632 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1633
1634 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1635
1636 isl_pw_qpolynomial_free(pwqp1);
1637
1638 str = "{ [i] -> ([(i)/2]) }";
1639 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1640 str = "{ [k] : exists a : k = 2a+1 }";
1641 set = isl_set_read_from_str(ctx, str, 0);
1642 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
1643 str = "{ [i] -> -1/2 + 1/2 * i }";
1644 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1645
1646 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1647
1648 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1649
1650 isl_pw_qpolynomial_free(pwqp1);
1651
1652 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
1653 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1654 str = "{ [i] -> ([(2 * [i/2])/5]) }";
1655 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1656
1657 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1658
1659 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1660
1661 isl_pw_qpolynomial_free(pwqp1);
1662
1663 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
1664 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
1665 str = "{ [x] -> x }";
1666 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
1667
1668 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
1669
1670 assert(isl_pw_qpolynomial_is_zero(pwqp1));
1671
1672 isl_pw_qpolynomial_free(pwqp1);
1673 }
1674
1675 void test_split_periods(isl_ctx *ctx)
1676 {
1677 const char *str;
1678 isl_pw_qpolynomial *pwqp;
1679
1680 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
1681 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
1682 "U >= 0; [U,V] -> U^2 : U >= 100 }";
1683 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1684
1685 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
1686 assert(pwqp);
1687
1688 isl_pw_qpolynomial_free(pwqp);
1689 }
1690
1691 void test_union(isl_ctx *ctx)
1692 {
1693 const char *str;
1694 isl_union_set *uset1, *uset2;
1695 isl_union_map *umap1, *umap2;
1696
1697 str = "{ [i] : 0 <= i <= 1 }";
1698 uset1 = isl_union_set_read_from_str(ctx, str);
1699 str = "{ [1] -> [0] }";
1700 umap1 = isl_union_map_read_from_str(ctx, str);
1701
1702 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
1703 assert(isl_union_map_is_equal(umap1, umap2));
1704
1705 isl_union_map_free(umap1);
1706 isl_union_map_free(umap2);
1707
1708 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
1709 umap1 = isl_union_map_read_from_str(ctx, str);
1710 str = "{ A[i]; B[i] }";
1711 uset1 = isl_union_set_read_from_str(ctx, str);
1712
1713 uset2 = isl_union_map_domain(umap1);
1714
1715 assert(isl_union_set_is_equal(uset1, uset2));
1716
1717 isl_union_set_free(uset1);
1718 isl_union_set_free(uset2);
1719 }
1720
1721 void test_bound(isl_ctx *ctx)
1722 {
1723 const char *str;
1724 isl_pw_qpolynomial *pwqp;
1725 isl_pw_qpolynomial_fold *pwf;
1726
1727 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
1728 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1729 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1730 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_set) == 4);
1731 isl_pw_qpolynomial_fold_free(pwf);
1732
1733 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
1734 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
1735 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
1736 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_set) == 1);
1737 isl_pw_qpolynomial_fold_free(pwf);
1738 }
1739
1740 void test_lift(isl_ctx *ctx)
1741 {
1742 const char *str;
1743 isl_basic_map *bmap;
1744 isl_basic_set *bset;
1745
1746 str = "{ [i0] : exists e0 : i0 = 4e0 }";
1747 bset = isl_basic_set_read_from_str(ctx, str, 0);
1748 bset = isl_basic_set_lift(bset);
1749 bmap = isl_basic_map_from_range(bset);
1750 bset = isl_basic_map_domain(bmap);
1751 isl_basic_set_free(bset);
1752 }
1753
1754 void test_subset(isl_ctx *ctx)
1755 {
1756 const char *str;
1757 isl_set *set1, *set2;
1758
1759 str = "{ [112, 0] }";
1760 set1 = isl_set_read_from_str(ctx, str, 0);
1761 str = "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
1762 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
1763 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }";
1764 set2 = isl_set_read_from_str(ctx, str, 0);
1765 assert(isl_set_is_subset(set1, set2));
1766 isl_set_free(set1);
1767 isl_set_free(set2);
1768 }
1769
1770 void test_factorize(isl_ctx *ctx)
1771 {
1772 const char *str;
1773 isl_basic_set *bset;
1774 isl_factorizer *f;
1775
1776 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
1777 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
1778 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
1779 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
1780 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
1781 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
1782 "3i5 >= -2i0 - i2 + 3i4 }";
1783 bset = isl_basic_set_read_from_str(ctx, str, 0);
1784 f = isl_basic_set_factorizer(bset);
1785 assert(f);
1786 isl_basic_set_free(bset);
1787 isl_factorizer_free(f);
1788
1789 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1790 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
1791 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
1792 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
1793 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
1794 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
1795 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
1796 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
1797 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
1798 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
1799 bset = isl_basic_set_read_from_str(ctx, str, 0);
1800 f = isl_basic_set_factorizer(bset);
1801 assert(f);
1802 isl_basic_set_free(bset);
1803 isl_factorizer_free(f);
1804 }
1805
1806 static int check_injective(__isl_take isl_map *map, void *user)
1807 {
1808 int *injective = user;
1809
1810 *injective = isl_map_is_injective(map);
1811 isl_map_free(map);
1812
1813 if (*injective < 0 || !*injective)
1814 return -1;
1815
1816 return 0;
1817 }
1818
1819 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
1820 const char *r, const char *s, int tilable, int parallel)
1821 {
1822 int i;
1823 isl_union_set *D;
1824 isl_union_map *W, *R, *S;
1825 isl_union_map *empty;
1826 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
1827 isl_union_map *validity, *proximity;
1828 isl_union_map *schedule;
1829 isl_union_map *test;
1830 isl_union_set *delta;
1831 isl_union_set *domain;
1832 isl_set *delta_set;
1833 isl_set *slice;
1834 isl_set *origin;
1835 isl_schedule *sched;
1836 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
1837
1838 D = isl_union_set_read_from_str(ctx, d);
1839 W = isl_union_map_read_from_str(ctx, w);
1840 R = isl_union_map_read_from_str(ctx, r);
1841 S = isl_union_map_read_from_str(ctx, s);
1842
1843 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
1844 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
1845
1846 empty = isl_union_map_empty(isl_union_map_get_dim(S));
1847 isl_union_map_compute_flow(isl_union_map_copy(R),
1848 isl_union_map_copy(W), empty,
1849 isl_union_map_copy(S),
1850 &dep_raw, NULL, NULL, NULL);
1851 isl_union_map_compute_flow(isl_union_map_copy(W),
1852 isl_union_map_copy(W),
1853 isl_union_map_copy(R),
1854 isl_union_map_copy(S),
1855 &dep_waw, &dep_war, NULL, NULL);
1856
1857 dep = isl_union_map_union(dep_waw, dep_war);
1858 dep = isl_union_map_union(dep, dep_raw);
1859 validity = isl_union_map_copy(dep);
1860 proximity = isl_union_map_copy(dep);
1861
1862 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
1863 validity, proximity);
1864 schedule = isl_schedule_get_map(sched);
1865 isl_schedule_free(sched);
1866 isl_union_map_free(W);
1867 isl_union_map_free(R);
1868 isl_union_map_free(S);
1869
1870 is_injection = 1;
1871 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
1872
1873 domain = isl_union_map_domain(isl_union_map_copy(schedule));
1874 is_complete = isl_union_set_is_subset(D, domain);
1875 isl_union_set_free(D);
1876 isl_union_set_free(domain);
1877
1878 test = isl_union_map_reverse(isl_union_map_copy(schedule));
1879 test = isl_union_map_apply_range(test, dep);
1880 test = isl_union_map_apply_range(test, schedule);
1881
1882 delta = isl_union_map_deltas(test);
1883 if (isl_union_set_n_set(delta) == 0) {
1884 is_tilable = 1;
1885 is_parallel = 1;
1886 is_nonneg = 1;
1887 } else {
1888 delta_set = isl_union_set_copy_set(delta);
1889
1890 slice = isl_set_universe(isl_set_get_dim(delta_set));
1891 for (i = 0; i < tilable; ++i)
1892 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
1893 is_tilable = isl_set_is_subset(delta_set, slice);
1894 isl_set_free(slice);
1895
1896 slice = isl_set_universe(isl_set_get_dim(delta_set));
1897 for (i = 0; i < parallel; ++i)
1898 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
1899 is_parallel = isl_set_is_subset(delta_set, slice);
1900 isl_set_free(slice);
1901
1902 origin = isl_set_universe(isl_set_get_dim(delta_set));
1903 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
1904 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
1905
1906 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
1907 delta_set = isl_set_lexmin(delta_set);
1908
1909 is_nonneg = isl_set_is_equal(delta_set, origin);
1910
1911 isl_set_free(origin);
1912 isl_set_free(delta_set);
1913 }
1914 isl_union_set_free(delta);
1915
1916 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
1917 is_injection < 0 || is_complete < 0)
1918 return -1;
1919 if (!is_complete)
1920 isl_die(ctx, isl_error_unknown,
1921 "generated schedule incomplete", return -1);
1922 if (!is_injection)
1923 isl_die(ctx, isl_error_unknown,
1924 "generated schedule not injective on each statement",
1925 return -1);
1926 if (!is_nonneg)
1927 isl_die(ctx, isl_error_unknown,
1928 "negative dependences in generated schedule",
1929 return -1);
1930 if (!is_tilable)
1931 isl_die(ctx, isl_error_unknown,
1932 "generated schedule not as tilable as expected",
1933 return -1);
1934 if (!is_parallel)
1935 isl_die(ctx, isl_error_unknown,
1936 "generated schedule not as parallel as expected",
1937 return -1);
1938
1939 return 0;
1940 }
1941
1942 int test_special_schedule(isl_ctx *ctx)
1943 {
1944 const char *str;
1945 isl_union_set *dom;
1946 isl_union_map *empty;
1947 isl_union_map *dep;
1948 isl_union_map *sched1, *sched2;
1949 isl_schedule *schedule;
1950 int equal;
1951
1952 str = "{ S[i,j] : 0 <= i <= 10 }";
1953 dom = isl_union_set_read_from_str(ctx, str);
1954 str = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
1955 dep = isl_union_map_read_from_str(ctx, str);
1956 empty = isl_union_map_read_from_str(ctx, "{}");
1957 schedule = isl_union_set_compute_schedule(dom, empty, dep);
1958 sched1 = isl_schedule_get_map(schedule);
1959 isl_schedule_free(schedule);
1960
1961 str = "{ S[i, j] -> [j, i] }";
1962 sched2 = isl_union_map_read_from_str(ctx, str);
1963
1964 equal = isl_union_map_is_equal(sched1, sched2);
1965 isl_union_map_free(sched1);
1966 isl_union_map_free(sched2);
1967
1968 if (equal < 0)
1969 return -1;
1970 if (!equal)
1971 isl_die(ctx, isl_error_unknown, "unexpected schedule",
1972 return -1);
1973
1974 return 0;
1975 }
1976
1977 int test_schedule(isl_ctx *ctx)
1978 {
1979 const char *D, *W, *R, *S;
1980
1981 /* Jacobi */
1982 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
1983 W = "{ S1[t,i] -> a[t,i] }";
1984 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
1985 "S1[t,i] -> a[t-1,i+1] }";
1986 S = "{ S1[t,i] -> [t,i] }";
1987 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
1988 return -1;
1989
1990 /* Fig. 5 of CC2008 */
1991 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
1992 "j <= -1 + N }";
1993 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
1994 "j >= 2 and j <= -1 + N }";
1995 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
1996 "j >= 2 and j <= -1 + N; "
1997 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
1998 "j >= 2 and j <= -1 + N }";
1999 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2000 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2001 return -1;
2002
2003 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2004 W = "{ S1[i] -> a[i] }";
2005 R = "{ S2[i] -> a[i+1] }";
2006 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2007 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2008 return -1;
2009
2010 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2011 W = "{ S1[i] -> a[i] }";
2012 R = "{ S2[i] -> a[9-i] }";
2013 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2014 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2015 return -1;
2016
2017 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2018 W = "{ S1[i] -> a[i] }";
2019 R = "[N] -> { S2[i] -> a[N-1-i] }";
2020 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2021 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2022 return -1;
2023
2024 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2025 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2026 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2027 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2028 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2029 return -1;
2030
2031 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2032 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2033 R = "{ S2[i,j] -> a[i-1,j] }";
2034 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2035 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2036 return -1;
2037
2038 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2039 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2040 R = "{ S2[i,j] -> a[i,j-1] }";
2041 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2042 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2043 return -1;
2044
2045 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2046 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2047 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2048 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2049 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2050 "S_0[] -> [0, 0, 0] }";
2051 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2052 return -1;
2053 ctx->opt->schedule_parametric = 0;
2054 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2055 return -1;
2056 ctx->opt->schedule_parametric = 1;
2057
2058 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2059 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2060 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2061 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2062 "S4[i] -> a[i,N] }";
2063 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2064 "S4[i] -> [4,i,0] }";
2065 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2066 return -1;
2067
2068 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2069 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2070 "j <= N }";
2071 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2072 "j <= N; "
2073 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2074 "j <= N }";
2075 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2076 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2077 return -1;
2078
2079 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2080 " S_2[t] : t >= 0 and t <= -1 + N; "
2081 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2082 "i <= -1 + N }";
2083 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2084 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2085 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2086 "i >= 0 and i <= -1 + N }";
2087 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2088 "i >= 0 and i <= -1 + N; "
2089 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2090 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2091 " S_0[t] -> [0, t, 0] }";
2092
2093 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2094 return -1;
2095 ctx->opt->schedule_parametric = 0;
2096 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2097 return -1;
2098 ctx->opt->schedule_parametric = 1;
2099
2100 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2101 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2102 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2103 return -1;
2104
2105 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2106 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2107 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2108 "j >= 0 and j <= -1 + N; "
2109 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2110 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2111 "j >= 0 and j <= -1 + N; "
2112 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2113 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2114 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2115 return -1;
2116
2117 D = "{ S_0[i] : i >= 0 }";
2118 W = "{ S_0[i] -> a[i] : i >= 0 }";
2119 R = "{ S_0[i] -> a[0] : i >= 0 }";
2120 S = "{ S_0[i] -> [0, i, 0] }";
2121 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2122 return -1;
2123
2124 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2125 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2126 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2127 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2128 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2129 return -1;
2130
2131 return test_special_schedule(ctx);
2132 }
2133
2134 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2135 {
2136 isl_union_map *umap;
2137 int test;
2138
2139 umap = isl_union_map_read_from_str(ctx, str);
2140 test = isl_union_map_plain_is_injective(umap);
2141 isl_union_map_free(umap);
2142 if (test < 0)
2143 return -1;
2144 if (test == injective)
2145 return 0;
2146 if (injective)
2147 isl_die(ctx, isl_error_unknown,
2148 "map not detected as injective", return -1);
2149 else
2150 isl_die(ctx, isl_error_unknown,
2151 "map detected as injective", return -1);
2152 }
2153
2154 int test_injective(isl_ctx *ctx)
2155 {
2156 const char *str;
2157
2158 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2159 return -1;
2160 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2161 return -1;
2162 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2163 return -1;
2164 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2165 return -1;
2166 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2167 return -1;
2168 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2169 return -1;
2170 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2171 return -1;
2172 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2173 return -1;
2174
2175 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2176 if (test_plain_injective(ctx, str, 1))
2177 return -1;
2178 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2179 if (test_plain_injective(ctx, str, 0))
2180 return -1;
2181
2182 return 0;
2183 }
2184
2185 int main()
2186 {
2187 struct isl_ctx *ctx;
2188
2189 srcdir = getenv("srcdir");
2190 assert(srcdir);
2191
2192 ctx = isl_ctx_alloc();
2193 if (test_injective(ctx) < 0)
2194 goto error;
2195 if (test_schedule(ctx) < 0)
2196 goto error;
2197 test_factorize(ctx);
2198 test_subset(ctx);
2199 test_lift(ctx);
2200 test_bound(ctx);
2201 test_union(ctx);
2202 test_split_periods(ctx);
2203 test_parse(ctx);
2204 test_pwqp(ctx);
2205 test_lex(ctx);
2206 if (test_sv(ctx) < 0)
2207 goto error;
2208 test_bijective(ctx);
2209 test_dep(ctx);
2210 test_read(ctx);
2211 test_bounded(ctx);
2212 test_construction(ctx);
2213 test_dim(ctx);
2214 test_div(ctx);
2215 test_application(ctx);
2216 test_affine_hull(ctx);
2217 test_convex_hull(ctx);
2218 test_gist(ctx);
2219 test_coalesce(ctx);
2220 test_closure(ctx);
2221 test_lexmin(ctx);
2222 isl_ctx_free(ctx);
2223 return 0;
2224 error:
2225 isl_ctx_free(ctx);
2226 return -1;
2227 }
Integer set library