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a5085349d27d0de3dfcf6b7d43251df00414e918
[isl.git] / isl_test.c
bloba5085349d27d0de3dfcf6b7d43251df00414e918
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the MIT license
5 *
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
9
10 #include <assert.h>
11 #include <stdio.h>
12 #include <limits.h>
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_aff_private.h>
16 #include <isl/set.h>
17 #include <isl/flow.h>
18 #include <isl/constraint.h>
19 #include <isl/polynomial.h>
20 #include <isl/union_map.h>
21 #include <isl_factorization.h>
22 #include <isl/schedule.h>
23 #include <isl_options_private.h>
24 #include <isl/vertices.h>
25 #include <isl/ast_build.h>
26 #include <isl/val.h>
27
28 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
29
30 static char *srcdir;
31
32 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
33 char *filename;
34 int length;
35 char *pattern = "%s/test_inputs/%s.%s";
36
37 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
38 + strlen(suffix) + 1;
39 filename = isl_alloc_array(ctx, char, length);
40
41 if (!filename)
42 return NULL;
43
44 sprintf(filename, pattern, srcdir, name, suffix);
45
46 return filename;
47 }
48
49 void test_parse_map(isl_ctx *ctx, const char *str)
50 {
51 isl_map *map;
52
53 map = isl_map_read_from_str(ctx, str);
54 assert(map);
55 isl_map_free(map);
56 }
57
58 int test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
59 {
60 isl_map *map, *map2;
61 int equal;
62
63 map = isl_map_read_from_str(ctx, str);
64 map2 = isl_map_read_from_str(ctx, str2);
65 equal = isl_map_is_equal(map, map2);
66 isl_map_free(map);
67 isl_map_free(map2);
68
69 if (equal < 0)
70 return -1;
71 if (!equal)
72 isl_die(ctx, isl_error_unknown, "maps not equal",
73 return -1);
74
75 return 0;
76 }
77
78 void test_parse_pwqp(isl_ctx *ctx, const char *str)
79 {
80 isl_pw_qpolynomial *pwqp;
81
82 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
83 assert(pwqp);
84 isl_pw_qpolynomial_free(pwqp);
85 }
86
87 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
88 {
89 isl_pw_aff *pwaff;
90
91 pwaff = isl_pw_aff_read_from_str(ctx, str);
92 assert(pwaff);
93 isl_pw_aff_free(pwaff);
94 }
95
96 int test_parse(struct isl_ctx *ctx)
97 {
98 isl_map *map, *map2;
99 const char *str, *str2;
100
101 str = "{ [i] -> [-i] }";
102 map = isl_map_read_from_str(ctx, str);
103 assert(map);
104 isl_map_free(map);
105
106 str = "{ A[i] -> L[([i/3])] }";
107 map = isl_map_read_from_str(ctx, str);
108 assert(map);
109 isl_map_free(map);
110
111 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
112 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
113 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
114
115 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
116 str2 = "{ [x, y] : 2y >= 6 - x }";
117 if (test_parse_map_equal(ctx, str, str2) < 0)
118 return -1;
119
120 if (test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
121 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
122 return -1;
123 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
124 if (test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }",
125 str) < 0)
126 return -1;
127
128 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
129 map = isl_map_read_from_str(ctx, str);
130 str = "{ [new, old] -> [o0, o1] : "
131 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
132 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
133 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
134 map2 = isl_map_read_from_str(ctx, str);
135 assert(isl_map_is_equal(map, map2));
136 isl_map_free(map);
137 isl_map_free(map2);
138
139 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
140 map = isl_map_read_from_str(ctx, str);
141 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
142 map2 = isl_map_read_from_str(ctx, str);
143 assert(isl_map_is_equal(map, map2));
144 isl_map_free(map);
145 isl_map_free(map2);
146
147 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
148 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
149 if (test_parse_map_equal(ctx, str, str2) < 0)
150 return -1;
151
152 str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
153 str2 = "{ [i,j] -> [min(i,j)] }";
154 if (test_parse_map_equal(ctx, str, str2) < 0)
155 return -1;
156
157 str = "{ [i,j] : i != j }";
158 str2 = "{ [i,j] : i < j or i > j }";
159 if (test_parse_map_equal(ctx, str, str2) < 0)
160 return -1;
161
162 str = "{ [i,j] : (i+1)*2 >= j }";
163 str2 = "{ [i, j] : j <= 2 + 2i }";
164 if (test_parse_map_equal(ctx, str, str2) < 0)
165 return -1;
166
167 str = "{ [i] -> [i > 0 ? 4 : 5] }";
168 str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
169 if (test_parse_map_equal(ctx, str, str2) < 0)
170 return -1;
171
172 str = "[N=2,M] -> { [i=[(M+N)/4]] }";
173 str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
174 if (test_parse_map_equal(ctx, str, str2) < 0)
175 return -1;
176
177 str = "{ [x] : x >= 0 }";
178 str2 = "{ [x] : x-0 >= 0 }";
179 if (test_parse_map_equal(ctx, str, str2) < 0)
180 return -1;
181
182 str = "{ [i] : ((i > 10)) }";
183 str2 = "{ [i] : i >= 11 }";
184 if (test_parse_map_equal(ctx, str, str2) < 0)
185 return -1;
186
187 str = "{ [i] -> [0] }";
188 str2 = "{ [i] -> [0 * i] }";
189 if (test_parse_map_equal(ctx, str, str2) < 0)
190 return -1;
191
192 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
193 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
194 test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
195 test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
196
197 if (test_parse_map_equal(ctx, "{ [a] -> [b] : (not false) }",
198 "{ [a] -> [b] : true }") < 0)
199 return -1;
200
201 if (test_parse_map_equal(ctx, "{ [i] : i/2 <= 5 }",
202 "{ [i] : i <= 10 }") < 0)
203 return -1;
204
205 if (test_parse_map_equal(ctx, "{Sym=[n] [i] : i <= n }",
206 "[n] -> { [i] : i <= n }") < 0)
207 return -1;
208
209 if (test_parse_map_equal(ctx, "{ [*] }", "{ [a] }") < 0)
210 return -1;
211
212 if (test_parse_map_equal(ctx, "{ [i] : 2*floor(i/2) = i }",
213 "{ [i] : exists a : i = 2 a }") < 0)
214 return -1;
215
216 if (test_parse_map_equal(ctx, "{ [a] -> [b] : a = 5 implies b = 5 }",
217 "{ [a] -> [b] : a != 5 or b = 5 }") < 0)
218 return -1;
219
220 return 0;
221 }
222
223 void test_read(struct isl_ctx *ctx)
224 {
225 char *filename;
226 FILE *input;
227 struct isl_basic_set *bset1, *bset2;
228 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
229
230 filename = get_filename(ctx, "set", "omega");
231 assert(filename);
232 input = fopen(filename, "r");
233 assert(input);
234
235 bset1 = isl_basic_set_read_from_file(ctx, input);
236 bset2 = isl_basic_set_read_from_str(ctx, str);
237
238 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
239
240 isl_basic_set_free(bset1);
241 isl_basic_set_free(bset2);
242 free(filename);
243
244 fclose(input);
245 }
246
247 void test_bounded(struct isl_ctx *ctx)
248 {
249 isl_set *set;
250 int bounded;
251
252 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
253 bounded = isl_set_is_bounded(set);
254 assert(bounded);
255 isl_set_free(set);
256
257 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
258 bounded = isl_set_is_bounded(set);
259 assert(!bounded);
260 isl_set_free(set);
261
262 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
263 bounded = isl_set_is_bounded(set);
264 assert(!bounded);
265 isl_set_free(set);
266 }
267
268 /* Construct the basic set { [i] : 5 <= i <= N } */
269 void test_construction(struct isl_ctx *ctx)
270 {
271 isl_int v;
272 isl_space *dim;
273 isl_local_space *ls;
274 struct isl_basic_set *bset;
275 struct isl_constraint *c;
276
277 isl_int_init(v);
278
279 dim = isl_space_set_alloc(ctx, 1, 1);
280 bset = isl_basic_set_universe(isl_space_copy(dim));
281 ls = isl_local_space_from_space(dim);
282
283 c = isl_inequality_alloc(isl_local_space_copy(ls));
284 isl_int_set_si(v, -1);
285 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
286 isl_int_set_si(v, 1);
287 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
288 bset = isl_basic_set_add_constraint(bset, c);
289
290 c = isl_inequality_alloc(isl_local_space_copy(ls));
291 isl_int_set_si(v, 1);
292 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
293 isl_int_set_si(v, -5);
294 isl_constraint_set_constant(c, v);
295 bset = isl_basic_set_add_constraint(bset, c);
296
297 isl_local_space_free(ls);
298 isl_basic_set_free(bset);
299
300 isl_int_clear(v);
301 }
302
303 void test_dim(struct isl_ctx *ctx)
304 {
305 const char *str;
306 isl_map *map1, *map2;
307
308 map1 = isl_map_read_from_str(ctx,
309 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
310 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
311 map2 = isl_map_read_from_str(ctx,
312 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
313 assert(isl_map_is_equal(map1, map2));
314 isl_map_free(map2);
315
316 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
317 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
318 assert(isl_map_is_equal(map1, map2));
319
320 isl_map_free(map1);
321 isl_map_free(map2);
322
323 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
324 map1 = isl_map_read_from_str(ctx, str);
325 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
326 map2 = isl_map_read_from_str(ctx, str);
327 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
328 assert(isl_map_is_equal(map1, map2));
329
330 isl_map_free(map1);
331 isl_map_free(map2);
332 }
333
334 struct {
335 __isl_give isl_val *(*op)(__isl_take isl_val *v);
336 const char *arg;
337 const char *res;
338 } val_un_tests[] = {
339 { &isl_val_neg, "0", "0" },
340 { &isl_val_abs, "0", "0" },
341 { &isl_val_2exp, "0", "1" },
342 { &isl_val_floor, "0", "0" },
343 { &isl_val_ceil, "0", "0" },
344 { &isl_val_neg, "1", "-1" },
345 { &isl_val_neg, "-1", "1" },
346 { &isl_val_neg, "1/2", "-1/2" },
347 { &isl_val_neg, "-1/2", "1/2" },
348 { &isl_val_neg, "infty", "-infty" },
349 { &isl_val_neg, "-infty", "infty" },
350 { &isl_val_neg, "NaN", "NaN" },
351 { &isl_val_abs, "1", "1" },
352 { &isl_val_abs, "-1", "1" },
353 { &isl_val_abs, "1/2", "1/2" },
354 { &isl_val_abs, "-1/2", "1/2" },
355 { &isl_val_abs, "infty", "infty" },
356 { &isl_val_abs, "-infty", "infty" },
357 { &isl_val_abs, "NaN", "NaN" },
358 { &isl_val_floor, "1", "1" },
359 { &isl_val_floor, "-1", "-1" },
360 { &isl_val_floor, "1/2", "0" },
361 { &isl_val_floor, "-1/2", "-1" },
362 { &isl_val_floor, "infty", "infty" },
363 { &isl_val_floor, "-infty", "-infty" },
364 { &isl_val_floor, "NaN", "NaN" },
365 { &isl_val_ceil, "1", "1" },
366 { &isl_val_ceil, "-1", "-1" },
367 { &isl_val_ceil, "1/2", "1" },
368 { &isl_val_ceil, "-1/2", "0" },
369 { &isl_val_ceil, "infty", "infty" },
370 { &isl_val_ceil, "-infty", "-infty" },
371 { &isl_val_ceil, "NaN", "NaN" },
372 { &isl_val_2exp, "-3", "1/8" },
373 { &isl_val_2exp, "-1", "1/2" },
374 { &isl_val_2exp, "1", "2" },
375 { &isl_val_2exp, "2", "4" },
376 { &isl_val_2exp, "3", "8" },
377 };
378
379 /* Perform some basic tests of unary operations on isl_val objects.
380 */
381 static int test_un_val(isl_ctx *ctx)
382 {
383 int i;
384 isl_val *v, *res;
385 __isl_give isl_val *(*fn)(__isl_take isl_val *v);
386 int ok;
387
388 for (i = 0; i < ARRAY_SIZE(val_un_tests); ++i) {
389 v = isl_val_read_from_str(ctx, val_un_tests[i].arg);
390 res = isl_val_read_from_str(ctx, val_un_tests[i].res);
391 fn = val_un_tests[i].op;
392 v = fn(v);
393 if (isl_val_is_nan(res))
394 ok = isl_val_is_nan(v);
395 else
396 ok = isl_val_eq(v, res);
397 isl_val_free(v);
398 isl_val_free(res);
399 if (ok < 0)
400 return -1;
401 if (!ok)
402 isl_die(ctx, isl_error_unknown,
403 "unexpected result", return -1);
404 }
405
406 return 0;
407 }
408
409 struct {
410 __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
411 __isl_take isl_val *v2);
412 } val_bin_op[] = {
413 ['+'] = { &isl_val_add },
414 ['-'] = { &isl_val_sub },
415 ['*'] = { &isl_val_mul },
416 ['/'] = { &isl_val_div },
417 ['g'] = { &isl_val_gcd },
418 ['m'] = { &isl_val_min },
419 ['M'] = { &isl_val_max },
420 };
421
422 struct {
423 const char *arg1;
424 unsigned char op;
425 const char *arg2;
426 const char *res;
427 } val_bin_tests[] = {
428 { "0", '+', "0", "0" },
429 { "1", '+', "0", "1" },
430 { "1", '+', "1", "2" },
431 { "1", '-', "1", "0" },
432 { "1", '*', "1", "1" },
433 { "1", '/', "1", "1" },
434 { "2", '*', "3", "6" },
435 { "2", '*', "1/2", "1" },
436 { "2", '*', "1/3", "2/3" },
437 { "2/3", '*', "3/5", "2/5" },
438 { "2/3", '*', "7/5", "14/15" },
439 { "2", '/', "1/2", "4" },
440 { "-2", '/', "-1/2", "4" },
441 { "-2", '/', "1/2", "-4" },
442 { "2", '/', "-1/2", "-4" },
443 { "2", '/', "2", "1" },
444 { "2", '/', "3", "2/3" },
445 { "2/3", '/', "5/3", "2/5" },
446 { "2/3", '/', "5/7", "14/15" },
447 { "0", '/', "0", "NaN" },
448 { "42", '/', "0", "NaN" },
449 { "-42", '/', "0", "NaN" },
450 { "infty", '/', "0", "NaN" },
451 { "-infty", '/', "0", "NaN" },
452 { "NaN", '/', "0", "NaN" },
453 { "0", '/', "NaN", "NaN" },
454 { "42", '/', "NaN", "NaN" },
455 { "-42", '/', "NaN", "NaN" },
456 { "infty", '/', "NaN", "NaN" },
457 { "-infty", '/', "NaN", "NaN" },
458 { "NaN", '/', "NaN", "NaN" },
459 { "0", '/', "infty", "0" },
460 { "42", '/', "infty", "0" },
461 { "-42", '/', "infty", "0" },
462 { "infty", '/', "infty", "NaN" },
463 { "-infty", '/', "infty", "NaN" },
464 { "NaN", '/', "infty", "NaN" },
465 { "0", '/', "-infty", "0" },
466 { "42", '/', "-infty", "0" },
467 { "-42", '/', "-infty", "0" },
468 { "infty", '/', "-infty", "NaN" },
469 { "-infty", '/', "-infty", "NaN" },
470 { "NaN", '/', "-infty", "NaN" },
471 { "1", '-', "1/3", "2/3" },
472 { "1/3", '+', "1/2", "5/6" },
473 { "1/2", '+', "1/2", "1" },
474 { "3/4", '-', "1/4", "1/2" },
475 { "1/2", '-', "1/3", "1/6" },
476 { "infty", '+', "42", "infty" },
477 { "infty", '+', "infty", "infty" },
478 { "42", '+', "infty", "infty" },
479 { "infty", '-', "infty", "NaN" },
480 { "infty", '*', "infty", "infty" },
481 { "infty", '*', "-infty", "-infty" },
482 { "-infty", '*', "infty", "-infty" },
483 { "-infty", '*', "-infty", "infty" },
484 { "0", '*', "infty", "NaN" },
485 { "1", '*', "infty", "infty" },
486 { "infty", '*', "0", "NaN" },
487 { "infty", '*', "42", "infty" },
488 { "42", '-', "infty", "-infty" },
489 { "infty", '+', "-infty", "NaN" },
490 { "4", 'g', "6", "2" },
491 { "5", 'g', "6", "1" },
492 { "42", 'm', "3", "3" },
493 { "42", 'M', "3", "42" },
494 { "3", 'm', "42", "3" },
495 { "3", 'M', "42", "42" },
496 { "42", 'm', "infty", "42" },
497 { "42", 'M', "infty", "infty" },
498 { "42", 'm', "-infty", "-infty" },
499 { "42", 'M', "-infty", "42" },
500 { "42", 'm', "NaN", "NaN" },
501 { "42", 'M', "NaN", "NaN" },
502 { "infty", 'm', "-infty", "-infty" },
503 { "infty", 'M', "-infty", "infty" },
504 };
505
506 /* Perform some basic tests of binary operations on isl_val objects.
507 */
508 static int test_bin_val(isl_ctx *ctx)
509 {
510 int i;
511 isl_val *v1, *v2, *res;
512 __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
513 __isl_take isl_val *v2);
514 int ok;
515
516 for (i = 0; i < ARRAY_SIZE(val_bin_tests); ++i) {
517 v1 = isl_val_read_from_str(ctx, val_bin_tests[i].arg1);
518 v2 = isl_val_read_from_str(ctx, val_bin_tests[i].arg2);
519 res = isl_val_read_from_str(ctx, val_bin_tests[i].res);
520 fn = val_bin_op[val_bin_tests[i].op].fn;
521 v1 = fn(v1, v2);
522 if (isl_val_is_nan(res))
523 ok = isl_val_is_nan(v1);
524 else
525 ok = isl_val_eq(v1, res);
526 isl_val_free(v1);
527 isl_val_free(res);
528 if (ok < 0)
529 return -1;
530 if (!ok)
531 isl_die(ctx, isl_error_unknown,
532 "unexpected result", return -1);
533 }
534
535 return 0;
536 }
537
538 /* Perform some basic tests on isl_val objects.
539 */
540 static int test_val(isl_ctx *ctx)
541 {
542 if (test_un_val(ctx) < 0)
543 return -1;
544 if (test_bin_val(ctx) < 0)
545 return -1;
546 return 0;
547 }
548
549 static int test_div(isl_ctx *ctx)
550 {
551 unsigned n;
552 const char *str;
553 int empty;
554 isl_int v;
555 isl_space *dim;
556 isl_set *set;
557 isl_local_space *ls;
558 struct isl_basic_set *bset;
559 struct isl_constraint *c;
560
561 isl_int_init(v);
562
563 /* test 1 */
564 dim = isl_space_set_alloc(ctx, 0, 3);
565 bset = isl_basic_set_universe(isl_space_copy(dim));
566 ls = isl_local_space_from_space(dim);
567
568 c = isl_equality_alloc(isl_local_space_copy(ls));
569 isl_int_set_si(v, -1);
570 isl_constraint_set_constant(c, v);
571 isl_int_set_si(v, 1);
572 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
573 isl_int_set_si(v, 3);
574 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
575 bset = isl_basic_set_add_constraint(bset, c);
576
577 c = isl_equality_alloc(isl_local_space_copy(ls));
578 isl_int_set_si(v, 1);
579 isl_constraint_set_constant(c, v);
580 isl_int_set_si(v, -1);
581 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
582 isl_int_set_si(v, 3);
583 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
584 bset = isl_basic_set_add_constraint(bset, c);
585
586 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
587
588 assert(bset && bset->n_div == 1);
589 isl_local_space_free(ls);
590 isl_basic_set_free(bset);
591
592 /* test 2 */
593 dim = isl_space_set_alloc(ctx, 0, 3);
594 bset = isl_basic_set_universe(isl_space_copy(dim));
595 ls = isl_local_space_from_space(dim);
596
597 c = isl_equality_alloc(isl_local_space_copy(ls));
598 isl_int_set_si(v, 1);
599 isl_constraint_set_constant(c, v);
600 isl_int_set_si(v, -1);
601 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
602 isl_int_set_si(v, 3);
603 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
604 bset = isl_basic_set_add_constraint(bset, c);
605
606 c = isl_equality_alloc(isl_local_space_copy(ls));
607 isl_int_set_si(v, -1);
608 isl_constraint_set_constant(c, v);
609 isl_int_set_si(v, 1);
610 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
611 isl_int_set_si(v, 3);
612 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
613 bset = isl_basic_set_add_constraint(bset, c);
614
615 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
616
617 assert(bset && bset->n_div == 1);
618 isl_local_space_free(ls);
619 isl_basic_set_free(bset);
620
621 /* test 3 */
622 dim = isl_space_set_alloc(ctx, 0, 3);
623 bset = isl_basic_set_universe(isl_space_copy(dim));
624 ls = isl_local_space_from_space(dim);
625
626 c = isl_equality_alloc(isl_local_space_copy(ls));
627 isl_int_set_si(v, 1);
628 isl_constraint_set_constant(c, v);
629 isl_int_set_si(v, -1);
630 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
631 isl_int_set_si(v, 3);
632 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
633 bset = isl_basic_set_add_constraint(bset, c);
634
635 c = isl_equality_alloc(isl_local_space_copy(ls));
636 isl_int_set_si(v, -3);
637 isl_constraint_set_constant(c, v);
638 isl_int_set_si(v, 1);
639 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
640 isl_int_set_si(v, 4);
641 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
642 bset = isl_basic_set_add_constraint(bset, c);
643
644 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
645
646 assert(bset && bset->n_div == 1);
647 isl_local_space_free(ls);
648 isl_basic_set_free(bset);
649
650 /* test 4 */
651 dim = isl_space_set_alloc(ctx, 0, 3);
652 bset = isl_basic_set_universe(isl_space_copy(dim));
653 ls = isl_local_space_from_space(dim);
654
655 c = isl_equality_alloc(isl_local_space_copy(ls));
656 isl_int_set_si(v, 2);
657 isl_constraint_set_constant(c, v);
658 isl_int_set_si(v, -1);
659 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
660 isl_int_set_si(v, 3);
661 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
662 bset = isl_basic_set_add_constraint(bset, c);
663
664 c = isl_equality_alloc(isl_local_space_copy(ls));
665 isl_int_set_si(v, -1);
666 isl_constraint_set_constant(c, v);
667 isl_int_set_si(v, 1);
668 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
669 isl_int_set_si(v, 6);
670 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
671 bset = isl_basic_set_add_constraint(bset, c);
672
673 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
674
675 assert(isl_basic_set_is_empty(bset));
676 isl_local_space_free(ls);
677 isl_basic_set_free(bset);
678
679 /* test 5 */
680 dim = isl_space_set_alloc(ctx, 0, 3);
681 bset = isl_basic_set_universe(isl_space_copy(dim));
682 ls = isl_local_space_from_space(dim);
683
684 c = isl_equality_alloc(isl_local_space_copy(ls));
685 isl_int_set_si(v, -1);
686 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
687 isl_int_set_si(v, 3);
688 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
689 bset = isl_basic_set_add_constraint(bset, c);
690
691 c = isl_equality_alloc(isl_local_space_copy(ls));
692 isl_int_set_si(v, 1);
693 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
694 isl_int_set_si(v, -3);
695 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
696 bset = isl_basic_set_add_constraint(bset, c);
697
698 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
699
700 assert(bset && bset->n_div == 0);
701 isl_basic_set_free(bset);
702 isl_local_space_free(ls);
703
704 /* test 6 */
705 dim = isl_space_set_alloc(ctx, 0, 3);
706 bset = isl_basic_set_universe(isl_space_copy(dim));
707 ls = isl_local_space_from_space(dim);
708
709 c = isl_equality_alloc(isl_local_space_copy(ls));
710 isl_int_set_si(v, -1);
711 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
712 isl_int_set_si(v, 6);
713 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
714 bset = isl_basic_set_add_constraint(bset, c);
715
716 c = isl_equality_alloc(isl_local_space_copy(ls));
717 isl_int_set_si(v, 1);
718 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
719 isl_int_set_si(v, -3);
720 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
721 bset = isl_basic_set_add_constraint(bset, c);
722
723 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
724
725 assert(bset && bset->n_div == 1);
726 isl_basic_set_free(bset);
727 isl_local_space_free(ls);
728
729 /* test 7 */
730 /* This test is a bit tricky. We set up an equality
731 * a + 3b + 3c = 6 e0
732 * Normalization of divs creates _two_ divs
733 * a = 3 e0
734 * c - b - e0 = 2 e1
735 * Afterwards e0 is removed again because it has coefficient -1
736 * and we end up with the original equality and div again.
737 * Perhaps we can avoid the introduction of this temporary div.
738 */
739 dim = isl_space_set_alloc(ctx, 0, 4);
740 bset = isl_basic_set_universe(isl_space_copy(dim));
741 ls = isl_local_space_from_space(dim);
742
743 c = isl_equality_alloc(isl_local_space_copy(ls));
744 isl_int_set_si(v, -1);
745 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
746 isl_int_set_si(v, -3);
747 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
748 isl_int_set_si(v, -3);
749 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
750 isl_int_set_si(v, 6);
751 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
752 bset = isl_basic_set_add_constraint(bset, c);
753
754 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
755
756 /* Test disabled for now */
757 /*
758 assert(bset && bset->n_div == 1);
759 */
760 isl_local_space_free(ls);
761 isl_basic_set_free(bset);
762
763 /* test 8 */
764 dim = isl_space_set_alloc(ctx, 0, 5);
765 bset = isl_basic_set_universe(isl_space_copy(dim));
766 ls = isl_local_space_from_space(dim);
767
768 c = isl_equality_alloc(isl_local_space_copy(ls));
769 isl_int_set_si(v, -1);
770 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
771 isl_int_set_si(v, -3);
772 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
773 isl_int_set_si(v, -3);
774 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
775 isl_int_set_si(v, 6);
776 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
777 bset = isl_basic_set_add_constraint(bset, c);
778
779 c = isl_equality_alloc(isl_local_space_copy(ls));
780 isl_int_set_si(v, -1);
781 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
782 isl_int_set_si(v, 1);
783 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
784 isl_int_set_si(v, 1);
785 isl_constraint_set_constant(c, v);
786 bset = isl_basic_set_add_constraint(bset, c);
787
788 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
789
790 /* Test disabled for now */
791 /*
792 assert(bset && bset->n_div == 1);
793 */
794 isl_local_space_free(ls);
795 isl_basic_set_free(bset);
796
797 /* test 9 */
798 dim = isl_space_set_alloc(ctx, 0, 4);
799 bset = isl_basic_set_universe(isl_space_copy(dim));
800 ls = isl_local_space_from_space(dim);
801
802 c = isl_equality_alloc(isl_local_space_copy(ls));
803 isl_int_set_si(v, 1);
804 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
805 isl_int_set_si(v, -1);
806 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
807 isl_int_set_si(v, -2);
808 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
809 bset = isl_basic_set_add_constraint(bset, c);
810
811 c = isl_equality_alloc(isl_local_space_copy(ls));
812 isl_int_set_si(v, -1);
813 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
814 isl_int_set_si(v, 3);
815 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
816 isl_int_set_si(v, 2);
817 isl_constraint_set_constant(c, v);
818 bset = isl_basic_set_add_constraint(bset, c);
819
820 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
821
822 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
823
824 assert(!isl_basic_set_is_empty(bset));
825
826 isl_local_space_free(ls);
827 isl_basic_set_free(bset);
828
829 /* test 10 */
830 dim = isl_space_set_alloc(ctx, 0, 3);
831 bset = isl_basic_set_universe(isl_space_copy(dim));
832 ls = isl_local_space_from_space(dim);
833
834 c = isl_equality_alloc(isl_local_space_copy(ls));
835 isl_int_set_si(v, 1);
836 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
837 isl_int_set_si(v, -2);
838 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
839 bset = isl_basic_set_add_constraint(bset, c);
840
841 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
842
843 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
844
845 isl_local_space_free(ls);
846 isl_basic_set_free(bset);
847
848 isl_int_clear(v);
849
850 str = "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
851 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
852 set = isl_set_read_from_str(ctx, str);
853 set = isl_set_compute_divs(set);
854 isl_set_free(set);
855 if (!set)
856 return -1;
857
858 str = "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
859 bset = isl_basic_set_read_from_str(ctx, str);
860 n = isl_basic_set_dim(bset, isl_dim_div);
861 isl_basic_set_free(bset);
862 if (!bset)
863 return -1;
864 if (n != 0)
865 isl_die(ctx, isl_error_unknown,
866 "expecting no existentials", return -1);
867
868 str = "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
869 set = isl_set_read_from_str(ctx, str);
870 set = isl_set_remove_divs_involving_dims(set, isl_dim_set, 0, 2);
871 set = isl_set_fix_si(set, isl_dim_set, 2, -3);
872 empty = isl_set_is_empty(set);
873 isl_set_free(set);
874 if (empty < 0)
875 return -1;
876 if (!empty)
877 isl_die(ctx, isl_error_unknown,
878 "result not as accurate as expected", return -1);
879
880 return 0;
881 }
882
883 void test_application_case(struct isl_ctx *ctx, const char *name)
884 {
885 char *filename;
886 FILE *input;
887 struct isl_basic_set *bset1, *bset2;
888 struct isl_basic_map *bmap;
889
890 filename = get_filename(ctx, name, "omega");
891 assert(filename);
892 input = fopen(filename, "r");
893 assert(input);
894
895 bset1 = isl_basic_set_read_from_file(ctx, input);
896 bmap = isl_basic_map_read_from_file(ctx, input);
897
898 bset1 = isl_basic_set_apply(bset1, bmap);
899
900 bset2 = isl_basic_set_read_from_file(ctx, input);
901
902 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
903
904 isl_basic_set_free(bset1);
905 isl_basic_set_free(bset2);
906 free(filename);
907
908 fclose(input);
909 }
910
911 void test_application(struct isl_ctx *ctx)
912 {
913 test_application_case(ctx, "application");
914 test_application_case(ctx, "application2");
915 }
916
917 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
918 {
919 char *filename;
920 FILE *input;
921 struct isl_basic_set *bset1, *bset2;
922
923 filename = get_filename(ctx, name, "polylib");
924 assert(filename);
925 input = fopen(filename, "r");
926 assert(input);
927
928 bset1 = isl_basic_set_read_from_file(ctx, input);
929 bset2 = isl_basic_set_read_from_file(ctx, input);
930
931 bset1 = isl_basic_set_affine_hull(bset1);
932
933 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
934
935 isl_basic_set_free(bset1);
936 isl_basic_set_free(bset2);
937 free(filename);
938
939 fclose(input);
940 }
941
942 int test_affine_hull(struct isl_ctx *ctx)
943 {
944 const char *str;
945 isl_set *set;
946 isl_basic_set *bset, *bset2;
947 int n;
948 int subset;
949
950 test_affine_hull_case(ctx, "affine2");
951 test_affine_hull_case(ctx, "affine");
952 test_affine_hull_case(ctx, "affine3");
953
954 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
955 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
956 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
957 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
958 set = isl_set_read_from_str(ctx, str);
959 bset = isl_set_affine_hull(set);
960 n = isl_basic_set_dim(bset, isl_dim_div);
961 isl_basic_set_free(bset);
962 if (n != 0)
963 isl_die(ctx, isl_error_unknown, "not expecting any divs",
964 return -1);
965
966 /* Check that isl_map_affine_hull is not confused by
967 * the reordering of divs in isl_map_align_divs.
968 */
969 str = "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
970 "32e0 = b and 32e1 = c); "
971 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
972 set = isl_set_read_from_str(ctx, str);
973 bset = isl_set_affine_hull(set);
974 isl_basic_set_free(bset);
975 if (!bset)
976 return -1;
977
978 str = "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
979 "32e2 = 31 + 31e0 }";
980 set = isl_set_read_from_str(ctx, str);
981 bset = isl_set_affine_hull(set);
982 str = "{ [a] : exists e : a = 32 e }";
983 bset2 = isl_basic_set_read_from_str(ctx, str);
984 subset = isl_basic_set_is_subset(bset, bset2);
985 isl_basic_set_free(bset);
986 isl_basic_set_free(bset2);
987 if (subset < 0)
988 return -1;
989 if (!subset)
990 isl_die(ctx, isl_error_unknown, "not as accurate as expected",
991 return -1);
992
993 return 0;
994 }
995
996 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
997 {
998 char *filename;
999 FILE *input;
1000 struct isl_basic_set *bset1, *bset2;
1001 struct isl_set *set;
1002
1003 filename = get_filename(ctx, name, "polylib");
1004 assert(filename);
1005 input = fopen(filename, "r");
1006 assert(input);
1007
1008 bset1 = isl_basic_set_read_from_file(ctx, input);
1009 bset2 = isl_basic_set_read_from_file(ctx, input);
1010
1011 set = isl_basic_set_union(bset1, bset2);
1012 bset1 = isl_set_convex_hull(set);
1013
1014 bset2 = isl_basic_set_read_from_file(ctx, input);
1015
1016 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1017
1018 isl_basic_set_free(bset1);
1019 isl_basic_set_free(bset2);
1020 free(filename);
1021
1022 fclose(input);
1023 }
1024
1025 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
1026 {
1027 const char *str1, *str2;
1028 isl_set *set1, *set2;
1029 int orig_convex = ctx->opt->convex;
1030 ctx->opt->convex = convex;
1031
1032 test_convex_hull_case(ctx, "convex0");
1033 test_convex_hull_case(ctx, "convex1");
1034 test_convex_hull_case(ctx, "convex2");
1035 test_convex_hull_case(ctx, "convex3");
1036 test_convex_hull_case(ctx, "convex4");
1037 test_convex_hull_case(ctx, "convex5");
1038 test_convex_hull_case(ctx, "convex6");
1039 test_convex_hull_case(ctx, "convex7");
1040 test_convex_hull_case(ctx, "convex8");
1041 test_convex_hull_case(ctx, "convex9");
1042 test_convex_hull_case(ctx, "convex10");
1043 test_convex_hull_case(ctx, "convex11");
1044 test_convex_hull_case(ctx, "convex12");
1045 test_convex_hull_case(ctx, "convex13");
1046 test_convex_hull_case(ctx, "convex14");
1047 test_convex_hull_case(ctx, "convex15");
1048
1049 str1 = "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1050 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1051 "(i0 = 0 and i1 = 0 and i2 = 0) }";
1052 str2 = "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
1053 set1 = isl_set_read_from_str(ctx, str1);
1054 set2 = isl_set_read_from_str(ctx, str2);
1055 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
1056 assert(isl_set_is_equal(set1, set2));
1057 isl_set_free(set1);
1058 isl_set_free(set2);
1059
1060 ctx->opt->convex = orig_convex;
1061 }
1062
1063 void test_convex_hull(struct isl_ctx *ctx)
1064 {
1065 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
1066 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
1067 }
1068
1069 void test_gist_case(struct isl_ctx *ctx, const char *name)
1070 {
1071 char *filename;
1072 FILE *input;
1073 struct isl_basic_set *bset1, *bset2;
1074
1075 filename = get_filename(ctx, name, "polylib");
1076 assert(filename);
1077 input = fopen(filename, "r");
1078 assert(input);
1079
1080 bset1 = isl_basic_set_read_from_file(ctx, input);
1081 bset2 = isl_basic_set_read_from_file(ctx, input);
1082
1083 bset1 = isl_basic_set_gist(bset1, bset2);
1084
1085 bset2 = isl_basic_set_read_from_file(ctx, input);
1086
1087 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1088
1089 isl_basic_set_free(bset1);
1090 isl_basic_set_free(bset2);
1091 free(filename);
1092
1093 fclose(input);
1094 }
1095
1096 static int test_gist(struct isl_ctx *ctx)
1097 {
1098 const char *str;
1099 isl_basic_set *bset1, *bset2;
1100 isl_map *map1, *map2;
1101
1102 test_gist_case(ctx, "gist1");
1103
1104 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
1105 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1106 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1107 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1108 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1109 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1110 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1111 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1112 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1113 bset1 = isl_basic_set_read_from_str(ctx, str);
1114 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1115 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1116 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1117 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1118 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1119 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1120 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1121 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1122 bset2 = isl_basic_set_read_from_str(ctx, str);
1123 bset1 = isl_basic_set_gist(bset1, bset2);
1124 assert(bset1 && bset1->n_div == 0);
1125 isl_basic_set_free(bset1);
1126
1127 /* Check that the integer divisions of the second disjunct
1128 * do not spread to the first disjunct.
1129 */
1130 str = "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1131 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1132 "(exists (e0 = [(-1 + t1)/16], "
1133 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1134 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1135 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1136 "o0 <= 4294967295 and t1 <= -1)) }";
1137 map1 = isl_map_read_from_str(ctx, str);
1138 str = "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1139 map2 = isl_map_read_from_str(ctx, str);
1140 map1 = isl_map_gist(map1, map2);
1141 if (!map1)
1142 return -1;
1143 if (map1->n != 1)
1144 isl_die(ctx, isl_error_unknown, "expecting single disjunct",
1145 isl_map_free(map1); return -1);
1146 if (isl_basic_map_dim(map1->p[0], isl_dim_div) != 1)
1147 isl_die(ctx, isl_error_unknown, "expecting single div",
1148 isl_map_free(map1); return -1);
1149 isl_map_free(map1);
1150
1151 return 0;
1152 }
1153
1154 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
1155 {
1156 isl_set *set, *set2;
1157 int equal;
1158 int one;
1159
1160 set = isl_set_read_from_str(ctx, str);
1161 set = isl_set_coalesce(set);
1162 set2 = isl_set_read_from_str(ctx, str);
1163 equal = isl_set_is_equal(set, set2);
1164 one = set && set->n == 1;
1165 isl_set_free(set);
1166 isl_set_free(set2);
1167
1168 if (equal < 0)
1169 return -1;
1170 if (!equal)
1171 isl_die(ctx, isl_error_unknown,
1172 "coalesced set not equal to input", return -1);
1173 if (check_one && !one)
1174 isl_die(ctx, isl_error_unknown,
1175 "coalesced set should not be a union", return -1);
1176
1177 return 0;
1178 }
1179
1180 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
1181 {
1182 int r = 0;
1183 int bounded;
1184
1185 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
1186 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
1187
1188 if (test_coalesce_set(ctx,
1189 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1190 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1191 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1192 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1193 "-10 <= y <= 0}", 1) < 0)
1194 goto error;
1195 if (test_coalesce_set(ctx,
1196 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
1197 goto error;
1198 if (test_coalesce_set(ctx,
1199 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
1200 goto error;
1201
1202 if (0) {
1203 error:
1204 r = -1;
1205 }
1206
1207 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
1208
1209 return r;
1210 }
1211
1212 /* Inputs for coalescing tests.
1213 * "str" is a string representation of the input set.
1214 * "single_disjunct" is set if we expect the result to consist of
1215 * a single disjunct.
1216 */
1217 struct {
1218 int single_disjunct;
1219 const char *str;
1220 } coalesce_tests[] = {
1221 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1222 "y >= x & x >= 2 & 5 >= y }" },
1223 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1224 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1225 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1226 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1227 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1228 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1229 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1230 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1231 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1232 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1233 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1234 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1235 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1236 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1237 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1238 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1239 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1240 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1241 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1242 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1243 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1244 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1245 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1246 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1247 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1248 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1249 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1250 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1251 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1252 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1253 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1254 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1255 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1256 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1257 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1258 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1259 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1260 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1261 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1262 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1263 "[o0, o1, o2, o3, o4, o5, o6]] : "
1264 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1265 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1266 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1267 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1268 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1269 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1270 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1271 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1272 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1273 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1274 "o6 >= i3 + i6 - o3 and M >= 0 and "
1275 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1276 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1277 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1278 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1279 "(o0 = 0 and M >= 2 and N >= 3) or "
1280 "(M = 0 and o0 = 0 and N >= 3) }" },
1281 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1282 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1283 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1284 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1285 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1286 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1287 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1288 "(y = 3 and x = 1) }" },
1289 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1290 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1291 "i1 <= M and i3 <= M and i4 <= M) or "
1292 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1293 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1294 "i4 <= -1 + M) }" },
1295 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1296 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1297 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1298 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1299 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1300 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1301 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1302 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1303 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1304 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1305 { 0, "{ [a, b] : exists e : 2e = a and "
1306 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1307 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1308 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1309 "j >= 1 and j' <= i + j - i' and i >= 1; "
1310 "[1, 1, 1, 1] }" },
1311 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1312 "[i,j] : exists a : j = 3a }" },
1313 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1314 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1315 "a >= 3) or "
1316 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1317 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1318 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1319 "c <= 6 + 8a and a >= 3; "
1320 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1321 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1322 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1323 "[x,0] : 3 <= x <= 4 }" },
1324 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1325 "[x,0] : 4 <= x <= 5 }" },
1326 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1327 "[x,0] : 3 <= x <= 5 }" },
1328 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1329 "[x,0] : 3 <= x <= 4 }" },
1330 { 1 , "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1331 "i1 <= 0; "
1332 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1333 };
1334
1335 /* Test the functionality of isl_set_coalesce.
1336 * That is, check that the output is always equal to the input
1337 * and in some cases that the result consists of a single disjunct.
1338 */
1339 static int test_coalesce(struct isl_ctx *ctx)
1340 {
1341 int i;
1342
1343 for (i = 0; i < ARRAY_SIZE(coalesce_tests); ++i) {
1344 const char *str = coalesce_tests[i].str;
1345 int check_one = coalesce_tests[i].single_disjunct;
1346 if (test_coalesce_set(ctx, str, check_one) < 0)
1347 return -1;
1348 }
1349
1350 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1351 return -1;
1352
1353 return 0;
1354 }
1355
1356 void test_closure(struct isl_ctx *ctx)
1357 {
1358 const char *str;
1359 isl_set *dom;
1360 isl_map *up, *right;
1361 isl_map *map, *map2;
1362 int exact;
1363
1364 /* COCOA example 1 */
1365 map = isl_map_read_from_str(ctx,
1366 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1367 "1 <= i and i < n and 1 <= j and j < n or "
1368 "i2 = i + 1 and j2 = j - 1 and "
1369 "1 <= i and i < n and 2 <= j and j <= n }");
1370 map = isl_map_power(map, &exact);
1371 assert(exact);
1372 isl_map_free(map);
1373
1374 /* COCOA example 1 */
1375 map = isl_map_read_from_str(ctx,
1376 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1377 "1 <= i and i < n and 1 <= j and j < n or "
1378 "i2 = i + 1 and j2 = j - 1 and "
1379 "1 <= i and i < n and 2 <= j and j <= n }");
1380 map = isl_map_transitive_closure(map, &exact);
1381 assert(exact);
1382 map2 = isl_map_read_from_str(ctx,
1383 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1384 "1 <= i and i < n and 1 <= j and j <= n and "
1385 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1386 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1387 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1388 assert(isl_map_is_equal(map, map2));
1389 isl_map_free(map2);
1390 isl_map_free(map);
1391
1392 map = isl_map_read_from_str(ctx,
1393 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1394 " 0 <= y and y <= n }");
1395 map = isl_map_transitive_closure(map, &exact);
1396 map2 = isl_map_read_from_str(ctx,
1397 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1398 " 0 <= y and y <= n }");
1399 assert(isl_map_is_equal(map, map2));
1400 isl_map_free(map2);
1401 isl_map_free(map);
1402
1403 /* COCOA example 2 */
1404 map = isl_map_read_from_str(ctx,
1405 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1406 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1407 "i2 = i + 2 and j2 = j - 2 and "
1408 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1409 map = isl_map_transitive_closure(map, &exact);
1410 assert(exact);
1411 map2 = isl_map_read_from_str(ctx,
1412 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1413 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1414 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1415 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1416 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1417 assert(isl_map_is_equal(map, map2));
1418 isl_map_free(map);
1419 isl_map_free(map2);
1420
1421 /* COCOA Fig.2 left */
1422 map = isl_map_read_from_str(ctx,
1423 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1424 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1425 "j <= n or "
1426 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1427 "j <= 2 i - 3 and j <= n - 2 or "
1428 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1429 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1430 map = isl_map_transitive_closure(map, &exact);
1431 assert(exact);
1432 isl_map_free(map);
1433
1434 /* COCOA Fig.2 right */
1435 map = isl_map_read_from_str(ctx,
1436 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1437 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1438 "j <= n or "
1439 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1440 "j <= 2 i - 4 and j <= n - 3 or "
1441 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1442 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1443 map = isl_map_power(map, &exact);
1444 assert(exact);
1445 isl_map_free(map);
1446
1447 /* COCOA Fig.2 right */
1448 map = isl_map_read_from_str(ctx,
1449 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1450 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1451 "j <= n or "
1452 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1453 "j <= 2 i - 4 and j <= n - 3 or "
1454 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1455 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1456 map = isl_map_transitive_closure(map, &exact);
1457 assert(exact);
1458 map2 = isl_map_read_from_str(ctx,
1459 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1460 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1461 "j <= n and 3 + i + 2 j <= 3 n and "
1462 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1463 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1464 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1465 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1466 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1467 assert(isl_map_is_equal(map, map2));
1468 isl_map_free(map2);
1469 isl_map_free(map);
1470
1471 /* COCOA Fig.1 right */
1472 dom = isl_set_read_from_str(ctx,
1473 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1474 "2 x - 3 y + 3 >= 0 }");
1475 right = isl_map_read_from_str(ctx,
1476 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1477 up = isl_map_read_from_str(ctx,
1478 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1479 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1480 right = isl_map_intersect_range(right, isl_set_copy(dom));
1481 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1482 up = isl_map_intersect_range(up, dom);
1483 map = isl_map_union(up, right);
1484 map = isl_map_transitive_closure(map, &exact);
1485 assert(exact);
1486 map2 = isl_map_read_from_str(ctx,
1487 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1488 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1489 assert(isl_map_is_equal(map, map2));
1490 isl_map_free(map2);
1491 isl_map_free(map);
1492
1493 /* COCOA Theorem 1 counter example */
1494 map = isl_map_read_from_str(ctx,
1495 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1496 "i2 = 1 and j2 = j or "
1497 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1498 map = isl_map_transitive_closure(map, &exact);
1499 assert(exact);
1500 isl_map_free(map);
1501
1502 map = isl_map_read_from_str(ctx,
1503 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1504 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1505 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1506 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1507 map = isl_map_transitive_closure(map, &exact);
1508 assert(exact);
1509 isl_map_free(map);
1510
1511 /* Kelly et al 1996, fig 12 */
1512 map = isl_map_read_from_str(ctx,
1513 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1514 "1 <= i,j,j+1 <= n or "
1515 "j = n and j2 = 1 and i2 = i + 1 and "
1516 "1 <= i,i+1 <= n }");
1517 map = isl_map_transitive_closure(map, &exact);
1518 assert(exact);
1519 map2 = isl_map_read_from_str(ctx,
1520 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1521 "1 <= i <= n and i = i2 or "
1522 "1 <= i < i2 <= n and 1 <= j <= n and "
1523 "1 <= j2 <= n }");
1524 assert(isl_map_is_equal(map, map2));
1525 isl_map_free(map2);
1526 isl_map_free(map);
1527
1528 /* Omega's closure4 */
1529 map = isl_map_read_from_str(ctx,
1530 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1531 "1 <= x,y <= 10 or "
1532 "x2 = x + 1 and y2 = y and "
1533 "1 <= x <= 20 && 5 <= y <= 15 }");
1534 map = isl_map_transitive_closure(map, &exact);
1535 assert(exact);
1536 isl_map_free(map);
1537
1538 map = isl_map_read_from_str(ctx,
1539 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1540 map = isl_map_transitive_closure(map, &exact);
1541 assert(!exact);
1542 map2 = isl_map_read_from_str(ctx,
1543 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1544 assert(isl_map_is_equal(map, map2));
1545 isl_map_free(map);
1546 isl_map_free(map2);
1547
1548 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1549 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1550 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1551 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1552 map = isl_map_read_from_str(ctx, str);
1553 map = isl_map_transitive_closure(map, &exact);
1554 assert(exact);
1555 map2 = isl_map_read_from_str(ctx, str);
1556 assert(isl_map_is_equal(map, map2));
1557 isl_map_free(map);
1558 isl_map_free(map2);
1559
1560 str = "{[0] -> [1]; [2] -> [3]}";
1561 map = isl_map_read_from_str(ctx, str);
1562 map = isl_map_transitive_closure(map, &exact);
1563 assert(exact);
1564 map2 = isl_map_read_from_str(ctx, str);
1565 assert(isl_map_is_equal(map, map2));
1566 isl_map_free(map);
1567 isl_map_free(map2);
1568
1569 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1570 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1571 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1572 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1573 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1574 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1575 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1576 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1577 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1578 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1579 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1580 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1581 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1582 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1583 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1584 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1585 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1586 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1587 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1588 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1589 map = isl_map_read_from_str(ctx, str);
1590 map = isl_map_transitive_closure(map, NULL);
1591 assert(map);
1592 isl_map_free(map);
1593 }
1594
1595 void test_lex(struct isl_ctx *ctx)
1596 {
1597 isl_space *dim;
1598 isl_map *map;
1599
1600 dim = isl_space_set_alloc(ctx, 0, 0);
1601 map = isl_map_lex_le(dim);
1602 assert(!isl_map_is_empty(map));
1603 isl_map_free(map);
1604 }
1605
1606 static int test_lexmin(struct isl_ctx *ctx)
1607 {
1608 int equal;
1609 const char *str;
1610 isl_basic_map *bmap;
1611 isl_map *map, *map2;
1612 isl_set *set;
1613 isl_set *set2;
1614 isl_pw_multi_aff *pma;
1615
1616 str = "[p0, p1] -> { [] -> [] : "
1617 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1618 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1619 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1620 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1621 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1622 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1623 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1624 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1625 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1626 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1627 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1628 map = isl_map_read_from_str(ctx, str);
1629 map = isl_map_lexmin(map);
1630 isl_map_free(map);
1631
1632 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1633 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1634 set = isl_set_read_from_str(ctx, str);
1635 set = isl_set_lexmax(set);
1636 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1637 set2 = isl_set_read_from_str(ctx, str);
1638 set = isl_set_intersect(set, set2);
1639 assert(!isl_set_is_empty(set));
1640 isl_set_free(set);
1641
1642 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1643 map = isl_map_read_from_str(ctx, str);
1644 map = isl_map_lexmin(map);
1645 str = "{ [x] -> [5] : 6 <= x <= 8; "
1646 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1647 map2 = isl_map_read_from_str(ctx, str);
1648 assert(isl_map_is_equal(map, map2));
1649 isl_map_free(map);
1650 isl_map_free(map2);
1651
1652 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1653 map = isl_map_read_from_str(ctx, str);
1654 map2 = isl_map_copy(map);
1655 map = isl_map_lexmin(map);
1656 assert(isl_map_is_equal(map, map2));
1657 isl_map_free(map);
1658 isl_map_free(map2);
1659
1660 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1661 map = isl_map_read_from_str(ctx, str);
1662 map = isl_map_lexmin(map);
1663 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1664 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1665 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1666 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1667 map2 = isl_map_read_from_str(ctx, str);
1668 assert(isl_map_is_equal(map, map2));
1669 isl_map_free(map);
1670 isl_map_free(map2);
1671
1672 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1673 " 8i' <= i and 8i' >= -7 + i }";
1674 bmap = isl_basic_map_read_from_str(ctx, str);
1675 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1676 map2 = isl_map_from_pw_multi_aff(pma);
1677 map = isl_map_from_basic_map(bmap);
1678 assert(isl_map_is_equal(map, map2));
1679 isl_map_free(map);
1680 isl_map_free(map2);
1681
1682 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1683 map = isl_map_read_from_str(ctx, str);
1684 map = isl_map_lexmin(map);
1685 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1686 map2 = isl_map_read_from_str(ctx, str);
1687 assert(isl_map_is_equal(map, map2));
1688 isl_map_free(map);
1689 isl_map_free(map2);
1690
1691 /* Check that empty pieces are properly combined. */
1692 str = "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
1693 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
1694 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
1695 map = isl_map_read_from_str(ctx, str);
1696 map = isl_map_lexmin(map);
1697 str = "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
1698 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
1699 "x >= 4 }";
1700 map2 = isl_map_read_from_str(ctx, str);
1701 assert(isl_map_is_equal(map, map2));
1702 isl_map_free(map);
1703 isl_map_free(map2);
1704
1705 str = "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1706 " 8i' <= i and 8i' >= -7 + i }";
1707 set = isl_set_read_from_str(ctx, str);
1708 pma = isl_set_lexmin_pw_multi_aff(isl_set_copy(set));
1709 set2 = isl_set_from_pw_multi_aff(pma);
1710 equal = isl_set_is_equal(set, set2);
1711 isl_set_free(set);
1712 isl_set_free(set2);
1713 if (equal < 0)
1714 return -1;
1715 if (!equal)
1716 isl_die(ctx, isl_error_unknown,
1717 "unexpected difference between set and "
1718 "piecewise affine expression", return -1);
1719
1720 return 0;
1721 }
1722
1723 struct must_may {
1724 isl_map *must;
1725 isl_map *may;
1726 };
1727
1728 static int collect_must_may(__isl_take isl_map *dep, int must,
1729 void *dep_user, void *user)
1730 {
1731 struct must_may *mm = (struct must_may *)user;
1732
1733 if (must)
1734 mm->must = isl_map_union(mm->must, dep);
1735 else
1736 mm->may = isl_map_union(mm->may, dep);
1737
1738 return 0;
1739 }
1740
1741 static int common_space(void *first, void *second)
1742 {
1743 int depth = *(int *)first;
1744 return 2 * depth;
1745 }
1746
1747 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1748 {
1749 isl_map *map2;
1750 int equal;
1751
1752 if (!map)
1753 return -1;
1754
1755 map2 = isl_map_read_from_str(map->ctx, str);
1756 equal = isl_map_is_equal(map, map2);
1757 isl_map_free(map2);
1758
1759 return equal;
1760 }
1761
1762 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1763 {
1764 int equal;
1765
1766 equal = map_is_equal(map, str);
1767 if (equal < 0)
1768 return -1;
1769 if (!equal)
1770 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1771 "result not as expected", return -1);
1772 return 0;
1773 }
1774
1775 void test_dep(struct isl_ctx *ctx)
1776 {
1777 const char *str;
1778 isl_space *dim;
1779 isl_map *map;
1780 isl_access_info *ai;
1781 isl_flow *flow;
1782 int depth;
1783 struct must_may mm;
1784
1785 depth = 3;
1786
1787 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1788 map = isl_map_read_from_str(ctx, str);
1789 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1790
1791 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1792 map = isl_map_read_from_str(ctx, str);
1793 ai = isl_access_info_add_source(ai, map, 1, &depth);
1794
1795 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1796 map = isl_map_read_from_str(ctx, str);
1797 ai = isl_access_info_add_source(ai, map, 1, &depth);
1798
1799 flow = isl_access_info_compute_flow(ai);
1800 dim = isl_space_alloc(ctx, 0, 3, 3);
1801 mm.must = isl_map_empty(isl_space_copy(dim));
1802 mm.may = isl_map_empty(dim);
1803
1804 isl_flow_foreach(flow, collect_must_may, &mm);
1805
1806 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1807 " [1,10,0] -> [2,5,0] }";
1808 assert(map_is_equal(mm.must, str));
1809 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1810 assert(map_is_equal(mm.may, str));
1811
1812 isl_map_free(mm.must);
1813 isl_map_free(mm.may);
1814 isl_flow_free(flow);
1815
1816
1817 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1818 map = isl_map_read_from_str(ctx, str);
1819 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1820
1821 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1822 map = isl_map_read_from_str(ctx, str);
1823 ai = isl_access_info_add_source(ai, map, 1, &depth);
1824
1825 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1826 map = isl_map_read_from_str(ctx, str);
1827 ai = isl_access_info_add_source(ai, map, 0, &depth);
1828
1829 flow = isl_access_info_compute_flow(ai);
1830 dim = isl_space_alloc(ctx, 0, 3, 3);
1831 mm.must = isl_map_empty(isl_space_copy(dim));
1832 mm.may = isl_map_empty(dim);
1833
1834 isl_flow_foreach(flow, collect_must_may, &mm);
1835
1836 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1837 assert(map_is_equal(mm.must, str));
1838 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1839 assert(map_is_equal(mm.may, str));
1840
1841 isl_map_free(mm.must);
1842 isl_map_free(mm.may);
1843 isl_flow_free(flow);
1844
1845
1846 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1847 map = isl_map_read_from_str(ctx, str);
1848 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1849
1850 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1851 map = isl_map_read_from_str(ctx, str);
1852 ai = isl_access_info_add_source(ai, map, 0, &depth);
1853
1854 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1855 map = isl_map_read_from_str(ctx, str);
1856 ai = isl_access_info_add_source(ai, map, 0, &depth);
1857
1858 flow = isl_access_info_compute_flow(ai);
1859 dim = isl_space_alloc(ctx, 0, 3, 3);
1860 mm.must = isl_map_empty(isl_space_copy(dim));
1861 mm.may = isl_map_empty(dim);
1862
1863 isl_flow_foreach(flow, collect_must_may, &mm);
1864
1865 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1866 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1867 assert(map_is_equal(mm.may, str));
1868 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1869 assert(map_is_equal(mm.must, str));
1870
1871 isl_map_free(mm.must);
1872 isl_map_free(mm.may);
1873 isl_flow_free(flow);
1874
1875
1876 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1877 map = isl_map_read_from_str(ctx, str);
1878 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1879
1880 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1881 map = isl_map_read_from_str(ctx, str);
1882 ai = isl_access_info_add_source(ai, map, 0, &depth);
1883
1884 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1885 map = isl_map_read_from_str(ctx, str);
1886 ai = isl_access_info_add_source(ai, map, 0, &depth);
1887
1888 flow = isl_access_info_compute_flow(ai);
1889 dim = isl_space_alloc(ctx, 0, 3, 3);
1890 mm.must = isl_map_empty(isl_space_copy(dim));
1891 mm.may = isl_map_empty(dim);
1892
1893 isl_flow_foreach(flow, collect_must_may, &mm);
1894
1895 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1896 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1897 assert(map_is_equal(mm.may, str));
1898 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1899 assert(map_is_equal(mm.must, str));
1900
1901 isl_map_free(mm.must);
1902 isl_map_free(mm.may);
1903 isl_flow_free(flow);
1904
1905
1906 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1907 map = isl_map_read_from_str(ctx, str);
1908 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1909
1910 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1911 map = isl_map_read_from_str(ctx, str);
1912 ai = isl_access_info_add_source(ai, map, 0, &depth);
1913
1914 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1915 map = isl_map_read_from_str(ctx, str);
1916 ai = isl_access_info_add_source(ai, map, 0, &depth);
1917
1918 flow = isl_access_info_compute_flow(ai);
1919 dim = isl_space_alloc(ctx, 0, 3, 3);
1920 mm.must = isl_map_empty(isl_space_copy(dim));
1921 mm.may = isl_map_empty(dim);
1922
1923 isl_flow_foreach(flow, collect_must_may, &mm);
1924
1925 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1926 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1927 assert(map_is_equal(mm.may, str));
1928 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1929 assert(map_is_equal(mm.must, str));
1930
1931 isl_map_free(mm.must);
1932 isl_map_free(mm.may);
1933 isl_flow_free(flow);
1934
1935
1936 depth = 5;
1937
1938 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1939 map = isl_map_read_from_str(ctx, str);
1940 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
1941
1942 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
1943 map = isl_map_read_from_str(ctx, str);
1944 ai = isl_access_info_add_source(ai, map, 1, &depth);
1945
1946 flow = isl_access_info_compute_flow(ai);
1947 dim = isl_space_alloc(ctx, 0, 5, 5);
1948 mm.must = isl_map_empty(isl_space_copy(dim));
1949 mm.may = isl_map_empty(dim);
1950
1951 isl_flow_foreach(flow, collect_must_may, &mm);
1952
1953 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
1954 assert(map_is_equal(mm.must, str));
1955 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
1956 assert(map_is_equal(mm.may, str));
1957
1958 isl_map_free(mm.must);
1959 isl_map_free(mm.may);
1960 isl_flow_free(flow);
1961 }
1962
1963 int test_sv(isl_ctx *ctx)
1964 {
1965 const char *str;
1966 isl_map *map;
1967 isl_union_map *umap;
1968 int sv;
1969
1970 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
1971 map = isl_map_read_from_str(ctx, str);
1972 sv = isl_map_is_single_valued(map);
1973 isl_map_free(map);
1974 if (sv < 0)
1975 return -1;
1976 if (!sv)
1977 isl_die(ctx, isl_error_internal,
1978 "map not detected as single valued", return -1);
1979
1980 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
1981 map = isl_map_read_from_str(ctx, str);
1982 sv = isl_map_is_single_valued(map);
1983 isl_map_free(map);
1984 if (sv < 0)
1985 return -1;
1986 if (sv)
1987 isl_die(ctx, isl_error_internal,
1988 "map detected as single valued", return -1);
1989
1990 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
1991 umap = isl_union_map_read_from_str(ctx, str);
1992 sv = isl_union_map_is_single_valued(umap);
1993 isl_union_map_free(umap);
1994 if (sv < 0)
1995 return -1;
1996 if (!sv)
1997 isl_die(ctx, isl_error_internal,
1998 "map not detected as single valued", return -1);
1999
2000 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
2001 umap = isl_union_map_read_from_str(ctx, str);
2002 sv = isl_union_map_is_single_valued(umap);
2003 isl_union_map_free(umap);
2004 if (sv < 0)
2005 return -1;
2006 if (sv)
2007 isl_die(ctx, isl_error_internal,
2008 "map detected as single valued", return -1);
2009
2010 return 0;
2011 }
2012
2013 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
2014 {
2015 isl_map *map;
2016
2017 map = isl_map_read_from_str(ctx, str);
2018 if (bijective)
2019 assert(isl_map_is_bijective(map));
2020 else
2021 assert(!isl_map_is_bijective(map));
2022 isl_map_free(map);
2023 }
2024
2025 void test_bijective(struct isl_ctx *ctx)
2026 {
2027 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
2028 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
2029 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
2030 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
2031 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
2032 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
2033 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
2034 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
2035 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
2036 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
2037 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
2038 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
2039 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
2040 }
2041
2042 static int test_pwqp(struct isl_ctx *ctx)
2043 {
2044 const char *str;
2045 isl_set *set;
2046 isl_pw_qpolynomial *pwqp1, *pwqp2;
2047 int equal;
2048
2049 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2050 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2051
2052 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
2053 isl_dim_in, 1, 1);
2054
2055 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2056 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2057
2058 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2059
2060 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2061
2062 isl_pw_qpolynomial_free(pwqp1);
2063
2064 str = "{ [i] -> i }";
2065 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2066 str = "{ [k] : exists a : k = 2a }";
2067 set = isl_set_read_from_str(ctx, str);
2068 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2069 str = "{ [i] -> i }";
2070 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2071
2072 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2073
2074 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2075
2076 isl_pw_qpolynomial_free(pwqp1);
2077
2078 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
2079 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2080 str = "{ [10] }";
2081 set = isl_set_read_from_str(ctx, str);
2082 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2083 str = "{ [i] -> 16 }";
2084 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2085
2086 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2087
2088 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2089
2090 isl_pw_qpolynomial_free(pwqp1);
2091
2092 str = "{ [i] -> ([(i)/2]) }";
2093 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2094 str = "{ [k] : exists a : k = 2a+1 }";
2095 set = isl_set_read_from_str(ctx, str);
2096 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2097 str = "{ [i] -> -1/2 + 1/2 * i }";
2098 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2099
2100 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2101
2102 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2103
2104 isl_pw_qpolynomial_free(pwqp1);
2105
2106 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
2107 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2108 str = "{ [i] -> ([(2 * [i/2])/5]) }";
2109 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2110
2111 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2112
2113 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2114
2115 isl_pw_qpolynomial_free(pwqp1);
2116
2117 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
2118 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2119 str = "{ [x] -> x }";
2120 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2121
2122 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2123
2124 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2125
2126 isl_pw_qpolynomial_free(pwqp1);
2127
2128 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2129 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2130 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2131 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
2132 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2133 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2134 isl_pw_qpolynomial_free(pwqp1);
2135
2136 str = "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2137 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2138 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2139 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2140 set = isl_set_read_from_str(ctx, "{ [a,b,a] }");
2141 pwqp1 = isl_pw_qpolynomial_intersect_domain(pwqp1, set);
2142 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2143 isl_pw_qpolynomial_free(pwqp1);
2144 isl_pw_qpolynomial_free(pwqp2);
2145 if (equal < 0)
2146 return -1;
2147 if (!equal)
2148 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2149
2150 str = "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2151 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2152 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2153 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2154 pwqp1 = isl_pw_qpolynomial_fix_val(pwqp1, isl_dim_set, 1,
2155 isl_val_one(ctx));
2156 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2157 isl_pw_qpolynomial_free(pwqp1);
2158 isl_pw_qpolynomial_free(pwqp2);
2159 if (equal < 0)
2160 return -1;
2161 if (!equal)
2162 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2163
2164 return 0;
2165 }
2166
2167 void test_split_periods(isl_ctx *ctx)
2168 {
2169 const char *str;
2170 isl_pw_qpolynomial *pwqp;
2171
2172 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2173 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2174 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2175 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2176
2177 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
2178 assert(pwqp);
2179
2180 isl_pw_qpolynomial_free(pwqp);
2181 }
2182
2183 void test_union(isl_ctx *ctx)
2184 {
2185 const char *str;
2186 isl_union_set *uset1, *uset2;
2187 isl_union_map *umap1, *umap2;
2188
2189 str = "{ [i] : 0 <= i <= 1 }";
2190 uset1 = isl_union_set_read_from_str(ctx, str);
2191 str = "{ [1] -> [0] }";
2192 umap1 = isl_union_map_read_from_str(ctx, str);
2193
2194 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
2195 assert(isl_union_map_is_equal(umap1, umap2));
2196
2197 isl_union_map_free(umap1);
2198 isl_union_map_free(umap2);
2199
2200 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2201 umap1 = isl_union_map_read_from_str(ctx, str);
2202 str = "{ A[i]; B[i] }";
2203 uset1 = isl_union_set_read_from_str(ctx, str);
2204
2205 uset2 = isl_union_map_domain(umap1);
2206
2207 assert(isl_union_set_is_equal(uset1, uset2));
2208
2209 isl_union_set_free(uset1);
2210 isl_union_set_free(uset2);
2211 }
2212
2213 void test_bound(isl_ctx *ctx)
2214 {
2215 const char *str;
2216 isl_pw_qpolynomial *pwqp;
2217 isl_pw_qpolynomial_fold *pwf;
2218
2219 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
2220 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2221 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2222 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
2223 isl_pw_qpolynomial_fold_free(pwf);
2224
2225 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2226 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2227 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2228 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
2229 isl_pw_qpolynomial_fold_free(pwf);
2230 }
2231
2232 void test_lift(isl_ctx *ctx)
2233 {
2234 const char *str;
2235 isl_basic_map *bmap;
2236 isl_basic_set *bset;
2237
2238 str = "{ [i0] : exists e0 : i0 = 4e0 }";
2239 bset = isl_basic_set_read_from_str(ctx, str);
2240 bset = isl_basic_set_lift(bset);
2241 bmap = isl_basic_map_from_range(bset);
2242 bset = isl_basic_map_domain(bmap);
2243 isl_basic_set_free(bset);
2244 }
2245
2246 struct {
2247 const char *set1;
2248 const char *set2;
2249 int subset;
2250 } subset_tests[] = {
2251 { "{ [112, 0] }",
2252 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2253 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2254 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2255 { "{ [65] }",
2256 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2257 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2258 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2259 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2260 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2261 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2262 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2263 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2264 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2265 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2266 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2267 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2268 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2269 };
2270
2271 static int test_subset(isl_ctx *ctx)
2272 {
2273 int i;
2274 isl_set *set1, *set2;
2275 int subset;
2276
2277 for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
2278 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
2279 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
2280 subset = isl_set_is_subset(set1, set2);
2281 isl_set_free(set1);
2282 isl_set_free(set2);
2283 if (subset < 0)
2284 return -1;
2285 if (subset != subset_tests[i].subset)
2286 isl_die(ctx, isl_error_unknown,
2287 "incorrect subset result", return -1);
2288 }
2289
2290 return 0;
2291 }
2292
2293 struct {
2294 const char *minuend;
2295 const char *subtrahend;
2296 const char *difference;
2297 } subtract_domain_tests[] = {
2298 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2299 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2300 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2301 };
2302
2303 static int test_subtract(isl_ctx *ctx)
2304 {
2305 int i;
2306 isl_union_map *umap1, *umap2;
2307 isl_union_set *uset;
2308 int equal;
2309
2310 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2311 umap1 = isl_union_map_read_from_str(ctx,
2312 subtract_domain_tests[i].minuend);
2313 uset = isl_union_set_read_from_str(ctx,
2314 subtract_domain_tests[i].subtrahend);
2315 umap2 = isl_union_map_read_from_str(ctx,
2316 subtract_domain_tests[i].difference);
2317 umap1 = isl_union_map_subtract_domain(umap1, uset);
2318 equal = isl_union_map_is_equal(umap1, umap2);
2319 isl_union_map_free(umap1);
2320 isl_union_map_free(umap2);
2321 if (equal < 0)
2322 return -1;
2323 if (!equal)
2324 isl_die(ctx, isl_error_unknown,
2325 "incorrect subtract domain result", return -1);
2326 }
2327
2328 return 0;
2329 }
2330
2331 int test_factorize(isl_ctx *ctx)
2332 {
2333 const char *str;
2334 isl_basic_set *bset;
2335 isl_factorizer *f;
2336
2337 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2338 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2339 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2340 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2341 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2342 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2343 "3i5 >= -2i0 - i2 + 3i4 }";
2344 bset = isl_basic_set_read_from_str(ctx, str);
2345 f = isl_basic_set_factorizer(bset);
2346 isl_basic_set_free(bset);
2347 isl_factorizer_free(f);
2348 if (!f)
2349 isl_die(ctx, isl_error_unknown,
2350 "failed to construct factorizer", return -1);
2351
2352 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2353 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2354 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2355 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2356 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2357 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2358 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2359 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2360 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2361 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2362 bset = isl_basic_set_read_from_str(ctx, str);
2363 f = isl_basic_set_factorizer(bset);
2364 isl_basic_set_free(bset);
2365 isl_factorizer_free(f);
2366 if (!f)
2367 isl_die(ctx, isl_error_unknown,
2368 "failed to construct factorizer", return -1);
2369
2370 return 0;
2371 }
2372
2373 static int check_injective(__isl_take isl_map *map, void *user)
2374 {
2375 int *injective = user;
2376
2377 *injective = isl_map_is_injective(map);
2378 isl_map_free(map);
2379
2380 if (*injective < 0 || !*injective)
2381 return -1;
2382
2383 return 0;
2384 }
2385
2386 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2387 const char *r, const char *s, int tilable, int parallel)
2388 {
2389 int i;
2390 isl_union_set *D;
2391 isl_union_map *W, *R, *S;
2392 isl_union_map *empty;
2393 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2394 isl_union_map *validity, *proximity;
2395 isl_union_map *schedule;
2396 isl_union_map *test;
2397 isl_union_set *delta;
2398 isl_union_set *domain;
2399 isl_set *delta_set;
2400 isl_set *slice;
2401 isl_set *origin;
2402 isl_schedule *sched;
2403 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2404
2405 D = isl_union_set_read_from_str(ctx, d);
2406 W = isl_union_map_read_from_str(ctx, w);
2407 R = isl_union_map_read_from_str(ctx, r);
2408 S = isl_union_map_read_from_str(ctx, s);
2409
2410 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2411 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2412
2413 empty = isl_union_map_empty(isl_union_map_get_space(S));
2414 isl_union_map_compute_flow(isl_union_map_copy(R),
2415 isl_union_map_copy(W), empty,
2416 isl_union_map_copy(S),
2417 &dep_raw, NULL, NULL, NULL);
2418 isl_union_map_compute_flow(isl_union_map_copy(W),
2419 isl_union_map_copy(W),
2420 isl_union_map_copy(R),
2421 isl_union_map_copy(S),
2422 &dep_waw, &dep_war, NULL, NULL);
2423
2424 dep = isl_union_map_union(dep_waw, dep_war);
2425 dep = isl_union_map_union(dep, dep_raw);
2426 validity = isl_union_map_copy(dep);
2427 proximity = isl_union_map_copy(dep);
2428
2429 sched = isl_union_set_compute_schedule(isl_union_set_copy(D),
2430 validity, proximity);
2431 schedule = isl_schedule_get_map(sched);
2432 isl_schedule_free(sched);
2433 isl_union_map_free(W);
2434 isl_union_map_free(R);
2435 isl_union_map_free(S);
2436
2437 is_injection = 1;
2438 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2439
2440 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2441 is_complete = isl_union_set_is_subset(D, domain);
2442 isl_union_set_free(D);
2443 isl_union_set_free(domain);
2444
2445 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2446 test = isl_union_map_apply_range(test, dep);
2447 test = isl_union_map_apply_range(test, schedule);
2448
2449 delta = isl_union_map_deltas(test);
2450 if (isl_union_set_n_set(delta) == 0) {
2451 is_tilable = 1;
2452 is_parallel = 1;
2453 is_nonneg = 1;
2454 isl_union_set_free(delta);
2455 } else {
2456 delta_set = isl_set_from_union_set(delta);
2457
2458 slice = isl_set_universe(isl_set_get_space(delta_set));
2459 for (i = 0; i < tilable; ++i)
2460 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2461 is_tilable = isl_set_is_subset(delta_set, slice);
2462 isl_set_free(slice);
2463
2464 slice = isl_set_universe(isl_set_get_space(delta_set));
2465 for (i = 0; i < parallel; ++i)
2466 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2467 is_parallel = isl_set_is_subset(delta_set, slice);
2468 isl_set_free(slice);
2469
2470 origin = isl_set_universe(isl_set_get_space(delta_set));
2471 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2472 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2473
2474 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2475 delta_set = isl_set_lexmin(delta_set);
2476
2477 is_nonneg = isl_set_is_equal(delta_set, origin);
2478
2479 isl_set_free(origin);
2480 isl_set_free(delta_set);
2481 }
2482
2483 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2484 is_injection < 0 || is_complete < 0)
2485 return -1;
2486 if (!is_complete)
2487 isl_die(ctx, isl_error_unknown,
2488 "generated schedule incomplete", return -1);
2489 if (!is_injection)
2490 isl_die(ctx, isl_error_unknown,
2491 "generated schedule not injective on each statement",
2492 return -1);
2493 if (!is_nonneg)
2494 isl_die(ctx, isl_error_unknown,
2495 "negative dependences in generated schedule",
2496 return -1);
2497 if (!is_tilable)
2498 isl_die(ctx, isl_error_unknown,
2499 "generated schedule not as tilable as expected",
2500 return -1);
2501 if (!is_parallel)
2502 isl_die(ctx, isl_error_unknown,
2503 "generated schedule not as parallel as expected",
2504 return -1);
2505
2506 return 0;
2507 }
2508
2509 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
2510 const char *domain, const char *validity, const char *proximity)
2511 {
2512 isl_union_set *dom;
2513 isl_union_map *dep;
2514 isl_union_map *prox;
2515 isl_schedule *schedule;
2516 isl_union_map *sched;
2517
2518 dom = isl_union_set_read_from_str(ctx, domain);
2519 dep = isl_union_map_read_from_str(ctx, validity);
2520 prox = isl_union_map_read_from_str(ctx, proximity);
2521 schedule = isl_union_set_compute_schedule(dom, dep, prox);
2522 sched = isl_schedule_get_map(schedule);
2523 isl_schedule_free(schedule);
2524
2525 return sched;
2526 }
2527
2528 /* Check that a schedule can be constructed on the given domain
2529 * with the given validity and proximity constraints.
2530 */
2531 static int test_has_schedule(isl_ctx *ctx, const char *domain,
2532 const char *validity, const char *proximity)
2533 {
2534 isl_union_map *sched;
2535
2536 sched = compute_schedule(ctx, domain, validity, proximity);
2537 if (!sched)
2538 return -1;
2539
2540 isl_union_map_free(sched);
2541 return 0;
2542 }
2543
2544 int test_special_schedule(isl_ctx *ctx, const char *domain,
2545 const char *validity, const char *proximity, const char *expected_sched)
2546 {
2547 isl_union_map *sched1, *sched2;
2548 int equal;
2549
2550 sched1 = compute_schedule(ctx, domain, validity, proximity);
2551 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2552
2553 equal = isl_union_map_is_equal(sched1, sched2);
2554 isl_union_map_free(sched1);
2555 isl_union_map_free(sched2);
2556
2557 if (equal < 0)
2558 return -1;
2559 if (!equal)
2560 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2561 return -1);
2562
2563 return 0;
2564 }
2565
2566 /* Check that the schedule map is properly padded, even after being
2567 * reconstructed from the band forest.
2568 */
2569 static int test_padded_schedule(isl_ctx *ctx)
2570 {
2571 const char *str;
2572 isl_union_set *D;
2573 isl_union_map *validity, *proximity;
2574 isl_schedule *sched;
2575 isl_union_map *map1, *map2;
2576 isl_band_list *list;
2577 int equal;
2578
2579 str = "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2580 D = isl_union_set_read_from_str(ctx, str);
2581 validity = isl_union_map_empty(isl_union_set_get_space(D));
2582 proximity = isl_union_map_copy(validity);
2583 sched = isl_union_set_compute_schedule(D, validity, proximity);
2584 map1 = isl_schedule_get_map(sched);
2585 list = isl_schedule_get_band_forest(sched);
2586 isl_band_list_free(list);
2587 map2 = isl_schedule_get_map(sched);
2588 isl_schedule_free(sched);
2589 equal = isl_union_map_is_equal(map1, map2);
2590 isl_union_map_free(map1);
2591 isl_union_map_free(map2);
2592
2593 if (equal < 0)
2594 return -1;
2595 if (!equal)
2596 isl_die(ctx, isl_error_unknown,
2597 "reconstructed schedule map not the same as original",
2598 return -1);
2599
2600 return 0;
2601 }
2602
2603 int test_schedule(isl_ctx *ctx)
2604 {
2605 const char *D, *W, *R, *V, *P, *S;
2606
2607 /* Handle resulting schedule with zero bands. */
2608 if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2609 return -1;
2610
2611 /* Jacobi */
2612 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2613 W = "{ S1[t,i] -> a[t,i] }";
2614 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2615 "S1[t,i] -> a[t-1,i+1] }";
2616 S = "{ S1[t,i] -> [t,i] }";
2617 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2618 return -1;
2619
2620 /* Fig. 5 of CC2008 */
2621 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2622 "j <= -1 + N }";
2623 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2624 "j >= 2 and j <= -1 + N }";
2625 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2626 "j >= 2 and j <= -1 + N; "
2627 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2628 "j >= 2 and j <= -1 + N }";
2629 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2630 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2631 return -1;
2632
2633 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2634 W = "{ S1[i] -> a[i] }";
2635 R = "{ S2[i] -> a[i+1] }";
2636 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2637 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2638 return -1;
2639
2640 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2641 W = "{ S1[i] -> a[i] }";
2642 R = "{ S2[i] -> a[9-i] }";
2643 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2644 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2645 return -1;
2646
2647 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2648 W = "{ S1[i] -> a[i] }";
2649 R = "[N] -> { S2[i] -> a[N-1-i] }";
2650 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2651 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2652 return -1;
2653
2654 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2655 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2656 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2657 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2658 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2659 return -1;
2660
2661 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2662 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2663 R = "{ S2[i,j] -> a[i-1,j] }";
2664 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2665 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2666 return -1;
2667
2668 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2669 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2670 R = "{ S2[i,j] -> a[i,j-1] }";
2671 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2672 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2673 return -1;
2674
2675 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2676 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2677 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2678 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2679 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2680 "S_0[] -> [0, 0, 0] }";
2681 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2682 return -1;
2683 ctx->opt->schedule_parametric = 0;
2684 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2685 return -1;
2686 ctx->opt->schedule_parametric = 1;
2687
2688 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2689 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2690 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2691 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2692 "S4[i] -> a[i,N] }";
2693 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2694 "S4[i] -> [4,i,0] }";
2695 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2696 return -1;
2697
2698 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2699 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2700 "j <= N }";
2701 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2702 "j <= N; "
2703 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2704 "j <= N }";
2705 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2706 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2707 return -1;
2708
2709 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2710 " S_2[t] : t >= 0 and t <= -1 + N; "
2711 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2712 "i <= -1 + N }";
2713 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2714 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2715 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2716 "i >= 0 and i <= -1 + N }";
2717 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2718 "i >= 0 and i <= -1 + N; "
2719 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2720 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2721 " S_0[t] -> [0, t, 0] }";
2722
2723 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2724 return -1;
2725 ctx->opt->schedule_parametric = 0;
2726 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2727 return -1;
2728 ctx->opt->schedule_parametric = 1;
2729
2730 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2731 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2732 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
2733 return -1;
2734
2735 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2736 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2737 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2738 "j >= 0 and j <= -1 + N; "
2739 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2740 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2741 "j >= 0 and j <= -1 + N; "
2742 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2743 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2744 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2745 return -1;
2746
2747 D = "{ S_0[i] : i >= 0 }";
2748 W = "{ S_0[i] -> a[i] : i >= 0 }";
2749 R = "{ S_0[i] -> a[0] : i >= 0 }";
2750 S = "{ S_0[i] -> [0, i, 0] }";
2751 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2752 return -1;
2753
2754 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
2755 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
2756 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
2757 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
2758 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2759 return -1;
2760
2761 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
2762 "k <= -1 + n and k >= 0 }";
2763 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
2764 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
2765 "k <= -1 + n and k >= 0; "
2766 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
2767 "k <= -1 + n and k >= 0; "
2768 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
2769 "k <= -1 + n and k >= 0 }";
2770 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
2771 ctx->opt->schedule_outer_zero_distance = 1;
2772 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2773 return -1;
2774 ctx->opt->schedule_outer_zero_distance = 0;
2775
2776 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
2777 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
2778 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
2779 "Stmt_for_body24[i0, i1, 1, 0]:"
2780 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
2781 "Stmt_for_body7[i0, i1, i2]:"
2782 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
2783 "i2 <= 7 }";
2784
2785 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
2786 "Stmt_for_body24[1, i1, i2, i3]:"
2787 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
2788 "i2 >= 1;"
2789 "Stmt_for_body24[0, i1, i2, i3] -> "
2790 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
2791 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
2792 "i3 >= 0;"
2793 "Stmt_for_body24[0, i1, i2, i3] ->"
2794 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
2795 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
2796 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
2797 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
2798 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
2799 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
2800 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
2801 "i1 <= 6 and i1 >= 0;"
2802 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
2803 "Stmt_for_body7[i0, i1, i2] -> "
2804 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
2805 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
2806 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
2807 "Stmt_for_body7[i0, i1, i2] -> "
2808 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
2809 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
2810 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
2811 P = V;
2812 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
2813 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
2814 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
2815
2816 if (test_special_schedule(ctx, D, V, P, S) < 0)
2817 return -1;
2818
2819 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
2820 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
2821 "j >= 1 and j <= 7;"
2822 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
2823 "j >= 1 and j <= 8 }";
2824 P = "{ }";
2825 S = "{ S_0[i, j] -> [i + j, j] }";
2826 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2827 if (test_special_schedule(ctx, D, V, P, S) < 0)
2828 return -1;
2829 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2830
2831 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
2832 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
2833 "j >= 0 and j <= -1 + i }";
2834 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
2835 "i <= -1 + N and j >= 0;"
2836 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
2837 "i <= -2 + N }";
2838 P = "{ }";
2839 S = "{ S_0[i, j] -> [i, j] }";
2840 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2841 if (test_special_schedule(ctx, D, V, P, S) < 0)
2842 return -1;
2843 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2844
2845 /* Test both algorithms on a case with only proximity dependences. */
2846 D = "{ S[i,j] : 0 <= i <= 10 }";
2847 V = "{ }";
2848 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
2849 S = "{ S[i, j] -> [j, i] }";
2850 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2851 if (test_special_schedule(ctx, D, V, P, S) < 0)
2852 return -1;
2853 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2854 if (test_special_schedule(ctx, D, V, P, S) < 0)
2855 return -1;
2856
2857 D = "{ A[a]; B[] }";
2858 V = "{}";
2859 P = "{ A[a] -> B[] }";
2860 if (test_has_schedule(ctx, D, V, P) < 0)
2861 return -1;
2862
2863 if (test_padded_schedule(ctx) < 0)
2864 return -1;
2865
2866 /* Check that check for progress is not confused by rational
2867 * solution.
2868 */
2869 D = "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
2870 V = "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
2871 "i0 <= -2 + N; "
2872 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
2873 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
2874 P = "{}";
2875 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
2876 if (test_has_schedule(ctx, D, V, P) < 0)
2877 return -1;
2878 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
2879
2880 return 0;
2881 }
2882
2883 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
2884 {
2885 isl_union_map *umap;
2886 int test;
2887
2888 umap = isl_union_map_read_from_str(ctx, str);
2889 test = isl_union_map_plain_is_injective(umap);
2890 isl_union_map_free(umap);
2891 if (test < 0)
2892 return -1;
2893 if (test == injective)
2894 return 0;
2895 if (injective)
2896 isl_die(ctx, isl_error_unknown,
2897 "map not detected as injective", return -1);
2898 else
2899 isl_die(ctx, isl_error_unknown,
2900 "map detected as injective", return -1);
2901 }
2902
2903 int test_injective(isl_ctx *ctx)
2904 {
2905 const char *str;
2906
2907 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
2908 return -1;
2909 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
2910 return -1;
2911 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
2912 return -1;
2913 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
2914 return -1;
2915 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
2916 return -1;
2917 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
2918 return -1;
2919 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
2920 return -1;
2921 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
2922 return -1;
2923
2924 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
2925 if (test_plain_injective(ctx, str, 1))
2926 return -1;
2927 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
2928 if (test_plain_injective(ctx, str, 0))
2929 return -1;
2930
2931 return 0;
2932 }
2933
2934 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
2935 {
2936 isl_aff *aff2;
2937 int equal;
2938
2939 if (!aff)
2940 return -1;
2941
2942 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
2943 equal = isl_aff_plain_is_equal(aff, aff2);
2944 isl_aff_free(aff2);
2945
2946 return equal;
2947 }
2948
2949 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
2950 {
2951 int equal;
2952
2953 equal = aff_plain_is_equal(aff, str);
2954 if (equal < 0)
2955 return -1;
2956 if (!equal)
2957 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
2958 "result not as expected", return -1);
2959 return 0;
2960 }
2961
2962 int test_aff(isl_ctx *ctx)
2963 {
2964 const char *str;
2965 isl_set *set;
2966 isl_space *space;
2967 isl_local_space *ls;
2968 isl_aff *aff;
2969 int zero, equal;
2970
2971 space = isl_space_set_alloc(ctx, 0, 1);
2972 ls = isl_local_space_from_space(space);
2973 aff = isl_aff_zero_on_domain(ls);
2974
2975 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2976 aff = isl_aff_scale_down_ui(aff, 3);
2977 aff = isl_aff_floor(aff);
2978 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2979 aff = isl_aff_scale_down_ui(aff, 2);
2980 aff = isl_aff_floor(aff);
2981 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
2982
2983 str = "{ [10] }";
2984 set = isl_set_read_from_str(ctx, str);
2985 aff = isl_aff_gist(aff, set);
2986
2987 aff = isl_aff_add_constant_si(aff, -16);
2988 zero = isl_aff_plain_is_zero(aff);
2989 isl_aff_free(aff);
2990
2991 if (zero < 0)
2992 return -1;
2993 if (!zero)
2994 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2995
2996 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
2997 aff = isl_aff_scale_down_ui(aff, 64);
2998 aff = isl_aff_floor(aff);
2999 equal = aff_check_plain_equal(aff, "{ [-1] }");
3000 isl_aff_free(aff);
3001 if (equal < 0)
3002 return -1;
3003
3004 return 0;
3005 }
3006
3007 int test_dim_max(isl_ctx *ctx)
3008 {
3009 int equal;
3010 const char *str;
3011 isl_set *set1, *set2;
3012 isl_set *set;
3013 isl_map *map;
3014 isl_pw_aff *pwaff;
3015
3016 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
3017 set = isl_set_read_from_str(ctx, str);
3018 pwaff = isl_set_dim_max(set, 0);
3019 set1 = isl_set_from_pw_aff(pwaff);
3020 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
3021 set2 = isl_set_read_from_str(ctx, str);
3022 equal = isl_set_is_equal(set1, set2);
3023 isl_set_free(set1);
3024 isl_set_free(set2);
3025 if (equal < 0)
3026 return -1;
3027 if (!equal)
3028 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3029
3030 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
3031 set = isl_set_read_from_str(ctx, str);
3032 pwaff = isl_set_dim_max(set, 0);
3033 set1 = isl_set_from_pw_aff(pwaff);
3034 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3035 set2 = isl_set_read_from_str(ctx, str);
3036 equal = isl_set_is_equal(set1, set2);
3037 isl_set_free(set1);
3038 isl_set_free(set2);
3039 if (equal < 0)
3040 return -1;
3041 if (!equal)
3042 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3043
3044 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
3045 set = isl_set_read_from_str(ctx, str);
3046 pwaff = isl_set_dim_max(set, 0);
3047 set1 = isl_set_from_pw_aff(pwaff);
3048 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3049 set2 = isl_set_read_from_str(ctx, str);
3050 equal = isl_set_is_equal(set1, set2);
3051 isl_set_free(set1);
3052 isl_set_free(set2);
3053 if (equal < 0)
3054 return -1;
3055 if (!equal)
3056 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3057
3058 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
3059 "0 <= i < N and 0 <= j < M }";
3060 map = isl_map_read_from_str(ctx, str);
3061 set = isl_map_range(map);
3062
3063 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
3064 set1 = isl_set_from_pw_aff(pwaff);
3065 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
3066 set2 = isl_set_read_from_str(ctx, str);
3067 equal = isl_set_is_equal(set1, set2);
3068 isl_set_free(set1);
3069 isl_set_free(set2);
3070
3071 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
3072 set1 = isl_set_from_pw_aff(pwaff);
3073 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
3074 set2 = isl_set_read_from_str(ctx, str);
3075 if (equal >= 0 && equal)
3076 equal = isl_set_is_equal(set1, set2);
3077 isl_set_free(set1);
3078 isl_set_free(set2);
3079
3080 isl_set_free(set);
3081
3082 if (equal < 0)
3083 return -1;
3084 if (!equal)
3085 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3086
3087 /* Check that solutions are properly merged. */
3088 str = "[n] -> { [a, b, c] : c >= -4a - 2b and "
3089 "c <= -1 + n - 4a - 2b and c >= -2b and "
3090 "4a >= -4 + n and c >= 0 }";
3091 set = isl_set_read_from_str(ctx, str);
3092 pwaff = isl_set_dim_min(set, 2);
3093 set1 = isl_set_from_pw_aff(pwaff);
3094 str = "[n] -> { [(0)] : n >= 1 }";
3095 set2 = isl_set_read_from_str(ctx, str);
3096 equal = isl_set_is_equal(set1, set2);
3097 isl_set_free(set1);
3098 isl_set_free(set2);
3099
3100 if (equal < 0)
3101 return -1;
3102 if (!equal)
3103 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3104
3105 return 0;
3106 }
3107
3108 int test_product(isl_ctx *ctx)
3109 {
3110 const char *str;
3111 isl_set *set;
3112 isl_union_set *uset1, *uset2;
3113 int ok;
3114
3115 str = "{ A[i] }";
3116 set = isl_set_read_from_str(ctx, str);
3117 set = isl_set_product(set, isl_set_copy(set));
3118 ok = isl_set_is_wrapping(set);
3119 isl_set_free(set);
3120 if (ok < 0)
3121 return -1;
3122 if (!ok)
3123 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3124
3125 str = "{ [] }";
3126 uset1 = isl_union_set_read_from_str(ctx, str);
3127 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
3128 str = "{ [[] -> []] }";
3129 uset2 = isl_union_set_read_from_str(ctx, str);
3130 ok = isl_union_set_is_equal(uset1, uset2);
3131 isl_union_set_free(uset1);
3132 isl_union_set_free(uset2);
3133 if (ok < 0)
3134 return -1;
3135 if (!ok)
3136 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3137
3138 return 0;
3139 }
3140
3141 int test_equal(isl_ctx *ctx)
3142 {
3143 const char *str;
3144 isl_set *set, *set2;
3145 int equal;
3146
3147 str = "{ S_6[i] }";
3148 set = isl_set_read_from_str(ctx, str);
3149 str = "{ S_7[i] }";
3150 set2 = isl_set_read_from_str(ctx, str);
3151 equal = isl_set_is_equal(set, set2);
3152 isl_set_free(set);
3153 isl_set_free(set2);
3154 if (equal < 0)
3155 return -1;
3156 if (equal)
3157 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3158
3159 return 0;
3160 }
3161
3162 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
3163 enum isl_dim_type type, unsigned pos, int fixed)
3164 {
3165 int test;
3166
3167 test = isl_map_plain_is_fixed(map, type, pos, NULL);
3168 isl_map_free(map);
3169 if (test < 0)
3170 return -1;
3171 if (test == fixed)
3172 return 0;
3173 if (fixed)
3174 isl_die(ctx, isl_error_unknown,
3175 "map not detected as fixed", return -1);
3176 else
3177 isl_die(ctx, isl_error_unknown,
3178 "map detected as fixed", return -1);
3179 }
3180
3181 int test_fixed(isl_ctx *ctx)
3182 {
3183 const char *str;
3184 isl_map *map;
3185
3186 str = "{ [i] -> [i] }";
3187 map = isl_map_read_from_str(ctx, str);
3188 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
3189 return -1;
3190 str = "{ [i] -> [1] }";
3191 map = isl_map_read_from_str(ctx, str);
3192 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3193 return -1;
3194 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
3195 map = isl_map_read_from_str(ctx, str);
3196 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3197 return -1;
3198 map = isl_map_read_from_str(ctx, str);
3199 map = isl_map_neg(map);
3200 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3201 return -1;
3202
3203 return 0;
3204 }
3205
3206 int test_vertices(isl_ctx *ctx)
3207 {
3208 const char *str;
3209 isl_basic_set *bset;
3210 isl_vertices *vertices;
3211
3212 str = "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }";
3213 bset = isl_basic_set_read_from_str(ctx, str);
3214 vertices = isl_basic_set_compute_vertices(bset);
3215 isl_basic_set_free(bset);
3216 isl_vertices_free(vertices);
3217 if (!vertices)
3218 return -1;
3219
3220 str = "{ A[t, i] : t = 14 and i = 1 }";
3221 bset = isl_basic_set_read_from_str(ctx, str);
3222 vertices = isl_basic_set_compute_vertices(bset);
3223 isl_basic_set_free(bset);
3224 isl_vertices_free(vertices);
3225 if (!vertices)
3226 return -1;
3227
3228 return 0;
3229 }
3230
3231 int test_union_pw(isl_ctx *ctx)
3232 {
3233 int equal;
3234 const char *str;
3235 isl_union_set *uset;
3236 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
3237
3238 str = "{ [x] -> x^2 }";
3239 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
3240 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
3241 uset = isl_union_pw_qpolynomial_domain(upwqp1);
3242 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
3243 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
3244 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
3245 isl_union_pw_qpolynomial_free(upwqp1);
3246 isl_union_pw_qpolynomial_free(upwqp2);
3247 if (equal < 0)
3248 return -1;
3249 if (!equal)
3250 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3251
3252 return 0;
3253 }
3254
3255 int test_output(isl_ctx *ctx)
3256 {
3257 char *s;
3258 const char *str;
3259 isl_pw_aff *pa;
3260 isl_printer *p;
3261 int equal;
3262
3263 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
3264 pa = isl_pw_aff_read_from_str(ctx, str);
3265
3266 p = isl_printer_to_str(ctx);
3267 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
3268 p = isl_printer_print_pw_aff(p, pa);
3269 s = isl_printer_get_str(p);
3270 isl_printer_free(p);
3271 isl_pw_aff_free(pa);
3272 if (!s)
3273 equal = -1;
3274 else
3275 equal = !strcmp(s, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
3276 free(s);
3277 if (equal < 0)
3278 return -1;
3279 if (!equal)
3280 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3281
3282 return 0;
3283 }
3284
3285 int test_sample(isl_ctx *ctx)
3286 {
3287 const char *str;
3288 isl_basic_set *bset1, *bset2;
3289 int empty, subset;
3290
3291 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
3292 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
3293 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
3294 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
3295 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
3296 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
3297 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
3298 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
3299 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3300 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3301 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3302 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3303 "d - 1073741821e and "
3304 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3305 "3j >= 1 - a + b + 2e and "
3306 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3307 "3i <= 4 - a + 4b - e and "
3308 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3309 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3310 "c <= -1 + a and 3i >= -2 - a + 3e and "
3311 "1073741822e <= 1073741823 - a + 1073741822b + c and "
3312 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3313 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3314 "1073741823e >= 1 + 1073741823b - d and "
3315 "3i >= 1073741823b + c - 1073741823e - f and "
3316 "3i >= 1 + 2b + e + 3g }";
3317 bset1 = isl_basic_set_read_from_str(ctx, str);
3318 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
3319 empty = isl_basic_set_is_empty(bset2);
3320 subset = isl_basic_set_is_subset(bset2, bset1);
3321 isl_basic_set_free(bset1);
3322 isl_basic_set_free(bset2);
3323 if (empty < 0 || subset < 0)
3324 return -1;
3325 if (empty)
3326 isl_die(ctx, isl_error_unknown, "point not found", return -1);
3327 if (!subset)
3328 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
3329
3330 return 0;
3331 }
3332
3333 int test_fixed_power(isl_ctx *ctx)
3334 {
3335 const char *str;
3336 isl_map *map;
3337 isl_int exp;
3338 int equal;
3339
3340 isl_int_init(exp);
3341 str = "{ [i] -> [i + 1] }";
3342 map = isl_map_read_from_str(ctx, str);
3343 isl_int_set_si(exp, 23);
3344 map = isl_map_fixed_power(map, exp);
3345 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
3346 isl_int_clear(exp);
3347 isl_map_free(map);
3348 if (equal < 0)
3349 return -1;
3350
3351 return 0;
3352 }
3353
3354 int test_slice(isl_ctx *ctx)
3355 {
3356 const char *str;
3357 isl_map *map;
3358 int equal;
3359
3360 str = "{ [i] -> [j] }";
3361 map = isl_map_read_from_str(ctx, str);
3362 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
3363 equal = map_check_equal(map, "{ [i] -> [i] }");
3364 isl_map_free(map);
3365 if (equal < 0)
3366 return -1;
3367
3368 str = "{ [i] -> [j] }";
3369 map = isl_map_read_from_str(ctx, str);
3370 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
3371 equal = map_check_equal(map, "{ [i] -> [j] }");
3372 isl_map_free(map);
3373 if (equal < 0)
3374 return -1;
3375
3376 str = "{ [i] -> [j] }";
3377 map = isl_map_read_from_str(ctx, str);
3378 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
3379 equal = map_check_equal(map, "{ [i] -> [-i] }");
3380 isl_map_free(map);
3381 if (equal < 0)
3382 return -1;
3383
3384 str = "{ [i] -> [j] }";
3385 map = isl_map_read_from_str(ctx, str);
3386 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
3387 equal = map_check_equal(map, "{ [0] -> [j] }");
3388 isl_map_free(map);
3389 if (equal < 0)
3390 return -1;
3391
3392 str = "{ [i] -> [j] }";
3393 map = isl_map_read_from_str(ctx, str);
3394 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
3395 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
3396 isl_map_free(map);
3397 if (equal < 0)
3398 return -1;
3399
3400 str = "{ [i] -> [j] }";
3401 map = isl_map_read_from_str(ctx, str);
3402 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
3403 equal = map_check_equal(map, "{ [i] -> [j] : false }");
3404 isl_map_free(map);
3405 if (equal < 0)
3406 return -1;
3407
3408 return 0;
3409 }
3410
3411 int test_eliminate(isl_ctx *ctx)
3412 {
3413 const char *str;
3414 isl_map *map;
3415 int equal;
3416
3417 str = "{ [i] -> [j] : i = 2j }";
3418 map = isl_map_read_from_str(ctx, str);
3419 map = isl_map_eliminate(map, isl_dim_out, 0, 1);
3420 equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
3421 isl_map_free(map);
3422 if (equal < 0)
3423 return -1;
3424
3425 return 0;
3426 }
3427
3428 /* Check that isl_set_dim_residue_class detects that the values of j
3429 * in the set below are all odd and that it does not detect any spurious
3430 * strides.
3431 */
3432 static int test_residue_class(isl_ctx *ctx)
3433 {
3434 const char *str;
3435 isl_set *set;
3436 isl_int m, r;
3437 int res;
3438
3439 str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3440 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3441 set = isl_set_read_from_str(ctx, str);
3442 isl_int_init(m);
3443 isl_int_init(r);
3444 res = isl_set_dim_residue_class(set, 1, &m, &r);
3445 if (res >= 0 &&
3446 (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
3447 isl_die(ctx, isl_error_unknown, "incorrect residue class",
3448 res = -1);
3449 isl_int_clear(r);
3450 isl_int_clear(m);
3451 isl_set_free(set);
3452
3453 return res;
3454 }
3455
3456 int test_align_parameters(isl_ctx *ctx)
3457 {
3458 const char *str;
3459 isl_space *space;
3460 isl_multi_aff *ma1, *ma2;
3461 int equal;
3462
3463 str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3464 ma1 = isl_multi_aff_read_from_str(ctx, str);
3465
3466 space = isl_space_params_alloc(ctx, 1);
3467 space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
3468 ma1 = isl_multi_aff_align_params(ma1, space);
3469
3470 str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3471 ma2 = isl_multi_aff_read_from_str(ctx, str);
3472
3473 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3474
3475 isl_multi_aff_free(ma1);
3476 isl_multi_aff_free(ma2);
3477
3478 if (equal < 0)
3479 return -1;
3480 if (!equal)
3481 isl_die(ctx, isl_error_unknown,
3482 "result not as expected", return -1);
3483
3484 return 0;
3485 }
3486
3487 static int test_list(isl_ctx *ctx)
3488 {
3489 isl_id *a, *b, *c, *d, *id;
3490 isl_id_list *list;
3491 int ok;
3492
3493 a = isl_id_alloc(ctx, "a", NULL);
3494 b = isl_id_alloc(ctx, "b", NULL);
3495 c = isl_id_alloc(ctx, "c", NULL);
3496 d = isl_id_alloc(ctx, "d", NULL);
3497
3498 list = isl_id_list_alloc(ctx, 4);
3499 list = isl_id_list_add(list, a);
3500 list = isl_id_list_add(list, b);
3501 list = isl_id_list_add(list, c);
3502 list = isl_id_list_add(list, d);
3503 list = isl_id_list_drop(list, 1, 1);
3504
3505 if (isl_id_list_n_id(list) != 3) {
3506 isl_id_list_free(list);
3507 isl_die(ctx, isl_error_unknown,
3508 "unexpected number of elements in list", return -1);
3509 }
3510
3511 id = isl_id_list_get_id(list, 0);
3512 ok = id == a;
3513 isl_id_free(id);
3514 id = isl_id_list_get_id(list, 1);
3515 ok = ok && id == c;
3516 isl_id_free(id);
3517 id = isl_id_list_get_id(list, 2);
3518 ok = ok && id == d;
3519 isl_id_free(id);
3520
3521 isl_id_list_free(list);
3522
3523 if (!ok)
3524 isl_die(ctx, isl_error_unknown,
3525 "unexpected elements in list", return -1);
3526
3527 return 0;
3528 }
3529
3530 const char *set_conversion_tests[] = {
3531 "[N] -> { [i] : N - 1 <= 2 i <= N }",
3532 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
3533 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3534 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
3535 };
3536
3537 /* Check that converting from isl_set to isl_pw_multi_aff and back
3538 * to isl_set produces the original isl_set.
3539 */
3540 static int test_set_conversion(isl_ctx *ctx)
3541 {
3542 int i;
3543 const char *str;
3544 isl_set *set1, *set2;
3545 isl_pw_multi_aff *pma;
3546 int equal;
3547
3548 for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
3549 str = set_conversion_tests[i];
3550 set1 = isl_set_read_from_str(ctx, str);
3551 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
3552 set2 = isl_set_from_pw_multi_aff(pma);
3553 equal = isl_set_is_equal(set1, set2);
3554 isl_set_free(set1);
3555 isl_set_free(set2);
3556
3557 if (equal < 0)
3558 return -1;
3559 if (!equal)
3560 isl_die(ctx, isl_error_unknown, "bad conversion",
3561 return -1);
3562 }
3563
3564 return 0;
3565 }
3566
3567 /* Check that converting from isl_map to isl_pw_multi_aff and back
3568 * to isl_map produces the original isl_map.
3569 */
3570 static int test_map_conversion(isl_ctx *ctx)
3571 {
3572 const char *str;
3573 isl_map *map1, *map2;
3574 isl_pw_multi_aff *pma;
3575 int equal;
3576
3577 str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
3578 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
3579 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
3580 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
3581 "9e <= -2 - 2a) }";
3582 map1 = isl_map_read_from_str(ctx, str);
3583 pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
3584 map2 = isl_map_from_pw_multi_aff(pma);
3585 equal = isl_map_is_equal(map1, map2);
3586 isl_map_free(map1);
3587 isl_map_free(map2);
3588
3589 if (equal < 0)
3590 return -1;
3591 if (!equal)
3592 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
3593
3594 return 0;
3595 }
3596
3597 static int test_conversion(isl_ctx *ctx)
3598 {
3599 if (test_set_conversion(ctx) < 0)
3600 return -1;
3601 if (test_map_conversion(ctx) < 0)
3602 return -1;
3603 return 0;
3604 }
3605
3606 /* Check that isl_basic_map_curry does not modify input.
3607 */
3608 static int test_curry(isl_ctx *ctx)
3609 {
3610 const char *str;
3611 isl_basic_map *bmap1, *bmap2;
3612 int equal;
3613
3614 str = "{ [A[] -> B[]] -> C[] }";
3615 bmap1 = isl_basic_map_read_from_str(ctx, str);
3616 bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
3617 equal = isl_basic_map_is_equal(bmap1, bmap2);
3618 isl_basic_map_free(bmap1);
3619 isl_basic_map_free(bmap2);
3620
3621 if (equal < 0)
3622 return -1;
3623 if (equal)
3624 isl_die(ctx, isl_error_unknown,
3625 "curried map should not be equal to original",
3626 return -1);
3627
3628 return 0;
3629 }
3630
3631 struct {
3632 const char *set;
3633 const char *ma;
3634 const char *res;
3635 } preimage_tests[] = {
3636 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
3637 "{ A[j,i] -> B[i,j] }",
3638 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
3639 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3640 "{ A[a,b] -> B[a/2,b/6] }",
3641 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
3642 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
3643 "{ A[a,b] -> B[a/2,b/6] }",
3644 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
3645 "exists i,j : a = 2 i and b = 6 j }" },
3646 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
3647 "[n] -> { : 0 <= n <= 100 }" },
3648 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3649 "{ A[a] -> B[2a] }",
3650 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
3651 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
3652 "{ A[a] -> B[([a/2])] }",
3653 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
3654 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
3655 "{ A[a] -> B[a,a,a/3] }",
3656 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
3657 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
3658 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
3659 };
3660
3661 static int test_preimage_basic_set(isl_ctx *ctx)
3662 {
3663 int i;
3664 isl_basic_set *bset1, *bset2;
3665 isl_multi_aff *ma;
3666 int equal;
3667
3668 for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
3669 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
3670 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
3671 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
3672 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
3673 equal = isl_basic_set_is_equal(bset1, bset2);
3674 isl_basic_set_free(bset1);
3675 isl_basic_set_free(bset2);
3676 if (equal < 0)
3677 return -1;
3678 if (!equal)
3679 isl_die(ctx, isl_error_unknown, "bad preimage",
3680 return -1);
3681 }
3682
3683 return 0;
3684 }
3685
3686 struct {
3687 const char *map;
3688 const char *ma;
3689 const char *res;
3690 } preimage_domain_tests[] = {
3691 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
3692 "{ A[j,i] -> B[i,j] }",
3693 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
3694 { "{ B[i] -> C[i]; D[i] -> E[i] }",
3695 "{ A[i] -> B[i + 1] }",
3696 "{ A[i] -> C[i + 1] }" },
3697 { "{ B[i] -> C[i]; B[i] -> E[i] }",
3698 "{ A[i] -> B[i + 1] }",
3699 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
3700 { "{ B[i] -> C[([i/2])] }",
3701 "{ A[i] -> B[2i] }",
3702 "{ A[i] -> C[i] }" },
3703 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
3704 "{ A[i] -> B[([i/5]), ([i/7])] }",
3705 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
3706 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
3707 "[N] -> { A[] -> B[([N/5])] }",
3708 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
3709 { "{ B[i] -> C[i] : exists a : i = 5 a }",
3710 "{ A[i] -> B[2i] }",
3711 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
3712 { "{ B[i] -> C[i] : exists a : i = 2 a; "
3713 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
3714 "{ A[i] -> B[2i] }",
3715 "{ A[i] -> C[2i] }" },
3716 };
3717
3718 static int test_preimage_union_map(isl_ctx *ctx)
3719 {
3720 int i;
3721 isl_union_map *umap1, *umap2;
3722 isl_multi_aff *ma;
3723 int equal;
3724
3725 for (i = 0; i < ARRAY_SIZE(preimage_domain_tests); ++i) {
3726 umap1 = isl_union_map_read_from_str(ctx,
3727 preimage_domain_tests[i].map);
3728 ma = isl_multi_aff_read_from_str(ctx,
3729 preimage_domain_tests[i].ma);
3730 umap2 = isl_union_map_read_from_str(ctx,
3731 preimage_domain_tests[i].res);
3732 umap1 = isl_union_map_preimage_domain_multi_aff(umap1, ma);
3733 equal = isl_union_map_is_equal(umap1, umap2);
3734 isl_union_map_free(umap1);
3735 isl_union_map_free(umap2);
3736 if (equal < 0)
3737 return -1;
3738 if (!equal)
3739 isl_die(ctx, isl_error_unknown, "bad preimage",
3740 return -1);
3741 }
3742
3743 return 0;
3744 }
3745
3746 static int test_preimage(isl_ctx *ctx)
3747 {
3748 if (test_preimage_basic_set(ctx) < 0)
3749 return -1;
3750 if (test_preimage_union_map(ctx) < 0)
3751 return -1;
3752
3753 return 0;
3754 }
3755
3756 struct {
3757 const char *ma1;
3758 const char *ma;
3759 const char *res;
3760 } pullback_tests[] = {
3761 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
3762 "{ A[a,b] -> C[b + 2a] }" },
3763 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
3764 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
3765 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
3766 "{ A[a] -> C[(a)/6] }" },
3767 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
3768 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
3769 "{ A[a] -> C[(2a)/3] }" },
3770 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
3771 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
3772 "{ A[i,j] -> C[i + j, i + j] }"},
3773 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
3774 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
3775 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
3776 };
3777
3778 static int test_pullback(isl_ctx *ctx)
3779 {
3780 int i;
3781 isl_multi_aff *ma1, *ma2;
3782 isl_multi_aff *ma;
3783 int equal;
3784
3785 for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
3786 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
3787 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
3788 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
3789 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
3790 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3791 isl_multi_aff_free(ma1);
3792 isl_multi_aff_free(ma2);
3793 if (equal < 0)
3794 return -1;
3795 if (!equal)
3796 isl_die(ctx, isl_error_unknown, "bad pullback",
3797 return -1);
3798 }
3799
3800 return 0;
3801 }
3802
3803 /* Check that negation is printed correctly.
3804 */
3805 static int test_ast(isl_ctx *ctx)
3806 {
3807 isl_ast_expr *expr, *expr1, *expr2, *expr3;
3808 char *str;
3809 int ok;
3810
3811 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
3812 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
3813 expr = isl_ast_expr_add(expr1, expr2);
3814 expr = isl_ast_expr_neg(expr);
3815 str = isl_ast_expr_to_str(expr);
3816 ok = str ? !strcmp(str, "-(A + B)") : -1;
3817 free(str);
3818 isl_ast_expr_free(expr);
3819
3820 if (ok < 0)
3821 return -1;
3822 if (!ok)
3823 isl_die(ctx, isl_error_unknown,
3824 "isl_ast_expr printed incorrectly", return -1);
3825
3826 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
3827 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
3828 expr = isl_ast_expr_add(expr1, expr2);
3829 expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
3830 expr = isl_ast_expr_sub(expr3, expr);
3831 str = isl_ast_expr_to_str(expr);
3832 ok = str ? !strcmp(str, "C - (A + B)") : -1;
3833 free(str);
3834 isl_ast_expr_free(expr);
3835
3836 if (ok < 0)
3837 return -1;
3838 if (!ok)
3839 isl_die(ctx, isl_error_unknown,
3840 "isl_ast_expr printed incorrectly", return -1);
3841
3842 return 0;
3843 }
3844
3845 /* Internal data structure for before_for and after_for callbacks.
3846 *
3847 * depth is the current depth
3848 * before is the number of times before_for has been called
3849 * after is the number of times after_for has been called
3850 */
3851 struct isl_test_codegen_data {
3852 int depth;
3853 int before;
3854 int after;
3855 };
3856
3857 /* This function is called before each for loop in the AST generated
3858 * from test_ast_gen1.
3859 *
3860 * Increment the number of calls and the depth.
3861 * Check that the space returned by isl_ast_build_get_schedule_space
3862 * matches the target space of the schedule returned by
3863 * isl_ast_build_get_schedule.
3864 * Return an isl_id that is checked by the corresponding call
3865 * to after_for.
3866 */
3867 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
3868 void *user)
3869 {
3870 struct isl_test_codegen_data *data = user;
3871 isl_ctx *ctx;
3872 isl_space *space;
3873 isl_union_map *schedule;
3874 isl_union_set *uset;
3875 isl_set *set;
3876 int empty;
3877 char name[] = "d0";
3878
3879 ctx = isl_ast_build_get_ctx(build);
3880
3881 if (data->before >= 3)
3882 isl_die(ctx, isl_error_unknown,
3883 "unexpected number of for nodes", return NULL);
3884 if (data->depth >= 2)
3885 isl_die(ctx, isl_error_unknown,
3886 "unexpected depth", return NULL);
3887
3888 snprintf(name, sizeof(name), "d%d", data->depth);
3889 data->before++;
3890 data->depth++;
3891
3892 schedule = isl_ast_build_get_schedule(build);
3893 uset = isl_union_map_range(schedule);
3894 if (!uset)
3895 return NULL;
3896 if (isl_union_set_n_set(uset) != 1) {
3897 isl_union_set_free(uset);
3898 isl_die(ctx, isl_error_unknown,
3899 "expecting single range space", return NULL);
3900 }
3901
3902 space = isl_ast_build_get_schedule_space(build);
3903 set = isl_union_set_extract_set(uset, space);
3904 isl_union_set_free(uset);
3905 empty = isl_set_is_empty(set);
3906 isl_set_free(set);
3907
3908 if (empty < 0)
3909 return NULL;
3910 if (empty)
3911 isl_die(ctx, isl_error_unknown,
3912 "spaces don't match", return NULL);
3913
3914 return isl_id_alloc(ctx, name, NULL);
3915 }
3916
3917 /* This function is called after each for loop in the AST generated
3918 * from test_ast_gen1.
3919 *
3920 * Increment the number of calls and decrement the depth.
3921 * Check that the annotation attached to the node matches
3922 * the isl_id returned by the corresponding call to before_for.
3923 */
3924 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
3925 __isl_keep isl_ast_build *build, void *user)
3926 {
3927 struct isl_test_codegen_data *data = user;
3928 isl_id *id;
3929 const char *name;
3930 int valid;
3931
3932 data->after++;
3933 data->depth--;
3934
3935 if (data->after > data->before)
3936 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3937 "mismatch in number of for nodes",
3938 return isl_ast_node_free(node));
3939
3940 id = isl_ast_node_get_annotation(node);
3941 if (!id)
3942 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3943 "missing annotation", return isl_ast_node_free(node));
3944
3945 name = isl_id_get_name(id);
3946 valid = name && atoi(name + 1) == data->depth;
3947 isl_id_free(id);
3948
3949 if (!valid)
3950 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
3951 "wrong annotation", return isl_ast_node_free(node));
3952
3953 return node;
3954 }
3955
3956 /* Check that the before_each_for and after_each_for callbacks
3957 * are called for each for loop in the generated code,
3958 * that they are called in the right order and that the isl_id
3959 * returned from the before_each_for callback is attached to
3960 * the isl_ast_node passed to the corresponding after_each_for call.
3961 */
3962 static int test_ast_gen1(isl_ctx *ctx)
3963 {
3964 const char *str;
3965 isl_set *set;
3966 isl_union_map *schedule;
3967 isl_ast_build *build;
3968 isl_ast_node *tree;
3969 struct isl_test_codegen_data data;
3970
3971 str = "[N] -> { : N >= 10 }";
3972 set = isl_set_read_from_str(ctx, str);
3973 str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
3974 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
3975 schedule = isl_union_map_read_from_str(ctx, str);
3976
3977 data.before = 0;
3978 data.after = 0;
3979 data.depth = 0;
3980 build = isl_ast_build_from_context(set);
3981 build = isl_ast_build_set_before_each_for(build,
3982 &before_for, &data);
3983 build = isl_ast_build_set_after_each_for(build,
3984 &after_for, &data);
3985 tree = isl_ast_build_ast_from_schedule(build, schedule);
3986 isl_ast_build_free(build);
3987 if (!tree)
3988 return -1;
3989
3990 isl_ast_node_free(tree);
3991
3992 if (data.before != 3 || data.after != 3)
3993 isl_die(ctx, isl_error_unknown,
3994 "unexpected number of for nodes", return -1);
3995
3996 return 0;
3997 }
3998
3999 /* Check that the AST generator handles domains that are integrally disjoint
4000 * but not ratinoally disjoint.
4001 */
4002 static int test_ast_gen2(isl_ctx *ctx)
4003 {
4004 const char *str;
4005 isl_set *set;
4006 isl_union_map *schedule;
4007 isl_union_map *options;
4008 isl_ast_build *build;
4009 isl_ast_node *tree;
4010
4011 str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
4012 schedule = isl_union_map_read_from_str(ctx, str);
4013 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4014 build = isl_ast_build_from_context(set);
4015
4016 str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
4017 options = isl_union_map_read_from_str(ctx, str);
4018 build = isl_ast_build_set_options(build, options);
4019 tree = isl_ast_build_ast_from_schedule(build, schedule);
4020 isl_ast_build_free(build);
4021 if (!tree)
4022 return -1;
4023 isl_ast_node_free(tree);
4024
4025 return 0;
4026 }
4027
4028 /* Increment *user on each call.
4029 */
4030 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
4031 __isl_keep isl_ast_build *build, void *user)
4032 {
4033 int *n = user;
4034
4035 (*n)++;
4036
4037 return node;
4038 }
4039
4040 /* Test that unrolling tries to minimize the number of instances.
4041 * In particular, for the schedule given below, make sure it generates
4042 * 3 nodes (rather than 101).
4043 */
4044 static int test_ast_gen3(isl_ctx *ctx)
4045 {
4046 const char *str;
4047 isl_set *set;
4048 isl_union_map *schedule;
4049 isl_union_map *options;
4050 isl_ast_build *build;
4051 isl_ast_node *tree;
4052 int n_domain = 0;
4053
4054 str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
4055 schedule = isl_union_map_read_from_str(ctx, str);
4056 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4057
4058 str = "{ [i] -> unroll[0] }";
4059 options = isl_union_map_read_from_str(ctx, str);
4060
4061 build = isl_ast_build_from_context(set);
4062 build = isl_ast_build_set_options(build, options);
4063 build = isl_ast_build_set_at_each_domain(build,
4064 &count_domains, &n_domain);
4065 tree = isl_ast_build_ast_from_schedule(build, schedule);
4066 isl_ast_build_free(build);
4067 if (!tree)
4068 return -1;
4069
4070 isl_ast_node_free(tree);
4071
4072 if (n_domain != 3)
4073 isl_die(ctx, isl_error_unknown,
4074 "unexpected number of for nodes", return -1);
4075
4076 return 0;
4077 }
4078
4079 /* Check that if the ast_build_exploit_nested_bounds options is set,
4080 * we do not get an outer if node in the generated AST,
4081 * while we do get such an outer if node if the options is not set.
4082 */
4083 static int test_ast_gen4(isl_ctx *ctx)
4084 {
4085 const char *str;
4086 isl_set *set;
4087 isl_union_map *schedule;
4088 isl_ast_build *build;
4089 isl_ast_node *tree;
4090 enum isl_ast_node_type type;
4091 int enb;
4092
4093 enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
4094 str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
4095
4096 isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
4097
4098 schedule = isl_union_map_read_from_str(ctx, str);
4099 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4100 build = isl_ast_build_from_context(set);
4101 tree = isl_ast_build_ast_from_schedule(build, schedule);
4102 isl_ast_build_free(build);
4103 if (!tree)
4104 return -1;
4105
4106 type = isl_ast_node_get_type(tree);
4107 isl_ast_node_free(tree);
4108
4109 if (type == isl_ast_node_if)
4110 isl_die(ctx, isl_error_unknown,
4111 "not expecting if node", return -1);
4112
4113 isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
4114
4115 schedule = isl_union_map_read_from_str(ctx, str);
4116 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4117 build = isl_ast_build_from_context(set);
4118 tree = isl_ast_build_ast_from_schedule(build, schedule);
4119 isl_ast_build_free(build);
4120 if (!tree)
4121 return -1;
4122
4123 type = isl_ast_node_get_type(tree);
4124 isl_ast_node_free(tree);
4125
4126 if (type != isl_ast_node_if)
4127 isl_die(ctx, isl_error_unknown,
4128 "expecting if node", return -1);
4129
4130 isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
4131
4132 return 0;
4133 }
4134
4135 /* This function is called for each leaf in the AST generated
4136 * from test_ast_gen5.
4137 *
4138 * We finalize the AST generation by extending the outer schedule
4139 * with a zero-dimensional schedule. If this results in any for loops,
4140 * then this means that we did not pass along enough information
4141 * about the outer schedule to the inner AST generation.
4142 */
4143 static __isl_give isl_ast_node *create_leaf(__isl_take isl_ast_build *build,
4144 void *user)
4145 {
4146 isl_union_map *schedule, *extra;
4147 isl_ast_node *tree;
4148
4149 schedule = isl_ast_build_get_schedule(build);
4150 extra = isl_union_map_copy(schedule);
4151 extra = isl_union_map_from_domain(isl_union_map_domain(extra));
4152 schedule = isl_union_map_range_product(schedule, extra);
4153 tree = isl_ast_build_ast_from_schedule(build, schedule);
4154 isl_ast_build_free(build);
4155
4156 if (!tree)
4157 return NULL;
4158
4159 if (isl_ast_node_get_type(tree) == isl_ast_node_for)
4160 isl_die(isl_ast_node_get_ctx(tree), isl_error_unknown,
4161 "code should not contain any for loop",
4162 return isl_ast_node_free(tree));
4163
4164 return tree;
4165 }
4166
4167 /* Check that we do not lose any information when going back and
4168 * forth between internal and external schedule.
4169 *
4170 * In particular, we create an AST where we unroll the only
4171 * non-constant dimension in the schedule. We therefore do
4172 * not expect any for loops in the AST. However, older versions
4173 * of isl would not pass along enough information about the outer
4174 * schedule when performing an inner code generation from a create_leaf
4175 * callback, resulting in the inner code generation producing a for loop.
4176 */
4177 static int test_ast_gen5(isl_ctx *ctx)
4178 {
4179 const char *str;
4180 isl_set *set;
4181 isl_union_map *schedule, *options;
4182 isl_ast_build *build;
4183 isl_ast_node *tree;
4184
4185 str = "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
4186 schedule = isl_union_map_read_from_str(ctx, str);
4187
4188 str = "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
4189 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
4190 options = isl_union_map_read_from_str(ctx, str);
4191
4192 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4193 build = isl_ast_build_from_context(set);
4194 build = isl_ast_build_set_options(build, options);
4195 build = isl_ast_build_set_create_leaf(build, &create_leaf, NULL);
4196 tree = isl_ast_build_ast_from_schedule(build, schedule);
4197 isl_ast_build_free(build);
4198 isl_ast_node_free(tree);
4199 if (!tree)
4200 return -1;
4201
4202 return 0;
4203 }
4204
4205 static int test_ast_gen(isl_ctx *ctx)
4206 {
4207 if (test_ast_gen1(ctx) < 0)
4208 return -1;
4209 if (test_ast_gen2(ctx) < 0)
4210 return -1;
4211 if (test_ast_gen3(ctx) < 0)
4212 return -1;
4213 if (test_ast_gen4(ctx) < 0)
4214 return -1;
4215 if (test_ast_gen5(ctx) < 0)
4216 return -1;
4217 return 0;
4218 }
4219
4220 /* Check if dropping output dimensions from an isl_pw_multi_aff
4221 * works properly.
4222 */
4223 static int test_pw_multi_aff(isl_ctx *ctx)
4224 {
4225 const char *str;
4226 isl_pw_multi_aff *pma1, *pma2;
4227 int equal;
4228
4229 str = "{ [i,j] -> [i+j, 4i-j] }";
4230 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
4231 str = "{ [i,j] -> [4i-j] }";
4232 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
4233
4234 pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
4235
4236 equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
4237
4238 isl_pw_multi_aff_free(pma1);
4239 isl_pw_multi_aff_free(pma2);
4240 if (equal < 0)
4241 return -1;
4242 if (!equal)
4243 isl_die(ctx, isl_error_unknown,
4244 "expressions not equal", return -1);
4245
4246 return 0;
4247 }
4248
4249 /* This is a regression test for a bug where isl_basic_map_simplify
4250 * would end up in an infinite loop. In particular, we construct
4251 * an empty basic set that is not obviously empty.
4252 * isl_basic_set_is_empty marks the basic set as empty.
4253 * After projecting out i3, the variable can be dropped completely,
4254 * but isl_basic_map_simplify refrains from doing so if the basic set
4255 * is empty and would end up in an infinite loop if it didn't test
4256 * explicitly for empty basic maps in the outer loop.
4257 */
4258 static int test_simplify(isl_ctx *ctx)
4259 {
4260 const char *str;
4261 isl_basic_set *bset;
4262 int empty;
4263
4264 str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
4265 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
4266 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
4267 "i3 >= i2 }";
4268 bset = isl_basic_set_read_from_str(ctx, str);
4269 empty = isl_basic_set_is_empty(bset);
4270 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
4271 isl_basic_set_free(bset);
4272 if (!bset)
4273 return -1;
4274 if (!empty)
4275 isl_die(ctx, isl_error_unknown,
4276 "basic set should be empty", return -1);
4277
4278 return 0;
4279 }
4280
4281 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
4282 * with gbr context would fail to disable the use of the shifted tableau
4283 * when transferring equalities for the input to the context, resulting
4284 * in invalid sample values.
4285 */
4286 static int test_partial_lexmin(isl_ctx *ctx)
4287 {
4288 const char *str;
4289 isl_basic_set *bset;
4290 isl_basic_map *bmap;
4291 isl_map *map;
4292
4293 str = "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
4294 bmap = isl_basic_map_read_from_str(ctx, str);
4295 str = "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
4296 bset = isl_basic_set_read_from_str(ctx, str);
4297 map = isl_basic_map_partial_lexmin(bmap, bset, NULL);
4298 isl_map_free(map);
4299
4300 if (!map)
4301 return -1;
4302
4303 return 0;
4304 }
4305
4306 /* Check that the variable compression performed on the existentially
4307 * quantified variables inside isl_basic_set_compute_divs is not confused
4308 * by the implicit equalities among the parameters.
4309 */
4310 static int test_compute_divs(isl_ctx *ctx)
4311 {
4312 const char *str;
4313 isl_basic_set *bset;
4314 isl_set *set;
4315
4316 str = "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
4317 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
4318 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
4319 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
4320 bset = isl_basic_set_read_from_str(ctx, str);
4321 set = isl_basic_set_compute_divs(bset);
4322 isl_set_free(set);
4323 if (!set)
4324 return -1;
4325
4326 return 0;
4327 }
4328
4329 struct {
4330 const char *name;
4331 int (*fn)(isl_ctx *ctx);
4332 } tests [] = {
4333 { "val", &test_val },
4334 { "compute divs", &test_compute_divs },
4335 { "partial lexmin", &test_partial_lexmin },
4336 { "simplify", &test_simplify },
4337 { "curry", &test_curry },
4338 { "piecewise multi affine expressions", &test_pw_multi_aff },
4339 { "conversion", &test_conversion },
4340 { "list", &test_list },
4341 { "align parameters", &test_align_parameters },
4342 { "preimage", &test_preimage },
4343 { "pullback", &test_pullback },
4344 { "AST", &test_ast },
4345 { "AST generation", &test_ast_gen },
4346 { "eliminate", &test_eliminate },
4347 { "residue class", &test_residue_class },
4348 { "div", &test_div },
4349 { "slice", &test_slice },
4350 { "fixed power", &test_fixed_power },
4351 { "sample", &test_sample },
4352 { "output", &test_output },
4353 { "vertices", &test_vertices },
4354 { "fixed", &test_fixed },
4355 { "equal", &test_equal },
4356 { "product", &test_product },
4357 { "dim_max", &test_dim_max },
4358 { "affine", &test_aff },
4359 { "injective", &test_injective },
4360 { "schedule", &test_schedule },
4361 { "union_pw", &test_union_pw },
4362 { "parse", &test_parse },
4363 { "single-valued", &test_sv },
4364 { "affine hull", &test_affine_hull },
4365 { "coalesce", &test_coalesce },
4366 { "factorize", &test_factorize },
4367 { "subset", &test_subset },
4368 { "subtract", &test_subtract },
4369 { "lexmin", &test_lexmin },
4370 { "gist", &test_gist },
4371 { "piecewise quasi-polynomials", &test_pwqp },
4372 };
4373
4374 int main()
4375 {
4376 int i;
4377 struct isl_ctx *ctx;
4378
4379 srcdir = getenv("srcdir");
4380 assert(srcdir);
4381
4382 ctx = isl_ctx_alloc();
4383 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
4384 printf("%s\n", tests[i].name);
4385 if (tests[i].fn(ctx) < 0)
4386 goto error;
4387 }
4388 test_lift(ctx);
4389 test_bound(ctx);
4390 test_union(ctx);
4391 test_split_periods(ctx);
4392 test_lex(ctx);
4393 test_bijective(ctx);
4394 test_dep(ctx);
4395 test_read(ctx);
4396 test_bounded(ctx);
4397 test_construction(ctx);
4398 test_dim(ctx);
4399 test_application(ctx);
4400 test_convex_hull(ctx);
4401 test_closure(ctx);
4402 isl_ctx_free(ctx);
4403 return 0;
4404 error:
4405 isl_ctx_free(ctx);
4406 return -1;
4407 }
Integer set library