?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
isl_basic_map_gist: avoid (temporarily) adding context constraints to input
[isl.git] / isl_test.c
blob058bc433caa8fd11b5b5dda6412c4588cab19e2f
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 *
6 * Use of this software is governed by the MIT license
7 *
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
13 */
14
15 #include <assert.h>
16 #include <stdio.h>
17 #include <limits.h>
18 #include <isl_ctx_private.h>
19 #include <isl_map_private.h>
20 #include <isl_aff_private.h>
21 #include <isl/set.h>
22 #include <isl/flow.h>
23 #include <isl_constraint_private.h>
24 #include <isl/polynomial.h>
25 #include <isl/union_map.h>
26 #include <isl_factorization.h>
27 #include <isl/schedule.h>
28 #include <isl_options_private.h>
29 #include <isl/vertices.h>
30 #include <isl/ast_build.h>
31 #include <isl/val.h>
32 #include <isl/ilp.h>
33 #include <isl_ast_build_expr.h>
34
35 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
36
37 static char *srcdir;
38
39 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
40 char *filename;
41 int length;
42 char *pattern = "%s/test_inputs/%s.%s";
43
44 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
45 + strlen(suffix) + 1;
46 filename = isl_alloc_array(ctx, char, length);
47
48 if (!filename)
49 return NULL;
50
51 sprintf(filename, pattern, srcdir, name, suffix);
52
53 return filename;
54 }
55
56 void test_parse_map(isl_ctx *ctx, const char *str)
57 {
58 isl_map *map;
59
60 map = isl_map_read_from_str(ctx, str);
61 assert(map);
62 isl_map_free(map);
63 }
64
65 int test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
66 {
67 isl_map *map, *map2;
68 int equal;
69
70 map = isl_map_read_from_str(ctx, str);
71 map2 = isl_map_read_from_str(ctx, str2);
72 equal = isl_map_is_equal(map, map2);
73 isl_map_free(map);
74 isl_map_free(map2);
75
76 if (equal < 0)
77 return -1;
78 if (!equal)
79 isl_die(ctx, isl_error_unknown, "maps not equal",
80 return -1);
81
82 return 0;
83 }
84
85 void test_parse_pwqp(isl_ctx *ctx, const char *str)
86 {
87 isl_pw_qpolynomial *pwqp;
88
89 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
90 assert(pwqp);
91 isl_pw_qpolynomial_free(pwqp);
92 }
93
94 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
95 {
96 isl_pw_aff *pwaff;
97
98 pwaff = isl_pw_aff_read_from_str(ctx, str);
99 assert(pwaff);
100 isl_pw_aff_free(pwaff);
101 }
102
103 int test_parse(struct isl_ctx *ctx)
104 {
105 isl_map *map, *map2;
106 const char *str, *str2;
107
108 str = "{ [i] -> [-i] }";
109 map = isl_map_read_from_str(ctx, str);
110 assert(map);
111 isl_map_free(map);
112
113 str = "{ A[i] -> L[([i/3])] }";
114 map = isl_map_read_from_str(ctx, str);
115 assert(map);
116 isl_map_free(map);
117
118 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
119 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
120 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
121
122 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
123 str2 = "{ [x, y] : 2y >= 6 - x }";
124 if (test_parse_map_equal(ctx, str, str2) < 0)
125 return -1;
126
127 if (test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
128 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
129 return -1;
130 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
131 if (test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }",
132 str) < 0)
133 return -1;
134
135 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
136 map = isl_map_read_from_str(ctx, str);
137 str = "{ [new, old] -> [o0, o1] : "
138 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
139 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
140 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
141 map2 = isl_map_read_from_str(ctx, str);
142 assert(isl_map_is_equal(map, map2));
143 isl_map_free(map);
144 isl_map_free(map2);
145
146 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
147 map = isl_map_read_from_str(ctx, str);
148 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
149 map2 = isl_map_read_from_str(ctx, str);
150 assert(isl_map_is_equal(map, map2));
151 isl_map_free(map);
152 isl_map_free(map2);
153
154 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
155 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
156 if (test_parse_map_equal(ctx, str, str2) < 0)
157 return -1;
158
159 str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
160 str2 = "{ [i,j] -> [min(i,j)] }";
161 if (test_parse_map_equal(ctx, str, str2) < 0)
162 return -1;
163
164 str = "{ [i,j] : i != j }";
165 str2 = "{ [i,j] : i < j or i > j }";
166 if (test_parse_map_equal(ctx, str, str2) < 0)
167 return -1;
168
169 str = "{ [i,j] : (i+1)*2 >= j }";
170 str2 = "{ [i, j] : j <= 2 + 2i }";
171 if (test_parse_map_equal(ctx, str, str2) < 0)
172 return -1;
173
174 str = "{ [i] -> [i > 0 ? 4 : 5] }";
175 str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
176 if (test_parse_map_equal(ctx, str, str2) < 0)
177 return -1;
178
179 str = "[N=2,M] -> { [i=[(M+N)/4]] }";
180 str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
181 if (test_parse_map_equal(ctx, str, str2) < 0)
182 return -1;
183
184 str = "{ [x] : x >= 0 }";
185 str2 = "{ [x] : x-0 >= 0 }";
186 if (test_parse_map_equal(ctx, str, str2) < 0)
187 return -1;
188
189 str = "{ [i] : ((i > 10)) }";
190 str2 = "{ [i] : i >= 11 }";
191 if (test_parse_map_equal(ctx, str, str2) < 0)
192 return -1;
193
194 str = "{ [i] -> [0] }";
195 str2 = "{ [i] -> [0 * i] }";
196 if (test_parse_map_equal(ctx, str, str2) < 0)
197 return -1;
198
199 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
200 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
201 test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
202 test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
203
204 if (test_parse_map_equal(ctx, "{ [a] -> [b] : (not false) }",
205 "{ [a] -> [b] : true }") < 0)
206 return -1;
207
208 if (test_parse_map_equal(ctx, "{ [i] : i/2 <= 5 }",
209 "{ [i] : i <= 10 }") < 0)
210 return -1;
211
212 if (test_parse_map_equal(ctx, "{Sym=[n] [i] : i <= n }",
213 "[n] -> { [i] : i <= n }") < 0)
214 return -1;
215
216 if (test_parse_map_equal(ctx, "{ [*] }", "{ [a] }") < 0)
217 return -1;
218
219 if (test_parse_map_equal(ctx, "{ [i] : 2*floor(i/2) = i }",
220 "{ [i] : exists a : i = 2 a }") < 0)
221 return -1;
222
223 if (test_parse_map_equal(ctx, "{ [a] -> [b] : a = 5 implies b = 5 }",
224 "{ [a] -> [b] : a != 5 or b = 5 }") < 0)
225 return -1;
226
227 if (test_parse_map_equal(ctx, "{ [a] -> [a - 1 : a > 0] }",
228 "{ [a] -> [a - 1] : a > 0 }") < 0)
229 return -1;
230 if (test_parse_map_equal(ctx,
231 "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
232 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }") < 0)
233 return -1;
234 if (test_parse_map_equal(ctx,
235 "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
236 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
237 return -1;
238 if (test_parse_map_equal(ctx,
239 "{ [a] -> [(a * 2) : a >= 0; 0 : a < 0] }",
240 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
241 return -1;
242 if (test_parse_map_equal(ctx,
243 "{ [a] -> [(a * 2 : a >= 0); 0 : a < 0] }",
244 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
245 return -1;
246 if (test_parse_map_equal(ctx,
247 "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
248 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
249 return -1;
250
251 return 0;
252 }
253
254 void test_read(struct isl_ctx *ctx)
255 {
256 char *filename;
257 FILE *input;
258 struct isl_basic_set *bset1, *bset2;
259 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
260
261 filename = get_filename(ctx, "set", "omega");
262 assert(filename);
263 input = fopen(filename, "r");
264 assert(input);
265
266 bset1 = isl_basic_set_read_from_file(ctx, input);
267 bset2 = isl_basic_set_read_from_str(ctx, str);
268
269 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
270
271 isl_basic_set_free(bset1);
272 isl_basic_set_free(bset2);
273 free(filename);
274
275 fclose(input);
276 }
277
278 void test_bounded(struct isl_ctx *ctx)
279 {
280 isl_set *set;
281 int bounded;
282
283 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
284 bounded = isl_set_is_bounded(set);
285 assert(bounded);
286 isl_set_free(set);
287
288 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
289 bounded = isl_set_is_bounded(set);
290 assert(!bounded);
291 isl_set_free(set);
292
293 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
294 bounded = isl_set_is_bounded(set);
295 assert(!bounded);
296 isl_set_free(set);
297 }
298
299 /* Construct the basic set { [i] : 5 <= i <= N } */
300 void test_construction(struct isl_ctx *ctx)
301 {
302 isl_int v;
303 isl_space *dim;
304 isl_local_space *ls;
305 struct isl_basic_set *bset;
306 struct isl_constraint *c;
307
308 isl_int_init(v);
309
310 dim = isl_space_set_alloc(ctx, 1, 1);
311 bset = isl_basic_set_universe(isl_space_copy(dim));
312 ls = isl_local_space_from_space(dim);
313
314 c = isl_inequality_alloc(isl_local_space_copy(ls));
315 isl_int_set_si(v, -1);
316 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
317 isl_int_set_si(v, 1);
318 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
319 bset = isl_basic_set_add_constraint(bset, c);
320
321 c = isl_inequality_alloc(isl_local_space_copy(ls));
322 isl_int_set_si(v, 1);
323 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
324 isl_int_set_si(v, -5);
325 isl_constraint_set_constant(c, v);
326 bset = isl_basic_set_add_constraint(bset, c);
327
328 isl_local_space_free(ls);
329 isl_basic_set_free(bset);
330
331 isl_int_clear(v);
332 }
333
334 void test_dim(struct isl_ctx *ctx)
335 {
336 const char *str;
337 isl_map *map1, *map2;
338
339 map1 = isl_map_read_from_str(ctx,
340 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
341 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
342 map2 = isl_map_read_from_str(ctx,
343 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
344 assert(isl_map_is_equal(map1, map2));
345 isl_map_free(map2);
346
347 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
348 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
349 assert(isl_map_is_equal(map1, map2));
350
351 isl_map_free(map1);
352 isl_map_free(map2);
353
354 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
355 map1 = isl_map_read_from_str(ctx, str);
356 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
357 map2 = isl_map_read_from_str(ctx, str);
358 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
359 assert(isl_map_is_equal(map1, map2));
360
361 isl_map_free(map1);
362 isl_map_free(map2);
363 }
364
365 struct {
366 __isl_give isl_val *(*op)(__isl_take isl_val *v);
367 const char *arg;
368 const char *res;
369 } val_un_tests[] = {
370 { &isl_val_neg, "0", "0" },
371 { &isl_val_abs, "0", "0" },
372 { &isl_val_2exp, "0", "1" },
373 { &isl_val_floor, "0", "0" },
374 { &isl_val_ceil, "0", "0" },
375 { &isl_val_neg, "1", "-1" },
376 { &isl_val_neg, "-1", "1" },
377 { &isl_val_neg, "1/2", "-1/2" },
378 { &isl_val_neg, "-1/2", "1/2" },
379 { &isl_val_neg, "infty", "-infty" },
380 { &isl_val_neg, "-infty", "infty" },
381 { &isl_val_neg, "NaN", "NaN" },
382 { &isl_val_abs, "1", "1" },
383 { &isl_val_abs, "-1", "1" },
384 { &isl_val_abs, "1/2", "1/2" },
385 { &isl_val_abs, "-1/2", "1/2" },
386 { &isl_val_abs, "infty", "infty" },
387 { &isl_val_abs, "-infty", "infty" },
388 { &isl_val_abs, "NaN", "NaN" },
389 { &isl_val_floor, "1", "1" },
390 { &isl_val_floor, "-1", "-1" },
391 { &isl_val_floor, "1/2", "0" },
392 { &isl_val_floor, "-1/2", "-1" },
393 { &isl_val_floor, "infty", "infty" },
394 { &isl_val_floor, "-infty", "-infty" },
395 { &isl_val_floor, "NaN", "NaN" },
396 { &isl_val_ceil, "1", "1" },
397 { &isl_val_ceil, "-1", "-1" },
398 { &isl_val_ceil, "1/2", "1" },
399 { &isl_val_ceil, "-1/2", "0" },
400 { &isl_val_ceil, "infty", "infty" },
401 { &isl_val_ceil, "-infty", "-infty" },
402 { &isl_val_ceil, "NaN", "NaN" },
403 { &isl_val_2exp, "-3", "1/8" },
404 { &isl_val_2exp, "-1", "1/2" },
405 { &isl_val_2exp, "1", "2" },
406 { &isl_val_2exp, "2", "4" },
407 { &isl_val_2exp, "3", "8" },
408 };
409
410 /* Perform some basic tests of unary operations on isl_val objects.
411 */
412 static int test_un_val(isl_ctx *ctx)
413 {
414 int i;
415 isl_val *v, *res;
416 __isl_give isl_val *(*fn)(__isl_take isl_val *v);
417 int ok;
418
419 for (i = 0; i < ARRAY_SIZE(val_un_tests); ++i) {
420 v = isl_val_read_from_str(ctx, val_un_tests[i].arg);
421 res = isl_val_read_from_str(ctx, val_un_tests[i].res);
422 fn = val_un_tests[i].op;
423 v = fn(v);
424 if (isl_val_is_nan(res))
425 ok = isl_val_is_nan(v);
426 else
427 ok = isl_val_eq(v, res);
428 isl_val_free(v);
429 isl_val_free(res);
430 if (ok < 0)
431 return -1;
432 if (!ok)
433 isl_die(ctx, isl_error_unknown,
434 "unexpected result", return -1);
435 }
436
437 return 0;
438 }
439
440 struct {
441 __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
442 __isl_take isl_val *v2);
443 } val_bin_op[] = {
444 ['+'] = { &isl_val_add },
445 ['-'] = { &isl_val_sub },
446 ['*'] = { &isl_val_mul },
447 ['/'] = { &isl_val_div },
448 ['g'] = { &isl_val_gcd },
449 ['m'] = { &isl_val_min },
450 ['M'] = { &isl_val_max },
451 };
452
453 struct {
454 const char *arg1;
455 unsigned char op;
456 const char *arg2;
457 const char *res;
458 } val_bin_tests[] = {
459 { "0", '+', "0", "0" },
460 { "1", '+', "0", "1" },
461 { "1", '+', "1", "2" },
462 { "1", '-', "1", "0" },
463 { "1", '*', "1", "1" },
464 { "1", '/', "1", "1" },
465 { "2", '*', "3", "6" },
466 { "2", '*', "1/2", "1" },
467 { "2", '*', "1/3", "2/3" },
468 { "2/3", '*', "3/5", "2/5" },
469 { "2/3", '*', "7/5", "14/15" },
470 { "2", '/', "1/2", "4" },
471 { "-2", '/', "-1/2", "4" },
472 { "-2", '/', "1/2", "-4" },
473 { "2", '/', "-1/2", "-4" },
474 { "2", '/', "2", "1" },
475 { "2", '/', "3", "2/3" },
476 { "2/3", '/', "5/3", "2/5" },
477 { "2/3", '/', "5/7", "14/15" },
478 { "0", '/', "0", "NaN" },
479 { "42", '/', "0", "NaN" },
480 { "-42", '/', "0", "NaN" },
481 { "infty", '/', "0", "NaN" },
482 { "-infty", '/', "0", "NaN" },
483 { "NaN", '/', "0", "NaN" },
484 { "0", '/', "NaN", "NaN" },
485 { "42", '/', "NaN", "NaN" },
486 { "-42", '/', "NaN", "NaN" },
487 { "infty", '/', "NaN", "NaN" },
488 { "-infty", '/', "NaN", "NaN" },
489 { "NaN", '/', "NaN", "NaN" },
490 { "0", '/', "infty", "0" },
491 { "42", '/', "infty", "0" },
492 { "-42", '/', "infty", "0" },
493 { "infty", '/', "infty", "NaN" },
494 { "-infty", '/', "infty", "NaN" },
495 { "NaN", '/', "infty", "NaN" },
496 { "0", '/', "-infty", "0" },
497 { "42", '/', "-infty", "0" },
498 { "-42", '/', "-infty", "0" },
499 { "infty", '/', "-infty", "NaN" },
500 { "-infty", '/', "-infty", "NaN" },
501 { "NaN", '/', "-infty", "NaN" },
502 { "1", '-', "1/3", "2/3" },
503 { "1/3", '+', "1/2", "5/6" },
504 { "1/2", '+', "1/2", "1" },
505 { "3/4", '-', "1/4", "1/2" },
506 { "1/2", '-', "1/3", "1/6" },
507 { "infty", '+', "42", "infty" },
508 { "infty", '+', "infty", "infty" },
509 { "42", '+', "infty", "infty" },
510 { "infty", '-', "infty", "NaN" },
511 { "infty", '*', "infty", "infty" },
512 { "infty", '*', "-infty", "-infty" },
513 { "-infty", '*', "infty", "-infty" },
514 { "-infty", '*', "-infty", "infty" },
515 { "0", '*', "infty", "NaN" },
516 { "1", '*', "infty", "infty" },
517 { "infty", '*', "0", "NaN" },
518 { "infty", '*', "42", "infty" },
519 { "42", '-', "infty", "-infty" },
520 { "infty", '+', "-infty", "NaN" },
521 { "4", 'g', "6", "2" },
522 { "5", 'g', "6", "1" },
523 { "42", 'm', "3", "3" },
524 { "42", 'M', "3", "42" },
525 { "3", 'm', "42", "3" },
526 { "3", 'M', "42", "42" },
527 { "42", 'm', "infty", "42" },
528 { "42", 'M', "infty", "infty" },
529 { "42", 'm', "-infty", "-infty" },
530 { "42", 'M', "-infty", "42" },
531 { "42", 'm', "NaN", "NaN" },
532 { "42", 'M', "NaN", "NaN" },
533 { "infty", 'm', "-infty", "-infty" },
534 { "infty", 'M', "-infty", "infty" },
535 };
536
537 /* Perform some basic tests of binary operations on isl_val objects.
538 */
539 static int test_bin_val(isl_ctx *ctx)
540 {
541 int i;
542 isl_val *v1, *v2, *res;
543 __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
544 __isl_take isl_val *v2);
545 int ok;
546
547 for (i = 0; i < ARRAY_SIZE(val_bin_tests); ++i) {
548 v1 = isl_val_read_from_str(ctx, val_bin_tests[i].arg1);
549 v2 = isl_val_read_from_str(ctx, val_bin_tests[i].arg2);
550 res = isl_val_read_from_str(ctx, val_bin_tests[i].res);
551 fn = val_bin_op[val_bin_tests[i].op].fn;
552 v1 = fn(v1, v2);
553 if (isl_val_is_nan(res))
554 ok = isl_val_is_nan(v1);
555 else
556 ok = isl_val_eq(v1, res);
557 isl_val_free(v1);
558 isl_val_free(res);
559 if (ok < 0)
560 return -1;
561 if (!ok)
562 isl_die(ctx, isl_error_unknown,
563 "unexpected result", return -1);
564 }
565
566 return 0;
567 }
568
569 /* Perform some basic tests on isl_val objects.
570 */
571 static int test_val(isl_ctx *ctx)
572 {
573 if (test_un_val(ctx) < 0)
574 return -1;
575 if (test_bin_val(ctx) < 0)
576 return -1;
577 return 0;
578 }
579
580 static int test_div(isl_ctx *ctx)
581 {
582 unsigned n;
583 const char *str;
584 int empty;
585 isl_int v;
586 isl_space *dim;
587 isl_set *set;
588 isl_local_space *ls;
589 struct isl_basic_set *bset;
590 struct isl_constraint *c;
591
592 isl_int_init(v);
593
594 /* test 1 */
595 dim = isl_space_set_alloc(ctx, 0, 3);
596 bset = isl_basic_set_universe(isl_space_copy(dim));
597 ls = isl_local_space_from_space(dim);
598
599 c = isl_equality_alloc(isl_local_space_copy(ls));
600 isl_int_set_si(v, -1);
601 isl_constraint_set_constant(c, v);
602 isl_int_set_si(v, 1);
603 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
604 isl_int_set_si(v, 3);
605 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
606 bset = isl_basic_set_add_constraint(bset, c);
607
608 c = isl_equality_alloc(isl_local_space_copy(ls));
609 isl_int_set_si(v, 1);
610 isl_constraint_set_constant(c, v);
611 isl_int_set_si(v, -1);
612 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
613 isl_int_set_si(v, 3);
614 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
615 bset = isl_basic_set_add_constraint(bset, c);
616
617 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
618
619 assert(bset && bset->n_div == 1);
620 isl_local_space_free(ls);
621 isl_basic_set_free(bset);
622
623 /* test 2 */
624 dim = isl_space_set_alloc(ctx, 0, 3);
625 bset = isl_basic_set_universe(isl_space_copy(dim));
626 ls = isl_local_space_from_space(dim);
627
628 c = isl_equality_alloc(isl_local_space_copy(ls));
629 isl_int_set_si(v, 1);
630 isl_constraint_set_constant(c, v);
631 isl_int_set_si(v, -1);
632 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
633 isl_int_set_si(v, 3);
634 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
635 bset = isl_basic_set_add_constraint(bset, c);
636
637 c = isl_equality_alloc(isl_local_space_copy(ls));
638 isl_int_set_si(v, -1);
639 isl_constraint_set_constant(c, v);
640 isl_int_set_si(v, 1);
641 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
642 isl_int_set_si(v, 3);
643 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
644 bset = isl_basic_set_add_constraint(bset, c);
645
646 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
647
648 assert(bset && bset->n_div == 1);
649 isl_local_space_free(ls);
650 isl_basic_set_free(bset);
651
652 /* test 3 */
653 dim = isl_space_set_alloc(ctx, 0, 3);
654 bset = isl_basic_set_universe(isl_space_copy(dim));
655 ls = isl_local_space_from_space(dim);
656
657 c = isl_equality_alloc(isl_local_space_copy(ls));
658 isl_int_set_si(v, 1);
659 isl_constraint_set_constant(c, v);
660 isl_int_set_si(v, -1);
661 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
662 isl_int_set_si(v, 3);
663 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
664 bset = isl_basic_set_add_constraint(bset, c);
665
666 c = isl_equality_alloc(isl_local_space_copy(ls));
667 isl_int_set_si(v, -3);
668 isl_constraint_set_constant(c, v);
669 isl_int_set_si(v, 1);
670 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
671 isl_int_set_si(v, 4);
672 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
673 bset = isl_basic_set_add_constraint(bset, c);
674
675 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
676
677 assert(bset && bset->n_div == 1);
678 isl_local_space_free(ls);
679 isl_basic_set_free(bset);
680
681 /* test 4 */
682 dim = isl_space_set_alloc(ctx, 0, 3);
683 bset = isl_basic_set_universe(isl_space_copy(dim));
684 ls = isl_local_space_from_space(dim);
685
686 c = isl_equality_alloc(isl_local_space_copy(ls));
687 isl_int_set_si(v, 2);
688 isl_constraint_set_constant(c, v);
689 isl_int_set_si(v, -1);
690 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
691 isl_int_set_si(v, 3);
692 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
693 bset = isl_basic_set_add_constraint(bset, c);
694
695 c = isl_equality_alloc(isl_local_space_copy(ls));
696 isl_int_set_si(v, -1);
697 isl_constraint_set_constant(c, v);
698 isl_int_set_si(v, 1);
699 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
700 isl_int_set_si(v, 6);
701 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
702 bset = isl_basic_set_add_constraint(bset, c);
703
704 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
705
706 assert(isl_basic_set_is_empty(bset));
707 isl_local_space_free(ls);
708 isl_basic_set_free(bset);
709
710 /* test 5 */
711 dim = isl_space_set_alloc(ctx, 0, 3);
712 bset = isl_basic_set_universe(isl_space_copy(dim));
713 ls = isl_local_space_from_space(dim);
714
715 c = isl_equality_alloc(isl_local_space_copy(ls));
716 isl_int_set_si(v, -1);
717 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
718 isl_int_set_si(v, 3);
719 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
720 bset = isl_basic_set_add_constraint(bset, c);
721
722 c = isl_equality_alloc(isl_local_space_copy(ls));
723 isl_int_set_si(v, 1);
724 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
725 isl_int_set_si(v, -3);
726 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
727 bset = isl_basic_set_add_constraint(bset, c);
728
729 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
730
731 assert(bset && bset->n_div == 0);
732 isl_basic_set_free(bset);
733 isl_local_space_free(ls);
734
735 /* test 6 */
736 dim = isl_space_set_alloc(ctx, 0, 3);
737 bset = isl_basic_set_universe(isl_space_copy(dim));
738 ls = isl_local_space_from_space(dim);
739
740 c = isl_equality_alloc(isl_local_space_copy(ls));
741 isl_int_set_si(v, -1);
742 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
743 isl_int_set_si(v, 6);
744 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
745 bset = isl_basic_set_add_constraint(bset, c);
746
747 c = isl_equality_alloc(isl_local_space_copy(ls));
748 isl_int_set_si(v, 1);
749 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
750 isl_int_set_si(v, -3);
751 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
752 bset = isl_basic_set_add_constraint(bset, c);
753
754 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
755
756 assert(bset && bset->n_div == 1);
757 isl_basic_set_free(bset);
758 isl_local_space_free(ls);
759
760 /* test 7 */
761 /* This test is a bit tricky. We set up an equality
762 * a + 3b + 3c = 6 e0
763 * Normalization of divs creates _two_ divs
764 * a = 3 e0
765 * c - b - e0 = 2 e1
766 * Afterwards e0 is removed again because it has coefficient -1
767 * and we end up with the original equality and div again.
768 * Perhaps we can avoid the introduction of this temporary div.
769 */
770 dim = isl_space_set_alloc(ctx, 0, 4);
771 bset = isl_basic_set_universe(isl_space_copy(dim));
772 ls = isl_local_space_from_space(dim);
773
774 c = isl_equality_alloc(isl_local_space_copy(ls));
775 isl_int_set_si(v, -1);
776 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
777 isl_int_set_si(v, -3);
778 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
779 isl_int_set_si(v, -3);
780 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
781 isl_int_set_si(v, 6);
782 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
783 bset = isl_basic_set_add_constraint(bset, c);
784
785 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
786
787 /* Test disabled for now */
788 /*
789 assert(bset && bset->n_div == 1);
790 */
791 isl_local_space_free(ls);
792 isl_basic_set_free(bset);
793
794 /* test 8 */
795 dim = isl_space_set_alloc(ctx, 0, 5);
796 bset = isl_basic_set_universe(isl_space_copy(dim));
797 ls = isl_local_space_from_space(dim);
798
799 c = isl_equality_alloc(isl_local_space_copy(ls));
800 isl_int_set_si(v, -1);
801 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
802 isl_int_set_si(v, -3);
803 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
804 isl_int_set_si(v, -3);
805 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
806 isl_int_set_si(v, 6);
807 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
808 bset = isl_basic_set_add_constraint(bset, c);
809
810 c = isl_equality_alloc(isl_local_space_copy(ls));
811 isl_int_set_si(v, -1);
812 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
813 isl_int_set_si(v, 1);
814 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
815 isl_int_set_si(v, 1);
816 isl_constraint_set_constant(c, v);
817 bset = isl_basic_set_add_constraint(bset, c);
818
819 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
820
821 /* Test disabled for now */
822 /*
823 assert(bset && bset->n_div == 1);
824 */
825 isl_local_space_free(ls);
826 isl_basic_set_free(bset);
827
828 /* test 9 */
829 dim = isl_space_set_alloc(ctx, 0, 4);
830 bset = isl_basic_set_universe(isl_space_copy(dim));
831 ls = isl_local_space_from_space(dim);
832
833 c = isl_equality_alloc(isl_local_space_copy(ls));
834 isl_int_set_si(v, 1);
835 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
836 isl_int_set_si(v, -1);
837 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
838 isl_int_set_si(v, -2);
839 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
840 bset = isl_basic_set_add_constraint(bset, c);
841
842 c = isl_equality_alloc(isl_local_space_copy(ls));
843 isl_int_set_si(v, -1);
844 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
845 isl_int_set_si(v, 3);
846 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
847 isl_int_set_si(v, 2);
848 isl_constraint_set_constant(c, v);
849 bset = isl_basic_set_add_constraint(bset, c);
850
851 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
852
853 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
854
855 assert(!isl_basic_set_is_empty(bset));
856
857 isl_local_space_free(ls);
858 isl_basic_set_free(bset);
859
860 /* test 10 */
861 dim = isl_space_set_alloc(ctx, 0, 3);
862 bset = isl_basic_set_universe(isl_space_copy(dim));
863 ls = isl_local_space_from_space(dim);
864
865 c = isl_equality_alloc(isl_local_space_copy(ls));
866 isl_int_set_si(v, 1);
867 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
868 isl_int_set_si(v, -2);
869 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
870 bset = isl_basic_set_add_constraint(bset, c);
871
872 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
873
874 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
875
876 isl_local_space_free(ls);
877 isl_basic_set_free(bset);
878
879 isl_int_clear(v);
880
881 str = "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
882 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
883 set = isl_set_read_from_str(ctx, str);
884 set = isl_set_compute_divs(set);
885 isl_set_free(set);
886 if (!set)
887 return -1;
888
889 str = "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
890 bset = isl_basic_set_read_from_str(ctx, str);
891 n = isl_basic_set_dim(bset, isl_dim_div);
892 isl_basic_set_free(bset);
893 if (!bset)
894 return -1;
895 if (n != 0)
896 isl_die(ctx, isl_error_unknown,
897 "expecting no existentials", return -1);
898
899 str = "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
900 set = isl_set_read_from_str(ctx, str);
901 set = isl_set_remove_divs_involving_dims(set, isl_dim_set, 0, 2);
902 set = isl_set_fix_si(set, isl_dim_set, 2, -3);
903 empty = isl_set_is_empty(set);
904 isl_set_free(set);
905 if (empty < 0)
906 return -1;
907 if (!empty)
908 isl_die(ctx, isl_error_unknown,
909 "result not as accurate as expected", return -1);
910
911 return 0;
912 }
913
914 void test_application_case(struct isl_ctx *ctx, const char *name)
915 {
916 char *filename;
917 FILE *input;
918 struct isl_basic_set *bset1, *bset2;
919 struct isl_basic_map *bmap;
920
921 filename = get_filename(ctx, name, "omega");
922 assert(filename);
923 input = fopen(filename, "r");
924 assert(input);
925
926 bset1 = isl_basic_set_read_from_file(ctx, input);
927 bmap = isl_basic_map_read_from_file(ctx, input);
928
929 bset1 = isl_basic_set_apply(bset1, bmap);
930
931 bset2 = isl_basic_set_read_from_file(ctx, input);
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 void test_application(struct isl_ctx *ctx)
943 {
944 test_application_case(ctx, "application");
945 test_application_case(ctx, "application2");
946 }
947
948 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
949 {
950 char *filename;
951 FILE *input;
952 struct isl_basic_set *bset1, *bset2;
953
954 filename = get_filename(ctx, name, "polylib");
955 assert(filename);
956 input = fopen(filename, "r");
957 assert(input);
958
959 bset1 = isl_basic_set_read_from_file(ctx, input);
960 bset2 = isl_basic_set_read_from_file(ctx, input);
961
962 bset1 = isl_basic_set_affine_hull(bset1);
963
964 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
965
966 isl_basic_set_free(bset1);
967 isl_basic_set_free(bset2);
968 free(filename);
969
970 fclose(input);
971 }
972
973 int test_affine_hull(struct isl_ctx *ctx)
974 {
975 const char *str;
976 isl_set *set;
977 isl_basic_set *bset, *bset2;
978 int n;
979 int subset;
980
981 test_affine_hull_case(ctx, "affine2");
982 test_affine_hull_case(ctx, "affine");
983 test_affine_hull_case(ctx, "affine3");
984
985 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
986 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
987 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
988 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
989 set = isl_set_read_from_str(ctx, str);
990 bset = isl_set_affine_hull(set);
991 n = isl_basic_set_dim(bset, isl_dim_div);
992 isl_basic_set_free(bset);
993 if (n != 0)
994 isl_die(ctx, isl_error_unknown, "not expecting any divs",
995 return -1);
996
997 /* Check that isl_map_affine_hull is not confused by
998 * the reordering of divs in isl_map_align_divs.
999 */
1000 str = "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1001 "32e0 = b and 32e1 = c); "
1002 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1003 set = isl_set_read_from_str(ctx, str);
1004 bset = isl_set_affine_hull(set);
1005 isl_basic_set_free(bset);
1006 if (!bset)
1007 return -1;
1008
1009 str = "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1010 "32e2 = 31 + 31e0 }";
1011 set = isl_set_read_from_str(ctx, str);
1012 bset = isl_set_affine_hull(set);
1013 str = "{ [a] : exists e : a = 32 e }";
1014 bset2 = isl_basic_set_read_from_str(ctx, str);
1015 subset = isl_basic_set_is_subset(bset, bset2);
1016 isl_basic_set_free(bset);
1017 isl_basic_set_free(bset2);
1018 if (subset < 0)
1019 return -1;
1020 if (!subset)
1021 isl_die(ctx, isl_error_unknown, "not as accurate as expected",
1022 return -1);
1023
1024 return 0;
1025 }
1026
1027 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
1028 {
1029 char *filename;
1030 FILE *input;
1031 struct isl_basic_set *bset1, *bset2;
1032 struct isl_set *set;
1033
1034 filename = get_filename(ctx, name, "polylib");
1035 assert(filename);
1036 input = fopen(filename, "r");
1037 assert(input);
1038
1039 bset1 = isl_basic_set_read_from_file(ctx, input);
1040 bset2 = isl_basic_set_read_from_file(ctx, input);
1041
1042 set = isl_basic_set_union(bset1, bset2);
1043 bset1 = isl_set_convex_hull(set);
1044
1045 bset2 = isl_basic_set_read_from_file(ctx, input);
1046
1047 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1048
1049 isl_basic_set_free(bset1);
1050 isl_basic_set_free(bset2);
1051 free(filename);
1052
1053 fclose(input);
1054 }
1055
1056 struct {
1057 const char *set;
1058 const char *hull;
1059 } convex_hull_tests[] = {
1060 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1061 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1062 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1063 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1064 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1065 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1066 "i2 <= 5 and i2 >= 4; "
1067 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1068 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1069 "i2 <= 5 + i0 and i2 >= i0 }" },
1070 };
1071
1072 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
1073 {
1074 int i;
1075 int orig_convex = ctx->opt->convex;
1076 ctx->opt->convex = convex;
1077
1078 test_convex_hull_case(ctx, "convex0");
1079 test_convex_hull_case(ctx, "convex1");
1080 test_convex_hull_case(ctx, "convex2");
1081 test_convex_hull_case(ctx, "convex3");
1082 test_convex_hull_case(ctx, "convex4");
1083 test_convex_hull_case(ctx, "convex5");
1084 test_convex_hull_case(ctx, "convex6");
1085 test_convex_hull_case(ctx, "convex7");
1086 test_convex_hull_case(ctx, "convex8");
1087 test_convex_hull_case(ctx, "convex9");
1088 test_convex_hull_case(ctx, "convex10");
1089 test_convex_hull_case(ctx, "convex11");
1090 test_convex_hull_case(ctx, "convex12");
1091 test_convex_hull_case(ctx, "convex13");
1092 test_convex_hull_case(ctx, "convex14");
1093 test_convex_hull_case(ctx, "convex15");
1094
1095 for (i = 0; i < ARRAY_SIZE(convex_hull_tests); ++i) {
1096 isl_set *set1, *set2;
1097
1098 set1 = isl_set_read_from_str(ctx, convex_hull_tests[i].set);
1099 set2 = isl_set_read_from_str(ctx, convex_hull_tests[i].hull);
1100 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
1101 assert(isl_set_is_equal(set1, set2));
1102 isl_set_free(set1);
1103 isl_set_free(set2);
1104 }
1105
1106 ctx->opt->convex = orig_convex;
1107 }
1108
1109 void test_convex_hull(struct isl_ctx *ctx)
1110 {
1111 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
1112 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
1113 }
1114
1115 void test_gist_case(struct isl_ctx *ctx, const char *name)
1116 {
1117 char *filename;
1118 FILE *input;
1119 struct isl_basic_set *bset1, *bset2;
1120
1121 filename = get_filename(ctx, name, "polylib");
1122 assert(filename);
1123 input = fopen(filename, "r");
1124 assert(input);
1125
1126 bset1 = isl_basic_set_read_from_file(ctx, input);
1127 bset2 = isl_basic_set_read_from_file(ctx, input);
1128
1129 bset1 = isl_basic_set_gist(bset1, bset2);
1130
1131 bset2 = isl_basic_set_read_from_file(ctx, input);
1132
1133 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1134
1135 isl_basic_set_free(bset1);
1136 isl_basic_set_free(bset2);
1137 free(filename);
1138
1139 fclose(input);
1140 }
1141
1142 static int test_gist(struct isl_ctx *ctx)
1143 {
1144 const char *str;
1145 isl_basic_set *bset1, *bset2;
1146 isl_map *map1, *map2;
1147
1148 test_gist_case(ctx, "gist1");
1149
1150 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
1151 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1152 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1153 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1154 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1155 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1156 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1157 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1158 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1159 bset1 = isl_basic_set_read_from_str(ctx, str);
1160 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1161 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1162 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1163 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1164 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1165 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1166 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1167 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1168 bset2 = isl_basic_set_read_from_str(ctx, str);
1169 bset1 = isl_basic_set_gist(bset1, bset2);
1170 assert(bset1 && bset1->n_div == 0);
1171 isl_basic_set_free(bset1);
1172
1173 /* Check that the integer divisions of the second disjunct
1174 * do not spread to the first disjunct.
1175 */
1176 str = "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1177 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1178 "(exists (e0 = [(-1 + t1)/16], "
1179 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1180 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1181 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1182 "o0 <= 4294967295 and t1 <= -1)) }";
1183 map1 = isl_map_read_from_str(ctx, str);
1184 str = "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1185 map2 = isl_map_read_from_str(ctx, str);
1186 map1 = isl_map_gist(map1, map2);
1187 if (!map1)
1188 return -1;
1189 if (map1->n != 1)
1190 isl_die(ctx, isl_error_unknown, "expecting single disjunct",
1191 isl_map_free(map1); return -1);
1192 if (isl_basic_map_dim(map1->p[0], isl_dim_div) != 1)
1193 isl_die(ctx, isl_error_unknown, "expecting single div",
1194 isl_map_free(map1); return -1);
1195 isl_map_free(map1);
1196
1197 return 0;
1198 }
1199
1200 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
1201 {
1202 isl_set *set, *set2;
1203 int equal;
1204 int one;
1205
1206 set = isl_set_read_from_str(ctx, str);
1207 set = isl_set_coalesce(set);
1208 set2 = isl_set_read_from_str(ctx, str);
1209 equal = isl_set_is_equal(set, set2);
1210 one = set && set->n == 1;
1211 isl_set_free(set);
1212 isl_set_free(set2);
1213
1214 if (equal < 0)
1215 return -1;
1216 if (!equal)
1217 isl_die(ctx, isl_error_unknown,
1218 "coalesced set not equal to input", return -1);
1219 if (check_one && !one)
1220 isl_die(ctx, isl_error_unknown,
1221 "coalesced set should not be a union", return -1);
1222
1223 return 0;
1224 }
1225
1226 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
1227 {
1228 int r = 0;
1229 int bounded;
1230
1231 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
1232 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
1233
1234 if (test_coalesce_set(ctx,
1235 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1236 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1237 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1238 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1239 "-10 <= y <= 0}", 1) < 0)
1240 goto error;
1241 if (test_coalesce_set(ctx,
1242 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
1243 goto error;
1244 if (test_coalesce_set(ctx,
1245 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
1246 goto error;
1247
1248 if (0) {
1249 error:
1250 r = -1;
1251 }
1252
1253 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
1254
1255 return r;
1256 }
1257
1258 /* Inputs for coalescing tests.
1259 * "str" is a string representation of the input set.
1260 * "single_disjunct" is set if we expect the result to consist of
1261 * a single disjunct.
1262 */
1263 struct {
1264 int single_disjunct;
1265 const char *str;
1266 } coalesce_tests[] = {
1267 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1268 "y >= x & x >= 2 & 5 >= y }" },
1269 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1270 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1271 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1272 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1273 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1274 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1275 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1276 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1277 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1278 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1279 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1280 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1281 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1282 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1283 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1284 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1285 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1286 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1287 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1288 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1289 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1290 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1291 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1292 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1293 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1294 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1295 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1296 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1297 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1298 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1299 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1300 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1301 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1302 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1303 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1304 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1305 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1306 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1307 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1308 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1309 "[o0, o1, o2, o3, o4, o5, o6]] : "
1310 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1311 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1312 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1313 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1314 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1315 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1316 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1317 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1318 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1319 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1320 "o6 >= i3 + i6 - o3 and M >= 0 and "
1321 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1322 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1323 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1324 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1325 "(o0 = 0 and M >= 2 and N >= 3) or "
1326 "(M = 0 and o0 = 0 and N >= 3) }" },
1327 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1328 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1329 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1330 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1331 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1332 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1333 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1334 "(y = 3 and x = 1) }" },
1335 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1336 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1337 "i1 <= M and i3 <= M and i4 <= M) or "
1338 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1339 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1340 "i4 <= -1 + M) }" },
1341 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1342 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1343 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1344 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1345 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1346 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1347 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1348 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1349 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1350 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1351 { 0, "{ [a, b] : exists e : 2e = a and "
1352 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1353 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1354 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1355 "j >= 1 and j' <= i + j - i' and i >= 1; "
1356 "[1, 1, 1, 1] }" },
1357 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1358 "[i,j] : exists a : j = 3a }" },
1359 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1360 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1361 "a >= 3) or "
1362 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1363 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1364 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1365 "c <= 6 + 8a and a >= 3; "
1366 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1367 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1368 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1369 "[x,0] : 3 <= x <= 4 }" },
1370 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1371 "[x,0] : 4 <= x <= 5 }" },
1372 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1373 "[x,0] : 3 <= x <= 5 }" },
1374 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1375 "[x,0] : 3 <= x <= 4 }" },
1376 { 1 , "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1377 "i1 <= 0; "
1378 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1379 };
1380
1381 /* Test the functionality of isl_set_coalesce.
1382 * That is, check that the output is always equal to the input
1383 * and in some cases that the result consists of a single disjunct.
1384 */
1385 static int test_coalesce(struct isl_ctx *ctx)
1386 {
1387 int i;
1388
1389 for (i = 0; i < ARRAY_SIZE(coalesce_tests); ++i) {
1390 const char *str = coalesce_tests[i].str;
1391 int check_one = coalesce_tests[i].single_disjunct;
1392 if (test_coalesce_set(ctx, str, check_one) < 0)
1393 return -1;
1394 }
1395
1396 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1397 return -1;
1398
1399 return 0;
1400 }
1401
1402 void test_closure(struct isl_ctx *ctx)
1403 {
1404 const char *str;
1405 isl_set *dom;
1406 isl_map *up, *right;
1407 isl_map *map, *map2;
1408 int exact;
1409
1410 /* COCOA example 1 */
1411 map = isl_map_read_from_str(ctx,
1412 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1413 "1 <= i and i < n and 1 <= j and j < n or "
1414 "i2 = i + 1 and j2 = j - 1 and "
1415 "1 <= i and i < n and 2 <= j and j <= n }");
1416 map = isl_map_power(map, &exact);
1417 assert(exact);
1418 isl_map_free(map);
1419
1420 /* COCOA example 1 */
1421 map = isl_map_read_from_str(ctx,
1422 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1423 "1 <= i and i < n and 1 <= j and j < n or "
1424 "i2 = i + 1 and j2 = j - 1 and "
1425 "1 <= i and i < n and 2 <= j and j <= n }");
1426 map = isl_map_transitive_closure(map, &exact);
1427 assert(exact);
1428 map2 = isl_map_read_from_str(ctx,
1429 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1430 "1 <= i and i < n and 1 <= j and j <= n and "
1431 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1432 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1433 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1434 assert(isl_map_is_equal(map, map2));
1435 isl_map_free(map2);
1436 isl_map_free(map);
1437
1438 map = isl_map_read_from_str(ctx,
1439 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1440 " 0 <= y and y <= n }");
1441 map = isl_map_transitive_closure(map, &exact);
1442 map2 = isl_map_read_from_str(ctx,
1443 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1444 " 0 <= y and y <= n }");
1445 assert(isl_map_is_equal(map, map2));
1446 isl_map_free(map2);
1447 isl_map_free(map);
1448
1449 /* COCOA example 2 */
1450 map = isl_map_read_from_str(ctx,
1451 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1452 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1453 "i2 = i + 2 and j2 = j - 2 and "
1454 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1455 map = isl_map_transitive_closure(map, &exact);
1456 assert(exact);
1457 map2 = isl_map_read_from_str(ctx,
1458 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1459 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1460 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1461 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1462 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1463 assert(isl_map_is_equal(map, map2));
1464 isl_map_free(map);
1465 isl_map_free(map2);
1466
1467 /* COCOA Fig.2 left */
1468 map = isl_map_read_from_str(ctx,
1469 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1470 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1471 "j <= n or "
1472 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1473 "j <= 2 i - 3 and j <= n - 2 or "
1474 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1475 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1476 map = isl_map_transitive_closure(map, &exact);
1477 assert(exact);
1478 isl_map_free(map);
1479
1480 /* COCOA Fig.2 right */
1481 map = isl_map_read_from_str(ctx,
1482 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1483 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1484 "j <= n or "
1485 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1486 "j <= 2 i - 4 and j <= n - 3 or "
1487 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1488 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1489 map = isl_map_power(map, &exact);
1490 assert(exact);
1491 isl_map_free(map);
1492
1493 /* COCOA Fig.2 right */
1494 map = isl_map_read_from_str(ctx,
1495 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1496 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1497 "j <= n or "
1498 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1499 "j <= 2 i - 4 and j <= n - 3 or "
1500 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1501 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1502 map = isl_map_transitive_closure(map, &exact);
1503 assert(exact);
1504 map2 = isl_map_read_from_str(ctx,
1505 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1506 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1507 "j <= n and 3 + i + 2 j <= 3 n and "
1508 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1509 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1510 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1511 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1512 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1513 assert(isl_map_is_equal(map, map2));
1514 isl_map_free(map2);
1515 isl_map_free(map);
1516
1517 /* COCOA Fig.1 right */
1518 dom = isl_set_read_from_str(ctx,
1519 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1520 "2 x - 3 y + 3 >= 0 }");
1521 right = isl_map_read_from_str(ctx,
1522 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1523 up = isl_map_read_from_str(ctx,
1524 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1525 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1526 right = isl_map_intersect_range(right, isl_set_copy(dom));
1527 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1528 up = isl_map_intersect_range(up, dom);
1529 map = isl_map_union(up, right);
1530 map = isl_map_transitive_closure(map, &exact);
1531 assert(exact);
1532 map2 = isl_map_read_from_str(ctx,
1533 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1534 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1535 assert(isl_map_is_equal(map, map2));
1536 isl_map_free(map2);
1537 isl_map_free(map);
1538
1539 /* COCOA Theorem 1 counter example */
1540 map = isl_map_read_from_str(ctx,
1541 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1542 "i2 = 1 and j2 = j or "
1543 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1544 map = isl_map_transitive_closure(map, &exact);
1545 assert(exact);
1546 isl_map_free(map);
1547
1548 map = isl_map_read_from_str(ctx,
1549 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1550 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1551 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1552 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1553 map = isl_map_transitive_closure(map, &exact);
1554 assert(exact);
1555 isl_map_free(map);
1556
1557 /* Kelly et al 1996, fig 12 */
1558 map = isl_map_read_from_str(ctx,
1559 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1560 "1 <= i,j,j+1 <= n or "
1561 "j = n and j2 = 1 and i2 = i + 1 and "
1562 "1 <= i,i+1 <= n }");
1563 map = isl_map_transitive_closure(map, &exact);
1564 assert(exact);
1565 map2 = isl_map_read_from_str(ctx,
1566 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1567 "1 <= i <= n and i = i2 or "
1568 "1 <= i < i2 <= n and 1 <= j <= n and "
1569 "1 <= j2 <= n }");
1570 assert(isl_map_is_equal(map, map2));
1571 isl_map_free(map2);
1572 isl_map_free(map);
1573
1574 /* Omega's closure4 */
1575 map = isl_map_read_from_str(ctx,
1576 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1577 "1 <= x,y <= 10 or "
1578 "x2 = x + 1 and y2 = y and "
1579 "1 <= x <= 20 && 5 <= y <= 15 }");
1580 map = isl_map_transitive_closure(map, &exact);
1581 assert(exact);
1582 isl_map_free(map);
1583
1584 map = isl_map_read_from_str(ctx,
1585 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1586 map = isl_map_transitive_closure(map, &exact);
1587 assert(!exact);
1588 map2 = isl_map_read_from_str(ctx,
1589 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1590 assert(isl_map_is_equal(map, map2));
1591 isl_map_free(map);
1592 isl_map_free(map2);
1593
1594 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1595 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1596 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1597 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1598 map = isl_map_read_from_str(ctx, str);
1599 map = isl_map_transitive_closure(map, &exact);
1600 assert(exact);
1601 map2 = isl_map_read_from_str(ctx, str);
1602 assert(isl_map_is_equal(map, map2));
1603 isl_map_free(map);
1604 isl_map_free(map2);
1605
1606 str = "{[0] -> [1]; [2] -> [3]}";
1607 map = isl_map_read_from_str(ctx, str);
1608 map = isl_map_transitive_closure(map, &exact);
1609 assert(exact);
1610 map2 = isl_map_read_from_str(ctx, str);
1611 assert(isl_map_is_equal(map, map2));
1612 isl_map_free(map);
1613 isl_map_free(map2);
1614
1615 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1616 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1617 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1618 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1619 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1620 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1621 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1622 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1623 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1624 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1625 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1626 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1627 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1628 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1629 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1630 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1631 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1632 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1633 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1634 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1635 map = isl_map_read_from_str(ctx, str);
1636 map = isl_map_transitive_closure(map, NULL);
1637 assert(map);
1638 isl_map_free(map);
1639 }
1640
1641 void test_lex(struct isl_ctx *ctx)
1642 {
1643 isl_space *dim;
1644 isl_map *map;
1645
1646 dim = isl_space_set_alloc(ctx, 0, 0);
1647 map = isl_map_lex_le(dim);
1648 assert(!isl_map_is_empty(map));
1649 isl_map_free(map);
1650 }
1651
1652 static int test_lexmin(struct isl_ctx *ctx)
1653 {
1654 int equal;
1655 const char *str;
1656 isl_basic_map *bmap;
1657 isl_map *map, *map2;
1658 isl_set *set;
1659 isl_set *set2;
1660 isl_pw_multi_aff *pma;
1661
1662 str = "[p0, p1] -> { [] -> [] : "
1663 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1664 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1665 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1666 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1667 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1668 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1669 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1670 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1671 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1672 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1673 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1674 map = isl_map_read_from_str(ctx, str);
1675 map = isl_map_lexmin(map);
1676 isl_map_free(map);
1677
1678 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1679 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1680 set = isl_set_read_from_str(ctx, str);
1681 set = isl_set_lexmax(set);
1682 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1683 set2 = isl_set_read_from_str(ctx, str);
1684 set = isl_set_intersect(set, set2);
1685 assert(!isl_set_is_empty(set));
1686 isl_set_free(set);
1687
1688 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1689 map = isl_map_read_from_str(ctx, str);
1690 map = isl_map_lexmin(map);
1691 str = "{ [x] -> [5] : 6 <= x <= 8; "
1692 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1693 map2 = isl_map_read_from_str(ctx, str);
1694 assert(isl_map_is_equal(map, map2));
1695 isl_map_free(map);
1696 isl_map_free(map2);
1697
1698 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1699 map = isl_map_read_from_str(ctx, str);
1700 map2 = isl_map_copy(map);
1701 map = isl_map_lexmin(map);
1702 assert(isl_map_is_equal(map, map2));
1703 isl_map_free(map);
1704 isl_map_free(map2);
1705
1706 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1707 map = isl_map_read_from_str(ctx, str);
1708 map = isl_map_lexmin(map);
1709 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1710 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1711 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1712 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1713 map2 = isl_map_read_from_str(ctx, str);
1714 assert(isl_map_is_equal(map, map2));
1715 isl_map_free(map);
1716 isl_map_free(map2);
1717
1718 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1719 " 8i' <= i and 8i' >= -7 + i }";
1720 bmap = isl_basic_map_read_from_str(ctx, str);
1721 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1722 map2 = isl_map_from_pw_multi_aff(pma);
1723 map = isl_map_from_basic_map(bmap);
1724 assert(isl_map_is_equal(map, map2));
1725 isl_map_free(map);
1726 isl_map_free(map2);
1727
1728 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1729 map = isl_map_read_from_str(ctx, str);
1730 map = isl_map_lexmin(map);
1731 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1732 map2 = isl_map_read_from_str(ctx, str);
1733 assert(isl_map_is_equal(map, map2));
1734 isl_map_free(map);
1735 isl_map_free(map2);
1736
1737 /* Check that empty pieces are properly combined. */
1738 str = "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
1739 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
1740 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
1741 map = isl_map_read_from_str(ctx, str);
1742 map = isl_map_lexmin(map);
1743 str = "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
1744 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
1745 "x >= 4 }";
1746 map2 = isl_map_read_from_str(ctx, str);
1747 assert(isl_map_is_equal(map, map2));
1748 isl_map_free(map);
1749 isl_map_free(map2);
1750
1751 str = "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1752 " 8i' <= i and 8i' >= -7 + i }";
1753 set = isl_set_read_from_str(ctx, str);
1754 pma = isl_set_lexmin_pw_multi_aff(isl_set_copy(set));
1755 set2 = isl_set_from_pw_multi_aff(pma);
1756 equal = isl_set_is_equal(set, set2);
1757 isl_set_free(set);
1758 isl_set_free(set2);
1759 if (equal < 0)
1760 return -1;
1761 if (!equal)
1762 isl_die(ctx, isl_error_unknown,
1763 "unexpected difference between set and "
1764 "piecewise affine expression", return -1);
1765
1766 return 0;
1767 }
1768
1769 /* Check that isl_set_min_val and isl_set_max_val compute the correct
1770 * result on non-convex inputs.
1771 */
1772 static int test_min(struct isl_ctx *ctx)
1773 {
1774 isl_set *set;
1775 isl_aff *aff;
1776 isl_val *val;
1777 int min_ok, max_ok;
1778
1779 set = isl_set_read_from_str(ctx, "{ [-1]; [1] }");
1780 aff = isl_aff_read_from_str(ctx, "{ [x] -> [x] }");
1781 val = isl_set_min_val(set, aff);
1782 min_ok = isl_val_is_negone(val);
1783 isl_val_free(val);
1784 val = isl_set_max_val(set, aff);
1785 max_ok = isl_val_is_one(val);
1786 isl_val_free(val);
1787 isl_aff_free(aff);
1788 isl_set_free(set);
1789
1790 if (min_ok < 0 || max_ok < 0)
1791 return -1;
1792 if (!min_ok)
1793 isl_die(ctx, isl_error_unknown,
1794 "unexpected minimum", return -1);
1795 if (!max_ok)
1796 isl_die(ctx, isl_error_unknown,
1797 "unexpected maximum", return -1);
1798
1799 return 0;
1800 }
1801
1802 struct must_may {
1803 isl_map *must;
1804 isl_map *may;
1805 };
1806
1807 static int collect_must_may(__isl_take isl_map *dep, int must,
1808 void *dep_user, void *user)
1809 {
1810 struct must_may *mm = (struct must_may *)user;
1811
1812 if (must)
1813 mm->must = isl_map_union(mm->must, dep);
1814 else
1815 mm->may = isl_map_union(mm->may, dep);
1816
1817 return 0;
1818 }
1819
1820 static int common_space(void *first, void *second)
1821 {
1822 int depth = *(int *)first;
1823 return 2 * depth;
1824 }
1825
1826 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1827 {
1828 isl_map *map2;
1829 int equal;
1830
1831 if (!map)
1832 return -1;
1833
1834 map2 = isl_map_read_from_str(map->ctx, str);
1835 equal = isl_map_is_equal(map, map2);
1836 isl_map_free(map2);
1837
1838 return equal;
1839 }
1840
1841 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1842 {
1843 int equal;
1844
1845 equal = map_is_equal(map, str);
1846 if (equal < 0)
1847 return -1;
1848 if (!equal)
1849 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1850 "result not as expected", return -1);
1851 return 0;
1852 }
1853
1854 void test_dep(struct isl_ctx *ctx)
1855 {
1856 const char *str;
1857 isl_space *dim;
1858 isl_map *map;
1859 isl_access_info *ai;
1860 isl_flow *flow;
1861 int depth;
1862 struct must_may mm;
1863
1864 depth = 3;
1865
1866 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1867 map = isl_map_read_from_str(ctx, str);
1868 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1869
1870 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1871 map = isl_map_read_from_str(ctx, str);
1872 ai = isl_access_info_add_source(ai, map, 1, &depth);
1873
1874 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1875 map = isl_map_read_from_str(ctx, str);
1876 ai = isl_access_info_add_source(ai, map, 1, &depth);
1877
1878 flow = isl_access_info_compute_flow(ai);
1879 dim = isl_space_alloc(ctx, 0, 3, 3);
1880 mm.must = isl_map_empty(isl_space_copy(dim));
1881 mm.may = isl_map_empty(dim);
1882
1883 isl_flow_foreach(flow, collect_must_may, &mm);
1884
1885 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1886 " [1,10,0] -> [2,5,0] }";
1887 assert(map_is_equal(mm.must, str));
1888 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1889 assert(map_is_equal(mm.may, str));
1890
1891 isl_map_free(mm.must);
1892 isl_map_free(mm.may);
1893 isl_flow_free(flow);
1894
1895
1896 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1897 map = isl_map_read_from_str(ctx, str);
1898 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1899
1900 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1901 map = isl_map_read_from_str(ctx, str);
1902 ai = isl_access_info_add_source(ai, map, 1, &depth);
1903
1904 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1905 map = isl_map_read_from_str(ctx, str);
1906 ai = isl_access_info_add_source(ai, map, 0, &depth);
1907
1908 flow = isl_access_info_compute_flow(ai);
1909 dim = isl_space_alloc(ctx, 0, 3, 3);
1910 mm.must = isl_map_empty(isl_space_copy(dim));
1911 mm.may = isl_map_empty(dim);
1912
1913 isl_flow_foreach(flow, collect_must_may, &mm);
1914
1915 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1916 assert(map_is_equal(mm.must, str));
1917 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1918 assert(map_is_equal(mm.may, str));
1919
1920 isl_map_free(mm.must);
1921 isl_map_free(mm.may);
1922 isl_flow_free(flow);
1923
1924
1925 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1926 map = isl_map_read_from_str(ctx, str);
1927 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1928
1929 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1930 map = isl_map_read_from_str(ctx, str);
1931 ai = isl_access_info_add_source(ai, map, 0, &depth);
1932
1933 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1934 map = isl_map_read_from_str(ctx, str);
1935 ai = isl_access_info_add_source(ai, map, 0, &depth);
1936
1937 flow = isl_access_info_compute_flow(ai);
1938 dim = isl_space_alloc(ctx, 0, 3, 3);
1939 mm.must = isl_map_empty(isl_space_copy(dim));
1940 mm.may = isl_map_empty(dim);
1941
1942 isl_flow_foreach(flow, collect_must_may, &mm);
1943
1944 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1945 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1946 assert(map_is_equal(mm.may, str));
1947 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1948 assert(map_is_equal(mm.must, str));
1949
1950 isl_map_free(mm.must);
1951 isl_map_free(mm.may);
1952 isl_flow_free(flow);
1953
1954
1955 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1956 map = isl_map_read_from_str(ctx, str);
1957 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1958
1959 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1960 map = isl_map_read_from_str(ctx, str);
1961 ai = isl_access_info_add_source(ai, map, 0, &depth);
1962
1963 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1964 map = isl_map_read_from_str(ctx, str);
1965 ai = isl_access_info_add_source(ai, map, 0, &depth);
1966
1967 flow = isl_access_info_compute_flow(ai);
1968 dim = isl_space_alloc(ctx, 0, 3, 3);
1969 mm.must = isl_map_empty(isl_space_copy(dim));
1970 mm.may = isl_map_empty(dim);
1971
1972 isl_flow_foreach(flow, collect_must_may, &mm);
1973
1974 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1975 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1976 assert(map_is_equal(mm.may, str));
1977 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1978 assert(map_is_equal(mm.must, str));
1979
1980 isl_map_free(mm.must);
1981 isl_map_free(mm.may);
1982 isl_flow_free(flow);
1983
1984
1985 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1986 map = isl_map_read_from_str(ctx, str);
1987 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1988
1989 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1990 map = isl_map_read_from_str(ctx, str);
1991 ai = isl_access_info_add_source(ai, map, 0, &depth);
1992
1993 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1994 map = isl_map_read_from_str(ctx, str);
1995 ai = isl_access_info_add_source(ai, map, 0, &depth);
1996
1997 flow = isl_access_info_compute_flow(ai);
1998 dim = isl_space_alloc(ctx, 0, 3, 3);
1999 mm.must = isl_map_empty(isl_space_copy(dim));
2000 mm.may = isl_map_empty(dim);
2001
2002 isl_flow_foreach(flow, collect_must_may, &mm);
2003
2004 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2005 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2006 assert(map_is_equal(mm.may, str));
2007 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2008 assert(map_is_equal(mm.must, str));
2009
2010 isl_map_free(mm.must);
2011 isl_map_free(mm.may);
2012 isl_flow_free(flow);
2013
2014
2015 depth = 5;
2016
2017 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2018 map = isl_map_read_from_str(ctx, str);
2019 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
2020
2021 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2022 map = isl_map_read_from_str(ctx, str);
2023 ai = isl_access_info_add_source(ai, map, 1, &depth);
2024
2025 flow = isl_access_info_compute_flow(ai);
2026 dim = isl_space_alloc(ctx, 0, 5, 5);
2027 mm.must = isl_map_empty(isl_space_copy(dim));
2028 mm.may = isl_map_empty(dim);
2029
2030 isl_flow_foreach(flow, collect_must_may, &mm);
2031
2032 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2033 assert(map_is_equal(mm.must, str));
2034 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2035 assert(map_is_equal(mm.may, str));
2036
2037 isl_map_free(mm.must);
2038 isl_map_free(mm.may);
2039 isl_flow_free(flow);
2040 }
2041
2042 /* Check that the dependence analysis proceeds without errors.
2043 * Earlier versions of isl would break down during the analysis
2044 * due to the use of the wrong spaces.
2045 */
2046 static int test_flow(isl_ctx *ctx)
2047 {
2048 const char *str;
2049 isl_union_map *access, *schedule;
2050 isl_union_map *must_dep, *may_dep;
2051 int r;
2052
2053 str = "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2054 access = isl_union_map_read_from_str(ctx, str);
2055 str = "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2056 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2057 "S2[] -> [1,0,0,0]; "
2058 "S3[] -> [-1,0,0,0] }";
2059 schedule = isl_union_map_read_from_str(ctx, str);
2060 r = isl_union_map_compute_flow(access, isl_union_map_copy(access),
2061 isl_union_map_copy(access), schedule,
2062 &must_dep, &may_dep, NULL, NULL);
2063 isl_union_map_free(may_dep);
2064 isl_union_map_free(must_dep);
2065
2066 return r;
2067 }
2068
2069 int test_sv(isl_ctx *ctx)
2070 {
2071 const char *str;
2072 isl_map *map;
2073 isl_union_map *umap;
2074 int sv;
2075
2076 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
2077 map = isl_map_read_from_str(ctx, str);
2078 sv = isl_map_is_single_valued(map);
2079 isl_map_free(map);
2080 if (sv < 0)
2081 return -1;
2082 if (!sv)
2083 isl_die(ctx, isl_error_internal,
2084 "map not detected as single valued", return -1);
2085
2086 str = "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
2087 map = isl_map_read_from_str(ctx, str);
2088 sv = isl_map_is_single_valued(map);
2089 isl_map_free(map);
2090 if (sv < 0)
2091 return -1;
2092 if (sv)
2093 isl_die(ctx, isl_error_internal,
2094 "map detected as single valued", return -1);
2095
2096 str = "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
2097 umap = isl_union_map_read_from_str(ctx, str);
2098 sv = isl_union_map_is_single_valued(umap);
2099 isl_union_map_free(umap);
2100 if (sv < 0)
2101 return -1;
2102 if (!sv)
2103 isl_die(ctx, isl_error_internal,
2104 "map not detected as single valued", return -1);
2105
2106 str = "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
2107 umap = isl_union_map_read_from_str(ctx, str);
2108 sv = isl_union_map_is_single_valued(umap);
2109 isl_union_map_free(umap);
2110 if (sv < 0)
2111 return -1;
2112 if (sv)
2113 isl_die(ctx, isl_error_internal,
2114 "map detected as single valued", return -1);
2115
2116 return 0;
2117 }
2118
2119 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
2120 {
2121 isl_map *map;
2122
2123 map = isl_map_read_from_str(ctx, str);
2124 if (bijective)
2125 assert(isl_map_is_bijective(map));
2126 else
2127 assert(!isl_map_is_bijective(map));
2128 isl_map_free(map);
2129 }
2130
2131 void test_bijective(struct isl_ctx *ctx)
2132 {
2133 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
2134 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
2135 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
2136 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
2137 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
2138 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
2139 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
2140 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
2141 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
2142 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
2143 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
2144 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
2145 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
2146 }
2147
2148 static int test_pwqp(struct isl_ctx *ctx)
2149 {
2150 const char *str;
2151 isl_set *set;
2152 isl_pw_qpolynomial *pwqp1, *pwqp2;
2153 int equal;
2154
2155 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2156 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2157
2158 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
2159 isl_dim_in, 1, 1);
2160
2161 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2162 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2163
2164 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2165
2166 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2167
2168 isl_pw_qpolynomial_free(pwqp1);
2169
2170 str = "{ [i] -> i }";
2171 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2172 str = "{ [k] : exists a : k = 2a }";
2173 set = isl_set_read_from_str(ctx, str);
2174 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2175 str = "{ [i] -> i }";
2176 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2177
2178 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2179
2180 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2181
2182 isl_pw_qpolynomial_free(pwqp1);
2183
2184 str = "{ [i] -> i + [ (i + [i/3])/2 ] }";
2185 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2186 str = "{ [10] }";
2187 set = isl_set_read_from_str(ctx, str);
2188 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2189 str = "{ [i] -> 16 }";
2190 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2191
2192 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2193
2194 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2195
2196 isl_pw_qpolynomial_free(pwqp1);
2197
2198 str = "{ [i] -> ([(i)/2]) }";
2199 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2200 str = "{ [k] : exists a : k = 2a+1 }";
2201 set = isl_set_read_from_str(ctx, str);
2202 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2203 str = "{ [i] -> -1/2 + 1/2 * i }";
2204 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2205
2206 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2207
2208 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2209
2210 isl_pw_qpolynomial_free(pwqp1);
2211
2212 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
2213 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2214 str = "{ [i] -> ([(2 * [i/2])/5]) }";
2215 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2216
2217 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2218
2219 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2220
2221 isl_pw_qpolynomial_free(pwqp1);
2222
2223 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
2224 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2225 str = "{ [x] -> x }";
2226 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2227
2228 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2229
2230 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2231
2232 isl_pw_qpolynomial_free(pwqp1);
2233
2234 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2235 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2236 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2237 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
2238 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2239 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2240 isl_pw_qpolynomial_free(pwqp1);
2241
2242 str = "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2243 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2244 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2245 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2246 set = isl_set_read_from_str(ctx, "{ [a,b,a] }");
2247 pwqp1 = isl_pw_qpolynomial_intersect_domain(pwqp1, set);
2248 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2249 isl_pw_qpolynomial_free(pwqp1);
2250 isl_pw_qpolynomial_free(pwqp2);
2251 if (equal < 0)
2252 return -1;
2253 if (!equal)
2254 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2255
2256 str = "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2257 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2258 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2259 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2260 pwqp1 = isl_pw_qpolynomial_fix_val(pwqp1, isl_dim_set, 1,
2261 isl_val_one(ctx));
2262 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2263 isl_pw_qpolynomial_free(pwqp1);
2264 isl_pw_qpolynomial_free(pwqp2);
2265 if (equal < 0)
2266 return -1;
2267 if (!equal)
2268 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2269
2270 return 0;
2271 }
2272
2273 void test_split_periods(isl_ctx *ctx)
2274 {
2275 const char *str;
2276 isl_pw_qpolynomial *pwqp;
2277
2278 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2279 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2280 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2281 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2282
2283 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
2284 assert(pwqp);
2285
2286 isl_pw_qpolynomial_free(pwqp);
2287 }
2288
2289 void test_union(isl_ctx *ctx)
2290 {
2291 const char *str;
2292 isl_union_set *uset1, *uset2;
2293 isl_union_map *umap1, *umap2;
2294
2295 str = "{ [i] : 0 <= i <= 1 }";
2296 uset1 = isl_union_set_read_from_str(ctx, str);
2297 str = "{ [1] -> [0] }";
2298 umap1 = isl_union_map_read_from_str(ctx, str);
2299
2300 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
2301 assert(isl_union_map_is_equal(umap1, umap2));
2302
2303 isl_union_map_free(umap1);
2304 isl_union_map_free(umap2);
2305
2306 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2307 umap1 = isl_union_map_read_from_str(ctx, str);
2308 str = "{ A[i]; B[i] }";
2309 uset1 = isl_union_set_read_from_str(ctx, str);
2310
2311 uset2 = isl_union_map_domain(umap1);
2312
2313 assert(isl_union_set_is_equal(uset1, uset2));
2314
2315 isl_union_set_free(uset1);
2316 isl_union_set_free(uset2);
2317 }
2318
2319 void test_bound(isl_ctx *ctx)
2320 {
2321 const char *str;
2322 isl_pw_qpolynomial *pwqp;
2323 isl_pw_qpolynomial_fold *pwf;
2324
2325 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
2326 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2327 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2328 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
2329 isl_pw_qpolynomial_fold_free(pwf);
2330
2331 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2332 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2333 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2334 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
2335 isl_pw_qpolynomial_fold_free(pwf);
2336 }
2337
2338 void test_lift(isl_ctx *ctx)
2339 {
2340 const char *str;
2341 isl_basic_map *bmap;
2342 isl_basic_set *bset;
2343
2344 str = "{ [i0] : exists e0 : i0 = 4e0 }";
2345 bset = isl_basic_set_read_from_str(ctx, str);
2346 bset = isl_basic_set_lift(bset);
2347 bmap = isl_basic_map_from_range(bset);
2348 bset = isl_basic_map_domain(bmap);
2349 isl_basic_set_free(bset);
2350 }
2351
2352 struct {
2353 const char *set1;
2354 const char *set2;
2355 int subset;
2356 } subset_tests[] = {
2357 { "{ [112, 0] }",
2358 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2359 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2360 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2361 { "{ [65] }",
2362 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2363 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2364 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2365 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2366 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2367 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2368 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2369 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2370 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2371 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2372 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2373 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2374 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2375 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2376 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2377 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2378 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2379 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2380 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2381 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2382 "4e0 <= -57 + i0 + i1)) or "
2383 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2384 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2385 "4e0 >= -61 + i0 + i1)) or "
2386 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2387 };
2388
2389 static int test_subset(isl_ctx *ctx)
2390 {
2391 int i;
2392 isl_set *set1, *set2;
2393 int subset;
2394
2395 for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
2396 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
2397 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
2398 subset = isl_set_is_subset(set1, set2);
2399 isl_set_free(set1);
2400 isl_set_free(set2);
2401 if (subset < 0)
2402 return -1;
2403 if (subset != subset_tests[i].subset)
2404 isl_die(ctx, isl_error_unknown,
2405 "incorrect subset result", return -1);
2406 }
2407
2408 return 0;
2409 }
2410
2411 struct {
2412 const char *minuend;
2413 const char *subtrahend;
2414 const char *difference;
2415 } subtract_domain_tests[] = {
2416 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2417 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2418 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2419 };
2420
2421 static int test_subtract(isl_ctx *ctx)
2422 {
2423 int i;
2424 isl_union_map *umap1, *umap2;
2425 isl_union_set *uset;
2426 int equal;
2427
2428 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2429 umap1 = isl_union_map_read_from_str(ctx,
2430 subtract_domain_tests[i].minuend);
2431 uset = isl_union_set_read_from_str(ctx,
2432 subtract_domain_tests[i].subtrahend);
2433 umap2 = isl_union_map_read_from_str(ctx,
2434 subtract_domain_tests[i].difference);
2435 umap1 = isl_union_map_subtract_domain(umap1, uset);
2436 equal = isl_union_map_is_equal(umap1, umap2);
2437 isl_union_map_free(umap1);
2438 isl_union_map_free(umap2);
2439 if (equal < 0)
2440 return -1;
2441 if (!equal)
2442 isl_die(ctx, isl_error_unknown,
2443 "incorrect subtract domain result", return -1);
2444 }
2445
2446 return 0;
2447 }
2448
2449 int test_factorize(isl_ctx *ctx)
2450 {
2451 const char *str;
2452 isl_basic_set *bset;
2453 isl_factorizer *f;
2454
2455 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2456 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2457 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2458 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2459 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2460 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2461 "3i5 >= -2i0 - i2 + 3i4 }";
2462 bset = isl_basic_set_read_from_str(ctx, str);
2463 f = isl_basic_set_factorizer(bset);
2464 isl_basic_set_free(bset);
2465 isl_factorizer_free(f);
2466 if (!f)
2467 isl_die(ctx, isl_error_unknown,
2468 "failed to construct factorizer", return -1);
2469
2470 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2471 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2472 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2473 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2474 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2475 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2476 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2477 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2478 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2479 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2480 bset = isl_basic_set_read_from_str(ctx, str);
2481 f = isl_basic_set_factorizer(bset);
2482 isl_basic_set_free(bset);
2483 isl_factorizer_free(f);
2484 if (!f)
2485 isl_die(ctx, isl_error_unknown,
2486 "failed to construct factorizer", return -1);
2487
2488 return 0;
2489 }
2490
2491 static int check_injective(__isl_take isl_map *map, void *user)
2492 {
2493 int *injective = user;
2494
2495 *injective = isl_map_is_injective(map);
2496 isl_map_free(map);
2497
2498 if (*injective < 0 || !*injective)
2499 return -1;
2500
2501 return 0;
2502 }
2503
2504 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2505 const char *r, const char *s, int tilable, int parallel)
2506 {
2507 int i;
2508 isl_union_set *D;
2509 isl_union_map *W, *R, *S;
2510 isl_union_map *empty;
2511 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2512 isl_union_map *validity, *proximity, *coincidence;
2513 isl_union_map *schedule;
2514 isl_union_map *test;
2515 isl_union_set *delta;
2516 isl_union_set *domain;
2517 isl_set *delta_set;
2518 isl_set *slice;
2519 isl_set *origin;
2520 isl_schedule_constraints *sc;
2521 isl_schedule *sched;
2522 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2523
2524 D = isl_union_set_read_from_str(ctx, d);
2525 W = isl_union_map_read_from_str(ctx, w);
2526 R = isl_union_map_read_from_str(ctx, r);
2527 S = isl_union_map_read_from_str(ctx, s);
2528
2529 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2530 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2531
2532 empty = isl_union_map_empty(isl_union_map_get_space(S));
2533 isl_union_map_compute_flow(isl_union_map_copy(R),
2534 isl_union_map_copy(W), empty,
2535 isl_union_map_copy(S),
2536 &dep_raw, NULL, NULL, NULL);
2537 isl_union_map_compute_flow(isl_union_map_copy(W),
2538 isl_union_map_copy(W),
2539 isl_union_map_copy(R),
2540 isl_union_map_copy(S),
2541 &dep_waw, &dep_war, NULL, NULL);
2542
2543 dep = isl_union_map_union(dep_waw, dep_war);
2544 dep = isl_union_map_union(dep, dep_raw);
2545 validity = isl_union_map_copy(dep);
2546 coincidence = isl_union_map_copy(dep);
2547 proximity = isl_union_map_copy(dep);
2548
2549 sc = isl_schedule_constraints_on_domain(isl_union_set_copy(D));
2550 sc = isl_schedule_constraints_set_validity(sc, validity);
2551 sc = isl_schedule_constraints_set_coincidence(sc, coincidence);
2552 sc = isl_schedule_constraints_set_proximity(sc, proximity);
2553 sched = isl_schedule_constraints_compute_schedule(sc);
2554 schedule = isl_schedule_get_map(sched);
2555 isl_schedule_free(sched);
2556 isl_union_map_free(W);
2557 isl_union_map_free(R);
2558 isl_union_map_free(S);
2559
2560 is_injection = 1;
2561 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2562
2563 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2564 is_complete = isl_union_set_is_subset(D, domain);
2565 isl_union_set_free(D);
2566 isl_union_set_free(domain);
2567
2568 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2569 test = isl_union_map_apply_range(test, dep);
2570 test = isl_union_map_apply_range(test, schedule);
2571
2572 delta = isl_union_map_deltas(test);
2573 if (isl_union_set_n_set(delta) == 0) {
2574 is_tilable = 1;
2575 is_parallel = 1;
2576 is_nonneg = 1;
2577 isl_union_set_free(delta);
2578 } else {
2579 delta_set = isl_set_from_union_set(delta);
2580
2581 slice = isl_set_universe(isl_set_get_space(delta_set));
2582 for (i = 0; i < tilable; ++i)
2583 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2584 is_tilable = isl_set_is_subset(delta_set, slice);
2585 isl_set_free(slice);
2586
2587 slice = isl_set_universe(isl_set_get_space(delta_set));
2588 for (i = 0; i < parallel; ++i)
2589 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2590 is_parallel = isl_set_is_subset(delta_set, slice);
2591 isl_set_free(slice);
2592
2593 origin = isl_set_universe(isl_set_get_space(delta_set));
2594 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2595 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2596
2597 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2598 delta_set = isl_set_lexmin(delta_set);
2599
2600 is_nonneg = isl_set_is_equal(delta_set, origin);
2601
2602 isl_set_free(origin);
2603 isl_set_free(delta_set);
2604 }
2605
2606 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2607 is_injection < 0 || is_complete < 0)
2608 return -1;
2609 if (!is_complete)
2610 isl_die(ctx, isl_error_unknown,
2611 "generated schedule incomplete", return -1);
2612 if (!is_injection)
2613 isl_die(ctx, isl_error_unknown,
2614 "generated schedule not injective on each statement",
2615 return -1);
2616 if (!is_nonneg)
2617 isl_die(ctx, isl_error_unknown,
2618 "negative dependences in generated schedule",
2619 return -1);
2620 if (!is_tilable)
2621 isl_die(ctx, isl_error_unknown,
2622 "generated schedule not as tilable as expected",
2623 return -1);
2624 if (!is_parallel)
2625 isl_die(ctx, isl_error_unknown,
2626 "generated schedule not as parallel as expected",
2627 return -1);
2628
2629 return 0;
2630 }
2631
2632 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
2633 const char *domain, const char *validity, const char *proximity)
2634 {
2635 isl_union_set *dom;
2636 isl_union_map *dep;
2637 isl_union_map *prox;
2638 isl_schedule_constraints *sc;
2639 isl_schedule *schedule;
2640 isl_union_map *sched;
2641
2642 dom = isl_union_set_read_from_str(ctx, domain);
2643 dep = isl_union_map_read_from_str(ctx, validity);
2644 prox = isl_union_map_read_from_str(ctx, proximity);
2645 sc = isl_schedule_constraints_on_domain(dom);
2646 sc = isl_schedule_constraints_set_validity(sc, dep);
2647 sc = isl_schedule_constraints_set_proximity(sc, prox);
2648 schedule = isl_schedule_constraints_compute_schedule(sc);
2649 sched = isl_schedule_get_map(schedule);
2650 isl_schedule_free(schedule);
2651
2652 return sched;
2653 }
2654
2655 /* Check that a schedule can be constructed on the given domain
2656 * with the given validity and proximity constraints.
2657 */
2658 static int test_has_schedule(isl_ctx *ctx, const char *domain,
2659 const char *validity, const char *proximity)
2660 {
2661 isl_union_map *sched;
2662
2663 sched = compute_schedule(ctx, domain, validity, proximity);
2664 if (!sched)
2665 return -1;
2666
2667 isl_union_map_free(sched);
2668 return 0;
2669 }
2670
2671 int test_special_schedule(isl_ctx *ctx, const char *domain,
2672 const char *validity, const char *proximity, const char *expected_sched)
2673 {
2674 isl_union_map *sched1, *sched2;
2675 int equal;
2676
2677 sched1 = compute_schedule(ctx, domain, validity, proximity);
2678 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2679
2680 equal = isl_union_map_is_equal(sched1, sched2);
2681 isl_union_map_free(sched1);
2682 isl_union_map_free(sched2);
2683
2684 if (equal < 0)
2685 return -1;
2686 if (!equal)
2687 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2688 return -1);
2689
2690 return 0;
2691 }
2692
2693 /* Check that the schedule map is properly padded, even after being
2694 * reconstructed from the band forest.
2695 */
2696 static int test_padded_schedule(isl_ctx *ctx)
2697 {
2698 const char *str;
2699 isl_union_set *D;
2700 isl_union_map *validity, *proximity;
2701 isl_schedule_constraints *sc;
2702 isl_schedule *sched;
2703 isl_union_map *map1, *map2;
2704 isl_band_list *list;
2705 int equal;
2706
2707 str = "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2708 D = isl_union_set_read_from_str(ctx, str);
2709 validity = isl_union_map_empty(isl_union_set_get_space(D));
2710 proximity = isl_union_map_copy(validity);
2711 sc = isl_schedule_constraints_on_domain(D);
2712 sc = isl_schedule_constraints_set_validity(sc, validity);
2713 sc = isl_schedule_constraints_set_proximity(sc, proximity);
2714 sched = isl_schedule_constraints_compute_schedule(sc);
2715 map1 = isl_schedule_get_map(sched);
2716 list = isl_schedule_get_band_forest(sched);
2717 isl_band_list_free(list);
2718 map2 = isl_schedule_get_map(sched);
2719 isl_schedule_free(sched);
2720 equal = isl_union_map_is_equal(map1, map2);
2721 isl_union_map_free(map1);
2722 isl_union_map_free(map2);
2723
2724 if (equal < 0)
2725 return -1;
2726 if (!equal)
2727 isl_die(ctx, isl_error_unknown,
2728 "reconstructed schedule map not the same as original",
2729 return -1);
2730
2731 return 0;
2732 }
2733
2734 /* Input for testing of schedule construction based on
2735 * conditional constraints.
2736 *
2737 * domain is the iteration domain
2738 * flow are the flow dependences, which determine the validity and
2739 * proximity constraints
2740 * condition are the conditions on the conditional validity constraints
2741 * conditional_validity are the conditional validity constraints
2742 * outer_band_n is the expected number of members in the outer band
2743 */
2744 struct {
2745 const char *domain;
2746 const char *flow;
2747 const char *condition;
2748 const char *conditional_validity;
2749 int outer_band_n;
2750 } live_range_tests[] = {
2751 /* Contrived example that illustrates that we need to keep
2752 * track of tagged condition dependences and
2753 * tagged conditional validity dependences
2754 * in isl_sched_edge separately.
2755 * In particular, the conditional validity constraints on A
2756 * cannot be satisfied,
2757 * but they can be ignored because there are no corresponding
2758 * condition constraints. However, we do have an additional
2759 * conditional validity constraint that maps to the same
2760 * dependence relation
2761 * as the condition constraint on B. If we did not make a distinction
2762 * between tagged condition and tagged conditional validity
2763 * dependences, then we
2764 * could end up treating this shared dependence as an condition
2765 * constraint on A, forcing a localization of the conditions,
2766 * which is impossible.
2767 */
2768 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
2769 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
2770 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
2771 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2772 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2773 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
2774 1
2775 },
2776 /* TACO 2013 Fig. 7 */
2777 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2778 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2779 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2780 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
2781 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
2782 "0 <= i < n and 0 <= j < n - 1 }",
2783 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
2784 "0 <= i < n and 0 <= j < j' < n;"
2785 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
2786 "0 <= i < i' < n and 0 <= j,j' < n;"
2787 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
2788 "0 <= i,j,j' < n and j < j' }",
2789 2
2790 },
2791 /* TACO 2013 Fig. 7, without tags */
2792 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2793 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2794 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2795 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2796 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2797 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
2798 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
2799 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
2800 1
2801 },
2802 /* TACO 2013 Fig. 12 */
2803 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
2804 "S3[i,3] : 0 <= i <= 1 }",
2805 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
2806 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
2807 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
2808 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
2809 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2810 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
2811 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2812 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
2813 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
2814 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
2815 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
2816 1
2817 }
2818 };
2819
2820 /* Test schedule construction based on conditional constraints.
2821 * In particular, check the number of members in the outer band
2822 * as an indication of whether tiling is possible or not.
2823 */
2824 static int test_conditional_schedule_constraints(isl_ctx *ctx)
2825 {
2826 int i;
2827 isl_union_set *domain;
2828 isl_union_map *condition;
2829 isl_union_map *flow;
2830 isl_union_map *validity;
2831 isl_schedule_constraints *sc;
2832 isl_schedule *schedule;
2833 isl_band_list *list;
2834 isl_band *band;
2835 int n_member;
2836
2837 for (i = 0; i < ARRAY_SIZE(live_range_tests); ++i) {
2838 domain = isl_union_set_read_from_str(ctx,
2839 live_range_tests[i].domain);
2840 flow = isl_union_map_read_from_str(ctx,
2841 live_range_tests[i].flow);
2842 condition = isl_union_map_read_from_str(ctx,
2843 live_range_tests[i].condition);
2844 validity = isl_union_map_read_from_str(ctx,
2845 live_range_tests[i].conditional_validity);
2846 sc = isl_schedule_constraints_on_domain(domain);
2847 sc = isl_schedule_constraints_set_validity(sc,
2848 isl_union_map_copy(flow));
2849 sc = isl_schedule_constraints_set_proximity(sc, flow);
2850 sc = isl_schedule_constraints_set_conditional_validity(sc,
2851 condition, validity);
2852 schedule = isl_schedule_constraints_compute_schedule(sc);
2853 list = isl_schedule_get_band_forest(schedule);
2854 band = isl_band_list_get_band(list, 0);
2855 n_member = isl_band_n_member(band);
2856 isl_band_free(band);
2857 isl_band_list_free(list);
2858 isl_schedule_free(schedule);
2859
2860 if (!schedule)
2861 return -1;
2862 if (n_member != live_range_tests[i].outer_band_n)
2863 isl_die(ctx, isl_error_unknown,
2864 "unexpected number of members in outer band",
2865 return -1);
2866 }
2867 return 0;
2868 }
2869
2870 int test_schedule(isl_ctx *ctx)
2871 {
2872 const char *D, *W, *R, *V, *P, *S;
2873
2874 /* Handle resulting schedule with zero bands. */
2875 if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2876 return -1;
2877
2878 /* Jacobi */
2879 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2880 W = "{ S1[t,i] -> a[t,i] }";
2881 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2882 "S1[t,i] -> a[t-1,i+1] }";
2883 S = "{ S1[t,i] -> [t,i] }";
2884 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2885 return -1;
2886
2887 /* Fig. 5 of CC2008 */
2888 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2889 "j <= -1 + N }";
2890 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2891 "j >= 2 and j <= -1 + N }";
2892 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2893 "j >= 2 and j <= -1 + N; "
2894 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2895 "j >= 2 and j <= -1 + N }";
2896 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2897 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2898 return -1;
2899
2900 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2901 W = "{ S1[i] -> a[i] }";
2902 R = "{ S2[i] -> a[i+1] }";
2903 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2904 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2905 return -1;
2906
2907 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2908 W = "{ S1[i] -> a[i] }";
2909 R = "{ S2[i] -> a[9-i] }";
2910 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2911 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2912 return -1;
2913
2914 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2915 W = "{ S1[i] -> a[i] }";
2916 R = "[N] -> { S2[i] -> a[N-1-i] }";
2917 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2918 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2919 return -1;
2920
2921 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2922 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2923 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2924 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2925 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2926 return -1;
2927
2928 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2929 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2930 R = "{ S2[i,j] -> a[i-1,j] }";
2931 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2932 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2933 return -1;
2934
2935 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2936 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2937 R = "{ S2[i,j] -> a[i,j-1] }";
2938 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2939 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2940 return -1;
2941
2942 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2943 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2944 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2945 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2946 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2947 "S_0[] -> [0, 0, 0] }";
2948 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
2949 return -1;
2950 ctx->opt->schedule_parametric = 0;
2951 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2952 return -1;
2953 ctx->opt->schedule_parametric = 1;
2954
2955 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2956 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2957 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2958 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2959 "S4[i] -> a[i,N] }";
2960 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2961 "S4[i] -> [4,i,0] }";
2962 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2963 return -1;
2964
2965 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2966 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2967 "j <= N }";
2968 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2969 "j <= N; "
2970 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2971 "j <= N }";
2972 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2973 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2974 return -1;
2975
2976 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2977 " S_2[t] : t >= 0 and t <= -1 + N; "
2978 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2979 "i <= -1 + N }";
2980 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2981 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2982 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2983 "i >= 0 and i <= -1 + N }";
2984 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2985 "i >= 0 and i <= -1 + N; "
2986 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2987 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2988 " S_0[t] -> [0, t, 0] }";
2989
2990 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2991 return -1;
2992 ctx->opt->schedule_parametric = 0;
2993 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2994 return -1;
2995 ctx->opt->schedule_parametric = 1;
2996
2997 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2998 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2999 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
3000 return -1;
3001
3002 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3003 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3004 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3005 "j >= 0 and j <= -1 + N; "
3006 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3007 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3008 "j >= 0 and j <= -1 + N; "
3009 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3010 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3011 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3012 return -1;
3013
3014 D = "{ S_0[i] : i >= 0 }";
3015 W = "{ S_0[i] -> a[i] : i >= 0 }";
3016 R = "{ S_0[i] -> a[0] : i >= 0 }";
3017 S = "{ S_0[i] -> [0, i, 0] }";
3018 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3019 return -1;
3020
3021 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3022 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3023 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3024 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3025 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3026 return -1;
3027
3028 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3029 "k <= -1 + n and k >= 0 }";
3030 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3031 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3032 "k <= -1 + n and k >= 0; "
3033 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3034 "k <= -1 + n and k >= 0; "
3035 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3036 "k <= -1 + n and k >= 0 }";
3037 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
3038 ctx->opt->schedule_outer_coincidence = 1;
3039 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3040 return -1;
3041 ctx->opt->schedule_outer_coincidence = 0;
3042
3043 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
3044 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3045 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3046 "Stmt_for_body24[i0, i1, 1, 0]:"
3047 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3048 "Stmt_for_body7[i0, i1, i2]:"
3049 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3050 "i2 <= 7 }";
3051
3052 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
3053 "Stmt_for_body24[1, i1, i2, i3]:"
3054 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3055 "i2 >= 1;"
3056 "Stmt_for_body24[0, i1, i2, i3] -> "
3057 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3058 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3059 "i3 >= 0;"
3060 "Stmt_for_body24[0, i1, i2, i3] ->"
3061 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3062 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3063 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3064 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3065 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3066 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3067 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3068 "i1 <= 6 and i1 >= 0;"
3069 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3070 "Stmt_for_body7[i0, i1, i2] -> "
3071 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3072 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3073 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3074 "Stmt_for_body7[i0, i1, i2] -> "
3075 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3076 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3077 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3078 P = V;
3079 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3080 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3081 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3082
3083 if (test_special_schedule(ctx, D, V, P, S) < 0)
3084 return -1;
3085
3086 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3087 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3088 "j >= 1 and j <= 7;"
3089 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3090 "j >= 1 and j <= 8 }";
3091 P = "{ }";
3092 S = "{ S_0[i, j] -> [i + j, j] }";
3093 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3094 if (test_special_schedule(ctx, D, V, P, S) < 0)
3095 return -1;
3096 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3097
3098 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3099 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3100 "j >= 0 and j <= -1 + i }";
3101 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3102 "i <= -1 + N and j >= 0;"
3103 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3104 "i <= -2 + N }";
3105 P = "{ }";
3106 S = "{ S_0[i, j] -> [i, j] }";
3107 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3108 if (test_special_schedule(ctx, D, V, P, S) < 0)
3109 return -1;
3110 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3111
3112 /* Test both algorithms on a case with only proximity dependences. */
3113 D = "{ S[i,j] : 0 <= i <= 10 }";
3114 V = "{ }";
3115 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3116 S = "{ S[i, j] -> [j, i] }";
3117 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3118 if (test_special_schedule(ctx, D, V, P, S) < 0)
3119 return -1;
3120 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3121 if (test_special_schedule(ctx, D, V, P, S) < 0)
3122 return -1;
3123
3124 D = "{ A[a]; B[] }";
3125 V = "{}";
3126 P = "{ A[a] -> B[] }";
3127 if (test_has_schedule(ctx, D, V, P) < 0)
3128 return -1;
3129
3130 if (test_padded_schedule(ctx) < 0)
3131 return -1;
3132
3133 /* Check that check for progress is not confused by rational
3134 * solution.
3135 */
3136 D = "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3137 V = "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3138 "i0 <= -2 + N; "
3139 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3140 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3141 P = "{}";
3142 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3143 if (test_has_schedule(ctx, D, V, P) < 0)
3144 return -1;
3145 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3146
3147 if (test_conditional_schedule_constraints(ctx) < 0)
3148 return -1;
3149
3150 return 0;
3151 }
3152
3153 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
3154 {
3155 isl_union_map *umap;
3156 int test;
3157
3158 umap = isl_union_map_read_from_str(ctx, str);
3159 test = isl_union_map_plain_is_injective(umap);
3160 isl_union_map_free(umap);
3161 if (test < 0)
3162 return -1;
3163 if (test == injective)
3164 return 0;
3165 if (injective)
3166 isl_die(ctx, isl_error_unknown,
3167 "map not detected as injective", return -1);
3168 else
3169 isl_die(ctx, isl_error_unknown,
3170 "map detected as injective", return -1);
3171 }
3172
3173 int test_injective(isl_ctx *ctx)
3174 {
3175 const char *str;
3176
3177 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3178 return -1;
3179 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
3180 return -1;
3181 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
3182 return -1;
3183 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
3184 return -1;
3185 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3186 return -1;
3187 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3188 return -1;
3189 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3190 return -1;
3191 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3192 return -1;
3193
3194 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3195 if (test_plain_injective(ctx, str, 1))
3196 return -1;
3197 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3198 if (test_plain_injective(ctx, str, 0))
3199 return -1;
3200
3201 return 0;
3202 }
3203
3204 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
3205 {
3206 isl_aff *aff2;
3207 int equal;
3208
3209 if (!aff)
3210 return -1;
3211
3212 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
3213 equal = isl_aff_plain_is_equal(aff, aff2);
3214 isl_aff_free(aff2);
3215
3216 return equal;
3217 }
3218
3219 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
3220 {
3221 int equal;
3222
3223 equal = aff_plain_is_equal(aff, str);
3224 if (equal < 0)
3225 return -1;
3226 if (!equal)
3227 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
3228 "result not as expected", return -1);
3229 return 0;
3230 }
3231
3232 struct {
3233 __isl_give isl_aff *(*fn)(__isl_take isl_aff *aff1,
3234 __isl_take isl_aff *aff2);
3235 } aff_bin_op[] = {
3236 ['+'] = { &isl_aff_add },
3237 ['-'] = { &isl_aff_sub },
3238 ['*'] = { &isl_aff_mul },
3239 ['/'] = { &isl_aff_div },
3240 };
3241
3242 struct {
3243 const char *arg1;
3244 unsigned char op;
3245 const char *arg2;
3246 const char *res;
3247 } aff_bin_tests[] = {
3248 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3249 "{ [i] -> [2i] }" },
3250 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3251 "{ [i] -> [0] }" },
3252 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3253 "{ [i] -> [2i] }" },
3254 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3255 "{ [i] -> [2i] }" },
3256 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
3257 "{ [i] -> [i/2] }" },
3258 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
3259 "{ [i] -> [i] }" },
3260 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3261 "{ [i] -> [NaN] }" },
3262 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3263 "{ [i] -> [NaN] }" },
3264 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3265 "{ [i] -> [NaN] }" },
3266 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3267 "{ [i] -> [NaN] }" },
3268 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
3269 "{ [i] -> [NaN] }" },
3270 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
3271 "{ [i] -> [NaN] }" },
3272 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3273 "{ [i] -> [NaN] }" },
3274 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3275 "{ [i] -> [NaN] }" },
3276 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3277 "{ [i] -> [NaN] }" },
3278 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3279 "{ [i] -> [NaN] }" },
3280 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
3281 "{ [i] -> [NaN] }" },
3282 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
3283 "{ [i] -> [NaN] }" },
3284 };
3285
3286 /* Perform some basic tests of binary operations on isl_aff objects.
3287 */
3288 static int test_bin_aff(isl_ctx *ctx)
3289 {
3290 int i;
3291 isl_aff *aff1, *aff2, *res;
3292 __isl_give isl_aff *(*fn)(__isl_take isl_aff *aff1,
3293 __isl_take isl_aff *aff2);
3294 int ok;
3295
3296 for (i = 0; i < ARRAY_SIZE(aff_bin_tests); ++i) {
3297 aff1 = isl_aff_read_from_str(ctx, aff_bin_tests[i].arg1);
3298 aff2 = isl_aff_read_from_str(ctx, aff_bin_tests[i].arg2);
3299 res = isl_aff_read_from_str(ctx, aff_bin_tests[i].res);
3300 fn = aff_bin_op[aff_bin_tests[i].op].fn;
3301 aff1 = fn(aff1, aff2);
3302 if (isl_aff_is_nan(res))
3303 ok = isl_aff_is_nan(aff1);
3304 else
3305 ok = isl_aff_plain_is_equal(aff1, res);
3306 isl_aff_free(aff1);
3307 isl_aff_free(res);
3308 if (ok < 0)
3309 return -1;
3310 if (!ok)
3311 isl_die(ctx, isl_error_unknown,
3312 "unexpected result", return -1);
3313 }
3314
3315 return 0;
3316 }
3317
3318 int test_aff(isl_ctx *ctx)
3319 {
3320 const char *str;
3321 isl_set *set;
3322 isl_space *space;
3323 isl_local_space *ls;
3324 isl_aff *aff;
3325 int zero, equal;
3326
3327 if (test_bin_aff(ctx) < 0)
3328 return -1;
3329
3330 space = isl_space_set_alloc(ctx, 0, 1);
3331 ls = isl_local_space_from_space(space);
3332 aff = isl_aff_zero_on_domain(ls);
3333
3334 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3335 aff = isl_aff_scale_down_ui(aff, 3);
3336 aff = isl_aff_floor(aff);
3337 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3338 aff = isl_aff_scale_down_ui(aff, 2);
3339 aff = isl_aff_floor(aff);
3340 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3341
3342 str = "{ [10] }";
3343 set = isl_set_read_from_str(ctx, str);
3344 aff = isl_aff_gist(aff, set);
3345
3346 aff = isl_aff_add_constant_si(aff, -16);
3347 zero = isl_aff_plain_is_zero(aff);
3348 isl_aff_free(aff);
3349
3350 if (zero < 0)
3351 return -1;
3352 if (!zero)
3353 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3354
3355 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
3356 aff = isl_aff_scale_down_ui(aff, 64);
3357 aff = isl_aff_floor(aff);
3358 equal = aff_check_plain_equal(aff, "{ [-1] }");
3359 isl_aff_free(aff);
3360 if (equal < 0)
3361 return -1;
3362
3363 return 0;
3364 }
3365
3366 int test_dim_max(isl_ctx *ctx)
3367 {
3368 int equal;
3369 const char *str;
3370 isl_set *set1, *set2;
3371 isl_set *set;
3372 isl_map *map;
3373 isl_pw_aff *pwaff;
3374
3375 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
3376 set = isl_set_read_from_str(ctx, str);
3377 pwaff = isl_set_dim_max(set, 0);
3378 set1 = isl_set_from_pw_aff(pwaff);
3379 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
3380 set2 = isl_set_read_from_str(ctx, str);
3381 equal = isl_set_is_equal(set1, set2);
3382 isl_set_free(set1);
3383 isl_set_free(set2);
3384 if (equal < 0)
3385 return -1;
3386 if (!equal)
3387 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3388
3389 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
3390 set = isl_set_read_from_str(ctx, str);
3391 pwaff = isl_set_dim_max(set, 0);
3392 set1 = isl_set_from_pw_aff(pwaff);
3393 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3394 set2 = isl_set_read_from_str(ctx, str);
3395 equal = isl_set_is_equal(set1, set2);
3396 isl_set_free(set1);
3397 isl_set_free(set2);
3398 if (equal < 0)
3399 return -1;
3400 if (!equal)
3401 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3402
3403 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
3404 set = isl_set_read_from_str(ctx, str);
3405 pwaff = isl_set_dim_max(set, 0);
3406 set1 = isl_set_from_pw_aff(pwaff);
3407 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3408 set2 = isl_set_read_from_str(ctx, str);
3409 equal = isl_set_is_equal(set1, set2);
3410 isl_set_free(set1);
3411 isl_set_free(set2);
3412 if (equal < 0)
3413 return -1;
3414 if (!equal)
3415 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3416
3417 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
3418 "0 <= i < N and 0 <= j < M }";
3419 map = isl_map_read_from_str(ctx, str);
3420 set = isl_map_range(map);
3421
3422 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
3423 set1 = isl_set_from_pw_aff(pwaff);
3424 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
3425 set2 = isl_set_read_from_str(ctx, str);
3426 equal = isl_set_is_equal(set1, set2);
3427 isl_set_free(set1);
3428 isl_set_free(set2);
3429
3430 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
3431 set1 = isl_set_from_pw_aff(pwaff);
3432 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
3433 set2 = isl_set_read_from_str(ctx, str);
3434 if (equal >= 0 && equal)
3435 equal = isl_set_is_equal(set1, set2);
3436 isl_set_free(set1);
3437 isl_set_free(set2);
3438
3439 isl_set_free(set);
3440
3441 if (equal < 0)
3442 return -1;
3443 if (!equal)
3444 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3445
3446 /* Check that solutions are properly merged. */
3447 str = "[n] -> { [a, b, c] : c >= -4a - 2b and "
3448 "c <= -1 + n - 4a - 2b and c >= -2b and "
3449 "4a >= -4 + n and c >= 0 }";
3450 set = isl_set_read_from_str(ctx, str);
3451 pwaff = isl_set_dim_min(set, 2);
3452 set1 = isl_set_from_pw_aff(pwaff);
3453 str = "[n] -> { [(0)] : n >= 1 }";
3454 set2 = isl_set_read_from_str(ctx, str);
3455 equal = isl_set_is_equal(set1, set2);
3456 isl_set_free(set1);
3457 isl_set_free(set2);
3458
3459 if (equal < 0)
3460 return -1;
3461 if (!equal)
3462 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3463
3464 /* Check that empty solution lie in the right space. */
3465 str = "[n] -> { [t,a] : 1 = 0 }";
3466 set = isl_set_read_from_str(ctx, str);
3467 pwaff = isl_set_dim_max(set, 0);
3468 set1 = isl_set_from_pw_aff(pwaff);
3469 str = "[n] -> { [t] : 1 = 0 }";
3470 set2 = isl_set_read_from_str(ctx, str);
3471 equal = isl_set_is_equal(set1, set2);
3472 isl_set_free(set1);
3473 isl_set_free(set2);
3474
3475 if (equal < 0)
3476 return -1;
3477 if (!equal)
3478 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3479
3480 return 0;
3481 }
3482
3483 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
3484 */
3485 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff *pma,
3486 const char *str)
3487 {
3488 isl_ctx *ctx;
3489 isl_pw_multi_aff *pma2;
3490 int equal;
3491
3492 if (!pma)
3493 return -1;
3494
3495 ctx = isl_pw_multi_aff_get_ctx(pma);
3496 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3497 equal = isl_pw_multi_aff_plain_is_equal(pma, pma2);
3498 isl_pw_multi_aff_free(pma2);
3499
3500 return equal;
3501 }
3502
3503 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
3504 * represented by "str".
3505 */
3506 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff *pma,
3507 const char *str)
3508 {
3509 int equal;
3510
3511 equal = pw_multi_aff_plain_is_equal(pma, str);
3512 if (equal < 0)
3513 return -1;
3514 if (!equal)
3515 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_unknown,
3516 "result not as expected", return -1);
3517 return 0;
3518 }
3519
3520 /* Basic test for isl_pw_multi_aff_product.
3521 *
3522 * Check that multiple pieces are properly handled.
3523 */
3524 static int test_product_pma(isl_ctx *ctx)
3525 {
3526 int equal;
3527 const char *str;
3528 isl_pw_multi_aff *pma1, *pma2;
3529
3530 str = "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
3531 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
3532 str = "{ C[] -> D[] }";
3533 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3534 pma1 = isl_pw_multi_aff_product(pma1, pma2);
3535 str = "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
3536 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
3537 equal = pw_multi_aff_check_plain_equal(pma1, str);
3538 isl_pw_multi_aff_free(pma1);
3539 if (equal < 0)
3540 return -1;
3541
3542 return 0;
3543 }
3544
3545 int test_product(isl_ctx *ctx)
3546 {
3547 const char *str;
3548 isl_set *set;
3549 isl_union_set *uset1, *uset2;
3550 int ok;
3551
3552 str = "{ A[i] }";
3553 set = isl_set_read_from_str(ctx, str);
3554 set = isl_set_product(set, isl_set_copy(set));
3555 ok = isl_set_is_wrapping(set);
3556 isl_set_free(set);
3557 if (ok < 0)
3558 return -1;
3559 if (!ok)
3560 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3561
3562 str = "{ [] }";
3563 uset1 = isl_union_set_read_from_str(ctx, str);
3564 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
3565 str = "{ [[] -> []] }";
3566 uset2 = isl_union_set_read_from_str(ctx, str);
3567 ok = isl_union_set_is_equal(uset1, uset2);
3568 isl_union_set_free(uset1);
3569 isl_union_set_free(uset2);
3570 if (ok < 0)
3571 return -1;
3572 if (!ok)
3573 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3574
3575 if (test_product_pma(ctx) < 0)
3576 return -1;
3577
3578 return 0;
3579 }
3580
3581 /* Check that two sets are not considered disjoint just because
3582 * they have a different set of (named) parameters.
3583 */
3584 static int test_disjoint(isl_ctx *ctx)
3585 {
3586 const char *str;
3587 isl_set *set, *set2;
3588 int disjoint;
3589
3590 str = "[n] -> { [[]->[]] }";
3591 set = isl_set_read_from_str(ctx, str);
3592 str = "{ [[]->[]] }";
3593 set2 = isl_set_read_from_str(ctx, str);
3594 disjoint = isl_set_is_disjoint(set, set2);
3595 isl_set_free(set);
3596 isl_set_free(set2);
3597 if (disjoint < 0)
3598 return -1;
3599 if (disjoint)
3600 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3601
3602 return 0;
3603 }
3604
3605 int test_equal(isl_ctx *ctx)
3606 {
3607 const char *str;
3608 isl_set *set, *set2;
3609 int equal;
3610
3611 str = "{ S_6[i] }";
3612 set = isl_set_read_from_str(ctx, str);
3613 str = "{ S_7[i] }";
3614 set2 = isl_set_read_from_str(ctx, str);
3615 equal = isl_set_is_equal(set, set2);
3616 isl_set_free(set);
3617 isl_set_free(set2);
3618 if (equal < 0)
3619 return -1;
3620 if (equal)
3621 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3622
3623 return 0;
3624 }
3625
3626 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
3627 enum isl_dim_type type, unsigned pos, int fixed)
3628 {
3629 int test;
3630
3631 test = isl_map_plain_is_fixed(map, type, pos, NULL);
3632 isl_map_free(map);
3633 if (test < 0)
3634 return -1;
3635 if (test == fixed)
3636 return 0;
3637 if (fixed)
3638 isl_die(ctx, isl_error_unknown,
3639 "map not detected as fixed", return -1);
3640 else
3641 isl_die(ctx, isl_error_unknown,
3642 "map detected as fixed", return -1);
3643 }
3644
3645 int test_fixed(isl_ctx *ctx)
3646 {
3647 const char *str;
3648 isl_map *map;
3649
3650 str = "{ [i] -> [i] }";
3651 map = isl_map_read_from_str(ctx, str);
3652 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
3653 return -1;
3654 str = "{ [i] -> [1] }";
3655 map = isl_map_read_from_str(ctx, str);
3656 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3657 return -1;
3658 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
3659 map = isl_map_read_from_str(ctx, str);
3660 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3661 return -1;
3662 map = isl_map_read_from_str(ctx, str);
3663 map = isl_map_neg(map);
3664 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3665 return -1;
3666
3667 return 0;
3668 }
3669
3670 struct isl_vertices_test_data {
3671 const char *set;
3672 int n;
3673 const char *vertex[2];
3674 } vertices_tests[] = {
3675 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
3676 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
3677 { "{ A[t, i] : t = 14 and i = 1 }",
3678 1, { "{ A[14, 1] }" } },
3679 };
3680
3681 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
3682 */
3683 static int find_vertex(__isl_take isl_vertex *vertex, void *user)
3684 {
3685 struct isl_vertices_test_data *data = user;
3686 isl_ctx *ctx;
3687 isl_multi_aff *ma;
3688 isl_basic_set *bset;
3689 isl_pw_multi_aff *pma;
3690 int i;
3691 int equal;
3692
3693 ctx = isl_vertex_get_ctx(vertex);
3694 bset = isl_vertex_get_domain(vertex);
3695 ma = isl_vertex_get_expr(vertex);
3696 pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset), ma);
3697
3698 for (i = 0; i < data->n; ++i) {
3699 isl_pw_multi_aff *pma_i;
3700
3701 pma_i = isl_pw_multi_aff_read_from_str(ctx, data->vertex[i]);
3702 equal = isl_pw_multi_aff_plain_is_equal(pma, pma_i);
3703 isl_pw_multi_aff_free(pma_i);
3704
3705 if (equal < 0 || equal)
3706 break;
3707 }
3708
3709 isl_pw_multi_aff_free(pma);
3710 isl_vertex_free(vertex);
3711
3712 if (equal < 0)
3713 return -1;
3714
3715 return equal ? 0 : - 1;
3716 }
3717
3718 int test_vertices(isl_ctx *ctx)
3719 {
3720 int i;
3721
3722 for (i = 0; i < ARRAY_SIZE(vertices_tests); ++i) {
3723 isl_basic_set *bset;
3724 isl_vertices *vertices;
3725 int ok = 1;
3726 int n;
3727
3728 bset = isl_basic_set_read_from_str(ctx, vertices_tests[i].set);
3729 vertices = isl_basic_set_compute_vertices(bset);
3730 n = isl_vertices_get_n_vertices(vertices);
3731 if (vertices_tests[i].n != n)
3732 ok = 0;
3733 if (isl_vertices_foreach_vertex(vertices, &find_vertex,
3734 &vertices_tests[i]) < 0)
3735 ok = 0;
3736 isl_vertices_free(vertices);
3737 isl_basic_set_free(bset);
3738
3739 if (!vertices)
3740 return -1;
3741 if (!ok)
3742 isl_die(ctx, isl_error_unknown, "unexpected vertices",
3743 return -1);
3744 }
3745
3746 return 0;
3747 }
3748
3749 int test_union_pw(isl_ctx *ctx)
3750 {
3751 int equal;
3752 const char *str;
3753 isl_union_set *uset;
3754 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
3755
3756 str = "{ [x] -> x^2 }";
3757 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
3758 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
3759 uset = isl_union_pw_qpolynomial_domain(upwqp1);
3760 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
3761 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
3762 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
3763 isl_union_pw_qpolynomial_free(upwqp1);
3764 isl_union_pw_qpolynomial_free(upwqp2);
3765 if (equal < 0)
3766 return -1;
3767 if (!equal)
3768 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3769
3770 return 0;
3771 }
3772
3773 int test_output(isl_ctx *ctx)
3774 {
3775 char *s;
3776 const char *str;
3777 isl_pw_aff *pa;
3778 isl_printer *p;
3779 int equal;
3780
3781 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
3782 pa = isl_pw_aff_read_from_str(ctx, str);
3783
3784 p = isl_printer_to_str(ctx);
3785 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
3786 p = isl_printer_print_pw_aff(p, pa);
3787 s = isl_printer_get_str(p);
3788 isl_printer_free(p);
3789 isl_pw_aff_free(pa);
3790 if (!s)
3791 equal = -1;
3792 else
3793 equal = !strcmp(s, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
3794 free(s);
3795 if (equal < 0)
3796 return -1;
3797 if (!equal)
3798 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3799
3800 return 0;
3801 }
3802
3803 int test_sample(isl_ctx *ctx)
3804 {
3805 const char *str;
3806 isl_basic_set *bset1, *bset2;
3807 int empty, subset;
3808
3809 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
3810 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
3811 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
3812 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
3813 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
3814 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
3815 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
3816 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
3817 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3818 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3819 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3820 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3821 "d - 1073741821e and "
3822 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3823 "3j >= 1 - a + b + 2e and "
3824 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3825 "3i <= 4 - a + 4b - e and "
3826 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3827 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3828 "c <= -1 + a and 3i >= -2 - a + 3e and "
3829 "1073741822e <= 1073741823 - a + 1073741822b + c and "
3830 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3831 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3832 "1073741823e >= 1 + 1073741823b - d and "
3833 "3i >= 1073741823b + c - 1073741823e - f and "
3834 "3i >= 1 + 2b + e + 3g }";
3835 bset1 = isl_basic_set_read_from_str(ctx, str);
3836 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
3837 empty = isl_basic_set_is_empty(bset2);
3838 subset = isl_basic_set_is_subset(bset2, bset1);
3839 isl_basic_set_free(bset1);
3840 isl_basic_set_free(bset2);
3841 if (empty < 0 || subset < 0)
3842 return -1;
3843 if (empty)
3844 isl_die(ctx, isl_error_unknown, "point not found", return -1);
3845 if (!subset)
3846 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
3847
3848 return 0;
3849 }
3850
3851 int test_fixed_power(isl_ctx *ctx)
3852 {
3853 const char *str;
3854 isl_map *map;
3855 isl_int exp;
3856 int equal;
3857
3858 isl_int_init(exp);
3859 str = "{ [i] -> [i + 1] }";
3860 map = isl_map_read_from_str(ctx, str);
3861 isl_int_set_si(exp, 23);
3862 map = isl_map_fixed_power(map, exp);
3863 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
3864 isl_int_clear(exp);
3865 isl_map_free(map);
3866 if (equal < 0)
3867 return -1;
3868
3869 return 0;
3870 }
3871
3872 int test_slice(isl_ctx *ctx)
3873 {
3874 const char *str;
3875 isl_map *map;
3876 int equal;
3877
3878 str = "{ [i] -> [j] }";
3879 map = isl_map_read_from_str(ctx, str);
3880 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
3881 equal = map_check_equal(map, "{ [i] -> [i] }");
3882 isl_map_free(map);
3883 if (equal < 0)
3884 return -1;
3885
3886 str = "{ [i] -> [j] }";
3887 map = isl_map_read_from_str(ctx, str);
3888 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
3889 equal = map_check_equal(map, "{ [i] -> [j] }");
3890 isl_map_free(map);
3891 if (equal < 0)
3892 return -1;
3893
3894 str = "{ [i] -> [j] }";
3895 map = isl_map_read_from_str(ctx, str);
3896 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
3897 equal = map_check_equal(map, "{ [i] -> [-i] }");
3898 isl_map_free(map);
3899 if (equal < 0)
3900 return -1;
3901
3902 str = "{ [i] -> [j] }";
3903 map = isl_map_read_from_str(ctx, str);
3904 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
3905 equal = map_check_equal(map, "{ [0] -> [j] }");
3906 isl_map_free(map);
3907 if (equal < 0)
3908 return -1;
3909
3910 str = "{ [i] -> [j] }";
3911 map = isl_map_read_from_str(ctx, str);
3912 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
3913 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
3914 isl_map_free(map);
3915 if (equal < 0)
3916 return -1;
3917
3918 str = "{ [i] -> [j] }";
3919 map = isl_map_read_from_str(ctx, str);
3920 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
3921 equal = map_check_equal(map, "{ [i] -> [j] : false }");
3922 isl_map_free(map);
3923 if (equal < 0)
3924 return -1;
3925
3926 return 0;
3927 }
3928
3929 int test_eliminate(isl_ctx *ctx)
3930 {
3931 const char *str;
3932 isl_map *map;
3933 int equal;
3934
3935 str = "{ [i] -> [j] : i = 2j }";
3936 map = isl_map_read_from_str(ctx, str);
3937 map = isl_map_eliminate(map, isl_dim_out, 0, 1);
3938 equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
3939 isl_map_free(map);
3940 if (equal < 0)
3941 return -1;
3942
3943 return 0;
3944 }
3945
3946 /* Check that isl_set_dim_residue_class detects that the values of j
3947 * in the set below are all odd and that it does not detect any spurious
3948 * strides.
3949 */
3950 static int test_residue_class(isl_ctx *ctx)
3951 {
3952 const char *str;
3953 isl_set *set;
3954 isl_int m, r;
3955 int res;
3956
3957 str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3958 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3959 set = isl_set_read_from_str(ctx, str);
3960 isl_int_init(m);
3961 isl_int_init(r);
3962 res = isl_set_dim_residue_class(set, 1, &m, &r);
3963 if (res >= 0 &&
3964 (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
3965 isl_die(ctx, isl_error_unknown, "incorrect residue class",
3966 res = -1);
3967 isl_int_clear(r);
3968 isl_int_clear(m);
3969 isl_set_free(set);
3970
3971 return res;
3972 }
3973
3974 int test_align_parameters(isl_ctx *ctx)
3975 {
3976 const char *str;
3977 isl_space *space;
3978 isl_multi_aff *ma1, *ma2;
3979 int equal;
3980
3981 str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3982 ma1 = isl_multi_aff_read_from_str(ctx, str);
3983
3984 space = isl_space_params_alloc(ctx, 1);
3985 space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
3986 ma1 = isl_multi_aff_align_params(ma1, space);
3987
3988 str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3989 ma2 = isl_multi_aff_read_from_str(ctx, str);
3990
3991 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
3992
3993 isl_multi_aff_free(ma1);
3994 isl_multi_aff_free(ma2);
3995
3996 if (equal < 0)
3997 return -1;
3998 if (!equal)
3999 isl_die(ctx, isl_error_unknown,
4000 "result not as expected", return -1);
4001
4002 return 0;
4003 }
4004
4005 static int test_list(isl_ctx *ctx)
4006 {
4007 isl_id *a, *b, *c, *d, *id;
4008 isl_id_list *list;
4009 int ok;
4010
4011 a = isl_id_alloc(ctx, "a", NULL);
4012 b = isl_id_alloc(ctx, "b", NULL);
4013 c = isl_id_alloc(ctx, "c", NULL);
4014 d = isl_id_alloc(ctx, "d", NULL);
4015
4016 list = isl_id_list_alloc(ctx, 4);
4017 list = isl_id_list_add(list, a);
4018 list = isl_id_list_add(list, b);
4019 list = isl_id_list_add(list, c);
4020 list = isl_id_list_add(list, d);
4021 list = isl_id_list_drop(list, 1, 1);
4022
4023 if (isl_id_list_n_id(list) != 3) {
4024 isl_id_list_free(list);
4025 isl_die(ctx, isl_error_unknown,
4026 "unexpected number of elements in list", return -1);
4027 }
4028
4029 id = isl_id_list_get_id(list, 0);
4030 ok = id == a;
4031 isl_id_free(id);
4032 id = isl_id_list_get_id(list, 1);
4033 ok = ok && id == c;
4034 isl_id_free(id);
4035 id = isl_id_list_get_id(list, 2);
4036 ok = ok && id == d;
4037 isl_id_free(id);
4038
4039 isl_id_list_free(list);
4040
4041 if (!ok)
4042 isl_die(ctx, isl_error_unknown,
4043 "unexpected elements in list", return -1);
4044
4045 return 0;
4046 }
4047
4048 const char *set_conversion_tests[] = {
4049 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4050 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4051 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4052 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4053 };
4054
4055 /* Check that converting from isl_set to isl_pw_multi_aff and back
4056 * to isl_set produces the original isl_set.
4057 */
4058 static int test_set_conversion(isl_ctx *ctx)
4059 {
4060 int i;
4061 const char *str;
4062 isl_set *set1, *set2;
4063 isl_pw_multi_aff *pma;
4064 int equal;
4065
4066 for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
4067 str = set_conversion_tests[i];
4068 set1 = isl_set_read_from_str(ctx, str);
4069 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
4070 set2 = isl_set_from_pw_multi_aff(pma);
4071 equal = isl_set_is_equal(set1, set2);
4072 isl_set_free(set1);
4073 isl_set_free(set2);
4074
4075 if (equal < 0)
4076 return -1;
4077 if (!equal)
4078 isl_die(ctx, isl_error_unknown, "bad conversion",
4079 return -1);
4080 }
4081
4082 return 0;
4083 }
4084
4085 /* Check that converting from isl_map to isl_pw_multi_aff and back
4086 * to isl_map produces the original isl_map.
4087 */
4088 static int test_map_conversion(isl_ctx *ctx)
4089 {
4090 const char *str;
4091 isl_map *map1, *map2;
4092 isl_pw_multi_aff *pma;
4093 int equal;
4094
4095 str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
4096 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4097 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4098 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4099 "9e <= -2 - 2a) }";
4100 map1 = isl_map_read_from_str(ctx, str);
4101 pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
4102 map2 = isl_map_from_pw_multi_aff(pma);
4103 equal = isl_map_is_equal(map1, map2);
4104 isl_map_free(map1);
4105 isl_map_free(map2);
4106
4107 if (equal < 0)
4108 return -1;
4109 if (!equal)
4110 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
4111
4112 return 0;
4113 }
4114
4115 static int test_conversion(isl_ctx *ctx)
4116 {
4117 if (test_set_conversion(ctx) < 0)
4118 return -1;
4119 if (test_map_conversion(ctx) < 0)
4120 return -1;
4121 return 0;
4122 }
4123
4124 /* Check that isl_basic_map_curry does not modify input.
4125 */
4126 static int test_curry(isl_ctx *ctx)
4127 {
4128 const char *str;
4129 isl_basic_map *bmap1, *bmap2;
4130 int equal;
4131
4132 str = "{ [A[] -> B[]] -> C[] }";
4133 bmap1 = isl_basic_map_read_from_str(ctx, str);
4134 bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
4135 equal = isl_basic_map_is_equal(bmap1, bmap2);
4136 isl_basic_map_free(bmap1);
4137 isl_basic_map_free(bmap2);
4138
4139 if (equal < 0)
4140 return -1;
4141 if (equal)
4142 isl_die(ctx, isl_error_unknown,
4143 "curried map should not be equal to original",
4144 return -1);
4145
4146 return 0;
4147 }
4148
4149 struct {
4150 const char *set;
4151 const char *ma;
4152 const char *res;
4153 } preimage_tests[] = {
4154 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4155 "{ A[j,i] -> B[i,j] }",
4156 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4157 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4158 "{ A[a,b] -> B[a/2,b/6] }",
4159 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4160 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4161 "{ A[a,b] -> B[a/2,b/6] }",
4162 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4163 "exists i,j : a = 2 i and b = 6 j }" },
4164 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4165 "[n] -> { : 0 <= n <= 100 }" },
4166 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4167 "{ A[a] -> B[2a] }",
4168 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4169 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4170 "{ A[a] -> B[([a/2])] }",
4171 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4172 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4173 "{ A[a] -> B[a,a,a/3] }",
4174 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4175 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4176 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4177 };
4178
4179 static int test_preimage_basic_set(isl_ctx *ctx)
4180 {
4181 int i;
4182 isl_basic_set *bset1, *bset2;
4183 isl_multi_aff *ma;
4184 int equal;
4185
4186 for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
4187 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
4188 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
4189 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
4190 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
4191 equal = isl_basic_set_is_equal(bset1, bset2);
4192 isl_basic_set_free(bset1);
4193 isl_basic_set_free(bset2);
4194 if (equal < 0)
4195 return -1;
4196 if (!equal)
4197 isl_die(ctx, isl_error_unknown, "bad preimage",
4198 return -1);
4199 }
4200
4201 return 0;
4202 }
4203
4204 struct {
4205 const char *map;
4206 const char *ma;
4207 const char *res;
4208 } preimage_domain_tests[] = {
4209 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4210 "{ A[j,i] -> B[i,j] }",
4211 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4212 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4213 "{ A[i] -> B[i + 1] }",
4214 "{ A[i] -> C[i + 1] }" },
4215 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4216 "{ A[i] -> B[i + 1] }",
4217 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4218 { "{ B[i] -> C[([i/2])] }",
4219 "{ A[i] -> B[2i] }",
4220 "{ A[i] -> C[i] }" },
4221 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4222 "{ A[i] -> B[([i/5]), ([i/7])] }",
4223 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4224 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4225 "[N] -> { A[] -> B[([N/5])] }",
4226 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4227 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4228 "{ A[i] -> B[2i] }",
4229 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4230 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4231 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4232 "{ A[i] -> B[2i] }",
4233 "{ A[i] -> C[2i] }" },
4234 };
4235
4236 static int test_preimage_union_map(isl_ctx *ctx)
4237 {
4238 int i;
4239 isl_union_map *umap1, *umap2;
4240 isl_multi_aff *ma;
4241 int equal;
4242
4243 for (i = 0; i < ARRAY_SIZE(preimage_domain_tests); ++i) {
4244 umap1 = isl_union_map_read_from_str(ctx,
4245 preimage_domain_tests[i].map);
4246 ma = isl_multi_aff_read_from_str(ctx,
4247 preimage_domain_tests[i].ma);
4248 umap2 = isl_union_map_read_from_str(ctx,
4249 preimage_domain_tests[i].res);
4250 umap1 = isl_union_map_preimage_domain_multi_aff(umap1, ma);
4251 equal = isl_union_map_is_equal(umap1, umap2);
4252 isl_union_map_free(umap1);
4253 isl_union_map_free(umap2);
4254 if (equal < 0)
4255 return -1;
4256 if (!equal)
4257 isl_die(ctx, isl_error_unknown, "bad preimage",
4258 return -1);
4259 }
4260
4261 return 0;
4262 }
4263
4264 static int test_preimage(isl_ctx *ctx)
4265 {
4266 if (test_preimage_basic_set(ctx) < 0)
4267 return -1;
4268 if (test_preimage_union_map(ctx) < 0)
4269 return -1;
4270
4271 return 0;
4272 }
4273
4274 struct {
4275 const char *ma1;
4276 const char *ma;
4277 const char *res;
4278 } pullback_tests[] = {
4279 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
4280 "{ A[a,b] -> C[b + 2a] }" },
4281 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
4282 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
4283 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
4284 "{ A[a] -> C[(a)/6] }" },
4285 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
4286 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
4287 "{ A[a] -> C[(2a)/3] }" },
4288 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
4289 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
4290 "{ A[i,j] -> C[i + j, i + j] }"},
4291 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
4292 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
4293 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
4294 };
4295
4296 static int test_pullback(isl_ctx *ctx)
4297 {
4298 int i;
4299 isl_multi_aff *ma1, *ma2;
4300 isl_multi_aff *ma;
4301 int equal;
4302
4303 for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
4304 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
4305 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
4306 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
4307 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
4308 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
4309 isl_multi_aff_free(ma1);
4310 isl_multi_aff_free(ma2);
4311 if (equal < 0)
4312 return -1;
4313 if (!equal)
4314 isl_die(ctx, isl_error_unknown, "bad pullback",
4315 return -1);
4316 }
4317
4318 return 0;
4319 }
4320
4321 /* Check that negation is printed correctly.
4322 */
4323 static int test_ast(isl_ctx *ctx)
4324 {
4325 isl_ast_expr *expr, *expr1, *expr2, *expr3;
4326 char *str;
4327 int ok;
4328
4329 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
4330 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
4331 expr = isl_ast_expr_add(expr1, expr2);
4332 expr = isl_ast_expr_neg(expr);
4333 str = isl_ast_expr_to_str(expr);
4334 ok = str ? !strcmp(str, "-(A + B)") : -1;
4335 free(str);
4336 isl_ast_expr_free(expr);
4337
4338 if (ok < 0)
4339 return -1;
4340 if (!ok)
4341 isl_die(ctx, isl_error_unknown,
4342 "isl_ast_expr printed incorrectly", return -1);
4343
4344 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
4345 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
4346 expr = isl_ast_expr_add(expr1, expr2);
4347 expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
4348 expr = isl_ast_expr_sub(expr3, expr);
4349 str = isl_ast_expr_to_str(expr);
4350 ok = str ? !strcmp(str, "C - (A + B)") : -1;
4351 free(str);
4352 isl_ast_expr_free(expr);
4353
4354 if (ok < 0)
4355 return -1;
4356 if (!ok)
4357 isl_die(ctx, isl_error_unknown,
4358 "isl_ast_expr printed incorrectly", return -1);
4359
4360 return 0;
4361 }
4362
4363 /* Check that isl_ast_build_expr_from_set returns a valid expression
4364 * for an empty set. Note that isl_ast_build_expr_from_set getting
4365 * called on an empty set probably indicates a bug in the caller.
4366 */
4367 static int test_ast_build(isl_ctx *ctx)
4368 {
4369 isl_set *set;
4370 isl_ast_build *build;
4371 isl_ast_expr *expr;
4372
4373 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4374 build = isl_ast_build_from_context(set);
4375
4376 set = isl_set_empty(isl_space_params_alloc(ctx, 0));
4377 expr = isl_ast_build_expr_from_set(build, set);
4378
4379 isl_ast_expr_free(expr);
4380 isl_ast_build_free(build);
4381
4382 if (!expr)
4383 return -1;
4384
4385 return 0;
4386 }
4387
4388 /* Internal data structure for before_for and after_for callbacks.
4389 *
4390 * depth is the current depth
4391 * before is the number of times before_for has been called
4392 * after is the number of times after_for has been called
4393 */
4394 struct isl_test_codegen_data {
4395 int depth;
4396 int before;
4397 int after;
4398 };
4399
4400 /* This function is called before each for loop in the AST generated
4401 * from test_ast_gen1.
4402 *
4403 * Increment the number of calls and the depth.
4404 * Check that the space returned by isl_ast_build_get_schedule_space
4405 * matches the target space of the schedule returned by
4406 * isl_ast_build_get_schedule.
4407 * Return an isl_id that is checked by the corresponding call
4408 * to after_for.
4409 */
4410 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
4411 void *user)
4412 {
4413 struct isl_test_codegen_data *data = user;
4414 isl_ctx *ctx;
4415 isl_space *space;
4416 isl_union_map *schedule;
4417 isl_union_set *uset;
4418 isl_set *set;
4419 int empty;
4420 char name[] = "d0";
4421
4422 ctx = isl_ast_build_get_ctx(build);
4423
4424 if (data->before >= 3)
4425 isl_die(ctx, isl_error_unknown,
4426 "unexpected number of for nodes", return NULL);
4427 if (data->depth >= 2)
4428 isl_die(ctx, isl_error_unknown,
4429 "unexpected depth", return NULL);
4430
4431 snprintf(name, sizeof(name), "d%d", data->depth);
4432 data->before++;
4433 data->depth++;
4434
4435 schedule = isl_ast_build_get_schedule(build);
4436 uset = isl_union_map_range(schedule);
4437 if (!uset)
4438 return NULL;
4439 if (isl_union_set_n_set(uset) != 1) {
4440 isl_union_set_free(uset);
4441 isl_die(ctx, isl_error_unknown,
4442 "expecting single range space", return NULL);
4443 }
4444
4445 space = isl_ast_build_get_schedule_space(build);
4446 set = isl_union_set_extract_set(uset, space);
4447 isl_union_set_free(uset);
4448 empty = isl_set_is_empty(set);
4449 isl_set_free(set);
4450
4451 if (empty < 0)
4452 return NULL;
4453 if (empty)
4454 isl_die(ctx, isl_error_unknown,
4455 "spaces don't match", return NULL);
4456
4457 return isl_id_alloc(ctx, name, NULL);
4458 }
4459
4460 /* This function is called after each for loop in the AST generated
4461 * from test_ast_gen1.
4462 *
4463 * Increment the number of calls and decrement the depth.
4464 * Check that the annotation attached to the node matches
4465 * the isl_id returned by the corresponding call to before_for.
4466 */
4467 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
4468 __isl_keep isl_ast_build *build, void *user)
4469 {
4470 struct isl_test_codegen_data *data = user;
4471 isl_id *id;
4472 const char *name;
4473 int valid;
4474
4475 data->after++;
4476 data->depth--;
4477
4478 if (data->after > data->before)
4479 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4480 "mismatch in number of for nodes",
4481 return isl_ast_node_free(node));
4482
4483 id = isl_ast_node_get_annotation(node);
4484 if (!id)
4485 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4486 "missing annotation", return isl_ast_node_free(node));
4487
4488 name = isl_id_get_name(id);
4489 valid = name && atoi(name + 1) == data->depth;
4490 isl_id_free(id);
4491
4492 if (!valid)
4493 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4494 "wrong annotation", return isl_ast_node_free(node));
4495
4496 return node;
4497 }
4498
4499 /* Check that the before_each_for and after_each_for callbacks
4500 * are called for each for loop in the generated code,
4501 * that they are called in the right order and that the isl_id
4502 * returned from the before_each_for callback is attached to
4503 * the isl_ast_node passed to the corresponding after_each_for call.
4504 */
4505 static int test_ast_gen1(isl_ctx *ctx)
4506 {
4507 const char *str;
4508 isl_set *set;
4509 isl_union_map *schedule;
4510 isl_ast_build *build;
4511 isl_ast_node *tree;
4512 struct isl_test_codegen_data data;
4513
4514 str = "[N] -> { : N >= 10 }";
4515 set = isl_set_read_from_str(ctx, str);
4516 str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
4517 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
4518 schedule = isl_union_map_read_from_str(ctx, str);
4519
4520 data.before = 0;
4521 data.after = 0;
4522 data.depth = 0;
4523 build = isl_ast_build_from_context(set);
4524 build = isl_ast_build_set_before_each_for(build,
4525 &before_for, &data);
4526 build = isl_ast_build_set_after_each_for(build,
4527 &after_for, &data);
4528 tree = isl_ast_build_ast_from_schedule(build, schedule);
4529 isl_ast_build_free(build);
4530 if (!tree)
4531 return -1;
4532
4533 isl_ast_node_free(tree);
4534
4535 if (data.before != 3 || data.after != 3)
4536 isl_die(ctx, isl_error_unknown,
4537 "unexpected number of for nodes", return -1);
4538
4539 return 0;
4540 }
4541
4542 /* Check that the AST generator handles domains that are integrally disjoint
4543 * but not ratinoally disjoint.
4544 */
4545 static int test_ast_gen2(isl_ctx *ctx)
4546 {
4547 const char *str;
4548 isl_set *set;
4549 isl_union_map *schedule;
4550 isl_union_map *options;
4551 isl_ast_build *build;
4552 isl_ast_node *tree;
4553
4554 str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
4555 schedule = isl_union_map_read_from_str(ctx, str);
4556 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4557 build = isl_ast_build_from_context(set);
4558
4559 str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
4560 options = isl_union_map_read_from_str(ctx, str);
4561 build = isl_ast_build_set_options(build, options);
4562 tree = isl_ast_build_ast_from_schedule(build, schedule);
4563 isl_ast_build_free(build);
4564 if (!tree)
4565 return -1;
4566 isl_ast_node_free(tree);
4567
4568 return 0;
4569 }
4570
4571 /* Increment *user on each call.
4572 */
4573 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
4574 __isl_keep isl_ast_build *build, void *user)
4575 {
4576 int *n = user;
4577
4578 (*n)++;
4579
4580 return node;
4581 }
4582
4583 /* Test that unrolling tries to minimize the number of instances.
4584 * In particular, for the schedule given below, make sure it generates
4585 * 3 nodes (rather than 101).
4586 */
4587 static int test_ast_gen3(isl_ctx *ctx)
4588 {
4589 const char *str;
4590 isl_set *set;
4591 isl_union_map *schedule;
4592 isl_union_map *options;
4593 isl_ast_build *build;
4594 isl_ast_node *tree;
4595 int n_domain = 0;
4596
4597 str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
4598 schedule = isl_union_map_read_from_str(ctx, str);
4599 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4600
4601 str = "{ [i] -> unroll[0] }";
4602 options = isl_union_map_read_from_str(ctx, str);
4603
4604 build = isl_ast_build_from_context(set);
4605 build = isl_ast_build_set_options(build, options);
4606 build = isl_ast_build_set_at_each_domain(build,
4607 &count_domains, &n_domain);
4608 tree = isl_ast_build_ast_from_schedule(build, schedule);
4609 isl_ast_build_free(build);
4610 if (!tree)
4611 return -1;
4612
4613 isl_ast_node_free(tree);
4614
4615 if (n_domain != 3)
4616 isl_die(ctx, isl_error_unknown,
4617 "unexpected number of for nodes", return -1);
4618
4619 return 0;
4620 }
4621
4622 /* Check that if the ast_build_exploit_nested_bounds options is set,
4623 * we do not get an outer if node in the generated AST,
4624 * while we do get such an outer if node if the options is not set.
4625 */
4626 static int test_ast_gen4(isl_ctx *ctx)
4627 {
4628 const char *str;
4629 isl_set *set;
4630 isl_union_map *schedule;
4631 isl_ast_build *build;
4632 isl_ast_node *tree;
4633 enum isl_ast_node_type type;
4634 int enb;
4635
4636 enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
4637 str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
4638
4639 isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
4640
4641 schedule = isl_union_map_read_from_str(ctx, str);
4642 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4643 build = isl_ast_build_from_context(set);
4644 tree = isl_ast_build_ast_from_schedule(build, schedule);
4645 isl_ast_build_free(build);
4646 if (!tree)
4647 return -1;
4648
4649 type = isl_ast_node_get_type(tree);
4650 isl_ast_node_free(tree);
4651
4652 if (type == isl_ast_node_if)
4653 isl_die(ctx, isl_error_unknown,
4654 "not expecting if node", return -1);
4655
4656 isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
4657
4658 schedule = isl_union_map_read_from_str(ctx, str);
4659 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4660 build = isl_ast_build_from_context(set);
4661 tree = isl_ast_build_ast_from_schedule(build, schedule);
4662 isl_ast_build_free(build);
4663 if (!tree)
4664 return -1;
4665
4666 type = isl_ast_node_get_type(tree);
4667 isl_ast_node_free(tree);
4668
4669 if (type != isl_ast_node_if)
4670 isl_die(ctx, isl_error_unknown,
4671 "expecting if node", return -1);
4672
4673 isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
4674
4675 return 0;
4676 }
4677
4678 /* This function is called for each leaf in the AST generated
4679 * from test_ast_gen5.
4680 *
4681 * We finalize the AST generation by extending the outer schedule
4682 * with a zero-dimensional schedule. If this results in any for loops,
4683 * then this means that we did not pass along enough information
4684 * about the outer schedule to the inner AST generation.
4685 */
4686 static __isl_give isl_ast_node *create_leaf(__isl_take isl_ast_build *build,
4687 void *user)
4688 {
4689 isl_union_map *schedule, *extra;
4690 isl_ast_node *tree;
4691
4692 schedule = isl_ast_build_get_schedule(build);
4693 extra = isl_union_map_copy(schedule);
4694 extra = isl_union_map_from_domain(isl_union_map_domain(extra));
4695 schedule = isl_union_map_range_product(schedule, extra);
4696 tree = isl_ast_build_ast_from_schedule(build, schedule);
4697 isl_ast_build_free(build);
4698
4699 if (!tree)
4700 return NULL;
4701
4702 if (isl_ast_node_get_type(tree) == isl_ast_node_for)
4703 isl_die(isl_ast_node_get_ctx(tree), isl_error_unknown,
4704 "code should not contain any for loop",
4705 return isl_ast_node_free(tree));
4706
4707 return tree;
4708 }
4709
4710 /* Check that we do not lose any information when going back and
4711 * forth between internal and external schedule.
4712 *
4713 * In particular, we create an AST where we unroll the only
4714 * non-constant dimension in the schedule. We therefore do
4715 * not expect any for loops in the AST. However, older versions
4716 * of isl would not pass along enough information about the outer
4717 * schedule when performing an inner code generation from a create_leaf
4718 * callback, resulting in the inner code generation producing a for loop.
4719 */
4720 static int test_ast_gen5(isl_ctx *ctx)
4721 {
4722 const char *str;
4723 isl_set *set;
4724 isl_union_map *schedule, *options;
4725 isl_ast_build *build;
4726 isl_ast_node *tree;
4727
4728 str = "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
4729 schedule = isl_union_map_read_from_str(ctx, str);
4730
4731 str = "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
4732 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
4733 options = isl_union_map_read_from_str(ctx, str);
4734
4735 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4736 build = isl_ast_build_from_context(set);
4737 build = isl_ast_build_set_options(build, options);
4738 build = isl_ast_build_set_create_leaf(build, &create_leaf, NULL);
4739 tree = isl_ast_build_ast_from_schedule(build, schedule);
4740 isl_ast_build_free(build);
4741 isl_ast_node_free(tree);
4742 if (!tree)
4743 return -1;
4744
4745 return 0;
4746 }
4747
4748 static int test_ast_gen(isl_ctx *ctx)
4749 {
4750 if (test_ast_gen1(ctx) < 0)
4751 return -1;
4752 if (test_ast_gen2(ctx) < 0)
4753 return -1;
4754 if (test_ast_gen3(ctx) < 0)
4755 return -1;
4756 if (test_ast_gen4(ctx) < 0)
4757 return -1;
4758 if (test_ast_gen5(ctx) < 0)
4759 return -1;
4760 return 0;
4761 }
4762
4763 /* Check if dropping output dimensions from an isl_pw_multi_aff
4764 * works properly.
4765 */
4766 static int test_pw_multi_aff(isl_ctx *ctx)
4767 {
4768 const char *str;
4769 isl_pw_multi_aff *pma1, *pma2;
4770 int equal;
4771
4772 str = "{ [i,j] -> [i+j, 4i-j] }";
4773 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
4774 str = "{ [i,j] -> [4i-j] }";
4775 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
4776
4777 pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
4778
4779 equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
4780
4781 isl_pw_multi_aff_free(pma1);
4782 isl_pw_multi_aff_free(pma2);
4783 if (equal < 0)
4784 return -1;
4785 if (!equal)
4786 isl_die(ctx, isl_error_unknown,
4787 "expressions not equal", return -1);
4788
4789 return 0;
4790 }
4791
4792 /* Check that we can properly parse multi piecewise affine expressions
4793 * where the piecewise affine expressions have different domains.
4794 */
4795 static int test_multi_pw_aff(isl_ctx *ctx)
4796 {
4797 const char *str;
4798 isl_set *dom, *dom2;
4799 isl_multi_pw_aff *mpa1, *mpa2;
4800 isl_pw_aff *pa;
4801 int equal;
4802 int equal_domain;
4803
4804 mpa1 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [i] }");
4805 dom = isl_set_read_from_str(ctx, "{ [i] : i > 0 }");
4806 mpa1 = isl_multi_pw_aff_intersect_domain(mpa1, dom);
4807 mpa2 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [2i] }");
4808 mpa2 = isl_multi_pw_aff_flat_range_product(mpa1, mpa2);
4809 str = "{ [i] -> [(i : i > 0), 2i] }";
4810 mpa1 = isl_multi_pw_aff_read_from_str(ctx, str);
4811
4812 equal = isl_multi_pw_aff_plain_is_equal(mpa1, mpa2);
4813
4814 pa = isl_multi_pw_aff_get_pw_aff(mpa1, 0);
4815 dom = isl_pw_aff_domain(pa);
4816 pa = isl_multi_pw_aff_get_pw_aff(mpa1, 1);
4817 dom2 = isl_pw_aff_domain(pa);
4818 equal_domain = isl_set_is_equal(dom, dom2);
4819
4820 isl_set_free(dom);
4821 isl_set_free(dom2);
4822 isl_multi_pw_aff_free(mpa1);
4823 isl_multi_pw_aff_free(mpa2);
4824
4825 if (equal < 0)
4826 return -1;
4827 if (!equal)
4828 isl_die(ctx, isl_error_unknown,
4829 "expressions not equal", return -1);
4830
4831 if (equal_domain < 0)
4832 return -1;
4833 if (equal_domain)
4834 isl_die(ctx, isl_error_unknown,
4835 "domains unexpectedly equal", return -1);
4836
4837 return 0;
4838 }
4839
4840 /* This is a regression test for a bug where isl_basic_map_simplify
4841 * would end up in an infinite loop. In particular, we construct
4842 * an empty basic set that is not obviously empty.
4843 * isl_basic_set_is_empty marks the basic set as empty.
4844 * After projecting out i3, the variable can be dropped completely,
4845 * but isl_basic_map_simplify refrains from doing so if the basic set
4846 * is empty and would end up in an infinite loop if it didn't test
4847 * explicitly for empty basic maps in the outer loop.
4848 */
4849 static int test_simplify(isl_ctx *ctx)
4850 {
4851 const char *str;
4852 isl_basic_set *bset;
4853 int empty;
4854
4855 str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
4856 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
4857 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
4858 "i3 >= i2 }";
4859 bset = isl_basic_set_read_from_str(ctx, str);
4860 empty = isl_basic_set_is_empty(bset);
4861 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
4862 isl_basic_set_free(bset);
4863 if (!bset)
4864 return -1;
4865 if (!empty)
4866 isl_die(ctx, isl_error_unknown,
4867 "basic set should be empty", return -1);
4868
4869 return 0;
4870 }
4871
4872 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
4873 * with gbr context would fail to disable the use of the shifted tableau
4874 * when transferring equalities for the input to the context, resulting
4875 * in invalid sample values.
4876 */
4877 static int test_partial_lexmin(isl_ctx *ctx)
4878 {
4879 const char *str;
4880 isl_basic_set *bset;
4881 isl_basic_map *bmap;
4882 isl_map *map;
4883
4884 str = "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
4885 bmap = isl_basic_map_read_from_str(ctx, str);
4886 str = "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
4887 bset = isl_basic_set_read_from_str(ctx, str);
4888 map = isl_basic_map_partial_lexmin(bmap, bset, NULL);
4889 isl_map_free(map);
4890
4891 if (!map)
4892 return -1;
4893
4894 return 0;
4895 }
4896
4897 /* Check that the variable compression performed on the existentially
4898 * quantified variables inside isl_basic_set_compute_divs is not confused
4899 * by the implicit equalities among the parameters.
4900 */
4901 static int test_compute_divs(isl_ctx *ctx)
4902 {
4903 const char *str;
4904 isl_basic_set *bset;
4905 isl_set *set;
4906
4907 str = "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
4908 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
4909 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
4910 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
4911 bset = isl_basic_set_read_from_str(ctx, str);
4912 set = isl_basic_set_compute_divs(bset);
4913 isl_set_free(set);
4914 if (!set)
4915 return -1;
4916
4917 return 0;
4918 }
4919
4920 struct {
4921 const char *set;
4922 const char *dual;
4923 } coef_tests[] = {
4924 { "{ rat: [i] : 0 <= i <= 10 }",
4925 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
4926 { "{ rat: [i] : FALSE }",
4927 "{ rat: coefficients[[cst] -> [a]] }" },
4928 { "{ rat: [i] : }",
4929 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
4930 };
4931
4932 struct {
4933 const char *set;
4934 const char *dual;
4935 } sol_tests[] = {
4936 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
4937 "{ rat: [i] : 0 <= i <= 10 }" },
4938 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
4939 "{ rat: [i] }" },
4940 { "{ rat: coefficients[[cst] -> [a]] }",
4941 "{ rat: [i] : FALSE }" },
4942 };
4943
4944 /* Test the basic functionality of isl_basic_set_coefficients and
4945 * isl_basic_set_solutions.
4946 */
4947 static int test_dual(isl_ctx *ctx)
4948 {
4949 int i;
4950
4951 for (i = 0; i < ARRAY_SIZE(coef_tests); ++i) {
4952 int equal;
4953 isl_basic_set *bset1, *bset2;
4954
4955 bset1 = isl_basic_set_read_from_str(ctx, coef_tests[i].set);
4956 bset2 = isl_basic_set_read_from_str(ctx, coef_tests[i].dual);
4957 bset1 = isl_basic_set_coefficients(bset1);
4958 equal = isl_basic_set_is_equal(bset1, bset2);
4959 isl_basic_set_free(bset1);
4960 isl_basic_set_free(bset2);
4961 if (equal < 0)
4962 return -1;
4963 if (!equal)
4964 isl_die(ctx, isl_error_unknown,
4965 "incorrect dual", return -1);
4966 }
4967
4968 for (i = 0; i < ARRAY_SIZE(sol_tests); ++i) {
4969 int equal;
4970 isl_basic_set *bset1, *bset2;
4971
4972 bset1 = isl_basic_set_read_from_str(ctx, sol_tests[i].set);
4973 bset2 = isl_basic_set_read_from_str(ctx, sol_tests[i].dual);
4974 bset1 = isl_basic_set_solutions(bset1);
4975 equal = isl_basic_set_is_equal(bset1, bset2);
4976 isl_basic_set_free(bset1);
4977 isl_basic_set_free(bset2);
4978 if (equal < 0)
4979 return -1;
4980 if (!equal)
4981 isl_die(ctx, isl_error_unknown,
4982 "incorrect dual", return -1);
4983 }
4984
4985 return 0;
4986 }
4987
4988 struct {
4989 const char *name;
4990 int (*fn)(isl_ctx *ctx);
4991 } tests [] = {
4992 { "dual", &test_dual },
4993 { "dependence analysis", &test_flow },
4994 { "val", &test_val },
4995 { "compute divs", &test_compute_divs },
4996 { "partial lexmin", &test_partial_lexmin },
4997 { "simplify", &test_simplify },
4998 { "curry", &test_curry },
4999 { "piecewise multi affine expressions", &test_pw_multi_aff },
5000 { "multi piecewise affine expressions", &test_multi_pw_aff },
5001 { "conversion", &test_conversion },
5002 { "list", &test_list },
5003 { "align parameters", &test_align_parameters },
5004 { "preimage", &test_preimage },
5005 { "pullback", &test_pullback },
5006 { "AST", &test_ast },
5007 { "AST build", &test_ast_build },
5008 { "AST generation", &test_ast_gen },
5009 { "eliminate", &test_eliminate },
5010 { "residue class", &test_residue_class },
5011 { "div", &test_div },
5012 { "slice", &test_slice },
5013 { "fixed power", &test_fixed_power },
5014 { "sample", &test_sample },
5015 { "output", &test_output },
5016 { "vertices", &test_vertices },
5017 { "fixed", &test_fixed },
5018 { "equal", &test_equal },
5019 { "disjoint", &test_disjoint },
5020 { "product", &test_product },
5021 { "dim_max", &test_dim_max },
5022 { "affine", &test_aff },
5023 { "injective", &test_injective },
5024 { "schedule", &test_schedule },
5025 { "union_pw", &test_union_pw },
5026 { "parse", &test_parse },
5027 { "single-valued", &test_sv },
5028 { "affine hull", &test_affine_hull },
5029 { "coalesce", &test_coalesce },
5030 { "factorize", &test_factorize },
5031 { "subset", &test_subset },
5032 { "subtract", &test_subtract },
5033 { "lexmin", &test_lexmin },
5034 { "min", &test_min },
5035 { "gist", &test_gist },
5036 { "piecewise quasi-polynomials", &test_pwqp },
5037 };
5038
5039 int main()
5040 {
5041 int i;
5042 struct isl_ctx *ctx;
5043
5044 srcdir = getenv("srcdir");
5045 assert(srcdir);
5046
5047 ctx = isl_ctx_alloc();
5048 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
5049 printf("%s\n", tests[i].name);
5050 if (tests[i].fn(ctx) < 0)
5051 goto error;
5052 }
5053 test_lift(ctx);
5054 test_bound(ctx);
5055 test_union(ctx);
5056 test_split_periods(ctx);
5057 test_lex(ctx);
5058 test_bijective(ctx);
5059 test_dep(ctx);
5060 test_read(ctx);
5061 test_bounded(ctx);
5062 test_construction(ctx);
5063 test_dim(ctx);
5064 test_application(ctx);
5065 test_convex_hull(ctx);
5066 test_closure(ctx);
5067 isl_ctx_free(ctx);
5068 return 0;
5069 error:
5070 isl_ctx_free(ctx);
5071 return -1;
5072 }
Integer set library