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isl_map_coalesce: check for subsets with smaller number of divs
[isl.git] / isl_test.c
blob299c75ebb68929dcc44b018feea9a913317ca4aa
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
6 *
7 * Use of this software is governed by the MIT license
8 *
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
12 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
15 * B.P. 105 - 78153 Le Chesnay, France
16 */
17
18 #include <assert.h>
19 #include <stdio.h>
20 #include <limits.h>
21 #include <isl_ctx_private.h>
22 #include <isl_map_private.h>
23 #include <isl_aff_private.h>
24 #include <isl/set.h>
25 #include <isl/flow.h>
26 #include <isl_constraint_private.h>
27 #include <isl/polynomial.h>
28 #include <isl/union_map.h>
29 #include <isl_factorization.h>
30 #include <isl/schedule.h>
31 #include <isl_options_private.h>
32 #include <isl/vertices.h>
33 #include <isl/ast_build.h>
34 #include <isl/val.h>
35 #include <isl/ilp.h>
36 #include <isl_ast_build_expr.h>
37 #include <isl/options.h>
38
39 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
40
41 static char *srcdir;
42
43 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
44 char *filename;
45 int length;
46 char *pattern = "%s/test_inputs/%s.%s";
47
48 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
49 + strlen(suffix) + 1;
50 filename = isl_alloc_array(ctx, char, length);
51
52 if (!filename)
53 return NULL;
54
55 sprintf(filename, pattern, srcdir, name, suffix);
56
57 return filename;
58 }
59
60 void test_parse_map(isl_ctx *ctx, const char *str)
61 {
62 isl_map *map;
63
64 map = isl_map_read_from_str(ctx, str);
65 assert(map);
66 isl_map_free(map);
67 }
68
69 int test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
70 {
71 isl_map *map, *map2;
72 int equal;
73
74 map = isl_map_read_from_str(ctx, str);
75 map2 = isl_map_read_from_str(ctx, str2);
76 equal = isl_map_is_equal(map, map2);
77 isl_map_free(map);
78 isl_map_free(map2);
79
80 if (equal < 0)
81 return -1;
82 if (!equal)
83 isl_die(ctx, isl_error_unknown, "maps not equal",
84 return -1);
85
86 return 0;
87 }
88
89 void test_parse_pwqp(isl_ctx *ctx, const char *str)
90 {
91 isl_pw_qpolynomial *pwqp;
92
93 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
94 assert(pwqp);
95 isl_pw_qpolynomial_free(pwqp);
96 }
97
98 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
99 {
100 isl_pw_aff *pwaff;
101
102 pwaff = isl_pw_aff_read_from_str(ctx, str);
103 assert(pwaff);
104 isl_pw_aff_free(pwaff);
105 }
106
107 int test_parse(struct isl_ctx *ctx)
108 {
109 isl_map *map, *map2;
110 const char *str, *str2;
111
112 str = "{ [i] -> [-i] }";
113 map = isl_map_read_from_str(ctx, str);
114 assert(map);
115 isl_map_free(map);
116
117 str = "{ A[i] -> L[([i/3])] }";
118 map = isl_map_read_from_str(ctx, str);
119 assert(map);
120 isl_map_free(map);
121
122 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
123 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
124 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
125
126 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
127 str2 = "{ [x, y] : 2y >= 6 - x }";
128 if (test_parse_map_equal(ctx, str, str2) < 0)
129 return -1;
130
131 if (test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
132 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
133 return -1;
134 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
135 if (test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }",
136 str) < 0)
137 return -1;
138
139 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
140 map = isl_map_read_from_str(ctx, str);
141 str = "{ [new, old] -> [o0, o1] : "
142 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
143 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
144 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
145 map2 = isl_map_read_from_str(ctx, str);
146 assert(isl_map_is_equal(map, map2));
147 isl_map_free(map);
148 isl_map_free(map2);
149
150 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
151 map = isl_map_read_from_str(ctx, str);
152 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
153 map2 = isl_map_read_from_str(ctx, str);
154 assert(isl_map_is_equal(map, map2));
155 isl_map_free(map);
156 isl_map_free(map2);
157
158 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
159 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
160 if (test_parse_map_equal(ctx, str, str2) < 0)
161 return -1;
162
163 str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
164 str2 = "{ [i,j] -> [min(i,j)] }";
165 if (test_parse_map_equal(ctx, str, str2) < 0)
166 return -1;
167
168 str = "{ [i,j] : i != j }";
169 str2 = "{ [i,j] : i < j or i > j }";
170 if (test_parse_map_equal(ctx, str, str2) < 0)
171 return -1;
172
173 str = "{ [i,j] : (i+1)*2 >= j }";
174 str2 = "{ [i, j] : j <= 2 + 2i }";
175 if (test_parse_map_equal(ctx, str, str2) < 0)
176 return -1;
177
178 str = "{ [i] -> [i > 0 ? 4 : 5] }";
179 str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
180 if (test_parse_map_equal(ctx, str, str2) < 0)
181 return -1;
182
183 str = "[N=2,M] -> { [i=[(M+N)/4]] }";
184 str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
185 if (test_parse_map_equal(ctx, str, str2) < 0)
186 return -1;
187
188 str = "{ [x] : x >= 0 }";
189 str2 = "{ [x] : x-0 >= 0 }";
190 if (test_parse_map_equal(ctx, str, str2) < 0)
191 return -1;
192
193 str = "{ [i] : ((i > 10)) }";
194 str2 = "{ [i] : i >= 11 }";
195 if (test_parse_map_equal(ctx, str, str2) < 0)
196 return -1;
197
198 str = "{ [i] -> [0] }";
199 str2 = "{ [i] -> [0 * i] }";
200 if (test_parse_map_equal(ctx, str, str2) < 0)
201 return -1;
202
203 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
204 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
205 test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
206 test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
207
208 if (test_parse_map_equal(ctx, "{ [a] -> [b] : (not false) }",
209 "{ [a] -> [b] : true }") < 0)
210 return -1;
211
212 if (test_parse_map_equal(ctx, "{ [i] : i/2 <= 5 }",
213 "{ [i] : i <= 10 }") < 0)
214 return -1;
215
216 if (test_parse_map_equal(ctx, "{Sym=[n] [i] : i <= n }",
217 "[n] -> { [i] : i <= n }") < 0)
218 return -1;
219
220 if (test_parse_map_equal(ctx, "{ [*] }", "{ [a] }") < 0)
221 return -1;
222
223 if (test_parse_map_equal(ctx, "{ [i] : 2*floor(i/2) = i }",
224 "{ [i] : exists a : i = 2 a }") < 0)
225 return -1;
226
227 if (test_parse_map_equal(ctx, "{ [a] -> [b] : a = 5 implies b = 5 }",
228 "{ [a] -> [b] : a != 5 or b = 5 }") < 0)
229 return -1;
230
231 if (test_parse_map_equal(ctx, "{ [a] -> [a - 1 : a > 0] }",
232 "{ [a] -> [a - 1] : a > 0 }") < 0)
233 return -1;
234 if (test_parse_map_equal(ctx,
235 "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
236 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : 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 if (test_parse_map_equal(ctx,
251 "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
252 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
253 return -1;
254
255 return 0;
256 }
257
258 void test_read(struct isl_ctx *ctx)
259 {
260 char *filename;
261 FILE *input;
262 struct isl_basic_set *bset1, *bset2;
263 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
264
265 filename = get_filename(ctx, "set", "omega");
266 assert(filename);
267 input = fopen(filename, "r");
268 assert(input);
269
270 bset1 = isl_basic_set_read_from_file(ctx, input);
271 bset2 = isl_basic_set_read_from_str(ctx, str);
272
273 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
274
275 isl_basic_set_free(bset1);
276 isl_basic_set_free(bset2);
277 free(filename);
278
279 fclose(input);
280 }
281
282 void test_bounded(struct isl_ctx *ctx)
283 {
284 isl_set *set;
285 int bounded;
286
287 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
288 bounded = isl_set_is_bounded(set);
289 assert(bounded);
290 isl_set_free(set);
291
292 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
293 bounded = isl_set_is_bounded(set);
294 assert(!bounded);
295 isl_set_free(set);
296
297 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
298 bounded = isl_set_is_bounded(set);
299 assert(!bounded);
300 isl_set_free(set);
301 }
302
303 /* Construct the basic set { [i] : 5 <= i <= N } */
304 void test_construction(struct isl_ctx *ctx)
305 {
306 isl_int v;
307 isl_space *dim;
308 isl_local_space *ls;
309 struct isl_basic_set *bset;
310 struct isl_constraint *c;
311
312 isl_int_init(v);
313
314 dim = isl_space_set_alloc(ctx, 1, 1);
315 bset = isl_basic_set_universe(isl_space_copy(dim));
316 ls = isl_local_space_from_space(dim);
317
318 c = isl_inequality_alloc(isl_local_space_copy(ls));
319 isl_int_set_si(v, -1);
320 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
321 isl_int_set_si(v, 1);
322 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
323 bset = isl_basic_set_add_constraint(bset, c);
324
325 c = isl_inequality_alloc(isl_local_space_copy(ls));
326 isl_int_set_si(v, 1);
327 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
328 isl_int_set_si(v, -5);
329 isl_constraint_set_constant(c, v);
330 bset = isl_basic_set_add_constraint(bset, c);
331
332 isl_local_space_free(ls);
333 isl_basic_set_free(bset);
334
335 isl_int_clear(v);
336 }
337
338 void test_dim(struct isl_ctx *ctx)
339 {
340 const char *str;
341 isl_map *map1, *map2;
342
343 map1 = isl_map_read_from_str(ctx,
344 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
345 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
346 map2 = isl_map_read_from_str(ctx,
347 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
348 assert(isl_map_is_equal(map1, map2));
349 isl_map_free(map2);
350
351 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
352 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
353 assert(isl_map_is_equal(map1, map2));
354
355 isl_map_free(map1);
356 isl_map_free(map2);
357
358 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
359 map1 = isl_map_read_from_str(ctx, str);
360 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
361 map2 = isl_map_read_from_str(ctx, str);
362 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
363 assert(isl_map_is_equal(map1, map2));
364
365 isl_map_free(map1);
366 isl_map_free(map2);
367 }
368
369 struct {
370 __isl_give isl_val *(*op)(__isl_take isl_val *v);
371 const char *arg;
372 const char *res;
373 } val_un_tests[] = {
374 { &isl_val_neg, "0", "0" },
375 { &isl_val_abs, "0", "0" },
376 { &isl_val_2exp, "0", "1" },
377 { &isl_val_floor, "0", "0" },
378 { &isl_val_ceil, "0", "0" },
379 { &isl_val_neg, "1", "-1" },
380 { &isl_val_neg, "-1", "1" },
381 { &isl_val_neg, "1/2", "-1/2" },
382 { &isl_val_neg, "-1/2", "1/2" },
383 { &isl_val_neg, "infty", "-infty" },
384 { &isl_val_neg, "-infty", "infty" },
385 { &isl_val_neg, "NaN", "NaN" },
386 { &isl_val_abs, "1", "1" },
387 { &isl_val_abs, "-1", "1" },
388 { &isl_val_abs, "1/2", "1/2" },
389 { &isl_val_abs, "-1/2", "1/2" },
390 { &isl_val_abs, "infty", "infty" },
391 { &isl_val_abs, "-infty", "infty" },
392 { &isl_val_abs, "NaN", "NaN" },
393 { &isl_val_floor, "1", "1" },
394 { &isl_val_floor, "-1", "-1" },
395 { &isl_val_floor, "1/2", "0" },
396 { &isl_val_floor, "-1/2", "-1" },
397 { &isl_val_floor, "infty", "infty" },
398 { &isl_val_floor, "-infty", "-infty" },
399 { &isl_val_floor, "NaN", "NaN" },
400 { &isl_val_ceil, "1", "1" },
401 { &isl_val_ceil, "-1", "-1" },
402 { &isl_val_ceil, "1/2", "1" },
403 { &isl_val_ceil, "-1/2", "0" },
404 { &isl_val_ceil, "infty", "infty" },
405 { &isl_val_ceil, "-infty", "-infty" },
406 { &isl_val_ceil, "NaN", "NaN" },
407 { &isl_val_2exp, "-3", "1/8" },
408 { &isl_val_2exp, "-1", "1/2" },
409 { &isl_val_2exp, "1", "2" },
410 { &isl_val_2exp, "2", "4" },
411 { &isl_val_2exp, "3", "8" },
412 { &isl_val_inv, "1", "1" },
413 { &isl_val_inv, "2", "1/2" },
414 { &isl_val_inv, "1/2", "2" },
415 { &isl_val_inv, "-2", "-1/2" },
416 { &isl_val_inv, "-1/2", "-2" },
417 { &isl_val_inv, "0", "NaN" },
418 { &isl_val_inv, "NaN", "NaN" },
419 { &isl_val_inv, "infty", "0" },
420 { &isl_val_inv, "-infty", "0" },
421 };
422
423 /* Perform some basic tests of unary operations on isl_val objects.
424 */
425 static int test_un_val(isl_ctx *ctx)
426 {
427 int i;
428 isl_val *v, *res;
429 __isl_give isl_val *(*fn)(__isl_take isl_val *v);
430 int ok;
431
432 for (i = 0; i < ARRAY_SIZE(val_un_tests); ++i) {
433 v = isl_val_read_from_str(ctx, val_un_tests[i].arg);
434 res = isl_val_read_from_str(ctx, val_un_tests[i].res);
435 fn = val_un_tests[i].op;
436 v = fn(v);
437 if (isl_val_is_nan(res))
438 ok = isl_val_is_nan(v);
439 else
440 ok = isl_val_eq(v, res);
441 isl_val_free(v);
442 isl_val_free(res);
443 if (ok < 0)
444 return -1;
445 if (!ok)
446 isl_die(ctx, isl_error_unknown,
447 "unexpected result", return -1);
448 }
449
450 return 0;
451 }
452
453 struct {
454 __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
455 __isl_take isl_val *v2);
456 } val_bin_op[] = {
457 ['+'] = { &isl_val_add },
458 ['-'] = { &isl_val_sub },
459 ['*'] = { &isl_val_mul },
460 ['/'] = { &isl_val_div },
461 ['g'] = { &isl_val_gcd },
462 ['m'] = { &isl_val_min },
463 ['M'] = { &isl_val_max },
464 };
465
466 struct {
467 const char *arg1;
468 unsigned char op;
469 const char *arg2;
470 const char *res;
471 } val_bin_tests[] = {
472 { "0", '+', "0", "0" },
473 { "1", '+', "0", "1" },
474 { "1", '+', "1", "2" },
475 { "1", '-', "1", "0" },
476 { "1", '*', "1", "1" },
477 { "1", '/', "1", "1" },
478 { "2", '*', "3", "6" },
479 { "2", '*', "1/2", "1" },
480 { "2", '*', "1/3", "2/3" },
481 { "2/3", '*', "3/5", "2/5" },
482 { "2/3", '*', "7/5", "14/15" },
483 { "2", '/', "1/2", "4" },
484 { "-2", '/', "-1/2", "4" },
485 { "-2", '/', "1/2", "-4" },
486 { "2", '/', "-1/2", "-4" },
487 { "2", '/', "2", "1" },
488 { "2", '/', "3", "2/3" },
489 { "2/3", '/', "5/3", "2/5" },
490 { "2/3", '/', "5/7", "14/15" },
491 { "0", '/', "0", "NaN" },
492 { "42", '/', "0", "NaN" },
493 { "-42", '/', "0", "NaN" },
494 { "infty", '/', "0", "NaN" },
495 { "-infty", '/', "0", "NaN" },
496 { "NaN", '/', "0", "NaN" },
497 { "0", '/', "NaN", "NaN" },
498 { "42", '/', "NaN", "NaN" },
499 { "-42", '/', "NaN", "NaN" },
500 { "infty", '/', "NaN", "NaN" },
501 { "-infty", '/', "NaN", "NaN" },
502 { "NaN", '/', "NaN", "NaN" },
503 { "0", '/', "infty", "0" },
504 { "42", '/', "infty", "0" },
505 { "-42", '/', "infty", "0" },
506 { "infty", '/', "infty", "NaN" },
507 { "-infty", '/', "infty", "NaN" },
508 { "NaN", '/', "infty", "NaN" },
509 { "0", '/', "-infty", "0" },
510 { "42", '/', "-infty", "0" },
511 { "-42", '/', "-infty", "0" },
512 { "infty", '/', "-infty", "NaN" },
513 { "-infty", '/', "-infty", "NaN" },
514 { "NaN", '/', "-infty", "NaN" },
515 { "1", '-', "1/3", "2/3" },
516 { "1/3", '+', "1/2", "5/6" },
517 { "1/2", '+', "1/2", "1" },
518 { "3/4", '-', "1/4", "1/2" },
519 { "1/2", '-', "1/3", "1/6" },
520 { "infty", '+', "42", "infty" },
521 { "infty", '+', "infty", "infty" },
522 { "42", '+', "infty", "infty" },
523 { "infty", '-', "infty", "NaN" },
524 { "infty", '*', "infty", "infty" },
525 { "infty", '*', "-infty", "-infty" },
526 { "-infty", '*', "infty", "-infty" },
527 { "-infty", '*', "-infty", "infty" },
528 { "0", '*', "infty", "NaN" },
529 { "1", '*', "infty", "infty" },
530 { "infty", '*', "0", "NaN" },
531 { "infty", '*', "42", "infty" },
532 { "42", '-', "infty", "-infty" },
533 { "infty", '+', "-infty", "NaN" },
534 { "4", 'g', "6", "2" },
535 { "5", 'g', "6", "1" },
536 { "42", 'm', "3", "3" },
537 { "42", 'M', "3", "42" },
538 { "3", 'm', "42", "3" },
539 { "3", 'M', "42", "42" },
540 { "42", 'm', "infty", "42" },
541 { "42", 'M', "infty", "infty" },
542 { "42", 'm', "-infty", "-infty" },
543 { "42", 'M', "-infty", "42" },
544 { "42", 'm', "NaN", "NaN" },
545 { "42", 'M', "NaN", "NaN" },
546 { "infty", 'm', "-infty", "-infty" },
547 { "infty", 'M', "-infty", "infty" },
548 };
549
550 /* Perform some basic tests of binary operations on isl_val objects.
551 */
552 static int test_bin_val(isl_ctx *ctx)
553 {
554 int i;
555 isl_val *v1, *v2, *res;
556 __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
557 __isl_take isl_val *v2);
558 int ok;
559
560 for (i = 0; i < ARRAY_SIZE(val_bin_tests); ++i) {
561 v1 = isl_val_read_from_str(ctx, val_bin_tests[i].arg1);
562 v2 = isl_val_read_from_str(ctx, val_bin_tests[i].arg2);
563 res = isl_val_read_from_str(ctx, val_bin_tests[i].res);
564 fn = val_bin_op[val_bin_tests[i].op].fn;
565 v1 = fn(v1, v2);
566 if (isl_val_is_nan(res))
567 ok = isl_val_is_nan(v1);
568 else
569 ok = isl_val_eq(v1, res);
570 isl_val_free(v1);
571 isl_val_free(res);
572 if (ok < 0)
573 return -1;
574 if (!ok)
575 isl_die(ctx, isl_error_unknown,
576 "unexpected result", return -1);
577 }
578
579 return 0;
580 }
581
582 /* Perform some basic tests on isl_val objects.
583 */
584 static int test_val(isl_ctx *ctx)
585 {
586 if (test_un_val(ctx) < 0)
587 return -1;
588 if (test_bin_val(ctx) < 0)
589 return -1;
590 return 0;
591 }
592
593 static int test_div(isl_ctx *ctx)
594 {
595 unsigned n;
596 const char *str;
597 int empty;
598 isl_int v;
599 isl_space *dim;
600 isl_set *set;
601 isl_local_space *ls;
602 struct isl_basic_set *bset;
603 struct isl_constraint *c;
604
605 isl_int_init(v);
606
607 /* test 1 */
608 dim = isl_space_set_alloc(ctx, 0, 3);
609 bset = isl_basic_set_universe(isl_space_copy(dim));
610 ls = isl_local_space_from_space(dim);
611
612 c = isl_equality_alloc(isl_local_space_copy(ls));
613 isl_int_set_si(v, -1);
614 isl_constraint_set_constant(c, v);
615 isl_int_set_si(v, 1);
616 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
617 isl_int_set_si(v, 3);
618 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
619 bset = isl_basic_set_add_constraint(bset, c);
620
621 c = isl_equality_alloc(isl_local_space_copy(ls));
622 isl_int_set_si(v, 1);
623 isl_constraint_set_constant(c, v);
624 isl_int_set_si(v, -1);
625 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
626 isl_int_set_si(v, 3);
627 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
628 bset = isl_basic_set_add_constraint(bset, c);
629
630 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
631
632 assert(bset && bset->n_div == 1);
633 isl_local_space_free(ls);
634 isl_basic_set_free(bset);
635
636 /* test 2 */
637 dim = isl_space_set_alloc(ctx, 0, 3);
638 bset = isl_basic_set_universe(isl_space_copy(dim));
639 ls = isl_local_space_from_space(dim);
640
641 c = isl_equality_alloc(isl_local_space_copy(ls));
642 isl_int_set_si(v, 1);
643 isl_constraint_set_constant(c, v);
644 isl_int_set_si(v, -1);
645 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
646 isl_int_set_si(v, 3);
647 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
648 bset = isl_basic_set_add_constraint(bset, c);
649
650 c = isl_equality_alloc(isl_local_space_copy(ls));
651 isl_int_set_si(v, -1);
652 isl_constraint_set_constant(c, v);
653 isl_int_set_si(v, 1);
654 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
655 isl_int_set_si(v, 3);
656 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
657 bset = isl_basic_set_add_constraint(bset, c);
658
659 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
660
661 assert(bset && bset->n_div == 1);
662 isl_local_space_free(ls);
663 isl_basic_set_free(bset);
664
665 /* test 3 */
666 dim = isl_space_set_alloc(ctx, 0, 3);
667 bset = isl_basic_set_universe(isl_space_copy(dim));
668 ls = isl_local_space_from_space(dim);
669
670 c = isl_equality_alloc(isl_local_space_copy(ls));
671 isl_int_set_si(v, 1);
672 isl_constraint_set_constant(c, v);
673 isl_int_set_si(v, -1);
674 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
675 isl_int_set_si(v, 3);
676 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
677 bset = isl_basic_set_add_constraint(bset, c);
678
679 c = isl_equality_alloc(isl_local_space_copy(ls));
680 isl_int_set_si(v, -3);
681 isl_constraint_set_constant(c, v);
682 isl_int_set_si(v, 1);
683 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
684 isl_int_set_si(v, 4);
685 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
686 bset = isl_basic_set_add_constraint(bset, c);
687
688 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
689
690 assert(bset && bset->n_div == 1);
691 isl_local_space_free(ls);
692 isl_basic_set_free(bset);
693
694 /* test 4 */
695 dim = isl_space_set_alloc(ctx, 0, 3);
696 bset = isl_basic_set_universe(isl_space_copy(dim));
697 ls = isl_local_space_from_space(dim);
698
699 c = isl_equality_alloc(isl_local_space_copy(ls));
700 isl_int_set_si(v, 2);
701 isl_constraint_set_constant(c, v);
702 isl_int_set_si(v, -1);
703 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
704 isl_int_set_si(v, 3);
705 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
706 bset = isl_basic_set_add_constraint(bset, c);
707
708 c = isl_equality_alloc(isl_local_space_copy(ls));
709 isl_int_set_si(v, -1);
710 isl_constraint_set_constant(c, v);
711 isl_int_set_si(v, 1);
712 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
713 isl_int_set_si(v, 6);
714 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
715 bset = isl_basic_set_add_constraint(bset, c);
716
717 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
718
719 assert(isl_basic_set_is_empty(bset));
720 isl_local_space_free(ls);
721 isl_basic_set_free(bset);
722
723 /* test 5 */
724 dim = isl_space_set_alloc(ctx, 0, 3);
725 bset = isl_basic_set_universe(isl_space_copy(dim));
726 ls = isl_local_space_from_space(dim);
727
728 c = isl_equality_alloc(isl_local_space_copy(ls));
729 isl_int_set_si(v, -1);
730 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
731 isl_int_set_si(v, 3);
732 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
733 bset = isl_basic_set_add_constraint(bset, c);
734
735 c = isl_equality_alloc(isl_local_space_copy(ls));
736 isl_int_set_si(v, 1);
737 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
738 isl_int_set_si(v, -3);
739 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
740 bset = isl_basic_set_add_constraint(bset, c);
741
742 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
743
744 assert(bset && bset->n_div == 0);
745 isl_basic_set_free(bset);
746 isl_local_space_free(ls);
747
748 /* test 6 */
749 dim = isl_space_set_alloc(ctx, 0, 3);
750 bset = isl_basic_set_universe(isl_space_copy(dim));
751 ls = isl_local_space_from_space(dim);
752
753 c = isl_equality_alloc(isl_local_space_copy(ls));
754 isl_int_set_si(v, -1);
755 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
756 isl_int_set_si(v, 6);
757 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
758 bset = isl_basic_set_add_constraint(bset, c);
759
760 c = isl_equality_alloc(isl_local_space_copy(ls));
761 isl_int_set_si(v, 1);
762 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
763 isl_int_set_si(v, -3);
764 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
765 bset = isl_basic_set_add_constraint(bset, c);
766
767 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
768
769 assert(bset && bset->n_div == 1);
770 isl_basic_set_free(bset);
771 isl_local_space_free(ls);
772
773 /* test 7 */
774 /* This test is a bit tricky. We set up an equality
775 * a + 3b + 3c = 6 e0
776 * Normalization of divs creates _two_ divs
777 * a = 3 e0
778 * c - b - e0 = 2 e1
779 * Afterwards e0 is removed again because it has coefficient -1
780 * and we end up with the original equality and div again.
781 * Perhaps we can avoid the introduction of this temporary div.
782 */
783 dim = isl_space_set_alloc(ctx, 0, 4);
784 bset = isl_basic_set_universe(isl_space_copy(dim));
785 ls = isl_local_space_from_space(dim);
786
787 c = isl_equality_alloc(isl_local_space_copy(ls));
788 isl_int_set_si(v, -1);
789 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
790 isl_int_set_si(v, -3);
791 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
792 isl_int_set_si(v, -3);
793 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
794 isl_int_set_si(v, 6);
795 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
796 bset = isl_basic_set_add_constraint(bset, c);
797
798 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
799
800 /* Test disabled for now */
801 /*
802 assert(bset && bset->n_div == 1);
803 */
804 isl_local_space_free(ls);
805 isl_basic_set_free(bset);
806
807 /* test 8 */
808 dim = isl_space_set_alloc(ctx, 0, 5);
809 bset = isl_basic_set_universe(isl_space_copy(dim));
810 ls = isl_local_space_from_space(dim);
811
812 c = isl_equality_alloc(isl_local_space_copy(ls));
813 isl_int_set_si(v, -1);
814 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
815 isl_int_set_si(v, -3);
816 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
817 isl_int_set_si(v, -3);
818 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
819 isl_int_set_si(v, 6);
820 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
821 bset = isl_basic_set_add_constraint(bset, c);
822
823 c = isl_equality_alloc(isl_local_space_copy(ls));
824 isl_int_set_si(v, -1);
825 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
826 isl_int_set_si(v, 1);
827 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
828 isl_int_set_si(v, 1);
829 isl_constraint_set_constant(c, v);
830 bset = isl_basic_set_add_constraint(bset, c);
831
832 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
833
834 /* Test disabled for now */
835 /*
836 assert(bset && bset->n_div == 1);
837 */
838 isl_local_space_free(ls);
839 isl_basic_set_free(bset);
840
841 /* test 9 */
842 dim = isl_space_set_alloc(ctx, 0, 4);
843 bset = isl_basic_set_universe(isl_space_copy(dim));
844 ls = isl_local_space_from_space(dim);
845
846 c = isl_equality_alloc(isl_local_space_copy(ls));
847 isl_int_set_si(v, 1);
848 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
849 isl_int_set_si(v, -1);
850 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
851 isl_int_set_si(v, -2);
852 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
853 bset = isl_basic_set_add_constraint(bset, c);
854
855 c = isl_equality_alloc(isl_local_space_copy(ls));
856 isl_int_set_si(v, -1);
857 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
858 isl_int_set_si(v, 3);
859 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
860 isl_int_set_si(v, 2);
861 isl_constraint_set_constant(c, v);
862 bset = isl_basic_set_add_constraint(bset, c);
863
864 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
865
866 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
867
868 assert(!isl_basic_set_is_empty(bset));
869
870 isl_local_space_free(ls);
871 isl_basic_set_free(bset);
872
873 /* test 10 */
874 dim = isl_space_set_alloc(ctx, 0, 3);
875 bset = isl_basic_set_universe(isl_space_copy(dim));
876 ls = isl_local_space_from_space(dim);
877
878 c = isl_equality_alloc(isl_local_space_copy(ls));
879 isl_int_set_si(v, 1);
880 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
881 isl_int_set_si(v, -2);
882 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
883 bset = isl_basic_set_add_constraint(bset, c);
884
885 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
886
887 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
888
889 isl_local_space_free(ls);
890 isl_basic_set_free(bset);
891
892 isl_int_clear(v);
893
894 str = "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
895 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
896 set = isl_set_read_from_str(ctx, str);
897 set = isl_set_compute_divs(set);
898 isl_set_free(set);
899 if (!set)
900 return -1;
901
902 str = "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
903 bset = isl_basic_set_read_from_str(ctx, str);
904 n = isl_basic_set_dim(bset, isl_dim_div);
905 isl_basic_set_free(bset);
906 if (!bset)
907 return -1;
908 if (n != 0)
909 isl_die(ctx, isl_error_unknown,
910 "expecting no existentials", return -1);
911
912 str = "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
913 set = isl_set_read_from_str(ctx, str);
914 set = isl_set_remove_divs_involving_dims(set, isl_dim_set, 0, 2);
915 set = isl_set_fix_si(set, isl_dim_set, 2, -3);
916 empty = isl_set_is_empty(set);
917 isl_set_free(set);
918 if (empty < 0)
919 return -1;
920 if (!empty)
921 isl_die(ctx, isl_error_unknown,
922 "result not as accurate as expected", return -1);
923
924 return 0;
925 }
926
927 void test_application_case(struct isl_ctx *ctx, const char *name)
928 {
929 char *filename;
930 FILE *input;
931 struct isl_basic_set *bset1, *bset2;
932 struct isl_basic_map *bmap;
933
934 filename = get_filename(ctx, name, "omega");
935 assert(filename);
936 input = fopen(filename, "r");
937 assert(input);
938
939 bset1 = isl_basic_set_read_from_file(ctx, input);
940 bmap = isl_basic_map_read_from_file(ctx, input);
941
942 bset1 = isl_basic_set_apply(bset1, bmap);
943
944 bset2 = isl_basic_set_read_from_file(ctx, input);
945
946 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
947
948 isl_basic_set_free(bset1);
949 isl_basic_set_free(bset2);
950 free(filename);
951
952 fclose(input);
953 }
954
955 void test_application(struct isl_ctx *ctx)
956 {
957 test_application_case(ctx, "application");
958 test_application_case(ctx, "application2");
959 }
960
961 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
962 {
963 char *filename;
964 FILE *input;
965 struct isl_basic_set *bset1, *bset2;
966
967 filename = get_filename(ctx, name, "polylib");
968 assert(filename);
969 input = fopen(filename, "r");
970 assert(input);
971
972 bset1 = isl_basic_set_read_from_file(ctx, input);
973 bset2 = isl_basic_set_read_from_file(ctx, input);
974
975 bset1 = isl_basic_set_affine_hull(bset1);
976
977 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
978
979 isl_basic_set_free(bset1);
980 isl_basic_set_free(bset2);
981 free(filename);
982
983 fclose(input);
984 }
985
986 int test_affine_hull(struct isl_ctx *ctx)
987 {
988 const char *str;
989 isl_set *set;
990 isl_basic_set *bset, *bset2;
991 int n;
992 int subset;
993
994 test_affine_hull_case(ctx, "affine2");
995 test_affine_hull_case(ctx, "affine");
996 test_affine_hull_case(ctx, "affine3");
997
998 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
999 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
1000 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
1001 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
1002 set = isl_set_read_from_str(ctx, str);
1003 bset = isl_set_affine_hull(set);
1004 n = isl_basic_set_dim(bset, isl_dim_div);
1005 isl_basic_set_free(bset);
1006 if (n != 0)
1007 isl_die(ctx, isl_error_unknown, "not expecting any divs",
1008 return -1);
1009
1010 /* Check that isl_map_affine_hull is not confused by
1011 * the reordering of divs in isl_map_align_divs.
1012 */
1013 str = "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1014 "32e0 = b and 32e1 = c); "
1015 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1016 set = isl_set_read_from_str(ctx, str);
1017 bset = isl_set_affine_hull(set);
1018 isl_basic_set_free(bset);
1019 if (!bset)
1020 return -1;
1021
1022 str = "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1023 "32e2 = 31 + 31e0 }";
1024 set = isl_set_read_from_str(ctx, str);
1025 bset = isl_set_affine_hull(set);
1026 str = "{ [a] : exists e : a = 32 e }";
1027 bset2 = isl_basic_set_read_from_str(ctx, str);
1028 subset = isl_basic_set_is_subset(bset, bset2);
1029 isl_basic_set_free(bset);
1030 isl_basic_set_free(bset2);
1031 if (subset < 0)
1032 return -1;
1033 if (!subset)
1034 isl_die(ctx, isl_error_unknown, "not as accurate as expected",
1035 return -1);
1036
1037 return 0;
1038 }
1039
1040 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
1041 {
1042 char *filename;
1043 FILE *input;
1044 struct isl_basic_set *bset1, *bset2;
1045 struct isl_set *set;
1046
1047 filename = get_filename(ctx, name, "polylib");
1048 assert(filename);
1049 input = fopen(filename, "r");
1050 assert(input);
1051
1052 bset1 = isl_basic_set_read_from_file(ctx, input);
1053 bset2 = isl_basic_set_read_from_file(ctx, input);
1054
1055 set = isl_basic_set_union(bset1, bset2);
1056 bset1 = isl_set_convex_hull(set);
1057
1058 bset2 = isl_basic_set_read_from_file(ctx, input);
1059
1060 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1061
1062 isl_basic_set_free(bset1);
1063 isl_basic_set_free(bset2);
1064 free(filename);
1065
1066 fclose(input);
1067 }
1068
1069 struct {
1070 const char *set;
1071 const char *hull;
1072 } convex_hull_tests[] = {
1073 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1074 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1075 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1076 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1077 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1078 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1079 "i2 <= 5 and i2 >= 4; "
1080 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1081 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1082 "i2 <= 5 + i0 and i2 >= i0 }" },
1083 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1084 "{ [x, y] : 1 = 0 }" },
1085 };
1086
1087 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
1088 {
1089 int i;
1090 int orig_convex = ctx->opt->convex;
1091 ctx->opt->convex = convex;
1092
1093 test_convex_hull_case(ctx, "convex0");
1094 test_convex_hull_case(ctx, "convex1");
1095 test_convex_hull_case(ctx, "convex2");
1096 test_convex_hull_case(ctx, "convex3");
1097 test_convex_hull_case(ctx, "convex4");
1098 test_convex_hull_case(ctx, "convex5");
1099 test_convex_hull_case(ctx, "convex6");
1100 test_convex_hull_case(ctx, "convex7");
1101 test_convex_hull_case(ctx, "convex8");
1102 test_convex_hull_case(ctx, "convex9");
1103 test_convex_hull_case(ctx, "convex10");
1104 test_convex_hull_case(ctx, "convex11");
1105 test_convex_hull_case(ctx, "convex12");
1106 test_convex_hull_case(ctx, "convex13");
1107 test_convex_hull_case(ctx, "convex14");
1108 test_convex_hull_case(ctx, "convex15");
1109
1110 for (i = 0; i < ARRAY_SIZE(convex_hull_tests); ++i) {
1111 isl_set *set1, *set2;
1112
1113 set1 = isl_set_read_from_str(ctx, convex_hull_tests[i].set);
1114 set2 = isl_set_read_from_str(ctx, convex_hull_tests[i].hull);
1115 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
1116 assert(isl_set_is_equal(set1, set2));
1117 isl_set_free(set1);
1118 isl_set_free(set2);
1119 }
1120
1121 ctx->opt->convex = orig_convex;
1122 }
1123
1124 void test_convex_hull(struct isl_ctx *ctx)
1125 {
1126 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
1127 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
1128 }
1129
1130 void test_gist_case(struct isl_ctx *ctx, const char *name)
1131 {
1132 char *filename;
1133 FILE *input;
1134 struct isl_basic_set *bset1, *bset2;
1135
1136 filename = get_filename(ctx, name, "polylib");
1137 assert(filename);
1138 input = fopen(filename, "r");
1139 assert(input);
1140
1141 bset1 = isl_basic_set_read_from_file(ctx, input);
1142 bset2 = isl_basic_set_read_from_file(ctx, input);
1143
1144 bset1 = isl_basic_set_gist(bset1, bset2);
1145
1146 bset2 = isl_basic_set_read_from_file(ctx, input);
1147
1148 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1149
1150 isl_basic_set_free(bset1);
1151 isl_basic_set_free(bset2);
1152 free(filename);
1153
1154 fclose(input);
1155 }
1156
1157 struct {
1158 const char *set;
1159 const char *context;
1160 const char *gist;
1161 } gist_tests[] = {
1162 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1163 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1164 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1165 "{ [a, b, c] : a <= 15 }" },
1166 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1167 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1168 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1169 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1170 { "{ [m, n, a, b] : a <= 2147 + n }",
1171 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1172 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1173 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1174 "b >= 0) }",
1175 "{ [m, n, ku, kl] }" },
1176 };
1177
1178 static int test_gist(struct isl_ctx *ctx)
1179 {
1180 int i;
1181 const char *str;
1182 isl_basic_set *bset1, *bset2;
1183 isl_map *map1, *map2;
1184 int equal;
1185
1186 for (i = 0; i < ARRAY_SIZE(gist_tests); ++i) {
1187 int equal_input;
1188 isl_set *set1, *set2, *copy;
1189
1190 set1 = isl_set_read_from_str(ctx, gist_tests[i].set);
1191 set2 = isl_set_read_from_str(ctx, gist_tests[i].context);
1192 copy = isl_set_copy(set1);
1193 set1 = isl_set_gist(set1, set2);
1194 set2 = isl_set_read_from_str(ctx, gist_tests[i].gist);
1195 equal = isl_set_is_equal(set1, set2);
1196 isl_set_free(set1);
1197 isl_set_free(set2);
1198 set1 = isl_set_read_from_str(ctx, gist_tests[i].set);
1199 equal_input = isl_set_is_equal(set1, copy);
1200 isl_set_free(set1);
1201 isl_set_free(copy);
1202 if (equal < 0 || equal_input < 0)
1203 return -1;
1204 if (!equal)
1205 isl_die(ctx, isl_error_unknown,
1206 "incorrect gist result", return -1);
1207 if (!equal_input)
1208 isl_die(ctx, isl_error_unknown,
1209 "gist modified input", return -1);
1210 }
1211
1212 test_gist_case(ctx, "gist1");
1213
1214 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
1215 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1216 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1217 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1218 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1219 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1220 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1221 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1222 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1223 bset1 = isl_basic_set_read_from_str(ctx, str);
1224 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1225 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1226 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1227 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1228 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1229 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1230 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1231 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1232 bset2 = isl_basic_set_read_from_str(ctx, str);
1233 bset1 = isl_basic_set_gist(bset1, bset2);
1234 assert(bset1 && bset1->n_div == 0);
1235 isl_basic_set_free(bset1);
1236
1237 /* Check that the integer divisions of the second disjunct
1238 * do not spread to the first disjunct.
1239 */
1240 str = "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1241 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1242 "(exists (e0 = [(-1 + t1)/16], "
1243 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1244 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1245 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1246 "o0 <= 4294967295 and t1 <= -1)) }";
1247 map1 = isl_map_read_from_str(ctx, str);
1248 str = "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1249 map2 = isl_map_read_from_str(ctx, str);
1250 map1 = isl_map_gist(map1, map2);
1251 if (!map1)
1252 return -1;
1253 if (map1->n != 1)
1254 isl_die(ctx, isl_error_unknown, "expecting single disjunct",
1255 isl_map_free(map1); return -1);
1256 if (isl_basic_map_dim(map1->p[0], isl_dim_div) != 1)
1257 isl_die(ctx, isl_error_unknown, "expecting single div",
1258 isl_map_free(map1); return -1);
1259 isl_map_free(map1);
1260
1261 return 0;
1262 }
1263
1264 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
1265 {
1266 isl_set *set, *set2;
1267 int equal;
1268 int one;
1269
1270 set = isl_set_read_from_str(ctx, str);
1271 set = isl_set_coalesce(set);
1272 set2 = isl_set_read_from_str(ctx, str);
1273 equal = isl_set_is_equal(set, set2);
1274 one = set && set->n == 1;
1275 isl_set_free(set);
1276 isl_set_free(set2);
1277
1278 if (equal < 0)
1279 return -1;
1280 if (!equal)
1281 isl_die(ctx, isl_error_unknown,
1282 "coalesced set not equal to input", return -1);
1283 if (check_one && !one)
1284 isl_die(ctx, isl_error_unknown,
1285 "coalesced set should not be a union", return -1);
1286
1287 return 0;
1288 }
1289
1290 /* Inputs for coalescing tests with unbounded wrapping.
1291 * "str" is a string representation of the input set.
1292 * "single_disjunct" is set if we expect the result to consist of
1293 * a single disjunct.
1294 */
1295 struct {
1296 int single_disjunct;
1297 const char *str;
1298 } coalesce_unbounded_tests[] = {
1299 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1300 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1301 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1302 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1303 "-10 <= y <= 0}" },
1304 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1305 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1306 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1307 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1308 };
1309
1310 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1311 * option turned off.
1312 */
1313 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
1314 {
1315 int i;
1316 int r = 0;
1317 int bounded;
1318
1319 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
1320 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
1321
1322 for (i = 0; i < ARRAY_SIZE(coalesce_unbounded_tests); ++i) {
1323 const char *str = coalesce_unbounded_tests[i].str;
1324 int check_one = coalesce_unbounded_tests[i].single_disjunct;
1325 if (test_coalesce_set(ctx, str, check_one) >= 0)
1326 continue;
1327 r = -1;
1328 break;
1329 }
1330
1331 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
1332
1333 return r;
1334 }
1335
1336 /* Inputs for coalescing tests.
1337 * "str" is a string representation of the input set.
1338 * "single_disjunct" is set if we expect the result to consist of
1339 * a single disjunct.
1340 */
1341 struct {
1342 int single_disjunct;
1343 const char *str;
1344 } coalesce_tests[] = {
1345 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1346 "y >= x & x >= 2 & 5 >= y }" },
1347 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1348 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1349 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1350 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1351 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1352 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1353 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1354 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1355 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1356 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1357 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1358 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1359 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1360 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1361 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1362 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1363 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1364 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1365 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1366 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1367 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1368 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1369 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1370 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1371 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1372 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1373 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1374 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1375 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1376 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1377 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1378 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1379 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1380 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1381 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1382 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1383 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1384 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1385 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1386 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1387 "[o0, o1, o2, o3, o4, o5, o6]] : "
1388 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1389 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1390 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1391 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1392 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1393 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1394 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1395 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1396 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1397 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1398 "o6 >= i3 + i6 - o3 and M >= 0 and "
1399 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1400 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1401 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1402 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1403 "(o0 = 0 and M >= 2 and N >= 3) or "
1404 "(M = 0 and o0 = 0 and N >= 3) }" },
1405 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1406 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1407 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1408 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1409 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1410 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1411 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1412 "(y = 3 and x = 1) }" },
1413 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1414 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1415 "i1 <= M and i3 <= M and i4 <= M) or "
1416 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1417 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1418 "i4 <= -1 + M) }" },
1419 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1420 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1421 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1422 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1423 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1424 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1425 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1426 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1427 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1428 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1429 { 0, "{ [a, b] : exists e : 2e = a and "
1430 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1431 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1432 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1433 "j >= 1 and j' <= i + j - i' and i >= 1; "
1434 "[1, 1, 1, 1] }" },
1435 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1436 "[i,j] : exists a : j = 3a }" },
1437 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1438 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1439 "a >= 3) or "
1440 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1441 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1442 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1443 "c <= 6 + 8a and a >= 3; "
1444 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1445 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1446 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1447 "[x,0] : 3 <= x <= 4 }" },
1448 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1449 "[x,0] : 4 <= x <= 5 }" },
1450 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1451 "[x,0] : 3 <= x <= 5 }" },
1452 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1453 "[x,0] : 3 <= x <= 4 }" },
1454 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1455 "i1 <= 0; "
1456 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1457 { 1, "{ [0,0]; [1,1] }" },
1458 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1459 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1460 "ii <= k;"
1461 "[k, 0, k] : k <= 6 and k >= 1 }" },
1462 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1463 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1464 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1465 };
1466
1467 /* Test the functionality of isl_set_coalesce.
1468 * That is, check that the output is always equal to the input
1469 * and in some cases that the result consists of a single disjunct.
1470 */
1471 static int test_coalesce(struct isl_ctx *ctx)
1472 {
1473 int i;
1474
1475 for (i = 0; i < ARRAY_SIZE(coalesce_tests); ++i) {
1476 const char *str = coalesce_tests[i].str;
1477 int check_one = coalesce_tests[i].single_disjunct;
1478 if (test_coalesce_set(ctx, str, check_one) < 0)
1479 return -1;
1480 }
1481
1482 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1483 return -1;
1484
1485 return 0;
1486 }
1487
1488 void test_closure(struct isl_ctx *ctx)
1489 {
1490 const char *str;
1491 isl_set *dom;
1492 isl_map *up, *right;
1493 isl_map *map, *map2;
1494 int exact;
1495
1496 /* COCOA example 1 */
1497 map = isl_map_read_from_str(ctx,
1498 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1499 "1 <= i and i < n and 1 <= j and j < n or "
1500 "i2 = i + 1 and j2 = j - 1 and "
1501 "1 <= i and i < n and 2 <= j and j <= n }");
1502 map = isl_map_power(map, &exact);
1503 assert(exact);
1504 isl_map_free(map);
1505
1506 /* COCOA example 1 */
1507 map = isl_map_read_from_str(ctx,
1508 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1509 "1 <= i and i < n and 1 <= j and j < n or "
1510 "i2 = i + 1 and j2 = j - 1 and "
1511 "1 <= i and i < n and 2 <= j and j <= n }");
1512 map = isl_map_transitive_closure(map, &exact);
1513 assert(exact);
1514 map2 = isl_map_read_from_str(ctx,
1515 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1516 "1 <= i and i < n and 1 <= j and j <= n and "
1517 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1518 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1519 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1520 assert(isl_map_is_equal(map, map2));
1521 isl_map_free(map2);
1522 isl_map_free(map);
1523
1524 map = isl_map_read_from_str(ctx,
1525 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1526 " 0 <= y and y <= n }");
1527 map = isl_map_transitive_closure(map, &exact);
1528 map2 = isl_map_read_from_str(ctx,
1529 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1530 " 0 <= y and y <= n }");
1531 assert(isl_map_is_equal(map, map2));
1532 isl_map_free(map2);
1533 isl_map_free(map);
1534
1535 /* COCOA example 2 */
1536 map = isl_map_read_from_str(ctx,
1537 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1538 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1539 "i2 = i + 2 and j2 = j - 2 and "
1540 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1541 map = isl_map_transitive_closure(map, &exact);
1542 assert(exact);
1543 map2 = isl_map_read_from_str(ctx,
1544 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1545 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1546 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1547 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1548 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1549 assert(isl_map_is_equal(map, map2));
1550 isl_map_free(map);
1551 isl_map_free(map2);
1552
1553 /* COCOA Fig.2 left */
1554 map = isl_map_read_from_str(ctx,
1555 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1556 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1557 "j <= n or "
1558 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1559 "j <= 2 i - 3 and j <= n - 2 or "
1560 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1561 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1562 map = isl_map_transitive_closure(map, &exact);
1563 assert(exact);
1564 isl_map_free(map);
1565
1566 /* COCOA Fig.2 right */
1567 map = isl_map_read_from_str(ctx,
1568 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1569 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1570 "j <= n or "
1571 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1572 "j <= 2 i - 4 and j <= n - 3 or "
1573 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1574 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1575 map = isl_map_power(map, &exact);
1576 assert(exact);
1577 isl_map_free(map);
1578
1579 /* COCOA Fig.2 right */
1580 map = isl_map_read_from_str(ctx,
1581 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1582 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1583 "j <= n or "
1584 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1585 "j <= 2 i - 4 and j <= n - 3 or "
1586 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1587 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1588 map = isl_map_transitive_closure(map, &exact);
1589 assert(exact);
1590 map2 = isl_map_read_from_str(ctx,
1591 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1592 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1593 "j <= n and 3 + i + 2 j <= 3 n and "
1594 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1595 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1596 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1597 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1598 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1599 assert(isl_map_is_equal(map, map2));
1600 isl_map_free(map2);
1601 isl_map_free(map);
1602
1603 /* COCOA Fig.1 right */
1604 dom = isl_set_read_from_str(ctx,
1605 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1606 "2 x - 3 y + 3 >= 0 }");
1607 right = isl_map_read_from_str(ctx,
1608 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1609 up = isl_map_read_from_str(ctx,
1610 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1611 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1612 right = isl_map_intersect_range(right, isl_set_copy(dom));
1613 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1614 up = isl_map_intersect_range(up, dom);
1615 map = isl_map_union(up, right);
1616 map = isl_map_transitive_closure(map, &exact);
1617 assert(exact);
1618 map2 = isl_map_read_from_str(ctx,
1619 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1620 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1621 assert(isl_map_is_equal(map, map2));
1622 isl_map_free(map2);
1623 isl_map_free(map);
1624
1625 /* COCOA Theorem 1 counter example */
1626 map = isl_map_read_from_str(ctx,
1627 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1628 "i2 = 1 and j2 = j or "
1629 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1630 map = isl_map_transitive_closure(map, &exact);
1631 assert(exact);
1632 isl_map_free(map);
1633
1634 map = isl_map_read_from_str(ctx,
1635 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1636 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1637 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1638 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1639 map = isl_map_transitive_closure(map, &exact);
1640 assert(exact);
1641 isl_map_free(map);
1642
1643 /* Kelly et al 1996, fig 12 */
1644 map = isl_map_read_from_str(ctx,
1645 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1646 "1 <= i,j,j+1 <= n or "
1647 "j = n and j2 = 1 and i2 = i + 1 and "
1648 "1 <= i,i+1 <= n }");
1649 map = isl_map_transitive_closure(map, &exact);
1650 assert(exact);
1651 map2 = isl_map_read_from_str(ctx,
1652 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1653 "1 <= i <= n and i = i2 or "
1654 "1 <= i < i2 <= n and 1 <= j <= n and "
1655 "1 <= j2 <= n }");
1656 assert(isl_map_is_equal(map, map2));
1657 isl_map_free(map2);
1658 isl_map_free(map);
1659
1660 /* Omega's closure4 */
1661 map = isl_map_read_from_str(ctx,
1662 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1663 "1 <= x,y <= 10 or "
1664 "x2 = x + 1 and y2 = y and "
1665 "1 <= x <= 20 && 5 <= y <= 15 }");
1666 map = isl_map_transitive_closure(map, &exact);
1667 assert(exact);
1668 isl_map_free(map);
1669
1670 map = isl_map_read_from_str(ctx,
1671 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1672 map = isl_map_transitive_closure(map, &exact);
1673 assert(!exact);
1674 map2 = isl_map_read_from_str(ctx,
1675 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1676 assert(isl_map_is_equal(map, map2));
1677 isl_map_free(map);
1678 isl_map_free(map2);
1679
1680 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1681 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1682 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1683 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1684 map = isl_map_read_from_str(ctx, str);
1685 map = isl_map_transitive_closure(map, &exact);
1686 assert(exact);
1687 map2 = isl_map_read_from_str(ctx, str);
1688 assert(isl_map_is_equal(map, map2));
1689 isl_map_free(map);
1690 isl_map_free(map2);
1691
1692 str = "{[0] -> [1]; [2] -> [3]}";
1693 map = isl_map_read_from_str(ctx, str);
1694 map = isl_map_transitive_closure(map, &exact);
1695 assert(exact);
1696 map2 = isl_map_read_from_str(ctx, str);
1697 assert(isl_map_is_equal(map, map2));
1698 isl_map_free(map);
1699 isl_map_free(map2);
1700
1701 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1702 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1703 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1704 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1705 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1706 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1707 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1708 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1709 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1710 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1711 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1712 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1713 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1714 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1715 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1716 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1717 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1718 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1719 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1720 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1721 map = isl_map_read_from_str(ctx, str);
1722 map = isl_map_transitive_closure(map, NULL);
1723 assert(map);
1724 isl_map_free(map);
1725 }
1726
1727 void test_lex(struct isl_ctx *ctx)
1728 {
1729 isl_space *dim;
1730 isl_map *map;
1731
1732 dim = isl_space_set_alloc(ctx, 0, 0);
1733 map = isl_map_lex_le(dim);
1734 assert(!isl_map_is_empty(map));
1735 isl_map_free(map);
1736 }
1737
1738 static int test_lexmin(struct isl_ctx *ctx)
1739 {
1740 int equal;
1741 const char *str;
1742 isl_basic_map *bmap;
1743 isl_map *map, *map2;
1744 isl_set *set;
1745 isl_set *set2;
1746 isl_pw_multi_aff *pma;
1747
1748 str = "[p0, p1] -> { [] -> [] : "
1749 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1750 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1751 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1752 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1753 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1754 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1755 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1756 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1757 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1758 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1759 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1760 map = isl_map_read_from_str(ctx, str);
1761 map = isl_map_lexmin(map);
1762 isl_map_free(map);
1763
1764 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1765 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1766 set = isl_set_read_from_str(ctx, str);
1767 set = isl_set_lexmax(set);
1768 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1769 set2 = isl_set_read_from_str(ctx, str);
1770 set = isl_set_intersect(set, set2);
1771 assert(!isl_set_is_empty(set));
1772 isl_set_free(set);
1773
1774 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1775 map = isl_map_read_from_str(ctx, str);
1776 map = isl_map_lexmin(map);
1777 str = "{ [x] -> [5] : 6 <= x <= 8; "
1778 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1779 map2 = isl_map_read_from_str(ctx, str);
1780 assert(isl_map_is_equal(map, map2));
1781 isl_map_free(map);
1782 isl_map_free(map2);
1783
1784 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1785 map = isl_map_read_from_str(ctx, str);
1786 map2 = isl_map_copy(map);
1787 map = isl_map_lexmin(map);
1788 assert(isl_map_is_equal(map, map2));
1789 isl_map_free(map);
1790 isl_map_free(map2);
1791
1792 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1793 map = isl_map_read_from_str(ctx, str);
1794 map = isl_map_lexmin(map);
1795 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1796 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1797 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1798 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1799 map2 = isl_map_read_from_str(ctx, str);
1800 assert(isl_map_is_equal(map, map2));
1801 isl_map_free(map);
1802 isl_map_free(map2);
1803
1804 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1805 " 8i' <= i and 8i' >= -7 + i }";
1806 bmap = isl_basic_map_read_from_str(ctx, str);
1807 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1808 map2 = isl_map_from_pw_multi_aff(pma);
1809 map = isl_map_from_basic_map(bmap);
1810 assert(isl_map_is_equal(map, map2));
1811 isl_map_free(map);
1812 isl_map_free(map2);
1813
1814 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1815 map = isl_map_read_from_str(ctx, str);
1816 map = isl_map_lexmin(map);
1817 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1818 map2 = isl_map_read_from_str(ctx, str);
1819 assert(isl_map_is_equal(map, map2));
1820 isl_map_free(map);
1821 isl_map_free(map2);
1822
1823 /* Check that empty pieces are properly combined. */
1824 str = "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
1825 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
1826 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
1827 map = isl_map_read_from_str(ctx, str);
1828 map = isl_map_lexmin(map);
1829 str = "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
1830 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
1831 "x >= 4 }";
1832 map2 = isl_map_read_from_str(ctx, str);
1833 assert(isl_map_is_equal(map, map2));
1834 isl_map_free(map);
1835 isl_map_free(map2);
1836
1837 str = "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1838 " 8i' <= i and 8i' >= -7 + i }";
1839 set = isl_set_read_from_str(ctx, str);
1840 pma = isl_set_lexmin_pw_multi_aff(isl_set_copy(set));
1841 set2 = isl_set_from_pw_multi_aff(pma);
1842 equal = isl_set_is_equal(set, set2);
1843 isl_set_free(set);
1844 isl_set_free(set2);
1845 if (equal < 0)
1846 return -1;
1847 if (!equal)
1848 isl_die(ctx, isl_error_unknown,
1849 "unexpected difference between set and "
1850 "piecewise affine expression", return -1);
1851
1852 return 0;
1853 }
1854
1855 /* Check that isl_set_min_val and isl_set_max_val compute the correct
1856 * result on non-convex inputs.
1857 */
1858 static int test_min(struct isl_ctx *ctx)
1859 {
1860 isl_set *set;
1861 isl_aff *aff;
1862 isl_val *val;
1863 int min_ok, max_ok;
1864
1865 set = isl_set_read_from_str(ctx, "{ [-1]; [1] }");
1866 aff = isl_aff_read_from_str(ctx, "{ [x] -> [x] }");
1867 val = isl_set_min_val(set, aff);
1868 min_ok = isl_val_is_negone(val);
1869 isl_val_free(val);
1870 val = isl_set_max_val(set, aff);
1871 max_ok = isl_val_is_one(val);
1872 isl_val_free(val);
1873 isl_aff_free(aff);
1874 isl_set_free(set);
1875
1876 if (min_ok < 0 || max_ok < 0)
1877 return -1;
1878 if (!min_ok)
1879 isl_die(ctx, isl_error_unknown,
1880 "unexpected minimum", return -1);
1881 if (!max_ok)
1882 isl_die(ctx, isl_error_unknown,
1883 "unexpected maximum", return -1);
1884
1885 return 0;
1886 }
1887
1888 struct must_may {
1889 isl_map *must;
1890 isl_map *may;
1891 };
1892
1893 static int collect_must_may(__isl_take isl_map *dep, int must,
1894 void *dep_user, void *user)
1895 {
1896 struct must_may *mm = (struct must_may *)user;
1897
1898 if (must)
1899 mm->must = isl_map_union(mm->must, dep);
1900 else
1901 mm->may = isl_map_union(mm->may, dep);
1902
1903 return 0;
1904 }
1905
1906 static int common_space(void *first, void *second)
1907 {
1908 int depth = *(int *)first;
1909 return 2 * depth;
1910 }
1911
1912 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1913 {
1914 isl_map *map2;
1915 int equal;
1916
1917 if (!map)
1918 return -1;
1919
1920 map2 = isl_map_read_from_str(map->ctx, str);
1921 equal = isl_map_is_equal(map, map2);
1922 isl_map_free(map2);
1923
1924 return equal;
1925 }
1926
1927 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1928 {
1929 int equal;
1930
1931 equal = map_is_equal(map, str);
1932 if (equal < 0)
1933 return -1;
1934 if (!equal)
1935 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1936 "result not as expected", return -1);
1937 return 0;
1938 }
1939
1940 void test_dep(struct isl_ctx *ctx)
1941 {
1942 const char *str;
1943 isl_space *dim;
1944 isl_map *map;
1945 isl_access_info *ai;
1946 isl_flow *flow;
1947 int depth;
1948 struct must_may mm;
1949
1950 depth = 3;
1951
1952 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1953 map = isl_map_read_from_str(ctx, str);
1954 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1955
1956 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1957 map = isl_map_read_from_str(ctx, str);
1958 ai = isl_access_info_add_source(ai, map, 1, &depth);
1959
1960 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1961 map = isl_map_read_from_str(ctx, str);
1962 ai = isl_access_info_add_source(ai, map, 1, &depth);
1963
1964 flow = isl_access_info_compute_flow(ai);
1965 dim = isl_space_alloc(ctx, 0, 3, 3);
1966 mm.must = isl_map_empty(isl_space_copy(dim));
1967 mm.may = isl_map_empty(dim);
1968
1969 isl_flow_foreach(flow, collect_must_may, &mm);
1970
1971 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1972 " [1,10,0] -> [2,5,0] }";
1973 assert(map_is_equal(mm.must, str));
1974 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1975 assert(map_is_equal(mm.may, str));
1976
1977 isl_map_free(mm.must);
1978 isl_map_free(mm.may);
1979 isl_flow_free(flow);
1980
1981
1982 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1983 map = isl_map_read_from_str(ctx, str);
1984 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1985
1986 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1987 map = isl_map_read_from_str(ctx, str);
1988 ai = isl_access_info_add_source(ai, map, 1, &depth);
1989
1990 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1991 map = isl_map_read_from_str(ctx, str);
1992 ai = isl_access_info_add_source(ai, map, 0, &depth);
1993
1994 flow = isl_access_info_compute_flow(ai);
1995 dim = isl_space_alloc(ctx, 0, 3, 3);
1996 mm.must = isl_map_empty(isl_space_copy(dim));
1997 mm.may = isl_map_empty(dim);
1998
1999 isl_flow_foreach(flow, collect_must_may, &mm);
2000
2001 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2002 assert(map_is_equal(mm.must, str));
2003 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2004 assert(map_is_equal(mm.may, str));
2005
2006 isl_map_free(mm.must);
2007 isl_map_free(mm.may);
2008 isl_flow_free(flow);
2009
2010
2011 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2012 map = isl_map_read_from_str(ctx, str);
2013 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2014
2015 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2016 map = isl_map_read_from_str(ctx, str);
2017 ai = isl_access_info_add_source(ai, map, 0, &depth);
2018
2019 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2020 map = isl_map_read_from_str(ctx, str);
2021 ai = isl_access_info_add_source(ai, map, 0, &depth);
2022
2023 flow = isl_access_info_compute_flow(ai);
2024 dim = isl_space_alloc(ctx, 0, 3, 3);
2025 mm.must = isl_map_empty(isl_space_copy(dim));
2026 mm.may = isl_map_empty(dim);
2027
2028 isl_flow_foreach(flow, collect_must_may, &mm);
2029
2030 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2031 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2032 assert(map_is_equal(mm.may, str));
2033 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2034 assert(map_is_equal(mm.must, str));
2035
2036 isl_map_free(mm.must);
2037 isl_map_free(mm.may);
2038 isl_flow_free(flow);
2039
2040
2041 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2042 map = isl_map_read_from_str(ctx, str);
2043 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2044
2045 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2046 map = isl_map_read_from_str(ctx, str);
2047 ai = isl_access_info_add_source(ai, map, 0, &depth);
2048
2049 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2050 map = isl_map_read_from_str(ctx, str);
2051 ai = isl_access_info_add_source(ai, map, 0, &depth);
2052
2053 flow = isl_access_info_compute_flow(ai);
2054 dim = isl_space_alloc(ctx, 0, 3, 3);
2055 mm.must = isl_map_empty(isl_space_copy(dim));
2056 mm.may = isl_map_empty(dim);
2057
2058 isl_flow_foreach(flow, collect_must_may, &mm);
2059
2060 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2061 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2062 assert(map_is_equal(mm.may, str));
2063 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2064 assert(map_is_equal(mm.must, str));
2065
2066 isl_map_free(mm.must);
2067 isl_map_free(mm.may);
2068 isl_flow_free(flow);
2069
2070
2071 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2072 map = isl_map_read_from_str(ctx, str);
2073 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2074
2075 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2076 map = isl_map_read_from_str(ctx, str);
2077 ai = isl_access_info_add_source(ai, map, 0, &depth);
2078
2079 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2080 map = isl_map_read_from_str(ctx, str);
2081 ai = isl_access_info_add_source(ai, map, 0, &depth);
2082
2083 flow = isl_access_info_compute_flow(ai);
2084 dim = isl_space_alloc(ctx, 0, 3, 3);
2085 mm.must = isl_map_empty(isl_space_copy(dim));
2086 mm.may = isl_map_empty(dim);
2087
2088 isl_flow_foreach(flow, collect_must_may, &mm);
2089
2090 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2091 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2092 assert(map_is_equal(mm.may, str));
2093 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2094 assert(map_is_equal(mm.must, str));
2095
2096 isl_map_free(mm.must);
2097 isl_map_free(mm.may);
2098 isl_flow_free(flow);
2099
2100
2101 depth = 5;
2102
2103 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2104 map = isl_map_read_from_str(ctx, str);
2105 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
2106
2107 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2108 map = isl_map_read_from_str(ctx, str);
2109 ai = isl_access_info_add_source(ai, map, 1, &depth);
2110
2111 flow = isl_access_info_compute_flow(ai);
2112 dim = isl_space_alloc(ctx, 0, 5, 5);
2113 mm.must = isl_map_empty(isl_space_copy(dim));
2114 mm.may = isl_map_empty(dim);
2115
2116 isl_flow_foreach(flow, collect_must_may, &mm);
2117
2118 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2119 assert(map_is_equal(mm.must, str));
2120 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2121 assert(map_is_equal(mm.may, str));
2122
2123 isl_map_free(mm.must);
2124 isl_map_free(mm.may);
2125 isl_flow_free(flow);
2126 }
2127
2128 /* Check that the dependence analysis proceeds without errors.
2129 * Earlier versions of isl would break down during the analysis
2130 * due to the use of the wrong spaces.
2131 */
2132 static int test_flow(isl_ctx *ctx)
2133 {
2134 const char *str;
2135 isl_union_map *access, *schedule;
2136 isl_union_map *must_dep, *may_dep;
2137 int r;
2138
2139 str = "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2140 access = isl_union_map_read_from_str(ctx, str);
2141 str = "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2142 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2143 "S2[] -> [1,0,0,0]; "
2144 "S3[] -> [-1,0,0,0] }";
2145 schedule = isl_union_map_read_from_str(ctx, str);
2146 r = isl_union_map_compute_flow(access, isl_union_map_copy(access),
2147 isl_union_map_copy(access), schedule,
2148 &must_dep, &may_dep, NULL, NULL);
2149 isl_union_map_free(may_dep);
2150 isl_union_map_free(must_dep);
2151
2152 return r;
2153 }
2154
2155 struct {
2156 const char *map;
2157 int sv;
2158 } sv_tests[] = {
2159 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2160 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2161 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2162 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2163 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2164 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2165 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2166 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2167 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2168 };
2169
2170 int test_sv(isl_ctx *ctx)
2171 {
2172 isl_union_map *umap;
2173 int i;
2174 int sv;
2175
2176 for (i = 0; i < ARRAY_SIZE(sv_tests); ++i) {
2177 umap = isl_union_map_read_from_str(ctx, sv_tests[i].map);
2178 sv = isl_union_map_is_single_valued(umap);
2179 isl_union_map_free(umap);
2180 if (sv < 0)
2181 return -1;
2182 if (sv_tests[i].sv && !sv)
2183 isl_die(ctx, isl_error_internal,
2184 "map not detected as single valued", return -1);
2185 if (!sv_tests[i].sv && sv)
2186 isl_die(ctx, isl_error_internal,
2187 "map detected as single valued", return -1);
2188 }
2189
2190 return 0;
2191 }
2192
2193 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
2194 {
2195 isl_map *map;
2196
2197 map = isl_map_read_from_str(ctx, str);
2198 if (bijective)
2199 assert(isl_map_is_bijective(map));
2200 else
2201 assert(!isl_map_is_bijective(map));
2202 isl_map_free(map);
2203 }
2204
2205 void test_bijective(struct isl_ctx *ctx)
2206 {
2207 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
2208 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
2209 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
2210 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
2211 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
2212 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
2213 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
2214 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
2215 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
2216 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
2217 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
2218 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
2219 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
2220 }
2221
2222 /* Inputs for isl_pw_qpolynomial_gist tests.
2223 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2224 */
2225 struct {
2226 const char *pwqp;
2227 const char *set;
2228 const char *gist;
2229 } pwqp_gist_tests[] = {
2230 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2231 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2232 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2233 "{ [i] -> -1/2 + 1/2 * i }" },
2234 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2235 };
2236
2237 static int test_pwqp(struct isl_ctx *ctx)
2238 {
2239 int i;
2240 const char *str;
2241 isl_set *set;
2242 isl_pw_qpolynomial *pwqp1, *pwqp2;
2243 int equal;
2244
2245 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2246 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2247
2248 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
2249 isl_dim_in, 1, 1);
2250
2251 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2252 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2253
2254 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2255
2256 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2257
2258 isl_pw_qpolynomial_free(pwqp1);
2259
2260 for (i = 0; i < ARRAY_SIZE(pwqp_gist_tests); ++i) {
2261 str = pwqp_gist_tests[i].pwqp;
2262 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2263 str = pwqp_gist_tests[i].set;
2264 set = isl_set_read_from_str(ctx, str);
2265 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2266 str = pwqp_gist_tests[i].gist;
2267 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2268 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2269 equal = isl_pw_qpolynomial_is_zero(pwqp1);
2270 isl_pw_qpolynomial_free(pwqp1);
2271
2272 if (equal < 0)
2273 return -1;
2274 if (!equal)
2275 isl_die(ctx, isl_error_unknown,
2276 "unexpected result", return -1);
2277 }
2278
2279 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
2280 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2281 str = "{ [i] -> ([(2 * [i/2])/5]) }";
2282 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2283
2284 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2285
2286 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2287
2288 isl_pw_qpolynomial_free(pwqp1);
2289
2290 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
2291 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2292 str = "{ [x] -> x }";
2293 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2294
2295 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2296
2297 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2298
2299 isl_pw_qpolynomial_free(pwqp1);
2300
2301 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2302 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2303 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2304 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
2305 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2306 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2307 isl_pw_qpolynomial_free(pwqp1);
2308
2309 str = "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2310 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2311 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2312 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2313 set = isl_set_read_from_str(ctx, "{ [a,b,a] }");
2314 pwqp1 = isl_pw_qpolynomial_intersect_domain(pwqp1, set);
2315 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2316 isl_pw_qpolynomial_free(pwqp1);
2317 isl_pw_qpolynomial_free(pwqp2);
2318 if (equal < 0)
2319 return -1;
2320 if (!equal)
2321 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2322
2323 str = "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2324 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2325 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2326 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2327 pwqp1 = isl_pw_qpolynomial_fix_val(pwqp1, isl_dim_set, 1,
2328 isl_val_one(ctx));
2329 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2330 isl_pw_qpolynomial_free(pwqp1);
2331 isl_pw_qpolynomial_free(pwqp2);
2332 if (equal < 0)
2333 return -1;
2334 if (!equal)
2335 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2336
2337 return 0;
2338 }
2339
2340 void test_split_periods(isl_ctx *ctx)
2341 {
2342 const char *str;
2343 isl_pw_qpolynomial *pwqp;
2344
2345 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2346 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2347 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2348 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2349
2350 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
2351 assert(pwqp);
2352
2353 isl_pw_qpolynomial_free(pwqp);
2354 }
2355
2356 void test_union(isl_ctx *ctx)
2357 {
2358 const char *str;
2359 isl_union_set *uset1, *uset2;
2360 isl_union_map *umap1, *umap2;
2361
2362 str = "{ [i] : 0 <= i <= 1 }";
2363 uset1 = isl_union_set_read_from_str(ctx, str);
2364 str = "{ [1] -> [0] }";
2365 umap1 = isl_union_map_read_from_str(ctx, str);
2366
2367 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
2368 assert(isl_union_map_is_equal(umap1, umap2));
2369
2370 isl_union_map_free(umap1);
2371 isl_union_map_free(umap2);
2372
2373 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2374 umap1 = isl_union_map_read_from_str(ctx, str);
2375 str = "{ A[i]; B[i] }";
2376 uset1 = isl_union_set_read_from_str(ctx, str);
2377
2378 uset2 = isl_union_map_domain(umap1);
2379
2380 assert(isl_union_set_is_equal(uset1, uset2));
2381
2382 isl_union_set_free(uset1);
2383 isl_union_set_free(uset2);
2384 }
2385
2386 void test_bound(isl_ctx *ctx)
2387 {
2388 const char *str;
2389 isl_pw_qpolynomial *pwqp;
2390 isl_pw_qpolynomial_fold *pwf;
2391
2392 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
2393 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2394 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2395 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
2396 isl_pw_qpolynomial_fold_free(pwf);
2397
2398 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2399 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2400 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2401 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
2402 isl_pw_qpolynomial_fold_free(pwf);
2403 }
2404
2405 void test_lift(isl_ctx *ctx)
2406 {
2407 const char *str;
2408 isl_basic_map *bmap;
2409 isl_basic_set *bset;
2410
2411 str = "{ [i0] : exists e0 : i0 = 4e0 }";
2412 bset = isl_basic_set_read_from_str(ctx, str);
2413 bset = isl_basic_set_lift(bset);
2414 bmap = isl_basic_map_from_range(bset);
2415 bset = isl_basic_map_domain(bmap);
2416 isl_basic_set_free(bset);
2417 }
2418
2419 struct {
2420 const char *set1;
2421 const char *set2;
2422 int subset;
2423 } subset_tests[] = {
2424 { "{ [112, 0] }",
2425 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2426 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2427 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2428 { "{ [65] }",
2429 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2430 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2431 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2432 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2433 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2434 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2435 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2436 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2437 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2438 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2439 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2440 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2441 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2442 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2443 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2444 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2445 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2446 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2447 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2448 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2449 "4e0 <= -57 + i0 + i1)) or "
2450 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2451 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2452 "4e0 >= -61 + i0 + i1)) or "
2453 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2454 };
2455
2456 static int test_subset(isl_ctx *ctx)
2457 {
2458 int i;
2459 isl_set *set1, *set2;
2460 int subset;
2461
2462 for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
2463 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
2464 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
2465 subset = isl_set_is_subset(set1, set2);
2466 isl_set_free(set1);
2467 isl_set_free(set2);
2468 if (subset < 0)
2469 return -1;
2470 if (subset != subset_tests[i].subset)
2471 isl_die(ctx, isl_error_unknown,
2472 "incorrect subset result", return -1);
2473 }
2474
2475 return 0;
2476 }
2477
2478 struct {
2479 const char *minuend;
2480 const char *subtrahend;
2481 const char *difference;
2482 } subtract_domain_tests[] = {
2483 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2484 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2485 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2486 };
2487
2488 static int test_subtract(isl_ctx *ctx)
2489 {
2490 int i;
2491 isl_union_map *umap1, *umap2;
2492 isl_union_pw_multi_aff *upma1, *upma2;
2493 isl_union_set *uset;
2494 int equal;
2495
2496 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2497 umap1 = isl_union_map_read_from_str(ctx,
2498 subtract_domain_tests[i].minuend);
2499 uset = isl_union_set_read_from_str(ctx,
2500 subtract_domain_tests[i].subtrahend);
2501 umap2 = isl_union_map_read_from_str(ctx,
2502 subtract_domain_tests[i].difference);
2503 umap1 = isl_union_map_subtract_domain(umap1, uset);
2504 equal = isl_union_map_is_equal(umap1, umap2);
2505 isl_union_map_free(umap1);
2506 isl_union_map_free(umap2);
2507 if (equal < 0)
2508 return -1;
2509 if (!equal)
2510 isl_die(ctx, isl_error_unknown,
2511 "incorrect subtract domain result", return -1);
2512 }
2513
2514 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2515 upma1 = isl_union_pw_multi_aff_read_from_str(ctx,
2516 subtract_domain_tests[i].minuend);
2517 uset = isl_union_set_read_from_str(ctx,
2518 subtract_domain_tests[i].subtrahend);
2519 upma2 = isl_union_pw_multi_aff_read_from_str(ctx,
2520 subtract_domain_tests[i].difference);
2521 upma1 = isl_union_pw_multi_aff_subtract_domain(upma1, uset);
2522 equal = isl_union_pw_multi_aff_plain_is_equal(upma1, upma2);
2523 isl_union_pw_multi_aff_free(upma1);
2524 isl_union_pw_multi_aff_free(upma2);
2525 if (equal < 0)
2526 return -1;
2527 if (!equal)
2528 isl_die(ctx, isl_error_unknown,
2529 "incorrect subtract domain result", return -1);
2530 }
2531
2532 return 0;
2533 }
2534
2535 int test_factorize(isl_ctx *ctx)
2536 {
2537 const char *str;
2538 isl_basic_set *bset;
2539 isl_factorizer *f;
2540
2541 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2542 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2543 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2544 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2545 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2546 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2547 "3i5 >= -2i0 - i2 + 3i4 }";
2548 bset = isl_basic_set_read_from_str(ctx, str);
2549 f = isl_basic_set_factorizer(bset);
2550 isl_basic_set_free(bset);
2551 isl_factorizer_free(f);
2552 if (!f)
2553 isl_die(ctx, isl_error_unknown,
2554 "failed to construct factorizer", return -1);
2555
2556 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2557 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2558 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2559 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2560 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2561 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2562 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2563 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2564 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2565 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2566 bset = isl_basic_set_read_from_str(ctx, str);
2567 f = isl_basic_set_factorizer(bset);
2568 isl_basic_set_free(bset);
2569 isl_factorizer_free(f);
2570 if (!f)
2571 isl_die(ctx, isl_error_unknown,
2572 "failed to construct factorizer", return -1);
2573
2574 return 0;
2575 }
2576
2577 static int check_injective(__isl_take isl_map *map, void *user)
2578 {
2579 int *injective = user;
2580
2581 *injective = isl_map_is_injective(map);
2582 isl_map_free(map);
2583
2584 if (*injective < 0 || !*injective)
2585 return -1;
2586
2587 return 0;
2588 }
2589
2590 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2591 const char *r, const char *s, int tilable, int parallel)
2592 {
2593 int i;
2594 isl_union_set *D;
2595 isl_union_map *W, *R, *S;
2596 isl_union_map *empty;
2597 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2598 isl_union_map *validity, *proximity, *coincidence;
2599 isl_union_map *schedule;
2600 isl_union_map *test;
2601 isl_union_set *delta;
2602 isl_union_set *domain;
2603 isl_set *delta_set;
2604 isl_set *slice;
2605 isl_set *origin;
2606 isl_schedule_constraints *sc;
2607 isl_schedule *sched;
2608 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2609
2610 D = isl_union_set_read_from_str(ctx, d);
2611 W = isl_union_map_read_from_str(ctx, w);
2612 R = isl_union_map_read_from_str(ctx, r);
2613 S = isl_union_map_read_from_str(ctx, s);
2614
2615 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2616 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2617
2618 empty = isl_union_map_empty(isl_union_map_get_space(S));
2619 isl_union_map_compute_flow(isl_union_map_copy(R),
2620 isl_union_map_copy(W), empty,
2621 isl_union_map_copy(S),
2622 &dep_raw, NULL, NULL, NULL);
2623 isl_union_map_compute_flow(isl_union_map_copy(W),
2624 isl_union_map_copy(W),
2625 isl_union_map_copy(R),
2626 isl_union_map_copy(S),
2627 &dep_waw, &dep_war, NULL, NULL);
2628
2629 dep = isl_union_map_union(dep_waw, dep_war);
2630 dep = isl_union_map_union(dep, dep_raw);
2631 validity = isl_union_map_copy(dep);
2632 coincidence = isl_union_map_copy(dep);
2633 proximity = isl_union_map_copy(dep);
2634
2635 sc = isl_schedule_constraints_on_domain(isl_union_set_copy(D));
2636 sc = isl_schedule_constraints_set_validity(sc, validity);
2637 sc = isl_schedule_constraints_set_coincidence(sc, coincidence);
2638 sc = isl_schedule_constraints_set_proximity(sc, proximity);
2639 sched = isl_schedule_constraints_compute_schedule(sc);
2640 schedule = isl_schedule_get_map(sched);
2641 isl_schedule_free(sched);
2642 isl_union_map_free(W);
2643 isl_union_map_free(R);
2644 isl_union_map_free(S);
2645
2646 is_injection = 1;
2647 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2648
2649 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2650 is_complete = isl_union_set_is_subset(D, domain);
2651 isl_union_set_free(D);
2652 isl_union_set_free(domain);
2653
2654 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2655 test = isl_union_map_apply_range(test, dep);
2656 test = isl_union_map_apply_range(test, schedule);
2657
2658 delta = isl_union_map_deltas(test);
2659 if (isl_union_set_n_set(delta) == 0) {
2660 is_tilable = 1;
2661 is_parallel = 1;
2662 is_nonneg = 1;
2663 isl_union_set_free(delta);
2664 } else {
2665 delta_set = isl_set_from_union_set(delta);
2666
2667 slice = isl_set_universe(isl_set_get_space(delta_set));
2668 for (i = 0; i < tilable; ++i)
2669 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2670 is_tilable = isl_set_is_subset(delta_set, slice);
2671 isl_set_free(slice);
2672
2673 slice = isl_set_universe(isl_set_get_space(delta_set));
2674 for (i = 0; i < parallel; ++i)
2675 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2676 is_parallel = isl_set_is_subset(delta_set, slice);
2677 isl_set_free(slice);
2678
2679 origin = isl_set_universe(isl_set_get_space(delta_set));
2680 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2681 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2682
2683 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2684 delta_set = isl_set_lexmin(delta_set);
2685
2686 is_nonneg = isl_set_is_equal(delta_set, origin);
2687
2688 isl_set_free(origin);
2689 isl_set_free(delta_set);
2690 }
2691
2692 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2693 is_injection < 0 || is_complete < 0)
2694 return -1;
2695 if (!is_complete)
2696 isl_die(ctx, isl_error_unknown,
2697 "generated schedule incomplete", return -1);
2698 if (!is_injection)
2699 isl_die(ctx, isl_error_unknown,
2700 "generated schedule not injective on each statement",
2701 return -1);
2702 if (!is_nonneg)
2703 isl_die(ctx, isl_error_unknown,
2704 "negative dependences in generated schedule",
2705 return -1);
2706 if (!is_tilable)
2707 isl_die(ctx, isl_error_unknown,
2708 "generated schedule not as tilable as expected",
2709 return -1);
2710 if (!is_parallel)
2711 isl_die(ctx, isl_error_unknown,
2712 "generated schedule not as parallel as expected",
2713 return -1);
2714
2715 return 0;
2716 }
2717
2718 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
2719 const char *domain, const char *validity, const char *proximity)
2720 {
2721 isl_union_set *dom;
2722 isl_union_map *dep;
2723 isl_union_map *prox;
2724 isl_schedule_constraints *sc;
2725 isl_schedule *schedule;
2726 isl_union_map *sched;
2727
2728 dom = isl_union_set_read_from_str(ctx, domain);
2729 dep = isl_union_map_read_from_str(ctx, validity);
2730 prox = isl_union_map_read_from_str(ctx, proximity);
2731 sc = isl_schedule_constraints_on_domain(dom);
2732 sc = isl_schedule_constraints_set_validity(sc, dep);
2733 sc = isl_schedule_constraints_set_proximity(sc, prox);
2734 schedule = isl_schedule_constraints_compute_schedule(sc);
2735 sched = isl_schedule_get_map(schedule);
2736 isl_schedule_free(schedule);
2737
2738 return sched;
2739 }
2740
2741 /* Check that a schedule can be constructed on the given domain
2742 * with the given validity and proximity constraints.
2743 */
2744 static int test_has_schedule(isl_ctx *ctx, const char *domain,
2745 const char *validity, const char *proximity)
2746 {
2747 isl_union_map *sched;
2748
2749 sched = compute_schedule(ctx, domain, validity, proximity);
2750 if (!sched)
2751 return -1;
2752
2753 isl_union_map_free(sched);
2754 return 0;
2755 }
2756
2757 int test_special_schedule(isl_ctx *ctx, const char *domain,
2758 const char *validity, const char *proximity, const char *expected_sched)
2759 {
2760 isl_union_map *sched1, *sched2;
2761 int equal;
2762
2763 sched1 = compute_schedule(ctx, domain, validity, proximity);
2764 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2765
2766 equal = isl_union_map_is_equal(sched1, sched2);
2767 isl_union_map_free(sched1);
2768 isl_union_map_free(sched2);
2769
2770 if (equal < 0)
2771 return -1;
2772 if (!equal)
2773 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2774 return -1);
2775
2776 return 0;
2777 }
2778
2779 /* Check that the schedule map is properly padded, even after being
2780 * reconstructed from the band forest.
2781 */
2782 static int test_padded_schedule(isl_ctx *ctx)
2783 {
2784 const char *str;
2785 isl_union_set *D;
2786 isl_union_map *validity, *proximity;
2787 isl_schedule_constraints *sc;
2788 isl_schedule *sched;
2789 isl_union_map *map1, *map2;
2790 isl_band_list *list;
2791 int equal;
2792
2793 str = "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2794 D = isl_union_set_read_from_str(ctx, str);
2795 validity = isl_union_map_empty(isl_union_set_get_space(D));
2796 proximity = isl_union_map_copy(validity);
2797 sc = isl_schedule_constraints_on_domain(D);
2798 sc = isl_schedule_constraints_set_validity(sc, validity);
2799 sc = isl_schedule_constraints_set_proximity(sc, proximity);
2800 sched = isl_schedule_constraints_compute_schedule(sc);
2801 map1 = isl_schedule_get_map(sched);
2802 list = isl_schedule_get_band_forest(sched);
2803 isl_band_list_free(list);
2804 map2 = isl_schedule_get_map(sched);
2805 isl_schedule_free(sched);
2806 equal = isl_union_map_is_equal(map1, map2);
2807 isl_union_map_free(map1);
2808 isl_union_map_free(map2);
2809
2810 if (equal < 0)
2811 return -1;
2812 if (!equal)
2813 isl_die(ctx, isl_error_unknown,
2814 "reconstructed schedule map not the same as original",
2815 return -1);
2816
2817 return 0;
2818 }
2819
2820 /* Input for testing of schedule construction based on
2821 * conditional constraints.
2822 *
2823 * domain is the iteration domain
2824 * flow are the flow dependences, which determine the validity and
2825 * proximity constraints
2826 * condition are the conditions on the conditional validity constraints
2827 * conditional_validity are the conditional validity constraints
2828 * outer_band_n is the expected number of members in the outer band
2829 */
2830 struct {
2831 const char *domain;
2832 const char *flow;
2833 const char *condition;
2834 const char *conditional_validity;
2835 int outer_band_n;
2836 } live_range_tests[] = {
2837 /* Contrived example that illustrates that we need to keep
2838 * track of tagged condition dependences and
2839 * tagged conditional validity dependences
2840 * in isl_sched_edge separately.
2841 * In particular, the conditional validity constraints on A
2842 * cannot be satisfied,
2843 * but they can be ignored because there are no corresponding
2844 * condition constraints. However, we do have an additional
2845 * conditional validity constraint that maps to the same
2846 * dependence relation
2847 * as the condition constraint on B. If we did not make a distinction
2848 * between tagged condition and tagged conditional validity
2849 * dependences, then we
2850 * could end up treating this shared dependence as an condition
2851 * constraint on A, forcing a localization of the conditions,
2852 * which is impossible.
2853 */
2854 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
2855 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
2856 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
2857 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2858 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2859 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
2860 1
2861 },
2862 /* TACO 2013 Fig. 7 */
2863 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2864 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2865 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2866 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
2867 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
2868 "0 <= i < n and 0 <= j < n - 1 }",
2869 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
2870 "0 <= i < n and 0 <= j < j' < n;"
2871 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
2872 "0 <= i < i' < n and 0 <= j,j' < n;"
2873 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
2874 "0 <= i,j,j' < n and j < j' }",
2875 2
2876 },
2877 /* TACO 2013 Fig. 7, without tags */
2878 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2879 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2880 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2881 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2882 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2883 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
2884 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
2885 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
2886 1
2887 },
2888 /* TACO 2013 Fig. 12 */
2889 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
2890 "S3[i,3] : 0 <= i <= 1 }",
2891 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
2892 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
2893 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
2894 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
2895 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2896 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
2897 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2898 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
2899 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
2900 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
2901 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
2902 1
2903 }
2904 };
2905
2906 /* Test schedule construction based on conditional constraints.
2907 * In particular, check the number of members in the outer band
2908 * as an indication of whether tiling is possible or not.
2909 */
2910 static int test_conditional_schedule_constraints(isl_ctx *ctx)
2911 {
2912 int i;
2913 isl_union_set *domain;
2914 isl_union_map *condition;
2915 isl_union_map *flow;
2916 isl_union_map *validity;
2917 isl_schedule_constraints *sc;
2918 isl_schedule *schedule;
2919 isl_band_list *list;
2920 isl_band *band;
2921 int n_member;
2922
2923 for (i = 0; i < ARRAY_SIZE(live_range_tests); ++i) {
2924 domain = isl_union_set_read_from_str(ctx,
2925 live_range_tests[i].domain);
2926 flow = isl_union_map_read_from_str(ctx,
2927 live_range_tests[i].flow);
2928 condition = isl_union_map_read_from_str(ctx,
2929 live_range_tests[i].condition);
2930 validity = isl_union_map_read_from_str(ctx,
2931 live_range_tests[i].conditional_validity);
2932 sc = isl_schedule_constraints_on_domain(domain);
2933 sc = isl_schedule_constraints_set_validity(sc,
2934 isl_union_map_copy(flow));
2935 sc = isl_schedule_constraints_set_proximity(sc, flow);
2936 sc = isl_schedule_constraints_set_conditional_validity(sc,
2937 condition, validity);
2938 schedule = isl_schedule_constraints_compute_schedule(sc);
2939 list = isl_schedule_get_band_forest(schedule);
2940 band = isl_band_list_get_band(list, 0);
2941 n_member = isl_band_n_member(band);
2942 isl_band_free(band);
2943 isl_band_list_free(list);
2944 isl_schedule_free(schedule);
2945
2946 if (!schedule)
2947 return -1;
2948 if (n_member != live_range_tests[i].outer_band_n)
2949 isl_die(ctx, isl_error_unknown,
2950 "unexpected number of members in outer band",
2951 return -1);
2952 }
2953 return 0;
2954 }
2955
2956 int test_schedule(isl_ctx *ctx)
2957 {
2958 const char *D, *W, *R, *V, *P, *S;
2959
2960 /* Handle resulting schedule with zero bands. */
2961 if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2962 return -1;
2963
2964 /* Jacobi */
2965 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2966 W = "{ S1[t,i] -> a[t,i] }";
2967 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2968 "S1[t,i] -> a[t-1,i+1] }";
2969 S = "{ S1[t,i] -> [t,i] }";
2970 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2971 return -1;
2972
2973 /* Fig. 5 of CC2008 */
2974 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2975 "j <= -1 + N }";
2976 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2977 "j >= 2 and j <= -1 + N }";
2978 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2979 "j >= 2 and j <= -1 + N; "
2980 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2981 "j >= 2 and j <= -1 + N }";
2982 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2983 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2984 return -1;
2985
2986 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2987 W = "{ S1[i] -> a[i] }";
2988 R = "{ S2[i] -> a[i+1] }";
2989 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2990 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2991 return -1;
2992
2993 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2994 W = "{ S1[i] -> a[i] }";
2995 R = "{ S2[i] -> a[9-i] }";
2996 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2997 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2998 return -1;
2999
3000 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
3001 W = "{ S1[i] -> a[i] }";
3002 R = "[N] -> { S2[i] -> a[N-1-i] }";
3003 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3004 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
3005 return -1;
3006
3007 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
3008 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
3009 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
3010 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
3011 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3012 return -1;
3013
3014 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3015 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
3016 R = "{ S2[i,j] -> a[i-1,j] }";
3017 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3018 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3019 return -1;
3020
3021 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3022 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
3023 R = "{ S2[i,j] -> a[i,j-1] }";
3024 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3025 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3026 return -1;
3027
3028 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
3029 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
3030 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
3031 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
3032 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
3033 "S_0[] -> [0, 0, 0] }";
3034 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
3035 return -1;
3036 ctx->opt->schedule_parametric = 0;
3037 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3038 return -1;
3039 ctx->opt->schedule_parametric = 1;
3040
3041 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
3042 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
3043 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
3044 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
3045 "S4[i] -> a[i,N] }";
3046 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
3047 "S4[i] -> [4,i,0] }";
3048 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
3049 return -1;
3050
3051 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
3052 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3053 "j <= N }";
3054 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3055 "j <= N; "
3056 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
3057 "j <= N }";
3058 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3059 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3060 return -1;
3061
3062 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
3063 " S_2[t] : t >= 0 and t <= -1 + N; "
3064 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
3065 "i <= -1 + N }";
3066 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
3067 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
3068 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
3069 "i >= 0 and i <= -1 + N }";
3070 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
3071 "i >= 0 and i <= -1 + N; "
3072 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
3073 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
3074 " S_0[t] -> [0, t, 0] }";
3075
3076 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3077 return -1;
3078 ctx->opt->schedule_parametric = 0;
3079 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3080 return -1;
3081 ctx->opt->schedule_parametric = 1;
3082
3083 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
3084 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
3085 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
3086 return -1;
3087
3088 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3089 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3090 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3091 "j >= 0 and j <= -1 + N; "
3092 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3093 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3094 "j >= 0 and j <= -1 + N; "
3095 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3096 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3097 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3098 return -1;
3099
3100 D = "{ S_0[i] : i >= 0 }";
3101 W = "{ S_0[i] -> a[i] : i >= 0 }";
3102 R = "{ S_0[i] -> a[0] : i >= 0 }";
3103 S = "{ S_0[i] -> [0, i, 0] }";
3104 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3105 return -1;
3106
3107 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3108 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3109 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3110 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3111 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3112 return -1;
3113
3114 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3115 "k <= -1 + n and k >= 0 }";
3116 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3117 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3118 "k <= -1 + n and k >= 0; "
3119 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3120 "k <= -1 + n and k >= 0; "
3121 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3122 "k <= -1 + n and k >= 0 }";
3123 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
3124 ctx->opt->schedule_outer_coincidence = 1;
3125 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3126 return -1;
3127 ctx->opt->schedule_outer_coincidence = 0;
3128
3129 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
3130 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3131 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3132 "Stmt_for_body24[i0, i1, 1, 0]:"
3133 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3134 "Stmt_for_body7[i0, i1, i2]:"
3135 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3136 "i2 <= 7 }";
3137
3138 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
3139 "Stmt_for_body24[1, i1, i2, i3]:"
3140 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3141 "i2 >= 1;"
3142 "Stmt_for_body24[0, i1, i2, i3] -> "
3143 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3144 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3145 "i3 >= 0;"
3146 "Stmt_for_body24[0, i1, i2, i3] ->"
3147 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3148 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3149 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3150 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3151 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3152 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3153 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3154 "i1 <= 6 and i1 >= 0;"
3155 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3156 "Stmt_for_body7[i0, i1, i2] -> "
3157 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3158 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3159 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3160 "Stmt_for_body7[i0, i1, i2] -> "
3161 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3162 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3163 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3164 P = V;
3165 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3166 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3167 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3168
3169 if (test_special_schedule(ctx, D, V, P, S) < 0)
3170 return -1;
3171
3172 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3173 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3174 "j >= 1 and j <= 7;"
3175 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3176 "j >= 1 and j <= 8 }";
3177 P = "{ }";
3178 S = "{ S_0[i, j] -> [i + j, j] }";
3179 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3180 if (test_special_schedule(ctx, D, V, P, S) < 0)
3181 return -1;
3182 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3183
3184 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3185 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3186 "j >= 0 and j <= -1 + i }";
3187 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3188 "i <= -1 + N and j >= 0;"
3189 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3190 "i <= -2 + N }";
3191 P = "{ }";
3192 S = "{ S_0[i, j] -> [i, j] }";
3193 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3194 if (test_special_schedule(ctx, D, V, P, S) < 0)
3195 return -1;
3196 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3197
3198 /* Test both algorithms on a case with only proximity dependences. */
3199 D = "{ S[i,j] : 0 <= i <= 10 }";
3200 V = "{ }";
3201 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3202 S = "{ S[i, j] -> [j, i] }";
3203 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3204 if (test_special_schedule(ctx, D, V, P, S) < 0)
3205 return -1;
3206 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3207 if (test_special_schedule(ctx, D, V, P, S) < 0)
3208 return -1;
3209
3210 D = "{ A[a]; B[] }";
3211 V = "{}";
3212 P = "{ A[a] -> B[] }";
3213 if (test_has_schedule(ctx, D, V, P) < 0)
3214 return -1;
3215
3216 if (test_padded_schedule(ctx) < 0)
3217 return -1;
3218
3219 /* Check that check for progress is not confused by rational
3220 * solution.
3221 */
3222 D = "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3223 V = "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3224 "i0 <= -2 + N; "
3225 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3226 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3227 P = "{}";
3228 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3229 if (test_has_schedule(ctx, D, V, P) < 0)
3230 return -1;
3231 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3232
3233 /* Check that we allow schedule rows that are only non-trivial
3234 * on some full-dimensional domains.
3235 */
3236 D = "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
3237 V = "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
3238 "S1[j] -> S2[1] : 0 <= j <= 1 }";
3239 P = "{}";
3240 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3241 if (test_has_schedule(ctx, D, V, P) < 0)
3242 return -1;
3243 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3244
3245 if (test_conditional_schedule_constraints(ctx) < 0)
3246 return -1;
3247
3248 return 0;
3249 }
3250
3251 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
3252 {
3253 isl_union_map *umap;
3254 int test;
3255
3256 umap = isl_union_map_read_from_str(ctx, str);
3257 test = isl_union_map_plain_is_injective(umap);
3258 isl_union_map_free(umap);
3259 if (test < 0)
3260 return -1;
3261 if (test == injective)
3262 return 0;
3263 if (injective)
3264 isl_die(ctx, isl_error_unknown,
3265 "map not detected as injective", return -1);
3266 else
3267 isl_die(ctx, isl_error_unknown,
3268 "map detected as injective", return -1);
3269 }
3270
3271 int test_injective(isl_ctx *ctx)
3272 {
3273 const char *str;
3274
3275 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3276 return -1;
3277 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
3278 return -1;
3279 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
3280 return -1;
3281 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
3282 return -1;
3283 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3284 return -1;
3285 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3286 return -1;
3287 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3288 return -1;
3289 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3290 return -1;
3291
3292 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3293 if (test_plain_injective(ctx, str, 1))
3294 return -1;
3295 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3296 if (test_plain_injective(ctx, str, 0))
3297 return -1;
3298
3299 return 0;
3300 }
3301
3302 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
3303 {
3304 isl_aff *aff2;
3305 int equal;
3306
3307 if (!aff)
3308 return -1;
3309
3310 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
3311 equal = isl_aff_plain_is_equal(aff, aff2);
3312 isl_aff_free(aff2);
3313
3314 return equal;
3315 }
3316
3317 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
3318 {
3319 int equal;
3320
3321 equal = aff_plain_is_equal(aff, str);
3322 if (equal < 0)
3323 return -1;
3324 if (!equal)
3325 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
3326 "result not as expected", return -1);
3327 return 0;
3328 }
3329
3330 struct {
3331 __isl_give isl_aff *(*fn)(__isl_take isl_aff *aff1,
3332 __isl_take isl_aff *aff2);
3333 } aff_bin_op[] = {
3334 ['+'] = { &isl_aff_add },
3335 ['-'] = { &isl_aff_sub },
3336 ['*'] = { &isl_aff_mul },
3337 ['/'] = { &isl_aff_div },
3338 };
3339
3340 struct {
3341 const char *arg1;
3342 unsigned char op;
3343 const char *arg2;
3344 const char *res;
3345 } aff_bin_tests[] = {
3346 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3347 "{ [i] -> [2i] }" },
3348 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3349 "{ [i] -> [0] }" },
3350 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3351 "{ [i] -> [2i] }" },
3352 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3353 "{ [i] -> [2i] }" },
3354 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
3355 "{ [i] -> [i/2] }" },
3356 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
3357 "{ [i] -> [i] }" },
3358 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3359 "{ [i] -> [NaN] }" },
3360 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3361 "{ [i] -> [NaN] }" },
3362 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3363 "{ [i] -> [NaN] }" },
3364 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3365 "{ [i] -> [NaN] }" },
3366 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
3367 "{ [i] -> [NaN] }" },
3368 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
3369 "{ [i] -> [NaN] }" },
3370 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3371 "{ [i] -> [NaN] }" },
3372 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3373 "{ [i] -> [NaN] }" },
3374 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3375 "{ [i] -> [NaN] }" },
3376 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3377 "{ [i] -> [NaN] }" },
3378 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
3379 "{ [i] -> [NaN] }" },
3380 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
3381 "{ [i] -> [NaN] }" },
3382 };
3383
3384 /* Perform some basic tests of binary operations on isl_aff objects.
3385 */
3386 static int test_bin_aff(isl_ctx *ctx)
3387 {
3388 int i;
3389 isl_aff *aff1, *aff2, *res;
3390 __isl_give isl_aff *(*fn)(__isl_take isl_aff *aff1,
3391 __isl_take isl_aff *aff2);
3392 int ok;
3393
3394 for (i = 0; i < ARRAY_SIZE(aff_bin_tests); ++i) {
3395 aff1 = isl_aff_read_from_str(ctx, aff_bin_tests[i].arg1);
3396 aff2 = isl_aff_read_from_str(ctx, aff_bin_tests[i].arg2);
3397 res = isl_aff_read_from_str(ctx, aff_bin_tests[i].res);
3398 fn = aff_bin_op[aff_bin_tests[i].op].fn;
3399 aff1 = fn(aff1, aff2);
3400 if (isl_aff_is_nan(res))
3401 ok = isl_aff_is_nan(aff1);
3402 else
3403 ok = isl_aff_plain_is_equal(aff1, res);
3404 isl_aff_free(aff1);
3405 isl_aff_free(res);
3406 if (ok < 0)
3407 return -1;
3408 if (!ok)
3409 isl_die(ctx, isl_error_unknown,
3410 "unexpected result", return -1);
3411 }
3412
3413 return 0;
3414 }
3415
3416 struct {
3417 __isl_give isl_union_pw_multi_aff *(*fn)(
3418 __isl_take isl_union_pw_multi_aff *upma1,
3419 __isl_take isl_union_pw_multi_aff *upma2);
3420 const char *arg1;
3421 const char *arg2;
3422 const char *res;
3423 } upma_bin_tests[] = {
3424 { &isl_union_pw_multi_aff_add, "{ A[] -> [0]; B[0] -> [1] }",
3425 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
3426 { &isl_union_pw_multi_aff_union_add, "{ A[] -> [0]; B[0] -> [1] }",
3427 "{ B[x] -> [2] : x >= 0 }",
3428 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
3429 };
3430
3431 /* Perform some basic tests of binary operations on
3432 * isl_union_pw_multi_aff objects.
3433 */
3434 static int test_bin_upma(isl_ctx *ctx)
3435 {
3436 int i;
3437 isl_union_pw_multi_aff *upma1, *upma2, *res;
3438 int ok;
3439
3440 for (i = 0; i < ARRAY_SIZE(upma_bin_tests); ++i) {
3441 upma1 = isl_union_pw_multi_aff_read_from_str(ctx,
3442 upma_bin_tests[i].arg1);
3443 upma2 = isl_union_pw_multi_aff_read_from_str(ctx,
3444 upma_bin_tests[i].arg2);
3445 res = isl_union_pw_multi_aff_read_from_str(ctx,
3446 upma_bin_tests[i].res);
3447 upma1 = upma_bin_tests[i].fn(upma1, upma2);
3448 ok = isl_union_pw_multi_aff_plain_is_equal(upma1, res);
3449 isl_union_pw_multi_aff_free(upma1);
3450 isl_union_pw_multi_aff_free(res);
3451 if (ok < 0)
3452 return -1;
3453 if (!ok)
3454 isl_die(ctx, isl_error_unknown,
3455 "unexpected result", return -1);
3456 }
3457
3458 return 0;
3459 }
3460
3461 int test_aff(isl_ctx *ctx)
3462 {
3463 const char *str;
3464 isl_set *set;
3465 isl_space *space;
3466 isl_local_space *ls;
3467 isl_aff *aff;
3468 int zero, equal;
3469
3470 if (test_bin_aff(ctx) < 0)
3471 return -1;
3472 if (test_bin_upma(ctx) < 0)
3473 return -1;
3474
3475 space = isl_space_set_alloc(ctx, 0, 1);
3476 ls = isl_local_space_from_space(space);
3477 aff = isl_aff_zero_on_domain(ls);
3478
3479 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3480 aff = isl_aff_scale_down_ui(aff, 3);
3481 aff = isl_aff_floor(aff);
3482 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3483 aff = isl_aff_scale_down_ui(aff, 2);
3484 aff = isl_aff_floor(aff);
3485 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3486
3487 str = "{ [10] }";
3488 set = isl_set_read_from_str(ctx, str);
3489 aff = isl_aff_gist(aff, set);
3490
3491 aff = isl_aff_add_constant_si(aff, -16);
3492 zero = isl_aff_plain_is_zero(aff);
3493 isl_aff_free(aff);
3494
3495 if (zero < 0)
3496 return -1;
3497 if (!zero)
3498 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3499
3500 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
3501 aff = isl_aff_scale_down_ui(aff, 64);
3502 aff = isl_aff_floor(aff);
3503 equal = aff_check_plain_equal(aff, "{ [-1] }");
3504 isl_aff_free(aff);
3505 if (equal < 0)
3506 return -1;
3507
3508 return 0;
3509 }
3510
3511 int test_dim_max(isl_ctx *ctx)
3512 {
3513 int equal;
3514 const char *str;
3515 isl_set *set1, *set2;
3516 isl_set *set;
3517 isl_map *map;
3518 isl_pw_aff *pwaff;
3519
3520 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
3521 set = isl_set_read_from_str(ctx, str);
3522 pwaff = isl_set_dim_max(set, 0);
3523 set1 = isl_set_from_pw_aff(pwaff);
3524 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
3525 set2 = isl_set_read_from_str(ctx, str);
3526 equal = isl_set_is_equal(set1, set2);
3527 isl_set_free(set1);
3528 isl_set_free(set2);
3529 if (equal < 0)
3530 return -1;
3531 if (!equal)
3532 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3533
3534 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
3535 set = isl_set_read_from_str(ctx, str);
3536 pwaff = isl_set_dim_max(set, 0);
3537 set1 = isl_set_from_pw_aff(pwaff);
3538 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3539 set2 = isl_set_read_from_str(ctx, str);
3540 equal = isl_set_is_equal(set1, set2);
3541 isl_set_free(set1);
3542 isl_set_free(set2);
3543 if (equal < 0)
3544 return -1;
3545 if (!equal)
3546 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3547
3548 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
3549 set = isl_set_read_from_str(ctx, str);
3550 pwaff = isl_set_dim_max(set, 0);
3551 set1 = isl_set_from_pw_aff(pwaff);
3552 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3553 set2 = isl_set_read_from_str(ctx, str);
3554 equal = isl_set_is_equal(set1, set2);
3555 isl_set_free(set1);
3556 isl_set_free(set2);
3557 if (equal < 0)
3558 return -1;
3559 if (!equal)
3560 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3561
3562 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
3563 "0 <= i < N and 0 <= j < M }";
3564 map = isl_map_read_from_str(ctx, str);
3565 set = isl_map_range(map);
3566
3567 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
3568 set1 = isl_set_from_pw_aff(pwaff);
3569 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
3570 set2 = isl_set_read_from_str(ctx, str);
3571 equal = isl_set_is_equal(set1, set2);
3572 isl_set_free(set1);
3573 isl_set_free(set2);
3574
3575 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
3576 set1 = isl_set_from_pw_aff(pwaff);
3577 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
3578 set2 = isl_set_read_from_str(ctx, str);
3579 if (equal >= 0 && equal)
3580 equal = isl_set_is_equal(set1, set2);
3581 isl_set_free(set1);
3582 isl_set_free(set2);
3583
3584 isl_set_free(set);
3585
3586 if (equal < 0)
3587 return -1;
3588 if (!equal)
3589 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3590
3591 /* Check that solutions are properly merged. */
3592 str = "[n] -> { [a, b, c] : c >= -4a - 2b and "
3593 "c <= -1 + n - 4a - 2b and c >= -2b and "
3594 "4a >= -4 + n and c >= 0 }";
3595 set = isl_set_read_from_str(ctx, str);
3596 pwaff = isl_set_dim_min(set, 2);
3597 set1 = isl_set_from_pw_aff(pwaff);
3598 str = "[n] -> { [(0)] : n >= 1 }";
3599 set2 = isl_set_read_from_str(ctx, str);
3600 equal = isl_set_is_equal(set1, set2);
3601 isl_set_free(set1);
3602 isl_set_free(set2);
3603
3604 if (equal < 0)
3605 return -1;
3606 if (!equal)
3607 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3608
3609 /* Check that empty solution lie in the right space. */
3610 str = "[n] -> { [t,a] : 1 = 0 }";
3611 set = isl_set_read_from_str(ctx, str);
3612 pwaff = isl_set_dim_max(set, 0);
3613 set1 = isl_set_from_pw_aff(pwaff);
3614 str = "[n] -> { [t] : 1 = 0 }";
3615 set2 = isl_set_read_from_str(ctx, str);
3616 equal = isl_set_is_equal(set1, set2);
3617 isl_set_free(set1);
3618 isl_set_free(set2);
3619
3620 if (equal < 0)
3621 return -1;
3622 if (!equal)
3623 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3624
3625 return 0;
3626 }
3627
3628 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
3629 */
3630 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff *pma,
3631 const char *str)
3632 {
3633 isl_ctx *ctx;
3634 isl_pw_multi_aff *pma2;
3635 int equal;
3636
3637 if (!pma)
3638 return -1;
3639
3640 ctx = isl_pw_multi_aff_get_ctx(pma);
3641 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3642 equal = isl_pw_multi_aff_plain_is_equal(pma, pma2);
3643 isl_pw_multi_aff_free(pma2);
3644
3645 return equal;
3646 }
3647
3648 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
3649 * represented by "str".
3650 */
3651 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff *pma,
3652 const char *str)
3653 {
3654 int equal;
3655
3656 equal = pw_multi_aff_plain_is_equal(pma, str);
3657 if (equal < 0)
3658 return -1;
3659 if (!equal)
3660 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_unknown,
3661 "result not as expected", return -1);
3662 return 0;
3663 }
3664
3665 /* Basic test for isl_pw_multi_aff_product.
3666 *
3667 * Check that multiple pieces are properly handled.
3668 */
3669 static int test_product_pma(isl_ctx *ctx)
3670 {
3671 int equal;
3672 const char *str;
3673 isl_pw_multi_aff *pma1, *pma2;
3674
3675 str = "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
3676 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
3677 str = "{ C[] -> D[] }";
3678 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3679 pma1 = isl_pw_multi_aff_product(pma1, pma2);
3680 str = "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
3681 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
3682 equal = pw_multi_aff_check_plain_equal(pma1, str);
3683 isl_pw_multi_aff_free(pma1);
3684 if (equal < 0)
3685 return -1;
3686
3687 return 0;
3688 }
3689
3690 int test_product(isl_ctx *ctx)
3691 {
3692 const char *str;
3693 isl_set *set;
3694 isl_union_set *uset1, *uset2;
3695 int ok;
3696
3697 str = "{ A[i] }";
3698 set = isl_set_read_from_str(ctx, str);
3699 set = isl_set_product(set, isl_set_copy(set));
3700 ok = isl_set_is_wrapping(set);
3701 isl_set_free(set);
3702 if (ok < 0)
3703 return -1;
3704 if (!ok)
3705 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3706
3707 str = "{ [] }";
3708 uset1 = isl_union_set_read_from_str(ctx, str);
3709 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
3710 str = "{ [[] -> []] }";
3711 uset2 = isl_union_set_read_from_str(ctx, str);
3712 ok = isl_union_set_is_equal(uset1, uset2);
3713 isl_union_set_free(uset1);
3714 isl_union_set_free(uset2);
3715 if (ok < 0)
3716 return -1;
3717 if (!ok)
3718 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3719
3720 if (test_product_pma(ctx) < 0)
3721 return -1;
3722
3723 return 0;
3724 }
3725
3726 /* Check that two sets are not considered disjoint just because
3727 * they have a different set of (named) parameters.
3728 */
3729 static int test_disjoint(isl_ctx *ctx)
3730 {
3731 const char *str;
3732 isl_set *set, *set2;
3733 int disjoint;
3734
3735 str = "[n] -> { [[]->[]] }";
3736 set = isl_set_read_from_str(ctx, str);
3737 str = "{ [[]->[]] }";
3738 set2 = isl_set_read_from_str(ctx, str);
3739 disjoint = isl_set_is_disjoint(set, set2);
3740 isl_set_free(set);
3741 isl_set_free(set2);
3742 if (disjoint < 0)
3743 return -1;
3744 if (disjoint)
3745 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3746
3747 return 0;
3748 }
3749
3750 int test_equal(isl_ctx *ctx)
3751 {
3752 const char *str;
3753 isl_set *set, *set2;
3754 int equal;
3755
3756 str = "{ S_6[i] }";
3757 set = isl_set_read_from_str(ctx, str);
3758 str = "{ S_7[i] }";
3759 set2 = isl_set_read_from_str(ctx, str);
3760 equal = isl_set_is_equal(set, set2);
3761 isl_set_free(set);
3762 isl_set_free(set2);
3763 if (equal < 0)
3764 return -1;
3765 if (equal)
3766 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3767
3768 return 0;
3769 }
3770
3771 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
3772 enum isl_dim_type type, unsigned pos, int fixed)
3773 {
3774 int test;
3775
3776 test = isl_map_plain_is_fixed(map, type, pos, NULL);
3777 isl_map_free(map);
3778 if (test < 0)
3779 return -1;
3780 if (test == fixed)
3781 return 0;
3782 if (fixed)
3783 isl_die(ctx, isl_error_unknown,
3784 "map not detected as fixed", return -1);
3785 else
3786 isl_die(ctx, isl_error_unknown,
3787 "map detected as fixed", return -1);
3788 }
3789
3790 int test_fixed(isl_ctx *ctx)
3791 {
3792 const char *str;
3793 isl_map *map;
3794
3795 str = "{ [i] -> [i] }";
3796 map = isl_map_read_from_str(ctx, str);
3797 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
3798 return -1;
3799 str = "{ [i] -> [1] }";
3800 map = isl_map_read_from_str(ctx, str);
3801 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3802 return -1;
3803 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
3804 map = isl_map_read_from_str(ctx, str);
3805 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3806 return -1;
3807 map = isl_map_read_from_str(ctx, str);
3808 map = isl_map_neg(map);
3809 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3810 return -1;
3811
3812 return 0;
3813 }
3814
3815 struct isl_vertices_test_data {
3816 const char *set;
3817 int n;
3818 const char *vertex[2];
3819 } vertices_tests[] = {
3820 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
3821 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
3822 { "{ A[t, i] : t = 14 and i = 1 }",
3823 1, { "{ A[14, 1] }" } },
3824 };
3825
3826 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
3827 */
3828 static int find_vertex(__isl_take isl_vertex *vertex, void *user)
3829 {
3830 struct isl_vertices_test_data *data = user;
3831 isl_ctx *ctx;
3832 isl_multi_aff *ma;
3833 isl_basic_set *bset;
3834 isl_pw_multi_aff *pma;
3835 int i;
3836 int equal;
3837
3838 ctx = isl_vertex_get_ctx(vertex);
3839 bset = isl_vertex_get_domain(vertex);
3840 ma = isl_vertex_get_expr(vertex);
3841 pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset), ma);
3842
3843 for (i = 0; i < data->n; ++i) {
3844 isl_pw_multi_aff *pma_i;
3845
3846 pma_i = isl_pw_multi_aff_read_from_str(ctx, data->vertex[i]);
3847 equal = isl_pw_multi_aff_plain_is_equal(pma, pma_i);
3848 isl_pw_multi_aff_free(pma_i);
3849
3850 if (equal < 0 || equal)
3851 break;
3852 }
3853
3854 isl_pw_multi_aff_free(pma);
3855 isl_vertex_free(vertex);
3856
3857 if (equal < 0)
3858 return -1;
3859
3860 return equal ? 0 : - 1;
3861 }
3862
3863 int test_vertices(isl_ctx *ctx)
3864 {
3865 int i;
3866
3867 for (i = 0; i < ARRAY_SIZE(vertices_tests); ++i) {
3868 isl_basic_set *bset;
3869 isl_vertices *vertices;
3870 int ok = 1;
3871 int n;
3872
3873 bset = isl_basic_set_read_from_str(ctx, vertices_tests[i].set);
3874 vertices = isl_basic_set_compute_vertices(bset);
3875 n = isl_vertices_get_n_vertices(vertices);
3876 if (vertices_tests[i].n != n)
3877 ok = 0;
3878 if (isl_vertices_foreach_vertex(vertices, &find_vertex,
3879 &vertices_tests[i]) < 0)
3880 ok = 0;
3881 isl_vertices_free(vertices);
3882 isl_basic_set_free(bset);
3883
3884 if (!vertices)
3885 return -1;
3886 if (!ok)
3887 isl_die(ctx, isl_error_unknown, "unexpected vertices",
3888 return -1);
3889 }
3890
3891 return 0;
3892 }
3893
3894 int test_union_pw(isl_ctx *ctx)
3895 {
3896 int equal;
3897 const char *str;
3898 isl_union_set *uset;
3899 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
3900
3901 str = "{ [x] -> x^2 }";
3902 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
3903 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
3904 uset = isl_union_pw_qpolynomial_domain(upwqp1);
3905 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
3906 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
3907 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
3908 isl_union_pw_qpolynomial_free(upwqp1);
3909 isl_union_pw_qpolynomial_free(upwqp2);
3910 if (equal < 0)
3911 return -1;
3912 if (!equal)
3913 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3914
3915 return 0;
3916 }
3917
3918 int test_output(isl_ctx *ctx)
3919 {
3920 char *s;
3921 const char *str;
3922 isl_pw_aff *pa;
3923 isl_printer *p;
3924 int equal;
3925
3926 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
3927 pa = isl_pw_aff_read_from_str(ctx, str);
3928
3929 p = isl_printer_to_str(ctx);
3930 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
3931 p = isl_printer_print_pw_aff(p, pa);
3932 s = isl_printer_get_str(p);
3933 isl_printer_free(p);
3934 isl_pw_aff_free(pa);
3935 if (!s)
3936 equal = -1;
3937 else
3938 equal = !strcmp(s, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
3939 free(s);
3940 if (equal < 0)
3941 return -1;
3942 if (!equal)
3943 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3944
3945 return 0;
3946 }
3947
3948 int test_sample(isl_ctx *ctx)
3949 {
3950 const char *str;
3951 isl_basic_set *bset1, *bset2;
3952 int empty, subset;
3953
3954 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
3955 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
3956 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
3957 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
3958 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
3959 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
3960 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
3961 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
3962 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3963 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3964 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3965 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3966 "d - 1073741821e and "
3967 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3968 "3j >= 1 - a + b + 2e and "
3969 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3970 "3i <= 4 - a + 4b - e and "
3971 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3972 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3973 "c <= -1 + a and 3i >= -2 - a + 3e and "
3974 "1073741822e <= 1073741823 - a + 1073741822b + c and "
3975 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3976 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3977 "1073741823e >= 1 + 1073741823b - d and "
3978 "3i >= 1073741823b + c - 1073741823e - f and "
3979 "3i >= 1 + 2b + e + 3g }";
3980 bset1 = isl_basic_set_read_from_str(ctx, str);
3981 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
3982 empty = isl_basic_set_is_empty(bset2);
3983 subset = isl_basic_set_is_subset(bset2, bset1);
3984 isl_basic_set_free(bset1);
3985 isl_basic_set_free(bset2);
3986 if (empty < 0 || subset < 0)
3987 return -1;
3988 if (empty)
3989 isl_die(ctx, isl_error_unknown, "point not found", return -1);
3990 if (!subset)
3991 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
3992
3993 return 0;
3994 }
3995
3996 int test_fixed_power(isl_ctx *ctx)
3997 {
3998 const char *str;
3999 isl_map *map;
4000 isl_int exp;
4001 int equal;
4002
4003 isl_int_init(exp);
4004 str = "{ [i] -> [i + 1] }";
4005 map = isl_map_read_from_str(ctx, str);
4006 isl_int_set_si(exp, 23);
4007 map = isl_map_fixed_power(map, exp);
4008 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
4009 isl_int_clear(exp);
4010 isl_map_free(map);
4011 if (equal < 0)
4012 return -1;
4013
4014 return 0;
4015 }
4016
4017 int test_slice(isl_ctx *ctx)
4018 {
4019 const char *str;
4020 isl_map *map;
4021 int equal;
4022
4023 str = "{ [i] -> [j] }";
4024 map = isl_map_read_from_str(ctx, str);
4025 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
4026 equal = map_check_equal(map, "{ [i] -> [i] }");
4027 isl_map_free(map);
4028 if (equal < 0)
4029 return -1;
4030
4031 str = "{ [i] -> [j] }";
4032 map = isl_map_read_from_str(ctx, str);
4033 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
4034 equal = map_check_equal(map, "{ [i] -> [j] }");
4035 isl_map_free(map);
4036 if (equal < 0)
4037 return -1;
4038
4039 str = "{ [i] -> [j] }";
4040 map = isl_map_read_from_str(ctx, str);
4041 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
4042 equal = map_check_equal(map, "{ [i] -> [-i] }");
4043 isl_map_free(map);
4044 if (equal < 0)
4045 return -1;
4046
4047 str = "{ [i] -> [j] }";
4048 map = isl_map_read_from_str(ctx, str);
4049 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
4050 equal = map_check_equal(map, "{ [0] -> [j] }");
4051 isl_map_free(map);
4052 if (equal < 0)
4053 return -1;
4054
4055 str = "{ [i] -> [j] }";
4056 map = isl_map_read_from_str(ctx, str);
4057 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
4058 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
4059 isl_map_free(map);
4060 if (equal < 0)
4061 return -1;
4062
4063 str = "{ [i] -> [j] }";
4064 map = isl_map_read_from_str(ctx, str);
4065 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
4066 equal = map_check_equal(map, "{ [i] -> [j] : false }");
4067 isl_map_free(map);
4068 if (equal < 0)
4069 return -1;
4070
4071 return 0;
4072 }
4073
4074 int test_eliminate(isl_ctx *ctx)
4075 {
4076 const char *str;
4077 isl_map *map;
4078 int equal;
4079
4080 str = "{ [i] -> [j] : i = 2j }";
4081 map = isl_map_read_from_str(ctx, str);
4082 map = isl_map_eliminate(map, isl_dim_out, 0, 1);
4083 equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
4084 isl_map_free(map);
4085 if (equal < 0)
4086 return -1;
4087
4088 return 0;
4089 }
4090
4091 /* Check that isl_set_dim_residue_class detects that the values of j
4092 * in the set below are all odd and that it does not detect any spurious
4093 * strides.
4094 */
4095 static int test_residue_class(isl_ctx *ctx)
4096 {
4097 const char *str;
4098 isl_set *set;
4099 isl_int m, r;
4100 int res;
4101
4102 str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
4103 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
4104 set = isl_set_read_from_str(ctx, str);
4105 isl_int_init(m);
4106 isl_int_init(r);
4107 res = isl_set_dim_residue_class(set, 1, &m, &r);
4108 if (res >= 0 &&
4109 (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
4110 isl_die(ctx, isl_error_unknown, "incorrect residue class",
4111 res = -1);
4112 isl_int_clear(r);
4113 isl_int_clear(m);
4114 isl_set_free(set);
4115
4116 return res;
4117 }
4118
4119 int test_align_parameters(isl_ctx *ctx)
4120 {
4121 const char *str;
4122 isl_space *space;
4123 isl_multi_aff *ma1, *ma2;
4124 int equal;
4125
4126 str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
4127 ma1 = isl_multi_aff_read_from_str(ctx, str);
4128
4129 space = isl_space_params_alloc(ctx, 1);
4130 space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
4131 ma1 = isl_multi_aff_align_params(ma1, space);
4132
4133 str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
4134 ma2 = isl_multi_aff_read_from_str(ctx, str);
4135
4136 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
4137
4138 isl_multi_aff_free(ma1);
4139 isl_multi_aff_free(ma2);
4140
4141 if (equal < 0)
4142 return -1;
4143 if (!equal)
4144 isl_die(ctx, isl_error_unknown,
4145 "result not as expected", return -1);
4146
4147 return 0;
4148 }
4149
4150 static int test_list(isl_ctx *ctx)
4151 {
4152 isl_id *a, *b, *c, *d, *id;
4153 isl_id_list *list;
4154 int ok;
4155
4156 a = isl_id_alloc(ctx, "a", NULL);
4157 b = isl_id_alloc(ctx, "b", NULL);
4158 c = isl_id_alloc(ctx, "c", NULL);
4159 d = isl_id_alloc(ctx, "d", NULL);
4160
4161 list = isl_id_list_alloc(ctx, 4);
4162 list = isl_id_list_add(list, a);
4163 list = isl_id_list_add(list, b);
4164 list = isl_id_list_add(list, c);
4165 list = isl_id_list_add(list, d);
4166 list = isl_id_list_drop(list, 1, 1);
4167
4168 if (isl_id_list_n_id(list) != 3) {
4169 isl_id_list_free(list);
4170 isl_die(ctx, isl_error_unknown,
4171 "unexpected number of elements in list", return -1);
4172 }
4173
4174 id = isl_id_list_get_id(list, 0);
4175 ok = id == a;
4176 isl_id_free(id);
4177 id = isl_id_list_get_id(list, 1);
4178 ok = ok && id == c;
4179 isl_id_free(id);
4180 id = isl_id_list_get_id(list, 2);
4181 ok = ok && id == d;
4182 isl_id_free(id);
4183
4184 isl_id_list_free(list);
4185
4186 if (!ok)
4187 isl_die(ctx, isl_error_unknown,
4188 "unexpected elements in list", return -1);
4189
4190 return 0;
4191 }
4192
4193 const char *set_conversion_tests[] = {
4194 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4195 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4196 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4197 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4198 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
4199 };
4200
4201 /* Check that converting from isl_set to isl_pw_multi_aff and back
4202 * to isl_set produces the original isl_set.
4203 */
4204 static int test_set_conversion(isl_ctx *ctx)
4205 {
4206 int i;
4207 const char *str;
4208 isl_set *set1, *set2;
4209 isl_pw_multi_aff *pma;
4210 int equal;
4211
4212 for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
4213 str = set_conversion_tests[i];
4214 set1 = isl_set_read_from_str(ctx, str);
4215 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
4216 set2 = isl_set_from_pw_multi_aff(pma);
4217 equal = isl_set_is_equal(set1, set2);
4218 isl_set_free(set1);
4219 isl_set_free(set2);
4220
4221 if (equal < 0)
4222 return -1;
4223 if (!equal)
4224 isl_die(ctx, isl_error_unknown, "bad conversion",
4225 return -1);
4226 }
4227
4228 return 0;
4229 }
4230
4231 /* Check that converting from isl_map to isl_pw_multi_aff and back
4232 * to isl_map produces the original isl_map.
4233 */
4234 static int test_map_conversion(isl_ctx *ctx)
4235 {
4236 const char *str;
4237 isl_map *map1, *map2;
4238 isl_pw_multi_aff *pma;
4239 int equal;
4240
4241 str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
4242 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4243 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4244 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4245 "9e <= -2 - 2a) }";
4246 map1 = isl_map_read_from_str(ctx, str);
4247 pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
4248 map2 = isl_map_from_pw_multi_aff(pma);
4249 equal = isl_map_is_equal(map1, map2);
4250 isl_map_free(map1);
4251 isl_map_free(map2);
4252
4253 if (equal < 0)
4254 return -1;
4255 if (!equal)
4256 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
4257
4258 return 0;
4259 }
4260
4261 static int test_conversion(isl_ctx *ctx)
4262 {
4263 if (test_set_conversion(ctx) < 0)
4264 return -1;
4265 if (test_map_conversion(ctx) < 0)
4266 return -1;
4267 return 0;
4268 }
4269
4270 /* Check that isl_basic_map_curry does not modify input.
4271 */
4272 static int test_curry(isl_ctx *ctx)
4273 {
4274 const char *str;
4275 isl_basic_map *bmap1, *bmap2;
4276 int equal;
4277
4278 str = "{ [A[] -> B[]] -> C[] }";
4279 bmap1 = isl_basic_map_read_from_str(ctx, str);
4280 bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
4281 equal = isl_basic_map_is_equal(bmap1, bmap2);
4282 isl_basic_map_free(bmap1);
4283 isl_basic_map_free(bmap2);
4284
4285 if (equal < 0)
4286 return -1;
4287 if (equal)
4288 isl_die(ctx, isl_error_unknown,
4289 "curried map should not be equal to original",
4290 return -1);
4291
4292 return 0;
4293 }
4294
4295 struct {
4296 const char *set;
4297 const char *ma;
4298 const char *res;
4299 } preimage_tests[] = {
4300 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4301 "{ A[j,i] -> B[i,j] }",
4302 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4303 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4304 "{ A[a,b] -> B[a/2,b/6] }",
4305 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4306 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4307 "{ A[a,b] -> B[a/2,b/6] }",
4308 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4309 "exists i,j : a = 2 i and b = 6 j }" },
4310 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4311 "[n] -> { : 0 <= n <= 100 }" },
4312 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4313 "{ A[a] -> B[2a] }",
4314 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4315 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4316 "{ A[a] -> B[([a/2])] }",
4317 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4318 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4319 "{ A[a] -> B[a,a,a/3] }",
4320 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4321 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4322 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4323 };
4324
4325 static int test_preimage_basic_set(isl_ctx *ctx)
4326 {
4327 int i;
4328 isl_basic_set *bset1, *bset2;
4329 isl_multi_aff *ma;
4330 int equal;
4331
4332 for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
4333 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
4334 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
4335 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
4336 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
4337 equal = isl_basic_set_is_equal(bset1, bset2);
4338 isl_basic_set_free(bset1);
4339 isl_basic_set_free(bset2);
4340 if (equal < 0)
4341 return -1;
4342 if (!equal)
4343 isl_die(ctx, isl_error_unknown, "bad preimage",
4344 return -1);
4345 }
4346
4347 return 0;
4348 }
4349
4350 struct {
4351 const char *map;
4352 const char *ma;
4353 const char *res;
4354 } preimage_domain_tests[] = {
4355 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4356 "{ A[j,i] -> B[i,j] }",
4357 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4358 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4359 "{ A[i] -> B[i + 1] }",
4360 "{ A[i] -> C[i + 1] }" },
4361 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4362 "{ A[i] -> B[i + 1] }",
4363 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4364 { "{ B[i] -> C[([i/2])] }",
4365 "{ A[i] -> B[2i] }",
4366 "{ A[i] -> C[i] }" },
4367 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4368 "{ A[i] -> B[([i/5]), ([i/7])] }",
4369 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4370 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4371 "[N] -> { A[] -> B[([N/5])] }",
4372 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4373 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4374 "{ A[i] -> B[2i] }",
4375 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4376 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4377 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4378 "{ A[i] -> B[2i] }",
4379 "{ A[i] -> C[2i] }" },
4380 };
4381
4382 static int test_preimage_union_map(isl_ctx *ctx)
4383 {
4384 int i;
4385 isl_union_map *umap1, *umap2;
4386 isl_multi_aff *ma;
4387 int equal;
4388
4389 for (i = 0; i < ARRAY_SIZE(preimage_domain_tests); ++i) {
4390 umap1 = isl_union_map_read_from_str(ctx,
4391 preimage_domain_tests[i].map);
4392 ma = isl_multi_aff_read_from_str(ctx,
4393 preimage_domain_tests[i].ma);
4394 umap2 = isl_union_map_read_from_str(ctx,
4395 preimage_domain_tests[i].res);
4396 umap1 = isl_union_map_preimage_domain_multi_aff(umap1, ma);
4397 equal = isl_union_map_is_equal(umap1, umap2);
4398 isl_union_map_free(umap1);
4399 isl_union_map_free(umap2);
4400 if (equal < 0)
4401 return -1;
4402 if (!equal)
4403 isl_die(ctx, isl_error_unknown, "bad preimage",
4404 return -1);
4405 }
4406
4407 return 0;
4408 }
4409
4410 static int test_preimage(isl_ctx *ctx)
4411 {
4412 if (test_preimage_basic_set(ctx) < 0)
4413 return -1;
4414 if (test_preimage_union_map(ctx) < 0)
4415 return -1;
4416
4417 return 0;
4418 }
4419
4420 struct {
4421 const char *ma1;
4422 const char *ma;
4423 const char *res;
4424 } pullback_tests[] = {
4425 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
4426 "{ A[a,b] -> C[b + 2a] }" },
4427 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
4428 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
4429 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
4430 "{ A[a] -> C[(a)/6] }" },
4431 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
4432 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
4433 "{ A[a] -> C[(2a)/3] }" },
4434 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
4435 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
4436 "{ A[i,j] -> C[i + j, i + j] }"},
4437 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
4438 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
4439 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
4440 };
4441
4442 static int test_pullback(isl_ctx *ctx)
4443 {
4444 int i;
4445 isl_multi_aff *ma1, *ma2;
4446 isl_multi_aff *ma;
4447 int equal;
4448
4449 for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
4450 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
4451 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
4452 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
4453 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
4454 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
4455 isl_multi_aff_free(ma1);
4456 isl_multi_aff_free(ma2);
4457 if (equal < 0)
4458 return -1;
4459 if (!equal)
4460 isl_die(ctx, isl_error_unknown, "bad pullback",
4461 return -1);
4462 }
4463
4464 return 0;
4465 }
4466
4467 /* Check that negation is printed correctly.
4468 */
4469 static int test_ast(isl_ctx *ctx)
4470 {
4471 isl_ast_expr *expr, *expr1, *expr2, *expr3;
4472 char *str;
4473 int ok;
4474
4475 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
4476 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
4477 expr = isl_ast_expr_add(expr1, expr2);
4478 expr = isl_ast_expr_neg(expr);
4479 str = isl_ast_expr_to_str(expr);
4480 ok = str ? !strcmp(str, "-(A + B)") : -1;
4481 free(str);
4482 isl_ast_expr_free(expr);
4483
4484 if (ok < 0)
4485 return -1;
4486 if (!ok)
4487 isl_die(ctx, isl_error_unknown,
4488 "isl_ast_expr printed incorrectly", return -1);
4489
4490 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
4491 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
4492 expr = isl_ast_expr_add(expr1, expr2);
4493 expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
4494 expr = isl_ast_expr_sub(expr3, expr);
4495 str = isl_ast_expr_to_str(expr);
4496 ok = str ? !strcmp(str, "C - (A + B)") : -1;
4497 free(str);
4498 isl_ast_expr_free(expr);
4499
4500 if (ok < 0)
4501 return -1;
4502 if (!ok)
4503 isl_die(ctx, isl_error_unknown,
4504 "isl_ast_expr printed incorrectly", return -1);
4505
4506 return 0;
4507 }
4508
4509 /* Check that isl_ast_build_expr_from_set returns a valid expression
4510 * for an empty set. Note that isl_ast_build_expr_from_set getting
4511 * called on an empty set probably indicates a bug in the caller.
4512 */
4513 static int test_ast_build(isl_ctx *ctx)
4514 {
4515 isl_set *set;
4516 isl_ast_build *build;
4517 isl_ast_expr *expr;
4518
4519 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4520 build = isl_ast_build_from_context(set);
4521
4522 set = isl_set_empty(isl_space_params_alloc(ctx, 0));
4523 expr = isl_ast_build_expr_from_set(build, set);
4524
4525 isl_ast_expr_free(expr);
4526 isl_ast_build_free(build);
4527
4528 if (!expr)
4529 return -1;
4530
4531 return 0;
4532 }
4533
4534 /* Internal data structure for before_for and after_for callbacks.
4535 *
4536 * depth is the current depth
4537 * before is the number of times before_for has been called
4538 * after is the number of times after_for has been called
4539 */
4540 struct isl_test_codegen_data {
4541 int depth;
4542 int before;
4543 int after;
4544 };
4545
4546 /* This function is called before each for loop in the AST generated
4547 * from test_ast_gen1.
4548 *
4549 * Increment the number of calls and the depth.
4550 * Check that the space returned by isl_ast_build_get_schedule_space
4551 * matches the target space of the schedule returned by
4552 * isl_ast_build_get_schedule.
4553 * Return an isl_id that is checked by the corresponding call
4554 * to after_for.
4555 */
4556 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
4557 void *user)
4558 {
4559 struct isl_test_codegen_data *data = user;
4560 isl_ctx *ctx;
4561 isl_space *space;
4562 isl_union_map *schedule;
4563 isl_union_set *uset;
4564 isl_set *set;
4565 int empty;
4566 char name[] = "d0";
4567
4568 ctx = isl_ast_build_get_ctx(build);
4569
4570 if (data->before >= 3)
4571 isl_die(ctx, isl_error_unknown,
4572 "unexpected number of for nodes", return NULL);
4573 if (data->depth >= 2)
4574 isl_die(ctx, isl_error_unknown,
4575 "unexpected depth", return NULL);
4576
4577 snprintf(name, sizeof(name), "d%d", data->depth);
4578 data->before++;
4579 data->depth++;
4580
4581 schedule = isl_ast_build_get_schedule(build);
4582 uset = isl_union_map_range(schedule);
4583 if (!uset)
4584 return NULL;
4585 if (isl_union_set_n_set(uset) != 1) {
4586 isl_union_set_free(uset);
4587 isl_die(ctx, isl_error_unknown,
4588 "expecting single range space", return NULL);
4589 }
4590
4591 space = isl_ast_build_get_schedule_space(build);
4592 set = isl_union_set_extract_set(uset, space);
4593 isl_union_set_free(uset);
4594 empty = isl_set_is_empty(set);
4595 isl_set_free(set);
4596
4597 if (empty < 0)
4598 return NULL;
4599 if (empty)
4600 isl_die(ctx, isl_error_unknown,
4601 "spaces don't match", return NULL);
4602
4603 return isl_id_alloc(ctx, name, NULL);
4604 }
4605
4606 /* This function is called after each for loop in the AST generated
4607 * from test_ast_gen1.
4608 *
4609 * Increment the number of calls and decrement the depth.
4610 * Check that the annotation attached to the node matches
4611 * the isl_id returned by the corresponding call to before_for.
4612 */
4613 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
4614 __isl_keep isl_ast_build *build, void *user)
4615 {
4616 struct isl_test_codegen_data *data = user;
4617 isl_id *id;
4618 const char *name;
4619 int valid;
4620
4621 data->after++;
4622 data->depth--;
4623
4624 if (data->after > data->before)
4625 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4626 "mismatch in number of for nodes",
4627 return isl_ast_node_free(node));
4628
4629 id = isl_ast_node_get_annotation(node);
4630 if (!id)
4631 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4632 "missing annotation", return isl_ast_node_free(node));
4633
4634 name = isl_id_get_name(id);
4635 valid = name && atoi(name + 1) == data->depth;
4636 isl_id_free(id);
4637
4638 if (!valid)
4639 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4640 "wrong annotation", return isl_ast_node_free(node));
4641
4642 return node;
4643 }
4644
4645 /* Check that the before_each_for and after_each_for callbacks
4646 * are called for each for loop in the generated code,
4647 * that they are called in the right order and that the isl_id
4648 * returned from the before_each_for callback is attached to
4649 * the isl_ast_node passed to the corresponding after_each_for call.
4650 */
4651 static int test_ast_gen1(isl_ctx *ctx)
4652 {
4653 const char *str;
4654 isl_set *set;
4655 isl_union_map *schedule;
4656 isl_ast_build *build;
4657 isl_ast_node *tree;
4658 struct isl_test_codegen_data data;
4659
4660 str = "[N] -> { : N >= 10 }";
4661 set = isl_set_read_from_str(ctx, str);
4662 str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
4663 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
4664 schedule = isl_union_map_read_from_str(ctx, str);
4665
4666 data.before = 0;
4667 data.after = 0;
4668 data.depth = 0;
4669 build = isl_ast_build_from_context(set);
4670 build = isl_ast_build_set_before_each_for(build,
4671 &before_for, &data);
4672 build = isl_ast_build_set_after_each_for(build,
4673 &after_for, &data);
4674 tree = isl_ast_build_ast_from_schedule(build, schedule);
4675 isl_ast_build_free(build);
4676 if (!tree)
4677 return -1;
4678
4679 isl_ast_node_free(tree);
4680
4681 if (data.before != 3 || data.after != 3)
4682 isl_die(ctx, isl_error_unknown,
4683 "unexpected number of for nodes", return -1);
4684
4685 return 0;
4686 }
4687
4688 /* Check that the AST generator handles domains that are integrally disjoint
4689 * but not ratinoally disjoint.
4690 */
4691 static int test_ast_gen2(isl_ctx *ctx)
4692 {
4693 const char *str;
4694 isl_set *set;
4695 isl_union_map *schedule;
4696 isl_union_map *options;
4697 isl_ast_build *build;
4698 isl_ast_node *tree;
4699
4700 str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
4701 schedule = isl_union_map_read_from_str(ctx, str);
4702 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4703 build = isl_ast_build_from_context(set);
4704
4705 str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
4706 options = isl_union_map_read_from_str(ctx, str);
4707 build = isl_ast_build_set_options(build, options);
4708 tree = isl_ast_build_ast_from_schedule(build, schedule);
4709 isl_ast_build_free(build);
4710 if (!tree)
4711 return -1;
4712 isl_ast_node_free(tree);
4713
4714 return 0;
4715 }
4716
4717 /* Increment *user on each call.
4718 */
4719 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
4720 __isl_keep isl_ast_build *build, void *user)
4721 {
4722 int *n = user;
4723
4724 (*n)++;
4725
4726 return node;
4727 }
4728
4729 /* Test that unrolling tries to minimize the number of instances.
4730 * In particular, for the schedule given below, make sure it generates
4731 * 3 nodes (rather than 101).
4732 */
4733 static int test_ast_gen3(isl_ctx *ctx)
4734 {
4735 const char *str;
4736 isl_set *set;
4737 isl_union_map *schedule;
4738 isl_union_map *options;
4739 isl_ast_build *build;
4740 isl_ast_node *tree;
4741 int n_domain = 0;
4742
4743 str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
4744 schedule = isl_union_map_read_from_str(ctx, str);
4745 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4746
4747 str = "{ [i] -> unroll[0] }";
4748 options = isl_union_map_read_from_str(ctx, str);
4749
4750 build = isl_ast_build_from_context(set);
4751 build = isl_ast_build_set_options(build, options);
4752 build = isl_ast_build_set_at_each_domain(build,
4753 &count_domains, &n_domain);
4754 tree = isl_ast_build_ast_from_schedule(build, schedule);
4755 isl_ast_build_free(build);
4756 if (!tree)
4757 return -1;
4758
4759 isl_ast_node_free(tree);
4760
4761 if (n_domain != 3)
4762 isl_die(ctx, isl_error_unknown,
4763 "unexpected number of for nodes", return -1);
4764
4765 return 0;
4766 }
4767
4768 /* Check that if the ast_build_exploit_nested_bounds options is set,
4769 * we do not get an outer if node in the generated AST,
4770 * while we do get such an outer if node if the options is not set.
4771 */
4772 static int test_ast_gen4(isl_ctx *ctx)
4773 {
4774 const char *str;
4775 isl_set *set;
4776 isl_union_map *schedule;
4777 isl_ast_build *build;
4778 isl_ast_node *tree;
4779 enum isl_ast_node_type type;
4780 int enb;
4781
4782 enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
4783 str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
4784
4785 isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
4786
4787 schedule = isl_union_map_read_from_str(ctx, str);
4788 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4789 build = isl_ast_build_from_context(set);
4790 tree = isl_ast_build_ast_from_schedule(build, schedule);
4791 isl_ast_build_free(build);
4792 if (!tree)
4793 return -1;
4794
4795 type = isl_ast_node_get_type(tree);
4796 isl_ast_node_free(tree);
4797
4798 if (type == isl_ast_node_if)
4799 isl_die(ctx, isl_error_unknown,
4800 "not expecting if node", return -1);
4801
4802 isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
4803
4804 schedule = isl_union_map_read_from_str(ctx, str);
4805 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4806 build = isl_ast_build_from_context(set);
4807 tree = isl_ast_build_ast_from_schedule(build, schedule);
4808 isl_ast_build_free(build);
4809 if (!tree)
4810 return -1;
4811
4812 type = isl_ast_node_get_type(tree);
4813 isl_ast_node_free(tree);
4814
4815 if (type != isl_ast_node_if)
4816 isl_die(ctx, isl_error_unknown,
4817 "expecting if node", return -1);
4818
4819 isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
4820
4821 return 0;
4822 }
4823
4824 /* This function is called for each leaf in the AST generated
4825 * from test_ast_gen5.
4826 *
4827 * We finalize the AST generation by extending the outer schedule
4828 * with a zero-dimensional schedule. If this results in any for loops,
4829 * then this means that we did not pass along enough information
4830 * about the outer schedule to the inner AST generation.
4831 */
4832 static __isl_give isl_ast_node *create_leaf(__isl_take isl_ast_build *build,
4833 void *user)
4834 {
4835 isl_union_map *schedule, *extra;
4836 isl_ast_node *tree;
4837
4838 schedule = isl_ast_build_get_schedule(build);
4839 extra = isl_union_map_copy(schedule);
4840 extra = isl_union_map_from_domain(isl_union_map_domain(extra));
4841 schedule = isl_union_map_range_product(schedule, extra);
4842 tree = isl_ast_build_ast_from_schedule(build, schedule);
4843 isl_ast_build_free(build);
4844
4845 if (!tree)
4846 return NULL;
4847
4848 if (isl_ast_node_get_type(tree) == isl_ast_node_for)
4849 isl_die(isl_ast_node_get_ctx(tree), isl_error_unknown,
4850 "code should not contain any for loop",
4851 return isl_ast_node_free(tree));
4852
4853 return tree;
4854 }
4855
4856 /* Check that we do not lose any information when going back and
4857 * forth between internal and external schedule.
4858 *
4859 * In particular, we create an AST where we unroll the only
4860 * non-constant dimension in the schedule. We therefore do
4861 * not expect any for loops in the AST. However, older versions
4862 * of isl would not pass along enough information about the outer
4863 * schedule when performing an inner code generation from a create_leaf
4864 * callback, resulting in the inner code generation producing a for loop.
4865 */
4866 static int test_ast_gen5(isl_ctx *ctx)
4867 {
4868 const char *str;
4869 isl_set *set;
4870 isl_union_map *schedule, *options;
4871 isl_ast_build *build;
4872 isl_ast_node *tree;
4873
4874 str = "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
4875 schedule = isl_union_map_read_from_str(ctx, str);
4876
4877 str = "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
4878 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
4879 options = isl_union_map_read_from_str(ctx, str);
4880
4881 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4882 build = isl_ast_build_from_context(set);
4883 build = isl_ast_build_set_options(build, options);
4884 build = isl_ast_build_set_create_leaf(build, &create_leaf, NULL);
4885 tree = isl_ast_build_ast_from_schedule(build, schedule);
4886 isl_ast_build_free(build);
4887 isl_ast_node_free(tree);
4888 if (!tree)
4889 return -1;
4890
4891 return 0;
4892 }
4893
4894 static int test_ast_gen(isl_ctx *ctx)
4895 {
4896 if (test_ast_gen1(ctx) < 0)
4897 return -1;
4898 if (test_ast_gen2(ctx) < 0)
4899 return -1;
4900 if (test_ast_gen3(ctx) < 0)
4901 return -1;
4902 if (test_ast_gen4(ctx) < 0)
4903 return -1;
4904 if (test_ast_gen5(ctx) < 0)
4905 return -1;
4906 return 0;
4907 }
4908
4909 /* Check if dropping output dimensions from an isl_pw_multi_aff
4910 * works properly.
4911 */
4912 static int test_pw_multi_aff(isl_ctx *ctx)
4913 {
4914 const char *str;
4915 isl_pw_multi_aff *pma1, *pma2;
4916 int equal;
4917
4918 str = "{ [i,j] -> [i+j, 4i-j] }";
4919 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
4920 str = "{ [i,j] -> [4i-j] }";
4921 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
4922
4923 pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
4924
4925 equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
4926
4927 isl_pw_multi_aff_free(pma1);
4928 isl_pw_multi_aff_free(pma2);
4929 if (equal < 0)
4930 return -1;
4931 if (!equal)
4932 isl_die(ctx, isl_error_unknown,
4933 "expressions not equal", return -1);
4934
4935 return 0;
4936 }
4937
4938 /* Check that we can properly parse multi piecewise affine expressions
4939 * where the piecewise affine expressions have different domains.
4940 */
4941 static int test_multi_pw_aff(isl_ctx *ctx)
4942 {
4943 const char *str;
4944 isl_set *dom, *dom2;
4945 isl_multi_pw_aff *mpa1, *mpa2;
4946 isl_pw_aff *pa;
4947 int equal;
4948 int equal_domain;
4949
4950 mpa1 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [i] }");
4951 dom = isl_set_read_from_str(ctx, "{ [i] : i > 0 }");
4952 mpa1 = isl_multi_pw_aff_intersect_domain(mpa1, dom);
4953 mpa2 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [2i] }");
4954 mpa2 = isl_multi_pw_aff_flat_range_product(mpa1, mpa2);
4955 str = "{ [i] -> [(i : i > 0), 2i] }";
4956 mpa1 = isl_multi_pw_aff_read_from_str(ctx, str);
4957
4958 equal = isl_multi_pw_aff_plain_is_equal(mpa1, mpa2);
4959
4960 pa = isl_multi_pw_aff_get_pw_aff(mpa1, 0);
4961 dom = isl_pw_aff_domain(pa);
4962 pa = isl_multi_pw_aff_get_pw_aff(mpa1, 1);
4963 dom2 = isl_pw_aff_domain(pa);
4964 equal_domain = isl_set_is_equal(dom, dom2);
4965
4966 isl_set_free(dom);
4967 isl_set_free(dom2);
4968 isl_multi_pw_aff_free(mpa1);
4969 isl_multi_pw_aff_free(mpa2);
4970
4971 if (equal < 0)
4972 return -1;
4973 if (!equal)
4974 isl_die(ctx, isl_error_unknown,
4975 "expressions not equal", return -1);
4976
4977 if (equal_domain < 0)
4978 return -1;
4979 if (equal_domain)
4980 isl_die(ctx, isl_error_unknown,
4981 "domains unexpectedly equal", return -1);
4982
4983 return 0;
4984 }
4985
4986 /* This is a regression test for a bug where isl_basic_map_simplify
4987 * would end up in an infinite loop. In particular, we construct
4988 * an empty basic set that is not obviously empty.
4989 * isl_basic_set_is_empty marks the basic set as empty.
4990 * After projecting out i3, the variable can be dropped completely,
4991 * but isl_basic_map_simplify refrains from doing so if the basic set
4992 * is empty and would end up in an infinite loop if it didn't test
4993 * explicitly for empty basic maps in the outer loop.
4994 */
4995 static int test_simplify(isl_ctx *ctx)
4996 {
4997 const char *str;
4998 isl_basic_set *bset;
4999 int empty;
5000
5001 str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
5002 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
5003 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
5004 "i3 >= i2 }";
5005 bset = isl_basic_set_read_from_str(ctx, str);
5006 empty = isl_basic_set_is_empty(bset);
5007 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
5008 isl_basic_set_free(bset);
5009 if (!bset)
5010 return -1;
5011 if (!empty)
5012 isl_die(ctx, isl_error_unknown,
5013 "basic set should be empty", return -1);
5014
5015 return 0;
5016 }
5017
5018 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
5019 * with gbr context would fail to disable the use of the shifted tableau
5020 * when transferring equalities for the input to the context, resulting
5021 * in invalid sample values.
5022 */
5023 static int test_partial_lexmin(isl_ctx *ctx)
5024 {
5025 const char *str;
5026 isl_basic_set *bset;
5027 isl_basic_map *bmap;
5028 isl_map *map;
5029
5030 str = "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
5031 bmap = isl_basic_map_read_from_str(ctx, str);
5032 str = "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
5033 bset = isl_basic_set_read_from_str(ctx, str);
5034 map = isl_basic_map_partial_lexmin(bmap, bset, NULL);
5035 isl_map_free(map);
5036
5037 if (!map)
5038 return -1;
5039
5040 return 0;
5041 }
5042
5043 /* Check that the variable compression performed on the existentially
5044 * quantified variables inside isl_basic_set_compute_divs is not confused
5045 * by the implicit equalities among the parameters.
5046 */
5047 static int test_compute_divs(isl_ctx *ctx)
5048 {
5049 const char *str;
5050 isl_basic_set *bset;
5051 isl_set *set;
5052
5053 str = "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
5054 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
5055 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
5056 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
5057 bset = isl_basic_set_read_from_str(ctx, str);
5058 set = isl_basic_set_compute_divs(bset);
5059 isl_set_free(set);
5060 if (!set)
5061 return -1;
5062
5063 return 0;
5064 }
5065
5066 struct {
5067 const char *set;
5068 const char *dual;
5069 } coef_tests[] = {
5070 { "{ rat: [i] : 0 <= i <= 10 }",
5071 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
5072 { "{ rat: [i] : FALSE }",
5073 "{ rat: coefficients[[cst] -> [a]] }" },
5074 { "{ rat: [i] : }",
5075 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
5076 };
5077
5078 struct {
5079 const char *set;
5080 const char *dual;
5081 } sol_tests[] = {
5082 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
5083 "{ rat: [i] : 0 <= i <= 10 }" },
5084 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
5085 "{ rat: [i] }" },
5086 { "{ rat: coefficients[[cst] -> [a]] }",
5087 "{ rat: [i] : FALSE }" },
5088 };
5089
5090 /* Test the basic functionality of isl_basic_set_coefficients and
5091 * isl_basic_set_solutions.
5092 */
5093 static int test_dual(isl_ctx *ctx)
5094 {
5095 int i;
5096
5097 for (i = 0; i < ARRAY_SIZE(coef_tests); ++i) {
5098 int equal;
5099 isl_basic_set *bset1, *bset2;
5100
5101 bset1 = isl_basic_set_read_from_str(ctx, coef_tests[i].set);
5102 bset2 = isl_basic_set_read_from_str(ctx, coef_tests[i].dual);
5103 bset1 = isl_basic_set_coefficients(bset1);
5104 equal = isl_basic_set_is_equal(bset1, bset2);
5105 isl_basic_set_free(bset1);
5106 isl_basic_set_free(bset2);
5107 if (equal < 0)
5108 return -1;
5109 if (!equal)
5110 isl_die(ctx, isl_error_unknown,
5111 "incorrect dual", return -1);
5112 }
5113
5114 for (i = 0; i < ARRAY_SIZE(sol_tests); ++i) {
5115 int equal;
5116 isl_basic_set *bset1, *bset2;
5117
5118 bset1 = isl_basic_set_read_from_str(ctx, sol_tests[i].set);
5119 bset2 = isl_basic_set_read_from_str(ctx, sol_tests[i].dual);
5120 bset1 = isl_basic_set_solutions(bset1);
5121 equal = isl_basic_set_is_equal(bset1, bset2);
5122 isl_basic_set_free(bset1);
5123 isl_basic_set_free(bset2);
5124 if (equal < 0)
5125 return -1;
5126 if (!equal)
5127 isl_die(ctx, isl_error_unknown,
5128 "incorrect dual", return -1);
5129 }
5130
5131 return 0;
5132 }
5133
5134 struct {
5135 const char *name;
5136 int (*fn)(isl_ctx *ctx);
5137 } tests [] = {
5138 { "dual", &test_dual },
5139 { "dependence analysis", &test_flow },
5140 { "val", &test_val },
5141 { "compute divs", &test_compute_divs },
5142 { "partial lexmin", &test_partial_lexmin },
5143 { "simplify", &test_simplify },
5144 { "curry", &test_curry },
5145 { "piecewise multi affine expressions", &test_pw_multi_aff },
5146 { "multi piecewise affine expressions", &test_multi_pw_aff },
5147 { "conversion", &test_conversion },
5148 { "list", &test_list },
5149 { "align parameters", &test_align_parameters },
5150 { "preimage", &test_preimage },
5151 { "pullback", &test_pullback },
5152 { "AST", &test_ast },
5153 { "AST build", &test_ast_build },
5154 { "AST generation", &test_ast_gen },
5155 { "eliminate", &test_eliminate },
5156 { "residue class", &test_residue_class },
5157 { "div", &test_div },
5158 { "slice", &test_slice },
5159 { "fixed power", &test_fixed_power },
5160 { "sample", &test_sample },
5161 { "output", &test_output },
5162 { "vertices", &test_vertices },
5163 { "fixed", &test_fixed },
5164 { "equal", &test_equal },
5165 { "disjoint", &test_disjoint },
5166 { "product", &test_product },
5167 { "dim_max", &test_dim_max },
5168 { "affine", &test_aff },
5169 { "injective", &test_injective },
5170 { "schedule", &test_schedule },
5171 { "union_pw", &test_union_pw },
5172 { "parse", &test_parse },
5173 { "single-valued", &test_sv },
5174 { "affine hull", &test_affine_hull },
5175 { "coalesce", &test_coalesce },
5176 { "factorize", &test_factorize },
5177 { "subset", &test_subset },
5178 { "subtract", &test_subtract },
5179 { "lexmin", &test_lexmin },
5180 { "min", &test_min },
5181 { "gist", &test_gist },
5182 { "piecewise quasi-polynomials", &test_pwqp },
5183 };
5184
5185 int main(int argc, char **argv)
5186 {
5187 int i;
5188 struct isl_ctx *ctx;
5189 struct isl_options *options;
5190
5191 srcdir = getenv("srcdir");
5192 assert(srcdir);
5193
5194 options = isl_options_new_with_defaults();
5195 assert(options);
5196 argc = isl_options_parse(options, argc, argv, ISL_ARG_ALL);
5197
5198 ctx = isl_ctx_alloc_with_options(&isl_options_args, options);
5199 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
5200 printf("%s\n", tests[i].name);
5201 if (tests[i].fn(ctx) < 0)
5202 goto error;
5203 }
5204 test_lift(ctx);
5205 test_bound(ctx);
5206 test_union(ctx);
5207 test_split_periods(ctx);
5208 test_lex(ctx);
5209 test_bijective(ctx);
5210 test_dep(ctx);
5211 test_read(ctx);
5212 test_bounded(ctx);
5213 test_construction(ctx);
5214 test_dim(ctx);
5215 test_application(ctx);
5216 test_convex_hull(ctx);
5217 test_closure(ctx);
5218 isl_ctx_free(ctx);
5219 return 0;
5220 error:
5221 isl_ctx_free(ctx);
5222 return -1;
5223 }
Integer set library