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isl_map_simplify.c: uset_gist_full: allow equalities in context
[isl.git] / isl_test.c
bloba618e9da09a510bf7336a192bae74d30308b449c
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_space_private.h>
25 #include <isl/set.h>
26 #include <isl/flow.h>
27 #include <isl_constraint_private.h>
28 #include <isl/polynomial.h>
29 #include <isl/union_set.h>
30 #include <isl/union_map.h>
31 #include <isl_factorization.h>
32 #include <isl/schedule.h>
33 #include <isl/schedule_node.h>
34 #include <isl_options_private.h>
35 #include <isl/vertices.h>
36 #include <isl/ast_build.h>
37 #include <isl/val.h>
38 #include <isl/ilp.h>
39 #include <isl_ast_build_expr.h>
40 #include <isl/options.h>
41
42 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
43
44 static char *srcdir;
45
46 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
47 char *filename;
48 int length;
49 char *pattern = "%s/test_inputs/%s.%s";
50
51 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
52 + strlen(suffix) + 1;
53 filename = isl_alloc_array(ctx, char, length);
54
55 if (!filename)
56 return NULL;
57
58 sprintf(filename, pattern, srcdir, name, suffix);
59
60 return filename;
61 }
62
63 void test_parse_map(isl_ctx *ctx, const char *str)
64 {
65 isl_map *map;
66
67 map = isl_map_read_from_str(ctx, str);
68 assert(map);
69 isl_map_free(map);
70 }
71
72 int test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
73 {
74 isl_map *map, *map2;
75 int equal;
76
77 map = isl_map_read_from_str(ctx, str);
78 map2 = isl_map_read_from_str(ctx, str2);
79 equal = isl_map_is_equal(map, map2);
80 isl_map_free(map);
81 isl_map_free(map2);
82
83 if (equal < 0)
84 return -1;
85 if (!equal)
86 isl_die(ctx, isl_error_unknown, "maps not equal",
87 return -1);
88
89 return 0;
90 }
91
92 void test_parse_pwqp(isl_ctx *ctx, const char *str)
93 {
94 isl_pw_qpolynomial *pwqp;
95
96 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
97 assert(pwqp);
98 isl_pw_qpolynomial_free(pwqp);
99 }
100
101 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
102 {
103 isl_pw_aff *pwaff;
104
105 pwaff = isl_pw_aff_read_from_str(ctx, str);
106 assert(pwaff);
107 isl_pw_aff_free(pwaff);
108 }
109
110 /* Check that we can read an isl_multi_val from "str" without errors.
111 */
112 static int test_parse_multi_val(isl_ctx *ctx, const char *str)
113 {
114 isl_multi_val *mv;
115
116 mv = isl_multi_val_read_from_str(ctx, str);
117 isl_multi_val_free(mv);
118
119 return mv ? 0 : -1;
120 }
121
122 int test_parse(struct isl_ctx *ctx)
123 {
124 isl_map *map, *map2;
125 const char *str, *str2;
126
127 if (test_parse_multi_val(ctx, "{ A[B[2] -> C[5, 7]] }") < 0)
128 return -1;
129 if (test_parse_multi_val(ctx, "[n] -> { [2] }") < 0)
130 return -1;
131 if (test_parse_multi_val(ctx, "{ A[4, infty, NaN, -1/2, 2/3] }") < 0)
132 return -1;
133
134 str = "{ [i] -> [-i] }";
135 map = isl_map_read_from_str(ctx, str);
136 assert(map);
137 isl_map_free(map);
138
139 str = "{ A[i] -> L[([i/3])] }";
140 map = isl_map_read_from_str(ctx, str);
141 assert(map);
142 isl_map_free(map);
143
144 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
145 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
146 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
147
148 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
149 str2 = "{ [x, y] : 2y >= 6 - x }";
150 if (test_parse_map_equal(ctx, str, str2) < 0)
151 return -1;
152
153 if (test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
154 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
155 return -1;
156 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
157 if (test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }",
158 str) < 0)
159 return -1;
160
161 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
162 map = isl_map_read_from_str(ctx, str);
163 str = "{ [new, old] -> [o0, o1] : "
164 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
165 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
166 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
167 map2 = isl_map_read_from_str(ctx, str);
168 assert(isl_map_is_equal(map, map2));
169 isl_map_free(map);
170 isl_map_free(map2);
171
172 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
173 map = isl_map_read_from_str(ctx, str);
174 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
175 map2 = isl_map_read_from_str(ctx, str);
176 assert(isl_map_is_equal(map, map2));
177 isl_map_free(map);
178 isl_map_free(map2);
179
180 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
181 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
182 if (test_parse_map_equal(ctx, str, str2) < 0)
183 return -1;
184
185 str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
186 str2 = "{ [i,j] -> [min(i,j)] }";
187 if (test_parse_map_equal(ctx, str, str2) < 0)
188 return -1;
189
190 str = "{ [i,j] : i != j }";
191 str2 = "{ [i,j] : i < j or i > j }";
192 if (test_parse_map_equal(ctx, str, str2) < 0)
193 return -1;
194
195 str = "{ [i,j] : (i+1)*2 >= j }";
196 str2 = "{ [i, j] : j <= 2 + 2i }";
197 if (test_parse_map_equal(ctx, str, str2) < 0)
198 return -1;
199
200 str = "{ [i] -> [i > 0 ? 4 : 5] }";
201 str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
202 if (test_parse_map_equal(ctx, str, str2) < 0)
203 return -1;
204
205 str = "[N=2,M] -> { [i=[(M+N)/4]] }";
206 str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
207 if (test_parse_map_equal(ctx, str, str2) < 0)
208 return -1;
209
210 str = "{ [x] : x >= 0 }";
211 str2 = "{ [x] : x-0 >= 0 }";
212 if (test_parse_map_equal(ctx, str, str2) < 0)
213 return -1;
214
215 str = "{ [i] : ((i > 10)) }";
216 str2 = "{ [i] : i >= 11 }";
217 if (test_parse_map_equal(ctx, str, str2) < 0)
218 return -1;
219
220 str = "{ [i] -> [0] }";
221 str2 = "{ [i] -> [0 * i] }";
222 if (test_parse_map_equal(ctx, str, str2) < 0)
223 return -1;
224
225 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
226 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
227 test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
228 test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
229
230 if (test_parse_map_equal(ctx, "{ [a] -> [b] : (not false) }",
231 "{ [a] -> [b] : true }") < 0)
232 return -1;
233
234 if (test_parse_map_equal(ctx, "{ [i] : i/2 <= 5 }",
235 "{ [i] : i <= 10 }") < 0)
236 return -1;
237
238 if (test_parse_map_equal(ctx, "{Sym=[n] [i] : i <= n }",
239 "[n] -> { [i] : i <= n }") < 0)
240 return -1;
241
242 if (test_parse_map_equal(ctx, "{ [*] }", "{ [a] }") < 0)
243 return -1;
244
245 if (test_parse_map_equal(ctx, "{ [i] : 2*floor(i/2) = i }",
246 "{ [i] : exists a : i = 2 a }") < 0)
247 return -1;
248
249 if (test_parse_map_equal(ctx, "{ [a] -> [b] : a = 5 implies b = 5 }",
250 "{ [a] -> [b] : a != 5 or b = 5 }") < 0)
251 return -1;
252
253 if (test_parse_map_equal(ctx, "{ [a] -> [a - 1 : a > 0] }",
254 "{ [a] -> [a - 1] : a > 0 }") < 0)
255 return -1;
256 if (test_parse_map_equal(ctx,
257 "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
258 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }") < 0)
259 return -1;
260 if (test_parse_map_equal(ctx,
261 "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
262 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
263 return -1;
264 if (test_parse_map_equal(ctx,
265 "{ [a] -> [(a * 2) : a >= 0; 0 : a < 0] }",
266 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
267 return -1;
268 if (test_parse_map_equal(ctx,
269 "{ [a] -> [(a * 2 : a >= 0); 0 : a < 0] }",
270 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
271 return -1;
272 if (test_parse_map_equal(ctx,
273 "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
274 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
275 return -1;
276
277 return 0;
278 }
279
280 static int test_read(isl_ctx *ctx)
281 {
282 char *filename;
283 FILE *input;
284 isl_basic_set *bset1, *bset2;
285 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
286 int equal;
287
288 filename = get_filename(ctx, "set", "omega");
289 assert(filename);
290 input = fopen(filename, "r");
291 assert(input);
292
293 bset1 = isl_basic_set_read_from_file(ctx, input);
294 bset2 = isl_basic_set_read_from_str(ctx, str);
295
296 equal = isl_basic_set_is_equal(bset1, bset2);
297
298 isl_basic_set_free(bset1);
299 isl_basic_set_free(bset2);
300 free(filename);
301
302 fclose(input);
303
304 if (equal < 0)
305 return -1;
306 if (!equal)
307 isl_die(ctx, isl_error_unknown,
308 "read sets not equal", return -1);
309
310 return 0;
311 }
312
313 static int test_bounded(isl_ctx *ctx)
314 {
315 isl_set *set;
316 int bounded;
317
318 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
319 bounded = isl_set_is_bounded(set);
320 isl_set_free(set);
321
322 if (bounded < 0)
323 return -1;
324 if (!bounded)
325 isl_die(ctx, isl_error_unknown,
326 "set not considered bounded", return -1);
327
328 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
329 bounded = isl_set_is_bounded(set);
330 assert(!bounded);
331 isl_set_free(set);
332
333 if (bounded < 0)
334 return -1;
335 if (bounded)
336 isl_die(ctx, isl_error_unknown,
337 "set considered bounded", return -1);
338
339 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
340 bounded = isl_set_is_bounded(set);
341 isl_set_free(set);
342
343 if (bounded < 0)
344 return -1;
345 if (bounded)
346 isl_die(ctx, isl_error_unknown,
347 "set considered bounded", return -1);
348
349 return 0;
350 }
351
352 /* Construct the basic set { [i] : 5 <= i <= N } */
353 static int test_construction(isl_ctx *ctx)
354 {
355 isl_int v;
356 isl_space *dim;
357 isl_local_space *ls;
358 isl_basic_set *bset;
359 isl_constraint *c;
360
361 isl_int_init(v);
362
363 dim = isl_space_set_alloc(ctx, 1, 1);
364 bset = isl_basic_set_universe(isl_space_copy(dim));
365 ls = isl_local_space_from_space(dim);
366
367 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
368 isl_int_set_si(v, -1);
369 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
370 isl_int_set_si(v, 1);
371 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
372 bset = isl_basic_set_add_constraint(bset, c);
373
374 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
375 isl_int_set_si(v, 1);
376 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
377 isl_int_set_si(v, -5);
378 isl_constraint_set_constant(c, v);
379 bset = isl_basic_set_add_constraint(bset, c);
380
381 isl_local_space_free(ls);
382 isl_basic_set_free(bset);
383
384 isl_int_clear(v);
385
386 return 0;
387 }
388
389 static int test_dim(isl_ctx *ctx)
390 {
391 const char *str;
392 isl_map *map1, *map2;
393 int equal;
394
395 map1 = isl_map_read_from_str(ctx,
396 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
397 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
398 map2 = isl_map_read_from_str(ctx,
399 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
400 equal = isl_map_is_equal(map1, map2);
401 isl_map_free(map2);
402
403 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
404 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
405 if (equal >= 0 && equal)
406 equal = isl_map_is_equal(map1, map2);
407
408 isl_map_free(map1);
409 isl_map_free(map2);
410
411 if (equal < 0)
412 return -1;
413 if (!equal)
414 isl_die(ctx, isl_error_unknown,
415 "unexpected result", return -1);
416
417 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
418 map1 = isl_map_read_from_str(ctx, str);
419 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
420 map2 = isl_map_read_from_str(ctx, str);
421 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
422 equal = isl_map_is_equal(map1, map2);
423 isl_map_free(map1);
424 isl_map_free(map2);
425
426 if (equal < 0)
427 return -1;
428 if (!equal)
429 isl_die(ctx, isl_error_unknown,
430 "unexpected result", return -1);
431
432 return 0;
433 }
434
435 struct {
436 __isl_give isl_val *(*op)(__isl_take isl_val *v);
437 const char *arg;
438 const char *res;
439 } val_un_tests[] = {
440 { &isl_val_neg, "0", "0" },
441 { &isl_val_abs, "0", "0" },
442 { &isl_val_2exp, "0", "1" },
443 { &isl_val_floor, "0", "0" },
444 { &isl_val_ceil, "0", "0" },
445 { &isl_val_neg, "1", "-1" },
446 { &isl_val_neg, "-1", "1" },
447 { &isl_val_neg, "1/2", "-1/2" },
448 { &isl_val_neg, "-1/2", "1/2" },
449 { &isl_val_neg, "infty", "-infty" },
450 { &isl_val_neg, "-infty", "infty" },
451 { &isl_val_neg, "NaN", "NaN" },
452 { &isl_val_abs, "1", "1" },
453 { &isl_val_abs, "-1", "1" },
454 { &isl_val_abs, "1/2", "1/2" },
455 { &isl_val_abs, "-1/2", "1/2" },
456 { &isl_val_abs, "infty", "infty" },
457 { &isl_val_abs, "-infty", "infty" },
458 { &isl_val_abs, "NaN", "NaN" },
459 { &isl_val_floor, "1", "1" },
460 { &isl_val_floor, "-1", "-1" },
461 { &isl_val_floor, "1/2", "0" },
462 { &isl_val_floor, "-1/2", "-1" },
463 { &isl_val_floor, "infty", "infty" },
464 { &isl_val_floor, "-infty", "-infty" },
465 { &isl_val_floor, "NaN", "NaN" },
466 { &isl_val_ceil, "1", "1" },
467 { &isl_val_ceil, "-1", "-1" },
468 { &isl_val_ceil, "1/2", "1" },
469 { &isl_val_ceil, "-1/2", "0" },
470 { &isl_val_ceil, "infty", "infty" },
471 { &isl_val_ceil, "-infty", "-infty" },
472 { &isl_val_ceil, "NaN", "NaN" },
473 { &isl_val_2exp, "-3", "1/8" },
474 { &isl_val_2exp, "-1", "1/2" },
475 { &isl_val_2exp, "1", "2" },
476 { &isl_val_2exp, "2", "4" },
477 { &isl_val_2exp, "3", "8" },
478 { &isl_val_inv, "1", "1" },
479 { &isl_val_inv, "2", "1/2" },
480 { &isl_val_inv, "1/2", "2" },
481 { &isl_val_inv, "-2", "-1/2" },
482 { &isl_val_inv, "-1/2", "-2" },
483 { &isl_val_inv, "0", "NaN" },
484 { &isl_val_inv, "NaN", "NaN" },
485 { &isl_val_inv, "infty", "0" },
486 { &isl_val_inv, "-infty", "0" },
487 };
488
489 /* Perform some basic tests of unary operations on isl_val objects.
490 */
491 static int test_un_val(isl_ctx *ctx)
492 {
493 int i;
494 isl_val *v, *res;
495 __isl_give isl_val *(*fn)(__isl_take isl_val *v);
496 int ok;
497
498 for (i = 0; i < ARRAY_SIZE(val_un_tests); ++i) {
499 v = isl_val_read_from_str(ctx, val_un_tests[i].arg);
500 res = isl_val_read_from_str(ctx, val_un_tests[i].res);
501 fn = val_un_tests[i].op;
502 v = fn(v);
503 if (isl_val_is_nan(res))
504 ok = isl_val_is_nan(v);
505 else
506 ok = isl_val_eq(v, res);
507 isl_val_free(v);
508 isl_val_free(res);
509 if (ok < 0)
510 return -1;
511 if (!ok)
512 isl_die(ctx, isl_error_unknown,
513 "unexpected result", return -1);
514 }
515
516 return 0;
517 }
518
519 struct {
520 __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
521 __isl_take isl_val *v2);
522 } val_bin_op[] = {
523 ['+'] = { &isl_val_add },
524 ['-'] = { &isl_val_sub },
525 ['*'] = { &isl_val_mul },
526 ['/'] = { &isl_val_div },
527 ['g'] = { &isl_val_gcd },
528 ['m'] = { &isl_val_min },
529 ['M'] = { &isl_val_max },
530 };
531
532 struct {
533 const char *arg1;
534 unsigned char op;
535 const char *arg2;
536 const char *res;
537 } val_bin_tests[] = {
538 { "0", '+', "0", "0" },
539 { "1", '+', "0", "1" },
540 { "1", '+', "1", "2" },
541 { "1", '-', "1", "0" },
542 { "1", '*', "1", "1" },
543 { "1", '/', "1", "1" },
544 { "2", '*', "3", "6" },
545 { "2", '*', "1/2", "1" },
546 { "2", '*', "1/3", "2/3" },
547 { "2/3", '*', "3/5", "2/5" },
548 { "2/3", '*', "7/5", "14/15" },
549 { "2", '/', "1/2", "4" },
550 { "-2", '/', "-1/2", "4" },
551 { "-2", '/', "1/2", "-4" },
552 { "2", '/', "-1/2", "-4" },
553 { "2", '/', "2", "1" },
554 { "2", '/', "3", "2/3" },
555 { "2/3", '/', "5/3", "2/5" },
556 { "2/3", '/', "5/7", "14/15" },
557 { "0", '/', "0", "NaN" },
558 { "42", '/', "0", "NaN" },
559 { "-42", '/', "0", "NaN" },
560 { "infty", '/', "0", "NaN" },
561 { "-infty", '/', "0", "NaN" },
562 { "NaN", '/', "0", "NaN" },
563 { "0", '/', "NaN", "NaN" },
564 { "42", '/', "NaN", "NaN" },
565 { "-42", '/', "NaN", "NaN" },
566 { "infty", '/', "NaN", "NaN" },
567 { "-infty", '/', "NaN", "NaN" },
568 { "NaN", '/', "NaN", "NaN" },
569 { "0", '/', "infty", "0" },
570 { "42", '/', "infty", "0" },
571 { "-42", '/', "infty", "0" },
572 { "infty", '/', "infty", "NaN" },
573 { "-infty", '/', "infty", "NaN" },
574 { "NaN", '/', "infty", "NaN" },
575 { "0", '/', "-infty", "0" },
576 { "42", '/', "-infty", "0" },
577 { "-42", '/', "-infty", "0" },
578 { "infty", '/', "-infty", "NaN" },
579 { "-infty", '/', "-infty", "NaN" },
580 { "NaN", '/', "-infty", "NaN" },
581 { "1", '-', "1/3", "2/3" },
582 { "1/3", '+', "1/2", "5/6" },
583 { "1/2", '+', "1/2", "1" },
584 { "3/4", '-', "1/4", "1/2" },
585 { "1/2", '-', "1/3", "1/6" },
586 { "infty", '+', "42", "infty" },
587 { "infty", '+', "infty", "infty" },
588 { "42", '+', "infty", "infty" },
589 { "infty", '-', "infty", "NaN" },
590 { "infty", '*', "infty", "infty" },
591 { "infty", '*', "-infty", "-infty" },
592 { "-infty", '*', "infty", "-infty" },
593 { "-infty", '*', "-infty", "infty" },
594 { "0", '*', "infty", "NaN" },
595 { "1", '*', "infty", "infty" },
596 { "infty", '*', "0", "NaN" },
597 { "infty", '*', "42", "infty" },
598 { "42", '-', "infty", "-infty" },
599 { "infty", '+', "-infty", "NaN" },
600 { "4", 'g', "6", "2" },
601 { "5", 'g', "6", "1" },
602 { "42", 'm', "3", "3" },
603 { "42", 'M', "3", "42" },
604 { "3", 'm', "42", "3" },
605 { "3", 'M', "42", "42" },
606 { "42", 'm', "infty", "42" },
607 { "42", 'M', "infty", "infty" },
608 { "42", 'm', "-infty", "-infty" },
609 { "42", 'M', "-infty", "42" },
610 { "42", 'm', "NaN", "NaN" },
611 { "42", 'M', "NaN", "NaN" },
612 { "infty", 'm', "-infty", "-infty" },
613 { "infty", 'M', "-infty", "infty" },
614 };
615
616 /* Perform some basic tests of binary operations on isl_val objects.
617 */
618 static int test_bin_val(isl_ctx *ctx)
619 {
620 int i;
621 isl_val *v1, *v2, *res;
622 __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
623 __isl_take isl_val *v2);
624 int ok;
625
626 for (i = 0; i < ARRAY_SIZE(val_bin_tests); ++i) {
627 v1 = isl_val_read_from_str(ctx, val_bin_tests[i].arg1);
628 v2 = isl_val_read_from_str(ctx, val_bin_tests[i].arg2);
629 res = isl_val_read_from_str(ctx, val_bin_tests[i].res);
630 fn = val_bin_op[val_bin_tests[i].op].fn;
631 v1 = fn(v1, v2);
632 if (isl_val_is_nan(res))
633 ok = isl_val_is_nan(v1);
634 else
635 ok = isl_val_eq(v1, res);
636 isl_val_free(v1);
637 isl_val_free(res);
638 if (ok < 0)
639 return -1;
640 if (!ok)
641 isl_die(ctx, isl_error_unknown,
642 "unexpected result", return -1);
643 }
644
645 return 0;
646 }
647
648 /* Perform some basic tests on isl_val objects.
649 */
650 static int test_val(isl_ctx *ctx)
651 {
652 if (test_un_val(ctx) < 0)
653 return -1;
654 if (test_bin_val(ctx) < 0)
655 return -1;
656 return 0;
657 }
658
659 static int test_div(isl_ctx *ctx)
660 {
661 unsigned n;
662 const char *str;
663 int empty;
664 isl_int v;
665 isl_space *dim;
666 isl_set *set;
667 isl_local_space *ls;
668 struct isl_basic_set *bset;
669 struct isl_constraint *c;
670
671 isl_int_init(v);
672
673 /* test 1 */
674 dim = isl_space_set_alloc(ctx, 0, 3);
675 bset = isl_basic_set_universe(isl_space_copy(dim));
676 ls = isl_local_space_from_space(dim);
677
678 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
679 isl_int_set_si(v, -1);
680 isl_constraint_set_constant(c, v);
681 isl_int_set_si(v, 1);
682 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
683 isl_int_set_si(v, 3);
684 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
685 bset = isl_basic_set_add_constraint(bset, c);
686
687 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
688 isl_int_set_si(v, 1);
689 isl_constraint_set_constant(c, v);
690 isl_int_set_si(v, -1);
691 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
692 isl_int_set_si(v, 3);
693 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
694 bset = isl_basic_set_add_constraint(bset, c);
695
696 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
697
698 assert(bset && bset->n_div == 1);
699 isl_local_space_free(ls);
700 isl_basic_set_free(bset);
701
702 /* test 2 */
703 dim = isl_space_set_alloc(ctx, 0, 3);
704 bset = isl_basic_set_universe(isl_space_copy(dim));
705 ls = isl_local_space_from_space(dim);
706
707 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
708 isl_int_set_si(v, 1);
709 isl_constraint_set_constant(c, v);
710 isl_int_set_si(v, -1);
711 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
712 isl_int_set_si(v, 3);
713 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
714 bset = isl_basic_set_add_constraint(bset, c);
715
716 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
717 isl_int_set_si(v, -1);
718 isl_constraint_set_constant(c, v);
719 isl_int_set_si(v, 1);
720 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
721 isl_int_set_si(v, 3);
722 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
723 bset = isl_basic_set_add_constraint(bset, c);
724
725 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
726
727 assert(bset && bset->n_div == 1);
728 isl_local_space_free(ls);
729 isl_basic_set_free(bset);
730
731 /* test 3 */
732 dim = isl_space_set_alloc(ctx, 0, 3);
733 bset = isl_basic_set_universe(isl_space_copy(dim));
734 ls = isl_local_space_from_space(dim);
735
736 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
737 isl_int_set_si(v, 1);
738 isl_constraint_set_constant(c, v);
739 isl_int_set_si(v, -1);
740 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
741 isl_int_set_si(v, 3);
742 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
743 bset = isl_basic_set_add_constraint(bset, c);
744
745 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
746 isl_int_set_si(v, -3);
747 isl_constraint_set_constant(c, v);
748 isl_int_set_si(v, 1);
749 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
750 isl_int_set_si(v, 4);
751 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
752 bset = isl_basic_set_add_constraint(bset, c);
753
754 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
755
756 assert(bset && bset->n_div == 1);
757 isl_local_space_free(ls);
758 isl_basic_set_free(bset);
759
760 /* test 4 */
761 dim = isl_space_set_alloc(ctx, 0, 3);
762 bset = isl_basic_set_universe(isl_space_copy(dim));
763 ls = isl_local_space_from_space(dim);
764
765 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
766 isl_int_set_si(v, 2);
767 isl_constraint_set_constant(c, v);
768 isl_int_set_si(v, -1);
769 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
770 isl_int_set_si(v, 3);
771 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
772 bset = isl_basic_set_add_constraint(bset, c);
773
774 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
775 isl_int_set_si(v, -1);
776 isl_constraint_set_constant(c, v);
777 isl_int_set_si(v, 1);
778 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
779 isl_int_set_si(v, 6);
780 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
781 bset = isl_basic_set_add_constraint(bset, c);
782
783 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
784
785 assert(isl_basic_set_is_empty(bset));
786 isl_local_space_free(ls);
787 isl_basic_set_free(bset);
788
789 /* test 5 */
790 dim = isl_space_set_alloc(ctx, 0, 3);
791 bset = isl_basic_set_universe(isl_space_copy(dim));
792 ls = isl_local_space_from_space(dim);
793
794 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
795 isl_int_set_si(v, -1);
796 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
797 isl_int_set_si(v, 3);
798 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
799 bset = isl_basic_set_add_constraint(bset, c);
800
801 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
802 isl_int_set_si(v, 1);
803 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
804 isl_int_set_si(v, -3);
805 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
806 bset = isl_basic_set_add_constraint(bset, c);
807
808 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
809
810 assert(bset && bset->n_div == 0);
811 isl_basic_set_free(bset);
812 isl_local_space_free(ls);
813
814 /* test 6 */
815 dim = isl_space_set_alloc(ctx, 0, 3);
816 bset = isl_basic_set_universe(isl_space_copy(dim));
817 ls = isl_local_space_from_space(dim);
818
819 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
820 isl_int_set_si(v, -1);
821 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
822 isl_int_set_si(v, 6);
823 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
824 bset = isl_basic_set_add_constraint(bset, c);
825
826 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
827 isl_int_set_si(v, 1);
828 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
829 isl_int_set_si(v, -3);
830 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
831 bset = isl_basic_set_add_constraint(bset, c);
832
833 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
834
835 assert(bset && bset->n_div == 1);
836 isl_basic_set_free(bset);
837 isl_local_space_free(ls);
838
839 /* test 7 */
840 /* This test is a bit tricky. We set up an equality
841 * a + 3b + 3c = 6 e0
842 * Normalization of divs creates _two_ divs
843 * a = 3 e0
844 * c - b - e0 = 2 e1
845 * Afterwards e0 is removed again because it has coefficient -1
846 * and we end up with the original equality and div again.
847 * Perhaps we can avoid the introduction of this temporary div.
848 */
849 dim = isl_space_set_alloc(ctx, 0, 4);
850 bset = isl_basic_set_universe(isl_space_copy(dim));
851 ls = isl_local_space_from_space(dim);
852
853 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
854 isl_int_set_si(v, -1);
855 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
856 isl_int_set_si(v, -3);
857 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
858 isl_int_set_si(v, -3);
859 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
860 isl_int_set_si(v, 6);
861 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
862 bset = isl_basic_set_add_constraint(bset, c);
863
864 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
865
866 /* Test disabled for now */
867 /*
868 assert(bset && bset->n_div == 1);
869 */
870 isl_local_space_free(ls);
871 isl_basic_set_free(bset);
872
873 /* test 8 */
874 dim = isl_space_set_alloc(ctx, 0, 5);
875 bset = isl_basic_set_universe(isl_space_copy(dim));
876 ls = isl_local_space_from_space(dim);
877
878 c = isl_constraint_alloc_equality(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, -3);
882 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
883 isl_int_set_si(v, -3);
884 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
885 isl_int_set_si(v, 6);
886 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
887 bset = isl_basic_set_add_constraint(bset, c);
888
889 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
890 isl_int_set_si(v, -1);
891 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
892 isl_int_set_si(v, 1);
893 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
894 isl_int_set_si(v, 1);
895 isl_constraint_set_constant(c, v);
896 bset = isl_basic_set_add_constraint(bset, c);
897
898 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
899
900 /* Test disabled for now */
901 /*
902 assert(bset && bset->n_div == 1);
903 */
904 isl_local_space_free(ls);
905 isl_basic_set_free(bset);
906
907 /* test 9 */
908 dim = isl_space_set_alloc(ctx, 0, 4);
909 bset = isl_basic_set_universe(isl_space_copy(dim));
910 ls = isl_local_space_from_space(dim);
911
912 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
913 isl_int_set_si(v, 1);
914 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
915 isl_int_set_si(v, -1);
916 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
917 isl_int_set_si(v, -2);
918 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
919 bset = isl_basic_set_add_constraint(bset, c);
920
921 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
922 isl_int_set_si(v, -1);
923 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
924 isl_int_set_si(v, 3);
925 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
926 isl_int_set_si(v, 2);
927 isl_constraint_set_constant(c, v);
928 bset = isl_basic_set_add_constraint(bset, c);
929
930 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
931
932 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
933
934 assert(!isl_basic_set_is_empty(bset));
935
936 isl_local_space_free(ls);
937 isl_basic_set_free(bset);
938
939 /* test 10 */
940 dim = isl_space_set_alloc(ctx, 0, 3);
941 bset = isl_basic_set_universe(isl_space_copy(dim));
942 ls = isl_local_space_from_space(dim);
943
944 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
945 isl_int_set_si(v, 1);
946 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
947 isl_int_set_si(v, -2);
948 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
949 bset = isl_basic_set_add_constraint(bset, c);
950
951 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
952
953 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
954
955 isl_local_space_free(ls);
956 isl_basic_set_free(bset);
957
958 isl_int_clear(v);
959
960 str = "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
961 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
962 set = isl_set_read_from_str(ctx, str);
963 set = isl_set_compute_divs(set);
964 isl_set_free(set);
965 if (!set)
966 return -1;
967
968 str = "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
969 bset = isl_basic_set_read_from_str(ctx, str);
970 n = isl_basic_set_dim(bset, isl_dim_div);
971 isl_basic_set_free(bset);
972 if (!bset)
973 return -1;
974 if (n != 0)
975 isl_die(ctx, isl_error_unknown,
976 "expecting no existentials", return -1);
977
978 str = "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
979 set = isl_set_read_from_str(ctx, str);
980 set = isl_set_remove_divs_involving_dims(set, isl_dim_set, 0, 2);
981 set = isl_set_fix_si(set, isl_dim_set, 2, -3);
982 empty = isl_set_is_empty(set);
983 isl_set_free(set);
984 if (empty < 0)
985 return -1;
986 if (!empty)
987 isl_die(ctx, isl_error_unknown,
988 "result not as accurate as expected", return -1);
989
990 return 0;
991 }
992
993 void test_application_case(struct isl_ctx *ctx, const char *name)
994 {
995 char *filename;
996 FILE *input;
997 struct isl_basic_set *bset1, *bset2;
998 struct isl_basic_map *bmap;
999
1000 filename = get_filename(ctx, name, "omega");
1001 assert(filename);
1002 input = fopen(filename, "r");
1003 assert(input);
1004
1005 bset1 = isl_basic_set_read_from_file(ctx, input);
1006 bmap = isl_basic_map_read_from_file(ctx, input);
1007
1008 bset1 = isl_basic_set_apply(bset1, bmap);
1009
1010 bset2 = isl_basic_set_read_from_file(ctx, input);
1011
1012 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1013
1014 isl_basic_set_free(bset1);
1015 isl_basic_set_free(bset2);
1016 free(filename);
1017
1018 fclose(input);
1019 }
1020
1021 static int test_application(isl_ctx *ctx)
1022 {
1023 test_application_case(ctx, "application");
1024 test_application_case(ctx, "application2");
1025
1026 return 0;
1027 }
1028
1029 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
1030 {
1031 char *filename;
1032 FILE *input;
1033 struct isl_basic_set *bset1, *bset2;
1034
1035 filename = get_filename(ctx, name, "polylib");
1036 assert(filename);
1037 input = fopen(filename, "r");
1038 assert(input);
1039
1040 bset1 = isl_basic_set_read_from_file(ctx, input);
1041 bset2 = isl_basic_set_read_from_file(ctx, input);
1042
1043 bset1 = isl_basic_set_affine_hull(bset1);
1044
1045 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1046
1047 isl_basic_set_free(bset1);
1048 isl_basic_set_free(bset2);
1049 free(filename);
1050
1051 fclose(input);
1052 }
1053
1054 int test_affine_hull(struct isl_ctx *ctx)
1055 {
1056 const char *str;
1057 isl_set *set;
1058 isl_basic_set *bset, *bset2;
1059 int n;
1060 int subset;
1061
1062 test_affine_hull_case(ctx, "affine2");
1063 test_affine_hull_case(ctx, "affine");
1064 test_affine_hull_case(ctx, "affine3");
1065
1066 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
1067 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
1068 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
1069 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
1070 set = isl_set_read_from_str(ctx, str);
1071 bset = isl_set_affine_hull(set);
1072 n = isl_basic_set_dim(bset, isl_dim_div);
1073 isl_basic_set_free(bset);
1074 if (n != 0)
1075 isl_die(ctx, isl_error_unknown, "not expecting any divs",
1076 return -1);
1077
1078 /* Check that isl_map_affine_hull is not confused by
1079 * the reordering of divs in isl_map_align_divs.
1080 */
1081 str = "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1082 "32e0 = b and 32e1 = c); "
1083 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1084 set = isl_set_read_from_str(ctx, str);
1085 bset = isl_set_affine_hull(set);
1086 isl_basic_set_free(bset);
1087 if (!bset)
1088 return -1;
1089
1090 str = "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1091 "32e2 = 31 + 31e0 }";
1092 set = isl_set_read_from_str(ctx, str);
1093 bset = isl_set_affine_hull(set);
1094 str = "{ [a] : exists e : a = 32 e }";
1095 bset2 = isl_basic_set_read_from_str(ctx, str);
1096 subset = isl_basic_set_is_subset(bset, bset2);
1097 isl_basic_set_free(bset);
1098 isl_basic_set_free(bset2);
1099 if (subset < 0)
1100 return -1;
1101 if (!subset)
1102 isl_die(ctx, isl_error_unknown, "not as accurate as expected",
1103 return -1);
1104
1105 return 0;
1106 }
1107
1108 static int test_simple_hull(struct isl_ctx *ctx)
1109 {
1110 const char *str;
1111 isl_set *set;
1112 isl_basic_set *bset;
1113 isl_bool is_empty;
1114
1115 str = "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x;"
1116 "[y, x] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }";
1117 set = isl_set_read_from_str(ctx, str);
1118 bset = isl_set_simple_hull(set);
1119 is_empty = isl_basic_set_is_empty(bset);
1120 isl_basic_set_free(bset);
1121
1122 if (is_empty == isl_bool_error)
1123 return -1;
1124
1125 if (is_empty == isl_bool_false)
1126 isl_die(ctx, isl_error_unknown, "Empty set should be detected",
1127 return -1);
1128
1129 return 0;
1130 }
1131
1132 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
1133 {
1134 char *filename;
1135 FILE *input;
1136 struct isl_basic_set *bset1, *bset2;
1137 struct isl_set *set;
1138
1139 filename = get_filename(ctx, name, "polylib");
1140 assert(filename);
1141 input = fopen(filename, "r");
1142 assert(input);
1143
1144 bset1 = isl_basic_set_read_from_file(ctx, input);
1145 bset2 = isl_basic_set_read_from_file(ctx, input);
1146
1147 set = isl_basic_set_union(bset1, bset2);
1148 bset1 = isl_set_convex_hull(set);
1149
1150 bset2 = isl_basic_set_read_from_file(ctx, input);
1151
1152 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1153
1154 isl_basic_set_free(bset1);
1155 isl_basic_set_free(bset2);
1156 free(filename);
1157
1158 fclose(input);
1159 }
1160
1161 struct {
1162 const char *set;
1163 const char *hull;
1164 } convex_hull_tests[] = {
1165 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1166 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1167 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1168 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1169 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1170 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1171 "i2 <= 5 and i2 >= 4; "
1172 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1173 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1174 "i2 <= 5 + i0 and i2 >= i0 }" },
1175 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1176 "{ [x, y] : 1 = 0 }" },
1177 };
1178
1179 static int test_convex_hull_algo(isl_ctx *ctx, int convex)
1180 {
1181 int i;
1182 int orig_convex = ctx->opt->convex;
1183 ctx->opt->convex = convex;
1184
1185 test_convex_hull_case(ctx, "convex0");
1186 test_convex_hull_case(ctx, "convex1");
1187 test_convex_hull_case(ctx, "convex2");
1188 test_convex_hull_case(ctx, "convex3");
1189 test_convex_hull_case(ctx, "convex4");
1190 test_convex_hull_case(ctx, "convex5");
1191 test_convex_hull_case(ctx, "convex6");
1192 test_convex_hull_case(ctx, "convex7");
1193 test_convex_hull_case(ctx, "convex8");
1194 test_convex_hull_case(ctx, "convex9");
1195 test_convex_hull_case(ctx, "convex10");
1196 test_convex_hull_case(ctx, "convex11");
1197 test_convex_hull_case(ctx, "convex12");
1198 test_convex_hull_case(ctx, "convex13");
1199 test_convex_hull_case(ctx, "convex14");
1200 test_convex_hull_case(ctx, "convex15");
1201
1202 for (i = 0; i < ARRAY_SIZE(convex_hull_tests); ++i) {
1203 isl_set *set1, *set2;
1204 int equal;
1205
1206 set1 = isl_set_read_from_str(ctx, convex_hull_tests[i].set);
1207 set2 = isl_set_read_from_str(ctx, convex_hull_tests[i].hull);
1208 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
1209 equal = isl_set_is_equal(set1, set2);
1210 isl_set_free(set1);
1211 isl_set_free(set2);
1212
1213 if (equal < 0)
1214 return -1;
1215 if (!equal)
1216 isl_die(ctx, isl_error_unknown,
1217 "unexpected convex hull", return -1);
1218 }
1219
1220 ctx->opt->convex = orig_convex;
1221
1222 return 0;
1223 }
1224
1225 static int test_convex_hull(isl_ctx *ctx)
1226 {
1227 if (test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM) < 0)
1228 return -1;
1229 if (test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP) < 0)
1230 return -1;
1231 return 0;
1232 }
1233
1234 void test_gist_case(struct isl_ctx *ctx, const char *name)
1235 {
1236 char *filename;
1237 FILE *input;
1238 struct isl_basic_set *bset1, *bset2;
1239
1240 filename = get_filename(ctx, name, "polylib");
1241 assert(filename);
1242 input = fopen(filename, "r");
1243 assert(input);
1244
1245 bset1 = isl_basic_set_read_from_file(ctx, input);
1246 bset2 = isl_basic_set_read_from_file(ctx, input);
1247
1248 bset1 = isl_basic_set_gist(bset1, bset2);
1249
1250 bset2 = isl_basic_set_read_from_file(ctx, input);
1251
1252 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1253
1254 isl_basic_set_free(bset1);
1255 isl_basic_set_free(bset2);
1256 free(filename);
1257
1258 fclose(input);
1259 }
1260
1261 struct {
1262 const char *set;
1263 const char *context;
1264 const char *gist;
1265 } gist_tests[] = {
1266 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1267 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1268 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1269 "{ [a, b, c] : a <= 15 }" },
1270 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1271 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1272 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1273 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1274 { "{ [m, n, a, b] : a <= 2147 + n }",
1275 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1276 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1277 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1278 "b >= 0) }",
1279 "{ [m, n, ku, kl] }" },
1280 };
1281
1282 static int test_gist(struct isl_ctx *ctx)
1283 {
1284 int i;
1285 const char *str;
1286 isl_basic_set *bset1, *bset2;
1287 isl_map *map1, *map2;
1288 int equal;
1289
1290 for (i = 0; i < ARRAY_SIZE(gist_tests); ++i) {
1291 int equal_input;
1292 isl_set *set1, *set2, *copy;
1293
1294 set1 = isl_set_read_from_str(ctx, gist_tests[i].set);
1295 set2 = isl_set_read_from_str(ctx, gist_tests[i].context);
1296 copy = isl_set_copy(set1);
1297 set1 = isl_set_gist(set1, set2);
1298 set2 = isl_set_read_from_str(ctx, gist_tests[i].gist);
1299 equal = isl_set_is_equal(set1, set2);
1300 isl_set_free(set1);
1301 isl_set_free(set2);
1302 set1 = isl_set_read_from_str(ctx, gist_tests[i].set);
1303 equal_input = isl_set_is_equal(set1, copy);
1304 isl_set_free(set1);
1305 isl_set_free(copy);
1306 if (equal < 0 || equal_input < 0)
1307 return -1;
1308 if (!equal)
1309 isl_die(ctx, isl_error_unknown,
1310 "incorrect gist result", return -1);
1311 if (!equal_input)
1312 isl_die(ctx, isl_error_unknown,
1313 "gist modified input", return -1);
1314 }
1315
1316 test_gist_case(ctx, "gist1");
1317
1318 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
1319 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1320 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1321 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1322 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1323 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1324 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1325 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1326 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1327 bset1 = isl_basic_set_read_from_str(ctx, str);
1328 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1329 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1330 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1331 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1332 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1333 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1334 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1335 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1336 bset2 = isl_basic_set_read_from_str(ctx, str);
1337 bset1 = isl_basic_set_gist(bset1, bset2);
1338 assert(bset1 && bset1->n_div == 0);
1339 isl_basic_set_free(bset1);
1340
1341 /* Check that the integer divisions of the second disjunct
1342 * do not spread to the first disjunct.
1343 */
1344 str = "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1345 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1346 "(exists (e0 = [(-1 + t1)/16], "
1347 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1348 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1349 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1350 "o0 <= 4294967295 and t1 <= -1)) }";
1351 map1 = isl_map_read_from_str(ctx, str);
1352 str = "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1353 map2 = isl_map_read_from_str(ctx, str);
1354 map1 = isl_map_gist(map1, map2);
1355 if (!map1)
1356 return -1;
1357 if (map1->n != 1)
1358 isl_die(ctx, isl_error_unknown, "expecting single disjunct",
1359 isl_map_free(map1); return -1);
1360 if (isl_basic_map_dim(map1->p[0], isl_dim_div) != 1)
1361 isl_die(ctx, isl_error_unknown, "expecting single div",
1362 isl_map_free(map1); return -1);
1363 isl_map_free(map1);
1364
1365 return 0;
1366 }
1367
1368 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
1369 {
1370 isl_set *set, *set2;
1371 int equal;
1372 int one;
1373
1374 set = isl_set_read_from_str(ctx, str);
1375 set = isl_set_coalesce(set);
1376 set2 = isl_set_read_from_str(ctx, str);
1377 equal = isl_set_is_equal(set, set2);
1378 one = set && set->n == 1;
1379 isl_set_free(set);
1380 isl_set_free(set2);
1381
1382 if (equal < 0)
1383 return -1;
1384 if (!equal)
1385 isl_die(ctx, isl_error_unknown,
1386 "coalesced set not equal to input", return -1);
1387 if (check_one && !one)
1388 isl_die(ctx, isl_error_unknown,
1389 "coalesced set should not be a union", return -1);
1390
1391 return 0;
1392 }
1393
1394 /* Inputs for coalescing tests with unbounded wrapping.
1395 * "str" is a string representation of the input set.
1396 * "single_disjunct" is set if we expect the result to consist of
1397 * a single disjunct.
1398 */
1399 struct {
1400 int single_disjunct;
1401 const char *str;
1402 } coalesce_unbounded_tests[] = {
1403 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1404 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1405 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1406 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1407 "-10 <= y <= 0}" },
1408 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1409 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1410 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1411 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1412 };
1413
1414 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1415 * option turned off.
1416 */
1417 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
1418 {
1419 int i;
1420 int r = 0;
1421 int bounded;
1422
1423 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
1424 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
1425
1426 for (i = 0; i < ARRAY_SIZE(coalesce_unbounded_tests); ++i) {
1427 const char *str = coalesce_unbounded_tests[i].str;
1428 int check_one = coalesce_unbounded_tests[i].single_disjunct;
1429 if (test_coalesce_set(ctx, str, check_one) >= 0)
1430 continue;
1431 r = -1;
1432 break;
1433 }
1434
1435 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
1436
1437 return r;
1438 }
1439
1440 /* Inputs for coalescing tests.
1441 * "str" is a string representation of the input set.
1442 * "single_disjunct" is set if we expect the result to consist of
1443 * a single disjunct.
1444 */
1445 struct {
1446 int single_disjunct;
1447 const char *str;
1448 } coalesce_tests[] = {
1449 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1450 "y >= x & x >= 2 & 5 >= y }" },
1451 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1452 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1453 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1454 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1455 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1456 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1457 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1458 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1459 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1460 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1461 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1462 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1463 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1464 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1465 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1466 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1467 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1468 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1469 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1470 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1471 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1472 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1473 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1474 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1475 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1476 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1477 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1478 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1479 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1480 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1481 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1482 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1483 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1484 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1485 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1486 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1487 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1488 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1489 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1490 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1491 "[o0, o1, o2, o3, o4, o5, o6]] : "
1492 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1493 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1494 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1495 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1496 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1497 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1498 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1499 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1500 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1501 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1502 "o6 >= i3 + i6 - o3 and M >= 0 and "
1503 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1504 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1505 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1506 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1507 "(o0 = 0 and M >= 2 and N >= 3) or "
1508 "(M = 0 and o0 = 0 and N >= 3) }" },
1509 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1510 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1511 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1512 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1513 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1514 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1515 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1516 "(y = 3 and x = 1) }" },
1517 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1518 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1519 "i1 <= M and i3 <= M and i4 <= M) or "
1520 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1521 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1522 "i4 <= -1 + M) }" },
1523 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1524 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1525 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1526 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1527 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1528 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1529 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1530 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1531 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1532 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1533 { 0, "{ [a, b] : exists e : 2e = a and "
1534 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1535 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1536 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1537 "j >= 1 and j' <= i + j - i' and i >= 1; "
1538 "[1, 1, 1, 1] }" },
1539 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1540 "[i,j] : exists a : j = 3a }" },
1541 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1542 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1543 "a >= 3) or "
1544 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1545 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1546 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1547 "c <= 6 + 8a and a >= 3; "
1548 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1549 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1550 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1551 "[x,0] : 3 <= x <= 4 }" },
1552 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1553 "[x,0] : 4 <= x <= 5 }" },
1554 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1555 "[x,0] : 3 <= x <= 5 }" },
1556 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1557 "[x,0] : 3 <= x <= 4 }" },
1558 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1559 "i1 <= 0; "
1560 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1561 { 1, "{ [0,0]; [1,1] }" },
1562 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1563 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1564 "ii <= k;"
1565 "[k, 0, k] : k <= 6 and k >= 1 }" },
1566 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1567 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1568 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1569 { 1, "[n] -> { [1] : n >= 0;"
1570 "[x] : exists (e0 = floor((x)/2): x >= 2 and "
1571 "2e0 >= -1 + x and 2e0 <= x and 2e0 <= n) }" },
1572 { 1, "[n] -> { [x, y] : exists (e0 = floor((x)/2), e1 = floor((y)/3): "
1573 "3e1 = y and x >= 2 and 2e0 >= -1 + x and "
1574 "2e0 <= x and 2e0 <= n);"
1575 "[1, y] : exists (e0 = floor((y)/3): 3e0 = y and "
1576 "n >= 0) }" },
1577 { 1, "[t1] -> { [i0] : (exists (e0 = floor((63t1)/64): "
1578 "128e0 >= -134 + 127t1 and t1 >= 2 and "
1579 "64e0 <= 63t1 and 64e0 >= -63 + 63t1)) or "
1580 "t1 = 1 }" },
1581 { 1, "{ [i, i] : exists (e0 = floor((1 + 2i)/3): 3e0 <= 2i and "
1582 "3e0 >= -1 + 2i and i <= 9 and i >= 1);"
1583 "[0, 0] }" },
1584 { 1, "{ [t1] : exists (e0 = floor((-11 + t1)/2): 2e0 = -11 + t1 and "
1585 "t1 >= 13 and t1 <= 16);"
1586 "[t1] : t1 <= 15 and t1 >= 12 }" },
1587 { 1, "{ [x,y] : x = 3y and 0 <= y <= 2; [-3,-1] }" },
1588 { 1, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-2] }" },
1589 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-2,-2] }" },
1590 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-1] }" },
1591 { 1, "{ [i] : exists j : i = 4 j and 0 <= i <= 100;"
1592 "[i] : exists j : 1 <= i <= 100 and i >= 4j + 1 and "
1593 "i <= 4j + 2 }" },
1594 { 1, "{ [c0] : (exists (e0 : c0 - 1 <= 3e0 <= c0)) or "
1595 "(exists (e0 : 3e0 = -2 + c0)) }" },
1596 { 0, "[n, b0, t0] -> "
1597 "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1598 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1599 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1600 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1601 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 >= 8 + n and "
1602 "3i4 <= -96 + 3t0 + i0 and 3i4 >= -95 - n + 3t0 + i0 and "
1603 "i8 >= -157 + i0 - 4i4 and i8 >= 0 and "
1604 "i8 <= -33 + i0 - 4i4 and 3i8 <= -91 + 4n - i0)) or "
1605 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1606 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1607 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1608 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 <= 7 + n and "
1609 "4i4 <= -3 + i0 and 3i4 <= -96 + 3t0 + i0 and "
1610 "3i4 >= -95 - n + 3t0 + i0 and i8 >= -157 + i0 - 4i4 and "
1611 "i8 >= 0 and i8 <= -4 + i0 - 3i4 and i8 <= -41 + i0));"
1612 "[i0, i1, i2, i3, 0, i5, i6, i7, i8, i9, i10, i11, i12] : "
1613 "(exists (e0 = floor((i8)/32): b0 = 0 and 32e0 = i8 and "
1614 "n <= 2147483647 and t0 <= 31 and t0 >= 0 and i0 >= 11 and "
1615 "i0 >= 96 - 3t0 and i0 <= 95 + n - 3t0 and i0 <= 7 + n and "
1616 "i8 >= -40 + i0 and i8 <= -10 + i0)) }" },
1617 { 0, "{ [i0, i1, i2] : "
1618 "(exists (e0, e1 = floor((i0)/32), e2 = floor((i1)/32): "
1619 "32e1 = i0 and 32e2 = i1 and i1 >= -31 + i0 and "
1620 "i1 <= 31 + i0 and i2 >= -30 + i0 and i2 >= -30 + i1 and "
1621 "32e0 >= -30 + i0 and 32e0 >= -30 + i1 and "
1622 "32e0 >= -31 + i2 and 32e0 <= 30 + i2 and 32e0 <= 31 + i1 and "
1623 "32e0 <= 31 + i0)) or "
1624 "i0 >= 0 }" },
1625 { 1, "{ [a, b, c] : 2b = 1 + a and 2c = 2 + a; [0, 0, 0] }" },
1626 };
1627
1628 /* A specialized coalescing test case that would result
1629 * in a segmentation fault or a failed assertion in earlier versions of isl.
1630 */
1631 static int test_coalesce_special(struct isl_ctx *ctx)
1632 {
1633 const char *str;
1634 isl_map *map1, *map2;
1635
1636 str = "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1637 "[[S_L309_IN[] -> T11[]] -> ce_imag2[1, o1]] : "
1638 "(y = 201 and o1 <= 239 and o1 >= 212) or "
1639 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 198 and y >= 3 and "
1640 "o1 <= 239 and o1 >= 212)) or "
1641 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 201 and y >= 3 and "
1642 "o1 <= 241 and o1 >= 240));"
1643 "[S_L220_OUT[] -> T7[]] -> "
1644 "[[S_L309_IN[] -> T11[]] -> ce_imag2[0, o1]] : "
1645 "(y = 2 and o1 <= 241 and o1 >= 212) or "
1646 "(exists (e0 = [(-2 + y)/3]: 3e0 = -2 + y and y <= 200 and "
1647 "y >= 5 and o1 <= 241 and o1 >= 212)) }";
1648 map1 = isl_map_read_from_str(ctx, str);
1649 map1 = isl_map_align_divs(map1);
1650 map1 = isl_map_coalesce(map1);
1651 str = "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1652 "[[S_L309_IN[] -> T11[]] -> ce_imag2[o0, o1]] : "
1653 "exists (e0 = [(-1 - y + o0)/3]: 3e0 = -1 - y + o0 and "
1654 "y <= 201 and o0 <= 2 and o1 >= 212 and o1 <= 241 and "
1655 "o0 >= 3 - y and o0 <= -2 + y and o0 >= 0) }";
1656 map2 = isl_map_read_from_str(ctx, str);
1657 map2 = isl_map_union(map2, map1);
1658 map2 = isl_map_align_divs(map2);
1659 map2 = isl_map_coalesce(map2);
1660 isl_map_free(map2);
1661 if (!map2)
1662 return -1;
1663
1664 return 0;
1665 }
1666
1667 /* Test the functionality of isl_set_coalesce.
1668 * That is, check that the output is always equal to the input
1669 * and in some cases that the result consists of a single disjunct.
1670 */
1671 static int test_coalesce(struct isl_ctx *ctx)
1672 {
1673 int i;
1674
1675 for (i = 0; i < ARRAY_SIZE(coalesce_tests); ++i) {
1676 const char *str = coalesce_tests[i].str;
1677 int check_one = coalesce_tests[i].single_disjunct;
1678 if (test_coalesce_set(ctx, str, check_one) < 0)
1679 return -1;
1680 }
1681
1682 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1683 return -1;
1684 if (test_coalesce_special(ctx) < 0)
1685 return -1;
1686
1687 return 0;
1688 }
1689
1690 static int test_closure(isl_ctx *ctx)
1691 {
1692 const char *str;
1693 isl_set *dom;
1694 isl_map *up, *right;
1695 isl_map *map, *map2;
1696 int exact;
1697
1698 /* COCOA example 1 */
1699 map = isl_map_read_from_str(ctx,
1700 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1701 "1 <= i and i < n and 1 <= j and j < n or "
1702 "i2 = i + 1 and j2 = j - 1 and "
1703 "1 <= i and i < n and 2 <= j and j <= n }");
1704 map = isl_map_power(map, &exact);
1705 assert(exact);
1706 isl_map_free(map);
1707
1708 /* COCOA example 1 */
1709 map = isl_map_read_from_str(ctx,
1710 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1711 "1 <= i and i < n and 1 <= j and j < n or "
1712 "i2 = i + 1 and j2 = j - 1 and "
1713 "1 <= i and i < n and 2 <= j and j <= n }");
1714 map = isl_map_transitive_closure(map, &exact);
1715 assert(exact);
1716 map2 = isl_map_read_from_str(ctx,
1717 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1718 "1 <= i and i < n and 1 <= j and j <= n and "
1719 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1720 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1721 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1722 assert(isl_map_is_equal(map, map2));
1723 isl_map_free(map2);
1724 isl_map_free(map);
1725
1726 map = isl_map_read_from_str(ctx,
1727 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1728 " 0 <= y and y <= n }");
1729 map = isl_map_transitive_closure(map, &exact);
1730 map2 = isl_map_read_from_str(ctx,
1731 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1732 " 0 <= y and y <= n }");
1733 assert(isl_map_is_equal(map, map2));
1734 isl_map_free(map2);
1735 isl_map_free(map);
1736
1737 /* COCOA example 2 */
1738 map = isl_map_read_from_str(ctx,
1739 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1740 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1741 "i2 = i + 2 and j2 = j - 2 and "
1742 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1743 map = isl_map_transitive_closure(map, &exact);
1744 assert(exact);
1745 map2 = isl_map_read_from_str(ctx,
1746 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1747 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1748 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1749 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1750 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1751 assert(isl_map_is_equal(map, map2));
1752 isl_map_free(map);
1753 isl_map_free(map2);
1754
1755 /* COCOA Fig.2 left */
1756 map = isl_map_read_from_str(ctx,
1757 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1758 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1759 "j <= n or "
1760 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1761 "j <= 2 i - 3 and j <= n - 2 or "
1762 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1763 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1764 map = isl_map_transitive_closure(map, &exact);
1765 assert(exact);
1766 isl_map_free(map);
1767
1768 /* COCOA Fig.2 right */
1769 map = isl_map_read_from_str(ctx,
1770 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1771 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1772 "j <= n or "
1773 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1774 "j <= 2 i - 4 and j <= n - 3 or "
1775 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1776 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1777 map = isl_map_power(map, &exact);
1778 assert(exact);
1779 isl_map_free(map);
1780
1781 /* COCOA Fig.2 right */
1782 map = isl_map_read_from_str(ctx,
1783 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1784 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1785 "j <= n or "
1786 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1787 "j <= 2 i - 4 and j <= n - 3 or "
1788 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1789 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1790 map = isl_map_transitive_closure(map, &exact);
1791 assert(exact);
1792 map2 = isl_map_read_from_str(ctx,
1793 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1794 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1795 "j <= n and 3 + i + 2 j <= 3 n and "
1796 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1797 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1798 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1799 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1800 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1801 assert(isl_map_is_equal(map, map2));
1802 isl_map_free(map2);
1803 isl_map_free(map);
1804
1805 /* COCOA Fig.1 right */
1806 dom = isl_set_read_from_str(ctx,
1807 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1808 "2 x - 3 y + 3 >= 0 }");
1809 right = isl_map_read_from_str(ctx,
1810 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1811 up = isl_map_read_from_str(ctx,
1812 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1813 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1814 right = isl_map_intersect_range(right, isl_set_copy(dom));
1815 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1816 up = isl_map_intersect_range(up, dom);
1817 map = isl_map_union(up, right);
1818 map = isl_map_transitive_closure(map, &exact);
1819 assert(exact);
1820 map2 = isl_map_read_from_str(ctx,
1821 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1822 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1823 assert(isl_map_is_equal(map, map2));
1824 isl_map_free(map2);
1825 isl_map_free(map);
1826
1827 /* COCOA Theorem 1 counter example */
1828 map = isl_map_read_from_str(ctx,
1829 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1830 "i2 = 1 and j2 = j or "
1831 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1832 map = isl_map_transitive_closure(map, &exact);
1833 assert(exact);
1834 isl_map_free(map);
1835
1836 map = isl_map_read_from_str(ctx,
1837 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1838 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1839 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1840 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1841 map = isl_map_transitive_closure(map, &exact);
1842 assert(exact);
1843 isl_map_free(map);
1844
1845 /* Kelly et al 1996, fig 12 */
1846 map = isl_map_read_from_str(ctx,
1847 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1848 "1 <= i,j,j+1 <= n or "
1849 "j = n and j2 = 1 and i2 = i + 1 and "
1850 "1 <= i,i+1 <= n }");
1851 map = isl_map_transitive_closure(map, &exact);
1852 assert(exact);
1853 map2 = isl_map_read_from_str(ctx,
1854 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1855 "1 <= i <= n and i = i2 or "
1856 "1 <= i < i2 <= n and 1 <= j <= n and "
1857 "1 <= j2 <= n }");
1858 assert(isl_map_is_equal(map, map2));
1859 isl_map_free(map2);
1860 isl_map_free(map);
1861
1862 /* Omega's closure4 */
1863 map = isl_map_read_from_str(ctx,
1864 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1865 "1 <= x,y <= 10 or "
1866 "x2 = x + 1 and y2 = y and "
1867 "1 <= x <= 20 && 5 <= y <= 15 }");
1868 map = isl_map_transitive_closure(map, &exact);
1869 assert(exact);
1870 isl_map_free(map);
1871
1872 map = isl_map_read_from_str(ctx,
1873 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1874 map = isl_map_transitive_closure(map, &exact);
1875 assert(!exact);
1876 map2 = isl_map_read_from_str(ctx,
1877 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1878 assert(isl_map_is_equal(map, map2));
1879 isl_map_free(map);
1880 isl_map_free(map2);
1881
1882 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1883 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1884 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1885 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1886 map = isl_map_read_from_str(ctx, str);
1887 map = isl_map_transitive_closure(map, &exact);
1888 assert(exact);
1889 map2 = isl_map_read_from_str(ctx, str);
1890 assert(isl_map_is_equal(map, map2));
1891 isl_map_free(map);
1892 isl_map_free(map2);
1893
1894 str = "{[0] -> [1]; [2] -> [3]}";
1895 map = isl_map_read_from_str(ctx, str);
1896 map = isl_map_transitive_closure(map, &exact);
1897 assert(exact);
1898 map2 = isl_map_read_from_str(ctx, str);
1899 assert(isl_map_is_equal(map, map2));
1900 isl_map_free(map);
1901 isl_map_free(map2);
1902
1903 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1904 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1905 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1906 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1907 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1908 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1909 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1910 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1911 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1912 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1913 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1914 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1915 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1916 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1917 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1918 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1919 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1920 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1921 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1922 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1923 map = isl_map_read_from_str(ctx, str);
1924 map = isl_map_transitive_closure(map, NULL);
1925 assert(map);
1926 isl_map_free(map);
1927
1928 return 0;
1929 }
1930
1931 static int test_lex(struct isl_ctx *ctx)
1932 {
1933 isl_space *dim;
1934 isl_map *map;
1935 int empty;
1936
1937 dim = isl_space_set_alloc(ctx, 0, 0);
1938 map = isl_map_lex_le(dim);
1939 empty = isl_map_is_empty(map);
1940 isl_map_free(map);
1941
1942 if (empty < 0)
1943 return -1;
1944 if (empty)
1945 isl_die(ctx, isl_error_unknown,
1946 "expecting non-empty result", return -1);
1947
1948 return 0;
1949 }
1950
1951 static int test_lexmin(struct isl_ctx *ctx)
1952 {
1953 int equal;
1954 const char *str;
1955 isl_basic_map *bmap;
1956 isl_map *map, *map2;
1957 isl_set *set;
1958 isl_set *set2;
1959 isl_pw_multi_aff *pma;
1960
1961 str = "[p0, p1] -> { [] -> [] : "
1962 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1963 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1964 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1965 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1966 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1967 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1968 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1969 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1970 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1971 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1972 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1973 map = isl_map_read_from_str(ctx, str);
1974 map = isl_map_lexmin(map);
1975 isl_map_free(map);
1976
1977 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1978 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1979 set = isl_set_read_from_str(ctx, str);
1980 set = isl_set_lexmax(set);
1981 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1982 set2 = isl_set_read_from_str(ctx, str);
1983 set = isl_set_intersect(set, set2);
1984 assert(!isl_set_is_empty(set));
1985 isl_set_free(set);
1986
1987 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1988 map = isl_map_read_from_str(ctx, str);
1989 map = isl_map_lexmin(map);
1990 str = "{ [x] -> [5] : 6 <= x <= 8; "
1991 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1992 map2 = isl_map_read_from_str(ctx, str);
1993 assert(isl_map_is_equal(map, map2));
1994 isl_map_free(map);
1995 isl_map_free(map2);
1996
1997 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1998 map = isl_map_read_from_str(ctx, str);
1999 map2 = isl_map_copy(map);
2000 map = isl_map_lexmin(map);
2001 assert(isl_map_is_equal(map, map2));
2002 isl_map_free(map);
2003 isl_map_free(map2);
2004
2005 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
2006 map = isl_map_read_from_str(ctx, str);
2007 map = isl_map_lexmin(map);
2008 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
2009 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
2010 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
2011 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
2012 map2 = isl_map_read_from_str(ctx, str);
2013 assert(isl_map_is_equal(map, map2));
2014 isl_map_free(map);
2015 isl_map_free(map2);
2016
2017 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2018 " 8i' <= i and 8i' >= -7 + i }";
2019 bmap = isl_basic_map_read_from_str(ctx, str);
2020 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
2021 map2 = isl_map_from_pw_multi_aff(pma);
2022 map = isl_map_from_basic_map(bmap);
2023 assert(isl_map_is_equal(map, map2));
2024 isl_map_free(map);
2025 isl_map_free(map2);
2026
2027 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
2028 map = isl_map_read_from_str(ctx, str);
2029 map = isl_map_lexmin(map);
2030 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
2031 map2 = isl_map_read_from_str(ctx, str);
2032 assert(isl_map_is_equal(map, map2));
2033 isl_map_free(map);
2034 isl_map_free(map2);
2035
2036 /* Check that empty pieces are properly combined. */
2037 str = "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
2038 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
2039 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
2040 map = isl_map_read_from_str(ctx, str);
2041 map = isl_map_lexmin(map);
2042 str = "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
2043 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
2044 "x >= 4 }";
2045 map2 = isl_map_read_from_str(ctx, str);
2046 assert(isl_map_is_equal(map, map2));
2047 isl_map_free(map);
2048 isl_map_free(map2);
2049
2050 str = "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2051 " 8i' <= i and 8i' >= -7 + i }";
2052 set = isl_set_read_from_str(ctx, str);
2053 pma = isl_set_lexmin_pw_multi_aff(isl_set_copy(set));
2054 set2 = isl_set_from_pw_multi_aff(pma);
2055 equal = isl_set_is_equal(set, set2);
2056 isl_set_free(set);
2057 isl_set_free(set2);
2058 if (equal < 0)
2059 return -1;
2060 if (!equal)
2061 isl_die(ctx, isl_error_unknown,
2062 "unexpected difference between set and "
2063 "piecewise affine expression", return -1);
2064
2065 return 0;
2066 }
2067
2068 /* Check that isl_set_min_val and isl_set_max_val compute the correct
2069 * result on non-convex inputs.
2070 */
2071 static int test_min(struct isl_ctx *ctx)
2072 {
2073 isl_set *set;
2074 isl_aff *aff;
2075 isl_val *val;
2076 int min_ok, max_ok;
2077
2078 set = isl_set_read_from_str(ctx, "{ [-1]; [1] }");
2079 aff = isl_aff_read_from_str(ctx, "{ [x] -> [x] }");
2080 val = isl_set_min_val(set, aff);
2081 min_ok = isl_val_is_negone(val);
2082 isl_val_free(val);
2083 val = isl_set_max_val(set, aff);
2084 max_ok = isl_val_is_one(val);
2085 isl_val_free(val);
2086 isl_aff_free(aff);
2087 isl_set_free(set);
2088
2089 if (min_ok < 0 || max_ok < 0)
2090 return -1;
2091 if (!min_ok)
2092 isl_die(ctx, isl_error_unknown,
2093 "unexpected minimum", return -1);
2094 if (!max_ok)
2095 isl_die(ctx, isl_error_unknown,
2096 "unexpected maximum", return -1);
2097
2098 return 0;
2099 }
2100
2101 struct must_may {
2102 isl_map *must;
2103 isl_map *may;
2104 };
2105
2106 static isl_stat collect_must_may(__isl_take isl_map *dep, int must,
2107 void *dep_user, void *user)
2108 {
2109 struct must_may *mm = (struct must_may *)user;
2110
2111 if (must)
2112 mm->must = isl_map_union(mm->must, dep);
2113 else
2114 mm->may = isl_map_union(mm->may, dep);
2115
2116 return isl_stat_ok;
2117 }
2118
2119 static int common_space(void *first, void *second)
2120 {
2121 int depth = *(int *)first;
2122 return 2 * depth;
2123 }
2124
2125 static int map_is_equal(__isl_keep isl_map *map, const char *str)
2126 {
2127 isl_map *map2;
2128 int equal;
2129
2130 if (!map)
2131 return -1;
2132
2133 map2 = isl_map_read_from_str(map->ctx, str);
2134 equal = isl_map_is_equal(map, map2);
2135 isl_map_free(map2);
2136
2137 return equal;
2138 }
2139
2140 static int map_check_equal(__isl_keep isl_map *map, const char *str)
2141 {
2142 int equal;
2143
2144 equal = map_is_equal(map, str);
2145 if (equal < 0)
2146 return -1;
2147 if (!equal)
2148 isl_die(isl_map_get_ctx(map), isl_error_unknown,
2149 "result not as expected", return -1);
2150 return 0;
2151 }
2152
2153 static int test_dep(struct isl_ctx *ctx)
2154 {
2155 const char *str;
2156 isl_space *dim;
2157 isl_map *map;
2158 isl_access_info *ai;
2159 isl_flow *flow;
2160 int depth;
2161 struct must_may mm;
2162
2163 depth = 3;
2164
2165 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2166 map = isl_map_read_from_str(ctx, str);
2167 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2168
2169 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2170 map = isl_map_read_from_str(ctx, str);
2171 ai = isl_access_info_add_source(ai, map, 1, &depth);
2172
2173 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2174 map = isl_map_read_from_str(ctx, str);
2175 ai = isl_access_info_add_source(ai, map, 1, &depth);
2176
2177 flow = isl_access_info_compute_flow(ai);
2178 dim = isl_space_alloc(ctx, 0, 3, 3);
2179 mm.must = isl_map_empty(isl_space_copy(dim));
2180 mm.may = isl_map_empty(dim);
2181
2182 isl_flow_foreach(flow, collect_must_may, &mm);
2183
2184 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
2185 " [1,10,0] -> [2,5,0] }";
2186 assert(map_is_equal(mm.must, str));
2187 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2188 assert(map_is_equal(mm.may, str));
2189
2190 isl_map_free(mm.must);
2191 isl_map_free(mm.may);
2192 isl_flow_free(flow);
2193
2194
2195 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2196 map = isl_map_read_from_str(ctx, str);
2197 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2198
2199 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2200 map = isl_map_read_from_str(ctx, str);
2201 ai = isl_access_info_add_source(ai, map, 1, &depth);
2202
2203 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2204 map = isl_map_read_from_str(ctx, str);
2205 ai = isl_access_info_add_source(ai, map, 0, &depth);
2206
2207 flow = isl_access_info_compute_flow(ai);
2208 dim = isl_space_alloc(ctx, 0, 3, 3);
2209 mm.must = isl_map_empty(isl_space_copy(dim));
2210 mm.may = isl_map_empty(dim);
2211
2212 isl_flow_foreach(flow, collect_must_may, &mm);
2213
2214 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2215 assert(map_is_equal(mm.must, str));
2216 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2217 assert(map_is_equal(mm.may, str));
2218
2219 isl_map_free(mm.must);
2220 isl_map_free(mm.may);
2221 isl_flow_free(flow);
2222
2223
2224 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2225 map = isl_map_read_from_str(ctx, str);
2226 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2227
2228 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2229 map = isl_map_read_from_str(ctx, str);
2230 ai = isl_access_info_add_source(ai, map, 0, &depth);
2231
2232 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2233 map = isl_map_read_from_str(ctx, str);
2234 ai = isl_access_info_add_source(ai, map, 0, &depth);
2235
2236 flow = isl_access_info_compute_flow(ai);
2237 dim = isl_space_alloc(ctx, 0, 3, 3);
2238 mm.must = isl_map_empty(isl_space_copy(dim));
2239 mm.may = isl_map_empty(dim);
2240
2241 isl_flow_foreach(flow, collect_must_may, &mm);
2242
2243 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2244 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2245 assert(map_is_equal(mm.may, str));
2246 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2247 assert(map_is_equal(mm.must, str));
2248
2249 isl_map_free(mm.must);
2250 isl_map_free(mm.may);
2251 isl_flow_free(flow);
2252
2253
2254 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2255 map = isl_map_read_from_str(ctx, str);
2256 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2257
2258 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2259 map = isl_map_read_from_str(ctx, str);
2260 ai = isl_access_info_add_source(ai, map, 0, &depth);
2261
2262 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2263 map = isl_map_read_from_str(ctx, str);
2264 ai = isl_access_info_add_source(ai, map, 0, &depth);
2265
2266 flow = isl_access_info_compute_flow(ai);
2267 dim = isl_space_alloc(ctx, 0, 3, 3);
2268 mm.must = isl_map_empty(isl_space_copy(dim));
2269 mm.may = isl_map_empty(dim);
2270
2271 isl_flow_foreach(flow, collect_must_may, &mm);
2272
2273 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2274 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2275 assert(map_is_equal(mm.may, str));
2276 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2277 assert(map_is_equal(mm.must, str));
2278
2279 isl_map_free(mm.must);
2280 isl_map_free(mm.may);
2281 isl_flow_free(flow);
2282
2283
2284 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2285 map = isl_map_read_from_str(ctx, str);
2286 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2287
2288 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2289 map = isl_map_read_from_str(ctx, str);
2290 ai = isl_access_info_add_source(ai, map, 0, &depth);
2291
2292 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2293 map = isl_map_read_from_str(ctx, str);
2294 ai = isl_access_info_add_source(ai, map, 0, &depth);
2295
2296 flow = isl_access_info_compute_flow(ai);
2297 dim = isl_space_alloc(ctx, 0, 3, 3);
2298 mm.must = isl_map_empty(isl_space_copy(dim));
2299 mm.may = isl_map_empty(dim);
2300
2301 isl_flow_foreach(flow, collect_must_may, &mm);
2302
2303 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2304 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2305 assert(map_is_equal(mm.may, str));
2306 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2307 assert(map_is_equal(mm.must, str));
2308
2309 isl_map_free(mm.must);
2310 isl_map_free(mm.may);
2311 isl_flow_free(flow);
2312
2313
2314 depth = 5;
2315
2316 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2317 map = isl_map_read_from_str(ctx, str);
2318 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
2319
2320 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2321 map = isl_map_read_from_str(ctx, str);
2322 ai = isl_access_info_add_source(ai, map, 1, &depth);
2323
2324 flow = isl_access_info_compute_flow(ai);
2325 dim = isl_space_alloc(ctx, 0, 5, 5);
2326 mm.must = isl_map_empty(isl_space_copy(dim));
2327 mm.may = isl_map_empty(dim);
2328
2329 isl_flow_foreach(flow, collect_must_may, &mm);
2330
2331 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2332 assert(map_is_equal(mm.must, str));
2333 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2334 assert(map_is_equal(mm.may, str));
2335
2336 isl_map_free(mm.must);
2337 isl_map_free(mm.may);
2338 isl_flow_free(flow);
2339
2340 return 0;
2341 }
2342
2343 /* Check that the dependence analysis proceeds without errors.
2344 * Earlier versions of isl would break down during the analysis
2345 * due to the use of the wrong spaces.
2346 */
2347 static int test_flow(isl_ctx *ctx)
2348 {
2349 const char *str;
2350 isl_union_map *access, *schedule;
2351 isl_union_map *must_dep, *may_dep;
2352 int r;
2353
2354 str = "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2355 access = isl_union_map_read_from_str(ctx, str);
2356 str = "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2357 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2358 "S2[] -> [1,0,0,0]; "
2359 "S3[] -> [-1,0,0,0] }";
2360 schedule = isl_union_map_read_from_str(ctx, str);
2361 r = isl_union_map_compute_flow(access, isl_union_map_copy(access),
2362 isl_union_map_copy(access), schedule,
2363 &must_dep, &may_dep, NULL, NULL);
2364 isl_union_map_free(may_dep);
2365 isl_union_map_free(must_dep);
2366
2367 return r;
2368 }
2369
2370 struct {
2371 const char *map;
2372 int sv;
2373 } sv_tests[] = {
2374 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2375 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2376 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2377 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2378 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2379 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2380 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2381 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2382 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2383 };
2384
2385 int test_sv(isl_ctx *ctx)
2386 {
2387 isl_union_map *umap;
2388 int i;
2389 int sv;
2390
2391 for (i = 0; i < ARRAY_SIZE(sv_tests); ++i) {
2392 umap = isl_union_map_read_from_str(ctx, sv_tests[i].map);
2393 sv = isl_union_map_is_single_valued(umap);
2394 isl_union_map_free(umap);
2395 if (sv < 0)
2396 return -1;
2397 if (sv_tests[i].sv && !sv)
2398 isl_die(ctx, isl_error_internal,
2399 "map not detected as single valued", return -1);
2400 if (!sv_tests[i].sv && sv)
2401 isl_die(ctx, isl_error_internal,
2402 "map detected as single valued", return -1);
2403 }
2404
2405 return 0;
2406 }
2407
2408 struct {
2409 const char *str;
2410 int bijective;
2411 } bijective_tests[] = {
2412 { "[N,M]->{[i,j] -> [i]}", 0 },
2413 { "[N,M]->{[i,j] -> [i] : j=i}", 1 },
2414 { "[N,M]->{[i,j] -> [i] : j=0}", 1 },
2415 { "[N,M]->{[i,j] -> [i] : j=N}", 1 },
2416 { "[N,M]->{[i,j] -> [j,i]}", 1 },
2417 { "[N,M]->{[i,j] -> [i+j]}", 0 },
2418 { "[N,M]->{[i,j] -> []}", 0 },
2419 { "[N,M]->{[i,j] -> [i,j,N]}", 1 },
2420 { "[N,M]->{[i,j] -> [2i]}", 0 },
2421 { "[N,M]->{[i,j] -> [i,i]}", 0 },
2422 { "[N,M]->{[i,j] -> [2i,i]}", 0 },
2423 { "[N,M]->{[i,j] -> [2i,j]}", 1 },
2424 { "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1 },
2425 };
2426
2427 static int test_bijective(struct isl_ctx *ctx)
2428 {
2429 isl_map *map;
2430 int i;
2431 int bijective;
2432
2433 for (i = 0; i < ARRAY_SIZE(bijective_tests); ++i) {
2434 map = isl_map_read_from_str(ctx, bijective_tests[i].str);
2435 bijective = isl_map_is_bijective(map);
2436 isl_map_free(map);
2437 if (bijective < 0)
2438 return -1;
2439 if (bijective_tests[i].bijective && !bijective)
2440 isl_die(ctx, isl_error_internal,
2441 "map not detected as bijective", return -1);
2442 if (!bijective_tests[i].bijective && bijective)
2443 isl_die(ctx, isl_error_internal,
2444 "map detected as bijective", return -1);
2445 }
2446
2447 return 0;
2448 }
2449
2450 /* Inputs for isl_pw_qpolynomial_gist tests.
2451 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2452 */
2453 struct {
2454 const char *pwqp;
2455 const char *set;
2456 const char *gist;
2457 } pwqp_gist_tests[] = {
2458 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2459 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2460 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2461 "{ [i] -> -1/2 + 1/2 * i }" },
2462 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2463 };
2464
2465 static int test_pwqp(struct isl_ctx *ctx)
2466 {
2467 int i;
2468 const char *str;
2469 isl_set *set;
2470 isl_pw_qpolynomial *pwqp1, *pwqp2;
2471 int equal;
2472
2473 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2474 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2475
2476 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
2477 isl_dim_in, 1, 1);
2478
2479 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2480 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2481
2482 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2483
2484 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2485
2486 isl_pw_qpolynomial_free(pwqp1);
2487
2488 for (i = 0; i < ARRAY_SIZE(pwqp_gist_tests); ++i) {
2489 str = pwqp_gist_tests[i].pwqp;
2490 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2491 str = pwqp_gist_tests[i].set;
2492 set = isl_set_read_from_str(ctx, str);
2493 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2494 str = pwqp_gist_tests[i].gist;
2495 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2496 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2497 equal = isl_pw_qpolynomial_is_zero(pwqp1);
2498 isl_pw_qpolynomial_free(pwqp1);
2499
2500 if (equal < 0)
2501 return -1;
2502 if (!equal)
2503 isl_die(ctx, isl_error_unknown,
2504 "unexpected result", return -1);
2505 }
2506
2507 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
2508 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2509 str = "{ [i] -> ([(2 * [i/2])/5]) }";
2510 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2511
2512 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2513
2514 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2515
2516 isl_pw_qpolynomial_free(pwqp1);
2517
2518 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
2519 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2520 str = "{ [x] -> x }";
2521 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2522
2523 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2524
2525 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2526
2527 isl_pw_qpolynomial_free(pwqp1);
2528
2529 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2530 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2531 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2532 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
2533 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2534 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2535 isl_pw_qpolynomial_free(pwqp1);
2536
2537 str = "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2538 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2539 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2540 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2541 set = isl_set_read_from_str(ctx, "{ [a,b,a] }");
2542 pwqp1 = isl_pw_qpolynomial_intersect_domain(pwqp1, set);
2543 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2544 isl_pw_qpolynomial_free(pwqp1);
2545 isl_pw_qpolynomial_free(pwqp2);
2546 if (equal < 0)
2547 return -1;
2548 if (!equal)
2549 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2550
2551 str = "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2552 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2553 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2554 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2555 pwqp1 = isl_pw_qpolynomial_fix_val(pwqp1, isl_dim_set, 1,
2556 isl_val_one(ctx));
2557 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2558 isl_pw_qpolynomial_free(pwqp1);
2559 isl_pw_qpolynomial_free(pwqp2);
2560 if (equal < 0)
2561 return -1;
2562 if (!equal)
2563 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2564
2565 return 0;
2566 }
2567
2568 static int test_split_periods(isl_ctx *ctx)
2569 {
2570 const char *str;
2571 isl_pw_qpolynomial *pwqp;
2572
2573 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2574 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2575 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2576 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2577
2578 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
2579
2580 isl_pw_qpolynomial_free(pwqp);
2581
2582 if (!pwqp)
2583 return -1;
2584
2585 return 0;
2586 }
2587
2588 static int test_union(isl_ctx *ctx)
2589 {
2590 const char *str;
2591 isl_union_set *uset1, *uset2;
2592 isl_union_map *umap1, *umap2;
2593 int equal;
2594
2595 str = "{ [i] : 0 <= i <= 1 }";
2596 uset1 = isl_union_set_read_from_str(ctx, str);
2597 str = "{ [1] -> [0] }";
2598 umap1 = isl_union_map_read_from_str(ctx, str);
2599
2600 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
2601 equal = isl_union_map_is_equal(umap1, umap2);
2602
2603 isl_union_map_free(umap1);
2604 isl_union_map_free(umap2);
2605
2606 if (equal < 0)
2607 return -1;
2608 if (!equal)
2609 isl_die(ctx, isl_error_unknown, "union maps not equal",
2610 return -1);
2611
2612 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2613 umap1 = isl_union_map_read_from_str(ctx, str);
2614 str = "{ A[i]; B[i] }";
2615 uset1 = isl_union_set_read_from_str(ctx, str);
2616
2617 uset2 = isl_union_map_domain(umap1);
2618
2619 equal = isl_union_set_is_equal(uset1, uset2);
2620
2621 isl_union_set_free(uset1);
2622 isl_union_set_free(uset2);
2623
2624 if (equal < 0)
2625 return -1;
2626 if (!equal)
2627 isl_die(ctx, isl_error_unknown, "union sets not equal",
2628 return -1);
2629
2630 return 0;
2631 }
2632
2633 /* Check that computing a bound of a non-zero polynomial over an unbounded
2634 * domain does not produce a rational value.
2635 * In particular, check that the upper bound is infinity.
2636 */
2637 static int test_bound_unbounded_domain(isl_ctx *ctx)
2638 {
2639 const char *str;
2640 isl_pw_qpolynomial *pwqp;
2641 isl_pw_qpolynomial_fold *pwf, *pwf2;
2642 isl_bool equal;
2643
2644 str = "{ [m,n] -> -m * n }";
2645 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2646 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2647 str = "{ infty }";
2648 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2649 pwf2 = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2650 equal = isl_pw_qpolynomial_fold_plain_is_equal(pwf, pwf2);
2651 isl_pw_qpolynomial_fold_free(pwf);
2652 isl_pw_qpolynomial_fold_free(pwf2);
2653
2654 if (equal < 0)
2655 return -1;
2656 if (!equal)
2657 isl_die(ctx, isl_error_unknown,
2658 "expecting infinite polynomial bound", return -1);
2659
2660 return 0;
2661 }
2662
2663 static int test_bound(isl_ctx *ctx)
2664 {
2665 const char *str;
2666 unsigned dim;
2667 isl_pw_qpolynomial *pwqp;
2668 isl_pw_qpolynomial_fold *pwf;
2669
2670 if (test_bound_unbounded_domain(ctx) < 0)
2671 return -1;
2672
2673 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
2674 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2675 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2676 dim = isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in);
2677 isl_pw_qpolynomial_fold_free(pwf);
2678 if (dim != 4)
2679 isl_die(ctx, isl_error_unknown, "unexpected input dimension",
2680 return -1);
2681
2682 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2683 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2684 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2685 dim = isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in);
2686 isl_pw_qpolynomial_fold_free(pwf);
2687 if (dim != 1)
2688 isl_die(ctx, isl_error_unknown, "unexpected input dimension",
2689 return -1);
2690
2691 return 0;
2692 }
2693
2694 static int test_lift(isl_ctx *ctx)
2695 {
2696 const char *str;
2697 isl_basic_map *bmap;
2698 isl_basic_set *bset;
2699
2700 str = "{ [i0] : exists e0 : i0 = 4e0 }";
2701 bset = isl_basic_set_read_from_str(ctx, str);
2702 bset = isl_basic_set_lift(bset);
2703 bmap = isl_basic_map_from_range(bset);
2704 bset = isl_basic_map_domain(bmap);
2705 isl_basic_set_free(bset);
2706
2707 return 0;
2708 }
2709
2710 struct {
2711 const char *set1;
2712 const char *set2;
2713 int subset;
2714 } subset_tests[] = {
2715 { "{ [112, 0] }",
2716 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2717 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2718 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2719 { "{ [65] }",
2720 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2721 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2722 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2723 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2724 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2725 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2726 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2727 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2728 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2729 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2730 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2731 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2732 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2733 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2734 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2735 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2736 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2737 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2738 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2739 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2740 "4e0 <= -57 + i0 + i1)) or "
2741 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2742 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2743 "4e0 >= -61 + i0 + i1)) or "
2744 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2745 };
2746
2747 static int test_subset(isl_ctx *ctx)
2748 {
2749 int i;
2750 isl_set *set1, *set2;
2751 int subset;
2752
2753 for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
2754 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
2755 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
2756 subset = isl_set_is_subset(set1, set2);
2757 isl_set_free(set1);
2758 isl_set_free(set2);
2759 if (subset < 0)
2760 return -1;
2761 if (subset != subset_tests[i].subset)
2762 isl_die(ctx, isl_error_unknown,
2763 "incorrect subset result", return -1);
2764 }
2765
2766 return 0;
2767 }
2768
2769 struct {
2770 const char *minuend;
2771 const char *subtrahend;
2772 const char *difference;
2773 } subtract_domain_tests[] = {
2774 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2775 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2776 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2777 };
2778
2779 static int test_subtract(isl_ctx *ctx)
2780 {
2781 int i;
2782 isl_union_map *umap1, *umap2;
2783 isl_union_pw_multi_aff *upma1, *upma2;
2784 isl_union_set *uset;
2785 int equal;
2786
2787 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2788 umap1 = isl_union_map_read_from_str(ctx,
2789 subtract_domain_tests[i].minuend);
2790 uset = isl_union_set_read_from_str(ctx,
2791 subtract_domain_tests[i].subtrahend);
2792 umap2 = isl_union_map_read_from_str(ctx,
2793 subtract_domain_tests[i].difference);
2794 umap1 = isl_union_map_subtract_domain(umap1, uset);
2795 equal = isl_union_map_is_equal(umap1, umap2);
2796 isl_union_map_free(umap1);
2797 isl_union_map_free(umap2);
2798 if (equal < 0)
2799 return -1;
2800 if (!equal)
2801 isl_die(ctx, isl_error_unknown,
2802 "incorrect subtract domain result", return -1);
2803 }
2804
2805 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2806 upma1 = isl_union_pw_multi_aff_read_from_str(ctx,
2807 subtract_domain_tests[i].minuend);
2808 uset = isl_union_set_read_from_str(ctx,
2809 subtract_domain_tests[i].subtrahend);
2810 upma2 = isl_union_pw_multi_aff_read_from_str(ctx,
2811 subtract_domain_tests[i].difference);
2812 upma1 = isl_union_pw_multi_aff_subtract_domain(upma1, uset);
2813 equal = isl_union_pw_multi_aff_plain_is_equal(upma1, upma2);
2814 isl_union_pw_multi_aff_free(upma1);
2815 isl_union_pw_multi_aff_free(upma2);
2816 if (equal < 0)
2817 return -1;
2818 if (!equal)
2819 isl_die(ctx, isl_error_unknown,
2820 "incorrect subtract domain result", return -1);
2821 }
2822
2823 return 0;
2824 }
2825
2826 int test_factorize(isl_ctx *ctx)
2827 {
2828 const char *str;
2829 isl_basic_set *bset;
2830 isl_factorizer *f;
2831
2832 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2833 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2834 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2835 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2836 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2837 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2838 "3i5 >= -2i0 - i2 + 3i4 }";
2839 bset = isl_basic_set_read_from_str(ctx, str);
2840 f = isl_basic_set_factorizer(bset);
2841 isl_basic_set_free(bset);
2842 isl_factorizer_free(f);
2843 if (!f)
2844 isl_die(ctx, isl_error_unknown,
2845 "failed to construct factorizer", return -1);
2846
2847 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2848 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2849 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2850 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2851 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2852 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2853 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2854 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2855 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2856 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2857 bset = isl_basic_set_read_from_str(ctx, str);
2858 f = isl_basic_set_factorizer(bset);
2859 isl_basic_set_free(bset);
2860 isl_factorizer_free(f);
2861 if (!f)
2862 isl_die(ctx, isl_error_unknown,
2863 "failed to construct factorizer", return -1);
2864
2865 return 0;
2866 }
2867
2868 static isl_stat check_injective(__isl_take isl_map *map, void *user)
2869 {
2870 int *injective = user;
2871
2872 *injective = isl_map_is_injective(map);
2873 isl_map_free(map);
2874
2875 if (*injective < 0 || !*injective)
2876 return isl_stat_error;
2877
2878 return isl_stat_ok;
2879 }
2880
2881 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2882 const char *r, const char *s, int tilable, int parallel)
2883 {
2884 int i;
2885 isl_union_set *D;
2886 isl_union_map *W, *R, *S;
2887 isl_union_map *empty;
2888 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2889 isl_union_map *validity, *proximity, *coincidence;
2890 isl_union_map *schedule;
2891 isl_union_map *test;
2892 isl_union_set *delta;
2893 isl_union_set *domain;
2894 isl_set *delta_set;
2895 isl_set *slice;
2896 isl_set *origin;
2897 isl_schedule_constraints *sc;
2898 isl_schedule *sched;
2899 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2900
2901 D = isl_union_set_read_from_str(ctx, d);
2902 W = isl_union_map_read_from_str(ctx, w);
2903 R = isl_union_map_read_from_str(ctx, r);
2904 S = isl_union_map_read_from_str(ctx, s);
2905
2906 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2907 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2908
2909 empty = isl_union_map_empty(isl_union_map_get_space(S));
2910 isl_union_map_compute_flow(isl_union_map_copy(R),
2911 isl_union_map_copy(W), empty,
2912 isl_union_map_copy(S),
2913 &dep_raw, NULL, NULL, NULL);
2914 isl_union_map_compute_flow(isl_union_map_copy(W),
2915 isl_union_map_copy(W),
2916 isl_union_map_copy(R),
2917 isl_union_map_copy(S),
2918 &dep_waw, &dep_war, NULL, NULL);
2919
2920 dep = isl_union_map_union(dep_waw, dep_war);
2921 dep = isl_union_map_union(dep, dep_raw);
2922 validity = isl_union_map_copy(dep);
2923 coincidence = isl_union_map_copy(dep);
2924 proximity = isl_union_map_copy(dep);
2925
2926 sc = isl_schedule_constraints_on_domain(isl_union_set_copy(D));
2927 sc = isl_schedule_constraints_set_validity(sc, validity);
2928 sc = isl_schedule_constraints_set_coincidence(sc, coincidence);
2929 sc = isl_schedule_constraints_set_proximity(sc, proximity);
2930 sched = isl_schedule_constraints_compute_schedule(sc);
2931 schedule = isl_schedule_get_map(sched);
2932 isl_schedule_free(sched);
2933 isl_union_map_free(W);
2934 isl_union_map_free(R);
2935 isl_union_map_free(S);
2936
2937 is_injection = 1;
2938 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2939
2940 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2941 is_complete = isl_union_set_is_subset(D, domain);
2942 isl_union_set_free(D);
2943 isl_union_set_free(domain);
2944
2945 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2946 test = isl_union_map_apply_range(test, dep);
2947 test = isl_union_map_apply_range(test, schedule);
2948
2949 delta = isl_union_map_deltas(test);
2950 if (isl_union_set_n_set(delta) == 0) {
2951 is_tilable = 1;
2952 is_parallel = 1;
2953 is_nonneg = 1;
2954 isl_union_set_free(delta);
2955 } else {
2956 delta_set = isl_set_from_union_set(delta);
2957
2958 slice = isl_set_universe(isl_set_get_space(delta_set));
2959 for (i = 0; i < tilable; ++i)
2960 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2961 is_tilable = isl_set_is_subset(delta_set, slice);
2962 isl_set_free(slice);
2963
2964 slice = isl_set_universe(isl_set_get_space(delta_set));
2965 for (i = 0; i < parallel; ++i)
2966 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2967 is_parallel = isl_set_is_subset(delta_set, slice);
2968 isl_set_free(slice);
2969
2970 origin = isl_set_universe(isl_set_get_space(delta_set));
2971 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2972 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2973
2974 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2975 delta_set = isl_set_lexmin(delta_set);
2976
2977 is_nonneg = isl_set_is_equal(delta_set, origin);
2978
2979 isl_set_free(origin);
2980 isl_set_free(delta_set);
2981 }
2982
2983 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2984 is_injection < 0 || is_complete < 0)
2985 return -1;
2986 if (!is_complete)
2987 isl_die(ctx, isl_error_unknown,
2988 "generated schedule incomplete", return -1);
2989 if (!is_injection)
2990 isl_die(ctx, isl_error_unknown,
2991 "generated schedule not injective on each statement",
2992 return -1);
2993 if (!is_nonneg)
2994 isl_die(ctx, isl_error_unknown,
2995 "negative dependences in generated schedule",
2996 return -1);
2997 if (!is_tilable)
2998 isl_die(ctx, isl_error_unknown,
2999 "generated schedule not as tilable as expected",
3000 return -1);
3001 if (!is_parallel)
3002 isl_die(ctx, isl_error_unknown,
3003 "generated schedule not as parallel as expected",
3004 return -1);
3005
3006 return 0;
3007 }
3008
3009 /* Compute a schedule for the given instance set, validity constraints,
3010 * proximity constraints and context and return a corresponding union map
3011 * representation.
3012 */
3013 static __isl_give isl_union_map *compute_schedule_with_context(isl_ctx *ctx,
3014 const char *domain, const char *validity, const char *proximity,
3015 const char *context)
3016 {
3017 isl_set *con;
3018 isl_union_set *dom;
3019 isl_union_map *dep;
3020 isl_union_map *prox;
3021 isl_schedule_constraints *sc;
3022 isl_schedule *schedule;
3023 isl_union_map *sched;
3024
3025 con = isl_set_read_from_str(ctx, context);
3026 dom = isl_union_set_read_from_str(ctx, domain);
3027 dep = isl_union_map_read_from_str(ctx, validity);
3028 prox = isl_union_map_read_from_str(ctx, proximity);
3029 sc = isl_schedule_constraints_on_domain(dom);
3030 sc = isl_schedule_constraints_set_context(sc, con);
3031 sc = isl_schedule_constraints_set_validity(sc, dep);
3032 sc = isl_schedule_constraints_set_proximity(sc, prox);
3033 schedule = isl_schedule_constraints_compute_schedule(sc);
3034 sched = isl_schedule_get_map(schedule);
3035 isl_schedule_free(schedule);
3036
3037 return sched;
3038 }
3039
3040 /* Compute a schedule for the given instance set, validity constraints and
3041 * proximity constraints and return a corresponding union map representation.
3042 */
3043 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
3044 const char *domain, const char *validity, const char *proximity)
3045 {
3046 return compute_schedule_with_context(ctx, domain, validity, proximity,
3047 "{ : }");
3048 }
3049
3050 /* Check that a schedule can be constructed on the given domain
3051 * with the given validity and proximity constraints.
3052 */
3053 static int test_has_schedule(isl_ctx *ctx, const char *domain,
3054 const char *validity, const char *proximity)
3055 {
3056 isl_union_map *sched;
3057
3058 sched = compute_schedule(ctx, domain, validity, proximity);
3059 if (!sched)
3060 return -1;
3061
3062 isl_union_map_free(sched);
3063 return 0;
3064 }
3065
3066 int test_special_schedule(isl_ctx *ctx, const char *domain,
3067 const char *validity, const char *proximity, const char *expected_sched)
3068 {
3069 isl_union_map *sched1, *sched2;
3070 int equal;
3071
3072 sched1 = compute_schedule(ctx, domain, validity, proximity);
3073 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
3074
3075 equal = isl_union_map_is_equal(sched1, sched2);
3076 isl_union_map_free(sched1);
3077 isl_union_map_free(sched2);
3078
3079 if (equal < 0)
3080 return -1;
3081 if (!equal)
3082 isl_die(ctx, isl_error_unknown, "unexpected schedule",
3083 return -1);
3084
3085 return 0;
3086 }
3087
3088 /* Check that the schedule map is properly padded, even after being
3089 * reconstructed from the band forest.
3090 */
3091 static int test_padded_schedule(isl_ctx *ctx)
3092 {
3093 const char *str;
3094 isl_union_set *D;
3095 isl_union_map *validity, *proximity;
3096 isl_schedule_constraints *sc;
3097 isl_schedule *sched;
3098 isl_union_map *map1, *map2;
3099 isl_band_list *list;
3100 int equal;
3101
3102 str = "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
3103 D = isl_union_set_read_from_str(ctx, str);
3104 validity = isl_union_map_empty(isl_union_set_get_space(D));
3105 proximity = isl_union_map_copy(validity);
3106 sc = isl_schedule_constraints_on_domain(D);
3107 sc = isl_schedule_constraints_set_validity(sc, validity);
3108 sc = isl_schedule_constraints_set_proximity(sc, proximity);
3109 sched = isl_schedule_constraints_compute_schedule(sc);
3110 map1 = isl_schedule_get_map(sched);
3111 list = isl_schedule_get_band_forest(sched);
3112 isl_band_list_free(list);
3113 map2 = isl_schedule_get_map(sched);
3114 isl_schedule_free(sched);
3115 equal = isl_union_map_is_equal(map1, map2);
3116 isl_union_map_free(map1);
3117 isl_union_map_free(map2);
3118
3119 if (equal < 0)
3120 return -1;
3121 if (!equal)
3122 isl_die(ctx, isl_error_unknown,
3123 "reconstructed schedule map not the same as original",
3124 return -1);
3125
3126 return 0;
3127 }
3128
3129 /* Check that conditional validity constraints are also taken into
3130 * account across bands.
3131 * In particular, try to make sure that live ranges D[1,0]->C[2,1] and
3132 * D[2,0]->C[3,0] are not local in the outer band of the generated schedule
3133 * and then check that the adjacent order constraint C[2,1]->D[2,0]
3134 * is enforced by the rest of the schedule.
3135 */
3136 static int test_special_conditional_schedule_constraints(isl_ctx *ctx)
3137 {
3138 const char *str;
3139 isl_union_set *domain;
3140 isl_union_map *validity, *proximity, *condition;
3141 isl_union_map *sink, *source, *dep;
3142 isl_schedule_constraints *sc;
3143 isl_schedule *schedule;
3144 isl_union_access_info *access;
3145 isl_union_flow *flow;
3146 int empty;
3147
3148 str = "[n] -> { C[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3149 "A[k] : k >= 1 and k <= -1 + n; "
3150 "B[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3151 "D[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k }";
3152 domain = isl_union_set_read_from_str(ctx, str);
3153 sc = isl_schedule_constraints_on_domain(domain);
3154 str = "[n] -> { D[k, i] -> C[1 + k, k - i] : "
3155 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3156 "D[k, i] -> C[1 + k, i] : "
3157 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3158 "D[k, 0] -> C[1 + k, k] : k >= 1 and k <= -2 + n; "
3159 "D[k, 0] -> C[1 + k, 0] : k >= 1 and k <= -2 + n }";
3160 validity = isl_union_map_read_from_str(ctx, str);
3161 sc = isl_schedule_constraints_set_validity(sc, validity);
3162 str = "[n] -> { C[k, i] -> D[k, i] : "
3163 "0 <= i <= -1 + k and k <= -1 + n }";
3164 proximity = isl_union_map_read_from_str(ctx, str);
3165 sc = isl_schedule_constraints_set_proximity(sc, proximity);
3166 str = "[n] -> { [D[k, i] -> a[]] -> [C[1 + k, k - i] -> b[]] : "
3167 "i <= -1 + k and i >= 1 and k <= -2 + n; "
3168 "[B[k, i] -> c[]] -> [B[k, 1 + i] -> c[]] : "
3169 "k <= -1 + n and i >= 0 and i <= -2 + k }";
3170 condition = isl_union_map_read_from_str(ctx, str);
3171 str = "[n] -> { [B[k, i] -> e[]] -> [D[k, i] -> a[]] : "
3172 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3173 "[C[k, i] -> b[]] -> [D[k', -1 + k - i] -> a[]] : "
3174 "i >= 0 and i <= -1 + k and k <= -1 + n and "
3175 "k' <= -1 + n and k' >= k - i and k' >= 1 + k; "
3176 "[C[k, i] -> b[]] -> [D[k, -1 + k - i] -> a[]] : "
3177 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3178 "[B[k, i] -> c[]] -> [A[k'] -> d[]] : "
3179 "k <= -1 + n and i >= 0 and i <= -1 + k and "
3180 "k' >= 1 and k' <= -1 + n and k' >= 1 + k }";
3181 validity = isl_union_map_read_from_str(ctx, str);
3182 sc = isl_schedule_constraints_set_conditional_validity(sc, condition,
3183 validity);
3184 schedule = isl_schedule_constraints_compute_schedule(sc);
3185 str = "{ D[2,0] -> [] }";
3186 sink = isl_union_map_read_from_str(ctx, str);
3187 access = isl_union_access_info_from_sink(sink);
3188 str = "{ C[2,1] -> [] }";
3189 source = isl_union_map_read_from_str(ctx, str);
3190 access = isl_union_access_info_set_must_source(access, source);
3191 access = isl_union_access_info_set_schedule(access, schedule);
3192 flow = isl_union_access_info_compute_flow(access);
3193 dep = isl_union_flow_get_must_dependence(flow);
3194 isl_union_flow_free(flow);
3195 empty = isl_union_map_is_empty(dep);
3196 isl_union_map_free(dep);
3197
3198 if (empty < 0)
3199 return -1;
3200 if (empty)
3201 isl_die(ctx, isl_error_unknown,
3202 "conditional validity not respected", return -1);
3203
3204 return 0;
3205 }
3206
3207 /* Input for testing of schedule construction based on
3208 * conditional constraints.
3209 *
3210 * domain is the iteration domain
3211 * flow are the flow dependences, which determine the validity and
3212 * proximity constraints
3213 * condition are the conditions on the conditional validity constraints
3214 * conditional_validity are the conditional validity constraints
3215 * outer_band_n is the expected number of members in the outer band
3216 */
3217 struct {
3218 const char *domain;
3219 const char *flow;
3220 const char *condition;
3221 const char *conditional_validity;
3222 int outer_band_n;
3223 } live_range_tests[] = {
3224 /* Contrived example that illustrates that we need to keep
3225 * track of tagged condition dependences and
3226 * tagged conditional validity dependences
3227 * in isl_sched_edge separately.
3228 * In particular, the conditional validity constraints on A
3229 * cannot be satisfied,
3230 * but they can be ignored because there are no corresponding
3231 * condition constraints. However, we do have an additional
3232 * conditional validity constraint that maps to the same
3233 * dependence relation
3234 * as the condition constraint on B. If we did not make a distinction
3235 * between tagged condition and tagged conditional validity
3236 * dependences, then we
3237 * could end up treating this shared dependence as an condition
3238 * constraint on A, forcing a localization of the conditions,
3239 * which is impossible.
3240 */
3241 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
3242 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
3243 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
3244 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3245 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3246 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
3247 1
3248 },
3249 /* TACO 2013 Fig. 7 */
3250 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3251 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3252 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3253 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
3254 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
3255 "0 <= i < n and 0 <= j < n - 1 }",
3256 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
3257 "0 <= i < n and 0 <= j < j' < n;"
3258 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
3259 "0 <= i < i' < n and 0 <= j,j' < n;"
3260 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
3261 "0 <= i,j,j' < n and j < j' }",
3262 2
3263 },
3264 /* TACO 2013 Fig. 7, without tags */
3265 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3266 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3267 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3268 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3269 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3270 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
3271 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
3272 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
3273 1
3274 },
3275 /* TACO 2013 Fig. 12 */
3276 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
3277 "S3[i,3] : 0 <= i <= 1 }",
3278 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
3279 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
3280 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
3281 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
3282 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3283 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
3284 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3285 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
3286 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
3287 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
3288 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
3289 1
3290 }
3291 };
3292
3293 /* Test schedule construction based on conditional constraints.
3294 * In particular, check the number of members in the outer band node
3295 * as an indication of whether tiling is possible or not.
3296 */
3297 static int test_conditional_schedule_constraints(isl_ctx *ctx)
3298 {
3299 int i;
3300 isl_union_set *domain;
3301 isl_union_map *condition;
3302 isl_union_map *flow;
3303 isl_union_map *validity;
3304 isl_schedule_constraints *sc;
3305 isl_schedule *schedule;
3306 isl_schedule_node *node;
3307 int n_member;
3308
3309 if (test_special_conditional_schedule_constraints(ctx) < 0)
3310 return -1;
3311
3312 for (i = 0; i < ARRAY_SIZE(live_range_tests); ++i) {
3313 domain = isl_union_set_read_from_str(ctx,
3314 live_range_tests[i].domain);
3315 flow = isl_union_map_read_from_str(ctx,
3316 live_range_tests[i].flow);
3317 condition = isl_union_map_read_from_str(ctx,
3318 live_range_tests[i].condition);
3319 validity = isl_union_map_read_from_str(ctx,
3320 live_range_tests[i].conditional_validity);
3321 sc = isl_schedule_constraints_on_domain(domain);
3322 sc = isl_schedule_constraints_set_validity(sc,
3323 isl_union_map_copy(flow));
3324 sc = isl_schedule_constraints_set_proximity(sc, flow);
3325 sc = isl_schedule_constraints_set_conditional_validity(sc,
3326 condition, validity);
3327 schedule = isl_schedule_constraints_compute_schedule(sc);
3328 node = isl_schedule_get_root(schedule);
3329 while (node &&
3330 isl_schedule_node_get_type(node) != isl_schedule_node_band)
3331 node = isl_schedule_node_first_child(node);
3332 n_member = isl_schedule_node_band_n_member(node);
3333 isl_schedule_node_free(node);
3334 isl_schedule_free(schedule);
3335
3336 if (!schedule)
3337 return -1;
3338 if (n_member != live_range_tests[i].outer_band_n)
3339 isl_die(ctx, isl_error_unknown,
3340 "unexpected number of members in outer band",
3341 return -1);
3342 }
3343 return 0;
3344 }
3345
3346 /* Check that the schedule computed for the given instance set and
3347 * dependence relation strongly satisfies the dependences.
3348 * In particular, check that no instance is scheduled before
3349 * or together with an instance on which it depends.
3350 * Earlier versions of isl would produce a schedule that
3351 * only weakly satisfies the dependences.
3352 */
3353 static int test_strongly_satisfying_schedule(isl_ctx *ctx)
3354 {
3355 const char *domain, *dep;
3356 isl_union_map *D, *schedule;
3357 isl_map *map, *ge;
3358 int empty;
3359
3360 domain = "{ B[i0, i1] : 0 <= i0 <= 1 and 0 <= i1 <= 11; "
3361 "A[i0] : 0 <= i0 <= 1 }";
3362 dep = "{ B[i0, i1] -> B[i0, 1 + i1] : 0 <= i0 <= 1 and 0 <= i1 <= 10; "
3363 "B[0, 11] -> A[1]; A[i0] -> B[i0, 0] : 0 <= i0 <= 1 }";
3364 schedule = compute_schedule(ctx, domain, dep, dep);
3365 D = isl_union_map_read_from_str(ctx, dep);
3366 D = isl_union_map_apply_domain(D, isl_union_map_copy(schedule));
3367 D = isl_union_map_apply_range(D, schedule);
3368 map = isl_map_from_union_map(D);
3369 ge = isl_map_lex_ge(isl_space_domain(isl_map_get_space(map)));
3370 map = isl_map_intersect(map, ge);
3371 empty = isl_map_is_empty(map);
3372 isl_map_free(map);
3373
3374 if (empty < 0)
3375 return -1;
3376 if (!empty)
3377 isl_die(ctx, isl_error_unknown,
3378 "dependences not strongly satisfied", return -1);
3379
3380 return 0;
3381 }
3382
3383 /* Compute a schedule for input where the instance set constraints
3384 * conflict with the context constraints.
3385 * Earlier versions of isl did not properly handle this situation.
3386 */
3387 static int test_conflicting_context_schedule(isl_ctx *ctx)
3388 {
3389 isl_union_map *schedule;
3390 const char *domain, *context;
3391
3392 domain = "[n] -> { A[] : n >= 0 }";
3393 context = "[n] -> { : n < 0 }";
3394 schedule = compute_schedule_with_context(ctx,
3395 domain, "{}", "{}", context);
3396 isl_union_map_free(schedule);
3397
3398 if (!schedule)
3399 return -1;
3400
3401 return 0;
3402 }
3403
3404 /* Check that the dependence carrying step is not confused by
3405 * a bound on the coefficient size.
3406 * In particular, force the scheduler to move to a dependence carrying
3407 * step by demanding outer coincidence and bound the size of
3408 * the coefficients. Earlier versions of isl would take this
3409 * bound into account while carrying dependences, breaking
3410 * fundamental assumptions.
3411 */
3412 static int test_bounded_coefficients_schedule(isl_ctx *ctx)
3413 {
3414 const char *domain, *dep;
3415 isl_union_set *I;
3416 isl_union_map *D;
3417 isl_schedule_constraints *sc;
3418 isl_schedule *schedule;
3419
3420 domain = "{ C[i0, i1] : 2 <= i0 <= 3999 and 0 <= i1 <= -1 + i0 }";
3421 dep = "{ C[i0, i1] -> C[i0, 1 + i1] : i0 <= 3999 and i1 >= 0 and "
3422 "i1 <= -2 + i0; "
3423 "C[i0, -1 + i0] -> C[1 + i0, 0] : i0 <= 3998 and i0 >= 1 }";
3424 I = isl_union_set_read_from_str(ctx, domain);
3425 D = isl_union_map_read_from_str(ctx, dep);
3426 sc = isl_schedule_constraints_on_domain(I);
3427 sc = isl_schedule_constraints_set_validity(sc, isl_union_map_copy(D));
3428 sc = isl_schedule_constraints_set_coincidence(sc, D);
3429 isl_options_set_schedule_outer_coincidence(ctx, 1);
3430 isl_options_set_schedule_max_coefficient(ctx, 20);
3431 schedule = isl_schedule_constraints_compute_schedule(sc);
3432 isl_options_set_schedule_max_coefficient(ctx, -1);
3433 isl_options_set_schedule_outer_coincidence(ctx, 0);
3434 isl_schedule_free(schedule);
3435
3436 if (!schedule)
3437 return -1;
3438
3439 return 0;
3440 }
3441
3442 int test_schedule(isl_ctx *ctx)
3443 {
3444 const char *D, *W, *R, *V, *P, *S;
3445
3446 /* Handle resulting schedule with zero bands. */
3447 if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
3448 return -1;
3449
3450 /* Jacobi */
3451 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
3452 W = "{ S1[t,i] -> a[t,i] }";
3453 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
3454 "S1[t,i] -> a[t-1,i+1] }";
3455 S = "{ S1[t,i] -> [t,i] }";
3456 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
3457 return -1;
3458
3459 /* Fig. 5 of CC2008 */
3460 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
3461 "j <= -1 + N }";
3462 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
3463 "j >= 2 and j <= -1 + N }";
3464 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
3465 "j >= 2 and j <= -1 + N; "
3466 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
3467 "j >= 2 and j <= -1 + N }";
3468 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3469 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
3470 return -1;
3471
3472 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
3473 W = "{ S1[i] -> a[i] }";
3474 R = "{ S2[i] -> a[i+1] }";
3475 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3476 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
3477 return -1;
3478
3479 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
3480 W = "{ S1[i] -> a[i] }";
3481 R = "{ S2[i] -> a[9-i] }";
3482 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3483 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
3484 return -1;
3485
3486 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
3487 W = "{ S1[i] -> a[i] }";
3488 R = "[N] -> { S2[i] -> a[N-1-i] }";
3489 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3490 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
3491 return -1;
3492
3493 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
3494 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
3495 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
3496 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
3497 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3498 return -1;
3499
3500 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3501 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
3502 R = "{ S2[i,j] -> a[i-1,j] }";
3503 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3504 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3505 return -1;
3506
3507 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3508 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
3509 R = "{ S2[i,j] -> a[i,j-1] }";
3510 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3511 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3512 return -1;
3513
3514 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
3515 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
3516 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
3517 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
3518 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
3519 "S_0[] -> [0, 0, 0] }";
3520 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
3521 return -1;
3522 ctx->opt->schedule_parametric = 0;
3523 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3524 return -1;
3525 ctx->opt->schedule_parametric = 1;
3526
3527 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
3528 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
3529 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
3530 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
3531 "S4[i] -> a[i,N] }";
3532 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
3533 "S4[i] -> [4,i,0] }";
3534 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
3535 return -1;
3536
3537 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
3538 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3539 "j <= N }";
3540 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3541 "j <= N; "
3542 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
3543 "j <= N }";
3544 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3545 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3546 return -1;
3547
3548 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
3549 " S_2[t] : t >= 0 and t <= -1 + N; "
3550 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
3551 "i <= -1 + N }";
3552 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
3553 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
3554 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
3555 "i >= 0 and i <= -1 + N }";
3556 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
3557 "i >= 0 and i <= -1 + N; "
3558 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
3559 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
3560 " S_0[t] -> [0, t, 0] }";
3561
3562 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3563 return -1;
3564 ctx->opt->schedule_parametric = 0;
3565 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3566 return -1;
3567 ctx->opt->schedule_parametric = 1;
3568
3569 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
3570 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
3571 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
3572 return -1;
3573
3574 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3575 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3576 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3577 "j >= 0 and j <= -1 + N; "
3578 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3579 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3580 "j >= 0 and j <= -1 + N; "
3581 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3582 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3583 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3584 return -1;
3585
3586 D = "{ S_0[i] : i >= 0 }";
3587 W = "{ S_0[i] -> a[i] : i >= 0 }";
3588 R = "{ S_0[i] -> a[0] : i >= 0 }";
3589 S = "{ S_0[i] -> [0, i, 0] }";
3590 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3591 return -1;
3592
3593 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3594 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3595 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3596 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3597 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3598 return -1;
3599
3600 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3601 "k <= -1 + n and k >= 0 }";
3602 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3603 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3604 "k <= -1 + n and k >= 0; "
3605 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3606 "k <= -1 + n and k >= 0; "
3607 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3608 "k <= -1 + n and k >= 0 }";
3609 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
3610 ctx->opt->schedule_outer_coincidence = 1;
3611 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3612 return -1;
3613 ctx->opt->schedule_outer_coincidence = 0;
3614
3615 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
3616 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3617 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3618 "Stmt_for_body24[i0, i1, 1, 0]:"
3619 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3620 "Stmt_for_body7[i0, i1, i2]:"
3621 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3622 "i2 <= 7 }";
3623
3624 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
3625 "Stmt_for_body24[1, i1, i2, i3]:"
3626 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3627 "i2 >= 1;"
3628 "Stmt_for_body24[0, i1, i2, i3] -> "
3629 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3630 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3631 "i3 >= 0;"
3632 "Stmt_for_body24[0, i1, i2, i3] ->"
3633 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3634 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3635 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3636 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3637 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3638 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3639 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3640 "i1 <= 6 and i1 >= 0;"
3641 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3642 "Stmt_for_body7[i0, i1, i2] -> "
3643 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3644 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3645 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3646 "Stmt_for_body7[i0, i1, i2] -> "
3647 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3648 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3649 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3650 P = V;
3651 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3652 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3653 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3654
3655 if (test_special_schedule(ctx, D, V, P, S) < 0)
3656 return -1;
3657
3658 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3659 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3660 "j >= 1 and j <= 7;"
3661 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3662 "j >= 1 and j <= 8 }";
3663 P = "{ }";
3664 S = "{ S_0[i, j] -> [i + j, j] }";
3665 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3666 if (test_special_schedule(ctx, D, V, P, S) < 0)
3667 return -1;
3668 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3669
3670 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3671 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3672 "j >= 0 and j <= -1 + i }";
3673 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3674 "i <= -1 + N and j >= 0;"
3675 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3676 "i <= -2 + N }";
3677 P = "{ }";
3678 S = "{ S_0[i, j] -> [i, j] }";
3679 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3680 if (test_special_schedule(ctx, D, V, P, S) < 0)
3681 return -1;
3682 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3683
3684 /* Test both algorithms on a case with only proximity dependences. */
3685 D = "{ S[i,j] : 0 <= i <= 10 }";
3686 V = "{ }";
3687 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3688 S = "{ S[i, j] -> [j, i] }";
3689 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3690 if (test_special_schedule(ctx, D, V, P, S) < 0)
3691 return -1;
3692 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3693 if (test_special_schedule(ctx, D, V, P, S) < 0)
3694 return -1;
3695
3696 D = "{ A[a]; B[] }";
3697 V = "{}";
3698 P = "{ A[a] -> B[] }";
3699 if (test_has_schedule(ctx, D, V, P) < 0)
3700 return -1;
3701
3702 if (test_padded_schedule(ctx) < 0)
3703 return -1;
3704
3705 /* Check that check for progress is not confused by rational
3706 * solution.
3707 */
3708 D = "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3709 V = "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3710 "i0 <= -2 + N; "
3711 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3712 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3713 P = "{}";
3714 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3715 if (test_has_schedule(ctx, D, V, P) < 0)
3716 return -1;
3717 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3718
3719 /* Check that we allow schedule rows that are only non-trivial
3720 * on some full-dimensional domains.
3721 */
3722 D = "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
3723 V = "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
3724 "S1[j] -> S2[1] : 0 <= j <= 1 }";
3725 P = "{}";
3726 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3727 if (test_has_schedule(ctx, D, V, P) < 0)
3728 return -1;
3729 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3730
3731 if (test_conditional_schedule_constraints(ctx) < 0)
3732 return -1;
3733
3734 if (test_strongly_satisfying_schedule(ctx) < 0)
3735 return -1;
3736
3737 if (test_conflicting_context_schedule(ctx) < 0)
3738 return -1;
3739
3740 if (test_bounded_coefficients_schedule(ctx) < 0)
3741 return -1;
3742
3743 return 0;
3744 }
3745
3746 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
3747 {
3748 isl_union_map *umap;
3749 int test;
3750
3751 umap = isl_union_map_read_from_str(ctx, str);
3752 test = isl_union_map_plain_is_injective(umap);
3753 isl_union_map_free(umap);
3754 if (test < 0)
3755 return -1;
3756 if (test == injective)
3757 return 0;
3758 if (injective)
3759 isl_die(ctx, isl_error_unknown,
3760 "map not detected as injective", return -1);
3761 else
3762 isl_die(ctx, isl_error_unknown,
3763 "map detected as injective", return -1);
3764 }
3765
3766 int test_injective(isl_ctx *ctx)
3767 {
3768 const char *str;
3769
3770 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3771 return -1;
3772 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
3773 return -1;
3774 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
3775 return -1;
3776 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
3777 return -1;
3778 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3779 return -1;
3780 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3781 return -1;
3782 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3783 return -1;
3784 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3785 return -1;
3786
3787 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3788 if (test_plain_injective(ctx, str, 1))
3789 return -1;
3790 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3791 if (test_plain_injective(ctx, str, 0))
3792 return -1;
3793
3794 return 0;
3795 }
3796
3797 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
3798 {
3799 isl_aff *aff2;
3800 int equal;
3801
3802 if (!aff)
3803 return -1;
3804
3805 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
3806 equal = isl_aff_plain_is_equal(aff, aff2);
3807 isl_aff_free(aff2);
3808
3809 return equal;
3810 }
3811
3812 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
3813 {
3814 int equal;
3815
3816 equal = aff_plain_is_equal(aff, str);
3817 if (equal < 0)
3818 return -1;
3819 if (!equal)
3820 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
3821 "result not as expected", return -1);
3822 return 0;
3823 }
3824
3825 struct {
3826 __isl_give isl_aff *(*fn)(__isl_take isl_aff *aff1,
3827 __isl_take isl_aff *aff2);
3828 } aff_bin_op[] = {
3829 ['+'] = { &isl_aff_add },
3830 ['-'] = { &isl_aff_sub },
3831 ['*'] = { &isl_aff_mul },
3832 ['/'] = { &isl_aff_div },
3833 };
3834
3835 struct {
3836 const char *arg1;
3837 unsigned char op;
3838 const char *arg2;
3839 const char *res;
3840 } aff_bin_tests[] = {
3841 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3842 "{ [i] -> [2i] }" },
3843 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3844 "{ [i] -> [0] }" },
3845 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3846 "{ [i] -> [2i] }" },
3847 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3848 "{ [i] -> [2i] }" },
3849 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
3850 "{ [i] -> [i/2] }" },
3851 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
3852 "{ [i] -> [i] }" },
3853 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3854 "{ [i] -> [NaN] }" },
3855 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3856 "{ [i] -> [NaN] }" },
3857 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3858 "{ [i] -> [NaN] }" },
3859 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3860 "{ [i] -> [NaN] }" },
3861 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
3862 "{ [i] -> [NaN] }" },
3863 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
3864 "{ [i] -> [NaN] }" },
3865 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3866 "{ [i] -> [NaN] }" },
3867 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3868 "{ [i] -> [NaN] }" },
3869 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3870 "{ [i] -> [NaN] }" },
3871 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3872 "{ [i] -> [NaN] }" },
3873 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
3874 "{ [i] -> [NaN] }" },
3875 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
3876 "{ [i] -> [NaN] }" },
3877 };
3878
3879 /* Perform some basic tests of binary operations on isl_aff objects.
3880 */
3881 static int test_bin_aff(isl_ctx *ctx)
3882 {
3883 int i;
3884 isl_aff *aff1, *aff2, *res;
3885 __isl_give isl_aff *(*fn)(__isl_take isl_aff *aff1,
3886 __isl_take isl_aff *aff2);
3887 int ok;
3888
3889 for (i = 0; i < ARRAY_SIZE(aff_bin_tests); ++i) {
3890 aff1 = isl_aff_read_from_str(ctx, aff_bin_tests[i].arg1);
3891 aff2 = isl_aff_read_from_str(ctx, aff_bin_tests[i].arg2);
3892 res = isl_aff_read_from_str(ctx, aff_bin_tests[i].res);
3893 fn = aff_bin_op[aff_bin_tests[i].op].fn;
3894 aff1 = fn(aff1, aff2);
3895 if (isl_aff_is_nan(res))
3896 ok = isl_aff_is_nan(aff1);
3897 else
3898 ok = isl_aff_plain_is_equal(aff1, res);
3899 isl_aff_free(aff1);
3900 isl_aff_free(res);
3901 if (ok < 0)
3902 return -1;
3903 if (!ok)
3904 isl_die(ctx, isl_error_unknown,
3905 "unexpected result", return -1);
3906 }
3907
3908 return 0;
3909 }
3910
3911 struct {
3912 __isl_give isl_union_pw_multi_aff *(*fn)(
3913 __isl_take isl_union_pw_multi_aff *upma1,
3914 __isl_take isl_union_pw_multi_aff *upma2);
3915 const char *arg1;
3916 const char *arg2;
3917 const char *res;
3918 } upma_bin_tests[] = {
3919 { &isl_union_pw_multi_aff_add, "{ A[] -> [0]; B[0] -> [1] }",
3920 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
3921 { &isl_union_pw_multi_aff_union_add, "{ A[] -> [0]; B[0] -> [1] }",
3922 "{ B[x] -> [2] : x >= 0 }",
3923 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
3924 { &isl_union_pw_multi_aff_pullback_union_pw_multi_aff,
3925 "{ A[] -> B[0]; C[x] -> B[1] : x < 10; C[y] -> B[2] : y >= 10 }",
3926 "{ D[i] -> A[] : i < 0; D[i] -> C[i + 5] : i >= 0 }",
3927 "{ D[i] -> B[0] : i < 0; D[i] -> B[1] : 0 <= i < 5; "
3928 "D[i] -> B[2] : i >= 5 }" },
3929 { &isl_union_pw_multi_aff_union_add, "{ B[x] -> A[1] : x <= 0 }",
3930 "{ B[x] -> C[2] : x > 0 }",
3931 "{ B[x] -> A[1] : x <= 0; B[x] -> C[2] : x > 0 }" },
3932 { &isl_union_pw_multi_aff_union_add, "{ B[x] -> A[1] : x <= 0 }",
3933 "{ B[x] -> A[2] : x >= 0 }",
3934 "{ B[x] -> A[1] : x < 0; B[x] -> A[2] : x > 0; B[0] -> A[3] }" },
3935 };
3936
3937 /* Perform some basic tests of binary operations on
3938 * isl_union_pw_multi_aff objects.
3939 */
3940 static int test_bin_upma(isl_ctx *ctx)
3941 {
3942 int i;
3943 isl_union_pw_multi_aff *upma1, *upma2, *res;
3944 int ok;
3945
3946 for (i = 0; i < ARRAY_SIZE(upma_bin_tests); ++i) {
3947 upma1 = isl_union_pw_multi_aff_read_from_str(ctx,
3948 upma_bin_tests[i].arg1);
3949 upma2 = isl_union_pw_multi_aff_read_from_str(ctx,
3950 upma_bin_tests[i].arg2);
3951 res = isl_union_pw_multi_aff_read_from_str(ctx,
3952 upma_bin_tests[i].res);
3953 upma1 = upma_bin_tests[i].fn(upma1, upma2);
3954 ok = isl_union_pw_multi_aff_plain_is_equal(upma1, res);
3955 isl_union_pw_multi_aff_free(upma1);
3956 isl_union_pw_multi_aff_free(res);
3957 if (ok < 0)
3958 return -1;
3959 if (!ok)
3960 isl_die(ctx, isl_error_unknown,
3961 "unexpected result", return -1);
3962 }
3963
3964 return 0;
3965 }
3966
3967 struct {
3968 __isl_give isl_union_pw_multi_aff *(*fn)(
3969 __isl_take isl_union_pw_multi_aff *upma1,
3970 __isl_take isl_union_pw_multi_aff *upma2);
3971 const char *arg1;
3972 const char *arg2;
3973 } upma_bin_fail_tests[] = {
3974 { &isl_union_pw_multi_aff_union_add, "{ B[x] -> A[1] : x <= 0 }",
3975 "{ B[x] -> C[2] : x >= 0 }" },
3976 };
3977
3978 /* Perform some basic tests of binary operations on
3979 * isl_union_pw_multi_aff objects that are expected to fail.
3980 */
3981 static int test_bin_upma_fail(isl_ctx *ctx)
3982 {
3983 int i, n;
3984 isl_union_pw_multi_aff *upma1, *upma2;
3985 int on_error;
3986
3987 on_error = isl_options_get_on_error(ctx);
3988 isl_options_set_on_error(ctx, ISL_ON_ERROR_CONTINUE);
3989 n = ARRAY_SIZE(upma_bin_fail_tests);
3990 for (i = 0; i < n; ++i) {
3991 upma1 = isl_union_pw_multi_aff_read_from_str(ctx,
3992 upma_bin_fail_tests[i].arg1);
3993 upma2 = isl_union_pw_multi_aff_read_from_str(ctx,
3994 upma_bin_fail_tests[i].arg2);
3995 upma1 = upma_bin_fail_tests[i].fn(upma1, upma2);
3996 isl_union_pw_multi_aff_free(upma1);
3997 if (upma1)
3998 break;
3999 }
4000 isl_options_set_on_error(ctx, on_error);
4001 if (i < n)
4002 isl_die(ctx, isl_error_unknown,
4003 "operation not expected to succeed", return -1);
4004
4005 return 0;
4006 }
4007
4008 int test_aff(isl_ctx *ctx)
4009 {
4010 const char *str;
4011 isl_set *set;
4012 isl_space *space;
4013 isl_local_space *ls;
4014 isl_aff *aff;
4015 int zero, equal;
4016
4017 if (test_bin_aff(ctx) < 0)
4018 return -1;
4019 if (test_bin_upma(ctx) < 0)
4020 return -1;
4021 if (test_bin_upma_fail(ctx) < 0)
4022 return -1;
4023
4024 space = isl_space_set_alloc(ctx, 0, 1);
4025 ls = isl_local_space_from_space(space);
4026 aff = isl_aff_zero_on_domain(ls);
4027
4028 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
4029 aff = isl_aff_scale_down_ui(aff, 3);
4030 aff = isl_aff_floor(aff);
4031 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
4032 aff = isl_aff_scale_down_ui(aff, 2);
4033 aff = isl_aff_floor(aff);
4034 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
4035
4036 str = "{ [10] }";
4037 set = isl_set_read_from_str(ctx, str);
4038 aff = isl_aff_gist(aff, set);
4039
4040 aff = isl_aff_add_constant_si(aff, -16);
4041 zero = isl_aff_plain_is_zero(aff);
4042 isl_aff_free(aff);
4043
4044 if (zero < 0)
4045 return -1;
4046 if (!zero)
4047 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4048
4049 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
4050 aff = isl_aff_scale_down_ui(aff, 64);
4051 aff = isl_aff_floor(aff);
4052 equal = aff_check_plain_equal(aff, "{ [-1] }");
4053 isl_aff_free(aff);
4054 if (equal < 0)
4055 return -1;
4056
4057 return 0;
4058 }
4059
4060 int test_dim_max(isl_ctx *ctx)
4061 {
4062 int equal;
4063 const char *str;
4064 isl_set *set1, *set2;
4065 isl_set *set;
4066 isl_map *map;
4067 isl_pw_aff *pwaff;
4068
4069 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
4070 set = isl_set_read_from_str(ctx, str);
4071 pwaff = isl_set_dim_max(set, 0);
4072 set1 = isl_set_from_pw_aff(pwaff);
4073 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
4074 set2 = isl_set_read_from_str(ctx, str);
4075 equal = isl_set_is_equal(set1, set2);
4076 isl_set_free(set1);
4077 isl_set_free(set2);
4078 if (equal < 0)
4079 return -1;
4080 if (!equal)
4081 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4082
4083 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
4084 set = isl_set_read_from_str(ctx, str);
4085 pwaff = isl_set_dim_max(set, 0);
4086 set1 = isl_set_from_pw_aff(pwaff);
4087 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4088 set2 = isl_set_read_from_str(ctx, str);
4089 equal = isl_set_is_equal(set1, set2);
4090 isl_set_free(set1);
4091 isl_set_free(set2);
4092 if (equal < 0)
4093 return -1;
4094 if (!equal)
4095 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4096
4097 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
4098 set = isl_set_read_from_str(ctx, str);
4099 pwaff = isl_set_dim_max(set, 0);
4100 set1 = isl_set_from_pw_aff(pwaff);
4101 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4102 set2 = isl_set_read_from_str(ctx, str);
4103 equal = isl_set_is_equal(set1, set2);
4104 isl_set_free(set1);
4105 isl_set_free(set2);
4106 if (equal < 0)
4107 return -1;
4108 if (!equal)
4109 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4110
4111 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
4112 "0 <= i < N and 0 <= j < M }";
4113 map = isl_map_read_from_str(ctx, str);
4114 set = isl_map_range(map);
4115
4116 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
4117 set1 = isl_set_from_pw_aff(pwaff);
4118 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
4119 set2 = isl_set_read_from_str(ctx, str);
4120 equal = isl_set_is_equal(set1, set2);
4121 isl_set_free(set1);
4122 isl_set_free(set2);
4123
4124 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
4125 set1 = isl_set_from_pw_aff(pwaff);
4126 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
4127 set2 = isl_set_read_from_str(ctx, str);
4128 if (equal >= 0 && equal)
4129 equal = isl_set_is_equal(set1, set2);
4130 isl_set_free(set1);
4131 isl_set_free(set2);
4132
4133 isl_set_free(set);
4134
4135 if (equal < 0)
4136 return -1;
4137 if (!equal)
4138 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4139
4140 /* Check that solutions are properly merged. */
4141 str = "[n] -> { [a, b, c] : c >= -4a - 2b and "
4142 "c <= -1 + n - 4a - 2b and c >= -2b and "
4143 "4a >= -4 + n and c >= 0 }";
4144 set = isl_set_read_from_str(ctx, str);
4145 pwaff = isl_set_dim_min(set, 2);
4146 set1 = isl_set_from_pw_aff(pwaff);
4147 str = "[n] -> { [(0)] : n >= 1 }";
4148 set2 = isl_set_read_from_str(ctx, str);
4149 equal = isl_set_is_equal(set1, set2);
4150 isl_set_free(set1);
4151 isl_set_free(set2);
4152
4153 if (equal < 0)
4154 return -1;
4155 if (!equal)
4156 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4157
4158 /* Check that empty solution lie in the right space. */
4159 str = "[n] -> { [t,a] : 1 = 0 }";
4160 set = isl_set_read_from_str(ctx, str);
4161 pwaff = isl_set_dim_max(set, 0);
4162 set1 = isl_set_from_pw_aff(pwaff);
4163 str = "[n] -> { [t] : 1 = 0 }";
4164 set2 = isl_set_read_from_str(ctx, str);
4165 equal = isl_set_is_equal(set1, set2);
4166 isl_set_free(set1);
4167 isl_set_free(set2);
4168
4169 if (equal < 0)
4170 return -1;
4171 if (!equal)
4172 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4173
4174 return 0;
4175 }
4176
4177 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
4178 */
4179 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff *pma,
4180 const char *str)
4181 {
4182 isl_ctx *ctx;
4183 isl_pw_multi_aff *pma2;
4184 int equal;
4185
4186 if (!pma)
4187 return -1;
4188
4189 ctx = isl_pw_multi_aff_get_ctx(pma);
4190 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
4191 equal = isl_pw_multi_aff_plain_is_equal(pma, pma2);
4192 isl_pw_multi_aff_free(pma2);
4193
4194 return equal;
4195 }
4196
4197 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
4198 * represented by "str".
4199 */
4200 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff *pma,
4201 const char *str)
4202 {
4203 int equal;
4204
4205 equal = pw_multi_aff_plain_is_equal(pma, str);
4206 if (equal < 0)
4207 return -1;
4208 if (!equal)
4209 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_unknown,
4210 "result not as expected", return -1);
4211 return 0;
4212 }
4213
4214 /* Basic test for isl_pw_multi_aff_product.
4215 *
4216 * Check that multiple pieces are properly handled.
4217 */
4218 static int test_product_pma(isl_ctx *ctx)
4219 {
4220 int equal;
4221 const char *str;
4222 isl_pw_multi_aff *pma1, *pma2;
4223
4224 str = "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
4225 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
4226 str = "{ C[] -> D[] }";
4227 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
4228 pma1 = isl_pw_multi_aff_product(pma1, pma2);
4229 str = "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
4230 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
4231 equal = pw_multi_aff_check_plain_equal(pma1, str);
4232 isl_pw_multi_aff_free(pma1);
4233 if (equal < 0)
4234 return -1;
4235
4236 return 0;
4237 }
4238
4239 int test_product(isl_ctx *ctx)
4240 {
4241 const char *str;
4242 isl_set *set;
4243 isl_union_set *uset1, *uset2;
4244 int ok;
4245
4246 str = "{ A[i] }";
4247 set = isl_set_read_from_str(ctx, str);
4248 set = isl_set_product(set, isl_set_copy(set));
4249 ok = isl_set_is_wrapping(set);
4250 isl_set_free(set);
4251 if (ok < 0)
4252 return -1;
4253 if (!ok)
4254 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4255
4256 str = "{ [] }";
4257 uset1 = isl_union_set_read_from_str(ctx, str);
4258 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
4259 str = "{ [[] -> []] }";
4260 uset2 = isl_union_set_read_from_str(ctx, str);
4261 ok = isl_union_set_is_equal(uset1, uset2);
4262 isl_union_set_free(uset1);
4263 isl_union_set_free(uset2);
4264 if (ok < 0)
4265 return -1;
4266 if (!ok)
4267 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4268
4269 if (test_product_pma(ctx) < 0)
4270 return -1;
4271
4272 return 0;
4273 }
4274
4275 /* Check that two sets are not considered disjoint just because
4276 * they have a different set of (named) parameters.
4277 */
4278 static int test_disjoint(isl_ctx *ctx)
4279 {
4280 const char *str;
4281 isl_set *set, *set2;
4282 int disjoint;
4283
4284 str = "[n] -> { [[]->[]] }";
4285 set = isl_set_read_from_str(ctx, str);
4286 str = "{ [[]->[]] }";
4287 set2 = isl_set_read_from_str(ctx, str);
4288 disjoint = isl_set_is_disjoint(set, set2);
4289 isl_set_free(set);
4290 isl_set_free(set2);
4291 if (disjoint < 0)
4292 return -1;
4293 if (disjoint)
4294 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4295
4296 return 0;
4297 }
4298
4299 int test_equal(isl_ctx *ctx)
4300 {
4301 const char *str;
4302 isl_set *set, *set2;
4303 int equal;
4304
4305 str = "{ S_6[i] }";
4306 set = isl_set_read_from_str(ctx, str);
4307 str = "{ S_7[i] }";
4308 set2 = isl_set_read_from_str(ctx, str);
4309 equal = isl_set_is_equal(set, set2);
4310 isl_set_free(set);
4311 isl_set_free(set2);
4312 if (equal < 0)
4313 return -1;
4314 if (equal)
4315 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4316
4317 return 0;
4318 }
4319
4320 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
4321 enum isl_dim_type type, unsigned pos, int fixed)
4322 {
4323 int test;
4324
4325 test = isl_map_plain_is_fixed(map, type, pos, NULL);
4326 isl_map_free(map);
4327 if (test < 0)
4328 return -1;
4329 if (test == fixed)
4330 return 0;
4331 if (fixed)
4332 isl_die(ctx, isl_error_unknown,
4333 "map not detected as fixed", return -1);
4334 else
4335 isl_die(ctx, isl_error_unknown,
4336 "map detected as fixed", return -1);
4337 }
4338
4339 int test_fixed(isl_ctx *ctx)
4340 {
4341 const char *str;
4342 isl_map *map;
4343
4344 str = "{ [i] -> [i] }";
4345 map = isl_map_read_from_str(ctx, str);
4346 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
4347 return -1;
4348 str = "{ [i] -> [1] }";
4349 map = isl_map_read_from_str(ctx, str);
4350 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
4351 return -1;
4352 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
4353 map = isl_map_read_from_str(ctx, str);
4354 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
4355 return -1;
4356 map = isl_map_read_from_str(ctx, str);
4357 map = isl_map_neg(map);
4358 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
4359 return -1;
4360
4361 return 0;
4362 }
4363
4364 struct isl_vertices_test_data {
4365 const char *set;
4366 int n;
4367 const char *vertex[2];
4368 } vertices_tests[] = {
4369 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
4370 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
4371 { "{ A[t, i] : t = 14 and i = 1 }",
4372 1, { "{ A[14, 1] }" } },
4373 };
4374
4375 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
4376 */
4377 static isl_stat find_vertex(__isl_take isl_vertex *vertex, void *user)
4378 {
4379 struct isl_vertices_test_data *data = user;
4380 isl_ctx *ctx;
4381 isl_multi_aff *ma;
4382 isl_basic_set *bset;
4383 isl_pw_multi_aff *pma;
4384 int i;
4385 isl_bool equal;
4386
4387 ctx = isl_vertex_get_ctx(vertex);
4388 bset = isl_vertex_get_domain(vertex);
4389 ma = isl_vertex_get_expr(vertex);
4390 pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset), ma);
4391
4392 for (i = 0; i < data->n; ++i) {
4393 isl_pw_multi_aff *pma_i;
4394
4395 pma_i = isl_pw_multi_aff_read_from_str(ctx, data->vertex[i]);
4396 equal = isl_pw_multi_aff_plain_is_equal(pma, pma_i);
4397 isl_pw_multi_aff_free(pma_i);
4398
4399 if (equal < 0 || equal)
4400 break;
4401 }
4402
4403 isl_pw_multi_aff_free(pma);
4404 isl_vertex_free(vertex);
4405
4406 if (equal < 0)
4407 return isl_stat_error;
4408
4409 return equal ? isl_stat_ok : isl_stat_error;
4410 }
4411
4412 int test_vertices(isl_ctx *ctx)
4413 {
4414 int i;
4415
4416 for (i = 0; i < ARRAY_SIZE(vertices_tests); ++i) {
4417 isl_basic_set *bset;
4418 isl_vertices *vertices;
4419 int ok = 1;
4420 int n;
4421
4422 bset = isl_basic_set_read_from_str(ctx, vertices_tests[i].set);
4423 vertices = isl_basic_set_compute_vertices(bset);
4424 n = isl_vertices_get_n_vertices(vertices);
4425 if (vertices_tests[i].n != n)
4426 ok = 0;
4427 if (isl_vertices_foreach_vertex(vertices, &find_vertex,
4428 &vertices_tests[i]) < 0)
4429 ok = 0;
4430 isl_vertices_free(vertices);
4431 isl_basic_set_free(bset);
4432
4433 if (!vertices)
4434 return -1;
4435 if (!ok)
4436 isl_die(ctx, isl_error_unknown, "unexpected vertices",
4437 return -1);
4438 }
4439
4440 return 0;
4441 }
4442
4443 int test_union_pw(isl_ctx *ctx)
4444 {
4445 int equal;
4446 const char *str;
4447 isl_union_set *uset;
4448 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
4449
4450 str = "{ [x] -> x^2 }";
4451 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
4452 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
4453 uset = isl_union_pw_qpolynomial_domain(upwqp1);
4454 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
4455 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
4456 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
4457 isl_union_pw_qpolynomial_free(upwqp1);
4458 isl_union_pw_qpolynomial_free(upwqp2);
4459 if (equal < 0)
4460 return -1;
4461 if (!equal)
4462 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4463
4464 return 0;
4465 }
4466
4467 /* Test that isl_union_pw_qpolynomial_eval picks up the function
4468 * defined over the correct domain space.
4469 */
4470 static int test_eval(isl_ctx *ctx)
4471 {
4472 const char *str;
4473 isl_point *pnt;
4474 isl_set *set;
4475 isl_union_pw_qpolynomial *upwqp;
4476 isl_val *v;
4477 int cmp;
4478
4479 str = "{ A[x] -> x^2; B[x] -> -x^2 }";
4480 upwqp = isl_union_pw_qpolynomial_read_from_str(ctx, str);
4481 str = "{ A[6] }";
4482 set = isl_set_read_from_str(ctx, str);
4483 pnt = isl_set_sample_point(set);
4484 v = isl_union_pw_qpolynomial_eval(upwqp, pnt);
4485 cmp = isl_val_cmp_si(v, 36);
4486 isl_val_free(v);
4487
4488 if (!v)
4489 return -1;
4490 if (cmp != 0)
4491 isl_die(ctx, isl_error_unknown, "unexpected value", return -1);
4492
4493 return 0;
4494 }
4495
4496 int test_output(isl_ctx *ctx)
4497 {
4498 char *s;
4499 const char *str;
4500 isl_pw_aff *pa;
4501 isl_printer *p;
4502 int equal;
4503
4504 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
4505 pa = isl_pw_aff_read_from_str(ctx, str);
4506
4507 p = isl_printer_to_str(ctx);
4508 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
4509 p = isl_printer_print_pw_aff(p, pa);
4510 s = isl_printer_get_str(p);
4511 isl_printer_free(p);
4512 isl_pw_aff_free(pa);
4513 if (!s)
4514 equal = -1;
4515 else
4516 equal = !strcmp(s, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
4517 free(s);
4518 if (equal < 0)
4519 return -1;
4520 if (!equal)
4521 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4522
4523 return 0;
4524 }
4525
4526 int test_sample(isl_ctx *ctx)
4527 {
4528 const char *str;
4529 isl_basic_set *bset1, *bset2;
4530 int empty, subset;
4531
4532 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
4533 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
4534 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
4535 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
4536 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
4537 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
4538 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
4539 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
4540 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
4541 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
4542 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
4543 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
4544 "d - 1073741821e and "
4545 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
4546 "3j >= 1 - a + b + 2e and "
4547 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
4548 "3i <= 4 - a + 4b - e and "
4549 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
4550 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
4551 "c <= -1 + a and 3i >= -2 - a + 3e and "
4552 "1073741822e <= 1073741823 - a + 1073741822b + c and "
4553 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
4554 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
4555 "1073741823e >= 1 + 1073741823b - d and "
4556 "3i >= 1073741823b + c - 1073741823e - f and "
4557 "3i >= 1 + 2b + e + 3g }";
4558 bset1 = isl_basic_set_read_from_str(ctx, str);
4559 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
4560 empty = isl_basic_set_is_empty(bset2);
4561 subset = isl_basic_set_is_subset(bset2, bset1);
4562 isl_basic_set_free(bset1);
4563 isl_basic_set_free(bset2);
4564 if (empty < 0 || subset < 0)
4565 return -1;
4566 if (empty)
4567 isl_die(ctx, isl_error_unknown, "point not found", return -1);
4568 if (!subset)
4569 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
4570
4571 return 0;
4572 }
4573
4574 int test_fixed_power(isl_ctx *ctx)
4575 {
4576 const char *str;
4577 isl_map *map;
4578 isl_int exp;
4579 int equal;
4580
4581 isl_int_init(exp);
4582 str = "{ [i] -> [i + 1] }";
4583 map = isl_map_read_from_str(ctx, str);
4584 isl_int_set_si(exp, 23);
4585 map = isl_map_fixed_power(map, exp);
4586 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
4587 isl_int_clear(exp);
4588 isl_map_free(map);
4589 if (equal < 0)
4590 return -1;
4591
4592 return 0;
4593 }
4594
4595 int test_slice(isl_ctx *ctx)
4596 {
4597 const char *str;
4598 isl_map *map;
4599 int equal;
4600
4601 str = "{ [i] -> [j] }";
4602 map = isl_map_read_from_str(ctx, str);
4603 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
4604 equal = map_check_equal(map, "{ [i] -> [i] }");
4605 isl_map_free(map);
4606 if (equal < 0)
4607 return -1;
4608
4609 str = "{ [i] -> [j] }";
4610 map = isl_map_read_from_str(ctx, str);
4611 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
4612 equal = map_check_equal(map, "{ [i] -> [j] }");
4613 isl_map_free(map);
4614 if (equal < 0)
4615 return -1;
4616
4617 str = "{ [i] -> [j] }";
4618 map = isl_map_read_from_str(ctx, str);
4619 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
4620 equal = map_check_equal(map, "{ [i] -> [-i] }");
4621 isl_map_free(map);
4622 if (equal < 0)
4623 return -1;
4624
4625 str = "{ [i] -> [j] }";
4626 map = isl_map_read_from_str(ctx, str);
4627 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
4628 equal = map_check_equal(map, "{ [0] -> [j] }");
4629 isl_map_free(map);
4630 if (equal < 0)
4631 return -1;
4632
4633 str = "{ [i] -> [j] }";
4634 map = isl_map_read_from_str(ctx, str);
4635 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
4636 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
4637 isl_map_free(map);
4638 if (equal < 0)
4639 return -1;
4640
4641 str = "{ [i] -> [j] }";
4642 map = isl_map_read_from_str(ctx, str);
4643 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
4644 equal = map_check_equal(map, "{ [i] -> [j] : false }");
4645 isl_map_free(map);
4646 if (equal < 0)
4647 return -1;
4648
4649 return 0;
4650 }
4651
4652 int test_eliminate(isl_ctx *ctx)
4653 {
4654 const char *str;
4655 isl_map *map;
4656 int equal;
4657
4658 str = "{ [i] -> [j] : i = 2j }";
4659 map = isl_map_read_from_str(ctx, str);
4660 map = isl_map_eliminate(map, isl_dim_out, 0, 1);
4661 equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
4662 isl_map_free(map);
4663 if (equal < 0)
4664 return -1;
4665
4666 return 0;
4667 }
4668
4669 /* Check that isl_set_dim_residue_class detects that the values of j
4670 * in the set below are all odd and that it does not detect any spurious
4671 * strides.
4672 */
4673 static int test_residue_class(isl_ctx *ctx)
4674 {
4675 const char *str;
4676 isl_set *set;
4677 isl_int m, r;
4678 int res;
4679
4680 str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
4681 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
4682 set = isl_set_read_from_str(ctx, str);
4683 isl_int_init(m);
4684 isl_int_init(r);
4685 res = isl_set_dim_residue_class(set, 1, &m, &r);
4686 if (res >= 0 &&
4687 (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
4688 isl_die(ctx, isl_error_unknown, "incorrect residue class",
4689 res = -1);
4690 isl_int_clear(r);
4691 isl_int_clear(m);
4692 isl_set_free(set);
4693
4694 return res;
4695 }
4696
4697 int test_align_parameters(isl_ctx *ctx)
4698 {
4699 const char *str;
4700 isl_space *space;
4701 isl_multi_aff *ma1, *ma2;
4702 int equal;
4703
4704 str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
4705 ma1 = isl_multi_aff_read_from_str(ctx, str);
4706
4707 space = isl_space_params_alloc(ctx, 1);
4708 space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
4709 ma1 = isl_multi_aff_align_params(ma1, space);
4710
4711 str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
4712 ma2 = isl_multi_aff_read_from_str(ctx, str);
4713
4714 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
4715
4716 isl_multi_aff_free(ma1);
4717 isl_multi_aff_free(ma2);
4718
4719 if (equal < 0)
4720 return -1;
4721 if (!equal)
4722 isl_die(ctx, isl_error_unknown,
4723 "result not as expected", return -1);
4724
4725 return 0;
4726 }
4727
4728 static int test_list(isl_ctx *ctx)
4729 {
4730 isl_id *a, *b, *c, *d, *id;
4731 isl_id_list *list;
4732 int ok;
4733
4734 a = isl_id_alloc(ctx, "a", NULL);
4735 b = isl_id_alloc(ctx, "b", NULL);
4736 c = isl_id_alloc(ctx, "c", NULL);
4737 d = isl_id_alloc(ctx, "d", NULL);
4738
4739 list = isl_id_list_alloc(ctx, 4);
4740 list = isl_id_list_add(list, a);
4741 list = isl_id_list_add(list, b);
4742 list = isl_id_list_add(list, c);
4743 list = isl_id_list_add(list, d);
4744 list = isl_id_list_drop(list, 1, 1);
4745
4746 if (isl_id_list_n_id(list) != 3) {
4747 isl_id_list_free(list);
4748 isl_die(ctx, isl_error_unknown,
4749 "unexpected number of elements in list", return -1);
4750 }
4751
4752 id = isl_id_list_get_id(list, 0);
4753 ok = id == a;
4754 isl_id_free(id);
4755 id = isl_id_list_get_id(list, 1);
4756 ok = ok && id == c;
4757 isl_id_free(id);
4758 id = isl_id_list_get_id(list, 2);
4759 ok = ok && id == d;
4760 isl_id_free(id);
4761
4762 isl_id_list_free(list);
4763
4764 if (!ok)
4765 isl_die(ctx, isl_error_unknown,
4766 "unexpected elements in list", return -1);
4767
4768 return 0;
4769 }
4770
4771 const char *set_conversion_tests[] = {
4772 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4773 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4774 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4775 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4776 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
4777 };
4778
4779 /* Check that converting from isl_set to isl_pw_multi_aff and back
4780 * to isl_set produces the original isl_set.
4781 */
4782 static int test_set_conversion(isl_ctx *ctx)
4783 {
4784 int i;
4785 const char *str;
4786 isl_set *set1, *set2;
4787 isl_pw_multi_aff *pma;
4788 int equal;
4789
4790 for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
4791 str = set_conversion_tests[i];
4792 set1 = isl_set_read_from_str(ctx, str);
4793 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
4794 set2 = isl_set_from_pw_multi_aff(pma);
4795 equal = isl_set_is_equal(set1, set2);
4796 isl_set_free(set1);
4797 isl_set_free(set2);
4798
4799 if (equal < 0)
4800 return -1;
4801 if (!equal)
4802 isl_die(ctx, isl_error_unknown, "bad conversion",
4803 return -1);
4804 }
4805
4806 return 0;
4807 }
4808
4809 /* Check that converting from isl_map to isl_pw_multi_aff and back
4810 * to isl_map produces the original isl_map.
4811 */
4812 static int test_map_conversion(isl_ctx *ctx)
4813 {
4814 const char *str;
4815 isl_map *map1, *map2;
4816 isl_pw_multi_aff *pma;
4817 int equal;
4818
4819 str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
4820 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4821 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4822 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4823 "9e <= -2 - 2a) }";
4824 map1 = isl_map_read_from_str(ctx, str);
4825 pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
4826 map2 = isl_map_from_pw_multi_aff(pma);
4827 equal = isl_map_is_equal(map1, map2);
4828 isl_map_free(map1);
4829 isl_map_free(map2);
4830
4831 if (equal < 0)
4832 return -1;
4833 if (!equal)
4834 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
4835
4836 return 0;
4837 }
4838
4839 static int test_conversion(isl_ctx *ctx)
4840 {
4841 if (test_set_conversion(ctx) < 0)
4842 return -1;
4843 if (test_map_conversion(ctx) < 0)
4844 return -1;
4845 return 0;
4846 }
4847
4848 /* Check that isl_basic_map_curry does not modify input.
4849 */
4850 static int test_curry(isl_ctx *ctx)
4851 {
4852 const char *str;
4853 isl_basic_map *bmap1, *bmap2;
4854 int equal;
4855
4856 str = "{ [A[] -> B[]] -> C[] }";
4857 bmap1 = isl_basic_map_read_from_str(ctx, str);
4858 bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
4859 equal = isl_basic_map_is_equal(bmap1, bmap2);
4860 isl_basic_map_free(bmap1);
4861 isl_basic_map_free(bmap2);
4862
4863 if (equal < 0)
4864 return -1;
4865 if (equal)
4866 isl_die(ctx, isl_error_unknown,
4867 "curried map should not be equal to original",
4868 return -1);
4869
4870 return 0;
4871 }
4872
4873 struct {
4874 const char *set;
4875 const char *ma;
4876 const char *res;
4877 } preimage_tests[] = {
4878 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4879 "{ A[j,i] -> B[i,j] }",
4880 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4881 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4882 "{ A[a,b] -> B[a/2,b/6] }",
4883 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4884 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4885 "{ A[a,b] -> B[a/2,b/6] }",
4886 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4887 "exists i,j : a = 2 i and b = 6 j }" },
4888 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4889 "[n] -> { : 0 <= n <= 100 }" },
4890 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4891 "{ A[a] -> B[2a] }",
4892 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4893 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4894 "{ A[a] -> B[([a/2])] }",
4895 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4896 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4897 "{ A[a] -> B[a,a,a/3] }",
4898 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4899 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4900 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4901 };
4902
4903 static int test_preimage_basic_set(isl_ctx *ctx)
4904 {
4905 int i;
4906 isl_basic_set *bset1, *bset2;
4907 isl_multi_aff *ma;
4908 int equal;
4909
4910 for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
4911 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
4912 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
4913 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
4914 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
4915 equal = isl_basic_set_is_equal(bset1, bset2);
4916 isl_basic_set_free(bset1);
4917 isl_basic_set_free(bset2);
4918 if (equal < 0)
4919 return -1;
4920 if (!equal)
4921 isl_die(ctx, isl_error_unknown, "bad preimage",
4922 return -1);
4923 }
4924
4925 return 0;
4926 }
4927
4928 struct {
4929 const char *map;
4930 const char *ma;
4931 const char *res;
4932 } preimage_domain_tests[] = {
4933 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4934 "{ A[j,i] -> B[i,j] }",
4935 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4936 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4937 "{ A[i] -> B[i + 1] }",
4938 "{ A[i] -> C[i + 1] }" },
4939 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4940 "{ A[i] -> B[i + 1] }",
4941 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4942 { "{ B[i] -> C[([i/2])] }",
4943 "{ A[i] -> B[2i] }",
4944 "{ A[i] -> C[i] }" },
4945 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4946 "{ A[i] -> B[([i/5]), ([i/7])] }",
4947 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4948 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4949 "[N] -> { A[] -> B[([N/5])] }",
4950 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4951 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4952 "{ A[i] -> B[2i] }",
4953 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4954 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4955 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4956 "{ A[i] -> B[2i] }",
4957 "{ A[i] -> C[2i] }" },
4958 };
4959
4960 static int test_preimage_union_map(isl_ctx *ctx)
4961 {
4962 int i;
4963 isl_union_map *umap1, *umap2;
4964 isl_multi_aff *ma;
4965 int equal;
4966
4967 for (i = 0; i < ARRAY_SIZE(preimage_domain_tests); ++i) {
4968 umap1 = isl_union_map_read_from_str(ctx,
4969 preimage_domain_tests[i].map);
4970 ma = isl_multi_aff_read_from_str(ctx,
4971 preimage_domain_tests[i].ma);
4972 umap2 = isl_union_map_read_from_str(ctx,
4973 preimage_domain_tests[i].res);
4974 umap1 = isl_union_map_preimage_domain_multi_aff(umap1, ma);
4975 equal = isl_union_map_is_equal(umap1, umap2);
4976 isl_union_map_free(umap1);
4977 isl_union_map_free(umap2);
4978 if (equal < 0)
4979 return -1;
4980 if (!equal)
4981 isl_die(ctx, isl_error_unknown, "bad preimage",
4982 return -1);
4983 }
4984
4985 return 0;
4986 }
4987
4988 static int test_preimage(isl_ctx *ctx)
4989 {
4990 if (test_preimage_basic_set(ctx) < 0)
4991 return -1;
4992 if (test_preimage_union_map(ctx) < 0)
4993 return -1;
4994
4995 return 0;
4996 }
4997
4998 struct {
4999 const char *ma1;
5000 const char *ma;
5001 const char *res;
5002 } pullback_tests[] = {
5003 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
5004 "{ A[a,b] -> C[b + 2a] }" },
5005 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
5006 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
5007 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
5008 "{ A[a] -> C[(a)/6] }" },
5009 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
5010 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
5011 "{ A[a] -> C[(2a)/3] }" },
5012 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
5013 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
5014 "{ A[i,j] -> C[i + j, i + j] }"},
5015 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
5016 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
5017 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
5018 { "{ [i, j] -> [floor((i)/4) + floor((2*i+j)/5)] }",
5019 "{ [i, j] -> [floor((i)/3), j] }",
5020 "{ [i, j] -> [(floor((i)/12) + floor((j + 2*floor((i)/3))/5))] }" },
5021 };
5022
5023 static int test_pullback(isl_ctx *ctx)
5024 {
5025 int i;
5026 isl_multi_aff *ma1, *ma2;
5027 isl_multi_aff *ma;
5028 int equal;
5029
5030 for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
5031 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
5032 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
5033 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
5034 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
5035 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
5036 isl_multi_aff_free(ma1);
5037 isl_multi_aff_free(ma2);
5038 if (equal < 0)
5039 return -1;
5040 if (!equal)
5041 isl_die(ctx, isl_error_unknown, "bad pullback",
5042 return -1);
5043 }
5044
5045 return 0;
5046 }
5047
5048 /* Check that negation is printed correctly and that equal expressions
5049 * are correctly identified.
5050 */
5051 static int test_ast(isl_ctx *ctx)
5052 {
5053 isl_ast_expr *expr, *expr1, *expr2, *expr3;
5054 char *str;
5055 int ok, equal;
5056
5057 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
5058 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
5059 expr = isl_ast_expr_add(expr1, expr2);
5060 expr2 = isl_ast_expr_copy(expr);
5061 expr = isl_ast_expr_neg(expr);
5062 expr2 = isl_ast_expr_neg(expr2);
5063 equal = isl_ast_expr_is_equal(expr, expr2);
5064 str = isl_ast_expr_to_str(expr);
5065 ok = str ? !strcmp(str, "-(A + B)") : -1;
5066 free(str);
5067 isl_ast_expr_free(expr);
5068 isl_ast_expr_free(expr2);
5069
5070 if (ok < 0 || equal < 0)
5071 return -1;
5072 if (!equal)
5073 isl_die(ctx, isl_error_unknown,
5074 "equal expressions not considered equal", return -1);
5075 if (!ok)
5076 isl_die(ctx, isl_error_unknown,
5077 "isl_ast_expr printed incorrectly", return -1);
5078
5079 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
5080 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
5081 expr = isl_ast_expr_add(expr1, expr2);
5082 expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
5083 expr = isl_ast_expr_sub(expr3, expr);
5084 str = isl_ast_expr_to_str(expr);
5085 ok = str ? !strcmp(str, "C - (A + B)") : -1;
5086 free(str);
5087 isl_ast_expr_free(expr);
5088
5089 if (ok < 0)
5090 return -1;
5091 if (!ok)
5092 isl_die(ctx, isl_error_unknown,
5093 "isl_ast_expr printed incorrectly", return -1);
5094
5095 return 0;
5096 }
5097
5098 /* Check that isl_ast_build_expr_from_set returns a valid expression
5099 * for an empty set. Note that isl_ast_build_expr_from_set getting
5100 * called on an empty set probably indicates a bug in the caller.
5101 */
5102 static int test_ast_build(isl_ctx *ctx)
5103 {
5104 isl_set *set;
5105 isl_ast_build *build;
5106 isl_ast_expr *expr;
5107
5108 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5109 build = isl_ast_build_from_context(set);
5110
5111 set = isl_set_empty(isl_space_params_alloc(ctx, 0));
5112 expr = isl_ast_build_expr_from_set(build, set);
5113
5114 isl_ast_expr_free(expr);
5115 isl_ast_build_free(build);
5116
5117 if (!expr)
5118 return -1;
5119
5120 return 0;
5121 }
5122
5123 /* Internal data structure for before_for and after_for callbacks.
5124 *
5125 * depth is the current depth
5126 * before is the number of times before_for has been called
5127 * after is the number of times after_for has been called
5128 */
5129 struct isl_test_codegen_data {
5130 int depth;
5131 int before;
5132 int after;
5133 };
5134
5135 /* This function is called before each for loop in the AST generated
5136 * from test_ast_gen1.
5137 *
5138 * Increment the number of calls and the depth.
5139 * Check that the space returned by isl_ast_build_get_schedule_space
5140 * matches the target space of the schedule returned by
5141 * isl_ast_build_get_schedule.
5142 * Return an isl_id that is checked by the corresponding call
5143 * to after_for.
5144 */
5145 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
5146 void *user)
5147 {
5148 struct isl_test_codegen_data *data = user;
5149 isl_ctx *ctx;
5150 isl_space *space;
5151 isl_union_map *schedule;
5152 isl_union_set *uset;
5153 isl_set *set;
5154 int empty;
5155 char name[] = "d0";
5156
5157 ctx = isl_ast_build_get_ctx(build);
5158
5159 if (data->before >= 3)
5160 isl_die(ctx, isl_error_unknown,
5161 "unexpected number of for nodes", return NULL);
5162 if (data->depth >= 2)
5163 isl_die(ctx, isl_error_unknown,
5164 "unexpected depth", return NULL);
5165
5166 snprintf(name, sizeof(name), "d%d", data->depth);
5167 data->before++;
5168 data->depth++;
5169
5170 schedule = isl_ast_build_get_schedule(build);
5171 uset = isl_union_map_range(schedule);
5172 if (!uset)
5173 return NULL;
5174 if (isl_union_set_n_set(uset) != 1) {
5175 isl_union_set_free(uset);
5176 isl_die(ctx, isl_error_unknown,
5177 "expecting single range space", return NULL);
5178 }
5179
5180 space = isl_ast_build_get_schedule_space(build);
5181 set = isl_union_set_extract_set(uset, space);
5182 isl_union_set_free(uset);
5183 empty = isl_set_is_empty(set);
5184 isl_set_free(set);
5185
5186 if (empty < 0)
5187 return NULL;
5188 if (empty)
5189 isl_die(ctx, isl_error_unknown,
5190 "spaces don't match", return NULL);
5191
5192 return isl_id_alloc(ctx, name, NULL);
5193 }
5194
5195 /* This function is called after each for loop in the AST generated
5196 * from test_ast_gen1.
5197 *
5198 * Increment the number of calls and decrement the depth.
5199 * Check that the annotation attached to the node matches
5200 * the isl_id returned by the corresponding call to before_for.
5201 */
5202 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
5203 __isl_keep isl_ast_build *build, void *user)
5204 {
5205 struct isl_test_codegen_data *data = user;
5206 isl_id *id;
5207 const char *name;
5208 int valid;
5209
5210 data->after++;
5211 data->depth--;
5212
5213 if (data->after > data->before)
5214 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
5215 "mismatch in number of for nodes",
5216 return isl_ast_node_free(node));
5217
5218 id = isl_ast_node_get_annotation(node);
5219 if (!id)
5220 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
5221 "missing annotation", return isl_ast_node_free(node));
5222
5223 name = isl_id_get_name(id);
5224 valid = name && atoi(name + 1) == data->depth;
5225 isl_id_free(id);
5226
5227 if (!valid)
5228 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
5229 "wrong annotation", return isl_ast_node_free(node));
5230
5231 return node;
5232 }
5233
5234 /* Check that the before_each_for and after_each_for callbacks
5235 * are called for each for loop in the generated code,
5236 * that they are called in the right order and that the isl_id
5237 * returned from the before_each_for callback is attached to
5238 * the isl_ast_node passed to the corresponding after_each_for call.
5239 */
5240 static int test_ast_gen1(isl_ctx *ctx)
5241 {
5242 const char *str;
5243 isl_set *set;
5244 isl_union_map *schedule;
5245 isl_ast_build *build;
5246 isl_ast_node *tree;
5247 struct isl_test_codegen_data data;
5248
5249 str = "[N] -> { : N >= 10 }";
5250 set = isl_set_read_from_str(ctx, str);
5251 str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
5252 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
5253 schedule = isl_union_map_read_from_str(ctx, str);
5254
5255 data.before = 0;
5256 data.after = 0;
5257 data.depth = 0;
5258 build = isl_ast_build_from_context(set);
5259 build = isl_ast_build_set_before_each_for(build,
5260 &before_for, &data);
5261 build = isl_ast_build_set_after_each_for(build,
5262 &after_for, &data);
5263 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5264 isl_ast_build_free(build);
5265 if (!tree)
5266 return -1;
5267
5268 isl_ast_node_free(tree);
5269
5270 if (data.before != 3 || data.after != 3)
5271 isl_die(ctx, isl_error_unknown,
5272 "unexpected number of for nodes", return -1);
5273
5274 return 0;
5275 }
5276
5277 /* Check that the AST generator handles domains that are integrally disjoint
5278 * but not rationally disjoint.
5279 */
5280 static int test_ast_gen2(isl_ctx *ctx)
5281 {
5282 const char *str;
5283 isl_set *set;
5284 isl_union_map *schedule;
5285 isl_union_map *options;
5286 isl_ast_build *build;
5287 isl_ast_node *tree;
5288
5289 str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
5290 schedule = isl_union_map_read_from_str(ctx, str);
5291 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5292 build = isl_ast_build_from_context(set);
5293
5294 str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
5295 options = isl_union_map_read_from_str(ctx, str);
5296 build = isl_ast_build_set_options(build, options);
5297 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5298 isl_ast_build_free(build);
5299 if (!tree)
5300 return -1;
5301 isl_ast_node_free(tree);
5302
5303 return 0;
5304 }
5305
5306 /* Increment *user on each call.
5307 */
5308 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
5309 __isl_keep isl_ast_build *build, void *user)
5310 {
5311 int *n = user;
5312
5313 (*n)++;
5314
5315 return node;
5316 }
5317
5318 /* Test that unrolling tries to minimize the number of instances.
5319 * In particular, for the schedule given below, make sure it generates
5320 * 3 nodes (rather than 101).
5321 */
5322 static int test_ast_gen3(isl_ctx *ctx)
5323 {
5324 const char *str;
5325 isl_set *set;
5326 isl_union_map *schedule;
5327 isl_union_map *options;
5328 isl_ast_build *build;
5329 isl_ast_node *tree;
5330 int n_domain = 0;
5331
5332 str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
5333 schedule = isl_union_map_read_from_str(ctx, str);
5334 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5335
5336 str = "{ [i] -> unroll[0] }";
5337 options = isl_union_map_read_from_str(ctx, str);
5338
5339 build = isl_ast_build_from_context(set);
5340 build = isl_ast_build_set_options(build, options);
5341 build = isl_ast_build_set_at_each_domain(build,
5342 &count_domains, &n_domain);
5343 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5344 isl_ast_build_free(build);
5345 if (!tree)
5346 return -1;
5347
5348 isl_ast_node_free(tree);
5349
5350 if (n_domain != 3)
5351 isl_die(ctx, isl_error_unknown,
5352 "unexpected number of for nodes", return -1);
5353
5354 return 0;
5355 }
5356
5357 /* Check that if the ast_build_exploit_nested_bounds options is set,
5358 * we do not get an outer if node in the generated AST,
5359 * while we do get such an outer if node if the options is not set.
5360 */
5361 static int test_ast_gen4(isl_ctx *ctx)
5362 {
5363 const char *str;
5364 isl_set *set;
5365 isl_union_map *schedule;
5366 isl_ast_build *build;
5367 isl_ast_node *tree;
5368 enum isl_ast_node_type type;
5369 int enb;
5370
5371 enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
5372 str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
5373
5374 isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
5375
5376 schedule = isl_union_map_read_from_str(ctx, str);
5377 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5378 build = isl_ast_build_from_context(set);
5379 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5380 isl_ast_build_free(build);
5381 if (!tree)
5382 return -1;
5383
5384 type = isl_ast_node_get_type(tree);
5385 isl_ast_node_free(tree);
5386
5387 if (type == isl_ast_node_if)
5388 isl_die(ctx, isl_error_unknown,
5389 "not expecting if node", return -1);
5390
5391 isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
5392
5393 schedule = isl_union_map_read_from_str(ctx, str);
5394 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5395 build = isl_ast_build_from_context(set);
5396 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5397 isl_ast_build_free(build);
5398 if (!tree)
5399 return -1;
5400
5401 type = isl_ast_node_get_type(tree);
5402 isl_ast_node_free(tree);
5403
5404 if (type != isl_ast_node_if)
5405 isl_die(ctx, isl_error_unknown,
5406 "expecting if node", return -1);
5407
5408 isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
5409
5410 return 0;
5411 }
5412
5413 /* This function is called for each leaf in the AST generated
5414 * from test_ast_gen5.
5415 *
5416 * We finalize the AST generation by extending the outer schedule
5417 * with a zero-dimensional schedule. If this results in any for loops,
5418 * then this means that we did not pass along enough information
5419 * about the outer schedule to the inner AST generation.
5420 */
5421 static __isl_give isl_ast_node *create_leaf(__isl_take isl_ast_build *build,
5422 void *user)
5423 {
5424 isl_union_map *schedule, *extra;
5425 isl_ast_node *tree;
5426
5427 schedule = isl_ast_build_get_schedule(build);
5428 extra = isl_union_map_copy(schedule);
5429 extra = isl_union_map_from_domain(isl_union_map_domain(extra));
5430 schedule = isl_union_map_range_product(schedule, extra);
5431 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5432 isl_ast_build_free(build);
5433
5434 if (!tree)
5435 return NULL;
5436
5437 if (isl_ast_node_get_type(tree) == isl_ast_node_for)
5438 isl_die(isl_ast_node_get_ctx(tree), isl_error_unknown,
5439 "code should not contain any for loop",
5440 return isl_ast_node_free(tree));
5441
5442 return tree;
5443 }
5444
5445 /* Check that we do not lose any information when going back and
5446 * forth between internal and external schedule.
5447 *
5448 * In particular, we create an AST where we unroll the only
5449 * non-constant dimension in the schedule. We therefore do
5450 * not expect any for loops in the AST. However, older versions
5451 * of isl would not pass along enough information about the outer
5452 * schedule when performing an inner code generation from a create_leaf
5453 * callback, resulting in the inner code generation producing a for loop.
5454 */
5455 static int test_ast_gen5(isl_ctx *ctx)
5456 {
5457 const char *str;
5458 isl_set *set;
5459 isl_union_map *schedule, *options;
5460 isl_ast_build *build;
5461 isl_ast_node *tree;
5462
5463 str = "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
5464 schedule = isl_union_map_read_from_str(ctx, str);
5465
5466 str = "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
5467 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
5468 options = isl_union_map_read_from_str(ctx, str);
5469
5470 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5471 build = isl_ast_build_from_context(set);
5472 build = isl_ast_build_set_options(build, options);
5473 build = isl_ast_build_set_create_leaf(build, &create_leaf, NULL);
5474 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5475 isl_ast_build_free(build);
5476 isl_ast_node_free(tree);
5477 if (!tree)
5478 return -1;
5479
5480 return 0;
5481 }
5482
5483 static int test_ast_gen(isl_ctx *ctx)
5484 {
5485 if (test_ast_gen1(ctx) < 0)
5486 return -1;
5487 if (test_ast_gen2(ctx) < 0)
5488 return -1;
5489 if (test_ast_gen3(ctx) < 0)
5490 return -1;
5491 if (test_ast_gen4(ctx) < 0)
5492 return -1;
5493 if (test_ast_gen5(ctx) < 0)
5494 return -1;
5495 return 0;
5496 }
5497
5498 /* Check if dropping output dimensions from an isl_pw_multi_aff
5499 * works properly.
5500 */
5501 static int test_pw_multi_aff(isl_ctx *ctx)
5502 {
5503 const char *str;
5504 isl_pw_multi_aff *pma1, *pma2;
5505 int equal;
5506
5507 str = "{ [i,j] -> [i+j, 4i-j] }";
5508 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
5509 str = "{ [i,j] -> [4i-j] }";
5510 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
5511
5512 pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
5513
5514 equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
5515
5516 isl_pw_multi_aff_free(pma1);
5517 isl_pw_multi_aff_free(pma2);
5518 if (equal < 0)
5519 return -1;
5520 if (!equal)
5521 isl_die(ctx, isl_error_unknown,
5522 "expressions not equal", return -1);
5523
5524 return 0;
5525 }
5526
5527 /* Check that we can properly parse multi piecewise affine expressions
5528 * where the piecewise affine expressions have different domains.
5529 */
5530 static int test_multi_pw_aff(isl_ctx *ctx)
5531 {
5532 const char *str;
5533 isl_set *dom, *dom2;
5534 isl_multi_pw_aff *mpa1, *mpa2;
5535 isl_pw_aff *pa;
5536 int equal;
5537 int equal_domain;
5538
5539 mpa1 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [i] }");
5540 dom = isl_set_read_from_str(ctx, "{ [i] : i > 0 }");
5541 mpa1 = isl_multi_pw_aff_intersect_domain(mpa1, dom);
5542 mpa2 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [2i] }");
5543 mpa2 = isl_multi_pw_aff_flat_range_product(mpa1, mpa2);
5544 str = "{ [i] -> [(i : i > 0), 2i] }";
5545 mpa1 = isl_multi_pw_aff_read_from_str(ctx, str);
5546
5547 equal = isl_multi_pw_aff_plain_is_equal(mpa1, mpa2);
5548
5549 pa = isl_multi_pw_aff_get_pw_aff(mpa1, 0);
5550 dom = isl_pw_aff_domain(pa);
5551 pa = isl_multi_pw_aff_get_pw_aff(mpa1, 1);
5552 dom2 = isl_pw_aff_domain(pa);
5553 equal_domain = isl_set_is_equal(dom, dom2);
5554
5555 isl_set_free(dom);
5556 isl_set_free(dom2);
5557 isl_multi_pw_aff_free(mpa1);
5558 isl_multi_pw_aff_free(mpa2);
5559
5560 if (equal < 0)
5561 return -1;
5562 if (!equal)
5563 isl_die(ctx, isl_error_unknown,
5564 "expressions not equal", return -1);
5565
5566 if (equal_domain < 0)
5567 return -1;
5568 if (equal_domain)
5569 isl_die(ctx, isl_error_unknown,
5570 "domains unexpectedly equal", return -1);
5571
5572 return 0;
5573 }
5574
5575 /* This is a regression test for a bug where isl_basic_map_simplify
5576 * would end up in an infinite loop. In particular, we construct
5577 * an empty basic set that is not obviously empty.
5578 * isl_basic_set_is_empty marks the basic set as empty.
5579 * After projecting out i3, the variable can be dropped completely,
5580 * but isl_basic_map_simplify refrains from doing so if the basic set
5581 * is empty and would end up in an infinite loop if it didn't test
5582 * explicitly for empty basic maps in the outer loop.
5583 */
5584 static int test_simplify(isl_ctx *ctx)
5585 {
5586 const char *str;
5587 isl_basic_set *bset;
5588 int empty;
5589
5590 str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
5591 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
5592 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
5593 "i3 >= i2 }";
5594 bset = isl_basic_set_read_from_str(ctx, str);
5595 empty = isl_basic_set_is_empty(bset);
5596 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
5597 isl_basic_set_free(bset);
5598 if (!bset)
5599 return -1;
5600 if (!empty)
5601 isl_die(ctx, isl_error_unknown,
5602 "basic set should be empty", return -1);
5603
5604 return 0;
5605 }
5606
5607 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
5608 * with gbr context would fail to disable the use of the shifted tableau
5609 * when transferring equalities for the input to the context, resulting
5610 * in invalid sample values.
5611 */
5612 static int test_partial_lexmin(isl_ctx *ctx)
5613 {
5614 const char *str;
5615 isl_basic_set *bset;
5616 isl_basic_map *bmap;
5617 isl_map *map;
5618
5619 str = "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
5620 bmap = isl_basic_map_read_from_str(ctx, str);
5621 str = "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
5622 bset = isl_basic_set_read_from_str(ctx, str);
5623 map = isl_basic_map_partial_lexmin(bmap, bset, NULL);
5624 isl_map_free(map);
5625
5626 if (!map)
5627 return -1;
5628
5629 return 0;
5630 }
5631
5632 /* Check that the variable compression performed on the existentially
5633 * quantified variables inside isl_basic_set_compute_divs is not confused
5634 * by the implicit equalities among the parameters.
5635 */
5636 static int test_compute_divs(isl_ctx *ctx)
5637 {
5638 const char *str;
5639 isl_basic_set *bset;
5640 isl_set *set;
5641
5642 str = "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
5643 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
5644 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
5645 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
5646 bset = isl_basic_set_read_from_str(ctx, str);
5647 set = isl_basic_set_compute_divs(bset);
5648 isl_set_free(set);
5649 if (!set)
5650 return -1;
5651
5652 return 0;
5653 }
5654
5655 /* Check that the reaching domain elements and the prefix schedule
5656 * at a leaf node are the same before and after grouping.
5657 */
5658 static int test_schedule_tree_group_1(isl_ctx *ctx)
5659 {
5660 int equal;
5661 const char *str;
5662 isl_id *id;
5663 isl_union_set *uset;
5664 isl_multi_union_pw_aff *mupa;
5665 isl_union_pw_multi_aff *upma1, *upma2;
5666 isl_union_set *domain1, *domain2;
5667 isl_union_map *umap1, *umap2;
5668 isl_schedule_node *node;
5669
5670 str = "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10 }";
5671 uset = isl_union_set_read_from_str(ctx, str);
5672 node = isl_schedule_node_from_domain(uset);
5673 node = isl_schedule_node_child(node, 0);
5674 str = "[{ S1[i,j] -> [i]; S2[i,j] -> [9 - i] }]";
5675 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5676 node = isl_schedule_node_insert_partial_schedule(node, mupa);
5677 node = isl_schedule_node_child(node, 0);
5678 str = "[{ S1[i,j] -> [j]; S2[i,j] -> [j] }]";
5679 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5680 node = isl_schedule_node_insert_partial_schedule(node, mupa);
5681 node = isl_schedule_node_child(node, 0);
5682 umap1 = isl_schedule_node_get_prefix_schedule_union_map(node);
5683 upma1 = isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node);
5684 domain1 = isl_schedule_node_get_domain(node);
5685 id = isl_id_alloc(ctx, "group", NULL);
5686 node = isl_schedule_node_parent(node);
5687 node = isl_schedule_node_group(node, id);
5688 node = isl_schedule_node_child(node, 0);
5689 umap2 = isl_schedule_node_get_prefix_schedule_union_map(node);
5690 upma2 = isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node);
5691 domain2 = isl_schedule_node_get_domain(node);
5692 equal = isl_union_pw_multi_aff_plain_is_equal(upma1, upma2);
5693 if (equal >= 0 && equal)
5694 equal = isl_union_set_is_equal(domain1, domain2);
5695 if (equal >= 0 && equal)
5696 equal = isl_union_map_is_equal(umap1, umap2);
5697 isl_union_map_free(umap1);
5698 isl_union_map_free(umap2);
5699 isl_union_set_free(domain1);
5700 isl_union_set_free(domain2);
5701 isl_union_pw_multi_aff_free(upma1);
5702 isl_union_pw_multi_aff_free(upma2);
5703 isl_schedule_node_free(node);
5704
5705 if (equal < 0)
5706 return -1;
5707 if (!equal)
5708 isl_die(ctx, isl_error_unknown,
5709 "expressions not equal", return -1);
5710
5711 return 0;
5712 }
5713
5714 /* Check that we can have nested groupings and that the union map
5715 * schedule representation is the same before and after the grouping.
5716 * Note that after the grouping, the union map representation contains
5717 * the domain constraints from the ranges of the expansion nodes,
5718 * while they are missing from the union map representation of
5719 * the tree without expansion nodes.
5720 *
5721 * Also check that the global expansion is as expected.
5722 */
5723 static int test_schedule_tree_group_2(isl_ctx *ctx)
5724 {
5725 int equal, equal_expansion;
5726 const char *str;
5727 isl_id *id;
5728 isl_union_set *uset;
5729 isl_union_map *umap1, *umap2;
5730 isl_union_map *expansion1, *expansion2;
5731 isl_union_set_list *filters;
5732 isl_multi_union_pw_aff *mupa;
5733 isl_schedule *schedule;
5734 isl_schedule_node *node;
5735
5736 str = "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10; "
5737 "S3[i,j] : 0 <= i,j < 10 }";
5738 uset = isl_union_set_read_from_str(ctx, str);
5739 node = isl_schedule_node_from_domain(uset);
5740 node = isl_schedule_node_child(node, 0);
5741 str = "[{ S1[i,j] -> [i]; S2[i,j] -> [i]; S3[i,j] -> [i] }]";
5742 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5743 node = isl_schedule_node_insert_partial_schedule(node, mupa);
5744 node = isl_schedule_node_child(node, 0);
5745 str = "{ S1[i,j] }";
5746 uset = isl_union_set_read_from_str(ctx, str);
5747 filters = isl_union_set_list_from_union_set(uset);
5748 str = "{ S2[i,j]; S3[i,j] }";
5749 uset = isl_union_set_read_from_str(ctx, str);
5750 filters = isl_union_set_list_add(filters, uset);
5751 node = isl_schedule_node_insert_sequence(node, filters);
5752 node = isl_schedule_node_child(node, 1);
5753 node = isl_schedule_node_child(node, 0);
5754 str = "{ S2[i,j] }";
5755 uset = isl_union_set_read_from_str(ctx, str);
5756 filters = isl_union_set_list_from_union_set(uset);
5757 str = "{ S3[i,j] }";
5758 uset = isl_union_set_read_from_str(ctx, str);
5759 filters = isl_union_set_list_add(filters, uset);
5760 node = isl_schedule_node_insert_sequence(node, filters);
5761
5762 schedule = isl_schedule_node_get_schedule(node);
5763 umap1 = isl_schedule_get_map(schedule);
5764 uset = isl_schedule_get_domain(schedule);
5765 umap1 = isl_union_map_intersect_domain(umap1, uset);
5766 isl_schedule_free(schedule);
5767
5768 node = isl_schedule_node_parent(node);
5769 node = isl_schedule_node_parent(node);
5770 id = isl_id_alloc(ctx, "group1", NULL);
5771 node = isl_schedule_node_group(node, id);
5772 node = isl_schedule_node_child(node, 1);
5773 node = isl_schedule_node_child(node, 0);
5774 id = isl_id_alloc(ctx, "group2", NULL);
5775 node = isl_schedule_node_group(node, id);
5776
5777 schedule = isl_schedule_node_get_schedule(node);
5778 umap2 = isl_schedule_get_map(schedule);
5779 isl_schedule_free(schedule);
5780
5781 node = isl_schedule_node_root(node);
5782 node = isl_schedule_node_child(node, 0);
5783 expansion1 = isl_schedule_node_get_subtree_expansion(node);
5784 isl_schedule_node_free(node);
5785
5786 str = "{ group1[i] -> S1[i,j] : 0 <= i,j < 10; "
5787 "group1[i] -> S2[i,j] : 0 <= i,j < 10; "
5788 "group1[i] -> S3[i,j] : 0 <= i,j < 10 }";
5789
5790 expansion2 = isl_union_map_read_from_str(ctx, str);
5791
5792 equal = isl_union_map_is_equal(umap1, umap2);
5793 equal_expansion = isl_union_map_is_equal(expansion1, expansion2);
5794
5795 isl_union_map_free(umap1);
5796 isl_union_map_free(umap2);
5797 isl_union_map_free(expansion1);
5798 isl_union_map_free(expansion2);
5799
5800 if (equal < 0 || equal_expansion < 0)
5801 return -1;
5802 if (!equal)
5803 isl_die(ctx, isl_error_unknown,
5804 "expressions not equal", return -1);
5805 if (!equal_expansion)
5806 isl_die(ctx, isl_error_unknown,
5807 "unexpected expansion", return -1);
5808
5809 return 0;
5810 }
5811
5812 /* Some tests for the isl_schedule_node_group function.
5813 */
5814 static int test_schedule_tree_group(isl_ctx *ctx)
5815 {
5816 if (test_schedule_tree_group_1(ctx) < 0)
5817 return -1;
5818 if (test_schedule_tree_group_2(ctx) < 0)
5819 return -1;
5820 return 0;
5821 }
5822
5823 struct {
5824 const char *set;
5825 const char *dual;
5826 } coef_tests[] = {
5827 { "{ rat: [i] : 0 <= i <= 10 }",
5828 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
5829 { "{ rat: [i] : FALSE }",
5830 "{ rat: coefficients[[cst] -> [a]] }" },
5831 { "{ rat: [i] : }",
5832 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
5833 };
5834
5835 struct {
5836 const char *set;
5837 const char *dual;
5838 } sol_tests[] = {
5839 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
5840 "{ rat: [i] : 0 <= i <= 10 }" },
5841 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
5842 "{ rat: [i] }" },
5843 { "{ rat: coefficients[[cst] -> [a]] }",
5844 "{ rat: [i] : FALSE }" },
5845 };
5846
5847 /* Test the basic functionality of isl_basic_set_coefficients and
5848 * isl_basic_set_solutions.
5849 */
5850 static int test_dual(isl_ctx *ctx)
5851 {
5852 int i;
5853
5854 for (i = 0; i < ARRAY_SIZE(coef_tests); ++i) {
5855 int equal;
5856 isl_basic_set *bset1, *bset2;
5857
5858 bset1 = isl_basic_set_read_from_str(ctx, coef_tests[i].set);
5859 bset2 = isl_basic_set_read_from_str(ctx, coef_tests[i].dual);
5860 bset1 = isl_basic_set_coefficients(bset1);
5861 equal = isl_basic_set_is_equal(bset1, bset2);
5862 isl_basic_set_free(bset1);
5863 isl_basic_set_free(bset2);
5864 if (equal < 0)
5865 return -1;
5866 if (!equal)
5867 isl_die(ctx, isl_error_unknown,
5868 "incorrect dual", return -1);
5869 }
5870
5871 for (i = 0; i < ARRAY_SIZE(sol_tests); ++i) {
5872 int equal;
5873 isl_basic_set *bset1, *bset2;
5874
5875 bset1 = isl_basic_set_read_from_str(ctx, sol_tests[i].set);
5876 bset2 = isl_basic_set_read_from_str(ctx, sol_tests[i].dual);
5877 bset1 = isl_basic_set_solutions(bset1);
5878 equal = isl_basic_set_is_equal(bset1, bset2);
5879 isl_basic_set_free(bset1);
5880 isl_basic_set_free(bset2);
5881 if (equal < 0)
5882 return -1;
5883 if (!equal)
5884 isl_die(ctx, isl_error_unknown,
5885 "incorrect dual", return -1);
5886 }
5887
5888 return 0;
5889 }
5890
5891 struct {
5892 int scale_tile;
5893 int shift_point;
5894 const char *domain;
5895 const char *schedule;
5896 const char *sizes;
5897 const char *tile;
5898 const char *point;
5899 } tile_tests[] = {
5900 { 0, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
5901 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5902 "{ [32,32] }",
5903 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
5904 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5905 },
5906 { 1, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
5907 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5908 "{ [32,32] }",
5909 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
5910 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5911 },
5912 { 0, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
5913 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5914 "{ [32,32] }",
5915 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
5916 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
5917 },
5918 { 1, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
5919 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5920 "{ [32,32] }",
5921 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
5922 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
5923 },
5924 };
5925
5926 /* Basic tiling tests. Create a schedule tree with a domain and a band node,
5927 * tile the band and then check if the tile and point bands have the
5928 * expected partial schedule.
5929 */
5930 static int test_tile(isl_ctx *ctx)
5931 {
5932 int i;
5933 int scale;
5934 int shift;
5935
5936 scale = isl_options_get_tile_scale_tile_loops(ctx);
5937 shift = isl_options_get_tile_shift_point_loops(ctx);
5938
5939 for (i = 0; i < ARRAY_SIZE(tile_tests); ++i) {
5940 int opt;
5941 int equal;
5942 const char *str;
5943 isl_union_set *domain;
5944 isl_multi_union_pw_aff *mupa, *mupa2;
5945 isl_schedule_node *node;
5946 isl_multi_val *sizes;
5947
5948 opt = tile_tests[i].scale_tile;
5949 isl_options_set_tile_scale_tile_loops(ctx, opt);
5950 opt = tile_tests[i].shift_point;
5951 isl_options_set_tile_shift_point_loops(ctx, opt);
5952
5953 str = tile_tests[i].domain;
5954 domain = isl_union_set_read_from_str(ctx, str);
5955 node = isl_schedule_node_from_domain(domain);
5956 node = isl_schedule_node_child(node, 0);
5957 str = tile_tests[i].schedule;
5958 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5959 node = isl_schedule_node_insert_partial_schedule(node, mupa);
5960 str = tile_tests[i].sizes;
5961 sizes = isl_multi_val_read_from_str(ctx, str);
5962 node = isl_schedule_node_band_tile(node, sizes);
5963
5964 str = tile_tests[i].tile;
5965 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5966 mupa2 = isl_schedule_node_band_get_partial_schedule(node);
5967 equal = isl_multi_union_pw_aff_plain_is_equal(mupa, mupa2);
5968 isl_multi_union_pw_aff_free(mupa);
5969 isl_multi_union_pw_aff_free(mupa2);
5970
5971 node = isl_schedule_node_child(node, 0);
5972
5973 str = tile_tests[i].point;
5974 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5975 mupa2 = isl_schedule_node_band_get_partial_schedule(node);
5976 if (equal >= 0 && equal)
5977 equal = isl_multi_union_pw_aff_plain_is_equal(mupa,
5978 mupa2);
5979 isl_multi_union_pw_aff_free(mupa);
5980 isl_multi_union_pw_aff_free(mupa2);
5981
5982 isl_schedule_node_free(node);
5983
5984 if (equal < 0)
5985 return -1;
5986 if (!equal)
5987 isl_die(ctx, isl_error_unknown,
5988 "unexpected result", return -1);
5989 }
5990
5991 isl_options_set_tile_scale_tile_loops(ctx, scale);
5992 isl_options_set_tile_shift_point_loops(ctx, shift);
5993
5994 return 0;
5995 }
5996
5997 /* Check that the domain hash of a space is equal to the hash
5998 * of the domain of the space.
5999 */
6000 static int test_domain_hash(isl_ctx *ctx)
6001 {
6002 isl_map *map;
6003 isl_space *space;
6004 uint32_t hash1, hash2;
6005
6006 map = isl_map_read_from_str(ctx, "[n] -> { A[B[x] -> C[]] -> D[] }");
6007 space = isl_map_get_space(map);
6008 isl_map_free(map);
6009 hash1 = isl_space_get_domain_hash(space);
6010 space = isl_space_domain(space);
6011 hash2 = isl_space_get_hash(space);
6012 isl_space_free(space);
6013
6014 if (!space)
6015 return -1;
6016 if (hash1 != hash2)
6017 isl_die(ctx, isl_error_unknown,
6018 "domain hash not equal to hash of domain", return -1);
6019
6020 return 0;
6021 }
6022
6023 struct {
6024 const char *name;
6025 int (*fn)(isl_ctx *ctx);
6026 } tests [] = {
6027 { "domain hash", &test_domain_hash },
6028 { "dual", &test_dual },
6029 { "dependence analysis", &test_flow },
6030 { "val", &test_val },
6031 { "compute divs", &test_compute_divs },
6032 { "partial lexmin", &test_partial_lexmin },
6033 { "simplify", &test_simplify },
6034 { "curry", &test_curry },
6035 { "piecewise multi affine expressions", &test_pw_multi_aff },
6036 { "multi piecewise affine expressions", &test_multi_pw_aff },
6037 { "conversion", &test_conversion },
6038 { "list", &test_list },
6039 { "align parameters", &test_align_parameters },
6040 { "preimage", &test_preimage },
6041 { "pullback", &test_pullback },
6042 { "AST", &test_ast },
6043 { "AST build", &test_ast_build },
6044 { "AST generation", &test_ast_gen },
6045 { "eliminate", &test_eliminate },
6046 { "residue class", &test_residue_class },
6047 { "div", &test_div },
6048 { "slice", &test_slice },
6049 { "fixed power", &test_fixed_power },
6050 { "sample", &test_sample },
6051 { "output", &test_output },
6052 { "vertices", &test_vertices },
6053 { "fixed", &test_fixed },
6054 { "equal", &test_equal },
6055 { "disjoint", &test_disjoint },
6056 { "product", &test_product },
6057 { "dim_max", &test_dim_max },
6058 { "affine", &test_aff },
6059 { "injective", &test_injective },
6060 { "schedule", &test_schedule },
6061 { "schedule tree grouping", &test_schedule_tree_group },
6062 { "tile", &test_tile },
6063 { "union_pw", &test_union_pw },
6064 { "eval", &test_eval },
6065 { "parse", &test_parse },
6066 { "single-valued", &test_sv },
6067 { "affine hull", &test_affine_hull },
6068 { "simple_hull", &test_simple_hull },
6069 { "coalesce", &test_coalesce },
6070 { "factorize", &test_factorize },
6071 { "subset", &test_subset },
6072 { "subtract", &test_subtract },
6073 { "lexmin", &test_lexmin },
6074 { "min", &test_min },
6075 { "gist", &test_gist },
6076 { "piecewise quasi-polynomials", &test_pwqp },
6077 { "lift", &test_lift },
6078 { "bound", &test_bound },
6079 { "union", &test_union },
6080 { "split periods", &test_split_periods },
6081 { "lexicographic order", &test_lex },
6082 { "bijectivity", &test_bijective },
6083 { "dataflow analysis", &test_dep },
6084 { "reading", &test_read },
6085 { "bounded", &test_bounded },
6086 { "construction", &test_construction },
6087 { "dimension manipulation", &test_dim },
6088 { "map application", &test_application },
6089 { "convex hull", &test_convex_hull },
6090 { "transitive closure", &test_closure },
6091 };
6092
6093 int main(int argc, char **argv)
6094 {
6095 int i;
6096 struct isl_ctx *ctx;
6097 struct isl_options *options;
6098
6099 srcdir = getenv("srcdir");
6100 assert(srcdir);
6101
6102 options = isl_options_new_with_defaults();
6103 assert(options);
6104 argc = isl_options_parse(options, argc, argv, ISL_ARG_ALL);
6105
6106 ctx = isl_ctx_alloc_with_options(&isl_options_args, options);
6107 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
6108 printf("%s\n", tests[i].name);
6109 if (tests[i].fn(ctx) < 0)
6110 goto error;
6111 }
6112 isl_ctx_free(ctx);
6113 return 0;
6114 error:
6115 isl_ctx_free(ctx);
6116 return -1;
6117 }
Integer set library