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isl_union_*_match_bin_op: use isl_union_*_foreach_*
[isl.git] / isl_test.c
blob250128f0ce4dfa5fc568be4f6272faca029206c3
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 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
1109 {
1110 char *filename;
1111 FILE *input;
1112 struct isl_basic_set *bset1, *bset2;
1113 struct isl_set *set;
1114
1115 filename = get_filename(ctx, name, "polylib");
1116 assert(filename);
1117 input = fopen(filename, "r");
1118 assert(input);
1119
1120 bset1 = isl_basic_set_read_from_file(ctx, input);
1121 bset2 = isl_basic_set_read_from_file(ctx, input);
1122
1123 set = isl_basic_set_union(bset1, bset2);
1124 bset1 = isl_set_convex_hull(set);
1125
1126 bset2 = isl_basic_set_read_from_file(ctx, input);
1127
1128 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1129
1130 isl_basic_set_free(bset1);
1131 isl_basic_set_free(bset2);
1132 free(filename);
1133
1134 fclose(input);
1135 }
1136
1137 struct {
1138 const char *set;
1139 const char *hull;
1140 } convex_hull_tests[] = {
1141 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1142 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1143 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1144 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1145 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1146 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1147 "i2 <= 5 and i2 >= 4; "
1148 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1149 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1150 "i2 <= 5 + i0 and i2 >= i0 }" },
1151 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1152 "{ [x, y] : 1 = 0 }" },
1153 };
1154
1155 static int test_convex_hull_algo(isl_ctx *ctx, int convex)
1156 {
1157 int i;
1158 int orig_convex = ctx->opt->convex;
1159 ctx->opt->convex = convex;
1160
1161 test_convex_hull_case(ctx, "convex0");
1162 test_convex_hull_case(ctx, "convex1");
1163 test_convex_hull_case(ctx, "convex2");
1164 test_convex_hull_case(ctx, "convex3");
1165 test_convex_hull_case(ctx, "convex4");
1166 test_convex_hull_case(ctx, "convex5");
1167 test_convex_hull_case(ctx, "convex6");
1168 test_convex_hull_case(ctx, "convex7");
1169 test_convex_hull_case(ctx, "convex8");
1170 test_convex_hull_case(ctx, "convex9");
1171 test_convex_hull_case(ctx, "convex10");
1172 test_convex_hull_case(ctx, "convex11");
1173 test_convex_hull_case(ctx, "convex12");
1174 test_convex_hull_case(ctx, "convex13");
1175 test_convex_hull_case(ctx, "convex14");
1176 test_convex_hull_case(ctx, "convex15");
1177
1178 for (i = 0; i < ARRAY_SIZE(convex_hull_tests); ++i) {
1179 isl_set *set1, *set2;
1180 int equal;
1181
1182 set1 = isl_set_read_from_str(ctx, convex_hull_tests[i].set);
1183 set2 = isl_set_read_from_str(ctx, convex_hull_tests[i].hull);
1184 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
1185 equal = isl_set_is_equal(set1, set2);
1186 isl_set_free(set1);
1187 isl_set_free(set2);
1188
1189 if (equal < 0)
1190 return -1;
1191 if (!equal)
1192 isl_die(ctx, isl_error_unknown,
1193 "unexpected convex hull", return -1);
1194 }
1195
1196 ctx->opt->convex = orig_convex;
1197
1198 return 0;
1199 }
1200
1201 static int test_convex_hull(isl_ctx *ctx)
1202 {
1203 if (test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM) < 0)
1204 return -1;
1205 if (test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP) < 0)
1206 return -1;
1207 return 0;
1208 }
1209
1210 void test_gist_case(struct isl_ctx *ctx, const char *name)
1211 {
1212 char *filename;
1213 FILE *input;
1214 struct isl_basic_set *bset1, *bset2;
1215
1216 filename = get_filename(ctx, name, "polylib");
1217 assert(filename);
1218 input = fopen(filename, "r");
1219 assert(input);
1220
1221 bset1 = isl_basic_set_read_from_file(ctx, input);
1222 bset2 = isl_basic_set_read_from_file(ctx, input);
1223
1224 bset1 = isl_basic_set_gist(bset1, bset2);
1225
1226 bset2 = isl_basic_set_read_from_file(ctx, input);
1227
1228 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1229
1230 isl_basic_set_free(bset1);
1231 isl_basic_set_free(bset2);
1232 free(filename);
1233
1234 fclose(input);
1235 }
1236
1237 struct {
1238 const char *set;
1239 const char *context;
1240 const char *gist;
1241 } gist_tests[] = {
1242 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1243 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1244 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1245 "{ [a, b, c] : a <= 15 }" },
1246 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1247 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1248 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1249 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1250 { "{ [m, n, a, b] : a <= 2147 + n }",
1251 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1252 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1253 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1254 "b >= 0) }",
1255 "{ [m, n, ku, kl] }" },
1256 };
1257
1258 static int test_gist(struct isl_ctx *ctx)
1259 {
1260 int i;
1261 const char *str;
1262 isl_basic_set *bset1, *bset2;
1263 isl_map *map1, *map2;
1264 int equal;
1265
1266 for (i = 0; i < ARRAY_SIZE(gist_tests); ++i) {
1267 int equal_input;
1268 isl_set *set1, *set2, *copy;
1269
1270 set1 = isl_set_read_from_str(ctx, gist_tests[i].set);
1271 set2 = isl_set_read_from_str(ctx, gist_tests[i].context);
1272 copy = isl_set_copy(set1);
1273 set1 = isl_set_gist(set1, set2);
1274 set2 = isl_set_read_from_str(ctx, gist_tests[i].gist);
1275 equal = isl_set_is_equal(set1, set2);
1276 isl_set_free(set1);
1277 isl_set_free(set2);
1278 set1 = isl_set_read_from_str(ctx, gist_tests[i].set);
1279 equal_input = isl_set_is_equal(set1, copy);
1280 isl_set_free(set1);
1281 isl_set_free(copy);
1282 if (equal < 0 || equal_input < 0)
1283 return -1;
1284 if (!equal)
1285 isl_die(ctx, isl_error_unknown,
1286 "incorrect gist result", return -1);
1287 if (!equal_input)
1288 isl_die(ctx, isl_error_unknown,
1289 "gist modified input", return -1);
1290 }
1291
1292 test_gist_case(ctx, "gist1");
1293
1294 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
1295 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1296 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1297 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1298 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1299 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1300 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1301 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1302 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1303 bset1 = isl_basic_set_read_from_str(ctx, str);
1304 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1305 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1306 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1307 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1308 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1309 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1310 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1311 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1312 bset2 = isl_basic_set_read_from_str(ctx, str);
1313 bset1 = isl_basic_set_gist(bset1, bset2);
1314 assert(bset1 && bset1->n_div == 0);
1315 isl_basic_set_free(bset1);
1316
1317 /* Check that the integer divisions of the second disjunct
1318 * do not spread to the first disjunct.
1319 */
1320 str = "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1321 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1322 "(exists (e0 = [(-1 + t1)/16], "
1323 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1324 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1325 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1326 "o0 <= 4294967295 and t1 <= -1)) }";
1327 map1 = isl_map_read_from_str(ctx, str);
1328 str = "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1329 map2 = isl_map_read_from_str(ctx, str);
1330 map1 = isl_map_gist(map1, map2);
1331 if (!map1)
1332 return -1;
1333 if (map1->n != 1)
1334 isl_die(ctx, isl_error_unknown, "expecting single disjunct",
1335 isl_map_free(map1); return -1);
1336 if (isl_basic_map_dim(map1->p[0], isl_dim_div) != 1)
1337 isl_die(ctx, isl_error_unknown, "expecting single div",
1338 isl_map_free(map1); return -1);
1339 isl_map_free(map1);
1340
1341 return 0;
1342 }
1343
1344 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
1345 {
1346 isl_set *set, *set2;
1347 int equal;
1348 int one;
1349
1350 set = isl_set_read_from_str(ctx, str);
1351 set = isl_set_coalesce(set);
1352 set2 = isl_set_read_from_str(ctx, str);
1353 equal = isl_set_is_equal(set, set2);
1354 one = set && set->n == 1;
1355 isl_set_free(set);
1356 isl_set_free(set2);
1357
1358 if (equal < 0)
1359 return -1;
1360 if (!equal)
1361 isl_die(ctx, isl_error_unknown,
1362 "coalesced set not equal to input", return -1);
1363 if (check_one && !one)
1364 isl_die(ctx, isl_error_unknown,
1365 "coalesced set should not be a union", return -1);
1366
1367 return 0;
1368 }
1369
1370 /* Inputs for coalescing tests with unbounded wrapping.
1371 * "str" is a string representation of the input set.
1372 * "single_disjunct" is set if we expect the result to consist of
1373 * a single disjunct.
1374 */
1375 struct {
1376 int single_disjunct;
1377 const char *str;
1378 } coalesce_unbounded_tests[] = {
1379 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1380 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1381 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1382 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1383 "-10 <= y <= 0}" },
1384 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1385 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1386 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1387 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1388 };
1389
1390 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1391 * option turned off.
1392 */
1393 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
1394 {
1395 int i;
1396 int r = 0;
1397 int bounded;
1398
1399 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
1400 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
1401
1402 for (i = 0; i < ARRAY_SIZE(coalesce_unbounded_tests); ++i) {
1403 const char *str = coalesce_unbounded_tests[i].str;
1404 int check_one = coalesce_unbounded_tests[i].single_disjunct;
1405 if (test_coalesce_set(ctx, str, check_one) >= 0)
1406 continue;
1407 r = -1;
1408 break;
1409 }
1410
1411 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
1412
1413 return r;
1414 }
1415
1416 /* Inputs for coalescing tests.
1417 * "str" is a string representation of the input set.
1418 * "single_disjunct" is set if we expect the result to consist of
1419 * a single disjunct.
1420 */
1421 struct {
1422 int single_disjunct;
1423 const char *str;
1424 } coalesce_tests[] = {
1425 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1426 "y >= x & x >= 2 & 5 >= y }" },
1427 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1428 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1429 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1430 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1431 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1432 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1433 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1434 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1435 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1436 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1437 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1438 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1439 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1440 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1441 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1442 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1443 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1444 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1445 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1446 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1447 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1448 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1449 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1450 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1451 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1452 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1453 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1454 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1455 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1456 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1457 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1458 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1459 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1460 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1461 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1462 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1463 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1464 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1465 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1466 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1467 "[o0, o1, o2, o3, o4, o5, o6]] : "
1468 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1469 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1470 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1471 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1472 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1473 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1474 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1475 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1476 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1477 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1478 "o6 >= i3 + i6 - o3 and M >= 0 and "
1479 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1480 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1481 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1482 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1483 "(o0 = 0 and M >= 2 and N >= 3) or "
1484 "(M = 0 and o0 = 0 and N >= 3) }" },
1485 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1486 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1487 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1488 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1489 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1490 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1491 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1492 "(y = 3 and x = 1) }" },
1493 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1494 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1495 "i1 <= M and i3 <= M and i4 <= M) or "
1496 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1497 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1498 "i4 <= -1 + M) }" },
1499 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1500 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1501 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1502 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1503 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1504 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1505 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1506 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1507 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1508 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1509 { 0, "{ [a, b] : exists e : 2e = a and "
1510 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1511 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1512 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1513 "j >= 1 and j' <= i + j - i' and i >= 1; "
1514 "[1, 1, 1, 1] }" },
1515 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1516 "[i,j] : exists a : j = 3a }" },
1517 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1518 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1519 "a >= 3) or "
1520 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1521 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1522 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1523 "c <= 6 + 8a and a >= 3; "
1524 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1525 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1526 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1527 "[x,0] : 3 <= x <= 4 }" },
1528 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1529 "[x,0] : 4 <= x <= 5 }" },
1530 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1531 "[x,0] : 3 <= x <= 5 }" },
1532 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1533 "[x,0] : 3 <= x <= 4 }" },
1534 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1535 "i1 <= 0; "
1536 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1537 { 1, "{ [0,0]; [1,1] }" },
1538 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1539 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1540 "ii <= k;"
1541 "[k, 0, k] : k <= 6 and k >= 1 }" },
1542 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1543 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1544 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1545 { 1, "[n] -> { [1] : n >= 0;"
1546 "[x] : exists (e0 = floor((x)/2): x >= 2 and "
1547 "2e0 >= -1 + x and 2e0 <= x and 2e0 <= n) }" },
1548 { 1, "[n] -> { [x, y] : exists (e0 = floor((x)/2), e1 = floor((y)/3): "
1549 "3e1 = y and x >= 2 and 2e0 >= -1 + x and "
1550 "2e0 <= x and 2e0 <= n);"
1551 "[1, y] : exists (e0 = floor((y)/3): 3e0 = y and "
1552 "n >= 0) }" },
1553 { 1, "[t1] -> { [i0] : (exists (e0 = floor((63t1)/64): "
1554 "128e0 >= -134 + 127t1 and t1 >= 2 and "
1555 "64e0 <= 63t1 and 64e0 >= -63 + 63t1)) or "
1556 "t1 = 1 }" },
1557 { 1, "{ [i, i] : exists (e0 = floor((1 + 2i)/3): 3e0 <= 2i and "
1558 "3e0 >= -1 + 2i and i <= 9 and i >= 1);"
1559 "[0, 0] }" },
1560 { 1, "{ [t1] : exists (e0 = floor((-11 + t1)/2): 2e0 = -11 + t1 and "
1561 "t1 >= 13 and t1 <= 16);"
1562 "[t1] : t1 <= 15 and t1 >= 12 }" },
1563 { 1, "{ [x,y] : x = 3y and 0 <= y <= 2; [-3,-1] }" },
1564 { 1, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-2] }" },
1565 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-2,-2] }" },
1566 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-1] }" },
1567 { 1, "{ [i] : exists j : i = 4 j and 0 <= i <= 100;"
1568 "[i] : exists j : 1 <= i <= 100 and i >= 4j + 1 and "
1569 "i <= 4j + 2 }" },
1570 { 1, "{ [c0] : (exists (e0 : c0 - 1 <= 3e0 <= c0)) or "
1571 "(exists (e0 : 3e0 = -2 + c0)) }" },
1572 { 0, "[n, b0, t0] -> "
1573 "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1574 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1575 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1576 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1577 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 >= 8 + n and "
1578 "3i4 <= -96 + 3t0 + i0 and 3i4 >= -95 - n + 3t0 + i0 and "
1579 "i8 >= -157 + i0 - 4i4 and i8 >= 0 and "
1580 "i8 <= -33 + i0 - 4i4 and 3i8 <= -91 + 4n - i0)) or "
1581 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1582 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1583 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1584 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 <= 7 + n and "
1585 "4i4 <= -3 + i0 and 3i4 <= -96 + 3t0 + i0 and "
1586 "3i4 >= -95 - n + 3t0 + i0 and i8 >= -157 + i0 - 4i4 and "
1587 "i8 >= 0 and i8 <= -4 + i0 - 3i4 and i8 <= -41 + i0));"
1588 "[i0, i1, i2, i3, 0, i5, i6, i7, i8, i9, i10, i11, i12] : "
1589 "(exists (e0 = floor((i8)/32): b0 = 0 and 32e0 = i8 and "
1590 "n <= 2147483647 and t0 <= 31 and t0 >= 0 and i0 >= 11 and "
1591 "i0 >= 96 - 3t0 and i0 <= 95 + n - 3t0 and i0 <= 7 + n and "
1592 "i8 >= -40 + i0 and i8 <= -10 + i0)) }" },
1593 { 0, "{ [i0, i1, i2] : "
1594 "(exists (e0, e1 = floor((i0)/32), e2 = floor((i1)/32): "
1595 "32e1 = i0 and 32e2 = i1 and i1 >= -31 + i0 and "
1596 "i1 <= 31 + i0 and i2 >= -30 + i0 and i2 >= -30 + i1 and "
1597 "32e0 >= -30 + i0 and 32e0 >= -30 + i1 and "
1598 "32e0 >= -31 + i2 and 32e0 <= 30 + i2 and 32e0 <= 31 + i1 and "
1599 "32e0 <= 31 + i0)) or "
1600 "i0 >= 0 }" },
1601 };
1602
1603 /* A specialized coalescing test case that would result
1604 * in a segmentation fault or a failed assertion in earlier versions of isl.
1605 */
1606 static int test_coalesce_special(struct isl_ctx *ctx)
1607 {
1608 const char *str;
1609 isl_map *map1, *map2;
1610
1611 str = "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1612 "[[S_L309_IN[] -> T11[]] -> ce_imag2[1, o1]] : "
1613 "(y = 201 and o1 <= 239 and o1 >= 212) or "
1614 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 198 and y >= 3 and "
1615 "o1 <= 239 and o1 >= 212)) or "
1616 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 201 and y >= 3 and "
1617 "o1 <= 241 and o1 >= 240));"
1618 "[S_L220_OUT[] -> T7[]] -> "
1619 "[[S_L309_IN[] -> T11[]] -> ce_imag2[0, o1]] : "
1620 "(y = 2 and o1 <= 241 and o1 >= 212) or "
1621 "(exists (e0 = [(-2 + y)/3]: 3e0 = -2 + y and y <= 200 and "
1622 "y >= 5 and o1 <= 241 and o1 >= 212)) }";
1623 map1 = isl_map_read_from_str(ctx, str);
1624 map1 = isl_map_align_divs(map1);
1625 map1 = isl_map_coalesce(map1);
1626 str = "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1627 "[[S_L309_IN[] -> T11[]] -> ce_imag2[o0, o1]] : "
1628 "exists (e0 = [(-1 - y + o0)/3]: 3e0 = -1 - y + o0 and "
1629 "y <= 201 and o0 <= 2 and o1 >= 212 and o1 <= 241 and "
1630 "o0 >= 3 - y and o0 <= -2 + y and o0 >= 0) }";
1631 map2 = isl_map_read_from_str(ctx, str);
1632 map2 = isl_map_union(map2, map1);
1633 map2 = isl_map_align_divs(map2);
1634 map2 = isl_map_coalesce(map2);
1635 isl_map_free(map2);
1636 if (!map2)
1637 return -1;
1638
1639 return 0;
1640 }
1641
1642 /* Test the functionality of isl_set_coalesce.
1643 * That is, check that the output is always equal to the input
1644 * and in some cases that the result consists of a single disjunct.
1645 */
1646 static int test_coalesce(struct isl_ctx *ctx)
1647 {
1648 int i;
1649
1650 for (i = 0; i < ARRAY_SIZE(coalesce_tests); ++i) {
1651 const char *str = coalesce_tests[i].str;
1652 int check_one = coalesce_tests[i].single_disjunct;
1653 if (test_coalesce_set(ctx, str, check_one) < 0)
1654 return -1;
1655 }
1656
1657 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1658 return -1;
1659 if (test_coalesce_special(ctx) < 0)
1660 return -1;
1661
1662 return 0;
1663 }
1664
1665 static int test_closure(isl_ctx *ctx)
1666 {
1667 const char *str;
1668 isl_set *dom;
1669 isl_map *up, *right;
1670 isl_map *map, *map2;
1671 int exact;
1672
1673 /* COCOA example 1 */
1674 map = isl_map_read_from_str(ctx,
1675 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1676 "1 <= i and i < n and 1 <= j and j < n or "
1677 "i2 = i + 1 and j2 = j - 1 and "
1678 "1 <= i and i < n and 2 <= j and j <= n }");
1679 map = isl_map_power(map, &exact);
1680 assert(exact);
1681 isl_map_free(map);
1682
1683 /* COCOA example 1 */
1684 map = isl_map_read_from_str(ctx,
1685 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1686 "1 <= i and i < n and 1 <= j and j < n or "
1687 "i2 = i + 1 and j2 = j - 1 and "
1688 "1 <= i and i < n and 2 <= j and j <= n }");
1689 map = isl_map_transitive_closure(map, &exact);
1690 assert(exact);
1691 map2 = isl_map_read_from_str(ctx,
1692 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1693 "1 <= i and i < n and 1 <= j and j <= n and "
1694 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1695 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1696 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1697 assert(isl_map_is_equal(map, map2));
1698 isl_map_free(map2);
1699 isl_map_free(map);
1700
1701 map = isl_map_read_from_str(ctx,
1702 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1703 " 0 <= y and y <= n }");
1704 map = isl_map_transitive_closure(map, &exact);
1705 map2 = isl_map_read_from_str(ctx,
1706 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1707 " 0 <= y and y <= n }");
1708 assert(isl_map_is_equal(map, map2));
1709 isl_map_free(map2);
1710 isl_map_free(map);
1711
1712 /* COCOA example 2 */
1713 map = isl_map_read_from_str(ctx,
1714 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1715 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1716 "i2 = i + 2 and j2 = j - 2 and "
1717 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1718 map = isl_map_transitive_closure(map, &exact);
1719 assert(exact);
1720 map2 = isl_map_read_from_str(ctx,
1721 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1722 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1723 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1724 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1725 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1726 assert(isl_map_is_equal(map, map2));
1727 isl_map_free(map);
1728 isl_map_free(map2);
1729
1730 /* COCOA Fig.2 left */
1731 map = isl_map_read_from_str(ctx,
1732 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1733 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1734 "j <= n or "
1735 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1736 "j <= 2 i - 3 and j <= n - 2 or "
1737 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1738 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1739 map = isl_map_transitive_closure(map, &exact);
1740 assert(exact);
1741 isl_map_free(map);
1742
1743 /* COCOA Fig.2 right */
1744 map = isl_map_read_from_str(ctx,
1745 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1746 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1747 "j <= n or "
1748 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1749 "j <= 2 i - 4 and j <= n - 3 or "
1750 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1751 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1752 map = isl_map_power(map, &exact);
1753 assert(exact);
1754 isl_map_free(map);
1755
1756 /* COCOA Fig.2 right */
1757 map = isl_map_read_from_str(ctx,
1758 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1759 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1760 "j <= n or "
1761 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1762 "j <= 2 i - 4 and j <= n - 3 or "
1763 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1764 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1765 map = isl_map_transitive_closure(map, &exact);
1766 assert(exact);
1767 map2 = isl_map_read_from_str(ctx,
1768 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1769 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1770 "j <= n and 3 + i + 2 j <= 3 n and "
1771 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1772 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1773 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1774 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1775 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1776 assert(isl_map_is_equal(map, map2));
1777 isl_map_free(map2);
1778 isl_map_free(map);
1779
1780 /* COCOA Fig.1 right */
1781 dom = isl_set_read_from_str(ctx,
1782 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1783 "2 x - 3 y + 3 >= 0 }");
1784 right = isl_map_read_from_str(ctx,
1785 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1786 up = isl_map_read_from_str(ctx,
1787 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1788 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1789 right = isl_map_intersect_range(right, isl_set_copy(dom));
1790 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1791 up = isl_map_intersect_range(up, dom);
1792 map = isl_map_union(up, right);
1793 map = isl_map_transitive_closure(map, &exact);
1794 assert(exact);
1795 map2 = isl_map_read_from_str(ctx,
1796 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1797 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1798 assert(isl_map_is_equal(map, map2));
1799 isl_map_free(map2);
1800 isl_map_free(map);
1801
1802 /* COCOA Theorem 1 counter example */
1803 map = isl_map_read_from_str(ctx,
1804 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1805 "i2 = 1 and j2 = j or "
1806 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1807 map = isl_map_transitive_closure(map, &exact);
1808 assert(exact);
1809 isl_map_free(map);
1810
1811 map = isl_map_read_from_str(ctx,
1812 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1813 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1814 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1815 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1816 map = isl_map_transitive_closure(map, &exact);
1817 assert(exact);
1818 isl_map_free(map);
1819
1820 /* Kelly et al 1996, fig 12 */
1821 map = isl_map_read_from_str(ctx,
1822 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1823 "1 <= i,j,j+1 <= n or "
1824 "j = n and j2 = 1 and i2 = i + 1 and "
1825 "1 <= i,i+1 <= n }");
1826 map = isl_map_transitive_closure(map, &exact);
1827 assert(exact);
1828 map2 = isl_map_read_from_str(ctx,
1829 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1830 "1 <= i <= n and i = i2 or "
1831 "1 <= i < i2 <= n and 1 <= j <= n and "
1832 "1 <= j2 <= n }");
1833 assert(isl_map_is_equal(map, map2));
1834 isl_map_free(map2);
1835 isl_map_free(map);
1836
1837 /* Omega's closure4 */
1838 map = isl_map_read_from_str(ctx,
1839 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1840 "1 <= x,y <= 10 or "
1841 "x2 = x + 1 and y2 = y and "
1842 "1 <= x <= 20 && 5 <= y <= 15 }");
1843 map = isl_map_transitive_closure(map, &exact);
1844 assert(exact);
1845 isl_map_free(map);
1846
1847 map = isl_map_read_from_str(ctx,
1848 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1849 map = isl_map_transitive_closure(map, &exact);
1850 assert(!exact);
1851 map2 = isl_map_read_from_str(ctx,
1852 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1853 assert(isl_map_is_equal(map, map2));
1854 isl_map_free(map);
1855 isl_map_free(map2);
1856
1857 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1858 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1859 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1860 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1861 map = isl_map_read_from_str(ctx, str);
1862 map = isl_map_transitive_closure(map, &exact);
1863 assert(exact);
1864 map2 = isl_map_read_from_str(ctx, str);
1865 assert(isl_map_is_equal(map, map2));
1866 isl_map_free(map);
1867 isl_map_free(map2);
1868
1869 str = "{[0] -> [1]; [2] -> [3]}";
1870 map = isl_map_read_from_str(ctx, str);
1871 map = isl_map_transitive_closure(map, &exact);
1872 assert(exact);
1873 map2 = isl_map_read_from_str(ctx, str);
1874 assert(isl_map_is_equal(map, map2));
1875 isl_map_free(map);
1876 isl_map_free(map2);
1877
1878 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1879 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1880 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1881 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1882 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1883 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1884 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1885 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1886 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1887 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1888 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1889 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1890 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1891 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1892 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1893 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1894 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1895 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1896 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1897 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1898 map = isl_map_read_from_str(ctx, str);
1899 map = isl_map_transitive_closure(map, NULL);
1900 assert(map);
1901 isl_map_free(map);
1902
1903 return 0;
1904 }
1905
1906 static int test_lex(struct isl_ctx *ctx)
1907 {
1908 isl_space *dim;
1909 isl_map *map;
1910 int empty;
1911
1912 dim = isl_space_set_alloc(ctx, 0, 0);
1913 map = isl_map_lex_le(dim);
1914 empty = isl_map_is_empty(map);
1915 isl_map_free(map);
1916
1917 if (empty < 0)
1918 return -1;
1919 if (empty)
1920 isl_die(ctx, isl_error_unknown,
1921 "expecting non-empty result", return -1);
1922
1923 return 0;
1924 }
1925
1926 static int test_lexmin(struct isl_ctx *ctx)
1927 {
1928 int equal;
1929 const char *str;
1930 isl_basic_map *bmap;
1931 isl_map *map, *map2;
1932 isl_set *set;
1933 isl_set *set2;
1934 isl_pw_multi_aff *pma;
1935
1936 str = "[p0, p1] -> { [] -> [] : "
1937 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1938 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1939 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1940 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1941 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1942 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1943 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1944 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1945 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1946 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1947 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1948 map = isl_map_read_from_str(ctx, str);
1949 map = isl_map_lexmin(map);
1950 isl_map_free(map);
1951
1952 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1953 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1954 set = isl_set_read_from_str(ctx, str);
1955 set = isl_set_lexmax(set);
1956 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1957 set2 = isl_set_read_from_str(ctx, str);
1958 set = isl_set_intersect(set, set2);
1959 assert(!isl_set_is_empty(set));
1960 isl_set_free(set);
1961
1962 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1963 map = isl_map_read_from_str(ctx, str);
1964 map = isl_map_lexmin(map);
1965 str = "{ [x] -> [5] : 6 <= x <= 8; "
1966 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1967 map2 = isl_map_read_from_str(ctx, str);
1968 assert(isl_map_is_equal(map, map2));
1969 isl_map_free(map);
1970 isl_map_free(map2);
1971
1972 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1973 map = isl_map_read_from_str(ctx, str);
1974 map2 = isl_map_copy(map);
1975 map = isl_map_lexmin(map);
1976 assert(isl_map_is_equal(map, map2));
1977 isl_map_free(map);
1978 isl_map_free(map2);
1979
1980 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1981 map = isl_map_read_from_str(ctx, str);
1982 map = isl_map_lexmin(map);
1983 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1984 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1985 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1986 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1987 map2 = isl_map_read_from_str(ctx, str);
1988 assert(isl_map_is_equal(map, map2));
1989 isl_map_free(map);
1990 isl_map_free(map2);
1991
1992 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1993 " 8i' <= i and 8i' >= -7 + i }";
1994 bmap = isl_basic_map_read_from_str(ctx, str);
1995 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1996 map2 = isl_map_from_pw_multi_aff(pma);
1997 map = isl_map_from_basic_map(bmap);
1998 assert(isl_map_is_equal(map, map2));
1999 isl_map_free(map);
2000 isl_map_free(map2);
2001
2002 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
2003 map = isl_map_read_from_str(ctx, str);
2004 map = isl_map_lexmin(map);
2005 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
2006 map2 = isl_map_read_from_str(ctx, str);
2007 assert(isl_map_is_equal(map, map2));
2008 isl_map_free(map);
2009 isl_map_free(map2);
2010
2011 /* Check that empty pieces are properly combined. */
2012 str = "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
2013 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
2014 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
2015 map = isl_map_read_from_str(ctx, str);
2016 map = isl_map_lexmin(map);
2017 str = "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
2018 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
2019 "x >= 4 }";
2020 map2 = isl_map_read_from_str(ctx, str);
2021 assert(isl_map_is_equal(map, map2));
2022 isl_map_free(map);
2023 isl_map_free(map2);
2024
2025 str = "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2026 " 8i' <= i and 8i' >= -7 + i }";
2027 set = isl_set_read_from_str(ctx, str);
2028 pma = isl_set_lexmin_pw_multi_aff(isl_set_copy(set));
2029 set2 = isl_set_from_pw_multi_aff(pma);
2030 equal = isl_set_is_equal(set, set2);
2031 isl_set_free(set);
2032 isl_set_free(set2);
2033 if (equal < 0)
2034 return -1;
2035 if (!equal)
2036 isl_die(ctx, isl_error_unknown,
2037 "unexpected difference between set and "
2038 "piecewise affine expression", return -1);
2039
2040 return 0;
2041 }
2042
2043 /* Check that isl_set_min_val and isl_set_max_val compute the correct
2044 * result on non-convex inputs.
2045 */
2046 static int test_min(struct isl_ctx *ctx)
2047 {
2048 isl_set *set;
2049 isl_aff *aff;
2050 isl_val *val;
2051 int min_ok, max_ok;
2052
2053 set = isl_set_read_from_str(ctx, "{ [-1]; [1] }");
2054 aff = isl_aff_read_from_str(ctx, "{ [x] -> [x] }");
2055 val = isl_set_min_val(set, aff);
2056 min_ok = isl_val_is_negone(val);
2057 isl_val_free(val);
2058 val = isl_set_max_val(set, aff);
2059 max_ok = isl_val_is_one(val);
2060 isl_val_free(val);
2061 isl_aff_free(aff);
2062 isl_set_free(set);
2063
2064 if (min_ok < 0 || max_ok < 0)
2065 return -1;
2066 if (!min_ok)
2067 isl_die(ctx, isl_error_unknown,
2068 "unexpected minimum", return -1);
2069 if (!max_ok)
2070 isl_die(ctx, isl_error_unknown,
2071 "unexpected maximum", return -1);
2072
2073 return 0;
2074 }
2075
2076 struct must_may {
2077 isl_map *must;
2078 isl_map *may;
2079 };
2080
2081 static isl_stat collect_must_may(__isl_take isl_map *dep, int must,
2082 void *dep_user, void *user)
2083 {
2084 struct must_may *mm = (struct must_may *)user;
2085
2086 if (must)
2087 mm->must = isl_map_union(mm->must, dep);
2088 else
2089 mm->may = isl_map_union(mm->may, dep);
2090
2091 return isl_stat_ok;
2092 }
2093
2094 static int common_space(void *first, void *second)
2095 {
2096 int depth = *(int *)first;
2097 return 2 * depth;
2098 }
2099
2100 static int map_is_equal(__isl_keep isl_map *map, const char *str)
2101 {
2102 isl_map *map2;
2103 int equal;
2104
2105 if (!map)
2106 return -1;
2107
2108 map2 = isl_map_read_from_str(map->ctx, str);
2109 equal = isl_map_is_equal(map, map2);
2110 isl_map_free(map2);
2111
2112 return equal;
2113 }
2114
2115 static int map_check_equal(__isl_keep isl_map *map, const char *str)
2116 {
2117 int equal;
2118
2119 equal = map_is_equal(map, str);
2120 if (equal < 0)
2121 return -1;
2122 if (!equal)
2123 isl_die(isl_map_get_ctx(map), isl_error_unknown,
2124 "result not as expected", return -1);
2125 return 0;
2126 }
2127
2128 static int test_dep(struct isl_ctx *ctx)
2129 {
2130 const char *str;
2131 isl_space *dim;
2132 isl_map *map;
2133 isl_access_info *ai;
2134 isl_flow *flow;
2135 int depth;
2136 struct must_may mm;
2137
2138 depth = 3;
2139
2140 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2141 map = isl_map_read_from_str(ctx, str);
2142 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2143
2144 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2145 map = isl_map_read_from_str(ctx, str);
2146 ai = isl_access_info_add_source(ai, map, 1, &depth);
2147
2148 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2149 map = isl_map_read_from_str(ctx, str);
2150 ai = isl_access_info_add_source(ai, map, 1, &depth);
2151
2152 flow = isl_access_info_compute_flow(ai);
2153 dim = isl_space_alloc(ctx, 0, 3, 3);
2154 mm.must = isl_map_empty(isl_space_copy(dim));
2155 mm.may = isl_map_empty(dim);
2156
2157 isl_flow_foreach(flow, collect_must_may, &mm);
2158
2159 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
2160 " [1,10,0] -> [2,5,0] }";
2161 assert(map_is_equal(mm.must, str));
2162 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2163 assert(map_is_equal(mm.may, str));
2164
2165 isl_map_free(mm.must);
2166 isl_map_free(mm.may);
2167 isl_flow_free(flow);
2168
2169
2170 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2171 map = isl_map_read_from_str(ctx, str);
2172 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2173
2174 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2175 map = isl_map_read_from_str(ctx, str);
2176 ai = isl_access_info_add_source(ai, map, 1, &depth);
2177
2178 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2179 map = isl_map_read_from_str(ctx, str);
2180 ai = isl_access_info_add_source(ai, map, 0, &depth);
2181
2182 flow = isl_access_info_compute_flow(ai);
2183 dim = isl_space_alloc(ctx, 0, 3, 3);
2184 mm.must = isl_map_empty(isl_space_copy(dim));
2185 mm.may = isl_map_empty(dim);
2186
2187 isl_flow_foreach(flow, collect_must_may, &mm);
2188
2189 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2190 assert(map_is_equal(mm.must, str));
2191 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2192 assert(map_is_equal(mm.may, str));
2193
2194 isl_map_free(mm.must);
2195 isl_map_free(mm.may);
2196 isl_flow_free(flow);
2197
2198
2199 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2200 map = isl_map_read_from_str(ctx, str);
2201 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2202
2203 str = "{ [0,i,0] -> [i] : 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 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2208 map = isl_map_read_from_str(ctx, str);
2209 ai = isl_access_info_add_source(ai, map, 0, &depth);
2210
2211 flow = isl_access_info_compute_flow(ai);
2212 dim = isl_space_alloc(ctx, 0, 3, 3);
2213 mm.must = isl_map_empty(isl_space_copy(dim));
2214 mm.may = isl_map_empty(dim);
2215
2216 isl_flow_foreach(flow, collect_must_may, &mm);
2217
2218 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2219 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2220 assert(map_is_equal(mm.may, str));
2221 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2222 assert(map_is_equal(mm.must, str));
2223
2224 isl_map_free(mm.must);
2225 isl_map_free(mm.may);
2226 isl_flow_free(flow);
2227
2228
2229 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2230 map = isl_map_read_from_str(ctx, str);
2231 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2232
2233 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2234 map = isl_map_read_from_str(ctx, str);
2235 ai = isl_access_info_add_source(ai, map, 0, &depth);
2236
2237 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2238 map = isl_map_read_from_str(ctx, str);
2239 ai = isl_access_info_add_source(ai, map, 0, &depth);
2240
2241 flow = isl_access_info_compute_flow(ai);
2242 dim = isl_space_alloc(ctx, 0, 3, 3);
2243 mm.must = isl_map_empty(isl_space_copy(dim));
2244 mm.may = isl_map_empty(dim);
2245
2246 isl_flow_foreach(flow, collect_must_may, &mm);
2247
2248 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2249 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2250 assert(map_is_equal(mm.may, str));
2251 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2252 assert(map_is_equal(mm.must, str));
2253
2254 isl_map_free(mm.must);
2255 isl_map_free(mm.may);
2256 isl_flow_free(flow);
2257
2258
2259 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2260 map = isl_map_read_from_str(ctx, str);
2261 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2262
2263 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2264 map = isl_map_read_from_str(ctx, str);
2265 ai = isl_access_info_add_source(ai, map, 0, &depth);
2266
2267 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2268 map = isl_map_read_from_str(ctx, str);
2269 ai = isl_access_info_add_source(ai, map, 0, &depth);
2270
2271 flow = isl_access_info_compute_flow(ai);
2272 dim = isl_space_alloc(ctx, 0, 3, 3);
2273 mm.must = isl_map_empty(isl_space_copy(dim));
2274 mm.may = isl_map_empty(dim);
2275
2276 isl_flow_foreach(flow, collect_must_may, &mm);
2277
2278 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2279 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2280 assert(map_is_equal(mm.may, str));
2281 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2282 assert(map_is_equal(mm.must, str));
2283
2284 isl_map_free(mm.must);
2285 isl_map_free(mm.may);
2286 isl_flow_free(flow);
2287
2288
2289 depth = 5;
2290
2291 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2292 map = isl_map_read_from_str(ctx, str);
2293 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
2294
2295 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2296 map = isl_map_read_from_str(ctx, str);
2297 ai = isl_access_info_add_source(ai, map, 1, &depth);
2298
2299 flow = isl_access_info_compute_flow(ai);
2300 dim = isl_space_alloc(ctx, 0, 5, 5);
2301 mm.must = isl_map_empty(isl_space_copy(dim));
2302 mm.may = isl_map_empty(dim);
2303
2304 isl_flow_foreach(flow, collect_must_may, &mm);
2305
2306 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2307 assert(map_is_equal(mm.must, str));
2308 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2309 assert(map_is_equal(mm.may, str));
2310
2311 isl_map_free(mm.must);
2312 isl_map_free(mm.may);
2313 isl_flow_free(flow);
2314
2315 return 0;
2316 }
2317
2318 /* Check that the dependence analysis proceeds without errors.
2319 * Earlier versions of isl would break down during the analysis
2320 * due to the use of the wrong spaces.
2321 */
2322 static int test_flow(isl_ctx *ctx)
2323 {
2324 const char *str;
2325 isl_union_map *access, *schedule;
2326 isl_union_map *must_dep, *may_dep;
2327 int r;
2328
2329 str = "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2330 access = isl_union_map_read_from_str(ctx, str);
2331 str = "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2332 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2333 "S2[] -> [1,0,0,0]; "
2334 "S3[] -> [-1,0,0,0] }";
2335 schedule = isl_union_map_read_from_str(ctx, str);
2336 r = isl_union_map_compute_flow(access, isl_union_map_copy(access),
2337 isl_union_map_copy(access), schedule,
2338 &must_dep, &may_dep, NULL, NULL);
2339 isl_union_map_free(may_dep);
2340 isl_union_map_free(must_dep);
2341
2342 return r;
2343 }
2344
2345 struct {
2346 const char *map;
2347 int sv;
2348 } sv_tests[] = {
2349 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2350 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2351 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2352 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2353 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2354 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2355 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2356 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2357 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2358 };
2359
2360 int test_sv(isl_ctx *ctx)
2361 {
2362 isl_union_map *umap;
2363 int i;
2364 int sv;
2365
2366 for (i = 0; i < ARRAY_SIZE(sv_tests); ++i) {
2367 umap = isl_union_map_read_from_str(ctx, sv_tests[i].map);
2368 sv = isl_union_map_is_single_valued(umap);
2369 isl_union_map_free(umap);
2370 if (sv < 0)
2371 return -1;
2372 if (sv_tests[i].sv && !sv)
2373 isl_die(ctx, isl_error_internal,
2374 "map not detected as single valued", return -1);
2375 if (!sv_tests[i].sv && sv)
2376 isl_die(ctx, isl_error_internal,
2377 "map detected as single valued", return -1);
2378 }
2379
2380 return 0;
2381 }
2382
2383 struct {
2384 const char *str;
2385 int bijective;
2386 } bijective_tests[] = {
2387 { "[N,M]->{[i,j] -> [i]}", 0 },
2388 { "[N,M]->{[i,j] -> [i] : j=i}", 1 },
2389 { "[N,M]->{[i,j] -> [i] : j=0}", 1 },
2390 { "[N,M]->{[i,j] -> [i] : j=N}", 1 },
2391 { "[N,M]->{[i,j] -> [j,i]}", 1 },
2392 { "[N,M]->{[i,j] -> [i+j]}", 0 },
2393 { "[N,M]->{[i,j] -> []}", 0 },
2394 { "[N,M]->{[i,j] -> [i,j,N]}", 1 },
2395 { "[N,M]->{[i,j] -> [2i]}", 0 },
2396 { "[N,M]->{[i,j] -> [i,i]}", 0 },
2397 { "[N,M]->{[i,j] -> [2i,i]}", 0 },
2398 { "[N,M]->{[i,j] -> [2i,j]}", 1 },
2399 { "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1 },
2400 };
2401
2402 static int test_bijective(struct isl_ctx *ctx)
2403 {
2404 isl_map *map;
2405 int i;
2406 int bijective;
2407
2408 for (i = 0; i < ARRAY_SIZE(bijective_tests); ++i) {
2409 map = isl_map_read_from_str(ctx, bijective_tests[i].str);
2410 bijective = isl_map_is_bijective(map);
2411 isl_map_free(map);
2412 if (bijective < 0)
2413 return -1;
2414 if (bijective_tests[i].bijective && !bijective)
2415 isl_die(ctx, isl_error_internal,
2416 "map not detected as bijective", return -1);
2417 if (!bijective_tests[i].bijective && bijective)
2418 isl_die(ctx, isl_error_internal,
2419 "map detected as bijective", return -1);
2420 }
2421
2422 return 0;
2423 }
2424
2425 /* Inputs for isl_pw_qpolynomial_gist tests.
2426 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2427 */
2428 struct {
2429 const char *pwqp;
2430 const char *set;
2431 const char *gist;
2432 } pwqp_gist_tests[] = {
2433 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2434 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2435 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2436 "{ [i] -> -1/2 + 1/2 * i }" },
2437 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2438 };
2439
2440 static int test_pwqp(struct isl_ctx *ctx)
2441 {
2442 int i;
2443 const char *str;
2444 isl_set *set;
2445 isl_pw_qpolynomial *pwqp1, *pwqp2;
2446 int equal;
2447
2448 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2449 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2450
2451 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
2452 isl_dim_in, 1, 1);
2453
2454 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2455 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2456
2457 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2458
2459 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2460
2461 isl_pw_qpolynomial_free(pwqp1);
2462
2463 for (i = 0; i < ARRAY_SIZE(pwqp_gist_tests); ++i) {
2464 str = pwqp_gist_tests[i].pwqp;
2465 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2466 str = pwqp_gist_tests[i].set;
2467 set = isl_set_read_from_str(ctx, str);
2468 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2469 str = pwqp_gist_tests[i].gist;
2470 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2471 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2472 equal = isl_pw_qpolynomial_is_zero(pwqp1);
2473 isl_pw_qpolynomial_free(pwqp1);
2474
2475 if (equal < 0)
2476 return -1;
2477 if (!equal)
2478 isl_die(ctx, isl_error_unknown,
2479 "unexpected result", return -1);
2480 }
2481
2482 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
2483 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2484 str = "{ [i] -> ([(2 * [i/2])/5]) }";
2485 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2486
2487 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2488
2489 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2490
2491 isl_pw_qpolynomial_free(pwqp1);
2492
2493 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
2494 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2495 str = "{ [x] -> x }";
2496 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2497
2498 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2499
2500 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2501
2502 isl_pw_qpolynomial_free(pwqp1);
2503
2504 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2505 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2506 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2507 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
2508 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2509 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2510 isl_pw_qpolynomial_free(pwqp1);
2511
2512 str = "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2513 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2514 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2515 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2516 set = isl_set_read_from_str(ctx, "{ [a,b,a] }");
2517 pwqp1 = isl_pw_qpolynomial_intersect_domain(pwqp1, set);
2518 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2519 isl_pw_qpolynomial_free(pwqp1);
2520 isl_pw_qpolynomial_free(pwqp2);
2521 if (equal < 0)
2522 return -1;
2523 if (!equal)
2524 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2525
2526 str = "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2527 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2528 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2529 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2530 pwqp1 = isl_pw_qpolynomial_fix_val(pwqp1, isl_dim_set, 1,
2531 isl_val_one(ctx));
2532 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2533 isl_pw_qpolynomial_free(pwqp1);
2534 isl_pw_qpolynomial_free(pwqp2);
2535 if (equal < 0)
2536 return -1;
2537 if (!equal)
2538 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2539
2540 return 0;
2541 }
2542
2543 static int test_split_periods(isl_ctx *ctx)
2544 {
2545 const char *str;
2546 isl_pw_qpolynomial *pwqp;
2547
2548 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2549 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2550 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2551 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2552
2553 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
2554
2555 isl_pw_qpolynomial_free(pwqp);
2556
2557 if (!pwqp)
2558 return -1;
2559
2560 return 0;
2561 }
2562
2563 static int test_union(isl_ctx *ctx)
2564 {
2565 const char *str;
2566 isl_union_set *uset1, *uset2;
2567 isl_union_map *umap1, *umap2;
2568 int equal;
2569
2570 str = "{ [i] : 0 <= i <= 1 }";
2571 uset1 = isl_union_set_read_from_str(ctx, str);
2572 str = "{ [1] -> [0] }";
2573 umap1 = isl_union_map_read_from_str(ctx, str);
2574
2575 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
2576 equal = isl_union_map_is_equal(umap1, umap2);
2577
2578 isl_union_map_free(umap1);
2579 isl_union_map_free(umap2);
2580
2581 if (equal < 0)
2582 return -1;
2583 if (!equal)
2584 isl_die(ctx, isl_error_unknown, "union maps not equal",
2585 return -1);
2586
2587 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2588 umap1 = isl_union_map_read_from_str(ctx, str);
2589 str = "{ A[i]; B[i] }";
2590 uset1 = isl_union_set_read_from_str(ctx, str);
2591
2592 uset2 = isl_union_map_domain(umap1);
2593
2594 equal = isl_union_set_is_equal(uset1, uset2);
2595
2596 isl_union_set_free(uset1);
2597 isl_union_set_free(uset2);
2598
2599 if (equal < 0)
2600 return -1;
2601 if (!equal)
2602 isl_die(ctx, isl_error_unknown, "union sets not equal",
2603 return -1);
2604
2605 return 0;
2606 }
2607
2608 /* Check that computing a bound of a non-zero polynomial over an unbounded
2609 * domain does not produce a rational value.
2610 * In particular, check that the upper bound is infinity.
2611 */
2612 static int test_bound_unbounded_domain(isl_ctx *ctx)
2613 {
2614 const char *str;
2615 isl_pw_qpolynomial *pwqp;
2616 isl_pw_qpolynomial_fold *pwf, *pwf2;
2617 isl_bool equal;
2618
2619 str = "{ [m,n] -> -m * n }";
2620 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2621 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2622 str = "{ infty }";
2623 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2624 pwf2 = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2625 equal = isl_pw_qpolynomial_fold_plain_is_equal(pwf, pwf2);
2626 isl_pw_qpolynomial_fold_free(pwf);
2627 isl_pw_qpolynomial_fold_free(pwf2);
2628
2629 if (equal < 0)
2630 return -1;
2631 if (!equal)
2632 isl_die(ctx, isl_error_unknown,
2633 "expecting infinite polynomial bound", return -1);
2634
2635 return 0;
2636 }
2637
2638 static int test_bound(isl_ctx *ctx)
2639 {
2640 const char *str;
2641 unsigned dim;
2642 isl_pw_qpolynomial *pwqp;
2643 isl_pw_qpolynomial_fold *pwf;
2644
2645 if (test_bound_unbounded_domain(ctx) < 0)
2646 return -1;
2647
2648 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
2649 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2650 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2651 dim = isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in);
2652 isl_pw_qpolynomial_fold_free(pwf);
2653 if (dim != 4)
2654 isl_die(ctx, isl_error_unknown, "unexpected input dimension",
2655 return -1);
2656
2657 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2658 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2659 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2660 dim = isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in);
2661 isl_pw_qpolynomial_fold_free(pwf);
2662 if (dim != 1)
2663 isl_die(ctx, isl_error_unknown, "unexpected input dimension",
2664 return -1);
2665
2666 return 0;
2667 }
2668
2669 static int test_lift(isl_ctx *ctx)
2670 {
2671 const char *str;
2672 isl_basic_map *bmap;
2673 isl_basic_set *bset;
2674
2675 str = "{ [i0] : exists e0 : i0 = 4e0 }";
2676 bset = isl_basic_set_read_from_str(ctx, str);
2677 bset = isl_basic_set_lift(bset);
2678 bmap = isl_basic_map_from_range(bset);
2679 bset = isl_basic_map_domain(bmap);
2680 isl_basic_set_free(bset);
2681
2682 return 0;
2683 }
2684
2685 struct {
2686 const char *set1;
2687 const char *set2;
2688 int subset;
2689 } subset_tests[] = {
2690 { "{ [112, 0] }",
2691 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2692 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2693 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2694 { "{ [65] }",
2695 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2696 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2697 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2698 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2699 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2700 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2701 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2702 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2703 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2704 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2705 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2706 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2707 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2708 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2709 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2710 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2711 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2712 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2713 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2714 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2715 "4e0 <= -57 + i0 + i1)) or "
2716 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2717 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2718 "4e0 >= -61 + i0 + i1)) or "
2719 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2720 };
2721
2722 static int test_subset(isl_ctx *ctx)
2723 {
2724 int i;
2725 isl_set *set1, *set2;
2726 int subset;
2727
2728 for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
2729 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
2730 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
2731 subset = isl_set_is_subset(set1, set2);
2732 isl_set_free(set1);
2733 isl_set_free(set2);
2734 if (subset < 0)
2735 return -1;
2736 if (subset != subset_tests[i].subset)
2737 isl_die(ctx, isl_error_unknown,
2738 "incorrect subset result", return -1);
2739 }
2740
2741 return 0;
2742 }
2743
2744 struct {
2745 const char *minuend;
2746 const char *subtrahend;
2747 const char *difference;
2748 } subtract_domain_tests[] = {
2749 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2750 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2751 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2752 };
2753
2754 static int test_subtract(isl_ctx *ctx)
2755 {
2756 int i;
2757 isl_union_map *umap1, *umap2;
2758 isl_union_pw_multi_aff *upma1, *upma2;
2759 isl_union_set *uset;
2760 int equal;
2761
2762 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2763 umap1 = isl_union_map_read_from_str(ctx,
2764 subtract_domain_tests[i].minuend);
2765 uset = isl_union_set_read_from_str(ctx,
2766 subtract_domain_tests[i].subtrahend);
2767 umap2 = isl_union_map_read_from_str(ctx,
2768 subtract_domain_tests[i].difference);
2769 umap1 = isl_union_map_subtract_domain(umap1, uset);
2770 equal = isl_union_map_is_equal(umap1, umap2);
2771 isl_union_map_free(umap1);
2772 isl_union_map_free(umap2);
2773 if (equal < 0)
2774 return -1;
2775 if (!equal)
2776 isl_die(ctx, isl_error_unknown,
2777 "incorrect subtract domain result", return -1);
2778 }
2779
2780 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2781 upma1 = isl_union_pw_multi_aff_read_from_str(ctx,
2782 subtract_domain_tests[i].minuend);
2783 uset = isl_union_set_read_from_str(ctx,
2784 subtract_domain_tests[i].subtrahend);
2785 upma2 = isl_union_pw_multi_aff_read_from_str(ctx,
2786 subtract_domain_tests[i].difference);
2787 upma1 = isl_union_pw_multi_aff_subtract_domain(upma1, uset);
2788 equal = isl_union_pw_multi_aff_plain_is_equal(upma1, upma2);
2789 isl_union_pw_multi_aff_free(upma1);
2790 isl_union_pw_multi_aff_free(upma2);
2791 if (equal < 0)
2792 return -1;
2793 if (!equal)
2794 isl_die(ctx, isl_error_unknown,
2795 "incorrect subtract domain result", return -1);
2796 }
2797
2798 return 0;
2799 }
2800
2801 int test_factorize(isl_ctx *ctx)
2802 {
2803 const char *str;
2804 isl_basic_set *bset;
2805 isl_factorizer *f;
2806
2807 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2808 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2809 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2810 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2811 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2812 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2813 "3i5 >= -2i0 - i2 + 3i4 }";
2814 bset = isl_basic_set_read_from_str(ctx, str);
2815 f = isl_basic_set_factorizer(bset);
2816 isl_basic_set_free(bset);
2817 isl_factorizer_free(f);
2818 if (!f)
2819 isl_die(ctx, isl_error_unknown,
2820 "failed to construct factorizer", return -1);
2821
2822 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2823 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2824 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2825 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2826 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2827 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2828 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2829 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2830 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2831 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2832 bset = isl_basic_set_read_from_str(ctx, str);
2833 f = isl_basic_set_factorizer(bset);
2834 isl_basic_set_free(bset);
2835 isl_factorizer_free(f);
2836 if (!f)
2837 isl_die(ctx, isl_error_unknown,
2838 "failed to construct factorizer", return -1);
2839
2840 return 0;
2841 }
2842
2843 static isl_stat check_injective(__isl_take isl_map *map, void *user)
2844 {
2845 int *injective = user;
2846
2847 *injective = isl_map_is_injective(map);
2848 isl_map_free(map);
2849
2850 if (*injective < 0 || !*injective)
2851 return isl_stat_error;
2852
2853 return isl_stat_ok;
2854 }
2855
2856 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2857 const char *r, const char *s, int tilable, int parallel)
2858 {
2859 int i;
2860 isl_union_set *D;
2861 isl_union_map *W, *R, *S;
2862 isl_union_map *empty;
2863 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2864 isl_union_map *validity, *proximity, *coincidence;
2865 isl_union_map *schedule;
2866 isl_union_map *test;
2867 isl_union_set *delta;
2868 isl_union_set *domain;
2869 isl_set *delta_set;
2870 isl_set *slice;
2871 isl_set *origin;
2872 isl_schedule_constraints *sc;
2873 isl_schedule *sched;
2874 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2875
2876 D = isl_union_set_read_from_str(ctx, d);
2877 W = isl_union_map_read_from_str(ctx, w);
2878 R = isl_union_map_read_from_str(ctx, r);
2879 S = isl_union_map_read_from_str(ctx, s);
2880
2881 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2882 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2883
2884 empty = isl_union_map_empty(isl_union_map_get_space(S));
2885 isl_union_map_compute_flow(isl_union_map_copy(R),
2886 isl_union_map_copy(W), empty,
2887 isl_union_map_copy(S),
2888 &dep_raw, NULL, NULL, NULL);
2889 isl_union_map_compute_flow(isl_union_map_copy(W),
2890 isl_union_map_copy(W),
2891 isl_union_map_copy(R),
2892 isl_union_map_copy(S),
2893 &dep_waw, &dep_war, NULL, NULL);
2894
2895 dep = isl_union_map_union(dep_waw, dep_war);
2896 dep = isl_union_map_union(dep, dep_raw);
2897 validity = isl_union_map_copy(dep);
2898 coincidence = isl_union_map_copy(dep);
2899 proximity = isl_union_map_copy(dep);
2900
2901 sc = isl_schedule_constraints_on_domain(isl_union_set_copy(D));
2902 sc = isl_schedule_constraints_set_validity(sc, validity);
2903 sc = isl_schedule_constraints_set_coincidence(sc, coincidence);
2904 sc = isl_schedule_constraints_set_proximity(sc, proximity);
2905 sched = isl_schedule_constraints_compute_schedule(sc);
2906 schedule = isl_schedule_get_map(sched);
2907 isl_schedule_free(sched);
2908 isl_union_map_free(W);
2909 isl_union_map_free(R);
2910 isl_union_map_free(S);
2911
2912 is_injection = 1;
2913 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2914
2915 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2916 is_complete = isl_union_set_is_subset(D, domain);
2917 isl_union_set_free(D);
2918 isl_union_set_free(domain);
2919
2920 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2921 test = isl_union_map_apply_range(test, dep);
2922 test = isl_union_map_apply_range(test, schedule);
2923
2924 delta = isl_union_map_deltas(test);
2925 if (isl_union_set_n_set(delta) == 0) {
2926 is_tilable = 1;
2927 is_parallel = 1;
2928 is_nonneg = 1;
2929 isl_union_set_free(delta);
2930 } else {
2931 delta_set = isl_set_from_union_set(delta);
2932
2933 slice = isl_set_universe(isl_set_get_space(delta_set));
2934 for (i = 0; i < tilable; ++i)
2935 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2936 is_tilable = isl_set_is_subset(delta_set, slice);
2937 isl_set_free(slice);
2938
2939 slice = isl_set_universe(isl_set_get_space(delta_set));
2940 for (i = 0; i < parallel; ++i)
2941 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2942 is_parallel = isl_set_is_subset(delta_set, slice);
2943 isl_set_free(slice);
2944
2945 origin = isl_set_universe(isl_set_get_space(delta_set));
2946 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2947 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2948
2949 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2950 delta_set = isl_set_lexmin(delta_set);
2951
2952 is_nonneg = isl_set_is_equal(delta_set, origin);
2953
2954 isl_set_free(origin);
2955 isl_set_free(delta_set);
2956 }
2957
2958 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2959 is_injection < 0 || is_complete < 0)
2960 return -1;
2961 if (!is_complete)
2962 isl_die(ctx, isl_error_unknown,
2963 "generated schedule incomplete", return -1);
2964 if (!is_injection)
2965 isl_die(ctx, isl_error_unknown,
2966 "generated schedule not injective on each statement",
2967 return -1);
2968 if (!is_nonneg)
2969 isl_die(ctx, isl_error_unknown,
2970 "negative dependences in generated schedule",
2971 return -1);
2972 if (!is_tilable)
2973 isl_die(ctx, isl_error_unknown,
2974 "generated schedule not as tilable as expected",
2975 return -1);
2976 if (!is_parallel)
2977 isl_die(ctx, isl_error_unknown,
2978 "generated schedule not as parallel as expected",
2979 return -1);
2980
2981 return 0;
2982 }
2983
2984 /* Compute a schedule for the given instance set, validity constraints,
2985 * proximity constraints and context and return a corresponding union map
2986 * representation.
2987 */
2988 static __isl_give isl_union_map *compute_schedule_with_context(isl_ctx *ctx,
2989 const char *domain, const char *validity, const char *proximity,
2990 const char *context)
2991 {
2992 isl_set *con;
2993 isl_union_set *dom;
2994 isl_union_map *dep;
2995 isl_union_map *prox;
2996 isl_schedule_constraints *sc;
2997 isl_schedule *schedule;
2998 isl_union_map *sched;
2999
3000 con = isl_set_read_from_str(ctx, context);
3001 dom = isl_union_set_read_from_str(ctx, domain);
3002 dep = isl_union_map_read_from_str(ctx, validity);
3003 prox = isl_union_map_read_from_str(ctx, proximity);
3004 sc = isl_schedule_constraints_on_domain(dom);
3005 sc = isl_schedule_constraints_set_context(sc, con);
3006 sc = isl_schedule_constraints_set_validity(sc, dep);
3007 sc = isl_schedule_constraints_set_proximity(sc, prox);
3008 schedule = isl_schedule_constraints_compute_schedule(sc);
3009 sched = isl_schedule_get_map(schedule);
3010 isl_schedule_free(schedule);
3011
3012 return sched;
3013 }
3014
3015 /* Compute a schedule for the given instance set, validity constraints and
3016 * proximity constraints and return a corresponding union map representation.
3017 */
3018 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
3019 const char *domain, const char *validity, const char *proximity)
3020 {
3021 return compute_schedule_with_context(ctx, domain, validity, proximity,
3022 "{ : }");
3023 }
3024
3025 /* Check that a schedule can be constructed on the given domain
3026 * with the given validity and proximity constraints.
3027 */
3028 static int test_has_schedule(isl_ctx *ctx, const char *domain,
3029 const char *validity, const char *proximity)
3030 {
3031 isl_union_map *sched;
3032
3033 sched = compute_schedule(ctx, domain, validity, proximity);
3034 if (!sched)
3035 return -1;
3036
3037 isl_union_map_free(sched);
3038 return 0;
3039 }
3040
3041 int test_special_schedule(isl_ctx *ctx, const char *domain,
3042 const char *validity, const char *proximity, const char *expected_sched)
3043 {
3044 isl_union_map *sched1, *sched2;
3045 int equal;
3046
3047 sched1 = compute_schedule(ctx, domain, validity, proximity);
3048 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
3049
3050 equal = isl_union_map_is_equal(sched1, sched2);
3051 isl_union_map_free(sched1);
3052 isl_union_map_free(sched2);
3053
3054 if (equal < 0)
3055 return -1;
3056 if (!equal)
3057 isl_die(ctx, isl_error_unknown, "unexpected schedule",
3058 return -1);
3059
3060 return 0;
3061 }
3062
3063 /* Check that the schedule map is properly padded, even after being
3064 * reconstructed from the band forest.
3065 */
3066 static int test_padded_schedule(isl_ctx *ctx)
3067 {
3068 const char *str;
3069 isl_union_set *D;
3070 isl_union_map *validity, *proximity;
3071 isl_schedule_constraints *sc;
3072 isl_schedule *sched;
3073 isl_union_map *map1, *map2;
3074 isl_band_list *list;
3075 int equal;
3076
3077 str = "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
3078 D = isl_union_set_read_from_str(ctx, str);
3079 validity = isl_union_map_empty(isl_union_set_get_space(D));
3080 proximity = isl_union_map_copy(validity);
3081 sc = isl_schedule_constraints_on_domain(D);
3082 sc = isl_schedule_constraints_set_validity(sc, validity);
3083 sc = isl_schedule_constraints_set_proximity(sc, proximity);
3084 sched = isl_schedule_constraints_compute_schedule(sc);
3085 map1 = isl_schedule_get_map(sched);
3086 list = isl_schedule_get_band_forest(sched);
3087 isl_band_list_free(list);
3088 map2 = isl_schedule_get_map(sched);
3089 isl_schedule_free(sched);
3090 equal = isl_union_map_is_equal(map1, map2);
3091 isl_union_map_free(map1);
3092 isl_union_map_free(map2);
3093
3094 if (equal < 0)
3095 return -1;
3096 if (!equal)
3097 isl_die(ctx, isl_error_unknown,
3098 "reconstructed schedule map not the same as original",
3099 return -1);
3100
3101 return 0;
3102 }
3103
3104 /* Check that conditional validity constraints are also taken into
3105 * account across bands.
3106 * In particular, try to make sure that live ranges D[1,0]->C[2,1] and
3107 * D[2,0]->C[3,0] are not local in the outer band of the generated schedule
3108 * and then check that the adjacent order constraint C[2,1]->D[2,0]
3109 * is enforced by the rest of the schedule.
3110 */
3111 static int test_special_conditional_schedule_constraints(isl_ctx *ctx)
3112 {
3113 const char *str;
3114 isl_union_set *domain;
3115 isl_union_map *validity, *proximity, *condition;
3116 isl_union_map *sink, *source, *dep;
3117 isl_schedule_constraints *sc;
3118 isl_schedule *schedule;
3119 isl_union_access_info *access;
3120 isl_union_flow *flow;
3121 int empty;
3122
3123 str = "[n] -> { C[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3124 "A[k] : k >= 1 and k <= -1 + n; "
3125 "B[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3126 "D[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k }";
3127 domain = isl_union_set_read_from_str(ctx, str);
3128 sc = isl_schedule_constraints_on_domain(domain);
3129 str = "[n] -> { D[k, i] -> C[1 + k, k - i] : "
3130 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3131 "D[k, i] -> C[1 + k, i] : "
3132 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3133 "D[k, 0] -> C[1 + k, k] : k >= 1 and k <= -2 + n; "
3134 "D[k, 0] -> C[1 + k, 0] : k >= 1 and k <= -2 + n }";
3135 validity = isl_union_map_read_from_str(ctx, str);
3136 sc = isl_schedule_constraints_set_validity(sc, validity);
3137 str = "[n] -> { C[k, i] -> D[k, i] : "
3138 "0 <= i <= -1 + k and k <= -1 + n }";
3139 proximity = isl_union_map_read_from_str(ctx, str);
3140 sc = isl_schedule_constraints_set_proximity(sc, proximity);
3141 str = "[n] -> { [D[k, i] -> a[]] -> [C[1 + k, k - i] -> b[]] : "
3142 "i <= -1 + k and i >= 1 and k <= -2 + n; "
3143 "[B[k, i] -> c[]] -> [B[k, 1 + i] -> c[]] : "
3144 "k <= -1 + n and i >= 0 and i <= -2 + k }";
3145 condition = isl_union_map_read_from_str(ctx, str);
3146 str = "[n] -> { [B[k, i] -> e[]] -> [D[k, i] -> a[]] : "
3147 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3148 "[C[k, i] -> b[]] -> [D[k', -1 + k - i] -> a[]] : "
3149 "i >= 0 and i <= -1 + k and k <= -1 + n and "
3150 "k' <= -1 + n and k' >= k - i and k' >= 1 + k; "
3151 "[C[k, i] -> b[]] -> [D[k, -1 + k - i] -> a[]] : "
3152 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3153 "[B[k, i] -> c[]] -> [A[k'] -> d[]] : "
3154 "k <= -1 + n and i >= 0 and i <= -1 + k and "
3155 "k' >= 1 and k' <= -1 + n and k' >= 1 + k }";
3156 validity = isl_union_map_read_from_str(ctx, str);
3157 sc = isl_schedule_constraints_set_conditional_validity(sc, condition,
3158 validity);
3159 schedule = isl_schedule_constraints_compute_schedule(sc);
3160 str = "{ D[2,0] -> [] }";
3161 sink = isl_union_map_read_from_str(ctx, str);
3162 access = isl_union_access_info_from_sink(sink);
3163 str = "{ C[2,1] -> [] }";
3164 source = isl_union_map_read_from_str(ctx, str);
3165 access = isl_union_access_info_set_must_source(access, source);
3166 access = isl_union_access_info_set_schedule(access, schedule);
3167 flow = isl_union_access_info_compute_flow(access);
3168 dep = isl_union_flow_get_must_dependence(flow);
3169 isl_union_flow_free(flow);
3170 empty = isl_union_map_is_empty(dep);
3171 isl_union_map_free(dep);
3172
3173 if (empty < 0)
3174 return -1;
3175 if (empty)
3176 isl_die(ctx, isl_error_unknown,
3177 "conditional validity not respected", return -1);
3178
3179 return 0;
3180 }
3181
3182 /* Input for testing of schedule construction based on
3183 * conditional constraints.
3184 *
3185 * domain is the iteration domain
3186 * flow are the flow dependences, which determine the validity and
3187 * proximity constraints
3188 * condition are the conditions on the conditional validity constraints
3189 * conditional_validity are the conditional validity constraints
3190 * outer_band_n is the expected number of members in the outer band
3191 */
3192 struct {
3193 const char *domain;
3194 const char *flow;
3195 const char *condition;
3196 const char *conditional_validity;
3197 int outer_band_n;
3198 } live_range_tests[] = {
3199 /* Contrived example that illustrates that we need to keep
3200 * track of tagged condition dependences and
3201 * tagged conditional validity dependences
3202 * in isl_sched_edge separately.
3203 * In particular, the conditional validity constraints on A
3204 * cannot be satisfied,
3205 * but they can be ignored because there are no corresponding
3206 * condition constraints. However, we do have an additional
3207 * conditional validity constraint that maps to the same
3208 * dependence relation
3209 * as the condition constraint on B. If we did not make a distinction
3210 * between tagged condition and tagged conditional validity
3211 * dependences, then we
3212 * could end up treating this shared dependence as an condition
3213 * constraint on A, forcing a localization of the conditions,
3214 * which is impossible.
3215 */
3216 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
3217 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
3218 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
3219 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3220 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3221 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
3222 1
3223 },
3224 /* TACO 2013 Fig. 7 */
3225 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3226 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3227 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3228 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
3229 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
3230 "0 <= i < n and 0 <= j < n - 1 }",
3231 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
3232 "0 <= i < n and 0 <= j < j' < n;"
3233 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
3234 "0 <= i < i' < n and 0 <= j,j' < n;"
3235 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
3236 "0 <= i,j,j' < n and j < j' }",
3237 2
3238 },
3239 /* TACO 2013 Fig. 7, without tags */
3240 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3241 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3242 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3243 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3244 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3245 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
3246 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
3247 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
3248 1
3249 },
3250 /* TACO 2013 Fig. 12 */
3251 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
3252 "S3[i,3] : 0 <= i <= 1 }",
3253 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
3254 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
3255 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
3256 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
3257 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3258 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
3259 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3260 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
3261 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
3262 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
3263 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
3264 1
3265 }
3266 };
3267
3268 /* Test schedule construction based on conditional constraints.
3269 * In particular, check the number of members in the outer band node
3270 * as an indication of whether tiling is possible or not.
3271 */
3272 static int test_conditional_schedule_constraints(isl_ctx *ctx)
3273 {
3274 int i;
3275 isl_union_set *domain;
3276 isl_union_map *condition;
3277 isl_union_map *flow;
3278 isl_union_map *validity;
3279 isl_schedule_constraints *sc;
3280 isl_schedule *schedule;
3281 isl_schedule_node *node;
3282 int n_member;
3283
3284 if (test_special_conditional_schedule_constraints(ctx) < 0)
3285 return -1;
3286
3287 for (i = 0; i < ARRAY_SIZE(live_range_tests); ++i) {
3288 domain = isl_union_set_read_from_str(ctx,
3289 live_range_tests[i].domain);
3290 flow = isl_union_map_read_from_str(ctx,
3291 live_range_tests[i].flow);
3292 condition = isl_union_map_read_from_str(ctx,
3293 live_range_tests[i].condition);
3294 validity = isl_union_map_read_from_str(ctx,
3295 live_range_tests[i].conditional_validity);
3296 sc = isl_schedule_constraints_on_domain(domain);
3297 sc = isl_schedule_constraints_set_validity(sc,
3298 isl_union_map_copy(flow));
3299 sc = isl_schedule_constraints_set_proximity(sc, flow);
3300 sc = isl_schedule_constraints_set_conditional_validity(sc,
3301 condition, validity);
3302 schedule = isl_schedule_constraints_compute_schedule(sc);
3303 node = isl_schedule_get_root(schedule);
3304 while (node &&
3305 isl_schedule_node_get_type(node) != isl_schedule_node_band)
3306 node = isl_schedule_node_first_child(node);
3307 n_member = isl_schedule_node_band_n_member(node);
3308 isl_schedule_node_free(node);
3309 isl_schedule_free(schedule);
3310
3311 if (!schedule)
3312 return -1;
3313 if (n_member != live_range_tests[i].outer_band_n)
3314 isl_die(ctx, isl_error_unknown,
3315 "unexpected number of members in outer band",
3316 return -1);
3317 }
3318 return 0;
3319 }
3320
3321 /* Check that the schedule computed for the given instance set and
3322 * dependence relation strongly satisfies the dependences.
3323 * In particular, check that no instance is scheduled before
3324 * or together with an instance on which it depends.
3325 * Earlier versions of isl would produce a schedule that
3326 * only weakly satisfies the dependences.
3327 */
3328 static int test_strongly_satisfying_schedule(isl_ctx *ctx)
3329 {
3330 const char *domain, *dep;
3331 isl_union_map *D, *schedule;
3332 isl_map *map, *ge;
3333 int empty;
3334
3335 domain = "{ B[i0, i1] : 0 <= i0 <= 1 and 0 <= i1 <= 11; "
3336 "A[i0] : 0 <= i0 <= 1 }";
3337 dep = "{ B[i0, i1] -> B[i0, 1 + i1] : 0 <= i0 <= 1 and 0 <= i1 <= 10; "
3338 "B[0, 11] -> A[1]; A[i0] -> B[i0, 0] : 0 <= i0 <= 1 }";
3339 schedule = compute_schedule(ctx, domain, dep, dep);
3340 D = isl_union_map_read_from_str(ctx, dep);
3341 D = isl_union_map_apply_domain(D, isl_union_map_copy(schedule));
3342 D = isl_union_map_apply_range(D, schedule);
3343 map = isl_map_from_union_map(D);
3344 ge = isl_map_lex_ge(isl_space_domain(isl_map_get_space(map)));
3345 map = isl_map_intersect(map, ge);
3346 empty = isl_map_is_empty(map);
3347 isl_map_free(map);
3348
3349 if (empty < 0)
3350 return -1;
3351 if (!empty)
3352 isl_die(ctx, isl_error_unknown,
3353 "dependences not strongly satisfied", return -1);
3354
3355 return 0;
3356 }
3357
3358 /* Compute a schedule for input where the instance set constraints
3359 * conflict with the context constraints.
3360 * Earlier versions of isl did not properly handle this situation.
3361 */
3362 static int test_conflicting_context_schedule(isl_ctx *ctx)
3363 {
3364 isl_union_map *schedule;
3365 const char *domain, *context;
3366
3367 domain = "[n] -> { A[] : n >= 0 }";
3368 context = "[n] -> { : n < 0 }";
3369 schedule = compute_schedule_with_context(ctx,
3370 domain, "{}", "{}", context);
3371 isl_union_map_free(schedule);
3372
3373 if (!schedule)
3374 return -1;
3375
3376 return 0;
3377 }
3378
3379 /* Check that the dependence carrying step is not confused by
3380 * a bound on the coefficient size.
3381 * In particular, force the scheduler to move to a dependence carrying
3382 * step by demanding outer coincidence and bound the size of
3383 * the coefficients. Earlier versions of isl would take this
3384 * bound into account while carrying dependences, breaking
3385 * fundamental assumptions.
3386 */
3387 static int test_bounded_coefficients_schedule(isl_ctx *ctx)
3388 {
3389 const char *domain, *dep;
3390 isl_union_set *I;
3391 isl_union_map *D;
3392 isl_schedule_constraints *sc;
3393 isl_schedule *schedule;
3394
3395 domain = "{ C[i0, i1] : 2 <= i0 <= 3999 and 0 <= i1 <= -1 + i0 }";
3396 dep = "{ C[i0, i1] -> C[i0, 1 + i1] : i0 <= 3999 and i1 >= 0 and "
3397 "i1 <= -2 + i0; "
3398 "C[i0, -1 + i0] -> C[1 + i0, 0] : i0 <= 3998 and i0 >= 1 }";
3399 I = isl_union_set_read_from_str(ctx, domain);
3400 D = isl_union_map_read_from_str(ctx, dep);
3401 sc = isl_schedule_constraints_on_domain(I);
3402 sc = isl_schedule_constraints_set_validity(sc, isl_union_map_copy(D));
3403 sc = isl_schedule_constraints_set_coincidence(sc, D);
3404 isl_options_set_schedule_outer_coincidence(ctx, 1);
3405 isl_options_set_schedule_max_coefficient(ctx, 20);
3406 schedule = isl_schedule_constraints_compute_schedule(sc);
3407 isl_options_set_schedule_max_coefficient(ctx, -1);
3408 isl_options_set_schedule_outer_coincidence(ctx, 0);
3409 isl_schedule_free(schedule);
3410
3411 if (!schedule)
3412 return -1;
3413
3414 return 0;
3415 }
3416
3417 int test_schedule(isl_ctx *ctx)
3418 {
3419 const char *D, *W, *R, *V, *P, *S;
3420
3421 /* Handle resulting schedule with zero bands. */
3422 if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
3423 return -1;
3424
3425 /* Jacobi */
3426 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
3427 W = "{ S1[t,i] -> a[t,i] }";
3428 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
3429 "S1[t,i] -> a[t-1,i+1] }";
3430 S = "{ S1[t,i] -> [t,i] }";
3431 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
3432 return -1;
3433
3434 /* Fig. 5 of CC2008 */
3435 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
3436 "j <= -1 + N }";
3437 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
3438 "j >= 2 and j <= -1 + N }";
3439 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
3440 "j >= 2 and j <= -1 + N; "
3441 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
3442 "j >= 2 and j <= -1 + N }";
3443 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3444 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
3445 return -1;
3446
3447 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
3448 W = "{ S1[i] -> a[i] }";
3449 R = "{ S2[i] -> a[i+1] }";
3450 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3451 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
3452 return -1;
3453
3454 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
3455 W = "{ S1[i] -> a[i] }";
3456 R = "{ S2[i] -> a[9-i] }";
3457 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3458 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
3459 return -1;
3460
3461 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
3462 W = "{ S1[i] -> a[i] }";
3463 R = "[N] -> { S2[i] -> a[N-1-i] }";
3464 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3465 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
3466 return -1;
3467
3468 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
3469 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
3470 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
3471 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
3472 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3473 return -1;
3474
3475 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3476 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
3477 R = "{ S2[i,j] -> a[i-1,j] }";
3478 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3479 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3480 return -1;
3481
3482 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3483 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
3484 R = "{ S2[i,j] -> a[i,j-1] }";
3485 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3486 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3487 return -1;
3488
3489 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
3490 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
3491 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
3492 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
3493 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
3494 "S_0[] -> [0, 0, 0] }";
3495 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
3496 return -1;
3497 ctx->opt->schedule_parametric = 0;
3498 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3499 return -1;
3500 ctx->opt->schedule_parametric = 1;
3501
3502 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
3503 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
3504 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
3505 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
3506 "S4[i] -> a[i,N] }";
3507 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
3508 "S4[i] -> [4,i,0] }";
3509 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
3510 return -1;
3511
3512 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
3513 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3514 "j <= N }";
3515 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3516 "j <= N; "
3517 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
3518 "j <= N }";
3519 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3520 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3521 return -1;
3522
3523 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
3524 " S_2[t] : t >= 0 and t <= -1 + N; "
3525 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
3526 "i <= -1 + N }";
3527 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
3528 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
3529 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
3530 "i >= 0 and i <= -1 + N }";
3531 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
3532 "i >= 0 and i <= -1 + N; "
3533 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
3534 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
3535 " S_0[t] -> [0, t, 0] }";
3536
3537 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3538 return -1;
3539 ctx->opt->schedule_parametric = 0;
3540 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3541 return -1;
3542 ctx->opt->schedule_parametric = 1;
3543
3544 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
3545 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
3546 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
3547 return -1;
3548
3549 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3550 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3551 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3552 "j >= 0 and j <= -1 + N; "
3553 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3554 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3555 "j >= 0 and j <= -1 + N; "
3556 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3557 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3558 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3559 return -1;
3560
3561 D = "{ S_0[i] : i >= 0 }";
3562 W = "{ S_0[i] -> a[i] : i >= 0 }";
3563 R = "{ S_0[i] -> a[0] : i >= 0 }";
3564 S = "{ S_0[i] -> [0, i, 0] }";
3565 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3566 return -1;
3567
3568 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3569 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3570 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3571 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3572 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3573 return -1;
3574
3575 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3576 "k <= -1 + n and k >= 0 }";
3577 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3578 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3579 "k <= -1 + n and k >= 0; "
3580 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3581 "k <= -1 + n and k >= 0; "
3582 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3583 "k <= -1 + n and k >= 0 }";
3584 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
3585 ctx->opt->schedule_outer_coincidence = 1;
3586 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3587 return -1;
3588 ctx->opt->schedule_outer_coincidence = 0;
3589
3590 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
3591 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3592 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3593 "Stmt_for_body24[i0, i1, 1, 0]:"
3594 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3595 "Stmt_for_body7[i0, i1, i2]:"
3596 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3597 "i2 <= 7 }";
3598
3599 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
3600 "Stmt_for_body24[1, i1, i2, i3]:"
3601 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3602 "i2 >= 1;"
3603 "Stmt_for_body24[0, i1, i2, i3] -> "
3604 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3605 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3606 "i3 >= 0;"
3607 "Stmt_for_body24[0, i1, i2, i3] ->"
3608 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3609 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3610 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3611 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3612 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3613 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3614 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3615 "i1 <= 6 and i1 >= 0;"
3616 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3617 "Stmt_for_body7[i0, i1, i2] -> "
3618 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3619 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3620 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3621 "Stmt_for_body7[i0, i1, i2] -> "
3622 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3623 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3624 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3625 P = V;
3626 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3627 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3628 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3629
3630 if (test_special_schedule(ctx, D, V, P, S) < 0)
3631 return -1;
3632
3633 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3634 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3635 "j >= 1 and j <= 7;"
3636 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3637 "j >= 1 and j <= 8 }";
3638 P = "{ }";
3639 S = "{ S_0[i, j] -> [i + j, j] }";
3640 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3641 if (test_special_schedule(ctx, D, V, P, S) < 0)
3642 return -1;
3643 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3644
3645 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3646 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3647 "j >= 0 and j <= -1 + i }";
3648 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3649 "i <= -1 + N and j >= 0;"
3650 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3651 "i <= -2 + N }";
3652 P = "{ }";
3653 S = "{ S_0[i, j] -> [i, j] }";
3654 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3655 if (test_special_schedule(ctx, D, V, P, S) < 0)
3656 return -1;
3657 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3658
3659 /* Test both algorithms on a case with only proximity dependences. */
3660 D = "{ S[i,j] : 0 <= i <= 10 }";
3661 V = "{ }";
3662 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3663 S = "{ S[i, j] -> [j, i] }";
3664 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3665 if (test_special_schedule(ctx, D, V, P, S) < 0)
3666 return -1;
3667 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3668 if (test_special_schedule(ctx, D, V, P, S) < 0)
3669 return -1;
3670
3671 D = "{ A[a]; B[] }";
3672 V = "{}";
3673 P = "{ A[a] -> B[] }";
3674 if (test_has_schedule(ctx, D, V, P) < 0)
3675 return -1;
3676
3677 if (test_padded_schedule(ctx) < 0)
3678 return -1;
3679
3680 /* Check that check for progress is not confused by rational
3681 * solution.
3682 */
3683 D = "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3684 V = "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3685 "i0 <= -2 + N; "
3686 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3687 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3688 P = "{}";
3689 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3690 if (test_has_schedule(ctx, D, V, P) < 0)
3691 return -1;
3692 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3693
3694 /* Check that we allow schedule rows that are only non-trivial
3695 * on some full-dimensional domains.
3696 */
3697 D = "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
3698 V = "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
3699 "S1[j] -> S2[1] : 0 <= j <= 1 }";
3700 P = "{}";
3701 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3702 if (test_has_schedule(ctx, D, V, P) < 0)
3703 return -1;
3704 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3705
3706 if (test_conditional_schedule_constraints(ctx) < 0)
3707 return -1;
3708
3709 if (test_strongly_satisfying_schedule(ctx) < 0)
3710 return -1;
3711
3712 if (test_conflicting_context_schedule(ctx) < 0)
3713 return -1;
3714
3715 if (test_bounded_coefficients_schedule(ctx) < 0)
3716 return -1;
3717
3718 return 0;
3719 }
3720
3721 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
3722 {
3723 isl_union_map *umap;
3724 int test;
3725
3726 umap = isl_union_map_read_from_str(ctx, str);
3727 test = isl_union_map_plain_is_injective(umap);
3728 isl_union_map_free(umap);
3729 if (test < 0)
3730 return -1;
3731 if (test == injective)
3732 return 0;
3733 if (injective)
3734 isl_die(ctx, isl_error_unknown,
3735 "map not detected as injective", return -1);
3736 else
3737 isl_die(ctx, isl_error_unknown,
3738 "map detected as injective", return -1);
3739 }
3740
3741 int test_injective(isl_ctx *ctx)
3742 {
3743 const char *str;
3744
3745 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3746 return -1;
3747 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
3748 return -1;
3749 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
3750 return -1;
3751 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
3752 return -1;
3753 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3754 return -1;
3755 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3756 return -1;
3757 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3758 return -1;
3759 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3760 return -1;
3761
3762 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3763 if (test_plain_injective(ctx, str, 1))
3764 return -1;
3765 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3766 if (test_plain_injective(ctx, str, 0))
3767 return -1;
3768
3769 return 0;
3770 }
3771
3772 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
3773 {
3774 isl_aff *aff2;
3775 int equal;
3776
3777 if (!aff)
3778 return -1;
3779
3780 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
3781 equal = isl_aff_plain_is_equal(aff, aff2);
3782 isl_aff_free(aff2);
3783
3784 return equal;
3785 }
3786
3787 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
3788 {
3789 int equal;
3790
3791 equal = aff_plain_is_equal(aff, str);
3792 if (equal < 0)
3793 return -1;
3794 if (!equal)
3795 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
3796 "result not as expected", return -1);
3797 return 0;
3798 }
3799
3800 struct {
3801 __isl_give isl_aff *(*fn)(__isl_take isl_aff *aff1,
3802 __isl_take isl_aff *aff2);
3803 } aff_bin_op[] = {
3804 ['+'] = { &isl_aff_add },
3805 ['-'] = { &isl_aff_sub },
3806 ['*'] = { &isl_aff_mul },
3807 ['/'] = { &isl_aff_div },
3808 };
3809
3810 struct {
3811 const char *arg1;
3812 unsigned char op;
3813 const char *arg2;
3814 const char *res;
3815 } aff_bin_tests[] = {
3816 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3817 "{ [i] -> [2i] }" },
3818 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3819 "{ [i] -> [0] }" },
3820 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3821 "{ [i] -> [2i] }" },
3822 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3823 "{ [i] -> [2i] }" },
3824 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
3825 "{ [i] -> [i/2] }" },
3826 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
3827 "{ [i] -> [i] }" },
3828 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3829 "{ [i] -> [NaN] }" },
3830 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3831 "{ [i] -> [NaN] }" },
3832 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3833 "{ [i] -> [NaN] }" },
3834 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3835 "{ [i] -> [NaN] }" },
3836 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
3837 "{ [i] -> [NaN] }" },
3838 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
3839 "{ [i] -> [NaN] }" },
3840 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3841 "{ [i] -> [NaN] }" },
3842 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3843 "{ [i] -> [NaN] }" },
3844 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3845 "{ [i] -> [NaN] }" },
3846 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3847 "{ [i] -> [NaN] }" },
3848 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
3849 "{ [i] -> [NaN] }" },
3850 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
3851 "{ [i] -> [NaN] }" },
3852 };
3853
3854 /* Perform some basic tests of binary operations on isl_aff objects.
3855 */
3856 static int test_bin_aff(isl_ctx *ctx)
3857 {
3858 int i;
3859 isl_aff *aff1, *aff2, *res;
3860 __isl_give isl_aff *(*fn)(__isl_take isl_aff *aff1,
3861 __isl_take isl_aff *aff2);
3862 int ok;
3863
3864 for (i = 0; i < ARRAY_SIZE(aff_bin_tests); ++i) {
3865 aff1 = isl_aff_read_from_str(ctx, aff_bin_tests[i].arg1);
3866 aff2 = isl_aff_read_from_str(ctx, aff_bin_tests[i].arg2);
3867 res = isl_aff_read_from_str(ctx, aff_bin_tests[i].res);
3868 fn = aff_bin_op[aff_bin_tests[i].op].fn;
3869 aff1 = fn(aff1, aff2);
3870 if (isl_aff_is_nan(res))
3871 ok = isl_aff_is_nan(aff1);
3872 else
3873 ok = isl_aff_plain_is_equal(aff1, res);
3874 isl_aff_free(aff1);
3875 isl_aff_free(res);
3876 if (ok < 0)
3877 return -1;
3878 if (!ok)
3879 isl_die(ctx, isl_error_unknown,
3880 "unexpected result", return -1);
3881 }
3882
3883 return 0;
3884 }
3885
3886 struct {
3887 __isl_give isl_union_pw_multi_aff *(*fn)(
3888 __isl_take isl_union_pw_multi_aff *upma1,
3889 __isl_take isl_union_pw_multi_aff *upma2);
3890 const char *arg1;
3891 const char *arg2;
3892 const char *res;
3893 } upma_bin_tests[] = {
3894 { &isl_union_pw_multi_aff_add, "{ A[] -> [0]; B[0] -> [1] }",
3895 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
3896 { &isl_union_pw_multi_aff_union_add, "{ A[] -> [0]; B[0] -> [1] }",
3897 "{ B[x] -> [2] : x >= 0 }",
3898 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
3899 };
3900
3901 /* Perform some basic tests of binary operations on
3902 * isl_union_pw_multi_aff objects.
3903 */
3904 static int test_bin_upma(isl_ctx *ctx)
3905 {
3906 int i;
3907 isl_union_pw_multi_aff *upma1, *upma2, *res;
3908 int ok;
3909
3910 for (i = 0; i < ARRAY_SIZE(upma_bin_tests); ++i) {
3911 upma1 = isl_union_pw_multi_aff_read_from_str(ctx,
3912 upma_bin_tests[i].arg1);
3913 upma2 = isl_union_pw_multi_aff_read_from_str(ctx,
3914 upma_bin_tests[i].arg2);
3915 res = isl_union_pw_multi_aff_read_from_str(ctx,
3916 upma_bin_tests[i].res);
3917 upma1 = upma_bin_tests[i].fn(upma1, upma2);
3918 ok = isl_union_pw_multi_aff_plain_is_equal(upma1, res);
3919 isl_union_pw_multi_aff_free(upma1);
3920 isl_union_pw_multi_aff_free(res);
3921 if (ok < 0)
3922 return -1;
3923 if (!ok)
3924 isl_die(ctx, isl_error_unknown,
3925 "unexpected result", return -1);
3926 }
3927
3928 return 0;
3929 }
3930
3931 int test_aff(isl_ctx *ctx)
3932 {
3933 const char *str;
3934 isl_set *set;
3935 isl_space *space;
3936 isl_local_space *ls;
3937 isl_aff *aff;
3938 int zero, equal;
3939
3940 if (test_bin_aff(ctx) < 0)
3941 return -1;
3942 if (test_bin_upma(ctx) < 0)
3943 return -1;
3944
3945 space = isl_space_set_alloc(ctx, 0, 1);
3946 ls = isl_local_space_from_space(space);
3947 aff = isl_aff_zero_on_domain(ls);
3948
3949 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3950 aff = isl_aff_scale_down_ui(aff, 3);
3951 aff = isl_aff_floor(aff);
3952 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3953 aff = isl_aff_scale_down_ui(aff, 2);
3954 aff = isl_aff_floor(aff);
3955 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3956
3957 str = "{ [10] }";
3958 set = isl_set_read_from_str(ctx, str);
3959 aff = isl_aff_gist(aff, set);
3960
3961 aff = isl_aff_add_constant_si(aff, -16);
3962 zero = isl_aff_plain_is_zero(aff);
3963 isl_aff_free(aff);
3964
3965 if (zero < 0)
3966 return -1;
3967 if (!zero)
3968 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3969
3970 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
3971 aff = isl_aff_scale_down_ui(aff, 64);
3972 aff = isl_aff_floor(aff);
3973 equal = aff_check_plain_equal(aff, "{ [-1] }");
3974 isl_aff_free(aff);
3975 if (equal < 0)
3976 return -1;
3977
3978 return 0;
3979 }
3980
3981 int test_dim_max(isl_ctx *ctx)
3982 {
3983 int equal;
3984 const char *str;
3985 isl_set *set1, *set2;
3986 isl_set *set;
3987 isl_map *map;
3988 isl_pw_aff *pwaff;
3989
3990 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
3991 set = isl_set_read_from_str(ctx, str);
3992 pwaff = isl_set_dim_max(set, 0);
3993 set1 = isl_set_from_pw_aff(pwaff);
3994 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
3995 set2 = isl_set_read_from_str(ctx, str);
3996 equal = isl_set_is_equal(set1, set2);
3997 isl_set_free(set1);
3998 isl_set_free(set2);
3999 if (equal < 0)
4000 return -1;
4001 if (!equal)
4002 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4003
4004 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
4005 set = isl_set_read_from_str(ctx, str);
4006 pwaff = isl_set_dim_max(set, 0);
4007 set1 = isl_set_from_pw_aff(pwaff);
4008 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4009 set2 = isl_set_read_from_str(ctx, str);
4010 equal = isl_set_is_equal(set1, set2);
4011 isl_set_free(set1);
4012 isl_set_free(set2);
4013 if (equal < 0)
4014 return -1;
4015 if (!equal)
4016 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4017
4018 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
4019 set = isl_set_read_from_str(ctx, str);
4020 pwaff = isl_set_dim_max(set, 0);
4021 set1 = isl_set_from_pw_aff(pwaff);
4022 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4023 set2 = isl_set_read_from_str(ctx, str);
4024 equal = isl_set_is_equal(set1, set2);
4025 isl_set_free(set1);
4026 isl_set_free(set2);
4027 if (equal < 0)
4028 return -1;
4029 if (!equal)
4030 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4031
4032 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
4033 "0 <= i < N and 0 <= j < M }";
4034 map = isl_map_read_from_str(ctx, str);
4035 set = isl_map_range(map);
4036
4037 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
4038 set1 = isl_set_from_pw_aff(pwaff);
4039 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
4040 set2 = isl_set_read_from_str(ctx, str);
4041 equal = isl_set_is_equal(set1, set2);
4042 isl_set_free(set1);
4043 isl_set_free(set2);
4044
4045 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
4046 set1 = isl_set_from_pw_aff(pwaff);
4047 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
4048 set2 = isl_set_read_from_str(ctx, str);
4049 if (equal >= 0 && equal)
4050 equal = isl_set_is_equal(set1, set2);
4051 isl_set_free(set1);
4052 isl_set_free(set2);
4053
4054 isl_set_free(set);
4055
4056 if (equal < 0)
4057 return -1;
4058 if (!equal)
4059 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4060
4061 /* Check that solutions are properly merged. */
4062 str = "[n] -> { [a, b, c] : c >= -4a - 2b and "
4063 "c <= -1 + n - 4a - 2b and c >= -2b and "
4064 "4a >= -4 + n and c >= 0 }";
4065 set = isl_set_read_from_str(ctx, str);
4066 pwaff = isl_set_dim_min(set, 2);
4067 set1 = isl_set_from_pw_aff(pwaff);
4068 str = "[n] -> { [(0)] : n >= 1 }";
4069 set2 = isl_set_read_from_str(ctx, str);
4070 equal = isl_set_is_equal(set1, set2);
4071 isl_set_free(set1);
4072 isl_set_free(set2);
4073
4074 if (equal < 0)
4075 return -1;
4076 if (!equal)
4077 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4078
4079 /* Check that empty solution lie in the right space. */
4080 str = "[n] -> { [t,a] : 1 = 0 }";
4081 set = isl_set_read_from_str(ctx, str);
4082 pwaff = isl_set_dim_max(set, 0);
4083 set1 = isl_set_from_pw_aff(pwaff);
4084 str = "[n] -> { [t] : 1 = 0 }";
4085 set2 = isl_set_read_from_str(ctx, str);
4086 equal = isl_set_is_equal(set1, set2);
4087 isl_set_free(set1);
4088 isl_set_free(set2);
4089
4090 if (equal < 0)
4091 return -1;
4092 if (!equal)
4093 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4094
4095 return 0;
4096 }
4097
4098 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
4099 */
4100 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff *pma,
4101 const char *str)
4102 {
4103 isl_ctx *ctx;
4104 isl_pw_multi_aff *pma2;
4105 int equal;
4106
4107 if (!pma)
4108 return -1;
4109
4110 ctx = isl_pw_multi_aff_get_ctx(pma);
4111 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
4112 equal = isl_pw_multi_aff_plain_is_equal(pma, pma2);
4113 isl_pw_multi_aff_free(pma2);
4114
4115 return equal;
4116 }
4117
4118 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
4119 * represented by "str".
4120 */
4121 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff *pma,
4122 const char *str)
4123 {
4124 int equal;
4125
4126 equal = pw_multi_aff_plain_is_equal(pma, str);
4127 if (equal < 0)
4128 return -1;
4129 if (!equal)
4130 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_unknown,
4131 "result not as expected", return -1);
4132 return 0;
4133 }
4134
4135 /* Basic test for isl_pw_multi_aff_product.
4136 *
4137 * Check that multiple pieces are properly handled.
4138 */
4139 static int test_product_pma(isl_ctx *ctx)
4140 {
4141 int equal;
4142 const char *str;
4143 isl_pw_multi_aff *pma1, *pma2;
4144
4145 str = "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
4146 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
4147 str = "{ C[] -> D[] }";
4148 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
4149 pma1 = isl_pw_multi_aff_product(pma1, pma2);
4150 str = "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
4151 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
4152 equal = pw_multi_aff_check_plain_equal(pma1, str);
4153 isl_pw_multi_aff_free(pma1);
4154 if (equal < 0)
4155 return -1;
4156
4157 return 0;
4158 }
4159
4160 int test_product(isl_ctx *ctx)
4161 {
4162 const char *str;
4163 isl_set *set;
4164 isl_union_set *uset1, *uset2;
4165 int ok;
4166
4167 str = "{ A[i] }";
4168 set = isl_set_read_from_str(ctx, str);
4169 set = isl_set_product(set, isl_set_copy(set));
4170 ok = isl_set_is_wrapping(set);
4171 isl_set_free(set);
4172 if (ok < 0)
4173 return -1;
4174 if (!ok)
4175 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4176
4177 str = "{ [] }";
4178 uset1 = isl_union_set_read_from_str(ctx, str);
4179 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
4180 str = "{ [[] -> []] }";
4181 uset2 = isl_union_set_read_from_str(ctx, str);
4182 ok = isl_union_set_is_equal(uset1, uset2);
4183 isl_union_set_free(uset1);
4184 isl_union_set_free(uset2);
4185 if (ok < 0)
4186 return -1;
4187 if (!ok)
4188 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4189
4190 if (test_product_pma(ctx) < 0)
4191 return -1;
4192
4193 return 0;
4194 }
4195
4196 /* Check that two sets are not considered disjoint just because
4197 * they have a different set of (named) parameters.
4198 */
4199 static int test_disjoint(isl_ctx *ctx)
4200 {
4201 const char *str;
4202 isl_set *set, *set2;
4203 int disjoint;
4204
4205 str = "[n] -> { [[]->[]] }";
4206 set = isl_set_read_from_str(ctx, str);
4207 str = "{ [[]->[]] }";
4208 set2 = isl_set_read_from_str(ctx, str);
4209 disjoint = isl_set_is_disjoint(set, set2);
4210 isl_set_free(set);
4211 isl_set_free(set2);
4212 if (disjoint < 0)
4213 return -1;
4214 if (disjoint)
4215 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4216
4217 return 0;
4218 }
4219
4220 int test_equal(isl_ctx *ctx)
4221 {
4222 const char *str;
4223 isl_set *set, *set2;
4224 int equal;
4225
4226 str = "{ S_6[i] }";
4227 set = isl_set_read_from_str(ctx, str);
4228 str = "{ S_7[i] }";
4229 set2 = isl_set_read_from_str(ctx, str);
4230 equal = isl_set_is_equal(set, set2);
4231 isl_set_free(set);
4232 isl_set_free(set2);
4233 if (equal < 0)
4234 return -1;
4235 if (equal)
4236 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4237
4238 return 0;
4239 }
4240
4241 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
4242 enum isl_dim_type type, unsigned pos, int fixed)
4243 {
4244 int test;
4245
4246 test = isl_map_plain_is_fixed(map, type, pos, NULL);
4247 isl_map_free(map);
4248 if (test < 0)
4249 return -1;
4250 if (test == fixed)
4251 return 0;
4252 if (fixed)
4253 isl_die(ctx, isl_error_unknown,
4254 "map not detected as fixed", return -1);
4255 else
4256 isl_die(ctx, isl_error_unknown,
4257 "map detected as fixed", return -1);
4258 }
4259
4260 int test_fixed(isl_ctx *ctx)
4261 {
4262 const char *str;
4263 isl_map *map;
4264
4265 str = "{ [i] -> [i] }";
4266 map = isl_map_read_from_str(ctx, str);
4267 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
4268 return -1;
4269 str = "{ [i] -> [1] }";
4270 map = isl_map_read_from_str(ctx, str);
4271 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
4272 return -1;
4273 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
4274 map = isl_map_read_from_str(ctx, str);
4275 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
4276 return -1;
4277 map = isl_map_read_from_str(ctx, str);
4278 map = isl_map_neg(map);
4279 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
4280 return -1;
4281
4282 return 0;
4283 }
4284
4285 struct isl_vertices_test_data {
4286 const char *set;
4287 int n;
4288 const char *vertex[2];
4289 } vertices_tests[] = {
4290 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
4291 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
4292 { "{ A[t, i] : t = 14 and i = 1 }",
4293 1, { "{ A[14, 1] }" } },
4294 };
4295
4296 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
4297 */
4298 static isl_stat find_vertex(__isl_take isl_vertex *vertex, void *user)
4299 {
4300 struct isl_vertices_test_data *data = user;
4301 isl_ctx *ctx;
4302 isl_multi_aff *ma;
4303 isl_basic_set *bset;
4304 isl_pw_multi_aff *pma;
4305 int i;
4306 isl_bool equal;
4307
4308 ctx = isl_vertex_get_ctx(vertex);
4309 bset = isl_vertex_get_domain(vertex);
4310 ma = isl_vertex_get_expr(vertex);
4311 pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset), ma);
4312
4313 for (i = 0; i < data->n; ++i) {
4314 isl_pw_multi_aff *pma_i;
4315
4316 pma_i = isl_pw_multi_aff_read_from_str(ctx, data->vertex[i]);
4317 equal = isl_pw_multi_aff_plain_is_equal(pma, pma_i);
4318 isl_pw_multi_aff_free(pma_i);
4319
4320 if (equal < 0 || equal)
4321 break;
4322 }
4323
4324 isl_pw_multi_aff_free(pma);
4325 isl_vertex_free(vertex);
4326
4327 if (equal < 0)
4328 return isl_stat_error;
4329
4330 return equal ? isl_stat_ok : isl_stat_error;
4331 }
4332
4333 int test_vertices(isl_ctx *ctx)
4334 {
4335 int i;
4336
4337 for (i = 0; i < ARRAY_SIZE(vertices_tests); ++i) {
4338 isl_basic_set *bset;
4339 isl_vertices *vertices;
4340 int ok = 1;
4341 int n;
4342
4343 bset = isl_basic_set_read_from_str(ctx, vertices_tests[i].set);
4344 vertices = isl_basic_set_compute_vertices(bset);
4345 n = isl_vertices_get_n_vertices(vertices);
4346 if (vertices_tests[i].n != n)
4347 ok = 0;
4348 if (isl_vertices_foreach_vertex(vertices, &find_vertex,
4349 &vertices_tests[i]) < 0)
4350 ok = 0;
4351 isl_vertices_free(vertices);
4352 isl_basic_set_free(bset);
4353
4354 if (!vertices)
4355 return -1;
4356 if (!ok)
4357 isl_die(ctx, isl_error_unknown, "unexpected vertices",
4358 return -1);
4359 }
4360
4361 return 0;
4362 }
4363
4364 int test_union_pw(isl_ctx *ctx)
4365 {
4366 int equal;
4367 const char *str;
4368 isl_union_set *uset;
4369 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
4370
4371 str = "{ [x] -> x^2 }";
4372 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
4373 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
4374 uset = isl_union_pw_qpolynomial_domain(upwqp1);
4375 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
4376 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
4377 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
4378 isl_union_pw_qpolynomial_free(upwqp1);
4379 isl_union_pw_qpolynomial_free(upwqp2);
4380 if (equal < 0)
4381 return -1;
4382 if (!equal)
4383 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4384
4385 return 0;
4386 }
4387
4388 /* Test that isl_union_pw_qpolynomial_eval picks up the function
4389 * defined over the correct domain space.
4390 */
4391 static int test_eval(isl_ctx *ctx)
4392 {
4393 const char *str;
4394 isl_point *pnt;
4395 isl_set *set;
4396 isl_union_pw_qpolynomial *upwqp;
4397 isl_val *v;
4398 int cmp;
4399
4400 str = "{ A[x] -> x^2; B[x] -> -x^2 }";
4401 upwqp = isl_union_pw_qpolynomial_read_from_str(ctx, str);
4402 str = "{ A[6] }";
4403 set = isl_set_read_from_str(ctx, str);
4404 pnt = isl_set_sample_point(set);
4405 v = isl_union_pw_qpolynomial_eval(upwqp, pnt);
4406 cmp = isl_val_cmp_si(v, 36);
4407 isl_val_free(v);
4408
4409 if (!v)
4410 return -1;
4411 if (cmp != 0)
4412 isl_die(ctx, isl_error_unknown, "unexpected value", return -1);
4413
4414 return 0;
4415 }
4416
4417 int test_output(isl_ctx *ctx)
4418 {
4419 char *s;
4420 const char *str;
4421 isl_pw_aff *pa;
4422 isl_printer *p;
4423 int equal;
4424
4425 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
4426 pa = isl_pw_aff_read_from_str(ctx, str);
4427
4428 p = isl_printer_to_str(ctx);
4429 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
4430 p = isl_printer_print_pw_aff(p, pa);
4431 s = isl_printer_get_str(p);
4432 isl_printer_free(p);
4433 isl_pw_aff_free(pa);
4434 if (!s)
4435 equal = -1;
4436 else
4437 equal = !strcmp(s, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
4438 free(s);
4439 if (equal < 0)
4440 return -1;
4441 if (!equal)
4442 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
4443
4444 return 0;
4445 }
4446
4447 int test_sample(isl_ctx *ctx)
4448 {
4449 const char *str;
4450 isl_basic_set *bset1, *bset2;
4451 int empty, subset;
4452
4453 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
4454 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
4455 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
4456 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
4457 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
4458 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
4459 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
4460 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
4461 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
4462 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
4463 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
4464 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
4465 "d - 1073741821e and "
4466 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
4467 "3j >= 1 - a + b + 2e and "
4468 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
4469 "3i <= 4 - a + 4b - e and "
4470 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
4471 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
4472 "c <= -1 + a and 3i >= -2 - a + 3e and "
4473 "1073741822e <= 1073741823 - a + 1073741822b + c and "
4474 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
4475 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
4476 "1073741823e >= 1 + 1073741823b - d and "
4477 "3i >= 1073741823b + c - 1073741823e - f and "
4478 "3i >= 1 + 2b + e + 3g }";
4479 bset1 = isl_basic_set_read_from_str(ctx, str);
4480 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
4481 empty = isl_basic_set_is_empty(bset2);
4482 subset = isl_basic_set_is_subset(bset2, bset1);
4483 isl_basic_set_free(bset1);
4484 isl_basic_set_free(bset2);
4485 if (empty < 0 || subset < 0)
4486 return -1;
4487 if (empty)
4488 isl_die(ctx, isl_error_unknown, "point not found", return -1);
4489 if (!subset)
4490 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
4491
4492 return 0;
4493 }
4494
4495 int test_fixed_power(isl_ctx *ctx)
4496 {
4497 const char *str;
4498 isl_map *map;
4499 isl_int exp;
4500 int equal;
4501
4502 isl_int_init(exp);
4503 str = "{ [i] -> [i + 1] }";
4504 map = isl_map_read_from_str(ctx, str);
4505 isl_int_set_si(exp, 23);
4506 map = isl_map_fixed_power(map, exp);
4507 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
4508 isl_int_clear(exp);
4509 isl_map_free(map);
4510 if (equal < 0)
4511 return -1;
4512
4513 return 0;
4514 }
4515
4516 int test_slice(isl_ctx *ctx)
4517 {
4518 const char *str;
4519 isl_map *map;
4520 int equal;
4521
4522 str = "{ [i] -> [j] }";
4523 map = isl_map_read_from_str(ctx, str);
4524 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
4525 equal = map_check_equal(map, "{ [i] -> [i] }");
4526 isl_map_free(map);
4527 if (equal < 0)
4528 return -1;
4529
4530 str = "{ [i] -> [j] }";
4531 map = isl_map_read_from_str(ctx, str);
4532 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
4533 equal = map_check_equal(map, "{ [i] -> [j] }");
4534 isl_map_free(map);
4535 if (equal < 0)
4536 return -1;
4537
4538 str = "{ [i] -> [j] }";
4539 map = isl_map_read_from_str(ctx, str);
4540 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
4541 equal = map_check_equal(map, "{ [i] -> [-i] }");
4542 isl_map_free(map);
4543 if (equal < 0)
4544 return -1;
4545
4546 str = "{ [i] -> [j] }";
4547 map = isl_map_read_from_str(ctx, str);
4548 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
4549 equal = map_check_equal(map, "{ [0] -> [j] }");
4550 isl_map_free(map);
4551 if (equal < 0)
4552 return -1;
4553
4554 str = "{ [i] -> [j] }";
4555 map = isl_map_read_from_str(ctx, str);
4556 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
4557 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
4558 isl_map_free(map);
4559 if (equal < 0)
4560 return -1;
4561
4562 str = "{ [i] -> [j] }";
4563 map = isl_map_read_from_str(ctx, str);
4564 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
4565 equal = map_check_equal(map, "{ [i] -> [j] : false }");
4566 isl_map_free(map);
4567 if (equal < 0)
4568 return -1;
4569
4570 return 0;
4571 }
4572
4573 int test_eliminate(isl_ctx *ctx)
4574 {
4575 const char *str;
4576 isl_map *map;
4577 int equal;
4578
4579 str = "{ [i] -> [j] : i = 2j }";
4580 map = isl_map_read_from_str(ctx, str);
4581 map = isl_map_eliminate(map, isl_dim_out, 0, 1);
4582 equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
4583 isl_map_free(map);
4584 if (equal < 0)
4585 return -1;
4586
4587 return 0;
4588 }
4589
4590 /* Check that isl_set_dim_residue_class detects that the values of j
4591 * in the set below are all odd and that it does not detect any spurious
4592 * strides.
4593 */
4594 static int test_residue_class(isl_ctx *ctx)
4595 {
4596 const char *str;
4597 isl_set *set;
4598 isl_int m, r;
4599 int res;
4600
4601 str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
4602 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
4603 set = isl_set_read_from_str(ctx, str);
4604 isl_int_init(m);
4605 isl_int_init(r);
4606 res = isl_set_dim_residue_class(set, 1, &m, &r);
4607 if (res >= 0 &&
4608 (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
4609 isl_die(ctx, isl_error_unknown, "incorrect residue class",
4610 res = -1);
4611 isl_int_clear(r);
4612 isl_int_clear(m);
4613 isl_set_free(set);
4614
4615 return res;
4616 }
4617
4618 int test_align_parameters(isl_ctx *ctx)
4619 {
4620 const char *str;
4621 isl_space *space;
4622 isl_multi_aff *ma1, *ma2;
4623 int equal;
4624
4625 str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
4626 ma1 = isl_multi_aff_read_from_str(ctx, str);
4627
4628 space = isl_space_params_alloc(ctx, 1);
4629 space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
4630 ma1 = isl_multi_aff_align_params(ma1, space);
4631
4632 str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
4633 ma2 = isl_multi_aff_read_from_str(ctx, str);
4634
4635 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
4636
4637 isl_multi_aff_free(ma1);
4638 isl_multi_aff_free(ma2);
4639
4640 if (equal < 0)
4641 return -1;
4642 if (!equal)
4643 isl_die(ctx, isl_error_unknown,
4644 "result not as expected", return -1);
4645
4646 return 0;
4647 }
4648
4649 static int test_list(isl_ctx *ctx)
4650 {
4651 isl_id *a, *b, *c, *d, *id;
4652 isl_id_list *list;
4653 int ok;
4654
4655 a = isl_id_alloc(ctx, "a", NULL);
4656 b = isl_id_alloc(ctx, "b", NULL);
4657 c = isl_id_alloc(ctx, "c", NULL);
4658 d = isl_id_alloc(ctx, "d", NULL);
4659
4660 list = isl_id_list_alloc(ctx, 4);
4661 list = isl_id_list_add(list, a);
4662 list = isl_id_list_add(list, b);
4663 list = isl_id_list_add(list, c);
4664 list = isl_id_list_add(list, d);
4665 list = isl_id_list_drop(list, 1, 1);
4666
4667 if (isl_id_list_n_id(list) != 3) {
4668 isl_id_list_free(list);
4669 isl_die(ctx, isl_error_unknown,
4670 "unexpected number of elements in list", return -1);
4671 }
4672
4673 id = isl_id_list_get_id(list, 0);
4674 ok = id == a;
4675 isl_id_free(id);
4676 id = isl_id_list_get_id(list, 1);
4677 ok = ok && id == c;
4678 isl_id_free(id);
4679 id = isl_id_list_get_id(list, 2);
4680 ok = ok && id == d;
4681 isl_id_free(id);
4682
4683 isl_id_list_free(list);
4684
4685 if (!ok)
4686 isl_die(ctx, isl_error_unknown,
4687 "unexpected elements in list", return -1);
4688
4689 return 0;
4690 }
4691
4692 const char *set_conversion_tests[] = {
4693 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4694 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4695 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4696 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4697 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
4698 };
4699
4700 /* Check that converting from isl_set to isl_pw_multi_aff and back
4701 * to isl_set produces the original isl_set.
4702 */
4703 static int test_set_conversion(isl_ctx *ctx)
4704 {
4705 int i;
4706 const char *str;
4707 isl_set *set1, *set2;
4708 isl_pw_multi_aff *pma;
4709 int equal;
4710
4711 for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
4712 str = set_conversion_tests[i];
4713 set1 = isl_set_read_from_str(ctx, str);
4714 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
4715 set2 = isl_set_from_pw_multi_aff(pma);
4716 equal = isl_set_is_equal(set1, set2);
4717 isl_set_free(set1);
4718 isl_set_free(set2);
4719
4720 if (equal < 0)
4721 return -1;
4722 if (!equal)
4723 isl_die(ctx, isl_error_unknown, "bad conversion",
4724 return -1);
4725 }
4726
4727 return 0;
4728 }
4729
4730 /* Check that converting from isl_map to isl_pw_multi_aff and back
4731 * to isl_map produces the original isl_map.
4732 */
4733 static int test_map_conversion(isl_ctx *ctx)
4734 {
4735 const char *str;
4736 isl_map *map1, *map2;
4737 isl_pw_multi_aff *pma;
4738 int equal;
4739
4740 str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
4741 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4742 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4743 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4744 "9e <= -2 - 2a) }";
4745 map1 = isl_map_read_from_str(ctx, str);
4746 pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
4747 map2 = isl_map_from_pw_multi_aff(pma);
4748 equal = isl_map_is_equal(map1, map2);
4749 isl_map_free(map1);
4750 isl_map_free(map2);
4751
4752 if (equal < 0)
4753 return -1;
4754 if (!equal)
4755 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
4756
4757 return 0;
4758 }
4759
4760 static int test_conversion(isl_ctx *ctx)
4761 {
4762 if (test_set_conversion(ctx) < 0)
4763 return -1;
4764 if (test_map_conversion(ctx) < 0)
4765 return -1;
4766 return 0;
4767 }
4768
4769 /* Check that isl_basic_map_curry does not modify input.
4770 */
4771 static int test_curry(isl_ctx *ctx)
4772 {
4773 const char *str;
4774 isl_basic_map *bmap1, *bmap2;
4775 int equal;
4776
4777 str = "{ [A[] -> B[]] -> C[] }";
4778 bmap1 = isl_basic_map_read_from_str(ctx, str);
4779 bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
4780 equal = isl_basic_map_is_equal(bmap1, bmap2);
4781 isl_basic_map_free(bmap1);
4782 isl_basic_map_free(bmap2);
4783
4784 if (equal < 0)
4785 return -1;
4786 if (equal)
4787 isl_die(ctx, isl_error_unknown,
4788 "curried map should not be equal to original",
4789 return -1);
4790
4791 return 0;
4792 }
4793
4794 struct {
4795 const char *set;
4796 const char *ma;
4797 const char *res;
4798 } preimage_tests[] = {
4799 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4800 "{ A[j,i] -> B[i,j] }",
4801 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4802 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4803 "{ A[a,b] -> B[a/2,b/6] }",
4804 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4805 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4806 "{ A[a,b] -> B[a/2,b/6] }",
4807 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4808 "exists i,j : a = 2 i and b = 6 j }" },
4809 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4810 "[n] -> { : 0 <= n <= 100 }" },
4811 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4812 "{ A[a] -> B[2a] }",
4813 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4814 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4815 "{ A[a] -> B[([a/2])] }",
4816 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4817 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4818 "{ A[a] -> B[a,a,a/3] }",
4819 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4820 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4821 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4822 };
4823
4824 static int test_preimage_basic_set(isl_ctx *ctx)
4825 {
4826 int i;
4827 isl_basic_set *bset1, *bset2;
4828 isl_multi_aff *ma;
4829 int equal;
4830
4831 for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
4832 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
4833 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
4834 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
4835 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
4836 equal = isl_basic_set_is_equal(bset1, bset2);
4837 isl_basic_set_free(bset1);
4838 isl_basic_set_free(bset2);
4839 if (equal < 0)
4840 return -1;
4841 if (!equal)
4842 isl_die(ctx, isl_error_unknown, "bad preimage",
4843 return -1);
4844 }
4845
4846 return 0;
4847 }
4848
4849 struct {
4850 const char *map;
4851 const char *ma;
4852 const char *res;
4853 } preimage_domain_tests[] = {
4854 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4855 "{ A[j,i] -> B[i,j] }",
4856 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4857 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4858 "{ A[i] -> B[i + 1] }",
4859 "{ A[i] -> C[i + 1] }" },
4860 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4861 "{ A[i] -> B[i + 1] }",
4862 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4863 { "{ B[i] -> C[([i/2])] }",
4864 "{ A[i] -> B[2i] }",
4865 "{ A[i] -> C[i] }" },
4866 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4867 "{ A[i] -> B[([i/5]), ([i/7])] }",
4868 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4869 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4870 "[N] -> { A[] -> B[([N/5])] }",
4871 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4872 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4873 "{ A[i] -> B[2i] }",
4874 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4875 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4876 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4877 "{ A[i] -> B[2i] }",
4878 "{ A[i] -> C[2i] }" },
4879 };
4880
4881 static int test_preimage_union_map(isl_ctx *ctx)
4882 {
4883 int i;
4884 isl_union_map *umap1, *umap2;
4885 isl_multi_aff *ma;
4886 int equal;
4887
4888 for (i = 0; i < ARRAY_SIZE(preimage_domain_tests); ++i) {
4889 umap1 = isl_union_map_read_from_str(ctx,
4890 preimage_domain_tests[i].map);
4891 ma = isl_multi_aff_read_from_str(ctx,
4892 preimage_domain_tests[i].ma);
4893 umap2 = isl_union_map_read_from_str(ctx,
4894 preimage_domain_tests[i].res);
4895 umap1 = isl_union_map_preimage_domain_multi_aff(umap1, ma);
4896 equal = isl_union_map_is_equal(umap1, umap2);
4897 isl_union_map_free(umap1);
4898 isl_union_map_free(umap2);
4899 if (equal < 0)
4900 return -1;
4901 if (!equal)
4902 isl_die(ctx, isl_error_unknown, "bad preimage",
4903 return -1);
4904 }
4905
4906 return 0;
4907 }
4908
4909 static int test_preimage(isl_ctx *ctx)
4910 {
4911 if (test_preimage_basic_set(ctx) < 0)
4912 return -1;
4913 if (test_preimage_union_map(ctx) < 0)
4914 return -1;
4915
4916 return 0;
4917 }
4918
4919 struct {
4920 const char *ma1;
4921 const char *ma;
4922 const char *res;
4923 } pullback_tests[] = {
4924 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
4925 "{ A[a,b] -> C[b + 2a] }" },
4926 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
4927 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
4928 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
4929 "{ A[a] -> C[(a)/6] }" },
4930 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
4931 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
4932 "{ A[a] -> C[(2a)/3] }" },
4933 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
4934 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
4935 "{ A[i,j] -> C[i + j, i + j] }"},
4936 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
4937 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
4938 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
4939 { "{ [i, j] -> [floor((i)/4) + floor((2*i+j)/5)] }",
4940 "{ [i, j] -> [floor((i)/3), j] }",
4941 "{ [i, j] -> [(floor((i)/12) + floor((j + 2*floor((i)/3))/5))] }" },
4942 };
4943
4944 static int test_pullback(isl_ctx *ctx)
4945 {
4946 int i;
4947 isl_multi_aff *ma1, *ma2;
4948 isl_multi_aff *ma;
4949 int equal;
4950
4951 for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
4952 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
4953 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
4954 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
4955 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
4956 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
4957 isl_multi_aff_free(ma1);
4958 isl_multi_aff_free(ma2);
4959 if (equal < 0)
4960 return -1;
4961 if (!equal)
4962 isl_die(ctx, isl_error_unknown, "bad pullback",
4963 return -1);
4964 }
4965
4966 return 0;
4967 }
4968
4969 /* Check that negation is printed correctly and that equal expressions
4970 * are correctly identified.
4971 */
4972 static int test_ast(isl_ctx *ctx)
4973 {
4974 isl_ast_expr *expr, *expr1, *expr2, *expr3;
4975 char *str;
4976 int ok, equal;
4977
4978 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
4979 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
4980 expr = isl_ast_expr_add(expr1, expr2);
4981 expr2 = isl_ast_expr_copy(expr);
4982 expr = isl_ast_expr_neg(expr);
4983 expr2 = isl_ast_expr_neg(expr2);
4984 equal = isl_ast_expr_is_equal(expr, expr2);
4985 str = isl_ast_expr_to_str(expr);
4986 ok = str ? !strcmp(str, "-(A + B)") : -1;
4987 free(str);
4988 isl_ast_expr_free(expr);
4989 isl_ast_expr_free(expr2);
4990
4991 if (ok < 0 || equal < 0)
4992 return -1;
4993 if (!equal)
4994 isl_die(ctx, isl_error_unknown,
4995 "equal expressions not considered equal", return -1);
4996 if (!ok)
4997 isl_die(ctx, isl_error_unknown,
4998 "isl_ast_expr printed incorrectly", return -1);
4999
5000 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
5001 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
5002 expr = isl_ast_expr_add(expr1, expr2);
5003 expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
5004 expr = isl_ast_expr_sub(expr3, expr);
5005 str = isl_ast_expr_to_str(expr);
5006 ok = str ? !strcmp(str, "C - (A + B)") : -1;
5007 free(str);
5008 isl_ast_expr_free(expr);
5009
5010 if (ok < 0)
5011 return -1;
5012 if (!ok)
5013 isl_die(ctx, isl_error_unknown,
5014 "isl_ast_expr printed incorrectly", return -1);
5015
5016 return 0;
5017 }
5018
5019 /* Check that isl_ast_build_expr_from_set returns a valid expression
5020 * for an empty set. Note that isl_ast_build_expr_from_set getting
5021 * called on an empty set probably indicates a bug in the caller.
5022 */
5023 static int test_ast_build(isl_ctx *ctx)
5024 {
5025 isl_set *set;
5026 isl_ast_build *build;
5027 isl_ast_expr *expr;
5028
5029 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5030 build = isl_ast_build_from_context(set);
5031
5032 set = isl_set_empty(isl_space_params_alloc(ctx, 0));
5033 expr = isl_ast_build_expr_from_set(build, set);
5034
5035 isl_ast_expr_free(expr);
5036 isl_ast_build_free(build);
5037
5038 if (!expr)
5039 return -1;
5040
5041 return 0;
5042 }
5043
5044 /* Internal data structure for before_for and after_for callbacks.
5045 *
5046 * depth is the current depth
5047 * before is the number of times before_for has been called
5048 * after is the number of times after_for has been called
5049 */
5050 struct isl_test_codegen_data {
5051 int depth;
5052 int before;
5053 int after;
5054 };
5055
5056 /* This function is called before each for loop in the AST generated
5057 * from test_ast_gen1.
5058 *
5059 * Increment the number of calls and the depth.
5060 * Check that the space returned by isl_ast_build_get_schedule_space
5061 * matches the target space of the schedule returned by
5062 * isl_ast_build_get_schedule.
5063 * Return an isl_id that is checked by the corresponding call
5064 * to after_for.
5065 */
5066 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
5067 void *user)
5068 {
5069 struct isl_test_codegen_data *data = user;
5070 isl_ctx *ctx;
5071 isl_space *space;
5072 isl_union_map *schedule;
5073 isl_union_set *uset;
5074 isl_set *set;
5075 int empty;
5076 char name[] = "d0";
5077
5078 ctx = isl_ast_build_get_ctx(build);
5079
5080 if (data->before >= 3)
5081 isl_die(ctx, isl_error_unknown,
5082 "unexpected number of for nodes", return NULL);
5083 if (data->depth >= 2)
5084 isl_die(ctx, isl_error_unknown,
5085 "unexpected depth", return NULL);
5086
5087 snprintf(name, sizeof(name), "d%d", data->depth);
5088 data->before++;
5089 data->depth++;
5090
5091 schedule = isl_ast_build_get_schedule(build);
5092 uset = isl_union_map_range(schedule);
5093 if (!uset)
5094 return NULL;
5095 if (isl_union_set_n_set(uset) != 1) {
5096 isl_union_set_free(uset);
5097 isl_die(ctx, isl_error_unknown,
5098 "expecting single range space", return NULL);
5099 }
5100
5101 space = isl_ast_build_get_schedule_space(build);
5102 set = isl_union_set_extract_set(uset, space);
5103 isl_union_set_free(uset);
5104 empty = isl_set_is_empty(set);
5105 isl_set_free(set);
5106
5107 if (empty < 0)
5108 return NULL;
5109 if (empty)
5110 isl_die(ctx, isl_error_unknown,
5111 "spaces don't match", return NULL);
5112
5113 return isl_id_alloc(ctx, name, NULL);
5114 }
5115
5116 /* This function is called after each for loop in the AST generated
5117 * from test_ast_gen1.
5118 *
5119 * Increment the number of calls and decrement the depth.
5120 * Check that the annotation attached to the node matches
5121 * the isl_id returned by the corresponding call to before_for.
5122 */
5123 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
5124 __isl_keep isl_ast_build *build, void *user)
5125 {
5126 struct isl_test_codegen_data *data = user;
5127 isl_id *id;
5128 const char *name;
5129 int valid;
5130
5131 data->after++;
5132 data->depth--;
5133
5134 if (data->after > data->before)
5135 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
5136 "mismatch in number of for nodes",
5137 return isl_ast_node_free(node));
5138
5139 id = isl_ast_node_get_annotation(node);
5140 if (!id)
5141 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
5142 "missing annotation", return isl_ast_node_free(node));
5143
5144 name = isl_id_get_name(id);
5145 valid = name && atoi(name + 1) == data->depth;
5146 isl_id_free(id);
5147
5148 if (!valid)
5149 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
5150 "wrong annotation", return isl_ast_node_free(node));
5151
5152 return node;
5153 }
5154
5155 /* Check that the before_each_for and after_each_for callbacks
5156 * are called for each for loop in the generated code,
5157 * that they are called in the right order and that the isl_id
5158 * returned from the before_each_for callback is attached to
5159 * the isl_ast_node passed to the corresponding after_each_for call.
5160 */
5161 static int test_ast_gen1(isl_ctx *ctx)
5162 {
5163 const char *str;
5164 isl_set *set;
5165 isl_union_map *schedule;
5166 isl_ast_build *build;
5167 isl_ast_node *tree;
5168 struct isl_test_codegen_data data;
5169
5170 str = "[N] -> { : N >= 10 }";
5171 set = isl_set_read_from_str(ctx, str);
5172 str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
5173 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
5174 schedule = isl_union_map_read_from_str(ctx, str);
5175
5176 data.before = 0;
5177 data.after = 0;
5178 data.depth = 0;
5179 build = isl_ast_build_from_context(set);
5180 build = isl_ast_build_set_before_each_for(build,
5181 &before_for, &data);
5182 build = isl_ast_build_set_after_each_for(build,
5183 &after_for, &data);
5184 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5185 isl_ast_build_free(build);
5186 if (!tree)
5187 return -1;
5188
5189 isl_ast_node_free(tree);
5190
5191 if (data.before != 3 || data.after != 3)
5192 isl_die(ctx, isl_error_unknown,
5193 "unexpected number of for nodes", return -1);
5194
5195 return 0;
5196 }
5197
5198 /* Check that the AST generator handles domains that are integrally disjoint
5199 * but not rationally disjoint.
5200 */
5201 static int test_ast_gen2(isl_ctx *ctx)
5202 {
5203 const char *str;
5204 isl_set *set;
5205 isl_union_map *schedule;
5206 isl_union_map *options;
5207 isl_ast_build *build;
5208 isl_ast_node *tree;
5209
5210 str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
5211 schedule = isl_union_map_read_from_str(ctx, str);
5212 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5213 build = isl_ast_build_from_context(set);
5214
5215 str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
5216 options = isl_union_map_read_from_str(ctx, str);
5217 build = isl_ast_build_set_options(build, options);
5218 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5219 isl_ast_build_free(build);
5220 if (!tree)
5221 return -1;
5222 isl_ast_node_free(tree);
5223
5224 return 0;
5225 }
5226
5227 /* Increment *user on each call.
5228 */
5229 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
5230 __isl_keep isl_ast_build *build, void *user)
5231 {
5232 int *n = user;
5233
5234 (*n)++;
5235
5236 return node;
5237 }
5238
5239 /* Test that unrolling tries to minimize the number of instances.
5240 * In particular, for the schedule given below, make sure it generates
5241 * 3 nodes (rather than 101).
5242 */
5243 static int test_ast_gen3(isl_ctx *ctx)
5244 {
5245 const char *str;
5246 isl_set *set;
5247 isl_union_map *schedule;
5248 isl_union_map *options;
5249 isl_ast_build *build;
5250 isl_ast_node *tree;
5251 int n_domain = 0;
5252
5253 str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
5254 schedule = isl_union_map_read_from_str(ctx, str);
5255 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5256
5257 str = "{ [i] -> unroll[0] }";
5258 options = isl_union_map_read_from_str(ctx, str);
5259
5260 build = isl_ast_build_from_context(set);
5261 build = isl_ast_build_set_options(build, options);
5262 build = isl_ast_build_set_at_each_domain(build,
5263 &count_domains, &n_domain);
5264 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5265 isl_ast_build_free(build);
5266 if (!tree)
5267 return -1;
5268
5269 isl_ast_node_free(tree);
5270
5271 if (n_domain != 3)
5272 isl_die(ctx, isl_error_unknown,
5273 "unexpected number of for nodes", return -1);
5274
5275 return 0;
5276 }
5277
5278 /* Check that if the ast_build_exploit_nested_bounds options is set,
5279 * we do not get an outer if node in the generated AST,
5280 * while we do get such an outer if node if the options is not set.
5281 */
5282 static int test_ast_gen4(isl_ctx *ctx)
5283 {
5284 const char *str;
5285 isl_set *set;
5286 isl_union_map *schedule;
5287 isl_ast_build *build;
5288 isl_ast_node *tree;
5289 enum isl_ast_node_type type;
5290 int enb;
5291
5292 enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
5293 str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
5294
5295 isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
5296
5297 schedule = isl_union_map_read_from_str(ctx, str);
5298 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5299 build = isl_ast_build_from_context(set);
5300 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5301 isl_ast_build_free(build);
5302 if (!tree)
5303 return -1;
5304
5305 type = isl_ast_node_get_type(tree);
5306 isl_ast_node_free(tree);
5307
5308 if (type == isl_ast_node_if)
5309 isl_die(ctx, isl_error_unknown,
5310 "not expecting if node", return -1);
5311
5312 isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
5313
5314 schedule = isl_union_map_read_from_str(ctx, str);
5315 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5316 build = isl_ast_build_from_context(set);
5317 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5318 isl_ast_build_free(build);
5319 if (!tree)
5320 return -1;
5321
5322 type = isl_ast_node_get_type(tree);
5323 isl_ast_node_free(tree);
5324
5325 if (type != isl_ast_node_if)
5326 isl_die(ctx, isl_error_unknown,
5327 "expecting if node", return -1);
5328
5329 isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
5330
5331 return 0;
5332 }
5333
5334 /* This function is called for each leaf in the AST generated
5335 * from test_ast_gen5.
5336 *
5337 * We finalize the AST generation by extending the outer schedule
5338 * with a zero-dimensional schedule. If this results in any for loops,
5339 * then this means that we did not pass along enough information
5340 * about the outer schedule to the inner AST generation.
5341 */
5342 static __isl_give isl_ast_node *create_leaf(__isl_take isl_ast_build *build,
5343 void *user)
5344 {
5345 isl_union_map *schedule, *extra;
5346 isl_ast_node *tree;
5347
5348 schedule = isl_ast_build_get_schedule(build);
5349 extra = isl_union_map_copy(schedule);
5350 extra = isl_union_map_from_domain(isl_union_map_domain(extra));
5351 schedule = isl_union_map_range_product(schedule, extra);
5352 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5353 isl_ast_build_free(build);
5354
5355 if (!tree)
5356 return NULL;
5357
5358 if (isl_ast_node_get_type(tree) == isl_ast_node_for)
5359 isl_die(isl_ast_node_get_ctx(tree), isl_error_unknown,
5360 "code should not contain any for loop",
5361 return isl_ast_node_free(tree));
5362
5363 return tree;
5364 }
5365
5366 /* Check that we do not lose any information when going back and
5367 * forth between internal and external schedule.
5368 *
5369 * In particular, we create an AST where we unroll the only
5370 * non-constant dimension in the schedule. We therefore do
5371 * not expect any for loops in the AST. However, older versions
5372 * of isl would not pass along enough information about the outer
5373 * schedule when performing an inner code generation from a create_leaf
5374 * callback, resulting in the inner code generation producing a for loop.
5375 */
5376 static int test_ast_gen5(isl_ctx *ctx)
5377 {
5378 const char *str;
5379 isl_set *set;
5380 isl_union_map *schedule, *options;
5381 isl_ast_build *build;
5382 isl_ast_node *tree;
5383
5384 str = "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
5385 schedule = isl_union_map_read_from_str(ctx, str);
5386
5387 str = "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
5388 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
5389 options = isl_union_map_read_from_str(ctx, str);
5390
5391 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
5392 build = isl_ast_build_from_context(set);
5393 build = isl_ast_build_set_options(build, options);
5394 build = isl_ast_build_set_create_leaf(build, &create_leaf, NULL);
5395 tree = isl_ast_build_node_from_schedule_map(build, schedule);
5396 isl_ast_build_free(build);
5397 isl_ast_node_free(tree);
5398 if (!tree)
5399 return -1;
5400
5401 return 0;
5402 }
5403
5404 static int test_ast_gen(isl_ctx *ctx)
5405 {
5406 if (test_ast_gen1(ctx) < 0)
5407 return -1;
5408 if (test_ast_gen2(ctx) < 0)
5409 return -1;
5410 if (test_ast_gen3(ctx) < 0)
5411 return -1;
5412 if (test_ast_gen4(ctx) < 0)
5413 return -1;
5414 if (test_ast_gen5(ctx) < 0)
5415 return -1;
5416 return 0;
5417 }
5418
5419 /* Check if dropping output dimensions from an isl_pw_multi_aff
5420 * works properly.
5421 */
5422 static int test_pw_multi_aff(isl_ctx *ctx)
5423 {
5424 const char *str;
5425 isl_pw_multi_aff *pma1, *pma2;
5426 int equal;
5427
5428 str = "{ [i,j] -> [i+j, 4i-j] }";
5429 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
5430 str = "{ [i,j] -> [4i-j] }";
5431 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
5432
5433 pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
5434
5435 equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
5436
5437 isl_pw_multi_aff_free(pma1);
5438 isl_pw_multi_aff_free(pma2);
5439 if (equal < 0)
5440 return -1;
5441 if (!equal)
5442 isl_die(ctx, isl_error_unknown,
5443 "expressions not equal", return -1);
5444
5445 return 0;
5446 }
5447
5448 /* Check that we can properly parse multi piecewise affine expressions
5449 * where the piecewise affine expressions have different domains.
5450 */
5451 static int test_multi_pw_aff(isl_ctx *ctx)
5452 {
5453 const char *str;
5454 isl_set *dom, *dom2;
5455 isl_multi_pw_aff *mpa1, *mpa2;
5456 isl_pw_aff *pa;
5457 int equal;
5458 int equal_domain;
5459
5460 mpa1 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [i] }");
5461 dom = isl_set_read_from_str(ctx, "{ [i] : i > 0 }");
5462 mpa1 = isl_multi_pw_aff_intersect_domain(mpa1, dom);
5463 mpa2 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [2i] }");
5464 mpa2 = isl_multi_pw_aff_flat_range_product(mpa1, mpa2);
5465 str = "{ [i] -> [(i : i > 0), 2i] }";
5466 mpa1 = isl_multi_pw_aff_read_from_str(ctx, str);
5467
5468 equal = isl_multi_pw_aff_plain_is_equal(mpa1, mpa2);
5469
5470 pa = isl_multi_pw_aff_get_pw_aff(mpa1, 0);
5471 dom = isl_pw_aff_domain(pa);
5472 pa = isl_multi_pw_aff_get_pw_aff(mpa1, 1);
5473 dom2 = isl_pw_aff_domain(pa);
5474 equal_domain = isl_set_is_equal(dom, dom2);
5475
5476 isl_set_free(dom);
5477 isl_set_free(dom2);
5478 isl_multi_pw_aff_free(mpa1);
5479 isl_multi_pw_aff_free(mpa2);
5480
5481 if (equal < 0)
5482 return -1;
5483 if (!equal)
5484 isl_die(ctx, isl_error_unknown,
5485 "expressions not equal", return -1);
5486
5487 if (equal_domain < 0)
5488 return -1;
5489 if (equal_domain)
5490 isl_die(ctx, isl_error_unknown,
5491 "domains unexpectedly equal", return -1);
5492
5493 return 0;
5494 }
5495
5496 /* This is a regression test for a bug where isl_basic_map_simplify
5497 * would end up in an infinite loop. In particular, we construct
5498 * an empty basic set that is not obviously empty.
5499 * isl_basic_set_is_empty marks the basic set as empty.
5500 * After projecting out i3, the variable can be dropped completely,
5501 * but isl_basic_map_simplify refrains from doing so if the basic set
5502 * is empty and would end up in an infinite loop if it didn't test
5503 * explicitly for empty basic maps in the outer loop.
5504 */
5505 static int test_simplify(isl_ctx *ctx)
5506 {
5507 const char *str;
5508 isl_basic_set *bset;
5509 int empty;
5510
5511 str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
5512 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
5513 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
5514 "i3 >= i2 }";
5515 bset = isl_basic_set_read_from_str(ctx, str);
5516 empty = isl_basic_set_is_empty(bset);
5517 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
5518 isl_basic_set_free(bset);
5519 if (!bset)
5520 return -1;
5521 if (!empty)
5522 isl_die(ctx, isl_error_unknown,
5523 "basic set should be empty", return -1);
5524
5525 return 0;
5526 }
5527
5528 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
5529 * with gbr context would fail to disable the use of the shifted tableau
5530 * when transferring equalities for the input to the context, resulting
5531 * in invalid sample values.
5532 */
5533 static int test_partial_lexmin(isl_ctx *ctx)
5534 {
5535 const char *str;
5536 isl_basic_set *bset;
5537 isl_basic_map *bmap;
5538 isl_map *map;
5539
5540 str = "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
5541 bmap = isl_basic_map_read_from_str(ctx, str);
5542 str = "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
5543 bset = isl_basic_set_read_from_str(ctx, str);
5544 map = isl_basic_map_partial_lexmin(bmap, bset, NULL);
5545 isl_map_free(map);
5546
5547 if (!map)
5548 return -1;
5549
5550 return 0;
5551 }
5552
5553 /* Check that the variable compression performed on the existentially
5554 * quantified variables inside isl_basic_set_compute_divs is not confused
5555 * by the implicit equalities among the parameters.
5556 */
5557 static int test_compute_divs(isl_ctx *ctx)
5558 {
5559 const char *str;
5560 isl_basic_set *bset;
5561 isl_set *set;
5562
5563 str = "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
5564 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
5565 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
5566 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
5567 bset = isl_basic_set_read_from_str(ctx, str);
5568 set = isl_basic_set_compute_divs(bset);
5569 isl_set_free(set);
5570 if (!set)
5571 return -1;
5572
5573 return 0;
5574 }
5575
5576 /* Check that the reaching domain elements and the prefix schedule
5577 * at a leaf node are the same before and after grouping.
5578 */
5579 static int test_schedule_tree_group_1(isl_ctx *ctx)
5580 {
5581 int equal;
5582 const char *str;
5583 isl_id *id;
5584 isl_union_set *uset;
5585 isl_multi_union_pw_aff *mupa;
5586 isl_union_pw_multi_aff *upma1, *upma2;
5587 isl_union_set *domain1, *domain2;
5588 isl_union_map *umap1, *umap2;
5589 isl_schedule_node *node;
5590
5591 str = "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10 }";
5592 uset = isl_union_set_read_from_str(ctx, str);
5593 node = isl_schedule_node_from_domain(uset);
5594 node = isl_schedule_node_child(node, 0);
5595 str = "[{ S1[i,j] -> [i]; S2[i,j] -> [9 - i] }]";
5596 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5597 node = isl_schedule_node_insert_partial_schedule(node, mupa);
5598 node = isl_schedule_node_child(node, 0);
5599 str = "[{ S1[i,j] -> [j]; S2[i,j] -> [j] }]";
5600 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5601 node = isl_schedule_node_insert_partial_schedule(node, mupa);
5602 node = isl_schedule_node_child(node, 0);
5603 umap1 = isl_schedule_node_get_prefix_schedule_union_map(node);
5604 upma1 = isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node);
5605 domain1 = isl_schedule_node_get_domain(node);
5606 id = isl_id_alloc(ctx, "group", NULL);
5607 node = isl_schedule_node_parent(node);
5608 node = isl_schedule_node_group(node, id);
5609 node = isl_schedule_node_child(node, 0);
5610 umap2 = isl_schedule_node_get_prefix_schedule_union_map(node);
5611 upma2 = isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node);
5612 domain2 = isl_schedule_node_get_domain(node);
5613 equal = isl_union_pw_multi_aff_plain_is_equal(upma1, upma2);
5614 if (equal >= 0 && equal)
5615 equal = isl_union_set_is_equal(domain1, domain2);
5616 if (equal >= 0 && equal)
5617 equal = isl_union_map_is_equal(umap1, umap2);
5618 isl_union_map_free(umap1);
5619 isl_union_map_free(umap2);
5620 isl_union_set_free(domain1);
5621 isl_union_set_free(domain2);
5622 isl_union_pw_multi_aff_free(upma1);
5623 isl_union_pw_multi_aff_free(upma2);
5624 isl_schedule_node_free(node);
5625
5626 if (equal < 0)
5627 return -1;
5628 if (!equal)
5629 isl_die(ctx, isl_error_unknown,
5630 "expressions not equal", return -1);
5631
5632 return 0;
5633 }
5634
5635 /* Check that we can have nested groupings and that the union map
5636 * schedule representation is the same before and after the grouping.
5637 * Note that after the grouping, the union map representation contains
5638 * the domain constraints from the ranges of the expansion nodes,
5639 * while they are missing from the union map representation of
5640 * the tree without expansion nodes.
5641 *
5642 * Also check that the global expansion is as expected.
5643 */
5644 static int test_schedule_tree_group_2(isl_ctx *ctx)
5645 {
5646 int equal, equal_expansion;
5647 const char *str;
5648 isl_id *id;
5649 isl_union_set *uset;
5650 isl_union_map *umap1, *umap2;
5651 isl_union_map *expansion1, *expansion2;
5652 isl_union_set_list *filters;
5653 isl_multi_union_pw_aff *mupa;
5654 isl_schedule *schedule;
5655 isl_schedule_node *node;
5656
5657 str = "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10; "
5658 "S3[i,j] : 0 <= i,j < 10 }";
5659 uset = isl_union_set_read_from_str(ctx, str);
5660 node = isl_schedule_node_from_domain(uset);
5661 node = isl_schedule_node_child(node, 0);
5662 str = "[{ S1[i,j] -> [i]; S2[i,j] -> [i]; S3[i,j] -> [i] }]";
5663 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5664 node = isl_schedule_node_insert_partial_schedule(node, mupa);
5665 node = isl_schedule_node_child(node, 0);
5666 str = "{ S1[i,j] }";
5667 uset = isl_union_set_read_from_str(ctx, str);
5668 filters = isl_union_set_list_from_union_set(uset);
5669 str = "{ S2[i,j]; S3[i,j] }";
5670 uset = isl_union_set_read_from_str(ctx, str);
5671 filters = isl_union_set_list_add(filters, uset);
5672 node = isl_schedule_node_insert_sequence(node, filters);
5673 node = isl_schedule_node_child(node, 1);
5674 node = isl_schedule_node_child(node, 0);
5675 str = "{ S2[i,j] }";
5676 uset = isl_union_set_read_from_str(ctx, str);
5677 filters = isl_union_set_list_from_union_set(uset);
5678 str = "{ S3[i,j] }";
5679 uset = isl_union_set_read_from_str(ctx, str);
5680 filters = isl_union_set_list_add(filters, uset);
5681 node = isl_schedule_node_insert_sequence(node, filters);
5682
5683 schedule = isl_schedule_node_get_schedule(node);
5684 umap1 = isl_schedule_get_map(schedule);
5685 uset = isl_schedule_get_domain(schedule);
5686 umap1 = isl_union_map_intersect_domain(umap1, uset);
5687 isl_schedule_free(schedule);
5688
5689 node = isl_schedule_node_parent(node);
5690 node = isl_schedule_node_parent(node);
5691 id = isl_id_alloc(ctx, "group1", NULL);
5692 node = isl_schedule_node_group(node, id);
5693 node = isl_schedule_node_child(node, 1);
5694 node = isl_schedule_node_child(node, 0);
5695 id = isl_id_alloc(ctx, "group2", NULL);
5696 node = isl_schedule_node_group(node, id);
5697
5698 schedule = isl_schedule_node_get_schedule(node);
5699 umap2 = isl_schedule_get_map(schedule);
5700 isl_schedule_free(schedule);
5701
5702 node = isl_schedule_node_root(node);
5703 node = isl_schedule_node_child(node, 0);
5704 expansion1 = isl_schedule_node_get_subtree_expansion(node);
5705 isl_schedule_node_free(node);
5706
5707 str = "{ group1[i] -> S1[i,j] : 0 <= i,j < 10; "
5708 "group1[i] -> S2[i,j] : 0 <= i,j < 10; "
5709 "group1[i] -> S3[i,j] : 0 <= i,j < 10 }";
5710
5711 expansion2 = isl_union_map_read_from_str(ctx, str);
5712
5713 equal = isl_union_map_is_equal(umap1, umap2);
5714 equal_expansion = isl_union_map_is_equal(expansion1, expansion2);
5715
5716 isl_union_map_free(umap1);
5717 isl_union_map_free(umap2);
5718 isl_union_map_free(expansion1);
5719 isl_union_map_free(expansion2);
5720
5721 if (equal < 0 || equal_expansion < 0)
5722 return -1;
5723 if (!equal)
5724 isl_die(ctx, isl_error_unknown,
5725 "expressions not equal", return -1);
5726 if (!equal_expansion)
5727 isl_die(ctx, isl_error_unknown,
5728 "unexpected expansion", return -1);
5729
5730 return 0;
5731 }
5732
5733 /* Some tests for the isl_schedule_node_group function.
5734 */
5735 static int test_schedule_tree_group(isl_ctx *ctx)
5736 {
5737 if (test_schedule_tree_group_1(ctx) < 0)
5738 return -1;
5739 if (test_schedule_tree_group_2(ctx) < 0)
5740 return -1;
5741 return 0;
5742 }
5743
5744 struct {
5745 const char *set;
5746 const char *dual;
5747 } coef_tests[] = {
5748 { "{ rat: [i] : 0 <= i <= 10 }",
5749 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
5750 { "{ rat: [i] : FALSE }",
5751 "{ rat: coefficients[[cst] -> [a]] }" },
5752 { "{ rat: [i] : }",
5753 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
5754 };
5755
5756 struct {
5757 const char *set;
5758 const char *dual;
5759 } sol_tests[] = {
5760 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
5761 "{ rat: [i] : 0 <= i <= 10 }" },
5762 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
5763 "{ rat: [i] }" },
5764 { "{ rat: coefficients[[cst] -> [a]] }",
5765 "{ rat: [i] : FALSE }" },
5766 };
5767
5768 /* Test the basic functionality of isl_basic_set_coefficients and
5769 * isl_basic_set_solutions.
5770 */
5771 static int test_dual(isl_ctx *ctx)
5772 {
5773 int i;
5774
5775 for (i = 0; i < ARRAY_SIZE(coef_tests); ++i) {
5776 int equal;
5777 isl_basic_set *bset1, *bset2;
5778
5779 bset1 = isl_basic_set_read_from_str(ctx, coef_tests[i].set);
5780 bset2 = isl_basic_set_read_from_str(ctx, coef_tests[i].dual);
5781 bset1 = isl_basic_set_coefficients(bset1);
5782 equal = isl_basic_set_is_equal(bset1, bset2);
5783 isl_basic_set_free(bset1);
5784 isl_basic_set_free(bset2);
5785 if (equal < 0)
5786 return -1;
5787 if (!equal)
5788 isl_die(ctx, isl_error_unknown,
5789 "incorrect dual", return -1);
5790 }
5791
5792 for (i = 0; i < ARRAY_SIZE(sol_tests); ++i) {
5793 int equal;
5794 isl_basic_set *bset1, *bset2;
5795
5796 bset1 = isl_basic_set_read_from_str(ctx, sol_tests[i].set);
5797 bset2 = isl_basic_set_read_from_str(ctx, sol_tests[i].dual);
5798 bset1 = isl_basic_set_solutions(bset1);
5799 equal = isl_basic_set_is_equal(bset1, bset2);
5800 isl_basic_set_free(bset1);
5801 isl_basic_set_free(bset2);
5802 if (equal < 0)
5803 return -1;
5804 if (!equal)
5805 isl_die(ctx, isl_error_unknown,
5806 "incorrect dual", return -1);
5807 }
5808
5809 return 0;
5810 }
5811
5812 struct {
5813 int scale_tile;
5814 int shift_point;
5815 const char *domain;
5816 const char *schedule;
5817 const char *sizes;
5818 const char *tile;
5819 const char *point;
5820 } tile_tests[] = {
5821 { 0, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
5822 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5823 "{ [32,32] }",
5824 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
5825 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5826 },
5827 { 1, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
5828 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5829 "{ [32,32] }",
5830 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
5831 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5832 },
5833 { 0, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
5834 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5835 "{ [32,32] }",
5836 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
5837 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
5838 },
5839 { 1, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
5840 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5841 "{ [32,32] }",
5842 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
5843 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
5844 },
5845 };
5846
5847 /* Basic tiling tests. Create a schedule tree with a domain and a band node,
5848 * tile the band and then check if the tile and point bands have the
5849 * expected partial schedule.
5850 */
5851 static int test_tile(isl_ctx *ctx)
5852 {
5853 int i;
5854 int scale;
5855 int shift;
5856
5857 scale = isl_options_get_tile_scale_tile_loops(ctx);
5858 shift = isl_options_get_tile_shift_point_loops(ctx);
5859
5860 for (i = 0; i < ARRAY_SIZE(tile_tests); ++i) {
5861 int opt;
5862 int equal;
5863 const char *str;
5864 isl_union_set *domain;
5865 isl_multi_union_pw_aff *mupa, *mupa2;
5866 isl_schedule_node *node;
5867 isl_multi_val *sizes;
5868
5869 opt = tile_tests[i].scale_tile;
5870 isl_options_set_tile_scale_tile_loops(ctx, opt);
5871 opt = tile_tests[i].shift_point;
5872 isl_options_set_tile_shift_point_loops(ctx, opt);
5873
5874 str = tile_tests[i].domain;
5875 domain = isl_union_set_read_from_str(ctx, str);
5876 node = isl_schedule_node_from_domain(domain);
5877 node = isl_schedule_node_child(node, 0);
5878 str = tile_tests[i].schedule;
5879 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5880 node = isl_schedule_node_insert_partial_schedule(node, mupa);
5881 str = tile_tests[i].sizes;
5882 sizes = isl_multi_val_read_from_str(ctx, str);
5883 node = isl_schedule_node_band_tile(node, sizes);
5884
5885 str = tile_tests[i].tile;
5886 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5887 mupa2 = isl_schedule_node_band_get_partial_schedule(node);
5888 equal = isl_multi_union_pw_aff_plain_is_equal(mupa, mupa2);
5889 isl_multi_union_pw_aff_free(mupa);
5890 isl_multi_union_pw_aff_free(mupa2);
5891
5892 node = isl_schedule_node_child(node, 0);
5893
5894 str = tile_tests[i].point;
5895 mupa = isl_multi_union_pw_aff_read_from_str(ctx, str);
5896 mupa2 = isl_schedule_node_band_get_partial_schedule(node);
5897 if (equal >= 0 && equal)
5898 equal = isl_multi_union_pw_aff_plain_is_equal(mupa,
5899 mupa2);
5900 isl_multi_union_pw_aff_free(mupa);
5901 isl_multi_union_pw_aff_free(mupa2);
5902
5903 isl_schedule_node_free(node);
5904
5905 if (equal < 0)
5906 return -1;
5907 if (!equal)
5908 isl_die(ctx, isl_error_unknown,
5909 "unexpected result", return -1);
5910 }
5911
5912 isl_options_set_tile_scale_tile_loops(ctx, scale);
5913 isl_options_set_tile_shift_point_loops(ctx, shift);
5914
5915 return 0;
5916 }
5917
5918 /* Check that the domain hash of a space is equal to the hash
5919 * of the domain of the space.
5920 */
5921 static int test_domain_hash(isl_ctx *ctx)
5922 {
5923 isl_map *map;
5924 isl_space *space;
5925 uint32_t hash1, hash2;
5926
5927 map = isl_map_read_from_str(ctx, "[n] -> { A[B[x] -> C[]] -> D[] }");
5928 space = isl_map_get_space(map);
5929 isl_map_free(map);
5930 hash1 = isl_space_get_domain_hash(space);
5931 space = isl_space_domain(space);
5932 hash2 = isl_space_get_hash(space);
5933 isl_space_free(space);
5934
5935 if (!space)
5936 return -1;
5937 if (hash1 != hash2)
5938 isl_die(ctx, isl_error_unknown,
5939 "domain hash not equal to hash of domain", return -1);
5940
5941 return 0;
5942 }
5943
5944 struct {
5945 const char *name;
5946 int (*fn)(isl_ctx *ctx);
5947 } tests [] = {
5948 { "domain hash", &test_domain_hash },
5949 { "dual", &test_dual },
5950 { "dependence analysis", &test_flow },
5951 { "val", &test_val },
5952 { "compute divs", &test_compute_divs },
5953 { "partial lexmin", &test_partial_lexmin },
5954 { "simplify", &test_simplify },
5955 { "curry", &test_curry },
5956 { "piecewise multi affine expressions", &test_pw_multi_aff },
5957 { "multi piecewise affine expressions", &test_multi_pw_aff },
5958 { "conversion", &test_conversion },
5959 { "list", &test_list },
5960 { "align parameters", &test_align_parameters },
5961 { "preimage", &test_preimage },
5962 { "pullback", &test_pullback },
5963 { "AST", &test_ast },
5964 { "AST build", &test_ast_build },
5965 { "AST generation", &test_ast_gen },
5966 { "eliminate", &test_eliminate },
5967 { "residue class", &test_residue_class },
5968 { "div", &test_div },
5969 { "slice", &test_slice },
5970 { "fixed power", &test_fixed_power },
5971 { "sample", &test_sample },
5972 { "output", &test_output },
5973 { "vertices", &test_vertices },
5974 { "fixed", &test_fixed },
5975 { "equal", &test_equal },
5976 { "disjoint", &test_disjoint },
5977 { "product", &test_product },
5978 { "dim_max", &test_dim_max },
5979 { "affine", &test_aff },
5980 { "injective", &test_injective },
5981 { "schedule", &test_schedule },
5982 { "schedule tree grouping", &test_schedule_tree_group },
5983 { "tile", &test_tile },
5984 { "union_pw", &test_union_pw },
5985 { "eval", &test_eval },
5986 { "parse", &test_parse },
5987 { "single-valued", &test_sv },
5988 { "affine hull", &test_affine_hull },
5989 { "coalesce", &test_coalesce },
5990 { "factorize", &test_factorize },
5991 { "subset", &test_subset },
5992 { "subtract", &test_subtract },
5993 { "lexmin", &test_lexmin },
5994 { "min", &test_min },
5995 { "gist", &test_gist },
5996 { "piecewise quasi-polynomials", &test_pwqp },
5997 { "lift", &test_lift },
5998 { "bound", &test_bound },
5999 { "union", &test_union },
6000 { "split periods", &test_split_periods },
6001 { "lexicographic order", &test_lex },
6002 { "bijectivity", &test_bijective },
6003 { "dataflow analysis", &test_dep },
6004 { "reading", &test_read },
6005 { "bounded", &test_bounded },
6006 { "construction", &test_construction },
6007 { "dimension manipulation", &test_dim },
6008 { "map application", &test_application },
6009 { "convex hull", &test_convex_hull },
6010 { "transitive closure", &test_closure },
6011 };
6012
6013 int main(int argc, char **argv)
6014 {
6015 int i;
6016 struct isl_ctx *ctx;
6017 struct isl_options *options;
6018
6019 srcdir = getenv("srcdir");
6020 assert(srcdir);
6021
6022 options = isl_options_new_with_defaults();
6023 assert(options);
6024 argc = isl_options_parse(options, argc, argv, ISL_ARG_ALL);
6025
6026 ctx = isl_ctx_alloc_with_options(&isl_options_args, options);
6027 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
6028 printf("%s\n", tests[i].name);
6029 if (tests[i].fn(ctx) < 0)
6030 goto error;
6031 }
6032 isl_ctx_free(ctx);
6033 return 0;
6034 error:
6035 isl_ctx_free(ctx);
6036 return -1;
6037 }
Integer set library