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isl_tab_relax: return int instead of isl_tab *
[isl.git] / isl_test.c
bloba730243ccee60ad5684e4070d36ca9b49cd13b32
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
6 *
7 * Use of this software is governed by the MIT license
8 *
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
12 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
15 * B.P. 105 - 78153 Le Chesnay, France
16 */
17
18 #include <assert.h>
19 #include <stdio.h>
20 #include <limits.h>
21 #include <isl_ctx_private.h>
22 #include <isl_map_private.h>
23 #include <isl_aff_private.h>
24 #include <isl/set.h>
25 #include <isl/flow.h>
26 #include <isl_constraint_private.h>
27 #include <isl/polynomial.h>
28 #include <isl/union_map.h>
29 #include <isl_factorization.h>
30 #include <isl/schedule.h>
31 #include <isl_options_private.h>
32 #include <isl/vertices.h>
33 #include <isl/ast_build.h>
34 #include <isl/val.h>
35 #include <isl/ilp.h>
36 #include <isl_ast_build_expr.h>
37 #include <isl/options.h>
38
39 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
40
41 static char *srcdir;
42
43 static char *get_filename(isl_ctx *ctx, const char *name, const char *suffix) {
44 char *filename;
45 int length;
46 char *pattern = "%s/test_inputs/%s.%s";
47
48 length = strlen(pattern) - 6 + strlen(srcdir) + strlen(name)
49 + strlen(suffix) + 1;
50 filename = isl_alloc_array(ctx, char, length);
51
52 if (!filename)
53 return NULL;
54
55 sprintf(filename, pattern, srcdir, name, suffix);
56
57 return filename;
58 }
59
60 void test_parse_map(isl_ctx *ctx, const char *str)
61 {
62 isl_map *map;
63
64 map = isl_map_read_from_str(ctx, str);
65 assert(map);
66 isl_map_free(map);
67 }
68
69 int test_parse_map_equal(isl_ctx *ctx, const char *str, const char *str2)
70 {
71 isl_map *map, *map2;
72 int equal;
73
74 map = isl_map_read_from_str(ctx, str);
75 map2 = isl_map_read_from_str(ctx, str2);
76 equal = isl_map_is_equal(map, map2);
77 isl_map_free(map);
78 isl_map_free(map2);
79
80 if (equal < 0)
81 return -1;
82 if (!equal)
83 isl_die(ctx, isl_error_unknown, "maps not equal",
84 return -1);
85
86 return 0;
87 }
88
89 void test_parse_pwqp(isl_ctx *ctx, const char *str)
90 {
91 isl_pw_qpolynomial *pwqp;
92
93 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
94 assert(pwqp);
95 isl_pw_qpolynomial_free(pwqp);
96 }
97
98 static void test_parse_pwaff(isl_ctx *ctx, const char *str)
99 {
100 isl_pw_aff *pwaff;
101
102 pwaff = isl_pw_aff_read_from_str(ctx, str);
103 assert(pwaff);
104 isl_pw_aff_free(pwaff);
105 }
106
107 int test_parse(struct isl_ctx *ctx)
108 {
109 isl_map *map, *map2;
110 const char *str, *str2;
111
112 str = "{ [i] -> [-i] }";
113 map = isl_map_read_from_str(ctx, str);
114 assert(map);
115 isl_map_free(map);
116
117 str = "{ A[i] -> L[([i/3])] }";
118 map = isl_map_read_from_str(ctx, str);
119 assert(map);
120 isl_map_free(map);
121
122 test_parse_map(ctx, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
123 test_parse_map(ctx, "{ [p1, y1, y2] -> [2, y1, y2] : "
124 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
125
126 str = "{ [x,y] : [([x/2]+y)/3] >= 1 }";
127 str2 = "{ [x, y] : 2y >= 6 - x }";
128 if (test_parse_map_equal(ctx, str, str2) < 0)
129 return -1;
130
131 if (test_parse_map_equal(ctx, "{ [x,y] : x <= min(y, 2*y+3) }",
132 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
133 return -1;
134 str = "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
135 if (test_parse_map_equal(ctx, "{ [x,y] : x >= min(y, 2*y+3) }",
136 str) < 0)
137 return -1;
138
139 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
140 map = isl_map_read_from_str(ctx, str);
141 str = "{ [new, old] -> [o0, o1] : "
142 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
143 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
144 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
145 map2 = isl_map_read_from_str(ctx, str);
146 assert(isl_map_is_equal(map, map2));
147 isl_map_free(map);
148 isl_map_free(map2);
149
150 str = "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
151 map = isl_map_read_from_str(ctx, str);
152 str = "{[new,old] -> [(new+1)%2,(old+1)%2]}";
153 map2 = isl_map_read_from_str(ctx, str);
154 assert(isl_map_is_equal(map, map2));
155 isl_map_free(map);
156 isl_map_free(map2);
157
158 str = "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
159 str2 = "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
160 if (test_parse_map_equal(ctx, str, str2) < 0)
161 return -1;
162
163 str = "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
164 str2 = "{ [i,j] -> [min(i,j)] }";
165 if (test_parse_map_equal(ctx, str, str2) < 0)
166 return -1;
167
168 str = "{ [i,j] : i != j }";
169 str2 = "{ [i,j] : i < j or i > j }";
170 if (test_parse_map_equal(ctx, str, str2) < 0)
171 return -1;
172
173 str = "{ [i,j] : (i+1)*2 >= j }";
174 str2 = "{ [i, j] : j <= 2 + 2i }";
175 if (test_parse_map_equal(ctx, str, str2) < 0)
176 return -1;
177
178 str = "{ [i] -> [i > 0 ? 4 : 5] }";
179 str2 = "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
180 if (test_parse_map_equal(ctx, str, str2) < 0)
181 return -1;
182
183 str = "[N=2,M] -> { [i=[(M+N)/4]] }";
184 str2 = "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
185 if (test_parse_map_equal(ctx, str, str2) < 0)
186 return -1;
187
188 str = "{ [x] : x >= 0 }";
189 str2 = "{ [x] : x-0 >= 0 }";
190 if (test_parse_map_equal(ctx, str, str2) < 0)
191 return -1;
192
193 str = "{ [i] : ((i > 10)) }";
194 str2 = "{ [i] : i >= 11 }";
195 if (test_parse_map_equal(ctx, str, str2) < 0)
196 return -1;
197
198 str = "{ [i] -> [0] }";
199 str2 = "{ [i] -> [0 * i] }";
200 if (test_parse_map_equal(ctx, str, str2) < 0)
201 return -1;
202
203 test_parse_pwqp(ctx, "{ [i] -> i + [ (i + [i/3])/2 ] }");
204 test_parse_map(ctx, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
205 test_parse_pwaff(ctx, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
206 test_parse_pwqp(ctx, "{ [x] -> ([(x)/2] * [(x)/3]) }");
207
208 if (test_parse_map_equal(ctx, "{ [a] -> [b] : (not false) }",
209 "{ [a] -> [b] : true }") < 0)
210 return -1;
211
212 if (test_parse_map_equal(ctx, "{ [i] : i/2 <= 5 }",
213 "{ [i] : i <= 10 }") < 0)
214 return -1;
215
216 if (test_parse_map_equal(ctx, "{Sym=[n] [i] : i <= n }",
217 "[n] -> { [i] : i <= n }") < 0)
218 return -1;
219
220 if (test_parse_map_equal(ctx, "{ [*] }", "{ [a] }") < 0)
221 return -1;
222
223 if (test_parse_map_equal(ctx, "{ [i] : 2*floor(i/2) = i }",
224 "{ [i] : exists a : i = 2 a }") < 0)
225 return -1;
226
227 if (test_parse_map_equal(ctx, "{ [a] -> [b] : a = 5 implies b = 5 }",
228 "{ [a] -> [b] : a != 5 or b = 5 }") < 0)
229 return -1;
230
231 if (test_parse_map_equal(ctx, "{ [a] -> [a - 1 : a > 0] }",
232 "{ [a] -> [a - 1] : a > 0 }") < 0)
233 return -1;
234 if (test_parse_map_equal(ctx,
235 "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
236 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }") < 0)
237 return -1;
238 if (test_parse_map_equal(ctx,
239 "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
240 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
241 return -1;
242 if (test_parse_map_equal(ctx,
243 "{ [a] -> [(a * 2) : a >= 0; 0 : a < 0] }",
244 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
245 return -1;
246 if (test_parse_map_equal(ctx,
247 "{ [a] -> [(a * 2 : a >= 0); 0 : a < 0] }",
248 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
249 return -1;
250 if (test_parse_map_equal(ctx,
251 "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
252 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
253 return -1;
254
255 return 0;
256 }
257
258 void test_read(struct isl_ctx *ctx)
259 {
260 char *filename;
261 FILE *input;
262 struct isl_basic_set *bset1, *bset2;
263 const char *str = "{[y]: Exists ( alpha : 2alpha = y)}";
264
265 filename = get_filename(ctx, "set", "omega");
266 assert(filename);
267 input = fopen(filename, "r");
268 assert(input);
269
270 bset1 = isl_basic_set_read_from_file(ctx, input);
271 bset2 = isl_basic_set_read_from_str(ctx, str);
272
273 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
274
275 isl_basic_set_free(bset1);
276 isl_basic_set_free(bset2);
277 free(filename);
278
279 fclose(input);
280 }
281
282 void test_bounded(struct isl_ctx *ctx)
283 {
284 isl_set *set;
285 int bounded;
286
287 set = isl_set_read_from_str(ctx, "[n] -> {[i] : 0 <= i <= n }");
288 bounded = isl_set_is_bounded(set);
289 assert(bounded);
290 isl_set_free(set);
291
292 set = isl_set_read_from_str(ctx, "{[n, i] : 0 <= i <= n }");
293 bounded = isl_set_is_bounded(set);
294 assert(!bounded);
295 isl_set_free(set);
296
297 set = isl_set_read_from_str(ctx, "[n] -> {[i] : i <= n }");
298 bounded = isl_set_is_bounded(set);
299 assert(!bounded);
300 isl_set_free(set);
301 }
302
303 /* Construct the basic set { [i] : 5 <= i <= N } */
304 void test_construction(struct isl_ctx *ctx)
305 {
306 isl_int v;
307 isl_space *dim;
308 isl_local_space *ls;
309 struct isl_basic_set *bset;
310 struct isl_constraint *c;
311
312 isl_int_init(v);
313
314 dim = isl_space_set_alloc(ctx, 1, 1);
315 bset = isl_basic_set_universe(isl_space_copy(dim));
316 ls = isl_local_space_from_space(dim);
317
318 c = isl_inequality_alloc(isl_local_space_copy(ls));
319 isl_int_set_si(v, -1);
320 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
321 isl_int_set_si(v, 1);
322 isl_constraint_set_coefficient(c, isl_dim_param, 0, v);
323 bset = isl_basic_set_add_constraint(bset, c);
324
325 c = isl_inequality_alloc(isl_local_space_copy(ls));
326 isl_int_set_si(v, 1);
327 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
328 isl_int_set_si(v, -5);
329 isl_constraint_set_constant(c, v);
330 bset = isl_basic_set_add_constraint(bset, c);
331
332 isl_local_space_free(ls);
333 isl_basic_set_free(bset);
334
335 isl_int_clear(v);
336 }
337
338 void test_dim(struct isl_ctx *ctx)
339 {
340 const char *str;
341 isl_map *map1, *map2;
342
343 map1 = isl_map_read_from_str(ctx,
344 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
345 map1 = isl_map_add_dims(map1, isl_dim_in, 1);
346 map2 = isl_map_read_from_str(ctx,
347 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
348 assert(isl_map_is_equal(map1, map2));
349 isl_map_free(map2);
350
351 map1 = isl_map_project_out(map1, isl_dim_in, 0, 1);
352 map2 = isl_map_read_from_str(ctx, "[n] -> { [i] -> [j] : n >= 0 }");
353 assert(isl_map_is_equal(map1, map2));
354
355 isl_map_free(map1);
356 isl_map_free(map2);
357
358 str = "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
359 map1 = isl_map_read_from_str(ctx, str);
360 str = "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
361 map2 = isl_map_read_from_str(ctx, str);
362 map1 = isl_map_move_dims(map1, isl_dim_out, 0, isl_dim_param, 0, 1);
363 assert(isl_map_is_equal(map1, map2));
364
365 isl_map_free(map1);
366 isl_map_free(map2);
367 }
368
369 struct {
370 __isl_give isl_val *(*op)(__isl_take isl_val *v);
371 const char *arg;
372 const char *res;
373 } val_un_tests[] = {
374 { &isl_val_neg, "0", "0" },
375 { &isl_val_abs, "0", "0" },
376 { &isl_val_2exp, "0", "1" },
377 { &isl_val_floor, "0", "0" },
378 { &isl_val_ceil, "0", "0" },
379 { &isl_val_neg, "1", "-1" },
380 { &isl_val_neg, "-1", "1" },
381 { &isl_val_neg, "1/2", "-1/2" },
382 { &isl_val_neg, "-1/2", "1/2" },
383 { &isl_val_neg, "infty", "-infty" },
384 { &isl_val_neg, "-infty", "infty" },
385 { &isl_val_neg, "NaN", "NaN" },
386 { &isl_val_abs, "1", "1" },
387 { &isl_val_abs, "-1", "1" },
388 { &isl_val_abs, "1/2", "1/2" },
389 { &isl_val_abs, "-1/2", "1/2" },
390 { &isl_val_abs, "infty", "infty" },
391 { &isl_val_abs, "-infty", "infty" },
392 { &isl_val_abs, "NaN", "NaN" },
393 { &isl_val_floor, "1", "1" },
394 { &isl_val_floor, "-1", "-1" },
395 { &isl_val_floor, "1/2", "0" },
396 { &isl_val_floor, "-1/2", "-1" },
397 { &isl_val_floor, "infty", "infty" },
398 { &isl_val_floor, "-infty", "-infty" },
399 { &isl_val_floor, "NaN", "NaN" },
400 { &isl_val_ceil, "1", "1" },
401 { &isl_val_ceil, "-1", "-1" },
402 { &isl_val_ceil, "1/2", "1" },
403 { &isl_val_ceil, "-1/2", "0" },
404 { &isl_val_ceil, "infty", "infty" },
405 { &isl_val_ceil, "-infty", "-infty" },
406 { &isl_val_ceil, "NaN", "NaN" },
407 { &isl_val_2exp, "-3", "1/8" },
408 { &isl_val_2exp, "-1", "1/2" },
409 { &isl_val_2exp, "1", "2" },
410 { &isl_val_2exp, "2", "4" },
411 { &isl_val_2exp, "3", "8" },
412 { &isl_val_inv, "1", "1" },
413 { &isl_val_inv, "2", "1/2" },
414 { &isl_val_inv, "1/2", "2" },
415 { &isl_val_inv, "-2", "-1/2" },
416 { &isl_val_inv, "-1/2", "-2" },
417 { &isl_val_inv, "0", "NaN" },
418 { &isl_val_inv, "NaN", "NaN" },
419 { &isl_val_inv, "infty", "0" },
420 { &isl_val_inv, "-infty", "0" },
421 };
422
423 /* Perform some basic tests of unary operations on isl_val objects.
424 */
425 static int test_un_val(isl_ctx *ctx)
426 {
427 int i;
428 isl_val *v, *res;
429 __isl_give isl_val *(*fn)(__isl_take isl_val *v);
430 int ok;
431
432 for (i = 0; i < ARRAY_SIZE(val_un_tests); ++i) {
433 v = isl_val_read_from_str(ctx, val_un_tests[i].arg);
434 res = isl_val_read_from_str(ctx, val_un_tests[i].res);
435 fn = val_un_tests[i].op;
436 v = fn(v);
437 if (isl_val_is_nan(res))
438 ok = isl_val_is_nan(v);
439 else
440 ok = isl_val_eq(v, res);
441 isl_val_free(v);
442 isl_val_free(res);
443 if (ok < 0)
444 return -1;
445 if (!ok)
446 isl_die(ctx, isl_error_unknown,
447 "unexpected result", return -1);
448 }
449
450 return 0;
451 }
452
453 struct {
454 __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
455 __isl_take isl_val *v2);
456 } val_bin_op[] = {
457 ['+'] = { &isl_val_add },
458 ['-'] = { &isl_val_sub },
459 ['*'] = { &isl_val_mul },
460 ['/'] = { &isl_val_div },
461 ['g'] = { &isl_val_gcd },
462 ['m'] = { &isl_val_min },
463 ['M'] = { &isl_val_max },
464 };
465
466 struct {
467 const char *arg1;
468 unsigned char op;
469 const char *arg2;
470 const char *res;
471 } val_bin_tests[] = {
472 { "0", '+', "0", "0" },
473 { "1", '+', "0", "1" },
474 { "1", '+', "1", "2" },
475 { "1", '-', "1", "0" },
476 { "1", '*', "1", "1" },
477 { "1", '/', "1", "1" },
478 { "2", '*', "3", "6" },
479 { "2", '*', "1/2", "1" },
480 { "2", '*', "1/3", "2/3" },
481 { "2/3", '*', "3/5", "2/5" },
482 { "2/3", '*', "7/5", "14/15" },
483 { "2", '/', "1/2", "4" },
484 { "-2", '/', "-1/2", "4" },
485 { "-2", '/', "1/2", "-4" },
486 { "2", '/', "-1/2", "-4" },
487 { "2", '/', "2", "1" },
488 { "2", '/', "3", "2/3" },
489 { "2/3", '/', "5/3", "2/5" },
490 { "2/3", '/', "5/7", "14/15" },
491 { "0", '/', "0", "NaN" },
492 { "42", '/', "0", "NaN" },
493 { "-42", '/', "0", "NaN" },
494 { "infty", '/', "0", "NaN" },
495 { "-infty", '/', "0", "NaN" },
496 { "NaN", '/', "0", "NaN" },
497 { "0", '/', "NaN", "NaN" },
498 { "42", '/', "NaN", "NaN" },
499 { "-42", '/', "NaN", "NaN" },
500 { "infty", '/', "NaN", "NaN" },
501 { "-infty", '/', "NaN", "NaN" },
502 { "NaN", '/', "NaN", "NaN" },
503 { "0", '/', "infty", "0" },
504 { "42", '/', "infty", "0" },
505 { "-42", '/', "infty", "0" },
506 { "infty", '/', "infty", "NaN" },
507 { "-infty", '/', "infty", "NaN" },
508 { "NaN", '/', "infty", "NaN" },
509 { "0", '/', "-infty", "0" },
510 { "42", '/', "-infty", "0" },
511 { "-42", '/', "-infty", "0" },
512 { "infty", '/', "-infty", "NaN" },
513 { "-infty", '/', "-infty", "NaN" },
514 { "NaN", '/', "-infty", "NaN" },
515 { "1", '-', "1/3", "2/3" },
516 { "1/3", '+', "1/2", "5/6" },
517 { "1/2", '+', "1/2", "1" },
518 { "3/4", '-', "1/4", "1/2" },
519 { "1/2", '-', "1/3", "1/6" },
520 { "infty", '+', "42", "infty" },
521 { "infty", '+', "infty", "infty" },
522 { "42", '+', "infty", "infty" },
523 { "infty", '-', "infty", "NaN" },
524 { "infty", '*', "infty", "infty" },
525 { "infty", '*', "-infty", "-infty" },
526 { "-infty", '*', "infty", "-infty" },
527 { "-infty", '*', "-infty", "infty" },
528 { "0", '*', "infty", "NaN" },
529 { "1", '*', "infty", "infty" },
530 { "infty", '*', "0", "NaN" },
531 { "infty", '*', "42", "infty" },
532 { "42", '-', "infty", "-infty" },
533 { "infty", '+', "-infty", "NaN" },
534 { "4", 'g', "6", "2" },
535 { "5", 'g', "6", "1" },
536 { "42", 'm', "3", "3" },
537 { "42", 'M', "3", "42" },
538 { "3", 'm', "42", "3" },
539 { "3", 'M', "42", "42" },
540 { "42", 'm', "infty", "42" },
541 { "42", 'M', "infty", "infty" },
542 { "42", 'm', "-infty", "-infty" },
543 { "42", 'M', "-infty", "42" },
544 { "42", 'm', "NaN", "NaN" },
545 { "42", 'M', "NaN", "NaN" },
546 { "infty", 'm', "-infty", "-infty" },
547 { "infty", 'M', "-infty", "infty" },
548 };
549
550 /* Perform some basic tests of binary operations on isl_val objects.
551 */
552 static int test_bin_val(isl_ctx *ctx)
553 {
554 int i;
555 isl_val *v1, *v2, *res;
556 __isl_give isl_val *(*fn)(__isl_take isl_val *v1,
557 __isl_take isl_val *v2);
558 int ok;
559
560 for (i = 0; i < ARRAY_SIZE(val_bin_tests); ++i) {
561 v1 = isl_val_read_from_str(ctx, val_bin_tests[i].arg1);
562 v2 = isl_val_read_from_str(ctx, val_bin_tests[i].arg2);
563 res = isl_val_read_from_str(ctx, val_bin_tests[i].res);
564 fn = val_bin_op[val_bin_tests[i].op].fn;
565 v1 = fn(v1, v2);
566 if (isl_val_is_nan(res))
567 ok = isl_val_is_nan(v1);
568 else
569 ok = isl_val_eq(v1, res);
570 isl_val_free(v1);
571 isl_val_free(res);
572 if (ok < 0)
573 return -1;
574 if (!ok)
575 isl_die(ctx, isl_error_unknown,
576 "unexpected result", return -1);
577 }
578
579 return 0;
580 }
581
582 /* Perform some basic tests on isl_val objects.
583 */
584 static int test_val(isl_ctx *ctx)
585 {
586 if (test_un_val(ctx) < 0)
587 return -1;
588 if (test_bin_val(ctx) < 0)
589 return -1;
590 return 0;
591 }
592
593 static int test_div(isl_ctx *ctx)
594 {
595 unsigned n;
596 const char *str;
597 int empty;
598 isl_int v;
599 isl_space *dim;
600 isl_set *set;
601 isl_local_space *ls;
602 struct isl_basic_set *bset;
603 struct isl_constraint *c;
604
605 isl_int_init(v);
606
607 /* test 1 */
608 dim = isl_space_set_alloc(ctx, 0, 3);
609 bset = isl_basic_set_universe(isl_space_copy(dim));
610 ls = isl_local_space_from_space(dim);
611
612 c = isl_equality_alloc(isl_local_space_copy(ls));
613 isl_int_set_si(v, -1);
614 isl_constraint_set_constant(c, v);
615 isl_int_set_si(v, 1);
616 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
617 isl_int_set_si(v, 3);
618 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
619 bset = isl_basic_set_add_constraint(bset, c);
620
621 c = isl_equality_alloc(isl_local_space_copy(ls));
622 isl_int_set_si(v, 1);
623 isl_constraint_set_constant(c, v);
624 isl_int_set_si(v, -1);
625 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
626 isl_int_set_si(v, 3);
627 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
628 bset = isl_basic_set_add_constraint(bset, c);
629
630 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
631
632 assert(bset && bset->n_div == 1);
633 isl_local_space_free(ls);
634 isl_basic_set_free(bset);
635
636 /* test 2 */
637 dim = isl_space_set_alloc(ctx, 0, 3);
638 bset = isl_basic_set_universe(isl_space_copy(dim));
639 ls = isl_local_space_from_space(dim);
640
641 c = isl_equality_alloc(isl_local_space_copy(ls));
642 isl_int_set_si(v, 1);
643 isl_constraint_set_constant(c, v);
644 isl_int_set_si(v, -1);
645 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
646 isl_int_set_si(v, 3);
647 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
648 bset = isl_basic_set_add_constraint(bset, c);
649
650 c = isl_equality_alloc(isl_local_space_copy(ls));
651 isl_int_set_si(v, -1);
652 isl_constraint_set_constant(c, v);
653 isl_int_set_si(v, 1);
654 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
655 isl_int_set_si(v, 3);
656 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
657 bset = isl_basic_set_add_constraint(bset, c);
658
659 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
660
661 assert(bset && bset->n_div == 1);
662 isl_local_space_free(ls);
663 isl_basic_set_free(bset);
664
665 /* test 3 */
666 dim = isl_space_set_alloc(ctx, 0, 3);
667 bset = isl_basic_set_universe(isl_space_copy(dim));
668 ls = isl_local_space_from_space(dim);
669
670 c = isl_equality_alloc(isl_local_space_copy(ls));
671 isl_int_set_si(v, 1);
672 isl_constraint_set_constant(c, v);
673 isl_int_set_si(v, -1);
674 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
675 isl_int_set_si(v, 3);
676 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
677 bset = isl_basic_set_add_constraint(bset, c);
678
679 c = isl_equality_alloc(isl_local_space_copy(ls));
680 isl_int_set_si(v, -3);
681 isl_constraint_set_constant(c, v);
682 isl_int_set_si(v, 1);
683 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
684 isl_int_set_si(v, 4);
685 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
686 bset = isl_basic_set_add_constraint(bset, c);
687
688 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
689
690 assert(bset && bset->n_div == 1);
691 isl_local_space_free(ls);
692 isl_basic_set_free(bset);
693
694 /* test 4 */
695 dim = isl_space_set_alloc(ctx, 0, 3);
696 bset = isl_basic_set_universe(isl_space_copy(dim));
697 ls = isl_local_space_from_space(dim);
698
699 c = isl_equality_alloc(isl_local_space_copy(ls));
700 isl_int_set_si(v, 2);
701 isl_constraint_set_constant(c, v);
702 isl_int_set_si(v, -1);
703 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
704 isl_int_set_si(v, 3);
705 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
706 bset = isl_basic_set_add_constraint(bset, c);
707
708 c = isl_equality_alloc(isl_local_space_copy(ls));
709 isl_int_set_si(v, -1);
710 isl_constraint_set_constant(c, v);
711 isl_int_set_si(v, 1);
712 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
713 isl_int_set_si(v, 6);
714 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
715 bset = isl_basic_set_add_constraint(bset, c);
716
717 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 2);
718
719 assert(isl_basic_set_is_empty(bset));
720 isl_local_space_free(ls);
721 isl_basic_set_free(bset);
722
723 /* test 5 */
724 dim = isl_space_set_alloc(ctx, 0, 3);
725 bset = isl_basic_set_universe(isl_space_copy(dim));
726 ls = isl_local_space_from_space(dim);
727
728 c = isl_equality_alloc(isl_local_space_copy(ls));
729 isl_int_set_si(v, -1);
730 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
731 isl_int_set_si(v, 3);
732 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
733 bset = isl_basic_set_add_constraint(bset, c);
734
735 c = isl_equality_alloc(isl_local_space_copy(ls));
736 isl_int_set_si(v, 1);
737 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
738 isl_int_set_si(v, -3);
739 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
740 bset = isl_basic_set_add_constraint(bset, c);
741
742 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
743
744 assert(bset && bset->n_div == 0);
745 isl_basic_set_free(bset);
746 isl_local_space_free(ls);
747
748 /* test 6 */
749 dim = isl_space_set_alloc(ctx, 0, 3);
750 bset = isl_basic_set_universe(isl_space_copy(dim));
751 ls = isl_local_space_from_space(dim);
752
753 c = isl_equality_alloc(isl_local_space_copy(ls));
754 isl_int_set_si(v, -1);
755 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
756 isl_int_set_si(v, 6);
757 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
758 bset = isl_basic_set_add_constraint(bset, c);
759
760 c = isl_equality_alloc(isl_local_space_copy(ls));
761 isl_int_set_si(v, 1);
762 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
763 isl_int_set_si(v, -3);
764 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
765 bset = isl_basic_set_add_constraint(bset, c);
766
767 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
768
769 assert(bset && bset->n_div == 1);
770 isl_basic_set_free(bset);
771 isl_local_space_free(ls);
772
773 /* test 7 */
774 /* This test is a bit tricky. We set up an equality
775 * a + 3b + 3c = 6 e0
776 * Normalization of divs creates _two_ divs
777 * a = 3 e0
778 * c - b - e0 = 2 e1
779 * Afterwards e0 is removed again because it has coefficient -1
780 * and we end up with the original equality and div again.
781 * Perhaps we can avoid the introduction of this temporary div.
782 */
783 dim = isl_space_set_alloc(ctx, 0, 4);
784 bset = isl_basic_set_universe(isl_space_copy(dim));
785 ls = isl_local_space_from_space(dim);
786
787 c = isl_equality_alloc(isl_local_space_copy(ls));
788 isl_int_set_si(v, -1);
789 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
790 isl_int_set_si(v, -3);
791 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
792 isl_int_set_si(v, -3);
793 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
794 isl_int_set_si(v, 6);
795 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
796 bset = isl_basic_set_add_constraint(bset, c);
797
798 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
799
800 /* Test disabled for now */
801 /*
802 assert(bset && bset->n_div == 1);
803 */
804 isl_local_space_free(ls);
805 isl_basic_set_free(bset);
806
807 /* test 8 */
808 dim = isl_space_set_alloc(ctx, 0, 5);
809 bset = isl_basic_set_universe(isl_space_copy(dim));
810 ls = isl_local_space_from_space(dim);
811
812 c = isl_equality_alloc(isl_local_space_copy(ls));
813 isl_int_set_si(v, -1);
814 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
815 isl_int_set_si(v, -3);
816 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
817 isl_int_set_si(v, -3);
818 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
819 isl_int_set_si(v, 6);
820 isl_constraint_set_coefficient(c, isl_dim_set, 4, v);
821 bset = isl_basic_set_add_constraint(bset, c);
822
823 c = isl_equality_alloc(isl_local_space_copy(ls));
824 isl_int_set_si(v, -1);
825 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
826 isl_int_set_si(v, 1);
827 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
828 isl_int_set_si(v, 1);
829 isl_constraint_set_constant(c, v);
830 bset = isl_basic_set_add_constraint(bset, c);
831
832 bset = isl_basic_set_project_out(bset, isl_dim_set, 4, 1);
833
834 /* Test disabled for now */
835 /*
836 assert(bset && bset->n_div == 1);
837 */
838 isl_local_space_free(ls);
839 isl_basic_set_free(bset);
840
841 /* test 9 */
842 dim = isl_space_set_alloc(ctx, 0, 4);
843 bset = isl_basic_set_universe(isl_space_copy(dim));
844 ls = isl_local_space_from_space(dim);
845
846 c = isl_equality_alloc(isl_local_space_copy(ls));
847 isl_int_set_si(v, 1);
848 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
849 isl_int_set_si(v, -1);
850 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
851 isl_int_set_si(v, -2);
852 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
853 bset = isl_basic_set_add_constraint(bset, c);
854
855 c = isl_equality_alloc(isl_local_space_copy(ls));
856 isl_int_set_si(v, -1);
857 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
858 isl_int_set_si(v, 3);
859 isl_constraint_set_coefficient(c, isl_dim_set, 3, v);
860 isl_int_set_si(v, 2);
861 isl_constraint_set_constant(c, v);
862 bset = isl_basic_set_add_constraint(bset, c);
863
864 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 2);
865
866 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
867
868 assert(!isl_basic_set_is_empty(bset));
869
870 isl_local_space_free(ls);
871 isl_basic_set_free(bset);
872
873 /* test 10 */
874 dim = isl_space_set_alloc(ctx, 0, 3);
875 bset = isl_basic_set_universe(isl_space_copy(dim));
876 ls = isl_local_space_from_space(dim);
877
878 c = isl_equality_alloc(isl_local_space_copy(ls));
879 isl_int_set_si(v, 1);
880 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
881 isl_int_set_si(v, -2);
882 isl_constraint_set_coefficient(c, isl_dim_set, 2, v);
883 bset = isl_basic_set_add_constraint(bset, c);
884
885 bset = isl_basic_set_project_out(bset, isl_dim_set, 2, 1);
886
887 bset = isl_basic_set_fix_si(bset, isl_dim_set, 0, 2);
888
889 isl_local_space_free(ls);
890 isl_basic_set_free(bset);
891
892 isl_int_clear(v);
893
894 str = "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
895 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
896 set = isl_set_read_from_str(ctx, str);
897 set = isl_set_compute_divs(set);
898 isl_set_free(set);
899 if (!set)
900 return -1;
901
902 str = "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
903 bset = isl_basic_set_read_from_str(ctx, str);
904 n = isl_basic_set_dim(bset, isl_dim_div);
905 isl_basic_set_free(bset);
906 if (!bset)
907 return -1;
908 if (n != 0)
909 isl_die(ctx, isl_error_unknown,
910 "expecting no existentials", return -1);
911
912 str = "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
913 set = isl_set_read_from_str(ctx, str);
914 set = isl_set_remove_divs_involving_dims(set, isl_dim_set, 0, 2);
915 set = isl_set_fix_si(set, isl_dim_set, 2, -3);
916 empty = isl_set_is_empty(set);
917 isl_set_free(set);
918 if (empty < 0)
919 return -1;
920 if (!empty)
921 isl_die(ctx, isl_error_unknown,
922 "result not as accurate as expected", return -1);
923
924 return 0;
925 }
926
927 void test_application_case(struct isl_ctx *ctx, const char *name)
928 {
929 char *filename;
930 FILE *input;
931 struct isl_basic_set *bset1, *bset2;
932 struct isl_basic_map *bmap;
933
934 filename = get_filename(ctx, name, "omega");
935 assert(filename);
936 input = fopen(filename, "r");
937 assert(input);
938
939 bset1 = isl_basic_set_read_from_file(ctx, input);
940 bmap = isl_basic_map_read_from_file(ctx, input);
941
942 bset1 = isl_basic_set_apply(bset1, bmap);
943
944 bset2 = isl_basic_set_read_from_file(ctx, input);
945
946 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
947
948 isl_basic_set_free(bset1);
949 isl_basic_set_free(bset2);
950 free(filename);
951
952 fclose(input);
953 }
954
955 void test_application(struct isl_ctx *ctx)
956 {
957 test_application_case(ctx, "application");
958 test_application_case(ctx, "application2");
959 }
960
961 void test_affine_hull_case(struct isl_ctx *ctx, const char *name)
962 {
963 char *filename;
964 FILE *input;
965 struct isl_basic_set *bset1, *bset2;
966
967 filename = get_filename(ctx, name, "polylib");
968 assert(filename);
969 input = fopen(filename, "r");
970 assert(input);
971
972 bset1 = isl_basic_set_read_from_file(ctx, input);
973 bset2 = isl_basic_set_read_from_file(ctx, input);
974
975 bset1 = isl_basic_set_affine_hull(bset1);
976
977 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
978
979 isl_basic_set_free(bset1);
980 isl_basic_set_free(bset2);
981 free(filename);
982
983 fclose(input);
984 }
985
986 int test_affine_hull(struct isl_ctx *ctx)
987 {
988 const char *str;
989 isl_set *set;
990 isl_basic_set *bset, *bset2;
991 int n;
992 int subset;
993
994 test_affine_hull_case(ctx, "affine2");
995 test_affine_hull_case(ctx, "affine");
996 test_affine_hull_case(ctx, "affine3");
997
998 str = "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
999 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
1000 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
1001 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
1002 set = isl_set_read_from_str(ctx, str);
1003 bset = isl_set_affine_hull(set);
1004 n = isl_basic_set_dim(bset, isl_dim_div);
1005 isl_basic_set_free(bset);
1006 if (n != 0)
1007 isl_die(ctx, isl_error_unknown, "not expecting any divs",
1008 return -1);
1009
1010 /* Check that isl_map_affine_hull is not confused by
1011 * the reordering of divs in isl_map_align_divs.
1012 */
1013 str = "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1014 "32e0 = b and 32e1 = c); "
1015 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1016 set = isl_set_read_from_str(ctx, str);
1017 bset = isl_set_affine_hull(set);
1018 isl_basic_set_free(bset);
1019 if (!bset)
1020 return -1;
1021
1022 str = "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1023 "32e2 = 31 + 31e0 }";
1024 set = isl_set_read_from_str(ctx, str);
1025 bset = isl_set_affine_hull(set);
1026 str = "{ [a] : exists e : a = 32 e }";
1027 bset2 = isl_basic_set_read_from_str(ctx, str);
1028 subset = isl_basic_set_is_subset(bset, bset2);
1029 isl_basic_set_free(bset);
1030 isl_basic_set_free(bset2);
1031 if (subset < 0)
1032 return -1;
1033 if (!subset)
1034 isl_die(ctx, isl_error_unknown, "not as accurate as expected",
1035 return -1);
1036
1037 return 0;
1038 }
1039
1040 void test_convex_hull_case(struct isl_ctx *ctx, const char *name)
1041 {
1042 char *filename;
1043 FILE *input;
1044 struct isl_basic_set *bset1, *bset2;
1045 struct isl_set *set;
1046
1047 filename = get_filename(ctx, name, "polylib");
1048 assert(filename);
1049 input = fopen(filename, "r");
1050 assert(input);
1051
1052 bset1 = isl_basic_set_read_from_file(ctx, input);
1053 bset2 = isl_basic_set_read_from_file(ctx, input);
1054
1055 set = isl_basic_set_union(bset1, bset2);
1056 bset1 = isl_set_convex_hull(set);
1057
1058 bset2 = isl_basic_set_read_from_file(ctx, input);
1059
1060 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1061
1062 isl_basic_set_free(bset1);
1063 isl_basic_set_free(bset2);
1064 free(filename);
1065
1066 fclose(input);
1067 }
1068
1069 struct {
1070 const char *set;
1071 const char *hull;
1072 } convex_hull_tests[] = {
1073 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1074 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1075 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1076 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1077 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1078 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1079 "i2 <= 5 and i2 >= 4; "
1080 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1081 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1082 "i2 <= 5 + i0 and i2 >= i0 }" },
1083 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1084 "{ [x, y] : 1 = 0 }" },
1085 };
1086
1087 void test_convex_hull_algo(struct isl_ctx *ctx, int convex)
1088 {
1089 int i;
1090 int orig_convex = ctx->opt->convex;
1091 ctx->opt->convex = convex;
1092
1093 test_convex_hull_case(ctx, "convex0");
1094 test_convex_hull_case(ctx, "convex1");
1095 test_convex_hull_case(ctx, "convex2");
1096 test_convex_hull_case(ctx, "convex3");
1097 test_convex_hull_case(ctx, "convex4");
1098 test_convex_hull_case(ctx, "convex5");
1099 test_convex_hull_case(ctx, "convex6");
1100 test_convex_hull_case(ctx, "convex7");
1101 test_convex_hull_case(ctx, "convex8");
1102 test_convex_hull_case(ctx, "convex9");
1103 test_convex_hull_case(ctx, "convex10");
1104 test_convex_hull_case(ctx, "convex11");
1105 test_convex_hull_case(ctx, "convex12");
1106 test_convex_hull_case(ctx, "convex13");
1107 test_convex_hull_case(ctx, "convex14");
1108 test_convex_hull_case(ctx, "convex15");
1109
1110 for (i = 0; i < ARRAY_SIZE(convex_hull_tests); ++i) {
1111 isl_set *set1, *set2;
1112
1113 set1 = isl_set_read_from_str(ctx, convex_hull_tests[i].set);
1114 set2 = isl_set_read_from_str(ctx, convex_hull_tests[i].hull);
1115 set1 = isl_set_from_basic_set(isl_set_convex_hull(set1));
1116 assert(isl_set_is_equal(set1, set2));
1117 isl_set_free(set1);
1118 isl_set_free(set2);
1119 }
1120
1121 ctx->opt->convex = orig_convex;
1122 }
1123
1124 void test_convex_hull(struct isl_ctx *ctx)
1125 {
1126 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_FM);
1127 test_convex_hull_algo(ctx, ISL_CONVEX_HULL_WRAP);
1128 }
1129
1130 void test_gist_case(struct isl_ctx *ctx, const char *name)
1131 {
1132 char *filename;
1133 FILE *input;
1134 struct isl_basic_set *bset1, *bset2;
1135
1136 filename = get_filename(ctx, name, "polylib");
1137 assert(filename);
1138 input = fopen(filename, "r");
1139 assert(input);
1140
1141 bset1 = isl_basic_set_read_from_file(ctx, input);
1142 bset2 = isl_basic_set_read_from_file(ctx, input);
1143
1144 bset1 = isl_basic_set_gist(bset1, bset2);
1145
1146 bset2 = isl_basic_set_read_from_file(ctx, input);
1147
1148 assert(isl_basic_set_is_equal(bset1, bset2) == 1);
1149
1150 isl_basic_set_free(bset1);
1151 isl_basic_set_free(bset2);
1152 free(filename);
1153
1154 fclose(input);
1155 }
1156
1157 struct {
1158 const char *set;
1159 const char *context;
1160 const char *gist;
1161 } gist_tests[] = {
1162 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1163 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1164 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1165 "{ [a, b, c] : a <= 15 }" },
1166 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1167 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1168 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1169 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1170 { "{ [m, n, a, b] : a <= 2147 + n }",
1171 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1172 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1173 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1174 "b >= 0) }",
1175 "{ [m, n, ku, kl] }" },
1176 };
1177
1178 static int test_gist(struct isl_ctx *ctx)
1179 {
1180 int i;
1181 const char *str;
1182 isl_basic_set *bset1, *bset2;
1183 isl_map *map1, *map2;
1184 int equal;
1185
1186 for (i = 0; i < ARRAY_SIZE(gist_tests); ++i) {
1187 int equal_input;
1188 isl_set *set1, *set2, *copy;
1189
1190 set1 = isl_set_read_from_str(ctx, gist_tests[i].set);
1191 set2 = isl_set_read_from_str(ctx, gist_tests[i].context);
1192 copy = isl_set_copy(set1);
1193 set1 = isl_set_gist(set1, set2);
1194 set2 = isl_set_read_from_str(ctx, gist_tests[i].gist);
1195 equal = isl_set_is_equal(set1, set2);
1196 isl_set_free(set1);
1197 isl_set_free(set2);
1198 set1 = isl_set_read_from_str(ctx, gist_tests[i].set);
1199 equal_input = isl_set_is_equal(set1, copy);
1200 isl_set_free(set1);
1201 isl_set_free(copy);
1202 if (equal < 0 || equal_input < 0)
1203 return -1;
1204 if (!equal)
1205 isl_die(ctx, isl_error_unknown,
1206 "incorrect gist result", return -1);
1207 if (!equal_input)
1208 isl_die(ctx, isl_error_unknown,
1209 "gist modified input", return -1);
1210 }
1211
1212 test_gist_case(ctx, "gist1");
1213
1214 str = "[p0, p2, p3, p5, p6, p10] -> { [] : "
1215 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1216 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1217 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1218 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1219 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1220 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1221 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1222 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1223 bset1 = isl_basic_set_read_from_str(ctx, str);
1224 str = "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1225 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1226 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1227 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1228 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1229 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1230 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1231 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1232 bset2 = isl_basic_set_read_from_str(ctx, str);
1233 bset1 = isl_basic_set_gist(bset1, bset2);
1234 assert(bset1 && bset1->n_div == 0);
1235 isl_basic_set_free(bset1);
1236
1237 /* Check that the integer divisions of the second disjunct
1238 * do not spread to the first disjunct.
1239 */
1240 str = "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1241 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1242 "(exists (e0 = [(-1 + t1)/16], "
1243 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1244 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1245 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1246 "o0 <= 4294967295 and t1 <= -1)) }";
1247 map1 = isl_map_read_from_str(ctx, str);
1248 str = "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1249 map2 = isl_map_read_from_str(ctx, str);
1250 map1 = isl_map_gist(map1, map2);
1251 if (!map1)
1252 return -1;
1253 if (map1->n != 1)
1254 isl_die(ctx, isl_error_unknown, "expecting single disjunct",
1255 isl_map_free(map1); return -1);
1256 if (isl_basic_map_dim(map1->p[0], isl_dim_div) != 1)
1257 isl_die(ctx, isl_error_unknown, "expecting single div",
1258 isl_map_free(map1); return -1);
1259 isl_map_free(map1);
1260
1261 return 0;
1262 }
1263
1264 int test_coalesce_set(isl_ctx *ctx, const char *str, int check_one)
1265 {
1266 isl_set *set, *set2;
1267 int equal;
1268 int one;
1269
1270 set = isl_set_read_from_str(ctx, str);
1271 set = isl_set_coalesce(set);
1272 set2 = isl_set_read_from_str(ctx, str);
1273 equal = isl_set_is_equal(set, set2);
1274 one = set && set->n == 1;
1275 isl_set_free(set);
1276 isl_set_free(set2);
1277
1278 if (equal < 0)
1279 return -1;
1280 if (!equal)
1281 isl_die(ctx, isl_error_unknown,
1282 "coalesced set not equal to input", return -1);
1283 if (check_one && !one)
1284 isl_die(ctx, isl_error_unknown,
1285 "coalesced set should not be a union", return -1);
1286
1287 return 0;
1288 }
1289
1290 int test_coalesce_unbounded_wrapping(isl_ctx *ctx)
1291 {
1292 int r = 0;
1293 int bounded;
1294
1295 bounded = isl_options_get_coalesce_bounded_wrapping(ctx);
1296 isl_options_set_coalesce_bounded_wrapping(ctx, 0);
1297
1298 if (test_coalesce_set(ctx,
1299 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1300 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1301 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1302 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1303 "-10 <= y <= 0}", 1) < 0)
1304 goto error;
1305 if (test_coalesce_set(ctx,
1306 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
1307 goto error;
1308 if (test_coalesce_set(ctx,
1309 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
1310 goto error;
1311
1312 if (0) {
1313 error:
1314 r = -1;
1315 }
1316
1317 isl_options_set_coalesce_bounded_wrapping(ctx, bounded);
1318
1319 return r;
1320 }
1321
1322 /* Inputs for coalescing tests.
1323 * "str" is a string representation of the input set.
1324 * "single_disjunct" is set if we expect the result to consist of
1325 * a single disjunct.
1326 */
1327 struct {
1328 int single_disjunct;
1329 const char *str;
1330 } coalesce_tests[] = {
1331 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1332 "y >= x & x >= 2 & 5 >= y }" },
1333 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1334 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1335 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1336 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1337 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1338 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1339 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1340 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1341 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1342 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1343 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1344 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1345 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1346 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1347 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1348 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1349 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1350 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1351 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1352 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1353 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1354 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1355 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1356 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1357 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1358 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1359 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1360 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1361 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1362 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1363 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1364 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1365 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1366 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1367 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1368 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1369 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1370 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1371 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1372 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1373 "[o0, o1, o2, o3, o4, o5, o6]] : "
1374 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1375 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1376 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1377 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1378 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1379 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1380 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1381 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1382 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1383 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1384 "o6 >= i3 + i6 - o3 and M >= 0 and "
1385 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1386 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1387 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1388 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1389 "(o0 = 0 and M >= 2 and N >= 3) or "
1390 "(M = 0 and o0 = 0 and N >= 3) }" },
1391 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1392 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1393 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1394 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1395 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1396 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1397 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1398 "(y = 3 and x = 1) }" },
1399 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1400 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1401 "i1 <= M and i3 <= M and i4 <= M) or "
1402 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1403 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1404 "i4 <= -1 + M) }" },
1405 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1406 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1407 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1408 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1409 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1410 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1411 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1412 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1413 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1414 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1415 { 0, "{ [a, b] : exists e : 2e = a and "
1416 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1417 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1418 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1419 "j >= 1 and j' <= i + j - i' and i >= 1; "
1420 "[1, 1, 1, 1] }" },
1421 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1422 "[i,j] : exists a : j = 3a }" },
1423 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1424 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1425 "a >= 3) or "
1426 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1427 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1428 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1429 "c <= 6 + 8a and a >= 3; "
1430 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1431 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1432 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1433 "[x,0] : 3 <= x <= 4 }" },
1434 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1435 "[x,0] : 4 <= x <= 5 }" },
1436 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1437 "[x,0] : 3 <= x <= 5 }" },
1438 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1439 "[x,0] : 3 <= x <= 4 }" },
1440 { 1 , "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1441 "i1 <= 0; "
1442 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1443 };
1444
1445 /* Test the functionality of isl_set_coalesce.
1446 * That is, check that the output is always equal to the input
1447 * and in some cases that the result consists of a single disjunct.
1448 */
1449 static int test_coalesce(struct isl_ctx *ctx)
1450 {
1451 int i;
1452
1453 for (i = 0; i < ARRAY_SIZE(coalesce_tests); ++i) {
1454 const char *str = coalesce_tests[i].str;
1455 int check_one = coalesce_tests[i].single_disjunct;
1456 if (test_coalesce_set(ctx, str, check_one) < 0)
1457 return -1;
1458 }
1459
1460 if (test_coalesce_unbounded_wrapping(ctx) < 0)
1461 return -1;
1462
1463 return 0;
1464 }
1465
1466 void test_closure(struct isl_ctx *ctx)
1467 {
1468 const char *str;
1469 isl_set *dom;
1470 isl_map *up, *right;
1471 isl_map *map, *map2;
1472 int exact;
1473
1474 /* COCOA example 1 */
1475 map = isl_map_read_from_str(ctx,
1476 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1477 "1 <= i and i < n and 1 <= j and j < n or "
1478 "i2 = i + 1 and j2 = j - 1 and "
1479 "1 <= i and i < n and 2 <= j and j <= n }");
1480 map = isl_map_power(map, &exact);
1481 assert(exact);
1482 isl_map_free(map);
1483
1484 /* COCOA example 1 */
1485 map = isl_map_read_from_str(ctx,
1486 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1487 "1 <= i and i < n and 1 <= j and j < n or "
1488 "i2 = i + 1 and j2 = j - 1 and "
1489 "1 <= i and i < n and 2 <= j and j <= n }");
1490 map = isl_map_transitive_closure(map, &exact);
1491 assert(exact);
1492 map2 = isl_map_read_from_str(ctx,
1493 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1494 "1 <= i and i < n and 1 <= j and j <= n and "
1495 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1496 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1497 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1498 assert(isl_map_is_equal(map, map2));
1499 isl_map_free(map2);
1500 isl_map_free(map);
1501
1502 map = isl_map_read_from_str(ctx,
1503 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1504 " 0 <= y and y <= n }");
1505 map = isl_map_transitive_closure(map, &exact);
1506 map2 = isl_map_read_from_str(ctx,
1507 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1508 " 0 <= y and y <= n }");
1509 assert(isl_map_is_equal(map, map2));
1510 isl_map_free(map2);
1511 isl_map_free(map);
1512
1513 /* COCOA example 2 */
1514 map = isl_map_read_from_str(ctx,
1515 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1516 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1517 "i2 = i + 2 and j2 = j - 2 and "
1518 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1519 map = isl_map_transitive_closure(map, &exact);
1520 assert(exact);
1521 map2 = isl_map_read_from_str(ctx,
1522 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1523 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1524 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1525 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1526 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1527 assert(isl_map_is_equal(map, map2));
1528 isl_map_free(map);
1529 isl_map_free(map2);
1530
1531 /* COCOA Fig.2 left */
1532 map = isl_map_read_from_str(ctx,
1533 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1534 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1535 "j <= n or "
1536 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1537 "j <= 2 i - 3 and j <= n - 2 or "
1538 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1539 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1540 map = isl_map_transitive_closure(map, &exact);
1541 assert(exact);
1542 isl_map_free(map);
1543
1544 /* COCOA Fig.2 right */
1545 map = isl_map_read_from_str(ctx,
1546 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1547 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1548 "j <= n or "
1549 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1550 "j <= 2 i - 4 and j <= n - 3 or "
1551 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1552 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1553 map = isl_map_power(map, &exact);
1554 assert(exact);
1555 isl_map_free(map);
1556
1557 /* COCOA Fig.2 right */
1558 map = isl_map_read_from_str(ctx,
1559 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1560 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1561 "j <= n or "
1562 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1563 "j <= 2 i - 4 and j <= n - 3 or "
1564 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1565 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1566 map = isl_map_transitive_closure(map, &exact);
1567 assert(exact);
1568 map2 = isl_map_read_from_str(ctx,
1569 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1570 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1571 "j <= n and 3 + i + 2 j <= 3 n and "
1572 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1573 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1574 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1575 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1576 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1577 assert(isl_map_is_equal(map, map2));
1578 isl_map_free(map2);
1579 isl_map_free(map);
1580
1581 /* COCOA Fig.1 right */
1582 dom = isl_set_read_from_str(ctx,
1583 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1584 "2 x - 3 y + 3 >= 0 }");
1585 right = isl_map_read_from_str(ctx,
1586 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1587 up = isl_map_read_from_str(ctx,
1588 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1589 right = isl_map_intersect_domain(right, isl_set_copy(dom));
1590 right = isl_map_intersect_range(right, isl_set_copy(dom));
1591 up = isl_map_intersect_domain(up, isl_set_copy(dom));
1592 up = isl_map_intersect_range(up, dom);
1593 map = isl_map_union(up, right);
1594 map = isl_map_transitive_closure(map, &exact);
1595 assert(exact);
1596 map2 = isl_map_read_from_str(ctx,
1597 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1598 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1599 assert(isl_map_is_equal(map, map2));
1600 isl_map_free(map2);
1601 isl_map_free(map);
1602
1603 /* COCOA Theorem 1 counter example */
1604 map = isl_map_read_from_str(ctx,
1605 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1606 "i2 = 1 and j2 = j or "
1607 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1608 map = isl_map_transitive_closure(map, &exact);
1609 assert(exact);
1610 isl_map_free(map);
1611
1612 map = isl_map_read_from_str(ctx,
1613 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1614 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1615 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1616 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1617 map = isl_map_transitive_closure(map, &exact);
1618 assert(exact);
1619 isl_map_free(map);
1620
1621 /* Kelly et al 1996, fig 12 */
1622 map = isl_map_read_from_str(ctx,
1623 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1624 "1 <= i,j,j+1 <= n or "
1625 "j = n and j2 = 1 and i2 = i + 1 and "
1626 "1 <= i,i+1 <= n }");
1627 map = isl_map_transitive_closure(map, &exact);
1628 assert(exact);
1629 map2 = isl_map_read_from_str(ctx,
1630 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1631 "1 <= i <= n and i = i2 or "
1632 "1 <= i < i2 <= n and 1 <= j <= n and "
1633 "1 <= j2 <= n }");
1634 assert(isl_map_is_equal(map, map2));
1635 isl_map_free(map2);
1636 isl_map_free(map);
1637
1638 /* Omega's closure4 */
1639 map = isl_map_read_from_str(ctx,
1640 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1641 "1 <= x,y <= 10 or "
1642 "x2 = x + 1 and y2 = y and "
1643 "1 <= x <= 20 && 5 <= y <= 15 }");
1644 map = isl_map_transitive_closure(map, &exact);
1645 assert(exact);
1646 isl_map_free(map);
1647
1648 map = isl_map_read_from_str(ctx,
1649 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1650 map = isl_map_transitive_closure(map, &exact);
1651 assert(!exact);
1652 map2 = isl_map_read_from_str(ctx,
1653 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1654 assert(isl_map_is_equal(map, map2));
1655 isl_map_free(map);
1656 isl_map_free(map2);
1657
1658 str = "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1659 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1660 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1661 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1662 map = isl_map_read_from_str(ctx, str);
1663 map = isl_map_transitive_closure(map, &exact);
1664 assert(exact);
1665 map2 = isl_map_read_from_str(ctx, str);
1666 assert(isl_map_is_equal(map, map2));
1667 isl_map_free(map);
1668 isl_map_free(map2);
1669
1670 str = "{[0] -> [1]; [2] -> [3]}";
1671 map = isl_map_read_from_str(ctx, str);
1672 map = isl_map_transitive_closure(map, &exact);
1673 assert(exact);
1674 map2 = isl_map_read_from_str(ctx, str);
1675 assert(isl_map_is_equal(map, map2));
1676 isl_map_free(map);
1677 isl_map_free(map2);
1678
1679 str = "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1680 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1681 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1682 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1683 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1684 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1685 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1686 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1687 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1688 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1689 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1690 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1691 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1692 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1693 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1694 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1695 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1696 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1697 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1698 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1699 map = isl_map_read_from_str(ctx, str);
1700 map = isl_map_transitive_closure(map, NULL);
1701 assert(map);
1702 isl_map_free(map);
1703 }
1704
1705 void test_lex(struct isl_ctx *ctx)
1706 {
1707 isl_space *dim;
1708 isl_map *map;
1709
1710 dim = isl_space_set_alloc(ctx, 0, 0);
1711 map = isl_map_lex_le(dim);
1712 assert(!isl_map_is_empty(map));
1713 isl_map_free(map);
1714 }
1715
1716 static int test_lexmin(struct isl_ctx *ctx)
1717 {
1718 int equal;
1719 const char *str;
1720 isl_basic_map *bmap;
1721 isl_map *map, *map2;
1722 isl_set *set;
1723 isl_set *set2;
1724 isl_pw_multi_aff *pma;
1725
1726 str = "[p0, p1] -> { [] -> [] : "
1727 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1728 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1729 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1730 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1731 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1732 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1733 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1734 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1735 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1736 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1737 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1738 map = isl_map_read_from_str(ctx, str);
1739 map = isl_map_lexmin(map);
1740 isl_map_free(map);
1741
1742 str = "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1743 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1744 set = isl_set_read_from_str(ctx, str);
1745 set = isl_set_lexmax(set);
1746 str = "[C] -> { [obj,a,b,c] : C = 8 }";
1747 set2 = isl_set_read_from_str(ctx, str);
1748 set = isl_set_intersect(set, set2);
1749 assert(!isl_set_is_empty(set));
1750 isl_set_free(set);
1751
1752 str = "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1753 map = isl_map_read_from_str(ctx, str);
1754 map = isl_map_lexmin(map);
1755 str = "{ [x] -> [5] : 6 <= x <= 8; "
1756 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1757 map2 = isl_map_read_from_str(ctx, str);
1758 assert(isl_map_is_equal(map, map2));
1759 isl_map_free(map);
1760 isl_map_free(map2);
1761
1762 str = "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1763 map = isl_map_read_from_str(ctx, str);
1764 map2 = isl_map_copy(map);
1765 map = isl_map_lexmin(map);
1766 assert(isl_map_is_equal(map, map2));
1767 isl_map_free(map);
1768 isl_map_free(map2);
1769
1770 str = "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1771 map = isl_map_read_from_str(ctx, str);
1772 map = isl_map_lexmin(map);
1773 str = "{ [x] -> [y] : (4y = x and x >= 0) or "
1774 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1775 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1776 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1777 map2 = isl_map_read_from_str(ctx, str);
1778 assert(isl_map_is_equal(map, map2));
1779 isl_map_free(map);
1780 isl_map_free(map2);
1781
1782 str = "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1783 " 8i' <= i and 8i' >= -7 + i }";
1784 bmap = isl_basic_map_read_from_str(ctx, str);
1785 pma = isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap));
1786 map2 = isl_map_from_pw_multi_aff(pma);
1787 map = isl_map_from_basic_map(bmap);
1788 assert(isl_map_is_equal(map, map2));
1789 isl_map_free(map);
1790 isl_map_free(map2);
1791
1792 str = "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1793 map = isl_map_read_from_str(ctx, str);
1794 map = isl_map_lexmin(map);
1795 str = "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1796 map2 = isl_map_read_from_str(ctx, str);
1797 assert(isl_map_is_equal(map, map2));
1798 isl_map_free(map);
1799 isl_map_free(map2);
1800
1801 /* Check that empty pieces are properly combined. */
1802 str = "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
1803 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
1804 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
1805 map = isl_map_read_from_str(ctx, str);
1806 map = isl_map_lexmin(map);
1807 str = "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
1808 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
1809 "x >= 4 }";
1810 map2 = isl_map_read_from_str(ctx, str);
1811 assert(isl_map_is_equal(map, map2));
1812 isl_map_free(map);
1813 isl_map_free(map2);
1814
1815 str = "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1816 " 8i' <= i and 8i' >= -7 + i }";
1817 set = isl_set_read_from_str(ctx, str);
1818 pma = isl_set_lexmin_pw_multi_aff(isl_set_copy(set));
1819 set2 = isl_set_from_pw_multi_aff(pma);
1820 equal = isl_set_is_equal(set, set2);
1821 isl_set_free(set);
1822 isl_set_free(set2);
1823 if (equal < 0)
1824 return -1;
1825 if (!equal)
1826 isl_die(ctx, isl_error_unknown,
1827 "unexpected difference between set and "
1828 "piecewise affine expression", return -1);
1829
1830 return 0;
1831 }
1832
1833 /* Check that isl_set_min_val and isl_set_max_val compute the correct
1834 * result on non-convex inputs.
1835 */
1836 static int test_min(struct isl_ctx *ctx)
1837 {
1838 isl_set *set;
1839 isl_aff *aff;
1840 isl_val *val;
1841 int min_ok, max_ok;
1842
1843 set = isl_set_read_from_str(ctx, "{ [-1]; [1] }");
1844 aff = isl_aff_read_from_str(ctx, "{ [x] -> [x] }");
1845 val = isl_set_min_val(set, aff);
1846 min_ok = isl_val_is_negone(val);
1847 isl_val_free(val);
1848 val = isl_set_max_val(set, aff);
1849 max_ok = isl_val_is_one(val);
1850 isl_val_free(val);
1851 isl_aff_free(aff);
1852 isl_set_free(set);
1853
1854 if (min_ok < 0 || max_ok < 0)
1855 return -1;
1856 if (!min_ok)
1857 isl_die(ctx, isl_error_unknown,
1858 "unexpected minimum", return -1);
1859 if (!max_ok)
1860 isl_die(ctx, isl_error_unknown,
1861 "unexpected maximum", return -1);
1862
1863 return 0;
1864 }
1865
1866 struct must_may {
1867 isl_map *must;
1868 isl_map *may;
1869 };
1870
1871 static int collect_must_may(__isl_take isl_map *dep, int must,
1872 void *dep_user, void *user)
1873 {
1874 struct must_may *mm = (struct must_may *)user;
1875
1876 if (must)
1877 mm->must = isl_map_union(mm->must, dep);
1878 else
1879 mm->may = isl_map_union(mm->may, dep);
1880
1881 return 0;
1882 }
1883
1884 static int common_space(void *first, void *second)
1885 {
1886 int depth = *(int *)first;
1887 return 2 * depth;
1888 }
1889
1890 static int map_is_equal(__isl_keep isl_map *map, const char *str)
1891 {
1892 isl_map *map2;
1893 int equal;
1894
1895 if (!map)
1896 return -1;
1897
1898 map2 = isl_map_read_from_str(map->ctx, str);
1899 equal = isl_map_is_equal(map, map2);
1900 isl_map_free(map2);
1901
1902 return equal;
1903 }
1904
1905 static int map_check_equal(__isl_keep isl_map *map, const char *str)
1906 {
1907 int equal;
1908
1909 equal = map_is_equal(map, str);
1910 if (equal < 0)
1911 return -1;
1912 if (!equal)
1913 isl_die(isl_map_get_ctx(map), isl_error_unknown,
1914 "result not as expected", return -1);
1915 return 0;
1916 }
1917
1918 void test_dep(struct isl_ctx *ctx)
1919 {
1920 const char *str;
1921 isl_space *dim;
1922 isl_map *map;
1923 isl_access_info *ai;
1924 isl_flow *flow;
1925 int depth;
1926 struct must_may mm;
1927
1928 depth = 3;
1929
1930 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1931 map = isl_map_read_from_str(ctx, str);
1932 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1933
1934 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1935 map = isl_map_read_from_str(ctx, str);
1936 ai = isl_access_info_add_source(ai, map, 1, &depth);
1937
1938 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1939 map = isl_map_read_from_str(ctx, str);
1940 ai = isl_access_info_add_source(ai, map, 1, &depth);
1941
1942 flow = isl_access_info_compute_flow(ai);
1943 dim = isl_space_alloc(ctx, 0, 3, 3);
1944 mm.must = isl_map_empty(isl_space_copy(dim));
1945 mm.may = isl_map_empty(dim);
1946
1947 isl_flow_foreach(flow, collect_must_may, &mm);
1948
1949 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1950 " [1,10,0] -> [2,5,0] }";
1951 assert(map_is_equal(mm.must, str));
1952 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1953 assert(map_is_equal(mm.may, str));
1954
1955 isl_map_free(mm.must);
1956 isl_map_free(mm.may);
1957 isl_flow_free(flow);
1958
1959
1960 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1961 map = isl_map_read_from_str(ctx, str);
1962 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1963
1964 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1965 map = isl_map_read_from_str(ctx, str);
1966 ai = isl_access_info_add_source(ai, map, 1, &depth);
1967
1968 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1969 map = isl_map_read_from_str(ctx, str);
1970 ai = isl_access_info_add_source(ai, map, 0, &depth);
1971
1972 flow = isl_access_info_compute_flow(ai);
1973 dim = isl_space_alloc(ctx, 0, 3, 3);
1974 mm.must = isl_map_empty(isl_space_copy(dim));
1975 mm.may = isl_map_empty(dim);
1976
1977 isl_flow_foreach(flow, collect_must_may, &mm);
1978
1979 str = "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1980 assert(map_is_equal(mm.must, str));
1981 str = "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1982 assert(map_is_equal(mm.may, str));
1983
1984 isl_map_free(mm.must);
1985 isl_map_free(mm.may);
1986 isl_flow_free(flow);
1987
1988
1989 str = "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1990 map = isl_map_read_from_str(ctx, str);
1991 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
1992
1993 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1994 map = isl_map_read_from_str(ctx, str);
1995 ai = isl_access_info_add_source(ai, map, 0, &depth);
1996
1997 str = "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1998 map = isl_map_read_from_str(ctx, str);
1999 ai = isl_access_info_add_source(ai, map, 0, &depth);
2000
2001 flow = isl_access_info_compute_flow(ai);
2002 dim = isl_space_alloc(ctx, 0, 3, 3);
2003 mm.must = isl_map_empty(isl_space_copy(dim));
2004 mm.may = isl_map_empty(dim);
2005
2006 isl_flow_foreach(flow, collect_must_may, &mm);
2007
2008 str = "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2009 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2010 assert(map_is_equal(mm.may, str));
2011 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2012 assert(map_is_equal(mm.must, str));
2013
2014 isl_map_free(mm.must);
2015 isl_map_free(mm.may);
2016 isl_flow_free(flow);
2017
2018
2019 str = "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2020 map = isl_map_read_from_str(ctx, str);
2021 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2022
2023 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2024 map = isl_map_read_from_str(ctx, str);
2025 ai = isl_access_info_add_source(ai, map, 0, &depth);
2026
2027 str = "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2028 map = isl_map_read_from_str(ctx, str);
2029 ai = isl_access_info_add_source(ai, map, 0, &depth);
2030
2031 flow = isl_access_info_compute_flow(ai);
2032 dim = isl_space_alloc(ctx, 0, 3, 3);
2033 mm.must = isl_map_empty(isl_space_copy(dim));
2034 mm.may = isl_map_empty(dim);
2035
2036 isl_flow_foreach(flow, collect_must_may, &mm);
2037
2038 str = "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2039 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2040 assert(map_is_equal(mm.may, str));
2041 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2042 assert(map_is_equal(mm.must, str));
2043
2044 isl_map_free(mm.must);
2045 isl_map_free(mm.may);
2046 isl_flow_free(flow);
2047
2048
2049 str = "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2050 map = isl_map_read_from_str(ctx, str);
2051 ai = isl_access_info_alloc(map, &depth, &common_space, 2);
2052
2053 str = "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2054 map = isl_map_read_from_str(ctx, str);
2055 ai = isl_access_info_add_source(ai, map, 0, &depth);
2056
2057 str = "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2058 map = isl_map_read_from_str(ctx, str);
2059 ai = isl_access_info_add_source(ai, map, 0, &depth);
2060
2061 flow = isl_access_info_compute_flow(ai);
2062 dim = isl_space_alloc(ctx, 0, 3, 3);
2063 mm.must = isl_map_empty(isl_space_copy(dim));
2064 mm.may = isl_map_empty(dim);
2065
2066 isl_flow_foreach(flow, collect_must_may, &mm);
2067
2068 str = "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2069 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2070 assert(map_is_equal(mm.may, str));
2071 str = "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2072 assert(map_is_equal(mm.must, str));
2073
2074 isl_map_free(mm.must);
2075 isl_map_free(mm.may);
2076 isl_flow_free(flow);
2077
2078
2079 depth = 5;
2080
2081 str = "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2082 map = isl_map_read_from_str(ctx, str);
2083 ai = isl_access_info_alloc(map, &depth, &common_space, 1);
2084
2085 str = "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2086 map = isl_map_read_from_str(ctx, str);
2087 ai = isl_access_info_add_source(ai, map, 1, &depth);
2088
2089 flow = isl_access_info_compute_flow(ai);
2090 dim = isl_space_alloc(ctx, 0, 5, 5);
2091 mm.must = isl_map_empty(isl_space_copy(dim));
2092 mm.may = isl_map_empty(dim);
2093
2094 isl_flow_foreach(flow, collect_must_may, &mm);
2095
2096 str = "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2097 assert(map_is_equal(mm.must, str));
2098 str = "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2099 assert(map_is_equal(mm.may, str));
2100
2101 isl_map_free(mm.must);
2102 isl_map_free(mm.may);
2103 isl_flow_free(flow);
2104 }
2105
2106 /* Check that the dependence analysis proceeds without errors.
2107 * Earlier versions of isl would break down during the analysis
2108 * due to the use of the wrong spaces.
2109 */
2110 static int test_flow(isl_ctx *ctx)
2111 {
2112 const char *str;
2113 isl_union_map *access, *schedule;
2114 isl_union_map *must_dep, *may_dep;
2115 int r;
2116
2117 str = "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2118 access = isl_union_map_read_from_str(ctx, str);
2119 str = "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2120 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2121 "S2[] -> [1,0,0,0]; "
2122 "S3[] -> [-1,0,0,0] }";
2123 schedule = isl_union_map_read_from_str(ctx, str);
2124 r = isl_union_map_compute_flow(access, isl_union_map_copy(access),
2125 isl_union_map_copy(access), schedule,
2126 &must_dep, &may_dep, NULL, NULL);
2127 isl_union_map_free(may_dep);
2128 isl_union_map_free(must_dep);
2129
2130 return r;
2131 }
2132
2133 struct {
2134 const char *map;
2135 int sv;
2136 } sv_tests[] = {
2137 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2138 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2139 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2140 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2141 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2142 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2143 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2144 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2145 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2146 };
2147
2148 int test_sv(isl_ctx *ctx)
2149 {
2150 isl_union_map *umap;
2151 int i;
2152 int sv;
2153
2154 for (i = 0; i < ARRAY_SIZE(sv_tests); ++i) {
2155 umap = isl_union_map_read_from_str(ctx, sv_tests[i].map);
2156 sv = isl_union_map_is_single_valued(umap);
2157 isl_union_map_free(umap);
2158 if (sv < 0)
2159 return -1;
2160 if (sv_tests[i].sv && !sv)
2161 isl_die(ctx, isl_error_internal,
2162 "map not detected as single valued", return -1);
2163 if (!sv_tests[i].sv && sv)
2164 isl_die(ctx, isl_error_internal,
2165 "map detected as single valued", return -1);
2166 }
2167
2168 return 0;
2169 }
2170
2171 void test_bijective_case(struct isl_ctx *ctx, const char *str, int bijective)
2172 {
2173 isl_map *map;
2174
2175 map = isl_map_read_from_str(ctx, str);
2176 if (bijective)
2177 assert(isl_map_is_bijective(map));
2178 else
2179 assert(!isl_map_is_bijective(map));
2180 isl_map_free(map);
2181 }
2182
2183 void test_bijective(struct isl_ctx *ctx)
2184 {
2185 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i]}", 0);
2186 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=i}", 1);
2187 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=0}", 1);
2188 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i] : j=N}", 1);
2189 test_bijective_case(ctx, "[N,M]->{[i,j] -> [j,i]}", 1);
2190 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i+j]}", 0);
2191 test_bijective_case(ctx, "[N,M]->{[i,j] -> []}", 0);
2192 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,j,N]}", 1);
2193 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i]}", 0);
2194 test_bijective_case(ctx, "[N,M]->{[i,j] -> [i,i]}", 0);
2195 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,i]}", 0);
2196 test_bijective_case(ctx, "[N,M]->{[i,j] -> [2i,j]}", 1);
2197 test_bijective_case(ctx, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
2198 }
2199
2200 /* Inputs for isl_pw_qpolynomial_gist tests.
2201 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2202 */
2203 struct {
2204 const char *pwqp;
2205 const char *set;
2206 const char *gist;
2207 } pwqp_gist_tests[] = {
2208 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2209 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2210 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2211 "{ [i] -> -1/2 + 1/2 * i }" },
2212 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2213 };
2214
2215 static int test_pwqp(struct isl_ctx *ctx)
2216 {
2217 int i;
2218 const char *str;
2219 isl_set *set;
2220 isl_pw_qpolynomial *pwqp1, *pwqp2;
2221 int equal;
2222
2223 str = "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2224 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2225
2226 pwqp1 = isl_pw_qpolynomial_move_dims(pwqp1, isl_dim_param, 0,
2227 isl_dim_in, 1, 1);
2228
2229 str = "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2230 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2231
2232 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2233
2234 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2235
2236 isl_pw_qpolynomial_free(pwqp1);
2237
2238 for (i = 0; i < ARRAY_SIZE(pwqp_gist_tests); ++i) {
2239 str = pwqp_gist_tests[i].pwqp;
2240 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2241 str = pwqp_gist_tests[i].set;
2242 set = isl_set_read_from_str(ctx, str);
2243 pwqp1 = isl_pw_qpolynomial_gist(pwqp1, set);
2244 str = pwqp_gist_tests[i].gist;
2245 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2246 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2247 equal = isl_pw_qpolynomial_is_zero(pwqp1);
2248 isl_pw_qpolynomial_free(pwqp1);
2249
2250 if (equal < 0)
2251 return -1;
2252 if (!equal)
2253 isl_die(ctx, isl_error_unknown,
2254 "unexpected result", return -1);
2255 }
2256
2257 str = "{ [i] -> ([([i/2] + [i/2])/5]) }";
2258 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2259 str = "{ [i] -> ([(2 * [i/2])/5]) }";
2260 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2261
2262 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2263
2264 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2265
2266 isl_pw_qpolynomial_free(pwqp1);
2267
2268 str = "{ [x] -> ([x/2] + [(x+1)/2]) }";
2269 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2270 str = "{ [x] -> x }";
2271 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2272
2273 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2274
2275 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2276
2277 isl_pw_qpolynomial_free(pwqp1);
2278
2279 str = "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2280 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2281 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2282 pwqp1 = isl_pw_qpolynomial_coalesce(pwqp1);
2283 pwqp1 = isl_pw_qpolynomial_sub(pwqp1, pwqp2);
2284 assert(isl_pw_qpolynomial_is_zero(pwqp1));
2285 isl_pw_qpolynomial_free(pwqp1);
2286
2287 str = "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2288 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2289 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2290 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2291 set = isl_set_read_from_str(ctx, "{ [a,b,a] }");
2292 pwqp1 = isl_pw_qpolynomial_intersect_domain(pwqp1, set);
2293 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2294 isl_pw_qpolynomial_free(pwqp1);
2295 isl_pw_qpolynomial_free(pwqp2);
2296 if (equal < 0)
2297 return -1;
2298 if (!equal)
2299 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2300
2301 str = "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2302 pwqp2 = isl_pw_qpolynomial_read_from_str(ctx, str);
2303 str = "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2304 pwqp1 = isl_pw_qpolynomial_read_from_str(ctx, str);
2305 pwqp1 = isl_pw_qpolynomial_fix_val(pwqp1, isl_dim_set, 1,
2306 isl_val_one(ctx));
2307 equal = isl_pw_qpolynomial_plain_is_equal(pwqp1, pwqp2);
2308 isl_pw_qpolynomial_free(pwqp1);
2309 isl_pw_qpolynomial_free(pwqp2);
2310 if (equal < 0)
2311 return -1;
2312 if (!equal)
2313 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
2314
2315 return 0;
2316 }
2317
2318 void test_split_periods(isl_ctx *ctx)
2319 {
2320 const char *str;
2321 isl_pw_qpolynomial *pwqp;
2322
2323 str = "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2324 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2325 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2326 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2327
2328 pwqp = isl_pw_qpolynomial_split_periods(pwqp, 2);
2329 assert(pwqp);
2330
2331 isl_pw_qpolynomial_free(pwqp);
2332 }
2333
2334 void test_union(isl_ctx *ctx)
2335 {
2336 const char *str;
2337 isl_union_set *uset1, *uset2;
2338 isl_union_map *umap1, *umap2;
2339
2340 str = "{ [i] : 0 <= i <= 1 }";
2341 uset1 = isl_union_set_read_from_str(ctx, str);
2342 str = "{ [1] -> [0] }";
2343 umap1 = isl_union_map_read_from_str(ctx, str);
2344
2345 umap2 = isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1), uset1);
2346 assert(isl_union_map_is_equal(umap1, umap2));
2347
2348 isl_union_map_free(umap1);
2349 isl_union_map_free(umap2);
2350
2351 str = "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2352 umap1 = isl_union_map_read_from_str(ctx, str);
2353 str = "{ A[i]; B[i] }";
2354 uset1 = isl_union_set_read_from_str(ctx, str);
2355
2356 uset2 = isl_union_map_domain(umap1);
2357
2358 assert(isl_union_set_is_equal(uset1, uset2));
2359
2360 isl_union_set_free(uset1);
2361 isl_union_set_free(uset2);
2362 }
2363
2364 void test_bound(isl_ctx *ctx)
2365 {
2366 const char *str;
2367 isl_pw_qpolynomial *pwqp;
2368 isl_pw_qpolynomial_fold *pwf;
2369
2370 str = "{ [[a, b, c, d] -> [e]] -> 0 }";
2371 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2372 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2373 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 4);
2374 isl_pw_qpolynomial_fold_free(pwf);
2375
2376 str = "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2377 pwqp = isl_pw_qpolynomial_read_from_str(ctx, str);
2378 pwf = isl_pw_qpolynomial_bound(pwqp, isl_fold_max, NULL);
2379 assert(isl_pw_qpolynomial_fold_dim(pwf, isl_dim_in) == 1);
2380 isl_pw_qpolynomial_fold_free(pwf);
2381 }
2382
2383 void test_lift(isl_ctx *ctx)
2384 {
2385 const char *str;
2386 isl_basic_map *bmap;
2387 isl_basic_set *bset;
2388
2389 str = "{ [i0] : exists e0 : i0 = 4e0 }";
2390 bset = isl_basic_set_read_from_str(ctx, str);
2391 bset = isl_basic_set_lift(bset);
2392 bmap = isl_basic_map_from_range(bset);
2393 bset = isl_basic_map_domain(bmap);
2394 isl_basic_set_free(bset);
2395 }
2396
2397 struct {
2398 const char *set1;
2399 const char *set2;
2400 int subset;
2401 } subset_tests[] = {
2402 { "{ [112, 0] }",
2403 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2404 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2405 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2406 { "{ [65] }",
2407 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2408 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2409 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2410 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2411 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2412 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2413 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2414 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2415 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2416 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2417 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2418 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2419 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2420 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2421 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2422 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2423 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2424 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2425 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2426 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2427 "4e0 <= -57 + i0 + i1)) or "
2428 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2429 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2430 "4e0 >= -61 + i0 + i1)) or "
2431 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2432 };
2433
2434 static int test_subset(isl_ctx *ctx)
2435 {
2436 int i;
2437 isl_set *set1, *set2;
2438 int subset;
2439
2440 for (i = 0; i < ARRAY_SIZE(subset_tests); ++i) {
2441 set1 = isl_set_read_from_str(ctx, subset_tests[i].set1);
2442 set2 = isl_set_read_from_str(ctx, subset_tests[i].set2);
2443 subset = isl_set_is_subset(set1, set2);
2444 isl_set_free(set1);
2445 isl_set_free(set2);
2446 if (subset < 0)
2447 return -1;
2448 if (subset != subset_tests[i].subset)
2449 isl_die(ctx, isl_error_unknown,
2450 "incorrect subset result", return -1);
2451 }
2452
2453 return 0;
2454 }
2455
2456 struct {
2457 const char *minuend;
2458 const char *subtrahend;
2459 const char *difference;
2460 } subtract_domain_tests[] = {
2461 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2462 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2463 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2464 };
2465
2466 static int test_subtract(isl_ctx *ctx)
2467 {
2468 int i;
2469 isl_union_map *umap1, *umap2;
2470 isl_union_pw_multi_aff *upma1, *upma2;
2471 isl_union_set *uset;
2472 int equal;
2473
2474 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2475 umap1 = isl_union_map_read_from_str(ctx,
2476 subtract_domain_tests[i].minuend);
2477 uset = isl_union_set_read_from_str(ctx,
2478 subtract_domain_tests[i].subtrahend);
2479 umap2 = isl_union_map_read_from_str(ctx,
2480 subtract_domain_tests[i].difference);
2481 umap1 = isl_union_map_subtract_domain(umap1, uset);
2482 equal = isl_union_map_is_equal(umap1, umap2);
2483 isl_union_map_free(umap1);
2484 isl_union_map_free(umap2);
2485 if (equal < 0)
2486 return -1;
2487 if (!equal)
2488 isl_die(ctx, isl_error_unknown,
2489 "incorrect subtract domain result", return -1);
2490 }
2491
2492 for (i = 0; i < ARRAY_SIZE(subtract_domain_tests); ++i) {
2493 upma1 = isl_union_pw_multi_aff_read_from_str(ctx,
2494 subtract_domain_tests[i].minuend);
2495 uset = isl_union_set_read_from_str(ctx,
2496 subtract_domain_tests[i].subtrahend);
2497 upma2 = isl_union_pw_multi_aff_read_from_str(ctx,
2498 subtract_domain_tests[i].difference);
2499 upma1 = isl_union_pw_multi_aff_subtract_domain(upma1, uset);
2500 equal = isl_union_pw_multi_aff_plain_is_equal(upma1, upma2);
2501 isl_union_pw_multi_aff_free(upma1);
2502 isl_union_pw_multi_aff_free(upma2);
2503 if (equal < 0)
2504 return -1;
2505 if (!equal)
2506 isl_die(ctx, isl_error_unknown,
2507 "incorrect subtract domain result", return -1);
2508 }
2509
2510 return 0;
2511 }
2512
2513 int test_factorize(isl_ctx *ctx)
2514 {
2515 const char *str;
2516 isl_basic_set *bset;
2517 isl_factorizer *f;
2518
2519 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2520 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2521 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2522 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2523 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2524 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2525 "3i5 >= -2i0 - i2 + 3i4 }";
2526 bset = isl_basic_set_read_from_str(ctx, str);
2527 f = isl_basic_set_factorizer(bset);
2528 isl_basic_set_free(bset);
2529 isl_factorizer_free(f);
2530 if (!f)
2531 isl_die(ctx, isl_error_unknown,
2532 "failed to construct factorizer", return -1);
2533
2534 str = "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2535 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2536 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2537 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2538 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2539 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2540 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2541 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2542 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2543 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2544 bset = isl_basic_set_read_from_str(ctx, str);
2545 f = isl_basic_set_factorizer(bset);
2546 isl_basic_set_free(bset);
2547 isl_factorizer_free(f);
2548 if (!f)
2549 isl_die(ctx, isl_error_unknown,
2550 "failed to construct factorizer", return -1);
2551
2552 return 0;
2553 }
2554
2555 static int check_injective(__isl_take isl_map *map, void *user)
2556 {
2557 int *injective = user;
2558
2559 *injective = isl_map_is_injective(map);
2560 isl_map_free(map);
2561
2562 if (*injective < 0 || !*injective)
2563 return -1;
2564
2565 return 0;
2566 }
2567
2568 int test_one_schedule(isl_ctx *ctx, const char *d, const char *w,
2569 const char *r, const char *s, int tilable, int parallel)
2570 {
2571 int i;
2572 isl_union_set *D;
2573 isl_union_map *W, *R, *S;
2574 isl_union_map *empty;
2575 isl_union_map *dep_raw, *dep_war, *dep_waw, *dep;
2576 isl_union_map *validity, *proximity, *coincidence;
2577 isl_union_map *schedule;
2578 isl_union_map *test;
2579 isl_union_set *delta;
2580 isl_union_set *domain;
2581 isl_set *delta_set;
2582 isl_set *slice;
2583 isl_set *origin;
2584 isl_schedule_constraints *sc;
2585 isl_schedule *sched;
2586 int is_nonneg, is_parallel, is_tilable, is_injection, is_complete;
2587
2588 D = isl_union_set_read_from_str(ctx, d);
2589 W = isl_union_map_read_from_str(ctx, w);
2590 R = isl_union_map_read_from_str(ctx, r);
2591 S = isl_union_map_read_from_str(ctx, s);
2592
2593 W = isl_union_map_intersect_domain(W, isl_union_set_copy(D));
2594 R = isl_union_map_intersect_domain(R, isl_union_set_copy(D));
2595
2596 empty = isl_union_map_empty(isl_union_map_get_space(S));
2597 isl_union_map_compute_flow(isl_union_map_copy(R),
2598 isl_union_map_copy(W), empty,
2599 isl_union_map_copy(S),
2600 &dep_raw, NULL, NULL, NULL);
2601 isl_union_map_compute_flow(isl_union_map_copy(W),
2602 isl_union_map_copy(W),
2603 isl_union_map_copy(R),
2604 isl_union_map_copy(S),
2605 &dep_waw, &dep_war, NULL, NULL);
2606
2607 dep = isl_union_map_union(dep_waw, dep_war);
2608 dep = isl_union_map_union(dep, dep_raw);
2609 validity = isl_union_map_copy(dep);
2610 coincidence = isl_union_map_copy(dep);
2611 proximity = isl_union_map_copy(dep);
2612
2613 sc = isl_schedule_constraints_on_domain(isl_union_set_copy(D));
2614 sc = isl_schedule_constraints_set_validity(sc, validity);
2615 sc = isl_schedule_constraints_set_coincidence(sc, coincidence);
2616 sc = isl_schedule_constraints_set_proximity(sc, proximity);
2617 sched = isl_schedule_constraints_compute_schedule(sc);
2618 schedule = isl_schedule_get_map(sched);
2619 isl_schedule_free(sched);
2620 isl_union_map_free(W);
2621 isl_union_map_free(R);
2622 isl_union_map_free(S);
2623
2624 is_injection = 1;
2625 isl_union_map_foreach_map(schedule, &check_injective, &is_injection);
2626
2627 domain = isl_union_map_domain(isl_union_map_copy(schedule));
2628 is_complete = isl_union_set_is_subset(D, domain);
2629 isl_union_set_free(D);
2630 isl_union_set_free(domain);
2631
2632 test = isl_union_map_reverse(isl_union_map_copy(schedule));
2633 test = isl_union_map_apply_range(test, dep);
2634 test = isl_union_map_apply_range(test, schedule);
2635
2636 delta = isl_union_map_deltas(test);
2637 if (isl_union_set_n_set(delta) == 0) {
2638 is_tilable = 1;
2639 is_parallel = 1;
2640 is_nonneg = 1;
2641 isl_union_set_free(delta);
2642 } else {
2643 delta_set = isl_set_from_union_set(delta);
2644
2645 slice = isl_set_universe(isl_set_get_space(delta_set));
2646 for (i = 0; i < tilable; ++i)
2647 slice = isl_set_lower_bound_si(slice, isl_dim_set, i, 0);
2648 is_tilable = isl_set_is_subset(delta_set, slice);
2649 isl_set_free(slice);
2650
2651 slice = isl_set_universe(isl_set_get_space(delta_set));
2652 for (i = 0; i < parallel; ++i)
2653 slice = isl_set_fix_si(slice, isl_dim_set, i, 0);
2654 is_parallel = isl_set_is_subset(delta_set, slice);
2655 isl_set_free(slice);
2656
2657 origin = isl_set_universe(isl_set_get_space(delta_set));
2658 for (i = 0; i < isl_set_dim(origin, isl_dim_set); ++i)
2659 origin = isl_set_fix_si(origin, isl_dim_set, i, 0);
2660
2661 delta_set = isl_set_union(delta_set, isl_set_copy(origin));
2662 delta_set = isl_set_lexmin(delta_set);
2663
2664 is_nonneg = isl_set_is_equal(delta_set, origin);
2665
2666 isl_set_free(origin);
2667 isl_set_free(delta_set);
2668 }
2669
2670 if (is_nonneg < 0 || is_parallel < 0 || is_tilable < 0 ||
2671 is_injection < 0 || is_complete < 0)
2672 return -1;
2673 if (!is_complete)
2674 isl_die(ctx, isl_error_unknown,
2675 "generated schedule incomplete", return -1);
2676 if (!is_injection)
2677 isl_die(ctx, isl_error_unknown,
2678 "generated schedule not injective on each statement",
2679 return -1);
2680 if (!is_nonneg)
2681 isl_die(ctx, isl_error_unknown,
2682 "negative dependences in generated schedule",
2683 return -1);
2684 if (!is_tilable)
2685 isl_die(ctx, isl_error_unknown,
2686 "generated schedule not as tilable as expected",
2687 return -1);
2688 if (!is_parallel)
2689 isl_die(ctx, isl_error_unknown,
2690 "generated schedule not as parallel as expected",
2691 return -1);
2692
2693 return 0;
2694 }
2695
2696 static __isl_give isl_union_map *compute_schedule(isl_ctx *ctx,
2697 const char *domain, const char *validity, const char *proximity)
2698 {
2699 isl_union_set *dom;
2700 isl_union_map *dep;
2701 isl_union_map *prox;
2702 isl_schedule_constraints *sc;
2703 isl_schedule *schedule;
2704 isl_union_map *sched;
2705
2706 dom = isl_union_set_read_from_str(ctx, domain);
2707 dep = isl_union_map_read_from_str(ctx, validity);
2708 prox = isl_union_map_read_from_str(ctx, proximity);
2709 sc = isl_schedule_constraints_on_domain(dom);
2710 sc = isl_schedule_constraints_set_validity(sc, dep);
2711 sc = isl_schedule_constraints_set_proximity(sc, prox);
2712 schedule = isl_schedule_constraints_compute_schedule(sc);
2713 sched = isl_schedule_get_map(schedule);
2714 isl_schedule_free(schedule);
2715
2716 return sched;
2717 }
2718
2719 /* Check that a schedule can be constructed on the given domain
2720 * with the given validity and proximity constraints.
2721 */
2722 static int test_has_schedule(isl_ctx *ctx, const char *domain,
2723 const char *validity, const char *proximity)
2724 {
2725 isl_union_map *sched;
2726
2727 sched = compute_schedule(ctx, domain, validity, proximity);
2728 if (!sched)
2729 return -1;
2730
2731 isl_union_map_free(sched);
2732 return 0;
2733 }
2734
2735 int test_special_schedule(isl_ctx *ctx, const char *domain,
2736 const char *validity, const char *proximity, const char *expected_sched)
2737 {
2738 isl_union_map *sched1, *sched2;
2739 int equal;
2740
2741 sched1 = compute_schedule(ctx, domain, validity, proximity);
2742 sched2 = isl_union_map_read_from_str(ctx, expected_sched);
2743
2744 equal = isl_union_map_is_equal(sched1, sched2);
2745 isl_union_map_free(sched1);
2746 isl_union_map_free(sched2);
2747
2748 if (equal < 0)
2749 return -1;
2750 if (!equal)
2751 isl_die(ctx, isl_error_unknown, "unexpected schedule",
2752 return -1);
2753
2754 return 0;
2755 }
2756
2757 /* Check that the schedule map is properly padded, even after being
2758 * reconstructed from the band forest.
2759 */
2760 static int test_padded_schedule(isl_ctx *ctx)
2761 {
2762 const char *str;
2763 isl_union_set *D;
2764 isl_union_map *validity, *proximity;
2765 isl_schedule_constraints *sc;
2766 isl_schedule *sched;
2767 isl_union_map *map1, *map2;
2768 isl_band_list *list;
2769 int equal;
2770
2771 str = "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2772 D = isl_union_set_read_from_str(ctx, str);
2773 validity = isl_union_map_empty(isl_union_set_get_space(D));
2774 proximity = isl_union_map_copy(validity);
2775 sc = isl_schedule_constraints_on_domain(D);
2776 sc = isl_schedule_constraints_set_validity(sc, validity);
2777 sc = isl_schedule_constraints_set_proximity(sc, proximity);
2778 sched = isl_schedule_constraints_compute_schedule(sc);
2779 map1 = isl_schedule_get_map(sched);
2780 list = isl_schedule_get_band_forest(sched);
2781 isl_band_list_free(list);
2782 map2 = isl_schedule_get_map(sched);
2783 isl_schedule_free(sched);
2784 equal = isl_union_map_is_equal(map1, map2);
2785 isl_union_map_free(map1);
2786 isl_union_map_free(map2);
2787
2788 if (equal < 0)
2789 return -1;
2790 if (!equal)
2791 isl_die(ctx, isl_error_unknown,
2792 "reconstructed schedule map not the same as original",
2793 return -1);
2794
2795 return 0;
2796 }
2797
2798 /* Input for testing of schedule construction based on
2799 * conditional constraints.
2800 *
2801 * domain is the iteration domain
2802 * flow are the flow dependences, which determine the validity and
2803 * proximity constraints
2804 * condition are the conditions on the conditional validity constraints
2805 * conditional_validity are the conditional validity constraints
2806 * outer_band_n is the expected number of members in the outer band
2807 */
2808 struct {
2809 const char *domain;
2810 const char *flow;
2811 const char *condition;
2812 const char *conditional_validity;
2813 int outer_band_n;
2814 } live_range_tests[] = {
2815 /* Contrived example that illustrates that we need to keep
2816 * track of tagged condition dependences and
2817 * tagged conditional validity dependences
2818 * in isl_sched_edge separately.
2819 * In particular, the conditional validity constraints on A
2820 * cannot be satisfied,
2821 * but they can be ignored because there are no corresponding
2822 * condition constraints. However, we do have an additional
2823 * conditional validity constraint that maps to the same
2824 * dependence relation
2825 * as the condition constraint on B. If we did not make a distinction
2826 * between tagged condition and tagged conditional validity
2827 * dependences, then we
2828 * could end up treating this shared dependence as an condition
2829 * constraint on A, forcing a localization of the conditions,
2830 * which is impossible.
2831 */
2832 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
2833 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
2834 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
2835 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2836 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2837 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
2838 1
2839 },
2840 /* TACO 2013 Fig. 7 */
2841 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2842 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2843 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2844 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
2845 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
2846 "0 <= i < n and 0 <= j < n - 1 }",
2847 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
2848 "0 <= i < n and 0 <= j < j' < n;"
2849 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
2850 "0 <= i < i' < n and 0 <= j,j' < n;"
2851 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
2852 "0 <= i,j,j' < n and j < j' }",
2853 2
2854 },
2855 /* TACO 2013 Fig. 7, without tags */
2856 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2857 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2858 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2859 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2860 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2861 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
2862 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
2863 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
2864 1
2865 },
2866 /* TACO 2013 Fig. 12 */
2867 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
2868 "S3[i,3] : 0 <= i <= 1 }",
2869 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
2870 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
2871 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
2872 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
2873 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2874 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
2875 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2876 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
2877 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
2878 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
2879 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
2880 1
2881 }
2882 };
2883
2884 /* Test schedule construction based on conditional constraints.
2885 * In particular, check the number of members in the outer band
2886 * as an indication of whether tiling is possible or not.
2887 */
2888 static int test_conditional_schedule_constraints(isl_ctx *ctx)
2889 {
2890 int i;
2891 isl_union_set *domain;
2892 isl_union_map *condition;
2893 isl_union_map *flow;
2894 isl_union_map *validity;
2895 isl_schedule_constraints *sc;
2896 isl_schedule *schedule;
2897 isl_band_list *list;
2898 isl_band *band;
2899 int n_member;
2900
2901 for (i = 0; i < ARRAY_SIZE(live_range_tests); ++i) {
2902 domain = isl_union_set_read_from_str(ctx,
2903 live_range_tests[i].domain);
2904 flow = isl_union_map_read_from_str(ctx,
2905 live_range_tests[i].flow);
2906 condition = isl_union_map_read_from_str(ctx,
2907 live_range_tests[i].condition);
2908 validity = isl_union_map_read_from_str(ctx,
2909 live_range_tests[i].conditional_validity);
2910 sc = isl_schedule_constraints_on_domain(domain);
2911 sc = isl_schedule_constraints_set_validity(sc,
2912 isl_union_map_copy(flow));
2913 sc = isl_schedule_constraints_set_proximity(sc, flow);
2914 sc = isl_schedule_constraints_set_conditional_validity(sc,
2915 condition, validity);
2916 schedule = isl_schedule_constraints_compute_schedule(sc);
2917 list = isl_schedule_get_band_forest(schedule);
2918 band = isl_band_list_get_band(list, 0);
2919 n_member = isl_band_n_member(band);
2920 isl_band_free(band);
2921 isl_band_list_free(list);
2922 isl_schedule_free(schedule);
2923
2924 if (!schedule)
2925 return -1;
2926 if (n_member != live_range_tests[i].outer_band_n)
2927 isl_die(ctx, isl_error_unknown,
2928 "unexpected number of members in outer band",
2929 return -1);
2930 }
2931 return 0;
2932 }
2933
2934 int test_schedule(isl_ctx *ctx)
2935 {
2936 const char *D, *W, *R, *V, *P, *S;
2937
2938 /* Handle resulting schedule with zero bands. */
2939 if (test_one_schedule(ctx, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2940 return -1;
2941
2942 /* Jacobi */
2943 D = "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2944 W = "{ S1[t,i] -> a[t,i] }";
2945 R = "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2946 "S1[t,i] -> a[t-1,i+1] }";
2947 S = "{ S1[t,i] -> [t,i] }";
2948 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2949 return -1;
2950
2951 /* Fig. 5 of CC2008 */
2952 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2953 "j <= -1 + N }";
2954 W = "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2955 "j >= 2 and j <= -1 + N }";
2956 R = "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2957 "j >= 2 and j <= -1 + N; "
2958 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2959 "j >= 2 and j <= -1 + N }";
2960 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2961 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
2962 return -1;
2963
2964 D = "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2965 W = "{ S1[i] -> a[i] }";
2966 R = "{ S2[i] -> a[i+1] }";
2967 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2968 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2969 return -1;
2970
2971 D = "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2972 W = "{ S1[i] -> a[i] }";
2973 R = "{ S2[i] -> a[9-i] }";
2974 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2975 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2976 return -1;
2977
2978 D = "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2979 W = "{ S1[i] -> a[i] }";
2980 R = "[N] -> { S2[i] -> a[N-1-i] }";
2981 S = "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2982 if (test_one_schedule(ctx, D, W, R, S, 1, 1) < 0)
2983 return -1;
2984
2985 D = "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2986 W = "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2987 R = "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2988 S = "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2989 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
2990 return -1;
2991
2992 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2993 W = "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2994 R = "{ S2[i,j] -> a[i-1,j] }";
2995 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2996 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
2997 return -1;
2998
2999 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3000 W = "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
3001 R = "{ S2[i,j] -> a[i,j-1] }";
3002 S = "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3003 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3004 return -1;
3005
3006 D = "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
3007 W = "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
3008 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
3009 R = "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
3010 S = "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
3011 "S_0[] -> [0, 0, 0] }";
3012 if (test_one_schedule(ctx, D, W, R, S, 1, 0) < 0)
3013 return -1;
3014 ctx->opt->schedule_parametric = 0;
3015 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3016 return -1;
3017 ctx->opt->schedule_parametric = 1;
3018
3019 D = "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
3020 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
3021 W = "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
3022 R = "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
3023 "S4[i] -> a[i,N] }";
3024 S = "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
3025 "S4[i] -> [4,i,0] }";
3026 if (test_one_schedule(ctx, D, W, R, S, 2, 0) < 0)
3027 return -1;
3028
3029 D = "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
3030 W = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3031 "j <= N }";
3032 R = "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3033 "j <= N; "
3034 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
3035 "j <= N }";
3036 S = "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3037 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3038 return -1;
3039
3040 D = "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
3041 " S_2[t] : t >= 0 and t <= -1 + N; "
3042 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
3043 "i <= -1 + N }";
3044 W = "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
3045 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
3046 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
3047 "i >= 0 and i <= -1 + N }";
3048 R = "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
3049 "i >= 0 and i <= -1 + N; "
3050 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
3051 S = "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
3052 " S_0[t] -> [0, t, 0] }";
3053
3054 if (test_one_schedule(ctx, D, W, R, S, 2, 1) < 0)
3055 return -1;
3056 ctx->opt->schedule_parametric = 0;
3057 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3058 return -1;
3059 ctx->opt->schedule_parametric = 1;
3060
3061 D = "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
3062 S = "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
3063 if (test_one_schedule(ctx, D, "{}", "{}", S, 2, 2) < 0)
3064 return -1;
3065
3066 D = "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3067 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3068 W = "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3069 "j >= 0 and j <= -1 + N; "
3070 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3071 R = "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3072 "j >= 0 and j <= -1 + N; "
3073 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3074 S = "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3075 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3076 return -1;
3077
3078 D = "{ S_0[i] : i >= 0 }";
3079 W = "{ S_0[i] -> a[i] : i >= 0 }";
3080 R = "{ S_0[i] -> a[0] : i >= 0 }";
3081 S = "{ S_0[i] -> [0, i, 0] }";
3082 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3083 return -1;
3084
3085 D = "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3086 W = "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3087 R = "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3088 S = "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3089 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3090 return -1;
3091
3092 D = "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3093 "k <= -1 + n and k >= 0 }";
3094 W = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3095 R = "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3096 "k <= -1 + n and k >= 0; "
3097 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3098 "k <= -1 + n and k >= 0; "
3099 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3100 "k <= -1 + n and k >= 0 }";
3101 S = "[n] -> { S_0[j, k] -> [2, j, k] }";
3102 ctx->opt->schedule_outer_coincidence = 1;
3103 if (test_one_schedule(ctx, D, W, R, S, 0, 0) < 0)
3104 return -1;
3105 ctx->opt->schedule_outer_coincidence = 0;
3106
3107 D = "{Stmt_for_body24[i0, i1, i2, i3]:"
3108 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3109 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3110 "Stmt_for_body24[i0, i1, 1, 0]:"
3111 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3112 "Stmt_for_body7[i0, i1, i2]:"
3113 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3114 "i2 <= 7 }";
3115
3116 V = "{Stmt_for_body24[0, i1, i2, i3] -> "
3117 "Stmt_for_body24[1, i1, i2, i3]:"
3118 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3119 "i2 >= 1;"
3120 "Stmt_for_body24[0, i1, i2, i3] -> "
3121 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3122 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3123 "i3 >= 0;"
3124 "Stmt_for_body24[0, i1, i2, i3] ->"
3125 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3126 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3127 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3128 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3129 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3130 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3131 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3132 "i1 <= 6 and i1 >= 0;"
3133 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3134 "Stmt_for_body7[i0, i1, i2] -> "
3135 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3136 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3137 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3138 "Stmt_for_body7[i0, i1, i2] -> "
3139 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3140 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3141 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3142 P = V;
3143 S = "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3144 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3145 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3146
3147 if (test_special_schedule(ctx, D, V, P, S) < 0)
3148 return -1;
3149
3150 D = "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3151 V = "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3152 "j >= 1 and j <= 7;"
3153 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3154 "j >= 1 and j <= 8 }";
3155 P = "{ }";
3156 S = "{ S_0[i, j] -> [i + j, j] }";
3157 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3158 if (test_special_schedule(ctx, D, V, P, S) < 0)
3159 return -1;
3160 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3161
3162 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3163 D = "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3164 "j >= 0 and j <= -1 + i }";
3165 V = "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3166 "i <= -1 + N and j >= 0;"
3167 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3168 "i <= -2 + N }";
3169 P = "{ }";
3170 S = "{ S_0[i, j] -> [i, j] }";
3171 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3172 if (test_special_schedule(ctx, D, V, P, S) < 0)
3173 return -1;
3174 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3175
3176 /* Test both algorithms on a case with only proximity dependences. */
3177 D = "{ S[i,j] : 0 <= i <= 10 }";
3178 V = "{ }";
3179 P = "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3180 S = "{ S[i, j] -> [j, i] }";
3181 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3182 if (test_special_schedule(ctx, D, V, P, S) < 0)
3183 return -1;
3184 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3185 if (test_special_schedule(ctx, D, V, P, S) < 0)
3186 return -1;
3187
3188 D = "{ A[a]; B[] }";
3189 V = "{}";
3190 P = "{ A[a] -> B[] }";
3191 if (test_has_schedule(ctx, D, V, P) < 0)
3192 return -1;
3193
3194 if (test_padded_schedule(ctx) < 0)
3195 return -1;
3196
3197 /* Check that check for progress is not confused by rational
3198 * solution.
3199 */
3200 D = "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3201 V = "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3202 "i0 <= -2 + N; "
3203 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3204 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3205 P = "{}";
3206 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3207 if (test_has_schedule(ctx, D, V, P) < 0)
3208 return -1;
3209 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3210
3211 /* Check that we allow schedule rows that are only non-trivial
3212 * on some full-dimensional domains.
3213 */
3214 D = "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
3215 V = "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
3216 "S1[j] -> S2[1] : 0 <= j <= 1 }";
3217 P = "{}";
3218 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_FEAUTRIER;
3219 if (test_has_schedule(ctx, D, V, P) < 0)
3220 return -1;
3221 ctx->opt->schedule_algorithm = ISL_SCHEDULE_ALGORITHM_ISL;
3222
3223 if (test_conditional_schedule_constraints(ctx) < 0)
3224 return -1;
3225
3226 return 0;
3227 }
3228
3229 int test_plain_injective(isl_ctx *ctx, const char *str, int injective)
3230 {
3231 isl_union_map *umap;
3232 int test;
3233
3234 umap = isl_union_map_read_from_str(ctx, str);
3235 test = isl_union_map_plain_is_injective(umap);
3236 isl_union_map_free(umap);
3237 if (test < 0)
3238 return -1;
3239 if (test == injective)
3240 return 0;
3241 if (injective)
3242 isl_die(ctx, isl_error_unknown,
3243 "map not detected as injective", return -1);
3244 else
3245 isl_die(ctx, isl_error_unknown,
3246 "map detected as injective", return -1);
3247 }
3248
3249 int test_injective(isl_ctx *ctx)
3250 {
3251 const char *str;
3252
3253 if (test_plain_injective(ctx, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3254 return -1;
3255 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> B[0]}", 1))
3256 return -1;
3257 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[1]}", 1))
3258 return -1;
3259 if (test_plain_injective(ctx, "{S[] -> A[0]; T[] -> A[0]}", 0))
3260 return -1;
3261 if (test_plain_injective(ctx, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3262 return -1;
3263 if (test_plain_injective(ctx, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3264 return -1;
3265 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3266 return -1;
3267 if (test_plain_injective(ctx, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3268 return -1;
3269
3270 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3271 if (test_plain_injective(ctx, str, 1))
3272 return -1;
3273 str = "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3274 if (test_plain_injective(ctx, str, 0))
3275 return -1;
3276
3277 return 0;
3278 }
3279
3280 static int aff_plain_is_equal(__isl_keep isl_aff *aff, const char *str)
3281 {
3282 isl_aff *aff2;
3283 int equal;
3284
3285 if (!aff)
3286 return -1;
3287
3288 aff2 = isl_aff_read_from_str(isl_aff_get_ctx(aff), str);
3289 equal = isl_aff_plain_is_equal(aff, aff2);
3290 isl_aff_free(aff2);
3291
3292 return equal;
3293 }
3294
3295 static int aff_check_plain_equal(__isl_keep isl_aff *aff, const char *str)
3296 {
3297 int equal;
3298
3299 equal = aff_plain_is_equal(aff, str);
3300 if (equal < 0)
3301 return -1;
3302 if (!equal)
3303 isl_die(isl_aff_get_ctx(aff), isl_error_unknown,
3304 "result not as expected", return -1);
3305 return 0;
3306 }
3307
3308 struct {
3309 __isl_give isl_aff *(*fn)(__isl_take isl_aff *aff1,
3310 __isl_take isl_aff *aff2);
3311 } aff_bin_op[] = {
3312 ['+'] = { &isl_aff_add },
3313 ['-'] = { &isl_aff_sub },
3314 ['*'] = { &isl_aff_mul },
3315 ['/'] = { &isl_aff_div },
3316 };
3317
3318 struct {
3319 const char *arg1;
3320 unsigned char op;
3321 const char *arg2;
3322 const char *res;
3323 } aff_bin_tests[] = {
3324 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3325 "{ [i] -> [2i] }" },
3326 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3327 "{ [i] -> [0] }" },
3328 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3329 "{ [i] -> [2i] }" },
3330 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3331 "{ [i] -> [2i] }" },
3332 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
3333 "{ [i] -> [i/2] }" },
3334 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
3335 "{ [i] -> [i] }" },
3336 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3337 "{ [i] -> [NaN] }" },
3338 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3339 "{ [i] -> [NaN] }" },
3340 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3341 "{ [i] -> [NaN] }" },
3342 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3343 "{ [i] -> [NaN] }" },
3344 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
3345 "{ [i] -> [NaN] }" },
3346 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
3347 "{ [i] -> [NaN] }" },
3348 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3349 "{ [i] -> [NaN] }" },
3350 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3351 "{ [i] -> [NaN] }" },
3352 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3353 "{ [i] -> [NaN] }" },
3354 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3355 "{ [i] -> [NaN] }" },
3356 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
3357 "{ [i] -> [NaN] }" },
3358 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
3359 "{ [i] -> [NaN] }" },
3360 };
3361
3362 /* Perform some basic tests of binary operations on isl_aff objects.
3363 */
3364 static int test_bin_aff(isl_ctx *ctx)
3365 {
3366 int i;
3367 isl_aff *aff1, *aff2, *res;
3368 __isl_give isl_aff *(*fn)(__isl_take isl_aff *aff1,
3369 __isl_take isl_aff *aff2);
3370 int ok;
3371
3372 for (i = 0; i < ARRAY_SIZE(aff_bin_tests); ++i) {
3373 aff1 = isl_aff_read_from_str(ctx, aff_bin_tests[i].arg1);
3374 aff2 = isl_aff_read_from_str(ctx, aff_bin_tests[i].arg2);
3375 res = isl_aff_read_from_str(ctx, aff_bin_tests[i].res);
3376 fn = aff_bin_op[aff_bin_tests[i].op].fn;
3377 aff1 = fn(aff1, aff2);
3378 if (isl_aff_is_nan(res))
3379 ok = isl_aff_is_nan(aff1);
3380 else
3381 ok = isl_aff_plain_is_equal(aff1, res);
3382 isl_aff_free(aff1);
3383 isl_aff_free(res);
3384 if (ok < 0)
3385 return -1;
3386 if (!ok)
3387 isl_die(ctx, isl_error_unknown,
3388 "unexpected result", return -1);
3389 }
3390
3391 return 0;
3392 }
3393
3394 struct {
3395 __isl_give isl_union_pw_multi_aff *(*fn)(
3396 __isl_take isl_union_pw_multi_aff *upma1,
3397 __isl_take isl_union_pw_multi_aff *upma2);
3398 const char *arg1;
3399 const char *arg2;
3400 const char *res;
3401 } upma_bin_tests[] = {
3402 { &isl_union_pw_multi_aff_add, "{ A[] -> [0]; B[0] -> [1] }",
3403 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
3404 { &isl_union_pw_multi_aff_union_add, "{ A[] -> [0]; B[0] -> [1] }",
3405 "{ B[x] -> [2] : x >= 0 }",
3406 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
3407 };
3408
3409 /* Perform some basic tests of binary operations on
3410 * isl_union_pw_multi_aff objects.
3411 */
3412 static int test_bin_upma(isl_ctx *ctx)
3413 {
3414 int i;
3415 isl_union_pw_multi_aff *upma1, *upma2, *res;
3416 int ok;
3417
3418 for (i = 0; i < ARRAY_SIZE(upma_bin_tests); ++i) {
3419 upma1 = isl_union_pw_multi_aff_read_from_str(ctx,
3420 upma_bin_tests[i].arg1);
3421 upma2 = isl_union_pw_multi_aff_read_from_str(ctx,
3422 upma_bin_tests[i].arg2);
3423 res = isl_union_pw_multi_aff_read_from_str(ctx,
3424 upma_bin_tests[i].res);
3425 upma1 = upma_bin_tests[i].fn(upma1, upma2);
3426 ok = isl_union_pw_multi_aff_plain_is_equal(upma1, res);
3427 isl_union_pw_multi_aff_free(upma1);
3428 isl_union_pw_multi_aff_free(res);
3429 if (ok < 0)
3430 return -1;
3431 if (!ok)
3432 isl_die(ctx, isl_error_unknown,
3433 "unexpected result", return -1);
3434 }
3435
3436 return 0;
3437 }
3438
3439 int test_aff(isl_ctx *ctx)
3440 {
3441 const char *str;
3442 isl_set *set;
3443 isl_space *space;
3444 isl_local_space *ls;
3445 isl_aff *aff;
3446 int zero, equal;
3447
3448 if (test_bin_aff(ctx) < 0)
3449 return -1;
3450 if (test_bin_upma(ctx) < 0)
3451 return -1;
3452
3453 space = isl_space_set_alloc(ctx, 0, 1);
3454 ls = isl_local_space_from_space(space);
3455 aff = isl_aff_zero_on_domain(ls);
3456
3457 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3458 aff = isl_aff_scale_down_ui(aff, 3);
3459 aff = isl_aff_floor(aff);
3460 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3461 aff = isl_aff_scale_down_ui(aff, 2);
3462 aff = isl_aff_floor(aff);
3463 aff = isl_aff_add_coefficient_si(aff, isl_dim_in, 0, 1);
3464
3465 str = "{ [10] }";
3466 set = isl_set_read_from_str(ctx, str);
3467 aff = isl_aff_gist(aff, set);
3468
3469 aff = isl_aff_add_constant_si(aff, -16);
3470 zero = isl_aff_plain_is_zero(aff);
3471 isl_aff_free(aff);
3472
3473 if (zero < 0)
3474 return -1;
3475 if (!zero)
3476 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3477
3478 aff = isl_aff_read_from_str(ctx, "{ [-1] }");
3479 aff = isl_aff_scale_down_ui(aff, 64);
3480 aff = isl_aff_floor(aff);
3481 equal = aff_check_plain_equal(aff, "{ [-1] }");
3482 isl_aff_free(aff);
3483 if (equal < 0)
3484 return -1;
3485
3486 return 0;
3487 }
3488
3489 int test_dim_max(isl_ctx *ctx)
3490 {
3491 int equal;
3492 const char *str;
3493 isl_set *set1, *set2;
3494 isl_set *set;
3495 isl_map *map;
3496 isl_pw_aff *pwaff;
3497
3498 str = "[N] -> { [i] : 0 <= i <= min(N,10) }";
3499 set = isl_set_read_from_str(ctx, str);
3500 pwaff = isl_set_dim_max(set, 0);
3501 set1 = isl_set_from_pw_aff(pwaff);
3502 str = "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
3503 set2 = isl_set_read_from_str(ctx, str);
3504 equal = isl_set_is_equal(set1, set2);
3505 isl_set_free(set1);
3506 isl_set_free(set2);
3507 if (equal < 0)
3508 return -1;
3509 if (!equal)
3510 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3511
3512 str = "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
3513 set = isl_set_read_from_str(ctx, str);
3514 pwaff = isl_set_dim_max(set, 0);
3515 set1 = isl_set_from_pw_aff(pwaff);
3516 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3517 set2 = isl_set_read_from_str(ctx, str);
3518 equal = isl_set_is_equal(set1, set2);
3519 isl_set_free(set1);
3520 isl_set_free(set2);
3521 if (equal < 0)
3522 return -1;
3523 if (!equal)
3524 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3525
3526 str = "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
3527 set = isl_set_read_from_str(ctx, str);
3528 pwaff = isl_set_dim_max(set, 0);
3529 set1 = isl_set_from_pw_aff(pwaff);
3530 str = "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3531 set2 = isl_set_read_from_str(ctx, str);
3532 equal = isl_set_is_equal(set1, set2);
3533 isl_set_free(set1);
3534 isl_set_free(set2);
3535 if (equal < 0)
3536 return -1;
3537 if (!equal)
3538 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3539
3540 str = "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
3541 "0 <= i < N and 0 <= j < M }";
3542 map = isl_map_read_from_str(ctx, str);
3543 set = isl_map_range(map);
3544
3545 pwaff = isl_set_dim_max(isl_set_copy(set), 0);
3546 set1 = isl_set_from_pw_aff(pwaff);
3547 str = "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
3548 set2 = isl_set_read_from_str(ctx, str);
3549 equal = isl_set_is_equal(set1, set2);
3550 isl_set_free(set1);
3551 isl_set_free(set2);
3552
3553 pwaff = isl_set_dim_max(isl_set_copy(set), 3);
3554 set1 = isl_set_from_pw_aff(pwaff);
3555 str = "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
3556 set2 = isl_set_read_from_str(ctx, str);
3557 if (equal >= 0 && equal)
3558 equal = isl_set_is_equal(set1, set2);
3559 isl_set_free(set1);
3560 isl_set_free(set2);
3561
3562 isl_set_free(set);
3563
3564 if (equal < 0)
3565 return -1;
3566 if (!equal)
3567 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3568
3569 /* Check that solutions are properly merged. */
3570 str = "[n] -> { [a, b, c] : c >= -4a - 2b and "
3571 "c <= -1 + n - 4a - 2b and c >= -2b and "
3572 "4a >= -4 + n and c >= 0 }";
3573 set = isl_set_read_from_str(ctx, str);
3574 pwaff = isl_set_dim_min(set, 2);
3575 set1 = isl_set_from_pw_aff(pwaff);
3576 str = "[n] -> { [(0)] : n >= 1 }";
3577 set2 = isl_set_read_from_str(ctx, str);
3578 equal = isl_set_is_equal(set1, set2);
3579 isl_set_free(set1);
3580 isl_set_free(set2);
3581
3582 if (equal < 0)
3583 return -1;
3584 if (!equal)
3585 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3586
3587 /* Check that empty solution lie in the right space. */
3588 str = "[n] -> { [t,a] : 1 = 0 }";
3589 set = isl_set_read_from_str(ctx, str);
3590 pwaff = isl_set_dim_max(set, 0);
3591 set1 = isl_set_from_pw_aff(pwaff);
3592 str = "[n] -> { [t] : 1 = 0 }";
3593 set2 = isl_set_read_from_str(ctx, str);
3594 equal = isl_set_is_equal(set1, set2);
3595 isl_set_free(set1);
3596 isl_set_free(set2);
3597
3598 if (equal < 0)
3599 return -1;
3600 if (!equal)
3601 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3602
3603 return 0;
3604 }
3605
3606 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
3607 */
3608 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff *pma,
3609 const char *str)
3610 {
3611 isl_ctx *ctx;
3612 isl_pw_multi_aff *pma2;
3613 int equal;
3614
3615 if (!pma)
3616 return -1;
3617
3618 ctx = isl_pw_multi_aff_get_ctx(pma);
3619 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3620 equal = isl_pw_multi_aff_plain_is_equal(pma, pma2);
3621 isl_pw_multi_aff_free(pma2);
3622
3623 return equal;
3624 }
3625
3626 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
3627 * represented by "str".
3628 */
3629 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff *pma,
3630 const char *str)
3631 {
3632 int equal;
3633
3634 equal = pw_multi_aff_plain_is_equal(pma, str);
3635 if (equal < 0)
3636 return -1;
3637 if (!equal)
3638 isl_die(isl_pw_multi_aff_get_ctx(pma), isl_error_unknown,
3639 "result not as expected", return -1);
3640 return 0;
3641 }
3642
3643 /* Basic test for isl_pw_multi_aff_product.
3644 *
3645 * Check that multiple pieces are properly handled.
3646 */
3647 static int test_product_pma(isl_ctx *ctx)
3648 {
3649 int equal;
3650 const char *str;
3651 isl_pw_multi_aff *pma1, *pma2;
3652
3653 str = "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
3654 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
3655 str = "{ C[] -> D[] }";
3656 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
3657 pma1 = isl_pw_multi_aff_product(pma1, pma2);
3658 str = "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
3659 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
3660 equal = pw_multi_aff_check_plain_equal(pma1, str);
3661 isl_pw_multi_aff_free(pma1);
3662 if (equal < 0)
3663 return -1;
3664
3665 return 0;
3666 }
3667
3668 int test_product(isl_ctx *ctx)
3669 {
3670 const char *str;
3671 isl_set *set;
3672 isl_union_set *uset1, *uset2;
3673 int ok;
3674
3675 str = "{ A[i] }";
3676 set = isl_set_read_from_str(ctx, str);
3677 set = isl_set_product(set, isl_set_copy(set));
3678 ok = isl_set_is_wrapping(set);
3679 isl_set_free(set);
3680 if (ok < 0)
3681 return -1;
3682 if (!ok)
3683 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3684
3685 str = "{ [] }";
3686 uset1 = isl_union_set_read_from_str(ctx, str);
3687 uset1 = isl_union_set_product(uset1, isl_union_set_copy(uset1));
3688 str = "{ [[] -> []] }";
3689 uset2 = isl_union_set_read_from_str(ctx, str);
3690 ok = isl_union_set_is_equal(uset1, uset2);
3691 isl_union_set_free(uset1);
3692 isl_union_set_free(uset2);
3693 if (ok < 0)
3694 return -1;
3695 if (!ok)
3696 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3697
3698 if (test_product_pma(ctx) < 0)
3699 return -1;
3700
3701 return 0;
3702 }
3703
3704 /* Check that two sets are not considered disjoint just because
3705 * they have a different set of (named) parameters.
3706 */
3707 static int test_disjoint(isl_ctx *ctx)
3708 {
3709 const char *str;
3710 isl_set *set, *set2;
3711 int disjoint;
3712
3713 str = "[n] -> { [[]->[]] }";
3714 set = isl_set_read_from_str(ctx, str);
3715 str = "{ [[]->[]] }";
3716 set2 = isl_set_read_from_str(ctx, str);
3717 disjoint = isl_set_is_disjoint(set, set2);
3718 isl_set_free(set);
3719 isl_set_free(set2);
3720 if (disjoint < 0)
3721 return -1;
3722 if (disjoint)
3723 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3724
3725 return 0;
3726 }
3727
3728 int test_equal(isl_ctx *ctx)
3729 {
3730 const char *str;
3731 isl_set *set, *set2;
3732 int equal;
3733
3734 str = "{ S_6[i] }";
3735 set = isl_set_read_from_str(ctx, str);
3736 str = "{ S_7[i] }";
3737 set2 = isl_set_read_from_str(ctx, str);
3738 equal = isl_set_is_equal(set, set2);
3739 isl_set_free(set);
3740 isl_set_free(set2);
3741 if (equal < 0)
3742 return -1;
3743 if (equal)
3744 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3745
3746 return 0;
3747 }
3748
3749 static int test_plain_fixed(isl_ctx *ctx, __isl_take isl_map *map,
3750 enum isl_dim_type type, unsigned pos, int fixed)
3751 {
3752 int test;
3753
3754 test = isl_map_plain_is_fixed(map, type, pos, NULL);
3755 isl_map_free(map);
3756 if (test < 0)
3757 return -1;
3758 if (test == fixed)
3759 return 0;
3760 if (fixed)
3761 isl_die(ctx, isl_error_unknown,
3762 "map not detected as fixed", return -1);
3763 else
3764 isl_die(ctx, isl_error_unknown,
3765 "map detected as fixed", return -1);
3766 }
3767
3768 int test_fixed(isl_ctx *ctx)
3769 {
3770 const char *str;
3771 isl_map *map;
3772
3773 str = "{ [i] -> [i] }";
3774 map = isl_map_read_from_str(ctx, str);
3775 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 0))
3776 return -1;
3777 str = "{ [i] -> [1] }";
3778 map = isl_map_read_from_str(ctx, str);
3779 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3780 return -1;
3781 str = "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
3782 map = isl_map_read_from_str(ctx, str);
3783 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3784 return -1;
3785 map = isl_map_read_from_str(ctx, str);
3786 map = isl_map_neg(map);
3787 if (test_plain_fixed(ctx, map, isl_dim_out, 0, 1))
3788 return -1;
3789
3790 return 0;
3791 }
3792
3793 struct isl_vertices_test_data {
3794 const char *set;
3795 int n;
3796 const char *vertex[2];
3797 } vertices_tests[] = {
3798 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
3799 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
3800 { "{ A[t, i] : t = 14 and i = 1 }",
3801 1, { "{ A[14, 1] }" } },
3802 };
3803
3804 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
3805 */
3806 static int find_vertex(__isl_take isl_vertex *vertex, void *user)
3807 {
3808 struct isl_vertices_test_data *data = user;
3809 isl_ctx *ctx;
3810 isl_multi_aff *ma;
3811 isl_basic_set *bset;
3812 isl_pw_multi_aff *pma;
3813 int i;
3814 int equal;
3815
3816 ctx = isl_vertex_get_ctx(vertex);
3817 bset = isl_vertex_get_domain(vertex);
3818 ma = isl_vertex_get_expr(vertex);
3819 pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset), ma);
3820
3821 for (i = 0; i < data->n; ++i) {
3822 isl_pw_multi_aff *pma_i;
3823
3824 pma_i = isl_pw_multi_aff_read_from_str(ctx, data->vertex[i]);
3825 equal = isl_pw_multi_aff_plain_is_equal(pma, pma_i);
3826 isl_pw_multi_aff_free(pma_i);
3827
3828 if (equal < 0 || equal)
3829 break;
3830 }
3831
3832 isl_pw_multi_aff_free(pma);
3833 isl_vertex_free(vertex);
3834
3835 if (equal < 0)
3836 return -1;
3837
3838 return equal ? 0 : - 1;
3839 }
3840
3841 int test_vertices(isl_ctx *ctx)
3842 {
3843 int i;
3844
3845 for (i = 0; i < ARRAY_SIZE(vertices_tests); ++i) {
3846 isl_basic_set *bset;
3847 isl_vertices *vertices;
3848 int ok = 1;
3849 int n;
3850
3851 bset = isl_basic_set_read_from_str(ctx, vertices_tests[i].set);
3852 vertices = isl_basic_set_compute_vertices(bset);
3853 n = isl_vertices_get_n_vertices(vertices);
3854 if (vertices_tests[i].n != n)
3855 ok = 0;
3856 if (isl_vertices_foreach_vertex(vertices, &find_vertex,
3857 &vertices_tests[i]) < 0)
3858 ok = 0;
3859 isl_vertices_free(vertices);
3860 isl_basic_set_free(bset);
3861
3862 if (!vertices)
3863 return -1;
3864 if (!ok)
3865 isl_die(ctx, isl_error_unknown, "unexpected vertices",
3866 return -1);
3867 }
3868
3869 return 0;
3870 }
3871
3872 int test_union_pw(isl_ctx *ctx)
3873 {
3874 int equal;
3875 const char *str;
3876 isl_union_set *uset;
3877 isl_union_pw_qpolynomial *upwqp1, *upwqp2;
3878
3879 str = "{ [x] -> x^2 }";
3880 upwqp1 = isl_union_pw_qpolynomial_read_from_str(ctx, str);
3881 upwqp2 = isl_union_pw_qpolynomial_copy(upwqp1);
3882 uset = isl_union_pw_qpolynomial_domain(upwqp1);
3883 upwqp1 = isl_union_pw_qpolynomial_copy(upwqp2);
3884 upwqp1 = isl_union_pw_qpolynomial_intersect_domain(upwqp1, uset);
3885 equal = isl_union_pw_qpolynomial_plain_is_equal(upwqp1, upwqp2);
3886 isl_union_pw_qpolynomial_free(upwqp1);
3887 isl_union_pw_qpolynomial_free(upwqp2);
3888 if (equal < 0)
3889 return -1;
3890 if (!equal)
3891 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3892
3893 return 0;
3894 }
3895
3896 int test_output(isl_ctx *ctx)
3897 {
3898 char *s;
3899 const char *str;
3900 isl_pw_aff *pa;
3901 isl_printer *p;
3902 int equal;
3903
3904 str = "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
3905 pa = isl_pw_aff_read_from_str(ctx, str);
3906
3907 p = isl_printer_to_str(ctx);
3908 p = isl_printer_set_output_format(p, ISL_FORMAT_C);
3909 p = isl_printer_print_pw_aff(p, pa);
3910 s = isl_printer_get_str(p);
3911 isl_printer_free(p);
3912 isl_pw_aff_free(pa);
3913 if (!s)
3914 equal = -1;
3915 else
3916 equal = !strcmp(s, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
3917 free(s);
3918 if (equal < 0)
3919 return -1;
3920 if (!equal)
3921 isl_die(ctx, isl_error_unknown, "unexpected result", return -1);
3922
3923 return 0;
3924 }
3925
3926 int test_sample(isl_ctx *ctx)
3927 {
3928 const char *str;
3929 isl_basic_set *bset1, *bset2;
3930 int empty, subset;
3931
3932 str = "{ [a, b, c, d, e, f, g, h, i, j, k] : "
3933 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
3934 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
3935 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
3936 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
3937 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
3938 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
3939 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
3940 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3941 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3942 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3943 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3944 "d - 1073741821e and "
3945 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3946 "3j >= 1 - a + b + 2e and "
3947 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3948 "3i <= 4 - a + 4b - e and "
3949 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3950 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3951 "c <= -1 + a and 3i >= -2 - a + 3e and "
3952 "1073741822e <= 1073741823 - a + 1073741822b + c and "
3953 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3954 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3955 "1073741823e >= 1 + 1073741823b - d and "
3956 "3i >= 1073741823b + c - 1073741823e - f and "
3957 "3i >= 1 + 2b + e + 3g }";
3958 bset1 = isl_basic_set_read_from_str(ctx, str);
3959 bset2 = isl_basic_set_sample(isl_basic_set_copy(bset1));
3960 empty = isl_basic_set_is_empty(bset2);
3961 subset = isl_basic_set_is_subset(bset2, bset1);
3962 isl_basic_set_free(bset1);
3963 isl_basic_set_free(bset2);
3964 if (empty < 0 || subset < 0)
3965 return -1;
3966 if (empty)
3967 isl_die(ctx, isl_error_unknown, "point not found", return -1);
3968 if (!subset)
3969 isl_die(ctx, isl_error_unknown, "bad point found", return -1);
3970
3971 return 0;
3972 }
3973
3974 int test_fixed_power(isl_ctx *ctx)
3975 {
3976 const char *str;
3977 isl_map *map;
3978 isl_int exp;
3979 int equal;
3980
3981 isl_int_init(exp);
3982 str = "{ [i] -> [i + 1] }";
3983 map = isl_map_read_from_str(ctx, str);
3984 isl_int_set_si(exp, 23);
3985 map = isl_map_fixed_power(map, exp);
3986 equal = map_check_equal(map, "{ [i] -> [i + 23] }");
3987 isl_int_clear(exp);
3988 isl_map_free(map);
3989 if (equal < 0)
3990 return -1;
3991
3992 return 0;
3993 }
3994
3995 int test_slice(isl_ctx *ctx)
3996 {
3997 const char *str;
3998 isl_map *map;
3999 int equal;
4000
4001 str = "{ [i] -> [j] }";
4002 map = isl_map_read_from_str(ctx, str);
4003 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_out, 0);
4004 equal = map_check_equal(map, "{ [i] -> [i] }");
4005 isl_map_free(map);
4006 if (equal < 0)
4007 return -1;
4008
4009 str = "{ [i] -> [j] }";
4010 map = isl_map_read_from_str(ctx, str);
4011 map = isl_map_equate(map, isl_dim_in, 0, isl_dim_in, 0);
4012 equal = map_check_equal(map, "{ [i] -> [j] }");
4013 isl_map_free(map);
4014 if (equal < 0)
4015 return -1;
4016
4017 str = "{ [i] -> [j] }";
4018 map = isl_map_read_from_str(ctx, str);
4019 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_out, 0);
4020 equal = map_check_equal(map, "{ [i] -> [-i] }");
4021 isl_map_free(map);
4022 if (equal < 0)
4023 return -1;
4024
4025 str = "{ [i] -> [j] }";
4026 map = isl_map_read_from_str(ctx, str);
4027 map = isl_map_oppose(map, isl_dim_in, 0, isl_dim_in, 0);
4028 equal = map_check_equal(map, "{ [0] -> [j] }");
4029 isl_map_free(map);
4030 if (equal < 0)
4031 return -1;
4032
4033 str = "{ [i] -> [j] }";
4034 map = isl_map_read_from_str(ctx, str);
4035 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_out, 0);
4036 equal = map_check_equal(map, "{ [i] -> [j] : i > j }");
4037 isl_map_free(map);
4038 if (equal < 0)
4039 return -1;
4040
4041 str = "{ [i] -> [j] }";
4042 map = isl_map_read_from_str(ctx, str);
4043 map = isl_map_order_gt(map, isl_dim_in, 0, isl_dim_in, 0);
4044 equal = map_check_equal(map, "{ [i] -> [j] : false }");
4045 isl_map_free(map);
4046 if (equal < 0)
4047 return -1;
4048
4049 return 0;
4050 }
4051
4052 int test_eliminate(isl_ctx *ctx)
4053 {
4054 const char *str;
4055 isl_map *map;
4056 int equal;
4057
4058 str = "{ [i] -> [j] : i = 2j }";
4059 map = isl_map_read_from_str(ctx, str);
4060 map = isl_map_eliminate(map, isl_dim_out, 0, 1);
4061 equal = map_check_equal(map, "{ [i] -> [j] : exists a : i = 2a }");
4062 isl_map_free(map);
4063 if (equal < 0)
4064 return -1;
4065
4066 return 0;
4067 }
4068
4069 /* Check that isl_set_dim_residue_class detects that the values of j
4070 * in the set below are all odd and that it does not detect any spurious
4071 * strides.
4072 */
4073 static int test_residue_class(isl_ctx *ctx)
4074 {
4075 const char *str;
4076 isl_set *set;
4077 isl_int m, r;
4078 int res;
4079
4080 str = "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
4081 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
4082 set = isl_set_read_from_str(ctx, str);
4083 isl_int_init(m);
4084 isl_int_init(r);
4085 res = isl_set_dim_residue_class(set, 1, &m, &r);
4086 if (res >= 0 &&
4087 (isl_int_cmp_si(m, 2) != 0 || isl_int_cmp_si(r, 1) != 0))
4088 isl_die(ctx, isl_error_unknown, "incorrect residue class",
4089 res = -1);
4090 isl_int_clear(r);
4091 isl_int_clear(m);
4092 isl_set_free(set);
4093
4094 return res;
4095 }
4096
4097 int test_align_parameters(isl_ctx *ctx)
4098 {
4099 const char *str;
4100 isl_space *space;
4101 isl_multi_aff *ma1, *ma2;
4102 int equal;
4103
4104 str = "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
4105 ma1 = isl_multi_aff_read_from_str(ctx, str);
4106
4107 space = isl_space_params_alloc(ctx, 1);
4108 space = isl_space_set_dim_name(space, isl_dim_param, 0, "N");
4109 ma1 = isl_multi_aff_align_params(ma1, space);
4110
4111 str = "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
4112 ma2 = isl_multi_aff_read_from_str(ctx, str);
4113
4114 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
4115
4116 isl_multi_aff_free(ma1);
4117 isl_multi_aff_free(ma2);
4118
4119 if (equal < 0)
4120 return -1;
4121 if (!equal)
4122 isl_die(ctx, isl_error_unknown,
4123 "result not as expected", return -1);
4124
4125 return 0;
4126 }
4127
4128 static int test_list(isl_ctx *ctx)
4129 {
4130 isl_id *a, *b, *c, *d, *id;
4131 isl_id_list *list;
4132 int ok;
4133
4134 a = isl_id_alloc(ctx, "a", NULL);
4135 b = isl_id_alloc(ctx, "b", NULL);
4136 c = isl_id_alloc(ctx, "c", NULL);
4137 d = isl_id_alloc(ctx, "d", NULL);
4138
4139 list = isl_id_list_alloc(ctx, 4);
4140 list = isl_id_list_add(list, a);
4141 list = isl_id_list_add(list, b);
4142 list = isl_id_list_add(list, c);
4143 list = isl_id_list_add(list, d);
4144 list = isl_id_list_drop(list, 1, 1);
4145
4146 if (isl_id_list_n_id(list) != 3) {
4147 isl_id_list_free(list);
4148 isl_die(ctx, isl_error_unknown,
4149 "unexpected number of elements in list", return -1);
4150 }
4151
4152 id = isl_id_list_get_id(list, 0);
4153 ok = id == a;
4154 isl_id_free(id);
4155 id = isl_id_list_get_id(list, 1);
4156 ok = ok && id == c;
4157 isl_id_free(id);
4158 id = isl_id_list_get_id(list, 2);
4159 ok = ok && id == d;
4160 isl_id_free(id);
4161
4162 isl_id_list_free(list);
4163
4164 if (!ok)
4165 isl_die(ctx, isl_error_unknown,
4166 "unexpected elements in list", return -1);
4167
4168 return 0;
4169 }
4170
4171 const char *set_conversion_tests[] = {
4172 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4173 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4174 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4175 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4176 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
4177 };
4178
4179 /* Check that converting from isl_set to isl_pw_multi_aff and back
4180 * to isl_set produces the original isl_set.
4181 */
4182 static int test_set_conversion(isl_ctx *ctx)
4183 {
4184 int i;
4185 const char *str;
4186 isl_set *set1, *set2;
4187 isl_pw_multi_aff *pma;
4188 int equal;
4189
4190 for (i = 0; i < ARRAY_SIZE(set_conversion_tests); ++i) {
4191 str = set_conversion_tests[i];
4192 set1 = isl_set_read_from_str(ctx, str);
4193 pma = isl_pw_multi_aff_from_set(isl_set_copy(set1));
4194 set2 = isl_set_from_pw_multi_aff(pma);
4195 equal = isl_set_is_equal(set1, set2);
4196 isl_set_free(set1);
4197 isl_set_free(set2);
4198
4199 if (equal < 0)
4200 return -1;
4201 if (!equal)
4202 isl_die(ctx, isl_error_unknown, "bad conversion",
4203 return -1);
4204 }
4205
4206 return 0;
4207 }
4208
4209 /* Check that converting from isl_map to isl_pw_multi_aff and back
4210 * to isl_map produces the original isl_map.
4211 */
4212 static int test_map_conversion(isl_ctx *ctx)
4213 {
4214 const char *str;
4215 isl_map *map1, *map2;
4216 isl_pw_multi_aff *pma;
4217 int equal;
4218
4219 str = "{ [a, b, c, d] -> s0[a, b, e, f] : "
4220 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4221 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4222 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4223 "9e <= -2 - 2a) }";
4224 map1 = isl_map_read_from_str(ctx, str);
4225 pma = isl_pw_multi_aff_from_map(isl_map_copy(map1));
4226 map2 = isl_map_from_pw_multi_aff(pma);
4227 equal = isl_map_is_equal(map1, map2);
4228 isl_map_free(map1);
4229 isl_map_free(map2);
4230
4231 if (equal < 0)
4232 return -1;
4233 if (!equal)
4234 isl_die(ctx, isl_error_unknown, "bad conversion", return -1);
4235
4236 return 0;
4237 }
4238
4239 static int test_conversion(isl_ctx *ctx)
4240 {
4241 if (test_set_conversion(ctx) < 0)
4242 return -1;
4243 if (test_map_conversion(ctx) < 0)
4244 return -1;
4245 return 0;
4246 }
4247
4248 /* Check that isl_basic_map_curry does not modify input.
4249 */
4250 static int test_curry(isl_ctx *ctx)
4251 {
4252 const char *str;
4253 isl_basic_map *bmap1, *bmap2;
4254 int equal;
4255
4256 str = "{ [A[] -> B[]] -> C[] }";
4257 bmap1 = isl_basic_map_read_from_str(ctx, str);
4258 bmap2 = isl_basic_map_curry(isl_basic_map_copy(bmap1));
4259 equal = isl_basic_map_is_equal(bmap1, bmap2);
4260 isl_basic_map_free(bmap1);
4261 isl_basic_map_free(bmap2);
4262
4263 if (equal < 0)
4264 return -1;
4265 if (equal)
4266 isl_die(ctx, isl_error_unknown,
4267 "curried map should not be equal to original",
4268 return -1);
4269
4270 return 0;
4271 }
4272
4273 struct {
4274 const char *set;
4275 const char *ma;
4276 const char *res;
4277 } preimage_tests[] = {
4278 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4279 "{ A[j,i] -> B[i,j] }",
4280 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4281 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4282 "{ A[a,b] -> B[a/2,b/6] }",
4283 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4284 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4285 "{ A[a,b] -> B[a/2,b/6] }",
4286 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4287 "exists i,j : a = 2 i and b = 6 j }" },
4288 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4289 "[n] -> { : 0 <= n <= 100 }" },
4290 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4291 "{ A[a] -> B[2a] }",
4292 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4293 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4294 "{ A[a] -> B[([a/2])] }",
4295 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4296 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4297 "{ A[a] -> B[a,a,a/3] }",
4298 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4299 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4300 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4301 };
4302
4303 static int test_preimage_basic_set(isl_ctx *ctx)
4304 {
4305 int i;
4306 isl_basic_set *bset1, *bset2;
4307 isl_multi_aff *ma;
4308 int equal;
4309
4310 for (i = 0; i < ARRAY_SIZE(preimage_tests); ++i) {
4311 bset1 = isl_basic_set_read_from_str(ctx, preimage_tests[i].set);
4312 ma = isl_multi_aff_read_from_str(ctx, preimage_tests[i].ma);
4313 bset2 = isl_basic_set_read_from_str(ctx, preimage_tests[i].res);
4314 bset1 = isl_basic_set_preimage_multi_aff(bset1, ma);
4315 equal = isl_basic_set_is_equal(bset1, bset2);
4316 isl_basic_set_free(bset1);
4317 isl_basic_set_free(bset2);
4318 if (equal < 0)
4319 return -1;
4320 if (!equal)
4321 isl_die(ctx, isl_error_unknown, "bad preimage",
4322 return -1);
4323 }
4324
4325 return 0;
4326 }
4327
4328 struct {
4329 const char *map;
4330 const char *ma;
4331 const char *res;
4332 } preimage_domain_tests[] = {
4333 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4334 "{ A[j,i] -> B[i,j] }",
4335 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4336 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4337 "{ A[i] -> B[i + 1] }",
4338 "{ A[i] -> C[i + 1] }" },
4339 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4340 "{ A[i] -> B[i + 1] }",
4341 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4342 { "{ B[i] -> C[([i/2])] }",
4343 "{ A[i] -> B[2i] }",
4344 "{ A[i] -> C[i] }" },
4345 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4346 "{ A[i] -> B[([i/5]), ([i/7])] }",
4347 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4348 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4349 "[N] -> { A[] -> B[([N/5])] }",
4350 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4351 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4352 "{ A[i] -> B[2i] }",
4353 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4354 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4355 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4356 "{ A[i] -> B[2i] }",
4357 "{ A[i] -> C[2i] }" },
4358 };
4359
4360 static int test_preimage_union_map(isl_ctx *ctx)
4361 {
4362 int i;
4363 isl_union_map *umap1, *umap2;
4364 isl_multi_aff *ma;
4365 int equal;
4366
4367 for (i = 0; i < ARRAY_SIZE(preimage_domain_tests); ++i) {
4368 umap1 = isl_union_map_read_from_str(ctx,
4369 preimage_domain_tests[i].map);
4370 ma = isl_multi_aff_read_from_str(ctx,
4371 preimage_domain_tests[i].ma);
4372 umap2 = isl_union_map_read_from_str(ctx,
4373 preimage_domain_tests[i].res);
4374 umap1 = isl_union_map_preimage_domain_multi_aff(umap1, ma);
4375 equal = isl_union_map_is_equal(umap1, umap2);
4376 isl_union_map_free(umap1);
4377 isl_union_map_free(umap2);
4378 if (equal < 0)
4379 return -1;
4380 if (!equal)
4381 isl_die(ctx, isl_error_unknown, "bad preimage",
4382 return -1);
4383 }
4384
4385 return 0;
4386 }
4387
4388 static int test_preimage(isl_ctx *ctx)
4389 {
4390 if (test_preimage_basic_set(ctx) < 0)
4391 return -1;
4392 if (test_preimage_union_map(ctx) < 0)
4393 return -1;
4394
4395 return 0;
4396 }
4397
4398 struct {
4399 const char *ma1;
4400 const char *ma;
4401 const char *res;
4402 } pullback_tests[] = {
4403 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
4404 "{ A[a,b] -> C[b + 2a] }" },
4405 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
4406 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
4407 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
4408 "{ A[a] -> C[(a)/6] }" },
4409 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
4410 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
4411 "{ A[a] -> C[(2a)/3] }" },
4412 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
4413 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
4414 "{ A[i,j] -> C[i + j, i + j] }"},
4415 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
4416 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
4417 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
4418 };
4419
4420 static int test_pullback(isl_ctx *ctx)
4421 {
4422 int i;
4423 isl_multi_aff *ma1, *ma2;
4424 isl_multi_aff *ma;
4425 int equal;
4426
4427 for (i = 0; i < ARRAY_SIZE(pullback_tests); ++i) {
4428 ma1 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma1);
4429 ma = isl_multi_aff_read_from_str(ctx, pullback_tests[i].ma);
4430 ma2 = isl_multi_aff_read_from_str(ctx, pullback_tests[i].res);
4431 ma1 = isl_multi_aff_pullback_multi_aff(ma1, ma);
4432 equal = isl_multi_aff_plain_is_equal(ma1, ma2);
4433 isl_multi_aff_free(ma1);
4434 isl_multi_aff_free(ma2);
4435 if (equal < 0)
4436 return -1;
4437 if (!equal)
4438 isl_die(ctx, isl_error_unknown, "bad pullback",
4439 return -1);
4440 }
4441
4442 return 0;
4443 }
4444
4445 /* Check that negation is printed correctly.
4446 */
4447 static int test_ast(isl_ctx *ctx)
4448 {
4449 isl_ast_expr *expr, *expr1, *expr2, *expr3;
4450 char *str;
4451 int ok;
4452
4453 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
4454 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
4455 expr = isl_ast_expr_add(expr1, expr2);
4456 expr = isl_ast_expr_neg(expr);
4457 str = isl_ast_expr_to_str(expr);
4458 ok = str ? !strcmp(str, "-(A + B)") : -1;
4459 free(str);
4460 isl_ast_expr_free(expr);
4461
4462 if (ok < 0)
4463 return -1;
4464 if (!ok)
4465 isl_die(ctx, isl_error_unknown,
4466 "isl_ast_expr printed incorrectly", return -1);
4467
4468 expr1 = isl_ast_expr_from_id(isl_id_alloc(ctx, "A", NULL));
4469 expr2 = isl_ast_expr_from_id(isl_id_alloc(ctx, "B", NULL));
4470 expr = isl_ast_expr_add(expr1, expr2);
4471 expr3 = isl_ast_expr_from_id(isl_id_alloc(ctx, "C", NULL));
4472 expr = isl_ast_expr_sub(expr3, expr);
4473 str = isl_ast_expr_to_str(expr);
4474 ok = str ? !strcmp(str, "C - (A + B)") : -1;
4475 free(str);
4476 isl_ast_expr_free(expr);
4477
4478 if (ok < 0)
4479 return -1;
4480 if (!ok)
4481 isl_die(ctx, isl_error_unknown,
4482 "isl_ast_expr printed incorrectly", return -1);
4483
4484 return 0;
4485 }
4486
4487 /* Check that isl_ast_build_expr_from_set returns a valid expression
4488 * for an empty set. Note that isl_ast_build_expr_from_set getting
4489 * called on an empty set probably indicates a bug in the caller.
4490 */
4491 static int test_ast_build(isl_ctx *ctx)
4492 {
4493 isl_set *set;
4494 isl_ast_build *build;
4495 isl_ast_expr *expr;
4496
4497 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4498 build = isl_ast_build_from_context(set);
4499
4500 set = isl_set_empty(isl_space_params_alloc(ctx, 0));
4501 expr = isl_ast_build_expr_from_set(build, set);
4502
4503 isl_ast_expr_free(expr);
4504 isl_ast_build_free(build);
4505
4506 if (!expr)
4507 return -1;
4508
4509 return 0;
4510 }
4511
4512 /* Internal data structure for before_for and after_for callbacks.
4513 *
4514 * depth is the current depth
4515 * before is the number of times before_for has been called
4516 * after is the number of times after_for has been called
4517 */
4518 struct isl_test_codegen_data {
4519 int depth;
4520 int before;
4521 int after;
4522 };
4523
4524 /* This function is called before each for loop in the AST generated
4525 * from test_ast_gen1.
4526 *
4527 * Increment the number of calls and the depth.
4528 * Check that the space returned by isl_ast_build_get_schedule_space
4529 * matches the target space of the schedule returned by
4530 * isl_ast_build_get_schedule.
4531 * Return an isl_id that is checked by the corresponding call
4532 * to after_for.
4533 */
4534 static __isl_give isl_id *before_for(__isl_keep isl_ast_build *build,
4535 void *user)
4536 {
4537 struct isl_test_codegen_data *data = user;
4538 isl_ctx *ctx;
4539 isl_space *space;
4540 isl_union_map *schedule;
4541 isl_union_set *uset;
4542 isl_set *set;
4543 int empty;
4544 char name[] = "d0";
4545
4546 ctx = isl_ast_build_get_ctx(build);
4547
4548 if (data->before >= 3)
4549 isl_die(ctx, isl_error_unknown,
4550 "unexpected number of for nodes", return NULL);
4551 if (data->depth >= 2)
4552 isl_die(ctx, isl_error_unknown,
4553 "unexpected depth", return NULL);
4554
4555 snprintf(name, sizeof(name), "d%d", data->depth);
4556 data->before++;
4557 data->depth++;
4558
4559 schedule = isl_ast_build_get_schedule(build);
4560 uset = isl_union_map_range(schedule);
4561 if (!uset)
4562 return NULL;
4563 if (isl_union_set_n_set(uset) != 1) {
4564 isl_union_set_free(uset);
4565 isl_die(ctx, isl_error_unknown,
4566 "expecting single range space", return NULL);
4567 }
4568
4569 space = isl_ast_build_get_schedule_space(build);
4570 set = isl_union_set_extract_set(uset, space);
4571 isl_union_set_free(uset);
4572 empty = isl_set_is_empty(set);
4573 isl_set_free(set);
4574
4575 if (empty < 0)
4576 return NULL;
4577 if (empty)
4578 isl_die(ctx, isl_error_unknown,
4579 "spaces don't match", return NULL);
4580
4581 return isl_id_alloc(ctx, name, NULL);
4582 }
4583
4584 /* This function is called after each for loop in the AST generated
4585 * from test_ast_gen1.
4586 *
4587 * Increment the number of calls and decrement the depth.
4588 * Check that the annotation attached to the node matches
4589 * the isl_id returned by the corresponding call to before_for.
4590 */
4591 static __isl_give isl_ast_node *after_for(__isl_take isl_ast_node *node,
4592 __isl_keep isl_ast_build *build, void *user)
4593 {
4594 struct isl_test_codegen_data *data = user;
4595 isl_id *id;
4596 const char *name;
4597 int valid;
4598
4599 data->after++;
4600 data->depth--;
4601
4602 if (data->after > data->before)
4603 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4604 "mismatch in number of for nodes",
4605 return isl_ast_node_free(node));
4606
4607 id = isl_ast_node_get_annotation(node);
4608 if (!id)
4609 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4610 "missing annotation", return isl_ast_node_free(node));
4611
4612 name = isl_id_get_name(id);
4613 valid = name && atoi(name + 1) == data->depth;
4614 isl_id_free(id);
4615
4616 if (!valid)
4617 isl_die(isl_ast_node_get_ctx(node), isl_error_unknown,
4618 "wrong annotation", return isl_ast_node_free(node));
4619
4620 return node;
4621 }
4622
4623 /* Check that the before_each_for and after_each_for callbacks
4624 * are called for each for loop in the generated code,
4625 * that they are called in the right order and that the isl_id
4626 * returned from the before_each_for callback is attached to
4627 * the isl_ast_node passed to the corresponding after_each_for call.
4628 */
4629 static int test_ast_gen1(isl_ctx *ctx)
4630 {
4631 const char *str;
4632 isl_set *set;
4633 isl_union_map *schedule;
4634 isl_ast_build *build;
4635 isl_ast_node *tree;
4636 struct isl_test_codegen_data data;
4637
4638 str = "[N] -> { : N >= 10 }";
4639 set = isl_set_read_from_str(ctx, str);
4640 str = "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
4641 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
4642 schedule = isl_union_map_read_from_str(ctx, str);
4643
4644 data.before = 0;
4645 data.after = 0;
4646 data.depth = 0;
4647 build = isl_ast_build_from_context(set);
4648 build = isl_ast_build_set_before_each_for(build,
4649 &before_for, &data);
4650 build = isl_ast_build_set_after_each_for(build,
4651 &after_for, &data);
4652 tree = isl_ast_build_ast_from_schedule(build, schedule);
4653 isl_ast_build_free(build);
4654 if (!tree)
4655 return -1;
4656
4657 isl_ast_node_free(tree);
4658
4659 if (data.before != 3 || data.after != 3)
4660 isl_die(ctx, isl_error_unknown,
4661 "unexpected number of for nodes", return -1);
4662
4663 return 0;
4664 }
4665
4666 /* Check that the AST generator handles domains that are integrally disjoint
4667 * but not ratinoally disjoint.
4668 */
4669 static int test_ast_gen2(isl_ctx *ctx)
4670 {
4671 const char *str;
4672 isl_set *set;
4673 isl_union_map *schedule;
4674 isl_union_map *options;
4675 isl_ast_build *build;
4676 isl_ast_node *tree;
4677
4678 str = "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
4679 schedule = isl_union_map_read_from_str(ctx, str);
4680 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4681 build = isl_ast_build_from_context(set);
4682
4683 str = "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
4684 options = isl_union_map_read_from_str(ctx, str);
4685 build = isl_ast_build_set_options(build, options);
4686 tree = isl_ast_build_ast_from_schedule(build, schedule);
4687 isl_ast_build_free(build);
4688 if (!tree)
4689 return -1;
4690 isl_ast_node_free(tree);
4691
4692 return 0;
4693 }
4694
4695 /* Increment *user on each call.
4696 */
4697 static __isl_give isl_ast_node *count_domains(__isl_take isl_ast_node *node,
4698 __isl_keep isl_ast_build *build, void *user)
4699 {
4700 int *n = user;
4701
4702 (*n)++;
4703
4704 return node;
4705 }
4706
4707 /* Test that unrolling tries to minimize the number of instances.
4708 * In particular, for the schedule given below, make sure it generates
4709 * 3 nodes (rather than 101).
4710 */
4711 static int test_ast_gen3(isl_ctx *ctx)
4712 {
4713 const char *str;
4714 isl_set *set;
4715 isl_union_map *schedule;
4716 isl_union_map *options;
4717 isl_ast_build *build;
4718 isl_ast_node *tree;
4719 int n_domain = 0;
4720
4721 str = "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
4722 schedule = isl_union_map_read_from_str(ctx, str);
4723 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4724
4725 str = "{ [i] -> unroll[0] }";
4726 options = isl_union_map_read_from_str(ctx, str);
4727
4728 build = isl_ast_build_from_context(set);
4729 build = isl_ast_build_set_options(build, options);
4730 build = isl_ast_build_set_at_each_domain(build,
4731 &count_domains, &n_domain);
4732 tree = isl_ast_build_ast_from_schedule(build, schedule);
4733 isl_ast_build_free(build);
4734 if (!tree)
4735 return -1;
4736
4737 isl_ast_node_free(tree);
4738
4739 if (n_domain != 3)
4740 isl_die(ctx, isl_error_unknown,
4741 "unexpected number of for nodes", return -1);
4742
4743 return 0;
4744 }
4745
4746 /* Check that if the ast_build_exploit_nested_bounds options is set,
4747 * we do not get an outer if node in the generated AST,
4748 * while we do get such an outer if node if the options is not set.
4749 */
4750 static int test_ast_gen4(isl_ctx *ctx)
4751 {
4752 const char *str;
4753 isl_set *set;
4754 isl_union_map *schedule;
4755 isl_ast_build *build;
4756 isl_ast_node *tree;
4757 enum isl_ast_node_type type;
4758 int enb;
4759
4760 enb = isl_options_get_ast_build_exploit_nested_bounds(ctx);
4761 str = "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
4762
4763 isl_options_set_ast_build_exploit_nested_bounds(ctx, 1);
4764
4765 schedule = isl_union_map_read_from_str(ctx, str);
4766 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4767 build = isl_ast_build_from_context(set);
4768 tree = isl_ast_build_ast_from_schedule(build, schedule);
4769 isl_ast_build_free(build);
4770 if (!tree)
4771 return -1;
4772
4773 type = isl_ast_node_get_type(tree);
4774 isl_ast_node_free(tree);
4775
4776 if (type == isl_ast_node_if)
4777 isl_die(ctx, isl_error_unknown,
4778 "not expecting if node", return -1);
4779
4780 isl_options_set_ast_build_exploit_nested_bounds(ctx, 0);
4781
4782 schedule = isl_union_map_read_from_str(ctx, str);
4783 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4784 build = isl_ast_build_from_context(set);
4785 tree = isl_ast_build_ast_from_schedule(build, schedule);
4786 isl_ast_build_free(build);
4787 if (!tree)
4788 return -1;
4789
4790 type = isl_ast_node_get_type(tree);
4791 isl_ast_node_free(tree);
4792
4793 if (type != isl_ast_node_if)
4794 isl_die(ctx, isl_error_unknown,
4795 "expecting if node", return -1);
4796
4797 isl_options_set_ast_build_exploit_nested_bounds(ctx, enb);
4798
4799 return 0;
4800 }
4801
4802 /* This function is called for each leaf in the AST generated
4803 * from test_ast_gen5.
4804 *
4805 * We finalize the AST generation by extending the outer schedule
4806 * with a zero-dimensional schedule. If this results in any for loops,
4807 * then this means that we did not pass along enough information
4808 * about the outer schedule to the inner AST generation.
4809 */
4810 static __isl_give isl_ast_node *create_leaf(__isl_take isl_ast_build *build,
4811 void *user)
4812 {
4813 isl_union_map *schedule, *extra;
4814 isl_ast_node *tree;
4815
4816 schedule = isl_ast_build_get_schedule(build);
4817 extra = isl_union_map_copy(schedule);
4818 extra = isl_union_map_from_domain(isl_union_map_domain(extra));
4819 schedule = isl_union_map_range_product(schedule, extra);
4820 tree = isl_ast_build_ast_from_schedule(build, schedule);
4821 isl_ast_build_free(build);
4822
4823 if (!tree)
4824 return NULL;
4825
4826 if (isl_ast_node_get_type(tree) == isl_ast_node_for)
4827 isl_die(isl_ast_node_get_ctx(tree), isl_error_unknown,
4828 "code should not contain any for loop",
4829 return isl_ast_node_free(tree));
4830
4831 return tree;
4832 }
4833
4834 /* Check that we do not lose any information when going back and
4835 * forth between internal and external schedule.
4836 *
4837 * In particular, we create an AST where we unroll the only
4838 * non-constant dimension in the schedule. We therefore do
4839 * not expect any for loops in the AST. However, older versions
4840 * of isl would not pass along enough information about the outer
4841 * schedule when performing an inner code generation from a create_leaf
4842 * callback, resulting in the inner code generation producing a for loop.
4843 */
4844 static int test_ast_gen5(isl_ctx *ctx)
4845 {
4846 const char *str;
4847 isl_set *set;
4848 isl_union_map *schedule, *options;
4849 isl_ast_build *build;
4850 isl_ast_node *tree;
4851
4852 str = "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
4853 schedule = isl_union_map_read_from_str(ctx, str);
4854
4855 str = "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
4856 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
4857 options = isl_union_map_read_from_str(ctx, str);
4858
4859 set = isl_set_universe(isl_space_params_alloc(ctx, 0));
4860 build = isl_ast_build_from_context(set);
4861 build = isl_ast_build_set_options(build, options);
4862 build = isl_ast_build_set_create_leaf(build, &create_leaf, NULL);
4863 tree = isl_ast_build_ast_from_schedule(build, schedule);
4864 isl_ast_build_free(build);
4865 isl_ast_node_free(tree);
4866 if (!tree)
4867 return -1;
4868
4869 return 0;
4870 }
4871
4872 static int test_ast_gen(isl_ctx *ctx)
4873 {
4874 if (test_ast_gen1(ctx) < 0)
4875 return -1;
4876 if (test_ast_gen2(ctx) < 0)
4877 return -1;
4878 if (test_ast_gen3(ctx) < 0)
4879 return -1;
4880 if (test_ast_gen4(ctx) < 0)
4881 return -1;
4882 if (test_ast_gen5(ctx) < 0)
4883 return -1;
4884 return 0;
4885 }
4886
4887 /* Check if dropping output dimensions from an isl_pw_multi_aff
4888 * works properly.
4889 */
4890 static int test_pw_multi_aff(isl_ctx *ctx)
4891 {
4892 const char *str;
4893 isl_pw_multi_aff *pma1, *pma2;
4894 int equal;
4895
4896 str = "{ [i,j] -> [i+j, 4i-j] }";
4897 pma1 = isl_pw_multi_aff_read_from_str(ctx, str);
4898 str = "{ [i,j] -> [4i-j] }";
4899 pma2 = isl_pw_multi_aff_read_from_str(ctx, str);
4900
4901 pma1 = isl_pw_multi_aff_drop_dims(pma1, isl_dim_out, 0, 1);
4902
4903 equal = isl_pw_multi_aff_plain_is_equal(pma1, pma2);
4904
4905 isl_pw_multi_aff_free(pma1);
4906 isl_pw_multi_aff_free(pma2);
4907 if (equal < 0)
4908 return -1;
4909 if (!equal)
4910 isl_die(ctx, isl_error_unknown,
4911 "expressions not equal", return -1);
4912
4913 return 0;
4914 }
4915
4916 /* Check that we can properly parse multi piecewise affine expressions
4917 * where the piecewise affine expressions have different domains.
4918 */
4919 static int test_multi_pw_aff(isl_ctx *ctx)
4920 {
4921 const char *str;
4922 isl_set *dom, *dom2;
4923 isl_multi_pw_aff *mpa1, *mpa2;
4924 isl_pw_aff *pa;
4925 int equal;
4926 int equal_domain;
4927
4928 mpa1 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [i] }");
4929 dom = isl_set_read_from_str(ctx, "{ [i] : i > 0 }");
4930 mpa1 = isl_multi_pw_aff_intersect_domain(mpa1, dom);
4931 mpa2 = isl_multi_pw_aff_read_from_str(ctx, "{ [i] -> [2i] }");
4932 mpa2 = isl_multi_pw_aff_flat_range_product(mpa1, mpa2);
4933 str = "{ [i] -> [(i : i > 0), 2i] }";
4934 mpa1 = isl_multi_pw_aff_read_from_str(ctx, str);
4935
4936 equal = isl_multi_pw_aff_plain_is_equal(mpa1, mpa2);
4937
4938 pa = isl_multi_pw_aff_get_pw_aff(mpa1, 0);
4939 dom = isl_pw_aff_domain(pa);
4940 pa = isl_multi_pw_aff_get_pw_aff(mpa1, 1);
4941 dom2 = isl_pw_aff_domain(pa);
4942 equal_domain = isl_set_is_equal(dom, dom2);
4943
4944 isl_set_free(dom);
4945 isl_set_free(dom2);
4946 isl_multi_pw_aff_free(mpa1);
4947 isl_multi_pw_aff_free(mpa2);
4948
4949 if (equal < 0)
4950 return -1;
4951 if (!equal)
4952 isl_die(ctx, isl_error_unknown,
4953 "expressions not equal", return -1);
4954
4955 if (equal_domain < 0)
4956 return -1;
4957 if (equal_domain)
4958 isl_die(ctx, isl_error_unknown,
4959 "domains unexpectedly equal", return -1);
4960
4961 return 0;
4962 }
4963
4964 /* This is a regression test for a bug where isl_basic_map_simplify
4965 * would end up in an infinite loop. In particular, we construct
4966 * an empty basic set that is not obviously empty.
4967 * isl_basic_set_is_empty marks the basic set as empty.
4968 * After projecting out i3, the variable can be dropped completely,
4969 * but isl_basic_map_simplify refrains from doing so if the basic set
4970 * is empty and would end up in an infinite loop if it didn't test
4971 * explicitly for empty basic maps in the outer loop.
4972 */
4973 static int test_simplify(isl_ctx *ctx)
4974 {
4975 const char *str;
4976 isl_basic_set *bset;
4977 int empty;
4978
4979 str = "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
4980 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
4981 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
4982 "i3 >= i2 }";
4983 bset = isl_basic_set_read_from_str(ctx, str);
4984 empty = isl_basic_set_is_empty(bset);
4985 bset = isl_basic_set_project_out(bset, isl_dim_set, 3, 1);
4986 isl_basic_set_free(bset);
4987 if (!bset)
4988 return -1;
4989 if (!empty)
4990 isl_die(ctx, isl_error_unknown,
4991 "basic set should be empty", return -1);
4992
4993 return 0;
4994 }
4995
4996 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
4997 * with gbr context would fail to disable the use of the shifted tableau
4998 * when transferring equalities for the input to the context, resulting
4999 * in invalid sample values.
5000 */
5001 static int test_partial_lexmin(isl_ctx *ctx)
5002 {
5003 const char *str;
5004 isl_basic_set *bset;
5005 isl_basic_map *bmap;
5006 isl_map *map;
5007
5008 str = "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
5009 bmap = isl_basic_map_read_from_str(ctx, str);
5010 str = "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
5011 bset = isl_basic_set_read_from_str(ctx, str);
5012 map = isl_basic_map_partial_lexmin(bmap, bset, NULL);
5013 isl_map_free(map);
5014
5015 if (!map)
5016 return -1;
5017
5018 return 0;
5019 }
5020
5021 /* Check that the variable compression performed on the existentially
5022 * quantified variables inside isl_basic_set_compute_divs is not confused
5023 * by the implicit equalities among the parameters.
5024 */
5025 static int test_compute_divs(isl_ctx *ctx)
5026 {
5027 const char *str;
5028 isl_basic_set *bset;
5029 isl_set *set;
5030
5031 str = "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
5032 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
5033 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
5034 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
5035 bset = isl_basic_set_read_from_str(ctx, str);
5036 set = isl_basic_set_compute_divs(bset);
5037 isl_set_free(set);
5038 if (!set)
5039 return -1;
5040
5041 return 0;
5042 }
5043
5044 struct {
5045 const char *set;
5046 const char *dual;
5047 } coef_tests[] = {
5048 { "{ rat: [i] : 0 <= i <= 10 }",
5049 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
5050 { "{ rat: [i] : FALSE }",
5051 "{ rat: coefficients[[cst] -> [a]] }" },
5052 { "{ rat: [i] : }",
5053 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
5054 };
5055
5056 struct {
5057 const char *set;
5058 const char *dual;
5059 } sol_tests[] = {
5060 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
5061 "{ rat: [i] : 0 <= i <= 10 }" },
5062 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
5063 "{ rat: [i] }" },
5064 { "{ rat: coefficients[[cst] -> [a]] }",
5065 "{ rat: [i] : FALSE }" },
5066 };
5067
5068 /* Test the basic functionality of isl_basic_set_coefficients and
5069 * isl_basic_set_solutions.
5070 */
5071 static int test_dual(isl_ctx *ctx)
5072 {
5073 int i;
5074
5075 for (i = 0; i < ARRAY_SIZE(coef_tests); ++i) {
5076 int equal;
5077 isl_basic_set *bset1, *bset2;
5078
5079 bset1 = isl_basic_set_read_from_str(ctx, coef_tests[i].set);
5080 bset2 = isl_basic_set_read_from_str(ctx, coef_tests[i].dual);
5081 bset1 = isl_basic_set_coefficients(bset1);
5082 equal = isl_basic_set_is_equal(bset1, bset2);
5083 isl_basic_set_free(bset1);
5084 isl_basic_set_free(bset2);
5085 if (equal < 0)
5086 return -1;
5087 if (!equal)
5088 isl_die(ctx, isl_error_unknown,
5089 "incorrect dual", return -1);
5090 }
5091
5092 for (i = 0; i < ARRAY_SIZE(sol_tests); ++i) {
5093 int equal;
5094 isl_basic_set *bset1, *bset2;
5095
5096 bset1 = isl_basic_set_read_from_str(ctx, sol_tests[i].set);
5097 bset2 = isl_basic_set_read_from_str(ctx, sol_tests[i].dual);
5098 bset1 = isl_basic_set_solutions(bset1);
5099 equal = isl_basic_set_is_equal(bset1, bset2);
5100 isl_basic_set_free(bset1);
5101 isl_basic_set_free(bset2);
5102 if (equal < 0)
5103 return -1;
5104 if (!equal)
5105 isl_die(ctx, isl_error_unknown,
5106 "incorrect dual", return -1);
5107 }
5108
5109 return 0;
5110 }
5111
5112 struct {
5113 const char *name;
5114 int (*fn)(isl_ctx *ctx);
5115 } tests [] = {
5116 { "dual", &test_dual },
5117 { "dependence analysis", &test_flow },
5118 { "val", &test_val },
5119 { "compute divs", &test_compute_divs },
5120 { "partial lexmin", &test_partial_lexmin },
5121 { "simplify", &test_simplify },
5122 { "curry", &test_curry },
5123 { "piecewise multi affine expressions", &test_pw_multi_aff },
5124 { "multi piecewise affine expressions", &test_multi_pw_aff },
5125 { "conversion", &test_conversion },
5126 { "list", &test_list },
5127 { "align parameters", &test_align_parameters },
5128 { "preimage", &test_preimage },
5129 { "pullback", &test_pullback },
5130 { "AST", &test_ast },
5131 { "AST build", &test_ast_build },
5132 { "AST generation", &test_ast_gen },
5133 { "eliminate", &test_eliminate },
5134 { "residue class", &test_residue_class },
5135 { "div", &test_div },
5136 { "slice", &test_slice },
5137 { "fixed power", &test_fixed_power },
5138 { "sample", &test_sample },
5139 { "output", &test_output },
5140 { "vertices", &test_vertices },
5141 { "fixed", &test_fixed },
5142 { "equal", &test_equal },
5143 { "disjoint", &test_disjoint },
5144 { "product", &test_product },
5145 { "dim_max", &test_dim_max },
5146 { "affine", &test_aff },
5147 { "injective", &test_injective },
5148 { "schedule", &test_schedule },
5149 { "union_pw", &test_union_pw },
5150 { "parse", &test_parse },
5151 { "single-valued", &test_sv },
5152 { "affine hull", &test_affine_hull },
5153 { "coalesce", &test_coalesce },
5154 { "factorize", &test_factorize },
5155 { "subset", &test_subset },
5156 { "subtract", &test_subtract },
5157 { "lexmin", &test_lexmin },
5158 { "min", &test_min },
5159 { "gist", &test_gist },
5160 { "piecewise quasi-polynomials", &test_pwqp },
5161 };
5162
5163 int main(int argc, char **argv)
5164 {
5165 int i;
5166 struct isl_ctx *ctx;
5167 struct isl_options *options;
5168
5169 srcdir = getenv("srcdir");
5170 assert(srcdir);
5171
5172 options = isl_options_new_with_defaults();
5173 assert(options);
5174 argc = isl_options_parse(options, argc, argv, ISL_ARG_ALL);
5175
5176 ctx = isl_ctx_alloc_with_options(&isl_options_args, options);
5177 for (i = 0; i < ARRAY_SIZE(tests); ++i) {
5178 printf("%s\n", tests[i].name);
5179 if (tests[i].fn(ctx) < 0)
5180 goto error;
5181 }
5182 test_lift(ctx);
5183 test_bound(ctx);
5184 test_union(ctx);
5185 test_split_periods(ctx);
5186 test_lex(ctx);
5187 test_bijective(ctx);
5188 test_dep(ctx);
5189 test_read(ctx);
5190 test_bounded(ctx);
5191 test_construction(ctx);
5192 test_dim(ctx);
5193 test_application(ctx);
5194 test_convex_hull(ctx);
5195 test_closure(ctx);
5196 isl_ctx_free(ctx);
5197 return 0;
5198 error:
5199 isl_ctx_free(ctx);
5200 return -1;
5201 }
Integer set library