2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
18 #include <isl_ctx_private.h>
19 #include <isl_map_private.h>
20 #include <isl_aff_private.h>
23 #include <isl_constraint_private.h>
24 #include <isl/polynomial.h>
25 #include <isl/union_map.h>
26 #include <isl_factorization.h>
27 #include <isl/schedule.h>
28 #include <isl_options_private.h>
29 #include <isl/vertices.h>
30 #include <isl/ast_build.h>
33 #include <isl_ast_build_expr.h>
35 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
39 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
42 char *pattern
= "%s/test_inputs/%s.%s";
44 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
46 filename
= isl_alloc_array(ctx
, char, length
);
51 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
56 void test_parse_map(isl_ctx
*ctx
, const char *str
)
60 map
= isl_map_read_from_str(ctx
, str
);
65 int test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
70 map
= isl_map_read_from_str(ctx
, str
);
71 map2
= isl_map_read_from_str(ctx
, str2
);
72 equal
= isl_map_is_equal(map
, map2
);
79 isl_die(ctx
, isl_error_unknown
, "maps not equal",
85 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
87 isl_pw_qpolynomial
*pwqp
;
89 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
91 isl_pw_qpolynomial_free(pwqp
);
94 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
98 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
100 isl_pw_aff_free(pwaff
);
103 int test_parse(struct isl_ctx
*ctx
)
106 const char *str
, *str2
;
108 str
= "{ [i] -> [-i] }";
109 map
= isl_map_read_from_str(ctx
, str
);
113 str
= "{ A[i] -> L[([i/3])] }";
114 map
= isl_map_read_from_str(ctx
, str
);
118 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
119 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
120 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
122 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
123 str2
= "{ [x, y] : 2y >= 6 - x }";
124 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
127 if (test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
128 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
130 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
131 if (test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }",
135 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
136 map
= isl_map_read_from_str(ctx
, str
);
137 str
= "{ [new, old] -> [o0, o1] : "
138 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
139 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
140 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
141 map2
= isl_map_read_from_str(ctx
, str
);
142 assert(isl_map_is_equal(map
, map2
));
146 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
147 map
= isl_map_read_from_str(ctx
, str
);
148 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
149 map2
= isl_map_read_from_str(ctx
, str
);
150 assert(isl_map_is_equal(map
, map2
));
154 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
155 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
156 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
159 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
160 str2
= "{ [i,j] -> [min(i,j)] }";
161 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
164 str
= "{ [i,j] : i != j }";
165 str2
= "{ [i,j] : i < j or i > j }";
166 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
169 str
= "{ [i,j] : (i+1)*2 >= j }";
170 str2
= "{ [i, j] : j <= 2 + 2i }";
171 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
174 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
175 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
176 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
179 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
180 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
181 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
184 str
= "{ [x] : x >= 0 }";
185 str2
= "{ [x] : x-0 >= 0 }";
186 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
189 str
= "{ [i] : ((i > 10)) }";
190 str2
= "{ [i] : i >= 11 }";
191 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
194 str
= "{ [i] -> [0] }";
195 str2
= "{ [i] -> [0 * i] }";
196 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
199 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
200 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
201 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
202 test_parse_pwqp(ctx
, "{ [x] -> ([(x)/2] * [(x)/3]) }");
204 if (test_parse_map_equal(ctx
, "{ [a] -> [b] : (not false) }",
205 "{ [a] -> [b] : true }") < 0)
208 if (test_parse_map_equal(ctx
, "{ [i] : i/2 <= 5 }",
209 "{ [i] : i <= 10 }") < 0)
212 if (test_parse_map_equal(ctx
, "{Sym=[n] [i] : i <= n }",
213 "[n] -> { [i] : i <= n }") < 0)
216 if (test_parse_map_equal(ctx
, "{ [*] }", "{ [a] }") < 0)
219 if (test_parse_map_equal(ctx
, "{ [i] : 2*floor(i/2) = i }",
220 "{ [i] : exists a : i = 2 a }") < 0)
223 if (test_parse_map_equal(ctx
, "{ [a] -> [b] : a = 5 implies b = 5 }",
224 "{ [a] -> [b] : a != 5 or b = 5 }") < 0)
227 if (test_parse_map_equal(ctx
, "{ [a] -> [a - 1 : a > 0] }",
228 "{ [a] -> [a - 1] : a > 0 }") < 0)
230 if (test_parse_map_equal(ctx
,
231 "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
232 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }") < 0)
234 if (test_parse_map_equal(ctx
,
235 "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
236 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
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)
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)
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)
254 void test_read(struct isl_ctx
*ctx
)
258 struct isl_basic_set
*bset1
, *bset2
;
259 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
261 filename
= get_filename(ctx
, "set", "omega");
263 input
= fopen(filename
, "r");
266 bset1
= isl_basic_set_read_from_file(ctx
, input
);
267 bset2
= isl_basic_set_read_from_str(ctx
, str
);
269 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
271 isl_basic_set_free(bset1
);
272 isl_basic_set_free(bset2
);
278 void test_bounded(struct isl_ctx
*ctx
)
283 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
284 bounded
= isl_set_is_bounded(set
);
288 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
289 bounded
= isl_set_is_bounded(set
);
293 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
294 bounded
= isl_set_is_bounded(set
);
299 /* Construct the basic set { [i] : 5 <= i <= N } */
300 void test_construction(struct isl_ctx
*ctx
)
305 struct isl_basic_set
*bset
;
306 struct isl_constraint
*c
;
310 dim
= isl_space_set_alloc(ctx
, 1, 1);
311 bset
= isl_basic_set_universe(isl_space_copy(dim
));
312 ls
= isl_local_space_from_space(dim
);
314 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
315 isl_int_set_si(v
, -1);
316 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
317 isl_int_set_si(v
, 1);
318 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
319 bset
= isl_basic_set_add_constraint(bset
, c
);
321 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
322 isl_int_set_si(v
, 1);
323 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
324 isl_int_set_si(v
, -5);
325 isl_constraint_set_constant(c
, v
);
326 bset
= isl_basic_set_add_constraint(bset
, c
);
328 isl_local_space_free(ls
);
329 isl_basic_set_free(bset
);
334 void test_dim(struct isl_ctx
*ctx
)
337 isl_map
*map1
, *map2
;
339 map1
= isl_map_read_from_str(ctx
,
340 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
341 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
342 map2
= isl_map_read_from_str(ctx
,
343 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
344 assert(isl_map_is_equal(map1
, map2
));
347 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
348 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
349 assert(isl_map_is_equal(map1
, map2
));
354 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
355 map1
= isl_map_read_from_str(ctx
, str
);
356 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
357 map2
= isl_map_read_from_str(ctx
, str
);
358 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
359 assert(isl_map_is_equal(map1
, map2
));
366 __isl_give isl_val
*(*op
)(__isl_take isl_val
*v
);
370 { &isl_val_neg
, "0", "0" },
371 { &isl_val_abs
, "0", "0" },
372 { &isl_val_2exp
, "0", "1" },
373 { &isl_val_floor
, "0", "0" },
374 { &isl_val_ceil
, "0", "0" },
375 { &isl_val_neg
, "1", "-1" },
376 { &isl_val_neg
, "-1", "1" },
377 { &isl_val_neg
, "1/2", "-1/2" },
378 { &isl_val_neg
, "-1/2", "1/2" },
379 { &isl_val_neg
, "infty", "-infty" },
380 { &isl_val_neg
, "-infty", "infty" },
381 { &isl_val_neg
, "NaN", "NaN" },
382 { &isl_val_abs
, "1", "1" },
383 { &isl_val_abs
, "-1", "1" },
384 { &isl_val_abs
, "1/2", "1/2" },
385 { &isl_val_abs
, "-1/2", "1/2" },
386 { &isl_val_abs
, "infty", "infty" },
387 { &isl_val_abs
, "-infty", "infty" },
388 { &isl_val_abs
, "NaN", "NaN" },
389 { &isl_val_floor
, "1", "1" },
390 { &isl_val_floor
, "-1", "-1" },
391 { &isl_val_floor
, "1/2", "0" },
392 { &isl_val_floor
, "-1/2", "-1" },
393 { &isl_val_floor
, "infty", "infty" },
394 { &isl_val_floor
, "-infty", "-infty" },
395 { &isl_val_floor
, "NaN", "NaN" },
396 { &isl_val_ceil
, "1", "1" },
397 { &isl_val_ceil
, "-1", "-1" },
398 { &isl_val_ceil
, "1/2", "1" },
399 { &isl_val_ceil
, "-1/2", "0" },
400 { &isl_val_ceil
, "infty", "infty" },
401 { &isl_val_ceil
, "-infty", "-infty" },
402 { &isl_val_ceil
, "NaN", "NaN" },
403 { &isl_val_2exp
, "-3", "1/8" },
404 { &isl_val_2exp
, "-1", "1/2" },
405 { &isl_val_2exp
, "1", "2" },
406 { &isl_val_2exp
, "2", "4" },
407 { &isl_val_2exp
, "3", "8" },
410 /* Perform some basic tests of unary operations on isl_val objects.
412 static int test_un_val(isl_ctx
*ctx
)
416 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v
);
419 for (i
= 0; i
< ARRAY_SIZE(val_un_tests
); ++i
) {
420 v
= isl_val_read_from_str(ctx
, val_un_tests
[i
].arg
);
421 res
= isl_val_read_from_str(ctx
, val_un_tests
[i
].res
);
422 fn
= val_un_tests
[i
].op
;
424 if (isl_val_is_nan(res
))
425 ok
= isl_val_is_nan(v
);
427 ok
= isl_val_eq(v
, res
);
433 isl_die(ctx
, isl_error_unknown
,
434 "unexpected result", return -1);
441 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
442 __isl_take isl_val
*v2
);
444 ['+'] = { &isl_val_add
},
445 ['-'] = { &isl_val_sub
},
446 ['*'] = { &isl_val_mul
},
447 ['/'] = { &isl_val_div
},
448 ['g'] = { &isl_val_gcd
},
449 ['m'] = { &isl_val_min
},
450 ['M'] = { &isl_val_max
},
458 } val_bin_tests
[] = {
459 { "0", '+', "0", "0" },
460 { "1", '+', "0", "1" },
461 { "1", '+', "1", "2" },
462 { "1", '-', "1", "0" },
463 { "1", '*', "1", "1" },
464 { "1", '/', "1", "1" },
465 { "2", '*', "3", "6" },
466 { "2", '*', "1/2", "1" },
467 { "2", '*', "1/3", "2/3" },
468 { "2/3", '*', "3/5", "2/5" },
469 { "2/3", '*', "7/5", "14/15" },
470 { "2", '/', "1/2", "4" },
471 { "-2", '/', "-1/2", "4" },
472 { "-2", '/', "1/2", "-4" },
473 { "2", '/', "-1/2", "-4" },
474 { "2", '/', "2", "1" },
475 { "2", '/', "3", "2/3" },
476 { "2/3", '/', "5/3", "2/5" },
477 { "2/3", '/', "5/7", "14/15" },
478 { "0", '/', "0", "NaN" },
479 { "42", '/', "0", "NaN" },
480 { "-42", '/', "0", "NaN" },
481 { "infty", '/', "0", "NaN" },
482 { "-infty", '/', "0", "NaN" },
483 { "NaN", '/', "0", "NaN" },
484 { "0", '/', "NaN", "NaN" },
485 { "42", '/', "NaN", "NaN" },
486 { "-42", '/', "NaN", "NaN" },
487 { "infty", '/', "NaN", "NaN" },
488 { "-infty", '/', "NaN", "NaN" },
489 { "NaN", '/', "NaN", "NaN" },
490 { "0", '/', "infty", "0" },
491 { "42", '/', "infty", "0" },
492 { "-42", '/', "infty", "0" },
493 { "infty", '/', "infty", "NaN" },
494 { "-infty", '/', "infty", "NaN" },
495 { "NaN", '/', "infty", "NaN" },
496 { "0", '/', "-infty", "0" },
497 { "42", '/', "-infty", "0" },
498 { "-42", '/', "-infty", "0" },
499 { "infty", '/', "-infty", "NaN" },
500 { "-infty", '/', "-infty", "NaN" },
501 { "NaN", '/', "-infty", "NaN" },
502 { "1", '-', "1/3", "2/3" },
503 { "1/3", '+', "1/2", "5/6" },
504 { "1/2", '+', "1/2", "1" },
505 { "3/4", '-', "1/4", "1/2" },
506 { "1/2", '-', "1/3", "1/6" },
507 { "infty", '+', "42", "infty" },
508 { "infty", '+', "infty", "infty" },
509 { "42", '+', "infty", "infty" },
510 { "infty", '-', "infty", "NaN" },
511 { "infty", '*', "infty", "infty" },
512 { "infty", '*', "-infty", "-infty" },
513 { "-infty", '*', "infty", "-infty" },
514 { "-infty", '*', "-infty", "infty" },
515 { "0", '*', "infty", "NaN" },
516 { "1", '*', "infty", "infty" },
517 { "infty", '*', "0", "NaN" },
518 { "infty", '*', "42", "infty" },
519 { "42", '-', "infty", "-infty" },
520 { "infty", '+', "-infty", "NaN" },
521 { "4", 'g', "6", "2" },
522 { "5", 'g', "6", "1" },
523 { "42", 'm', "3", "3" },
524 { "42", 'M', "3", "42" },
525 { "3", 'm', "42", "3" },
526 { "3", 'M', "42", "42" },
527 { "42", 'm', "infty", "42" },
528 { "42", 'M', "infty", "infty" },
529 { "42", 'm', "-infty", "-infty" },
530 { "42", 'M', "-infty", "42" },
531 { "42", 'm', "NaN", "NaN" },
532 { "42", 'M', "NaN", "NaN" },
533 { "infty", 'm', "-infty", "-infty" },
534 { "infty", 'M', "-infty", "infty" },
537 /* Perform some basic tests of binary operations on isl_val objects.
539 static int test_bin_val(isl_ctx
*ctx
)
542 isl_val
*v1
, *v2
, *res
;
543 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
544 __isl_take isl_val
*v2
);
547 for (i
= 0; i
< ARRAY_SIZE(val_bin_tests
); ++i
) {
548 v1
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg1
);
549 v2
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg2
);
550 res
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].res
);
551 fn
= val_bin_op
[val_bin_tests
[i
].op
].fn
;
553 if (isl_val_is_nan(res
))
554 ok
= isl_val_is_nan(v1
);
556 ok
= isl_val_eq(v1
, res
);
562 isl_die(ctx
, isl_error_unknown
,
563 "unexpected result", return -1);
569 /* Perform some basic tests on isl_val objects.
571 static int test_val(isl_ctx
*ctx
)
573 if (test_un_val(ctx
) < 0)
575 if (test_bin_val(ctx
) < 0)
580 static int test_div(isl_ctx
*ctx
)
589 struct isl_basic_set
*bset
;
590 struct isl_constraint
*c
;
595 dim
= isl_space_set_alloc(ctx
, 0, 3);
596 bset
= isl_basic_set_universe(isl_space_copy(dim
));
597 ls
= isl_local_space_from_space(dim
);
599 c
= isl_equality_alloc(isl_local_space_copy(ls
));
600 isl_int_set_si(v
, -1);
601 isl_constraint_set_constant(c
, v
);
602 isl_int_set_si(v
, 1);
603 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
604 isl_int_set_si(v
, 3);
605 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
606 bset
= isl_basic_set_add_constraint(bset
, c
);
608 c
= isl_equality_alloc(isl_local_space_copy(ls
));
609 isl_int_set_si(v
, 1);
610 isl_constraint_set_constant(c
, v
);
611 isl_int_set_si(v
, -1);
612 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
613 isl_int_set_si(v
, 3);
614 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
615 bset
= isl_basic_set_add_constraint(bset
, c
);
617 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
619 assert(bset
&& bset
->n_div
== 1);
620 isl_local_space_free(ls
);
621 isl_basic_set_free(bset
);
624 dim
= isl_space_set_alloc(ctx
, 0, 3);
625 bset
= isl_basic_set_universe(isl_space_copy(dim
));
626 ls
= isl_local_space_from_space(dim
);
628 c
= isl_equality_alloc(isl_local_space_copy(ls
));
629 isl_int_set_si(v
, 1);
630 isl_constraint_set_constant(c
, v
);
631 isl_int_set_si(v
, -1);
632 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
633 isl_int_set_si(v
, 3);
634 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
635 bset
= isl_basic_set_add_constraint(bset
, c
);
637 c
= isl_equality_alloc(isl_local_space_copy(ls
));
638 isl_int_set_si(v
, -1);
639 isl_constraint_set_constant(c
, v
);
640 isl_int_set_si(v
, 1);
641 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
642 isl_int_set_si(v
, 3);
643 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
644 bset
= isl_basic_set_add_constraint(bset
, c
);
646 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
648 assert(bset
&& bset
->n_div
== 1);
649 isl_local_space_free(ls
);
650 isl_basic_set_free(bset
);
653 dim
= isl_space_set_alloc(ctx
, 0, 3);
654 bset
= isl_basic_set_universe(isl_space_copy(dim
));
655 ls
= isl_local_space_from_space(dim
);
657 c
= isl_equality_alloc(isl_local_space_copy(ls
));
658 isl_int_set_si(v
, 1);
659 isl_constraint_set_constant(c
, v
);
660 isl_int_set_si(v
, -1);
661 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
662 isl_int_set_si(v
, 3);
663 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
664 bset
= isl_basic_set_add_constraint(bset
, c
);
666 c
= isl_equality_alloc(isl_local_space_copy(ls
));
667 isl_int_set_si(v
, -3);
668 isl_constraint_set_constant(c
, v
);
669 isl_int_set_si(v
, 1);
670 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
671 isl_int_set_si(v
, 4);
672 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
673 bset
= isl_basic_set_add_constraint(bset
, c
);
675 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
677 assert(bset
&& bset
->n_div
== 1);
678 isl_local_space_free(ls
);
679 isl_basic_set_free(bset
);
682 dim
= isl_space_set_alloc(ctx
, 0, 3);
683 bset
= isl_basic_set_universe(isl_space_copy(dim
));
684 ls
= isl_local_space_from_space(dim
);
686 c
= isl_equality_alloc(isl_local_space_copy(ls
));
687 isl_int_set_si(v
, 2);
688 isl_constraint_set_constant(c
, v
);
689 isl_int_set_si(v
, -1);
690 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
691 isl_int_set_si(v
, 3);
692 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
693 bset
= isl_basic_set_add_constraint(bset
, c
);
695 c
= isl_equality_alloc(isl_local_space_copy(ls
));
696 isl_int_set_si(v
, -1);
697 isl_constraint_set_constant(c
, v
);
698 isl_int_set_si(v
, 1);
699 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
700 isl_int_set_si(v
, 6);
701 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
702 bset
= isl_basic_set_add_constraint(bset
, c
);
704 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
706 assert(isl_basic_set_is_empty(bset
));
707 isl_local_space_free(ls
);
708 isl_basic_set_free(bset
);
711 dim
= isl_space_set_alloc(ctx
, 0, 3);
712 bset
= isl_basic_set_universe(isl_space_copy(dim
));
713 ls
= isl_local_space_from_space(dim
);
715 c
= isl_equality_alloc(isl_local_space_copy(ls
));
716 isl_int_set_si(v
, -1);
717 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
718 isl_int_set_si(v
, 3);
719 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
720 bset
= isl_basic_set_add_constraint(bset
, c
);
722 c
= isl_equality_alloc(isl_local_space_copy(ls
));
723 isl_int_set_si(v
, 1);
724 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
725 isl_int_set_si(v
, -3);
726 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
727 bset
= isl_basic_set_add_constraint(bset
, c
);
729 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
731 assert(bset
&& bset
->n_div
== 0);
732 isl_basic_set_free(bset
);
733 isl_local_space_free(ls
);
736 dim
= isl_space_set_alloc(ctx
, 0, 3);
737 bset
= isl_basic_set_universe(isl_space_copy(dim
));
738 ls
= isl_local_space_from_space(dim
);
740 c
= isl_equality_alloc(isl_local_space_copy(ls
));
741 isl_int_set_si(v
, -1);
742 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
743 isl_int_set_si(v
, 6);
744 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
745 bset
= isl_basic_set_add_constraint(bset
, c
);
747 c
= isl_equality_alloc(isl_local_space_copy(ls
));
748 isl_int_set_si(v
, 1);
749 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
750 isl_int_set_si(v
, -3);
751 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
752 bset
= isl_basic_set_add_constraint(bset
, c
);
754 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
756 assert(bset
&& bset
->n_div
== 1);
757 isl_basic_set_free(bset
);
758 isl_local_space_free(ls
);
761 /* This test is a bit tricky. We set up an equality
763 * Normalization of divs creates _two_ divs
766 * Afterwards e0 is removed again because it has coefficient -1
767 * and we end up with the original equality and div again.
768 * Perhaps we can avoid the introduction of this temporary div.
770 dim
= isl_space_set_alloc(ctx
, 0, 4);
771 bset
= isl_basic_set_universe(isl_space_copy(dim
));
772 ls
= isl_local_space_from_space(dim
);
774 c
= isl_equality_alloc(isl_local_space_copy(ls
));
775 isl_int_set_si(v
, -1);
776 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
777 isl_int_set_si(v
, -3);
778 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
779 isl_int_set_si(v
, -3);
780 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
781 isl_int_set_si(v
, 6);
782 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
783 bset
= isl_basic_set_add_constraint(bset
, c
);
785 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
787 /* Test disabled for now */
789 assert(bset && bset->n_div == 1);
791 isl_local_space_free(ls
);
792 isl_basic_set_free(bset
);
795 dim
= isl_space_set_alloc(ctx
, 0, 5);
796 bset
= isl_basic_set_universe(isl_space_copy(dim
));
797 ls
= isl_local_space_from_space(dim
);
799 c
= isl_equality_alloc(isl_local_space_copy(ls
));
800 isl_int_set_si(v
, -1);
801 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
802 isl_int_set_si(v
, -3);
803 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
804 isl_int_set_si(v
, -3);
805 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
806 isl_int_set_si(v
, 6);
807 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
808 bset
= isl_basic_set_add_constraint(bset
, c
);
810 c
= isl_equality_alloc(isl_local_space_copy(ls
));
811 isl_int_set_si(v
, -1);
812 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
813 isl_int_set_si(v
, 1);
814 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
815 isl_int_set_si(v
, 1);
816 isl_constraint_set_constant(c
, v
);
817 bset
= isl_basic_set_add_constraint(bset
, c
);
819 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
821 /* Test disabled for now */
823 assert(bset && bset->n_div == 1);
825 isl_local_space_free(ls
);
826 isl_basic_set_free(bset
);
829 dim
= isl_space_set_alloc(ctx
, 0, 4);
830 bset
= isl_basic_set_universe(isl_space_copy(dim
));
831 ls
= isl_local_space_from_space(dim
);
833 c
= isl_equality_alloc(isl_local_space_copy(ls
));
834 isl_int_set_si(v
, 1);
835 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
836 isl_int_set_si(v
, -1);
837 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
838 isl_int_set_si(v
, -2);
839 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
840 bset
= isl_basic_set_add_constraint(bset
, c
);
842 c
= isl_equality_alloc(isl_local_space_copy(ls
));
843 isl_int_set_si(v
, -1);
844 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
845 isl_int_set_si(v
, 3);
846 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
847 isl_int_set_si(v
, 2);
848 isl_constraint_set_constant(c
, v
);
849 bset
= isl_basic_set_add_constraint(bset
, c
);
851 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
853 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
855 assert(!isl_basic_set_is_empty(bset
));
857 isl_local_space_free(ls
);
858 isl_basic_set_free(bset
);
861 dim
= isl_space_set_alloc(ctx
, 0, 3);
862 bset
= isl_basic_set_universe(isl_space_copy(dim
));
863 ls
= isl_local_space_from_space(dim
);
865 c
= isl_equality_alloc(isl_local_space_copy(ls
));
866 isl_int_set_si(v
, 1);
867 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
868 isl_int_set_si(v
, -2);
869 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
870 bset
= isl_basic_set_add_constraint(bset
, c
);
872 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
874 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
876 isl_local_space_free(ls
);
877 isl_basic_set_free(bset
);
881 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
882 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
883 set
= isl_set_read_from_str(ctx
, str
);
884 set
= isl_set_compute_divs(set
);
889 str
= "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
890 bset
= isl_basic_set_read_from_str(ctx
, str
);
891 n
= isl_basic_set_dim(bset
, isl_dim_div
);
892 isl_basic_set_free(bset
);
896 isl_die(ctx
, isl_error_unknown
,
897 "expecting no existentials", return -1);
899 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
900 set
= isl_set_read_from_str(ctx
, str
);
901 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
902 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
903 empty
= isl_set_is_empty(set
);
908 isl_die(ctx
, isl_error_unknown
,
909 "result not as accurate as expected", return -1);
914 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
918 struct isl_basic_set
*bset1
, *bset2
;
919 struct isl_basic_map
*bmap
;
921 filename
= get_filename(ctx
, name
, "omega");
923 input
= fopen(filename
, "r");
926 bset1
= isl_basic_set_read_from_file(ctx
, input
);
927 bmap
= isl_basic_map_read_from_file(ctx
, input
);
929 bset1
= isl_basic_set_apply(bset1
, bmap
);
931 bset2
= isl_basic_set_read_from_file(ctx
, input
);
933 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
935 isl_basic_set_free(bset1
);
936 isl_basic_set_free(bset2
);
942 void test_application(struct isl_ctx
*ctx
)
944 test_application_case(ctx
, "application");
945 test_application_case(ctx
, "application2");
948 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
952 struct isl_basic_set
*bset1
, *bset2
;
954 filename
= get_filename(ctx
, name
, "polylib");
956 input
= fopen(filename
, "r");
959 bset1
= isl_basic_set_read_from_file(ctx
, input
);
960 bset2
= isl_basic_set_read_from_file(ctx
, input
);
962 bset1
= isl_basic_set_affine_hull(bset1
);
964 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
966 isl_basic_set_free(bset1
);
967 isl_basic_set_free(bset2
);
973 int test_affine_hull(struct isl_ctx
*ctx
)
977 isl_basic_set
*bset
, *bset2
;
981 test_affine_hull_case(ctx
, "affine2");
982 test_affine_hull_case(ctx
, "affine");
983 test_affine_hull_case(ctx
, "affine3");
985 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
986 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
987 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
988 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
989 set
= isl_set_read_from_str(ctx
, str
);
990 bset
= isl_set_affine_hull(set
);
991 n
= isl_basic_set_dim(bset
, isl_dim_div
);
992 isl_basic_set_free(bset
);
994 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
997 /* Check that isl_map_affine_hull is not confused by
998 * the reordering of divs in isl_map_align_divs.
1000 str
= "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1001 "32e0 = b and 32e1 = c); "
1002 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1003 set
= isl_set_read_from_str(ctx
, str
);
1004 bset
= isl_set_affine_hull(set
);
1005 isl_basic_set_free(bset
);
1009 str
= "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1010 "32e2 = 31 + 31e0 }";
1011 set
= isl_set_read_from_str(ctx
, str
);
1012 bset
= isl_set_affine_hull(set
);
1013 str
= "{ [a] : exists e : a = 32 e }";
1014 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1015 subset
= isl_basic_set_is_subset(bset
, bset2
);
1016 isl_basic_set_free(bset
);
1017 isl_basic_set_free(bset2
);
1021 isl_die(ctx
, isl_error_unknown
, "not as accurate as expected",
1027 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
1031 struct isl_basic_set
*bset1
, *bset2
;
1032 struct isl_set
*set
;
1034 filename
= get_filename(ctx
, name
, "polylib");
1036 input
= fopen(filename
, "r");
1039 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1040 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1042 set
= isl_basic_set_union(bset1
, bset2
);
1043 bset1
= isl_set_convex_hull(set
);
1045 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1047 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1049 isl_basic_set_free(bset1
);
1050 isl_basic_set_free(bset2
);
1056 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
1058 const char *str1
, *str2
;
1059 isl_set
*set1
, *set2
;
1060 int orig_convex
= ctx
->opt
->convex
;
1061 ctx
->opt
->convex
= convex
;
1063 test_convex_hull_case(ctx
, "convex0");
1064 test_convex_hull_case(ctx
, "convex1");
1065 test_convex_hull_case(ctx
, "convex2");
1066 test_convex_hull_case(ctx
, "convex3");
1067 test_convex_hull_case(ctx
, "convex4");
1068 test_convex_hull_case(ctx
, "convex5");
1069 test_convex_hull_case(ctx
, "convex6");
1070 test_convex_hull_case(ctx
, "convex7");
1071 test_convex_hull_case(ctx
, "convex8");
1072 test_convex_hull_case(ctx
, "convex9");
1073 test_convex_hull_case(ctx
, "convex10");
1074 test_convex_hull_case(ctx
, "convex11");
1075 test_convex_hull_case(ctx
, "convex12");
1076 test_convex_hull_case(ctx
, "convex13");
1077 test_convex_hull_case(ctx
, "convex14");
1078 test_convex_hull_case(ctx
, "convex15");
1080 str1
= "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1081 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1082 "(i0 = 0 and i1 = 0 and i2 = 0) }";
1083 str2
= "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }";
1084 set1
= isl_set_read_from_str(ctx
, str1
);
1085 set2
= isl_set_read_from_str(ctx
, str2
);
1086 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
1087 assert(isl_set_is_equal(set1
, set2
));
1091 ctx
->opt
->convex
= orig_convex
;
1094 void test_convex_hull(struct isl_ctx
*ctx
)
1096 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
1097 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
1100 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
1104 struct isl_basic_set
*bset1
, *bset2
;
1106 filename
= get_filename(ctx
, name
, "polylib");
1108 input
= fopen(filename
, "r");
1111 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1112 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1114 bset1
= isl_basic_set_gist(bset1
, bset2
);
1116 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1118 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1120 isl_basic_set_free(bset1
);
1121 isl_basic_set_free(bset2
);
1127 static int test_gist(struct isl_ctx
*ctx
)
1130 isl_basic_set
*bset1
, *bset2
;
1131 isl_map
*map1
, *map2
;
1133 test_gist_case(ctx
, "gist1");
1135 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1136 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1137 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1138 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1139 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1140 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1141 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1142 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1143 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1144 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1145 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1146 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1147 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1148 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1149 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1150 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1151 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1152 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1153 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1154 bset1
= isl_basic_set_gist(bset1
, bset2
);
1155 assert(bset1
&& bset1
->n_div
== 0);
1156 isl_basic_set_free(bset1
);
1158 /* Check that the integer divisions of the second disjunct
1159 * do not spread to the first disjunct.
1161 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1162 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1163 "(exists (e0 = [(-1 + t1)/16], "
1164 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1165 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1166 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1167 "o0 <= 4294967295 and t1 <= -1)) }";
1168 map1
= isl_map_read_from_str(ctx
, str
);
1169 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1170 map2
= isl_map_read_from_str(ctx
, str
);
1171 map1
= isl_map_gist(map1
, map2
);
1175 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1176 isl_map_free(map1
); return -1);
1177 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1178 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1179 isl_map_free(map1
); return -1);
1185 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1187 isl_set
*set
, *set2
;
1191 set
= isl_set_read_from_str(ctx
, str
);
1192 set
= isl_set_coalesce(set
);
1193 set2
= isl_set_read_from_str(ctx
, str
);
1194 equal
= isl_set_is_equal(set
, set2
);
1195 one
= set
&& set
->n
== 1;
1202 isl_die(ctx
, isl_error_unknown
,
1203 "coalesced set not equal to input", return -1);
1204 if (check_one
&& !one
)
1205 isl_die(ctx
, isl_error_unknown
,
1206 "coalesced set should not be a union", return -1);
1211 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1216 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1217 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1219 if (test_coalesce_set(ctx
,
1220 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1221 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1222 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1223 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1224 "-10 <= y <= 0}", 1) < 0)
1226 if (test_coalesce_set(ctx
,
1227 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
1229 if (test_coalesce_set(ctx
,
1230 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
1238 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1243 /* Inputs for coalescing tests.
1244 * "str" is a string representation of the input set.
1245 * "single_disjunct" is set if we expect the result to consist of
1246 * a single disjunct.
1249 int single_disjunct
;
1251 } coalesce_tests
[] = {
1252 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1253 "y >= x & x >= 2 & 5 >= y }" },
1254 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1255 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1256 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1257 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1258 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1259 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1260 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1261 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1262 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1263 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1264 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1265 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1266 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1267 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1268 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1269 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1270 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1271 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1272 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1273 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1274 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1275 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1276 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1277 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1278 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1279 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1280 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1281 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1282 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1283 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1284 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1285 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1286 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1287 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1288 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1289 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1290 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1291 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1292 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1293 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1294 "[o0, o1, o2, o3, o4, o5, o6]] : "
1295 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1296 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1297 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1298 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1299 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1300 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1301 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1302 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1303 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1304 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1305 "o6 >= i3 + i6 - o3 and M >= 0 and "
1306 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1307 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1308 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1309 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1310 "(o0 = 0 and M >= 2 and N >= 3) or "
1311 "(M = 0 and o0 = 0 and N >= 3) }" },
1312 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1313 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1314 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1315 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1316 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1317 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1318 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1319 "(y = 3 and x = 1) }" },
1320 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1321 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1322 "i1 <= M and i3 <= M and i4 <= M) or "
1323 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1324 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1325 "i4 <= -1 + M) }" },
1326 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1327 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1328 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1329 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1330 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1331 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1332 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1333 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1334 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1335 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1336 { 0, "{ [a, b] : exists e : 2e = a and "
1337 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1338 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1339 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1340 "j >= 1 and j' <= i + j - i' and i >= 1; "
1342 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1343 "[i,j] : exists a : j = 3a }" },
1344 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1345 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1347 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1348 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1349 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1350 "c <= 6 + 8a and a >= 3; "
1351 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1352 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1353 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1354 "[x,0] : 3 <= x <= 4 }" },
1355 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1356 "[x,0] : 4 <= x <= 5 }" },
1357 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1358 "[x,0] : 3 <= x <= 5 }" },
1359 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1360 "[x,0] : 3 <= x <= 4 }" },
1361 { 1 , "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1363 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1366 /* Test the functionality of isl_set_coalesce.
1367 * That is, check that the output is always equal to the input
1368 * and in some cases that the result consists of a single disjunct.
1370 static int test_coalesce(struct isl_ctx
*ctx
)
1374 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
1375 const char *str
= coalesce_tests
[i
].str
;
1376 int check_one
= coalesce_tests
[i
].single_disjunct
;
1377 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
1381 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1387 void test_closure(struct isl_ctx
*ctx
)
1391 isl_map
*up
, *right
;
1392 isl_map
*map
, *map2
;
1395 /* COCOA example 1 */
1396 map
= isl_map_read_from_str(ctx
,
1397 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1398 "1 <= i and i < n and 1 <= j and j < n or "
1399 "i2 = i + 1 and j2 = j - 1 and "
1400 "1 <= i and i < n and 2 <= j and j <= n }");
1401 map
= isl_map_power(map
, &exact
);
1405 /* COCOA example 1 */
1406 map
= isl_map_read_from_str(ctx
,
1407 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1408 "1 <= i and i < n and 1 <= j and j < n or "
1409 "i2 = i + 1 and j2 = j - 1 and "
1410 "1 <= i and i < n and 2 <= j and j <= n }");
1411 map
= isl_map_transitive_closure(map
, &exact
);
1413 map2
= isl_map_read_from_str(ctx
,
1414 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1415 "1 <= i and i < n and 1 <= j and j <= n and "
1416 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1417 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1418 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1419 assert(isl_map_is_equal(map
, map2
));
1423 map
= isl_map_read_from_str(ctx
,
1424 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1425 " 0 <= y and y <= n }");
1426 map
= isl_map_transitive_closure(map
, &exact
);
1427 map2
= isl_map_read_from_str(ctx
,
1428 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1429 " 0 <= y and y <= n }");
1430 assert(isl_map_is_equal(map
, map2
));
1434 /* COCOA example 2 */
1435 map
= isl_map_read_from_str(ctx
,
1436 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1437 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1438 "i2 = i + 2 and j2 = j - 2 and "
1439 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1440 map
= isl_map_transitive_closure(map
, &exact
);
1442 map2
= isl_map_read_from_str(ctx
,
1443 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1444 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1445 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1446 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1447 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1448 assert(isl_map_is_equal(map
, map2
));
1452 /* COCOA Fig.2 left */
1453 map
= isl_map_read_from_str(ctx
,
1454 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1455 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1457 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1458 "j <= 2 i - 3 and j <= n - 2 or "
1459 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1460 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1461 map
= isl_map_transitive_closure(map
, &exact
);
1465 /* COCOA Fig.2 right */
1466 map
= isl_map_read_from_str(ctx
,
1467 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1468 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1470 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1471 "j <= 2 i - 4 and j <= n - 3 or "
1472 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1473 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1474 map
= isl_map_power(map
, &exact
);
1478 /* COCOA Fig.2 right */
1479 map
= isl_map_read_from_str(ctx
,
1480 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1481 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1483 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1484 "j <= 2 i - 4 and j <= n - 3 or "
1485 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1486 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1487 map
= isl_map_transitive_closure(map
, &exact
);
1489 map2
= isl_map_read_from_str(ctx
,
1490 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1491 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1492 "j <= n and 3 + i + 2 j <= 3 n and "
1493 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1494 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1495 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1496 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1497 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1498 assert(isl_map_is_equal(map
, map2
));
1502 /* COCOA Fig.1 right */
1503 dom
= isl_set_read_from_str(ctx
,
1504 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1505 "2 x - 3 y + 3 >= 0 }");
1506 right
= isl_map_read_from_str(ctx
,
1507 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1508 up
= isl_map_read_from_str(ctx
,
1509 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1510 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1511 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1512 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1513 up
= isl_map_intersect_range(up
, dom
);
1514 map
= isl_map_union(up
, right
);
1515 map
= isl_map_transitive_closure(map
, &exact
);
1517 map2
= isl_map_read_from_str(ctx
,
1518 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1519 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1520 assert(isl_map_is_equal(map
, map2
));
1524 /* COCOA Theorem 1 counter example */
1525 map
= isl_map_read_from_str(ctx
,
1526 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1527 "i2 = 1 and j2 = j or "
1528 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1529 map
= isl_map_transitive_closure(map
, &exact
);
1533 map
= isl_map_read_from_str(ctx
,
1534 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1535 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1536 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1537 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1538 map
= isl_map_transitive_closure(map
, &exact
);
1542 /* Kelly et al 1996, fig 12 */
1543 map
= isl_map_read_from_str(ctx
,
1544 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1545 "1 <= i,j,j+1 <= n or "
1546 "j = n and j2 = 1 and i2 = i + 1 and "
1547 "1 <= i,i+1 <= n }");
1548 map
= isl_map_transitive_closure(map
, &exact
);
1550 map2
= isl_map_read_from_str(ctx
,
1551 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1552 "1 <= i <= n and i = i2 or "
1553 "1 <= i < i2 <= n and 1 <= j <= n and "
1555 assert(isl_map_is_equal(map
, map2
));
1559 /* Omega's closure4 */
1560 map
= isl_map_read_from_str(ctx
,
1561 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1562 "1 <= x,y <= 10 or "
1563 "x2 = x + 1 and y2 = y and "
1564 "1 <= x <= 20 && 5 <= y <= 15 }");
1565 map
= isl_map_transitive_closure(map
, &exact
);
1569 map
= isl_map_read_from_str(ctx
,
1570 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1571 map
= isl_map_transitive_closure(map
, &exact
);
1573 map2
= isl_map_read_from_str(ctx
,
1574 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1575 assert(isl_map_is_equal(map
, map2
));
1579 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1580 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1581 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1582 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1583 map
= isl_map_read_from_str(ctx
, str
);
1584 map
= isl_map_transitive_closure(map
, &exact
);
1586 map2
= isl_map_read_from_str(ctx
, str
);
1587 assert(isl_map_is_equal(map
, map2
));
1591 str
= "{[0] -> [1]; [2] -> [3]}";
1592 map
= isl_map_read_from_str(ctx
, str
);
1593 map
= isl_map_transitive_closure(map
, &exact
);
1595 map2
= isl_map_read_from_str(ctx
, str
);
1596 assert(isl_map_is_equal(map
, map2
));
1600 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1601 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1602 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1603 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1604 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1605 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1606 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1607 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1608 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1609 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1610 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1611 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1612 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1613 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1614 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1615 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1616 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1617 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1618 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1619 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1620 map
= isl_map_read_from_str(ctx
, str
);
1621 map
= isl_map_transitive_closure(map
, NULL
);
1626 void test_lex(struct isl_ctx
*ctx
)
1631 dim
= isl_space_set_alloc(ctx
, 0, 0);
1632 map
= isl_map_lex_le(dim
);
1633 assert(!isl_map_is_empty(map
));
1637 static int test_lexmin(struct isl_ctx
*ctx
)
1641 isl_basic_map
*bmap
;
1642 isl_map
*map
, *map2
;
1645 isl_pw_multi_aff
*pma
;
1647 str
= "[p0, p1] -> { [] -> [] : "
1648 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1649 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1650 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1651 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1652 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1653 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1654 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1655 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1656 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1657 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1658 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1659 map
= isl_map_read_from_str(ctx
, str
);
1660 map
= isl_map_lexmin(map
);
1663 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1664 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1665 set
= isl_set_read_from_str(ctx
, str
);
1666 set
= isl_set_lexmax(set
);
1667 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1668 set2
= isl_set_read_from_str(ctx
, str
);
1669 set
= isl_set_intersect(set
, set2
);
1670 assert(!isl_set_is_empty(set
));
1673 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1674 map
= isl_map_read_from_str(ctx
, str
);
1675 map
= isl_map_lexmin(map
);
1676 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1677 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1678 map2
= isl_map_read_from_str(ctx
, str
);
1679 assert(isl_map_is_equal(map
, map2
));
1683 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1684 map
= isl_map_read_from_str(ctx
, str
);
1685 map2
= isl_map_copy(map
);
1686 map
= isl_map_lexmin(map
);
1687 assert(isl_map_is_equal(map
, map2
));
1691 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1692 map
= isl_map_read_from_str(ctx
, str
);
1693 map
= isl_map_lexmin(map
);
1694 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1695 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1696 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1697 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1698 map2
= isl_map_read_from_str(ctx
, str
);
1699 assert(isl_map_is_equal(map
, map2
));
1703 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1704 " 8i' <= i and 8i' >= -7 + i }";
1705 bmap
= isl_basic_map_read_from_str(ctx
, str
);
1706 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
1707 map2
= isl_map_from_pw_multi_aff(pma
);
1708 map
= isl_map_from_basic_map(bmap
);
1709 assert(isl_map_is_equal(map
, map2
));
1713 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1714 map
= isl_map_read_from_str(ctx
, str
);
1715 map
= isl_map_lexmin(map
);
1716 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1717 map2
= isl_map_read_from_str(ctx
, str
);
1718 assert(isl_map_is_equal(map
, map2
));
1722 /* Check that empty pieces are properly combined. */
1723 str
= "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
1724 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
1725 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
1726 map
= isl_map_read_from_str(ctx
, str
);
1727 map
= isl_map_lexmin(map
);
1728 str
= "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
1729 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
1731 map2
= isl_map_read_from_str(ctx
, str
);
1732 assert(isl_map_is_equal(map
, map2
));
1736 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1737 " 8i' <= i and 8i' >= -7 + i }";
1738 set
= isl_set_read_from_str(ctx
, str
);
1739 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
1740 set2
= isl_set_from_pw_multi_aff(pma
);
1741 equal
= isl_set_is_equal(set
, set2
);
1747 isl_die(ctx
, isl_error_unknown
,
1748 "unexpected difference between set and "
1749 "piecewise affine expression", return -1);
1754 /* Check that isl_set_min_val and isl_set_max_val compute the correct
1755 * result on non-convex inputs.
1757 static int test_min(struct isl_ctx
*ctx
)
1764 set
= isl_set_read_from_str(ctx
, "{ [-1]; [1] }");
1765 aff
= isl_aff_read_from_str(ctx
, "{ [x] -> [x] }");
1766 val
= isl_set_min_val(set
, aff
);
1767 min_ok
= isl_val_is_negone(val
);
1769 val
= isl_set_max_val(set
, aff
);
1770 max_ok
= isl_val_is_one(val
);
1775 if (min_ok
< 0 || max_ok
< 0)
1778 isl_die(ctx
, isl_error_unknown
,
1779 "unexpected minimum", return -1);
1781 isl_die(ctx
, isl_error_unknown
,
1782 "unexpected maximum", return -1);
1792 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1793 void *dep_user
, void *user
)
1795 struct must_may
*mm
= (struct must_may
*)user
;
1798 mm
->must
= isl_map_union(mm
->must
, dep
);
1800 mm
->may
= isl_map_union(mm
->may
, dep
);
1805 static int common_space(void *first
, void *second
)
1807 int depth
= *(int *)first
;
1811 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1819 map2
= isl_map_read_from_str(map
->ctx
, str
);
1820 equal
= isl_map_is_equal(map
, map2
);
1826 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
1830 equal
= map_is_equal(map
, str
);
1834 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
1835 "result not as expected", return -1);
1839 void test_dep(struct isl_ctx
*ctx
)
1844 isl_access_info
*ai
;
1851 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1852 map
= isl_map_read_from_str(ctx
, str
);
1853 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1855 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1856 map
= isl_map_read_from_str(ctx
, str
);
1857 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1859 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1860 map
= isl_map_read_from_str(ctx
, str
);
1861 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1863 flow
= isl_access_info_compute_flow(ai
);
1864 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1865 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1866 mm
.may
= isl_map_empty(dim
);
1868 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1870 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1871 " [1,10,0] -> [2,5,0] }";
1872 assert(map_is_equal(mm
.must
, str
));
1873 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1874 assert(map_is_equal(mm
.may
, str
));
1876 isl_map_free(mm
.must
);
1877 isl_map_free(mm
.may
);
1878 isl_flow_free(flow
);
1881 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1882 map
= isl_map_read_from_str(ctx
, str
);
1883 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1885 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1886 map
= isl_map_read_from_str(ctx
, str
);
1887 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1889 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1890 map
= isl_map_read_from_str(ctx
, str
);
1891 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1893 flow
= isl_access_info_compute_flow(ai
);
1894 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1895 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1896 mm
.may
= isl_map_empty(dim
);
1898 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1900 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1901 assert(map_is_equal(mm
.must
, str
));
1902 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1903 assert(map_is_equal(mm
.may
, str
));
1905 isl_map_free(mm
.must
);
1906 isl_map_free(mm
.may
);
1907 isl_flow_free(flow
);
1910 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1911 map
= isl_map_read_from_str(ctx
, str
);
1912 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1914 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1915 map
= isl_map_read_from_str(ctx
, str
);
1916 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1918 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1919 map
= isl_map_read_from_str(ctx
, str
);
1920 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1922 flow
= isl_access_info_compute_flow(ai
);
1923 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1924 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1925 mm
.may
= isl_map_empty(dim
);
1927 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1929 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1930 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1931 assert(map_is_equal(mm
.may
, str
));
1932 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1933 assert(map_is_equal(mm
.must
, str
));
1935 isl_map_free(mm
.must
);
1936 isl_map_free(mm
.may
);
1937 isl_flow_free(flow
);
1940 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1941 map
= isl_map_read_from_str(ctx
, str
);
1942 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1944 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1945 map
= isl_map_read_from_str(ctx
, str
);
1946 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1948 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1949 map
= isl_map_read_from_str(ctx
, str
);
1950 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1952 flow
= isl_access_info_compute_flow(ai
);
1953 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1954 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1955 mm
.may
= isl_map_empty(dim
);
1957 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1959 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1960 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1961 assert(map_is_equal(mm
.may
, str
));
1962 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1963 assert(map_is_equal(mm
.must
, str
));
1965 isl_map_free(mm
.must
);
1966 isl_map_free(mm
.may
);
1967 isl_flow_free(flow
);
1970 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1971 map
= isl_map_read_from_str(ctx
, str
);
1972 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1974 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1975 map
= isl_map_read_from_str(ctx
, str
);
1976 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1978 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1979 map
= isl_map_read_from_str(ctx
, str
);
1980 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1982 flow
= isl_access_info_compute_flow(ai
);
1983 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1984 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1985 mm
.may
= isl_map_empty(dim
);
1987 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1989 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
1990 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
1991 assert(map_is_equal(mm
.may
, str
));
1992 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1993 assert(map_is_equal(mm
.must
, str
));
1995 isl_map_free(mm
.must
);
1996 isl_map_free(mm
.may
);
1997 isl_flow_free(flow
);
2002 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2003 map
= isl_map_read_from_str(ctx
, str
);
2004 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2006 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2007 map
= isl_map_read_from_str(ctx
, str
);
2008 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2010 flow
= isl_access_info_compute_flow(ai
);
2011 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2012 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2013 mm
.may
= isl_map_empty(dim
);
2015 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2017 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2018 assert(map_is_equal(mm
.must
, str
));
2019 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2020 assert(map_is_equal(mm
.may
, str
));
2022 isl_map_free(mm
.must
);
2023 isl_map_free(mm
.may
);
2024 isl_flow_free(flow
);
2027 /* Check that the dependence analysis proceeds without errors.
2028 * Earlier versions of isl would break down during the analysis
2029 * due to the use of the wrong spaces.
2031 static int test_flow(isl_ctx
*ctx
)
2034 isl_union_map
*access
, *schedule
;
2035 isl_union_map
*must_dep
, *may_dep
;
2038 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2039 access
= isl_union_map_read_from_str(ctx
, str
);
2040 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2041 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2042 "S2[] -> [1,0,0,0]; "
2043 "S3[] -> [-1,0,0,0] }";
2044 schedule
= isl_union_map_read_from_str(ctx
, str
);
2045 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2046 isl_union_map_copy(access
), schedule
,
2047 &must_dep
, &may_dep
, NULL
, NULL
);
2048 isl_union_map_free(may_dep
);
2049 isl_union_map_free(must_dep
);
2054 int test_sv(isl_ctx
*ctx
)
2058 isl_union_map
*umap
;
2061 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
2062 map
= isl_map_read_from_str(ctx
, str
);
2063 sv
= isl_map_is_single_valued(map
);
2068 isl_die(ctx
, isl_error_internal
,
2069 "map not detected as single valued", return -1);
2071 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
2072 map
= isl_map_read_from_str(ctx
, str
);
2073 sv
= isl_map_is_single_valued(map
);
2078 isl_die(ctx
, isl_error_internal
,
2079 "map detected as single valued", return -1);
2081 str
= "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
2082 umap
= isl_union_map_read_from_str(ctx
, str
);
2083 sv
= isl_union_map_is_single_valued(umap
);
2084 isl_union_map_free(umap
);
2088 isl_die(ctx
, isl_error_internal
,
2089 "map not detected as single valued", return -1);
2091 str
= "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
2092 umap
= isl_union_map_read_from_str(ctx
, str
);
2093 sv
= isl_union_map_is_single_valued(umap
);
2094 isl_union_map_free(umap
);
2098 isl_die(ctx
, isl_error_internal
,
2099 "map detected as single valued", return -1);
2104 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
2108 map
= isl_map_read_from_str(ctx
, str
);
2110 assert(isl_map_is_bijective(map
));
2112 assert(!isl_map_is_bijective(map
));
2116 void test_bijective(struct isl_ctx
*ctx
)
2118 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
2119 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
2120 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
2121 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
2122 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
2123 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
2124 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
2125 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
2126 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
2127 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
2128 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
2129 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
2130 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
2133 static int test_pwqp(struct isl_ctx
*ctx
)
2137 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
2140 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2141 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2143 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
2146 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2147 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2149 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2151 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2153 isl_pw_qpolynomial_free(pwqp1
);
2155 str
= "{ [i] -> i }";
2156 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2157 str
= "{ [k] : exists a : k = 2a }";
2158 set
= isl_set_read_from_str(ctx
, str
);
2159 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2160 str
= "{ [i] -> i }";
2161 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2163 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2165 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2167 isl_pw_qpolynomial_free(pwqp1
);
2169 str
= "{ [i] -> i + [ (i + [i/3])/2 ] }";
2170 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2172 set
= isl_set_read_from_str(ctx
, str
);
2173 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2174 str
= "{ [i] -> 16 }";
2175 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2177 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2179 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2181 isl_pw_qpolynomial_free(pwqp1
);
2183 str
= "{ [i] -> ([(i)/2]) }";
2184 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2185 str
= "{ [k] : exists a : k = 2a+1 }";
2186 set
= isl_set_read_from_str(ctx
, str
);
2187 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2188 str
= "{ [i] -> -1/2 + 1/2 * i }";
2189 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2191 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2193 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2195 isl_pw_qpolynomial_free(pwqp1
);
2197 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
2198 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2199 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
2200 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2202 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2204 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2206 isl_pw_qpolynomial_free(pwqp1
);
2208 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
2209 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2210 str
= "{ [x] -> x }";
2211 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2213 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2215 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2217 isl_pw_qpolynomial_free(pwqp1
);
2219 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2220 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2221 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2222 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
2223 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2224 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2225 isl_pw_qpolynomial_free(pwqp1
);
2227 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2228 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2229 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2230 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2231 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
2232 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
2233 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2234 isl_pw_qpolynomial_free(pwqp1
);
2235 isl_pw_qpolynomial_free(pwqp2
);
2239 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2241 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2242 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2243 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2244 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2245 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
2247 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2248 isl_pw_qpolynomial_free(pwqp1
);
2249 isl_pw_qpolynomial_free(pwqp2
);
2253 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2258 void test_split_periods(isl_ctx
*ctx
)
2261 isl_pw_qpolynomial
*pwqp
;
2263 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2264 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2265 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2266 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2268 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
2271 isl_pw_qpolynomial_free(pwqp
);
2274 void test_union(isl_ctx
*ctx
)
2277 isl_union_set
*uset1
, *uset2
;
2278 isl_union_map
*umap1
, *umap2
;
2280 str
= "{ [i] : 0 <= i <= 1 }";
2281 uset1
= isl_union_set_read_from_str(ctx
, str
);
2282 str
= "{ [1] -> [0] }";
2283 umap1
= isl_union_map_read_from_str(ctx
, str
);
2285 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
2286 assert(isl_union_map_is_equal(umap1
, umap2
));
2288 isl_union_map_free(umap1
);
2289 isl_union_map_free(umap2
);
2291 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2292 umap1
= isl_union_map_read_from_str(ctx
, str
);
2293 str
= "{ A[i]; B[i] }";
2294 uset1
= isl_union_set_read_from_str(ctx
, str
);
2296 uset2
= isl_union_map_domain(umap1
);
2298 assert(isl_union_set_is_equal(uset1
, uset2
));
2300 isl_union_set_free(uset1
);
2301 isl_union_set_free(uset2
);
2304 void test_bound(isl_ctx
*ctx
)
2307 isl_pw_qpolynomial
*pwqp
;
2308 isl_pw_qpolynomial_fold
*pwf
;
2310 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
2311 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2312 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2313 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 4);
2314 isl_pw_qpolynomial_fold_free(pwf
);
2316 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2317 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2318 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2319 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 1);
2320 isl_pw_qpolynomial_fold_free(pwf
);
2323 void test_lift(isl_ctx
*ctx
)
2326 isl_basic_map
*bmap
;
2327 isl_basic_set
*bset
;
2329 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
2330 bset
= isl_basic_set_read_from_str(ctx
, str
);
2331 bset
= isl_basic_set_lift(bset
);
2332 bmap
= isl_basic_map_from_range(bset
);
2333 bset
= isl_basic_map_domain(bmap
);
2334 isl_basic_set_free(bset
);
2341 } subset_tests
[] = {
2343 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2344 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2345 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2347 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2348 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2349 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2350 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2351 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2352 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2353 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2354 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2355 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2356 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2357 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2358 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2359 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2360 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2361 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2362 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2363 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2364 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2365 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2366 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2367 "4e0 <= -57 + i0 + i1)) or "
2368 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2369 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2370 "4e0 >= -61 + i0 + i1)) or "
2371 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2374 static int test_subset(isl_ctx
*ctx
)
2377 isl_set
*set1
, *set2
;
2380 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
2381 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
2382 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
2383 subset
= isl_set_is_subset(set1
, set2
);
2388 if (subset
!= subset_tests
[i
].subset
)
2389 isl_die(ctx
, isl_error_unknown
,
2390 "incorrect subset result", return -1);
2397 const char *minuend
;
2398 const char *subtrahend
;
2399 const char *difference
;
2400 } subtract_domain_tests
[] = {
2401 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2402 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2403 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2406 static int test_subtract(isl_ctx
*ctx
)
2409 isl_union_map
*umap1
, *umap2
;
2410 isl_union_set
*uset
;
2413 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2414 umap1
= isl_union_map_read_from_str(ctx
,
2415 subtract_domain_tests
[i
].minuend
);
2416 uset
= isl_union_set_read_from_str(ctx
,
2417 subtract_domain_tests
[i
].subtrahend
);
2418 umap2
= isl_union_map_read_from_str(ctx
,
2419 subtract_domain_tests
[i
].difference
);
2420 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
2421 equal
= isl_union_map_is_equal(umap1
, umap2
);
2422 isl_union_map_free(umap1
);
2423 isl_union_map_free(umap2
);
2427 isl_die(ctx
, isl_error_unknown
,
2428 "incorrect subtract domain result", return -1);
2434 int test_factorize(isl_ctx
*ctx
)
2437 isl_basic_set
*bset
;
2440 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2441 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2442 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2443 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2444 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2445 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2446 "3i5 >= -2i0 - i2 + 3i4 }";
2447 bset
= isl_basic_set_read_from_str(ctx
, str
);
2448 f
= isl_basic_set_factorizer(bset
);
2449 isl_basic_set_free(bset
);
2450 isl_factorizer_free(f
);
2452 isl_die(ctx
, isl_error_unknown
,
2453 "failed to construct factorizer", return -1);
2455 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2456 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2457 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2458 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2459 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2460 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2461 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2462 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2463 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2464 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2465 bset
= isl_basic_set_read_from_str(ctx
, str
);
2466 f
= isl_basic_set_factorizer(bset
);
2467 isl_basic_set_free(bset
);
2468 isl_factorizer_free(f
);
2470 isl_die(ctx
, isl_error_unknown
,
2471 "failed to construct factorizer", return -1);
2476 static int check_injective(__isl_take isl_map
*map
, void *user
)
2478 int *injective
= user
;
2480 *injective
= isl_map_is_injective(map
);
2483 if (*injective
< 0 || !*injective
)
2489 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
2490 const char *r
, const char *s
, int tilable
, int parallel
)
2494 isl_union_map
*W
, *R
, *S
;
2495 isl_union_map
*empty
;
2496 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
2497 isl_union_map
*validity
, *proximity
, *coincidence
;
2498 isl_union_map
*schedule
;
2499 isl_union_map
*test
;
2500 isl_union_set
*delta
;
2501 isl_union_set
*domain
;
2505 isl_schedule_constraints
*sc
;
2506 isl_schedule
*sched
;
2507 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
2509 D
= isl_union_set_read_from_str(ctx
, d
);
2510 W
= isl_union_map_read_from_str(ctx
, w
);
2511 R
= isl_union_map_read_from_str(ctx
, r
);
2512 S
= isl_union_map_read_from_str(ctx
, s
);
2514 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
2515 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
2517 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
2518 isl_union_map_compute_flow(isl_union_map_copy(R
),
2519 isl_union_map_copy(W
), empty
,
2520 isl_union_map_copy(S
),
2521 &dep_raw
, NULL
, NULL
, NULL
);
2522 isl_union_map_compute_flow(isl_union_map_copy(W
),
2523 isl_union_map_copy(W
),
2524 isl_union_map_copy(R
),
2525 isl_union_map_copy(S
),
2526 &dep_waw
, &dep_war
, NULL
, NULL
);
2528 dep
= isl_union_map_union(dep_waw
, dep_war
);
2529 dep
= isl_union_map_union(dep
, dep_raw
);
2530 validity
= isl_union_map_copy(dep
);
2531 coincidence
= isl_union_map_copy(dep
);
2532 proximity
= isl_union_map_copy(dep
);
2534 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
2535 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
2536 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
2537 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
2538 sched
= isl_schedule_constraints_compute_schedule(sc
);
2539 schedule
= isl_schedule_get_map(sched
);
2540 isl_schedule_free(sched
);
2541 isl_union_map_free(W
);
2542 isl_union_map_free(R
);
2543 isl_union_map_free(S
);
2546 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
2548 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
2549 is_complete
= isl_union_set_is_subset(D
, domain
);
2550 isl_union_set_free(D
);
2551 isl_union_set_free(domain
);
2553 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
2554 test
= isl_union_map_apply_range(test
, dep
);
2555 test
= isl_union_map_apply_range(test
, schedule
);
2557 delta
= isl_union_map_deltas(test
);
2558 if (isl_union_set_n_set(delta
) == 0) {
2562 isl_union_set_free(delta
);
2564 delta_set
= isl_set_from_union_set(delta
);
2566 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2567 for (i
= 0; i
< tilable
; ++i
)
2568 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
2569 is_tilable
= isl_set_is_subset(delta_set
, slice
);
2570 isl_set_free(slice
);
2572 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2573 for (i
= 0; i
< parallel
; ++i
)
2574 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
2575 is_parallel
= isl_set_is_subset(delta_set
, slice
);
2576 isl_set_free(slice
);
2578 origin
= isl_set_universe(isl_set_get_space(delta_set
));
2579 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
2580 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2582 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2583 delta_set
= isl_set_lexmin(delta_set
);
2585 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2587 isl_set_free(origin
);
2588 isl_set_free(delta_set
);
2591 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2592 is_injection
< 0 || is_complete
< 0)
2595 isl_die(ctx
, isl_error_unknown
,
2596 "generated schedule incomplete", return -1);
2598 isl_die(ctx
, isl_error_unknown
,
2599 "generated schedule not injective on each statement",
2602 isl_die(ctx
, isl_error_unknown
,
2603 "negative dependences in generated schedule",
2606 isl_die(ctx
, isl_error_unknown
,
2607 "generated schedule not as tilable as expected",
2610 isl_die(ctx
, isl_error_unknown
,
2611 "generated schedule not as parallel as expected",
2617 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
2618 const char *domain
, const char *validity
, const char *proximity
)
2622 isl_union_map
*prox
;
2623 isl_schedule_constraints
*sc
;
2624 isl_schedule
*schedule
;
2625 isl_union_map
*sched
;
2627 dom
= isl_union_set_read_from_str(ctx
, domain
);
2628 dep
= isl_union_map_read_from_str(ctx
, validity
);
2629 prox
= isl_union_map_read_from_str(ctx
, proximity
);
2630 sc
= isl_schedule_constraints_on_domain(dom
);
2631 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
2632 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
2633 schedule
= isl_schedule_constraints_compute_schedule(sc
);
2634 sched
= isl_schedule_get_map(schedule
);
2635 isl_schedule_free(schedule
);
2640 /* Check that a schedule can be constructed on the given domain
2641 * with the given validity and proximity constraints.
2643 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
2644 const char *validity
, const char *proximity
)
2646 isl_union_map
*sched
;
2648 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
2652 isl_union_map_free(sched
);
2656 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
2657 const char *validity
, const char *proximity
, const char *expected_sched
)
2659 isl_union_map
*sched1
, *sched2
;
2662 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
2663 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
2665 equal
= isl_union_map_is_equal(sched1
, sched2
);
2666 isl_union_map_free(sched1
);
2667 isl_union_map_free(sched2
);
2672 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2678 /* Check that the schedule map is properly padded, even after being
2679 * reconstructed from the band forest.
2681 static int test_padded_schedule(isl_ctx
*ctx
)
2685 isl_union_map
*validity
, *proximity
;
2686 isl_schedule_constraints
*sc
;
2687 isl_schedule
*sched
;
2688 isl_union_map
*map1
, *map2
;
2689 isl_band_list
*list
;
2692 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2693 D
= isl_union_set_read_from_str(ctx
, str
);
2694 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
2695 proximity
= isl_union_map_copy(validity
);
2696 sc
= isl_schedule_constraints_on_domain(D
);
2697 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
2698 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
2699 sched
= isl_schedule_constraints_compute_schedule(sc
);
2700 map1
= isl_schedule_get_map(sched
);
2701 list
= isl_schedule_get_band_forest(sched
);
2702 isl_band_list_free(list
);
2703 map2
= isl_schedule_get_map(sched
);
2704 isl_schedule_free(sched
);
2705 equal
= isl_union_map_is_equal(map1
, map2
);
2706 isl_union_map_free(map1
);
2707 isl_union_map_free(map2
);
2712 isl_die(ctx
, isl_error_unknown
,
2713 "reconstructed schedule map not the same as original",
2719 /* Input for testing of schedule construction based on
2720 * conditional constraints.
2722 * domain is the iteration domain
2723 * flow are the flow dependences, which determine the validity and
2724 * proximity constraints
2725 * condition are the conditions on the conditional validity constraints
2726 * conditional_validity are the conditional validity constraints
2727 * outer_band_n is the expected number of members in the outer band
2732 const char *condition
;
2733 const char *conditional_validity
;
2735 } live_range_tests
[] = {
2736 /* Contrived example that illustrates that we need to keep
2737 * track of tagged condition dependences and
2738 * tagged conditional validity dependences
2739 * in isl_sched_edge separately.
2740 * In particular, the conditional validity constraints on A
2741 * cannot be satisfied,
2742 * but they can be ignored because there are no corresponding
2743 * condition constraints. However, we do have an additional
2744 * conditional validity constraint that maps to the same
2745 * dependence relation
2746 * as the condition constraint on B. If we did not make a distinction
2747 * between tagged condition and tagged conditional validity
2748 * dependences, then we
2749 * could end up treating this shared dependence as an condition
2750 * constraint on A, forcing a localization of the conditions,
2751 * which is impossible.
2753 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
2754 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
2755 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
2756 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2757 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2758 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
2761 /* TACO 2013 Fig. 7 */
2762 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2763 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2764 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2765 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
2766 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
2767 "0 <= i < n and 0 <= j < n - 1 }",
2768 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
2769 "0 <= i < n and 0 <= j < j' < n;"
2770 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
2771 "0 <= i < i' < n and 0 <= j,j' < n;"
2772 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
2773 "0 <= i,j,j' < n and j < j' }",
2776 /* TACO 2013 Fig. 7, without tags */
2777 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2778 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2779 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2780 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2781 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2782 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
2783 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
2784 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
2787 /* TACO 2013 Fig. 12 */
2788 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
2789 "S3[i,3] : 0 <= i <= 1 }",
2790 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
2791 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
2792 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
2793 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
2794 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2795 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
2796 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2797 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
2798 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
2799 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
2800 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
2805 /* Test schedule construction based on conditional constraints.
2806 * In particular, check the number of members in the outer band
2807 * as an indication of whether tiling is possible or not.
2809 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
2812 isl_union_set
*domain
;
2813 isl_union_map
*condition
;
2814 isl_union_map
*flow
;
2815 isl_union_map
*validity
;
2816 isl_schedule_constraints
*sc
;
2817 isl_schedule
*schedule
;
2818 isl_band_list
*list
;
2822 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
2823 domain
= isl_union_set_read_from_str(ctx
,
2824 live_range_tests
[i
].domain
);
2825 flow
= isl_union_map_read_from_str(ctx
,
2826 live_range_tests
[i
].flow
);
2827 condition
= isl_union_map_read_from_str(ctx
,
2828 live_range_tests
[i
].condition
);
2829 validity
= isl_union_map_read_from_str(ctx
,
2830 live_range_tests
[i
].conditional_validity
);
2831 sc
= isl_schedule_constraints_on_domain(domain
);
2832 sc
= isl_schedule_constraints_set_validity(sc
,
2833 isl_union_map_copy(flow
));
2834 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
2835 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
2836 condition
, validity
);
2837 schedule
= isl_schedule_constraints_compute_schedule(sc
);
2838 list
= isl_schedule_get_band_forest(schedule
);
2839 band
= isl_band_list_get_band(list
, 0);
2840 n_member
= isl_band_n_member(band
);
2841 isl_band_free(band
);
2842 isl_band_list_free(list
);
2843 isl_schedule_free(schedule
);
2847 if (n_member
!= live_range_tests
[i
].outer_band_n
)
2848 isl_die(ctx
, isl_error_unknown
,
2849 "unexpected number of members in outer band",
2855 int test_schedule(isl_ctx
*ctx
)
2857 const char *D
, *W
, *R
, *V
, *P
, *S
;
2859 /* Handle resulting schedule with zero bands. */
2860 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2864 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2865 W
= "{ S1[t,i] -> a[t,i] }";
2866 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2867 "S1[t,i] -> a[t-1,i+1] }";
2868 S
= "{ S1[t,i] -> [t,i] }";
2869 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2872 /* Fig. 5 of CC2008 */
2873 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2875 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2876 "j >= 2 and j <= -1 + N }";
2877 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2878 "j >= 2 and j <= -1 + N; "
2879 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2880 "j >= 2 and j <= -1 + N }";
2881 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2882 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2885 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2886 W
= "{ S1[i] -> a[i] }";
2887 R
= "{ S2[i] -> a[i+1] }";
2888 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2889 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2892 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2893 W
= "{ S1[i] -> a[i] }";
2894 R
= "{ S2[i] -> a[9-i] }";
2895 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2896 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2899 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2900 W
= "{ S1[i] -> a[i] }";
2901 R
= "[N] -> { S2[i] -> a[N-1-i] }";
2902 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2903 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2906 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2907 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2908 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2909 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2910 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2913 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2914 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2915 R
= "{ S2[i,j] -> a[i-1,j] }";
2916 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2917 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2920 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2921 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2922 R
= "{ S2[i,j] -> a[i,j-1] }";
2923 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2924 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2927 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2928 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2929 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2930 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2931 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2932 "S_0[] -> [0, 0, 0] }";
2933 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
2935 ctx
->opt
->schedule_parametric
= 0;
2936 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2938 ctx
->opt
->schedule_parametric
= 1;
2940 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2941 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2942 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2943 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2944 "S4[i] -> a[i,N] }";
2945 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2946 "S4[i] -> [4,i,0] }";
2947 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2950 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2951 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2953 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2955 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2957 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2958 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2961 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2962 " S_2[t] : t >= 0 and t <= -1 + N; "
2963 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2965 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2966 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2967 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2968 "i >= 0 and i <= -1 + N }";
2969 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2970 "i >= 0 and i <= -1 + N; "
2971 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2972 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2973 " S_0[t] -> [0, t, 0] }";
2975 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2977 ctx
->opt
->schedule_parametric
= 0;
2978 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2980 ctx
->opt
->schedule_parametric
= 1;
2982 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2983 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2984 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
2987 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
2988 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
2989 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
2990 "j >= 0 and j <= -1 + N; "
2991 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2992 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
2993 "j >= 0 and j <= -1 + N; "
2994 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
2995 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
2996 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2999 D
= "{ S_0[i] : i >= 0 }";
3000 W
= "{ S_0[i] -> a[i] : i >= 0 }";
3001 R
= "{ S_0[i] -> a[0] : i >= 0 }";
3002 S
= "{ S_0[i] -> [0, i, 0] }";
3003 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3006 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3007 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3008 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3009 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3010 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3013 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3014 "k <= -1 + n and k >= 0 }";
3015 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3016 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3017 "k <= -1 + n and k >= 0; "
3018 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3019 "k <= -1 + n and k >= 0; "
3020 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3021 "k <= -1 + n and k >= 0 }";
3022 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
3023 ctx
->opt
->schedule_outer_coincidence
= 1;
3024 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3026 ctx
->opt
->schedule_outer_coincidence
= 0;
3028 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
3029 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3030 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3031 "Stmt_for_body24[i0, i1, 1, 0]:"
3032 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3033 "Stmt_for_body7[i0, i1, i2]:"
3034 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3037 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
3038 "Stmt_for_body24[1, i1, i2, i3]:"
3039 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3041 "Stmt_for_body24[0, i1, i2, i3] -> "
3042 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3043 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3045 "Stmt_for_body24[0, i1, i2, i3] ->"
3046 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3047 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3048 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3049 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3050 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3051 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3052 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3053 "i1 <= 6 and i1 >= 0;"
3054 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3055 "Stmt_for_body7[i0, i1, i2] -> "
3056 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3057 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3058 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3059 "Stmt_for_body7[i0, i1, i2] -> "
3060 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3061 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3062 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3064 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3065 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3066 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3068 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3071 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3072 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3073 "j >= 1 and j <= 7;"
3074 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3075 "j >= 1 and j <= 8 }";
3077 S
= "{ S_0[i, j] -> [i + j, j] }";
3078 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3079 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3081 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3083 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3084 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3085 "j >= 0 and j <= -1 + i }";
3086 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3087 "i <= -1 + N and j >= 0;"
3088 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3091 S
= "{ S_0[i, j] -> [i, j] }";
3092 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3093 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3095 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3097 /* Test both algorithms on a case with only proximity dependences. */
3098 D
= "{ S[i,j] : 0 <= i <= 10 }";
3100 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3101 S
= "{ S[i, j] -> [j, i] }";
3102 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3103 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3105 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3106 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3109 D
= "{ A[a]; B[] }";
3111 P
= "{ A[a] -> B[] }";
3112 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3115 if (test_padded_schedule(ctx
) < 0)
3118 /* Check that check for progress is not confused by rational
3121 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3122 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3124 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3125 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3127 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3128 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3130 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3132 if (test_conditional_schedule_constraints(ctx
) < 0)
3138 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
3140 isl_union_map
*umap
;
3143 umap
= isl_union_map_read_from_str(ctx
, str
);
3144 test
= isl_union_map_plain_is_injective(umap
);
3145 isl_union_map_free(umap
);
3148 if (test
== injective
)
3151 isl_die(ctx
, isl_error_unknown
,
3152 "map not detected as injective", return -1);
3154 isl_die(ctx
, isl_error_unknown
,
3155 "map detected as injective", return -1);
3158 int test_injective(isl_ctx
*ctx
)
3162 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3164 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
3166 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
3168 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
3170 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3172 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3174 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3176 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3179 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3180 if (test_plain_injective(ctx
, str
, 1))
3182 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3183 if (test_plain_injective(ctx
, str
, 0))
3189 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
3197 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
3198 equal
= isl_aff_plain_is_equal(aff
, aff2
);
3204 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
3208 equal
= aff_plain_is_equal(aff
, str
);
3212 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
3213 "result not as expected", return -1);
3218 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3219 __isl_take isl_aff
*aff2
);
3221 ['+'] = { &isl_aff_add
},
3222 ['-'] = { &isl_aff_sub
},
3223 ['*'] = { &isl_aff_mul
},
3231 } aff_bin_tests
[] = {
3232 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3233 "{ [i] -> [2i] }" },
3234 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3236 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3237 "{ [i] -> [2i] }" },
3238 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3239 "{ [i] -> [2i] }" },
3240 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3241 "{ [i] -> [NaN] }" },
3242 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3243 "{ [i] -> [NaN] }" },
3244 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3245 "{ [i] -> [NaN] }" },
3246 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3247 "{ [i] -> [NaN] }" },
3248 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3249 "{ [i] -> [NaN] }" },
3250 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3251 "{ [i] -> [NaN] }" },
3252 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3253 "{ [i] -> [NaN] }" },
3254 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3255 "{ [i] -> [NaN] }" },
3258 /* Perform some basic tests of binary operations on isl_aff objects.
3260 static int test_bin_aff(isl_ctx
*ctx
)
3263 isl_aff
*aff1
, *aff2
, *res
;
3264 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3265 __isl_take isl_aff
*aff2
);
3268 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
3269 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
3270 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
3271 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
3272 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
3273 aff1
= fn(aff1
, aff2
);
3274 if (isl_aff_is_nan(res
))
3275 ok
= isl_aff_is_nan(aff1
);
3277 ok
= isl_aff_plain_is_equal(aff1
, res
);
3283 isl_die(ctx
, isl_error_unknown
,
3284 "unexpected result", return -1);
3290 int test_aff(isl_ctx
*ctx
)
3295 isl_local_space
*ls
;
3299 if (test_bin_aff(ctx
) < 0)
3302 space
= isl_space_set_alloc(ctx
, 0, 1);
3303 ls
= isl_local_space_from_space(space
);
3304 aff
= isl_aff_zero_on_domain(ls
);
3306 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3307 aff
= isl_aff_scale_down_ui(aff
, 3);
3308 aff
= isl_aff_floor(aff
);
3309 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3310 aff
= isl_aff_scale_down_ui(aff
, 2);
3311 aff
= isl_aff_floor(aff
);
3312 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3315 set
= isl_set_read_from_str(ctx
, str
);
3316 aff
= isl_aff_gist(aff
, set
);
3318 aff
= isl_aff_add_constant_si(aff
, -16);
3319 zero
= isl_aff_plain_is_zero(aff
);
3325 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3327 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
3328 aff
= isl_aff_scale_down_ui(aff
, 64);
3329 aff
= isl_aff_floor(aff
);
3330 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
3338 int test_dim_max(isl_ctx
*ctx
)
3342 isl_set
*set1
, *set2
;
3347 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
3348 set
= isl_set_read_from_str(ctx
, str
);
3349 pwaff
= isl_set_dim_max(set
, 0);
3350 set1
= isl_set_from_pw_aff(pwaff
);
3351 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
3352 set2
= isl_set_read_from_str(ctx
, str
);
3353 equal
= isl_set_is_equal(set1
, set2
);
3359 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3361 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
3362 set
= isl_set_read_from_str(ctx
, str
);
3363 pwaff
= isl_set_dim_max(set
, 0);
3364 set1
= isl_set_from_pw_aff(pwaff
);
3365 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3366 set2
= isl_set_read_from_str(ctx
, str
);
3367 equal
= isl_set_is_equal(set1
, set2
);
3373 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3375 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
3376 set
= isl_set_read_from_str(ctx
, str
);
3377 pwaff
= isl_set_dim_max(set
, 0);
3378 set1
= isl_set_from_pw_aff(pwaff
);
3379 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3380 set2
= isl_set_read_from_str(ctx
, str
);
3381 equal
= isl_set_is_equal(set1
, set2
);
3387 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3389 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
3390 "0 <= i < N and 0 <= j < M }";
3391 map
= isl_map_read_from_str(ctx
, str
);
3392 set
= isl_map_range(map
);
3394 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
3395 set1
= isl_set_from_pw_aff(pwaff
);
3396 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
3397 set2
= isl_set_read_from_str(ctx
, str
);
3398 equal
= isl_set_is_equal(set1
, set2
);
3402 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
3403 set1
= isl_set_from_pw_aff(pwaff
);
3404 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
3405 set2
= isl_set_read_from_str(ctx
, str
);
3406 if (equal
>= 0 && equal
)
3407 equal
= isl_set_is_equal(set1
, set2
);
3416 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3418 /* Check that solutions are properly merged. */
3419 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
3420 "c <= -1 + n - 4a - 2b and c >= -2b and "
3421 "4a >= -4 + n and c >= 0 }";
3422 set
= isl_set_read_from_str(ctx
, str
);
3423 pwaff
= isl_set_dim_min(set
, 2);
3424 set1
= isl_set_from_pw_aff(pwaff
);
3425 str
= "[n] -> { [(0)] : n >= 1 }";
3426 set2
= isl_set_read_from_str(ctx
, str
);
3427 equal
= isl_set_is_equal(set1
, set2
);
3434 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3436 /* Check that empty solution lie in the right space. */
3437 str
= "[n] -> { [t,a] : 1 = 0 }";
3438 set
= isl_set_read_from_str(ctx
, str
);
3439 pwaff
= isl_set_dim_max(set
, 0);
3440 set1
= isl_set_from_pw_aff(pwaff
);
3441 str
= "[n] -> { [t] : 1 = 0 }";
3442 set2
= isl_set_read_from_str(ctx
, str
);
3443 equal
= isl_set_is_equal(set1
, set2
);
3450 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3455 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
3457 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
3461 isl_pw_multi_aff
*pma2
;
3467 ctx
= isl_pw_multi_aff_get_ctx(pma
);
3468 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3469 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
3470 isl_pw_multi_aff_free(pma2
);
3475 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
3476 * represented by "str".
3478 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
3483 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
3487 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
3488 "result not as expected", return -1);
3492 /* Basic test for isl_pw_multi_aff_product.
3494 * Check that multiple pieces are properly handled.
3496 static int test_product_pma(isl_ctx
*ctx
)
3500 isl_pw_multi_aff
*pma1
, *pma2
;
3502 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
3503 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3504 str
= "{ C[] -> D[] }";
3505 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3506 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
3507 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
3508 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
3509 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
3510 isl_pw_multi_aff_free(pma1
);
3517 int test_product(isl_ctx
*ctx
)
3521 isl_union_set
*uset1
, *uset2
;
3525 set
= isl_set_read_from_str(ctx
, str
);
3526 set
= isl_set_product(set
, isl_set_copy(set
));
3527 ok
= isl_set_is_wrapping(set
);
3532 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3535 uset1
= isl_union_set_read_from_str(ctx
, str
);
3536 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
3537 str
= "{ [[] -> []] }";
3538 uset2
= isl_union_set_read_from_str(ctx
, str
);
3539 ok
= isl_union_set_is_equal(uset1
, uset2
);
3540 isl_union_set_free(uset1
);
3541 isl_union_set_free(uset2
);
3545 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3547 if (test_product_pma(ctx
) < 0)
3553 /* Check that two sets are not considered disjoint just because
3554 * they have a different set of (named) parameters.
3556 static int test_disjoint(isl_ctx
*ctx
)
3559 isl_set
*set
, *set2
;
3562 str
= "[n] -> { [[]->[]] }";
3563 set
= isl_set_read_from_str(ctx
, str
);
3564 str
= "{ [[]->[]] }";
3565 set2
= isl_set_read_from_str(ctx
, str
);
3566 disjoint
= isl_set_is_disjoint(set
, set2
);
3572 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3577 int test_equal(isl_ctx
*ctx
)
3580 isl_set
*set
, *set2
;
3584 set
= isl_set_read_from_str(ctx
, str
);
3586 set2
= isl_set_read_from_str(ctx
, str
);
3587 equal
= isl_set_is_equal(set
, set2
);
3593 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3598 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
3599 enum isl_dim_type type
, unsigned pos
, int fixed
)
3603 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
3610 isl_die(ctx
, isl_error_unknown
,
3611 "map not detected as fixed", return -1);
3613 isl_die(ctx
, isl_error_unknown
,
3614 "map detected as fixed", return -1);
3617 int test_fixed(isl_ctx
*ctx
)
3622 str
= "{ [i] -> [i] }";
3623 map
= isl_map_read_from_str(ctx
, str
);
3624 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
3626 str
= "{ [i] -> [1] }";
3627 map
= isl_map_read_from_str(ctx
, str
);
3628 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
3630 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
3631 map
= isl_map_read_from_str(ctx
, str
);
3632 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
3634 map
= isl_map_read_from_str(ctx
, str
);
3635 map
= isl_map_neg(map
);
3636 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
3642 struct isl_vertices_test_data
{
3645 const char *vertex
[2];
3646 } vertices_tests
[] = {
3647 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
3648 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
3649 { "{ A[t, i] : t = 14 and i = 1 }",
3650 1, { "{ A[14, 1] }" } },
3653 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
3655 static int find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
3657 struct isl_vertices_test_data
*data
= user
;
3660 isl_basic_set
*bset
;
3661 isl_pw_multi_aff
*pma
;
3665 ctx
= isl_vertex_get_ctx(vertex
);
3666 bset
= isl_vertex_get_domain(vertex
);
3667 ma
= isl_vertex_get_expr(vertex
);
3668 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
3670 for (i
= 0; i
< data
->n
; ++i
) {
3671 isl_pw_multi_aff
*pma_i
;
3673 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
3674 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
3675 isl_pw_multi_aff_free(pma_i
);
3677 if (equal
< 0 || equal
)
3681 isl_pw_multi_aff_free(pma
);
3682 isl_vertex_free(vertex
);
3687 return equal
? 0 : - 1;
3690 int test_vertices(isl_ctx
*ctx
)
3694 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
3695 isl_basic_set
*bset
;
3696 isl_vertices
*vertices
;
3700 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
3701 vertices
= isl_basic_set_compute_vertices(bset
);
3702 n
= isl_vertices_get_n_vertices(vertices
);
3703 if (vertices_tests
[i
].n
!= n
)
3705 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
3706 &vertices_tests
[i
]) < 0)
3708 isl_vertices_free(vertices
);
3709 isl_basic_set_free(bset
);
3714 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
3721 int test_union_pw(isl_ctx
*ctx
)
3725 isl_union_set
*uset
;
3726 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
3728 str
= "{ [x] -> x^2 }";
3729 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
3730 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
3731 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
3732 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
3733 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
3734 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
3735 isl_union_pw_qpolynomial_free(upwqp1
);
3736 isl_union_pw_qpolynomial_free(upwqp2
);
3740 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3745 int test_output(isl_ctx
*ctx
)
3753 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
3754 pa
= isl_pw_aff_read_from_str(ctx
, str
);
3756 p
= isl_printer_to_str(ctx
);
3757 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
3758 p
= isl_printer_print_pw_aff(p
, pa
);
3759 s
= isl_printer_get_str(p
);
3760 isl_printer_free(p
);
3761 isl_pw_aff_free(pa
);
3765 equal
= !strcmp(s
, "(2 - x + 4*floord(x, 4) >= 0) ? (1) : 2");
3770 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3775 int test_sample(isl_ctx
*ctx
)
3778 isl_basic_set
*bset1
, *bset2
;
3781 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
3782 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
3783 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
3784 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
3785 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
3786 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
3787 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
3788 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
3789 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3790 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3791 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3792 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3793 "d - 1073741821e and "
3794 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3795 "3j >= 1 - a + b + 2e and "
3796 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3797 "3i <= 4 - a + 4b - e and "
3798 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3799 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3800 "c <= -1 + a and 3i >= -2 - a + 3e and "
3801 "1073741822e <= 1073741823 - a + 1073741822b + c and "
3802 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3803 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3804 "1073741823e >= 1 + 1073741823b - d and "
3805 "3i >= 1073741823b + c - 1073741823e - f and "
3806 "3i >= 1 + 2b + e + 3g }";
3807 bset1
= isl_basic_set_read_from_str(ctx
, str
);
3808 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
3809 empty
= isl_basic_set_is_empty(bset2
);
3810 subset
= isl_basic_set_is_subset(bset2
, bset1
);
3811 isl_basic_set_free(bset1
);
3812 isl_basic_set_free(bset2
);
3813 if (empty
< 0 || subset
< 0)
3816 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
3818 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
3823 int test_fixed_power(isl_ctx
*ctx
)
3831 str
= "{ [i] -> [i + 1] }";
3832 map
= isl_map_read_from_str(ctx
, str
);
3833 isl_int_set_si(exp
, 23);
3834 map
= isl_map_fixed_power(map
, exp
);
3835 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
3844 int test_slice(isl_ctx
*ctx
)
3850 str
= "{ [i] -> [j] }";
3851 map
= isl_map_read_from_str(ctx
, str
);
3852 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3853 equal
= map_check_equal(map
, "{ [i] -> [i] }");
3858 str
= "{ [i] -> [j] }";
3859 map
= isl_map_read_from_str(ctx
, str
);
3860 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3861 equal
= map_check_equal(map
, "{ [i] -> [j] }");
3866 str
= "{ [i] -> [j] }";
3867 map
= isl_map_read_from_str(ctx
, str
);
3868 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3869 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
3874 str
= "{ [i] -> [j] }";
3875 map
= isl_map_read_from_str(ctx
, str
);
3876 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3877 equal
= map_check_equal(map
, "{ [0] -> [j] }");
3882 str
= "{ [i] -> [j] }";
3883 map
= isl_map_read_from_str(ctx
, str
);
3884 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3885 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
3890 str
= "{ [i] -> [j] }";
3891 map
= isl_map_read_from_str(ctx
, str
);
3892 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3893 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
3901 int test_eliminate(isl_ctx
*ctx
)
3907 str
= "{ [i] -> [j] : i = 2j }";
3908 map
= isl_map_read_from_str(ctx
, str
);
3909 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
3910 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
3918 /* Check that isl_set_dim_residue_class detects that the values of j
3919 * in the set below are all odd and that it does not detect any spurious
3922 static int test_residue_class(isl_ctx
*ctx
)
3929 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3930 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3931 set
= isl_set_read_from_str(ctx
, str
);
3934 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
3936 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
3937 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
3946 int test_align_parameters(isl_ctx
*ctx
)
3950 isl_multi_aff
*ma1
, *ma2
;
3953 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3954 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
3956 space
= isl_space_params_alloc(ctx
, 1);
3957 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
3958 ma1
= isl_multi_aff_align_params(ma1
, space
);
3960 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3961 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
3963 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
3965 isl_multi_aff_free(ma1
);
3966 isl_multi_aff_free(ma2
);
3971 isl_die(ctx
, isl_error_unknown
,
3972 "result not as expected", return -1);
3977 static int test_list(isl_ctx
*ctx
)
3979 isl_id
*a
, *b
, *c
, *d
, *id
;
3983 a
= isl_id_alloc(ctx
, "a", NULL
);
3984 b
= isl_id_alloc(ctx
, "b", NULL
);
3985 c
= isl_id_alloc(ctx
, "c", NULL
);
3986 d
= isl_id_alloc(ctx
, "d", NULL
);
3988 list
= isl_id_list_alloc(ctx
, 4);
3989 list
= isl_id_list_add(list
, a
);
3990 list
= isl_id_list_add(list
, b
);
3991 list
= isl_id_list_add(list
, c
);
3992 list
= isl_id_list_add(list
, d
);
3993 list
= isl_id_list_drop(list
, 1, 1);
3995 if (isl_id_list_n_id(list
) != 3) {
3996 isl_id_list_free(list
);
3997 isl_die(ctx
, isl_error_unknown
,
3998 "unexpected number of elements in list", return -1);
4001 id
= isl_id_list_get_id(list
, 0);
4004 id
= isl_id_list_get_id(list
, 1);
4007 id
= isl_id_list_get_id(list
, 2);
4011 isl_id_list_free(list
);
4014 isl_die(ctx
, isl_error_unknown
,
4015 "unexpected elements in list", return -1);
4020 const char *set_conversion_tests
[] = {
4021 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4022 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4023 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4024 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4027 /* Check that converting from isl_set to isl_pw_multi_aff and back
4028 * to isl_set produces the original isl_set.
4030 static int test_set_conversion(isl_ctx
*ctx
)
4034 isl_set
*set1
, *set2
;
4035 isl_pw_multi_aff
*pma
;
4038 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
4039 str
= set_conversion_tests
[i
];
4040 set1
= isl_set_read_from_str(ctx
, str
);
4041 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
4042 set2
= isl_set_from_pw_multi_aff(pma
);
4043 equal
= isl_set_is_equal(set1
, set2
);
4050 isl_die(ctx
, isl_error_unknown
, "bad conversion",
4057 /* Check that converting from isl_map to isl_pw_multi_aff and back
4058 * to isl_map produces the original isl_map.
4060 static int test_map_conversion(isl_ctx
*ctx
)
4063 isl_map
*map1
, *map2
;
4064 isl_pw_multi_aff
*pma
;
4067 str
= "{ [a, b, c, d] -> s0[a, b, e, f] : "
4068 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4069 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4070 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4072 map1
= isl_map_read_from_str(ctx
, str
);
4073 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
4074 map2
= isl_map_from_pw_multi_aff(pma
);
4075 equal
= isl_map_is_equal(map1
, map2
);
4082 isl_die(ctx
, isl_error_unknown
, "bad conversion", return -1);
4087 static int test_conversion(isl_ctx
*ctx
)
4089 if (test_set_conversion(ctx
) < 0)
4091 if (test_map_conversion(ctx
) < 0)
4096 /* Check that isl_basic_map_curry does not modify input.
4098 static int test_curry(isl_ctx
*ctx
)
4101 isl_basic_map
*bmap1
, *bmap2
;
4104 str
= "{ [A[] -> B[]] -> C[] }";
4105 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
4106 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
4107 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
4108 isl_basic_map_free(bmap1
);
4109 isl_basic_map_free(bmap2
);
4114 isl_die(ctx
, isl_error_unknown
,
4115 "curried map should not be equal to original",
4125 } preimage_tests
[] = {
4126 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4127 "{ A[j,i] -> B[i,j] }",
4128 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4129 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4130 "{ A[a,b] -> B[a/2,b/6] }",
4131 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4132 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4133 "{ A[a,b] -> B[a/2,b/6] }",
4134 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4135 "exists i,j : a = 2 i and b = 6 j }" },
4136 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4137 "[n] -> { : 0 <= n <= 100 }" },
4138 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4139 "{ A[a] -> B[2a] }",
4140 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4141 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4142 "{ A[a] -> B[([a/2])] }",
4143 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4144 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4145 "{ A[a] -> B[a,a,a/3] }",
4146 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4147 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4148 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4151 static int test_preimage_basic_set(isl_ctx
*ctx
)
4154 isl_basic_set
*bset1
, *bset2
;
4158 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
4159 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
4160 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
4161 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
4162 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
4163 equal
= isl_basic_set_is_equal(bset1
, bset2
);
4164 isl_basic_set_free(bset1
);
4165 isl_basic_set_free(bset2
);
4169 isl_die(ctx
, isl_error_unknown
, "bad preimage",
4180 } preimage_domain_tests
[] = {
4181 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4182 "{ A[j,i] -> B[i,j] }",
4183 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4184 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4185 "{ A[i] -> B[i + 1] }",
4186 "{ A[i] -> C[i + 1] }" },
4187 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4188 "{ A[i] -> B[i + 1] }",
4189 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4190 { "{ B[i] -> C[([i/2])] }",
4191 "{ A[i] -> B[2i] }",
4192 "{ A[i] -> C[i] }" },
4193 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4194 "{ A[i] -> B[([i/5]), ([i/7])] }",
4195 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4196 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4197 "[N] -> { A[] -> B[([N/5])] }",
4198 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4199 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4200 "{ A[i] -> B[2i] }",
4201 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4202 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4203 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4204 "{ A[i] -> B[2i] }",
4205 "{ A[i] -> C[2i] }" },
4208 static int test_preimage_union_map(isl_ctx
*ctx
)
4211 isl_union_map
*umap1
, *umap2
;
4215 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
4216 umap1
= isl_union_map_read_from_str(ctx
,
4217 preimage_domain_tests
[i
].map
);
4218 ma
= isl_multi_aff_read_from_str(ctx
,
4219 preimage_domain_tests
[i
].ma
);
4220 umap2
= isl_union_map_read_from_str(ctx
,
4221 preimage_domain_tests
[i
].res
);
4222 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
4223 equal
= isl_union_map_is_equal(umap1
, umap2
);
4224 isl_union_map_free(umap1
);
4225 isl_union_map_free(umap2
);
4229 isl_die(ctx
, isl_error_unknown
, "bad preimage",
4236 static int test_preimage(isl_ctx
*ctx
)
4238 if (test_preimage_basic_set(ctx
) < 0)
4240 if (test_preimage_union_map(ctx
) < 0)
4250 } pullback_tests
[] = {
4251 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
4252 "{ A[a,b] -> C[b + 2a] }" },
4253 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
4254 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
4255 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
4256 "{ A[a] -> C[(a)/6] }" },
4257 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
4258 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
4259 "{ A[a] -> C[(2a)/3] }" },
4260 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
4261 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
4262 "{ A[i,j] -> C[i + j, i + j] }"},
4263 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
4264 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
4265 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
4268 static int test_pullback(isl_ctx
*ctx
)
4271 isl_multi_aff
*ma1
, *ma2
;
4275 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
4276 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
4277 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
4278 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
4279 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
4280 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
4281 isl_multi_aff_free(ma1
);
4282 isl_multi_aff_free(ma2
);
4286 isl_die(ctx
, isl_error_unknown
, "bad pullback",
4293 /* Check that negation is printed correctly.
4295 static int test_ast(isl_ctx
*ctx
)
4297 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
4301 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
4302 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
4303 expr
= isl_ast_expr_add(expr1
, expr2
);
4304 expr
= isl_ast_expr_neg(expr
);
4305 str
= isl_ast_expr_to_str(expr
);
4306 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
4308 isl_ast_expr_free(expr
);
4313 isl_die(ctx
, isl_error_unknown
,
4314 "isl_ast_expr printed incorrectly", return -1);
4316 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
4317 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
4318 expr
= isl_ast_expr_add(expr1
, expr2
);
4319 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
4320 expr
= isl_ast_expr_sub(expr3
, expr
);
4321 str
= isl_ast_expr_to_str(expr
);
4322 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
4324 isl_ast_expr_free(expr
);
4329 isl_die(ctx
, isl_error_unknown
,
4330 "isl_ast_expr printed incorrectly", return -1);
4335 /* Check that isl_ast_build_expr_from_set returns a valid expression
4336 * for an empty set. Note that isl_ast_build_expr_from_set getting
4337 * called on an empty set probably indicates a bug in the caller.
4339 static int test_ast_build(isl_ctx
*ctx
)
4342 isl_ast_build
*build
;
4345 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4346 build
= isl_ast_build_from_context(set
);
4348 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
4349 expr
= isl_ast_build_expr_from_set(build
, set
);
4351 isl_ast_expr_free(expr
);
4352 isl_ast_build_free(build
);
4360 /* Internal data structure for before_for and after_for callbacks.
4362 * depth is the current depth
4363 * before is the number of times before_for has been called
4364 * after is the number of times after_for has been called
4366 struct isl_test_codegen_data
{
4372 /* This function is called before each for loop in the AST generated
4373 * from test_ast_gen1.
4375 * Increment the number of calls and the depth.
4376 * Check that the space returned by isl_ast_build_get_schedule_space
4377 * matches the target space of the schedule returned by
4378 * isl_ast_build_get_schedule.
4379 * Return an isl_id that is checked by the corresponding call
4382 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
4385 struct isl_test_codegen_data
*data
= user
;
4388 isl_union_map
*schedule
;
4389 isl_union_set
*uset
;
4394 ctx
= isl_ast_build_get_ctx(build
);
4396 if (data
->before
>= 3)
4397 isl_die(ctx
, isl_error_unknown
,
4398 "unexpected number of for nodes", return NULL
);
4399 if (data
->depth
>= 2)
4400 isl_die(ctx
, isl_error_unknown
,
4401 "unexpected depth", return NULL
);
4403 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
4407 schedule
= isl_ast_build_get_schedule(build
);
4408 uset
= isl_union_map_range(schedule
);
4411 if (isl_union_set_n_set(uset
) != 1) {
4412 isl_union_set_free(uset
);
4413 isl_die(ctx
, isl_error_unknown
,
4414 "expecting single range space", return NULL
);
4417 space
= isl_ast_build_get_schedule_space(build
);
4418 set
= isl_union_set_extract_set(uset
, space
);
4419 isl_union_set_free(uset
);
4420 empty
= isl_set_is_empty(set
);
4426 isl_die(ctx
, isl_error_unknown
,
4427 "spaces don't match", return NULL
);
4429 return isl_id_alloc(ctx
, name
, NULL
);
4432 /* This function is called after each for loop in the AST generated
4433 * from test_ast_gen1.
4435 * Increment the number of calls and decrement the depth.
4436 * Check that the annotation attached to the node matches
4437 * the isl_id returned by the corresponding call to before_for.
4439 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
4440 __isl_keep isl_ast_build
*build
, void *user
)
4442 struct isl_test_codegen_data
*data
= user
;
4450 if (data
->after
> data
->before
)
4451 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
4452 "mismatch in number of for nodes",
4453 return isl_ast_node_free(node
));
4455 id
= isl_ast_node_get_annotation(node
);
4457 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
4458 "missing annotation", return isl_ast_node_free(node
));
4460 name
= isl_id_get_name(id
);
4461 valid
= name
&& atoi(name
+ 1) == data
->depth
;
4465 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
4466 "wrong annotation", return isl_ast_node_free(node
));
4471 /* Check that the before_each_for and after_each_for callbacks
4472 * are called for each for loop in the generated code,
4473 * that they are called in the right order and that the isl_id
4474 * returned from the before_each_for callback is attached to
4475 * the isl_ast_node passed to the corresponding after_each_for call.
4477 static int test_ast_gen1(isl_ctx
*ctx
)
4481 isl_union_map
*schedule
;
4482 isl_ast_build
*build
;
4484 struct isl_test_codegen_data data
;
4486 str
= "[N] -> { : N >= 10 }";
4487 set
= isl_set_read_from_str(ctx
, str
);
4488 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
4489 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
4490 schedule
= isl_union_map_read_from_str(ctx
, str
);
4495 build
= isl_ast_build_from_context(set
);
4496 build
= isl_ast_build_set_before_each_for(build
,
4497 &before_for
, &data
);
4498 build
= isl_ast_build_set_after_each_for(build
,
4500 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4501 isl_ast_build_free(build
);
4505 isl_ast_node_free(tree
);
4507 if (data
.before
!= 3 || data
.after
!= 3)
4508 isl_die(ctx
, isl_error_unknown
,
4509 "unexpected number of for nodes", return -1);
4514 /* Check that the AST generator handles domains that are integrally disjoint
4515 * but not ratinoally disjoint.
4517 static int test_ast_gen2(isl_ctx
*ctx
)
4521 isl_union_map
*schedule
;
4522 isl_union_map
*options
;
4523 isl_ast_build
*build
;
4526 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
4527 schedule
= isl_union_map_read_from_str(ctx
, str
);
4528 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4529 build
= isl_ast_build_from_context(set
);
4531 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
4532 options
= isl_union_map_read_from_str(ctx
, str
);
4533 build
= isl_ast_build_set_options(build
, options
);
4534 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4535 isl_ast_build_free(build
);
4538 isl_ast_node_free(tree
);
4543 /* Increment *user on each call.
4545 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
4546 __isl_keep isl_ast_build
*build
, void *user
)
4555 /* Test that unrolling tries to minimize the number of instances.
4556 * In particular, for the schedule given below, make sure it generates
4557 * 3 nodes (rather than 101).
4559 static int test_ast_gen3(isl_ctx
*ctx
)
4563 isl_union_map
*schedule
;
4564 isl_union_map
*options
;
4565 isl_ast_build
*build
;
4569 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
4570 schedule
= isl_union_map_read_from_str(ctx
, str
);
4571 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4573 str
= "{ [i] -> unroll[0] }";
4574 options
= isl_union_map_read_from_str(ctx
, str
);
4576 build
= isl_ast_build_from_context(set
);
4577 build
= isl_ast_build_set_options(build
, options
);
4578 build
= isl_ast_build_set_at_each_domain(build
,
4579 &count_domains
, &n_domain
);
4580 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4581 isl_ast_build_free(build
);
4585 isl_ast_node_free(tree
);
4588 isl_die(ctx
, isl_error_unknown
,
4589 "unexpected number of for nodes", return -1);
4594 /* Check that if the ast_build_exploit_nested_bounds options is set,
4595 * we do not get an outer if node in the generated AST,
4596 * while we do get such an outer if node if the options is not set.
4598 static int test_ast_gen4(isl_ctx
*ctx
)
4602 isl_union_map
*schedule
;
4603 isl_ast_build
*build
;
4605 enum isl_ast_node_type type
;
4608 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
4609 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
4611 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
4613 schedule
= isl_union_map_read_from_str(ctx
, str
);
4614 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4615 build
= isl_ast_build_from_context(set
);
4616 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4617 isl_ast_build_free(build
);
4621 type
= isl_ast_node_get_type(tree
);
4622 isl_ast_node_free(tree
);
4624 if (type
== isl_ast_node_if
)
4625 isl_die(ctx
, isl_error_unknown
,
4626 "not expecting if node", return -1);
4628 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
4630 schedule
= isl_union_map_read_from_str(ctx
, str
);
4631 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4632 build
= isl_ast_build_from_context(set
);
4633 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4634 isl_ast_build_free(build
);
4638 type
= isl_ast_node_get_type(tree
);
4639 isl_ast_node_free(tree
);
4641 if (type
!= isl_ast_node_if
)
4642 isl_die(ctx
, isl_error_unknown
,
4643 "expecting if node", return -1);
4645 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
4650 /* This function is called for each leaf in the AST generated
4651 * from test_ast_gen5.
4653 * We finalize the AST generation by extending the outer schedule
4654 * with a zero-dimensional schedule. If this results in any for loops,
4655 * then this means that we did not pass along enough information
4656 * about the outer schedule to the inner AST generation.
4658 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
4661 isl_union_map
*schedule
, *extra
;
4664 schedule
= isl_ast_build_get_schedule(build
);
4665 extra
= isl_union_map_copy(schedule
);
4666 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
4667 schedule
= isl_union_map_range_product(schedule
, extra
);
4668 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4669 isl_ast_build_free(build
);
4674 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
4675 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
4676 "code should not contain any for loop",
4677 return isl_ast_node_free(tree
));
4682 /* Check that we do not lose any information when going back and
4683 * forth between internal and external schedule.
4685 * In particular, we create an AST where we unroll the only
4686 * non-constant dimension in the schedule. We therefore do
4687 * not expect any for loops in the AST. However, older versions
4688 * of isl would not pass along enough information about the outer
4689 * schedule when performing an inner code generation from a create_leaf
4690 * callback, resulting in the inner code generation producing a for loop.
4692 static int test_ast_gen5(isl_ctx
*ctx
)
4696 isl_union_map
*schedule
, *options
;
4697 isl_ast_build
*build
;
4700 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
4701 schedule
= isl_union_map_read_from_str(ctx
, str
);
4703 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
4704 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
4705 options
= isl_union_map_read_from_str(ctx
, str
);
4707 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4708 build
= isl_ast_build_from_context(set
);
4709 build
= isl_ast_build_set_options(build
, options
);
4710 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
4711 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4712 isl_ast_build_free(build
);
4713 isl_ast_node_free(tree
);
4720 static int test_ast_gen(isl_ctx
*ctx
)
4722 if (test_ast_gen1(ctx
) < 0)
4724 if (test_ast_gen2(ctx
) < 0)
4726 if (test_ast_gen3(ctx
) < 0)
4728 if (test_ast_gen4(ctx
) < 0)
4730 if (test_ast_gen5(ctx
) < 0)
4735 /* Check if dropping output dimensions from an isl_pw_multi_aff
4738 static int test_pw_multi_aff(isl_ctx
*ctx
)
4741 isl_pw_multi_aff
*pma1
, *pma2
;
4744 str
= "{ [i,j] -> [i+j, 4i-j] }";
4745 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4746 str
= "{ [i,j] -> [4i-j] }";
4747 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4749 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
4751 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
4753 isl_pw_multi_aff_free(pma1
);
4754 isl_pw_multi_aff_free(pma2
);
4758 isl_die(ctx
, isl_error_unknown
,
4759 "expressions not equal", return -1);
4764 /* Check that we can properly parse multi piecewise affine expressions
4765 * where the piecewise affine expressions have different domains.
4767 static int test_multi_pw_aff(isl_ctx
*ctx
)
4770 isl_set
*dom
, *dom2
;
4771 isl_multi_pw_aff
*mpa1
, *mpa2
;
4776 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
4777 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
4778 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
4779 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
4780 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
4781 str
= "{ [i] -> [(i : i > 0), 2i] }";
4782 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
4784 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
4786 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
4787 dom
= isl_pw_aff_domain(pa
);
4788 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
4789 dom2
= isl_pw_aff_domain(pa
);
4790 equal_domain
= isl_set_is_equal(dom
, dom2
);
4794 isl_multi_pw_aff_free(mpa1
);
4795 isl_multi_pw_aff_free(mpa2
);
4800 isl_die(ctx
, isl_error_unknown
,
4801 "expressions not equal", return -1);
4803 if (equal_domain
< 0)
4806 isl_die(ctx
, isl_error_unknown
,
4807 "domains unexpectedly equal", return -1);
4812 /* This is a regression test for a bug where isl_basic_map_simplify
4813 * would end up in an infinite loop. In particular, we construct
4814 * an empty basic set that is not obviously empty.
4815 * isl_basic_set_is_empty marks the basic set as empty.
4816 * After projecting out i3, the variable can be dropped completely,
4817 * but isl_basic_map_simplify refrains from doing so if the basic set
4818 * is empty and would end up in an infinite loop if it didn't test
4819 * explicitly for empty basic maps in the outer loop.
4821 static int test_simplify(isl_ctx
*ctx
)
4824 isl_basic_set
*bset
;
4827 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
4828 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
4829 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
4831 bset
= isl_basic_set_read_from_str(ctx
, str
);
4832 empty
= isl_basic_set_is_empty(bset
);
4833 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
4834 isl_basic_set_free(bset
);
4838 isl_die(ctx
, isl_error_unknown
,
4839 "basic set should be empty", return -1);
4844 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
4845 * with gbr context would fail to disable the use of the shifted tableau
4846 * when transferring equalities for the input to the context, resulting
4847 * in invalid sample values.
4849 static int test_partial_lexmin(isl_ctx
*ctx
)
4852 isl_basic_set
*bset
;
4853 isl_basic_map
*bmap
;
4856 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
4857 bmap
= isl_basic_map_read_from_str(ctx
, str
);
4858 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
4859 bset
= isl_basic_set_read_from_str(ctx
, str
);
4860 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
4869 /* Check that the variable compression performed on the existentially
4870 * quantified variables inside isl_basic_set_compute_divs is not confused
4871 * by the implicit equalities among the parameters.
4873 static int test_compute_divs(isl_ctx
*ctx
)
4876 isl_basic_set
*bset
;
4879 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
4880 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
4881 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
4882 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
4883 bset
= isl_basic_set_read_from_str(ctx
, str
);
4884 set
= isl_basic_set_compute_divs(bset
);
4894 int (*fn
)(isl_ctx
*ctx
);
4896 { "dependence analysis", &test_flow
},
4897 { "val", &test_val
},
4898 { "compute divs", &test_compute_divs
},
4899 { "partial lexmin", &test_partial_lexmin
},
4900 { "simplify", &test_simplify
},
4901 { "curry", &test_curry
},
4902 { "piecewise multi affine expressions", &test_pw_multi_aff
},
4903 { "multi piecewise affine expressions", &test_multi_pw_aff
},
4904 { "conversion", &test_conversion
},
4905 { "list", &test_list
},
4906 { "align parameters", &test_align_parameters
},
4907 { "preimage", &test_preimage
},
4908 { "pullback", &test_pullback
},
4909 { "AST", &test_ast
},
4910 { "AST build", &test_ast_build
},
4911 { "AST generation", &test_ast_gen
},
4912 { "eliminate", &test_eliminate
},
4913 { "residue class", &test_residue_class
},
4914 { "div", &test_div
},
4915 { "slice", &test_slice
},
4916 { "fixed power", &test_fixed_power
},
4917 { "sample", &test_sample
},
4918 { "output", &test_output
},
4919 { "vertices", &test_vertices
},
4920 { "fixed", &test_fixed
},
4921 { "equal", &test_equal
},
4922 { "disjoint", &test_disjoint
},
4923 { "product", &test_product
},
4924 { "dim_max", &test_dim_max
},
4925 { "affine", &test_aff
},
4926 { "injective", &test_injective
},
4927 { "schedule", &test_schedule
},
4928 { "union_pw", &test_union_pw
},
4929 { "parse", &test_parse
},
4930 { "single-valued", &test_sv
},
4931 { "affine hull", &test_affine_hull
},
4932 { "coalesce", &test_coalesce
},
4933 { "factorize", &test_factorize
},
4934 { "subset", &test_subset
},
4935 { "subtract", &test_subtract
},
4936 { "lexmin", &test_lexmin
},
4937 { "min", &test_min
},
4938 { "gist", &test_gist
},
4939 { "piecewise quasi-polynomials", &test_pwqp
},
4945 struct isl_ctx
*ctx
;
4947 srcdir
= getenv("srcdir");
4950 ctx
= isl_ctx_alloc();
4951 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
4952 printf("%s\n", tests
[i
].name
);
4953 if (tests
[i
].fn(ctx
) < 0)
4959 test_split_periods(ctx
);
4961 test_bijective(ctx
);
4965 test_construction(ctx
);
4967 test_application(ctx
);
4968 test_convex_hull(ctx
);