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
);
1059 } convex_hull_tests
[] = {
1060 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1061 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1062 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1063 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1064 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1065 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1066 "i2 <= 5 and i2 >= 4; "
1067 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1068 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1069 "i2 <= 5 + i0 and i2 >= i0 }" },
1072 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
1075 int orig_convex
= ctx
->opt
->convex
;
1076 ctx
->opt
->convex
= convex
;
1078 test_convex_hull_case(ctx
, "convex0");
1079 test_convex_hull_case(ctx
, "convex1");
1080 test_convex_hull_case(ctx
, "convex2");
1081 test_convex_hull_case(ctx
, "convex3");
1082 test_convex_hull_case(ctx
, "convex4");
1083 test_convex_hull_case(ctx
, "convex5");
1084 test_convex_hull_case(ctx
, "convex6");
1085 test_convex_hull_case(ctx
, "convex7");
1086 test_convex_hull_case(ctx
, "convex8");
1087 test_convex_hull_case(ctx
, "convex9");
1088 test_convex_hull_case(ctx
, "convex10");
1089 test_convex_hull_case(ctx
, "convex11");
1090 test_convex_hull_case(ctx
, "convex12");
1091 test_convex_hull_case(ctx
, "convex13");
1092 test_convex_hull_case(ctx
, "convex14");
1093 test_convex_hull_case(ctx
, "convex15");
1095 for (i
= 0; i
< ARRAY_SIZE(convex_hull_tests
); ++i
) {
1096 isl_set
*set1
, *set2
;
1098 set1
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].set
);
1099 set2
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].hull
);
1100 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
1101 assert(isl_set_is_equal(set1
, set2
));
1106 ctx
->opt
->convex
= orig_convex
;
1109 void test_convex_hull(struct isl_ctx
*ctx
)
1111 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
1112 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
1115 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
1119 struct isl_basic_set
*bset1
, *bset2
;
1121 filename
= get_filename(ctx
, name
, "polylib");
1123 input
= fopen(filename
, "r");
1126 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1127 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1129 bset1
= isl_basic_set_gist(bset1
, bset2
);
1131 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1133 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1135 isl_basic_set_free(bset1
);
1136 isl_basic_set_free(bset2
);
1142 static int test_gist(struct isl_ctx
*ctx
)
1145 isl_basic_set
*bset1
, *bset2
;
1146 isl_map
*map1
, *map2
;
1148 test_gist_case(ctx
, "gist1");
1150 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1151 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1152 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1153 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1154 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1155 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1156 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1157 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1158 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1159 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1160 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1161 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1162 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1163 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1164 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1165 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1166 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1167 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1168 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1169 bset1
= isl_basic_set_gist(bset1
, bset2
);
1170 assert(bset1
&& bset1
->n_div
== 0);
1171 isl_basic_set_free(bset1
);
1173 /* Check that the integer divisions of the second disjunct
1174 * do not spread to the first disjunct.
1176 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1177 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1178 "(exists (e0 = [(-1 + t1)/16], "
1179 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1180 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1181 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1182 "o0 <= 4294967295 and t1 <= -1)) }";
1183 map1
= isl_map_read_from_str(ctx
, str
);
1184 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1185 map2
= isl_map_read_from_str(ctx
, str
);
1186 map1
= isl_map_gist(map1
, map2
);
1190 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1191 isl_map_free(map1
); return -1);
1192 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1193 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1194 isl_map_free(map1
); return -1);
1200 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1202 isl_set
*set
, *set2
;
1206 set
= isl_set_read_from_str(ctx
, str
);
1207 set
= isl_set_coalesce(set
);
1208 set2
= isl_set_read_from_str(ctx
, str
);
1209 equal
= isl_set_is_equal(set
, set2
);
1210 one
= set
&& set
->n
== 1;
1217 isl_die(ctx
, isl_error_unknown
,
1218 "coalesced set not equal to input", return -1);
1219 if (check_one
&& !one
)
1220 isl_die(ctx
, isl_error_unknown
,
1221 "coalesced set should not be a union", return -1);
1226 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1231 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1232 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1234 if (test_coalesce_set(ctx
,
1235 "{[x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1236 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1237 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1238 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1239 "-10 <= y <= 0}", 1) < 0)
1241 if (test_coalesce_set(ctx
,
1242 "{[x,y] : 0 <= x,y <= 10; [5,y]: 4 <=y <= 11}", 1) < 0)
1244 if (test_coalesce_set(ctx
,
1245 "{[x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }", 1) < 0)
1253 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1258 /* Inputs for coalescing tests.
1259 * "str" is a string representation of the input set.
1260 * "single_disjunct" is set if we expect the result to consist of
1261 * a single disjunct.
1264 int single_disjunct
;
1266 } coalesce_tests
[] = {
1267 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1268 "y >= x & x >= 2 & 5 >= y }" },
1269 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1270 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1271 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1272 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1273 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1274 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1275 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1276 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1277 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1278 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1279 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1280 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1281 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1282 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1283 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1284 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1285 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1286 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1287 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1288 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1289 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1290 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1291 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1292 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1293 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1294 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1295 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1296 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1297 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1298 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1299 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1300 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1301 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1302 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1303 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1304 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1305 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1306 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1307 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1308 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1309 "[o0, o1, o2, o3, o4, o5, o6]] : "
1310 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1311 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1312 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1313 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1314 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1315 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1316 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1317 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1318 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1319 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1320 "o6 >= i3 + i6 - o3 and M >= 0 and "
1321 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1322 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1323 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1324 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1325 "(o0 = 0 and M >= 2 and N >= 3) or "
1326 "(M = 0 and o0 = 0 and N >= 3) }" },
1327 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1328 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1329 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1330 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1331 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1332 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1333 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1334 "(y = 3 and x = 1) }" },
1335 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1336 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1337 "i1 <= M and i3 <= M and i4 <= M) or "
1338 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1339 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1340 "i4 <= -1 + M) }" },
1341 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1342 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1343 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1344 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1345 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1346 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1347 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1348 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1349 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1350 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1351 { 0, "{ [a, b] : exists e : 2e = a and "
1352 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1353 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1354 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1355 "j >= 1 and j' <= i + j - i' and i >= 1; "
1357 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1358 "[i,j] : exists a : j = 3a }" },
1359 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1360 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1362 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1363 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1364 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1365 "c <= 6 + 8a and a >= 3; "
1366 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1367 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1368 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1369 "[x,0] : 3 <= x <= 4 }" },
1370 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1371 "[x,0] : 4 <= x <= 5 }" },
1372 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1373 "[x,0] : 3 <= x <= 5 }" },
1374 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1375 "[x,0] : 3 <= x <= 4 }" },
1376 { 1 , "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1378 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1381 /* Test the functionality of isl_set_coalesce.
1382 * That is, check that the output is always equal to the input
1383 * and in some cases that the result consists of a single disjunct.
1385 static int test_coalesce(struct isl_ctx
*ctx
)
1389 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
1390 const char *str
= coalesce_tests
[i
].str
;
1391 int check_one
= coalesce_tests
[i
].single_disjunct
;
1392 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
1396 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1402 void test_closure(struct isl_ctx
*ctx
)
1406 isl_map
*up
, *right
;
1407 isl_map
*map
, *map2
;
1410 /* COCOA example 1 */
1411 map
= isl_map_read_from_str(ctx
,
1412 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1413 "1 <= i and i < n and 1 <= j and j < n or "
1414 "i2 = i + 1 and j2 = j - 1 and "
1415 "1 <= i and i < n and 2 <= j and j <= n }");
1416 map
= isl_map_power(map
, &exact
);
1420 /* COCOA example 1 */
1421 map
= isl_map_read_from_str(ctx
,
1422 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1423 "1 <= i and i < n and 1 <= j and j < n or "
1424 "i2 = i + 1 and j2 = j - 1 and "
1425 "1 <= i and i < n and 2 <= j and j <= n }");
1426 map
= isl_map_transitive_closure(map
, &exact
);
1428 map2
= isl_map_read_from_str(ctx
,
1429 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1430 "1 <= i and i < n and 1 <= j and j <= n and "
1431 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1432 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1433 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1434 assert(isl_map_is_equal(map
, map2
));
1438 map
= isl_map_read_from_str(ctx
,
1439 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1440 " 0 <= y and y <= n }");
1441 map
= isl_map_transitive_closure(map
, &exact
);
1442 map2
= isl_map_read_from_str(ctx
,
1443 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1444 " 0 <= y and y <= n }");
1445 assert(isl_map_is_equal(map
, map2
));
1449 /* COCOA example 2 */
1450 map
= isl_map_read_from_str(ctx
,
1451 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1452 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1453 "i2 = i + 2 and j2 = j - 2 and "
1454 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1455 map
= isl_map_transitive_closure(map
, &exact
);
1457 map2
= isl_map_read_from_str(ctx
,
1458 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1459 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1460 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1461 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1462 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1463 assert(isl_map_is_equal(map
, map2
));
1467 /* COCOA Fig.2 left */
1468 map
= isl_map_read_from_str(ctx
,
1469 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1470 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1472 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1473 "j <= 2 i - 3 and j <= n - 2 or "
1474 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1475 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1476 map
= isl_map_transitive_closure(map
, &exact
);
1480 /* COCOA Fig.2 right */
1481 map
= isl_map_read_from_str(ctx
,
1482 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1483 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1485 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1486 "j <= 2 i - 4 and j <= n - 3 or "
1487 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1488 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1489 map
= isl_map_power(map
, &exact
);
1493 /* COCOA Fig.2 right */
1494 map
= isl_map_read_from_str(ctx
,
1495 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1496 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1498 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1499 "j <= 2 i - 4 and j <= n - 3 or "
1500 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1501 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1502 map
= isl_map_transitive_closure(map
, &exact
);
1504 map2
= isl_map_read_from_str(ctx
,
1505 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1506 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1507 "j <= n and 3 + i + 2 j <= 3 n and "
1508 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1509 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1510 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1511 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1512 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1513 assert(isl_map_is_equal(map
, map2
));
1517 /* COCOA Fig.1 right */
1518 dom
= isl_set_read_from_str(ctx
,
1519 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1520 "2 x - 3 y + 3 >= 0 }");
1521 right
= isl_map_read_from_str(ctx
,
1522 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1523 up
= isl_map_read_from_str(ctx
,
1524 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1525 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1526 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1527 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1528 up
= isl_map_intersect_range(up
, dom
);
1529 map
= isl_map_union(up
, right
);
1530 map
= isl_map_transitive_closure(map
, &exact
);
1532 map2
= isl_map_read_from_str(ctx
,
1533 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1534 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1535 assert(isl_map_is_equal(map
, map2
));
1539 /* COCOA Theorem 1 counter example */
1540 map
= isl_map_read_from_str(ctx
,
1541 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1542 "i2 = 1 and j2 = j or "
1543 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1544 map
= isl_map_transitive_closure(map
, &exact
);
1548 map
= isl_map_read_from_str(ctx
,
1549 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1550 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1551 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1552 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1553 map
= isl_map_transitive_closure(map
, &exact
);
1557 /* Kelly et al 1996, fig 12 */
1558 map
= isl_map_read_from_str(ctx
,
1559 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1560 "1 <= i,j,j+1 <= n or "
1561 "j = n and j2 = 1 and i2 = i + 1 and "
1562 "1 <= i,i+1 <= n }");
1563 map
= isl_map_transitive_closure(map
, &exact
);
1565 map2
= isl_map_read_from_str(ctx
,
1566 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1567 "1 <= i <= n and i = i2 or "
1568 "1 <= i < i2 <= n and 1 <= j <= n and "
1570 assert(isl_map_is_equal(map
, map2
));
1574 /* Omega's closure4 */
1575 map
= isl_map_read_from_str(ctx
,
1576 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1577 "1 <= x,y <= 10 or "
1578 "x2 = x + 1 and y2 = y and "
1579 "1 <= x <= 20 && 5 <= y <= 15 }");
1580 map
= isl_map_transitive_closure(map
, &exact
);
1584 map
= isl_map_read_from_str(ctx
,
1585 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1586 map
= isl_map_transitive_closure(map
, &exact
);
1588 map2
= isl_map_read_from_str(ctx
,
1589 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1590 assert(isl_map_is_equal(map
, map2
));
1594 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1595 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1596 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1597 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1598 map
= isl_map_read_from_str(ctx
, str
);
1599 map
= isl_map_transitive_closure(map
, &exact
);
1601 map2
= isl_map_read_from_str(ctx
, str
);
1602 assert(isl_map_is_equal(map
, map2
));
1606 str
= "{[0] -> [1]; [2] -> [3]}";
1607 map
= isl_map_read_from_str(ctx
, str
);
1608 map
= isl_map_transitive_closure(map
, &exact
);
1610 map2
= isl_map_read_from_str(ctx
, str
);
1611 assert(isl_map_is_equal(map
, map2
));
1615 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1616 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1617 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 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 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1621 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1622 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1623 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1624 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1625 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1626 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1627 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1628 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1629 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1630 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1631 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1632 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1633 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1634 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1635 map
= isl_map_read_from_str(ctx
, str
);
1636 map
= isl_map_transitive_closure(map
, NULL
);
1641 void test_lex(struct isl_ctx
*ctx
)
1646 dim
= isl_space_set_alloc(ctx
, 0, 0);
1647 map
= isl_map_lex_le(dim
);
1648 assert(!isl_map_is_empty(map
));
1652 static int test_lexmin(struct isl_ctx
*ctx
)
1656 isl_basic_map
*bmap
;
1657 isl_map
*map
, *map2
;
1660 isl_pw_multi_aff
*pma
;
1662 str
= "[p0, p1] -> { [] -> [] : "
1663 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1664 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1665 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1666 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1667 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1668 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1669 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1670 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1671 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1672 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1673 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1674 map
= isl_map_read_from_str(ctx
, str
);
1675 map
= isl_map_lexmin(map
);
1678 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1679 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1680 set
= isl_set_read_from_str(ctx
, str
);
1681 set
= isl_set_lexmax(set
);
1682 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1683 set2
= isl_set_read_from_str(ctx
, str
);
1684 set
= isl_set_intersect(set
, set2
);
1685 assert(!isl_set_is_empty(set
));
1688 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1689 map
= isl_map_read_from_str(ctx
, str
);
1690 map
= isl_map_lexmin(map
);
1691 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1692 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1693 map2
= isl_map_read_from_str(ctx
, str
);
1694 assert(isl_map_is_equal(map
, map2
));
1698 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1699 map
= isl_map_read_from_str(ctx
, str
);
1700 map2
= isl_map_copy(map
);
1701 map
= isl_map_lexmin(map
);
1702 assert(isl_map_is_equal(map
, map2
));
1706 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1707 map
= isl_map_read_from_str(ctx
, str
);
1708 map
= isl_map_lexmin(map
);
1709 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1710 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1711 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1712 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1713 map2
= isl_map_read_from_str(ctx
, str
);
1714 assert(isl_map_is_equal(map
, map2
));
1718 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1719 " 8i' <= i and 8i' >= -7 + i }";
1720 bmap
= isl_basic_map_read_from_str(ctx
, str
);
1721 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
1722 map2
= isl_map_from_pw_multi_aff(pma
);
1723 map
= isl_map_from_basic_map(bmap
);
1724 assert(isl_map_is_equal(map
, map2
));
1728 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1729 map
= isl_map_read_from_str(ctx
, str
);
1730 map
= isl_map_lexmin(map
);
1731 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1732 map2
= isl_map_read_from_str(ctx
, str
);
1733 assert(isl_map_is_equal(map
, map2
));
1737 /* Check that empty pieces are properly combined. */
1738 str
= "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
1739 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
1740 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
1741 map
= isl_map_read_from_str(ctx
, str
);
1742 map
= isl_map_lexmin(map
);
1743 str
= "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
1744 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
1746 map2
= isl_map_read_from_str(ctx
, str
);
1747 assert(isl_map_is_equal(map
, map2
));
1751 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1752 " 8i' <= i and 8i' >= -7 + i }";
1753 set
= isl_set_read_from_str(ctx
, str
);
1754 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
1755 set2
= isl_set_from_pw_multi_aff(pma
);
1756 equal
= isl_set_is_equal(set
, set2
);
1762 isl_die(ctx
, isl_error_unknown
,
1763 "unexpected difference between set and "
1764 "piecewise affine expression", return -1);
1769 /* Check that isl_set_min_val and isl_set_max_val compute the correct
1770 * result on non-convex inputs.
1772 static int test_min(struct isl_ctx
*ctx
)
1779 set
= isl_set_read_from_str(ctx
, "{ [-1]; [1] }");
1780 aff
= isl_aff_read_from_str(ctx
, "{ [x] -> [x] }");
1781 val
= isl_set_min_val(set
, aff
);
1782 min_ok
= isl_val_is_negone(val
);
1784 val
= isl_set_max_val(set
, aff
);
1785 max_ok
= isl_val_is_one(val
);
1790 if (min_ok
< 0 || max_ok
< 0)
1793 isl_die(ctx
, isl_error_unknown
,
1794 "unexpected minimum", return -1);
1796 isl_die(ctx
, isl_error_unknown
,
1797 "unexpected maximum", return -1);
1807 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1808 void *dep_user
, void *user
)
1810 struct must_may
*mm
= (struct must_may
*)user
;
1813 mm
->must
= isl_map_union(mm
->must
, dep
);
1815 mm
->may
= isl_map_union(mm
->may
, dep
);
1820 static int common_space(void *first
, void *second
)
1822 int depth
= *(int *)first
;
1826 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1834 map2
= isl_map_read_from_str(map
->ctx
, str
);
1835 equal
= isl_map_is_equal(map
, map2
);
1841 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
1845 equal
= map_is_equal(map
, str
);
1849 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
1850 "result not as expected", return -1);
1854 void test_dep(struct isl_ctx
*ctx
)
1859 isl_access_info
*ai
;
1866 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1867 map
= isl_map_read_from_str(ctx
, str
);
1868 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1870 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1871 map
= isl_map_read_from_str(ctx
, str
);
1872 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1874 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1875 map
= isl_map_read_from_str(ctx
, str
);
1876 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1878 flow
= isl_access_info_compute_flow(ai
);
1879 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1880 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1881 mm
.may
= isl_map_empty(dim
);
1883 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1885 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1886 " [1,10,0] -> [2,5,0] }";
1887 assert(map_is_equal(mm
.must
, str
));
1888 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1889 assert(map_is_equal(mm
.may
, str
));
1891 isl_map_free(mm
.must
);
1892 isl_map_free(mm
.may
);
1893 isl_flow_free(flow
);
1896 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1897 map
= isl_map_read_from_str(ctx
, str
);
1898 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1900 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1901 map
= isl_map_read_from_str(ctx
, str
);
1902 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1904 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1905 map
= isl_map_read_from_str(ctx
, str
);
1906 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1908 flow
= isl_access_info_compute_flow(ai
);
1909 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1910 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1911 mm
.may
= isl_map_empty(dim
);
1913 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1915 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1916 assert(map_is_equal(mm
.must
, str
));
1917 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1918 assert(map_is_equal(mm
.may
, str
));
1920 isl_map_free(mm
.must
);
1921 isl_map_free(mm
.may
);
1922 isl_flow_free(flow
);
1925 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1926 map
= isl_map_read_from_str(ctx
, str
);
1927 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1929 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1930 map
= isl_map_read_from_str(ctx
, str
);
1931 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1933 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1934 map
= isl_map_read_from_str(ctx
, str
);
1935 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1937 flow
= isl_access_info_compute_flow(ai
);
1938 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1939 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1940 mm
.may
= isl_map_empty(dim
);
1942 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1944 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
1945 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1946 assert(map_is_equal(mm
.may
, str
));
1947 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1948 assert(map_is_equal(mm
.must
, str
));
1950 isl_map_free(mm
.must
);
1951 isl_map_free(mm
.may
);
1952 isl_flow_free(flow
);
1955 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
1956 map
= isl_map_read_from_str(ctx
, str
);
1957 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1959 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1960 map
= isl_map_read_from_str(ctx
, str
);
1961 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1963 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
1964 map
= isl_map_read_from_str(ctx
, str
);
1965 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1967 flow
= isl_access_info_compute_flow(ai
);
1968 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1969 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1970 mm
.may
= isl_map_empty(dim
);
1972 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1974 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
1975 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
1976 assert(map_is_equal(mm
.may
, str
));
1977 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1978 assert(map_is_equal(mm
.must
, str
));
1980 isl_map_free(mm
.must
);
1981 isl_map_free(mm
.may
);
1982 isl_flow_free(flow
);
1985 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
1986 map
= isl_map_read_from_str(ctx
, str
);
1987 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1989 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1990 map
= isl_map_read_from_str(ctx
, str
);
1991 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1993 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
1994 map
= isl_map_read_from_str(ctx
, str
);
1995 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1997 flow
= isl_access_info_compute_flow(ai
);
1998 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1999 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2000 mm
.may
= isl_map_empty(dim
);
2002 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2004 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2005 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2006 assert(map_is_equal(mm
.may
, str
));
2007 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2008 assert(map_is_equal(mm
.must
, str
));
2010 isl_map_free(mm
.must
);
2011 isl_map_free(mm
.may
);
2012 isl_flow_free(flow
);
2017 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2018 map
= isl_map_read_from_str(ctx
, str
);
2019 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2021 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2022 map
= isl_map_read_from_str(ctx
, str
);
2023 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2025 flow
= isl_access_info_compute_flow(ai
);
2026 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2027 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2028 mm
.may
= isl_map_empty(dim
);
2030 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2032 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2033 assert(map_is_equal(mm
.must
, str
));
2034 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2035 assert(map_is_equal(mm
.may
, str
));
2037 isl_map_free(mm
.must
);
2038 isl_map_free(mm
.may
);
2039 isl_flow_free(flow
);
2042 /* Check that the dependence analysis proceeds without errors.
2043 * Earlier versions of isl would break down during the analysis
2044 * due to the use of the wrong spaces.
2046 static int test_flow(isl_ctx
*ctx
)
2049 isl_union_map
*access
, *schedule
;
2050 isl_union_map
*must_dep
, *may_dep
;
2053 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2054 access
= isl_union_map_read_from_str(ctx
, str
);
2055 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2056 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2057 "S2[] -> [1,0,0,0]; "
2058 "S3[] -> [-1,0,0,0] }";
2059 schedule
= isl_union_map_read_from_str(ctx
, str
);
2060 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2061 isl_union_map_copy(access
), schedule
,
2062 &must_dep
, &may_dep
, NULL
, NULL
);
2063 isl_union_map_free(may_dep
);
2064 isl_union_map_free(must_dep
);
2069 int test_sv(isl_ctx
*ctx
)
2073 isl_union_map
*umap
;
2076 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }";
2077 map
= isl_map_read_from_str(ctx
, str
);
2078 sv
= isl_map_is_single_valued(map
);
2083 isl_die(ctx
, isl_error_internal
,
2084 "map not detected as single valued", return -1);
2086 str
= "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }";
2087 map
= isl_map_read_from_str(ctx
, str
);
2088 sv
= isl_map_is_single_valued(map
);
2093 isl_die(ctx
, isl_error_internal
,
2094 "map detected as single valued", return -1);
2096 str
= "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }";
2097 umap
= isl_union_map_read_from_str(ctx
, str
);
2098 sv
= isl_union_map_is_single_valued(umap
);
2099 isl_union_map_free(umap
);
2103 isl_die(ctx
, isl_error_internal
,
2104 "map not detected as single valued", return -1);
2106 str
= "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }";
2107 umap
= isl_union_map_read_from_str(ctx
, str
);
2108 sv
= isl_union_map_is_single_valued(umap
);
2109 isl_union_map_free(umap
);
2113 isl_die(ctx
, isl_error_internal
,
2114 "map detected as single valued", return -1);
2119 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
2123 map
= isl_map_read_from_str(ctx
, str
);
2125 assert(isl_map_is_bijective(map
));
2127 assert(!isl_map_is_bijective(map
));
2131 void test_bijective(struct isl_ctx
*ctx
)
2133 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
2134 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
2135 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
2136 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
2137 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
2138 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
2139 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
2140 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
2141 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
2142 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
2143 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
2144 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
2145 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
2148 static int test_pwqp(struct isl_ctx
*ctx
)
2152 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
2155 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2156 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2158 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
2161 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2162 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2164 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2166 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2168 isl_pw_qpolynomial_free(pwqp1
);
2170 str
= "{ [i] -> i }";
2171 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2172 str
= "{ [k] : exists a : k = 2a }";
2173 set
= isl_set_read_from_str(ctx
, str
);
2174 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2175 str
= "{ [i] -> i }";
2176 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2178 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2180 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2182 isl_pw_qpolynomial_free(pwqp1
);
2184 str
= "{ [i] -> i + [ (i + [i/3])/2 ] }";
2185 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2187 set
= isl_set_read_from_str(ctx
, str
);
2188 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2189 str
= "{ [i] -> 16 }";
2190 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2192 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2194 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2196 isl_pw_qpolynomial_free(pwqp1
);
2198 str
= "{ [i] -> ([(i)/2]) }";
2199 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2200 str
= "{ [k] : exists a : k = 2a+1 }";
2201 set
= isl_set_read_from_str(ctx
, str
);
2202 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2203 str
= "{ [i] -> -1/2 + 1/2 * i }";
2204 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2206 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2208 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2210 isl_pw_qpolynomial_free(pwqp1
);
2212 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
2213 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2214 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
2215 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2217 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2219 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2221 isl_pw_qpolynomial_free(pwqp1
);
2223 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
2224 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2225 str
= "{ [x] -> x }";
2226 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2228 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2230 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2232 isl_pw_qpolynomial_free(pwqp1
);
2234 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2235 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2236 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2237 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
2238 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2239 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2240 isl_pw_qpolynomial_free(pwqp1
);
2242 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2243 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2244 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2245 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2246 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
2247 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
2248 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2249 isl_pw_qpolynomial_free(pwqp1
);
2250 isl_pw_qpolynomial_free(pwqp2
);
2254 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2256 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2257 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2258 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2259 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2260 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
2262 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2263 isl_pw_qpolynomial_free(pwqp1
);
2264 isl_pw_qpolynomial_free(pwqp2
);
2268 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2273 void test_split_periods(isl_ctx
*ctx
)
2276 isl_pw_qpolynomial
*pwqp
;
2278 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2279 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2280 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2281 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2283 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
2286 isl_pw_qpolynomial_free(pwqp
);
2289 void test_union(isl_ctx
*ctx
)
2292 isl_union_set
*uset1
, *uset2
;
2293 isl_union_map
*umap1
, *umap2
;
2295 str
= "{ [i] : 0 <= i <= 1 }";
2296 uset1
= isl_union_set_read_from_str(ctx
, str
);
2297 str
= "{ [1] -> [0] }";
2298 umap1
= isl_union_map_read_from_str(ctx
, str
);
2300 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
2301 assert(isl_union_map_is_equal(umap1
, umap2
));
2303 isl_union_map_free(umap1
);
2304 isl_union_map_free(umap2
);
2306 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2307 umap1
= isl_union_map_read_from_str(ctx
, str
);
2308 str
= "{ A[i]; B[i] }";
2309 uset1
= isl_union_set_read_from_str(ctx
, str
);
2311 uset2
= isl_union_map_domain(umap1
);
2313 assert(isl_union_set_is_equal(uset1
, uset2
));
2315 isl_union_set_free(uset1
);
2316 isl_union_set_free(uset2
);
2319 void test_bound(isl_ctx
*ctx
)
2322 isl_pw_qpolynomial
*pwqp
;
2323 isl_pw_qpolynomial_fold
*pwf
;
2325 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
2326 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2327 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2328 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 4);
2329 isl_pw_qpolynomial_fold_free(pwf
);
2331 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2332 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2333 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2334 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 1);
2335 isl_pw_qpolynomial_fold_free(pwf
);
2338 void test_lift(isl_ctx
*ctx
)
2341 isl_basic_map
*bmap
;
2342 isl_basic_set
*bset
;
2344 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
2345 bset
= isl_basic_set_read_from_str(ctx
, str
);
2346 bset
= isl_basic_set_lift(bset
);
2347 bmap
= isl_basic_map_from_range(bset
);
2348 bset
= isl_basic_map_domain(bmap
);
2349 isl_basic_set_free(bset
);
2356 } subset_tests
[] = {
2358 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2359 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2360 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2362 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2363 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2364 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2365 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2366 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2367 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2368 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2369 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2370 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2371 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2372 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2373 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2374 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2375 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2376 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2377 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2378 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2379 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2380 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2381 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2382 "4e0 <= -57 + i0 + i1)) or "
2383 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2384 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2385 "4e0 >= -61 + i0 + i1)) or "
2386 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2389 static int test_subset(isl_ctx
*ctx
)
2392 isl_set
*set1
, *set2
;
2395 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
2396 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
2397 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
2398 subset
= isl_set_is_subset(set1
, set2
);
2403 if (subset
!= subset_tests
[i
].subset
)
2404 isl_die(ctx
, isl_error_unknown
,
2405 "incorrect subset result", return -1);
2412 const char *minuend
;
2413 const char *subtrahend
;
2414 const char *difference
;
2415 } subtract_domain_tests
[] = {
2416 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2417 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2418 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2421 static int test_subtract(isl_ctx
*ctx
)
2424 isl_union_map
*umap1
, *umap2
;
2425 isl_union_set
*uset
;
2428 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2429 umap1
= isl_union_map_read_from_str(ctx
,
2430 subtract_domain_tests
[i
].minuend
);
2431 uset
= isl_union_set_read_from_str(ctx
,
2432 subtract_domain_tests
[i
].subtrahend
);
2433 umap2
= isl_union_map_read_from_str(ctx
,
2434 subtract_domain_tests
[i
].difference
);
2435 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
2436 equal
= isl_union_map_is_equal(umap1
, umap2
);
2437 isl_union_map_free(umap1
);
2438 isl_union_map_free(umap2
);
2442 isl_die(ctx
, isl_error_unknown
,
2443 "incorrect subtract domain result", return -1);
2449 int test_factorize(isl_ctx
*ctx
)
2452 isl_basic_set
*bset
;
2455 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2456 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2457 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2458 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2459 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2460 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2461 "3i5 >= -2i0 - i2 + 3i4 }";
2462 bset
= isl_basic_set_read_from_str(ctx
, str
);
2463 f
= isl_basic_set_factorizer(bset
);
2464 isl_basic_set_free(bset
);
2465 isl_factorizer_free(f
);
2467 isl_die(ctx
, isl_error_unknown
,
2468 "failed to construct factorizer", return -1);
2470 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2471 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2472 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2473 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2474 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2475 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2476 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2477 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2478 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2479 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2480 bset
= isl_basic_set_read_from_str(ctx
, str
);
2481 f
= isl_basic_set_factorizer(bset
);
2482 isl_basic_set_free(bset
);
2483 isl_factorizer_free(f
);
2485 isl_die(ctx
, isl_error_unknown
,
2486 "failed to construct factorizer", return -1);
2491 static int check_injective(__isl_take isl_map
*map
, void *user
)
2493 int *injective
= user
;
2495 *injective
= isl_map_is_injective(map
);
2498 if (*injective
< 0 || !*injective
)
2504 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
2505 const char *r
, const char *s
, int tilable
, int parallel
)
2509 isl_union_map
*W
, *R
, *S
;
2510 isl_union_map
*empty
;
2511 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
2512 isl_union_map
*validity
, *proximity
, *coincidence
;
2513 isl_union_map
*schedule
;
2514 isl_union_map
*test
;
2515 isl_union_set
*delta
;
2516 isl_union_set
*domain
;
2520 isl_schedule_constraints
*sc
;
2521 isl_schedule
*sched
;
2522 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
2524 D
= isl_union_set_read_from_str(ctx
, d
);
2525 W
= isl_union_map_read_from_str(ctx
, w
);
2526 R
= isl_union_map_read_from_str(ctx
, r
);
2527 S
= isl_union_map_read_from_str(ctx
, s
);
2529 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
2530 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
2532 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
2533 isl_union_map_compute_flow(isl_union_map_copy(R
),
2534 isl_union_map_copy(W
), empty
,
2535 isl_union_map_copy(S
),
2536 &dep_raw
, NULL
, NULL
, NULL
);
2537 isl_union_map_compute_flow(isl_union_map_copy(W
),
2538 isl_union_map_copy(W
),
2539 isl_union_map_copy(R
),
2540 isl_union_map_copy(S
),
2541 &dep_waw
, &dep_war
, NULL
, NULL
);
2543 dep
= isl_union_map_union(dep_waw
, dep_war
);
2544 dep
= isl_union_map_union(dep
, dep_raw
);
2545 validity
= isl_union_map_copy(dep
);
2546 coincidence
= isl_union_map_copy(dep
);
2547 proximity
= isl_union_map_copy(dep
);
2549 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
2550 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
2551 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
2552 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
2553 sched
= isl_schedule_constraints_compute_schedule(sc
);
2554 schedule
= isl_schedule_get_map(sched
);
2555 isl_schedule_free(sched
);
2556 isl_union_map_free(W
);
2557 isl_union_map_free(R
);
2558 isl_union_map_free(S
);
2561 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
2563 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
2564 is_complete
= isl_union_set_is_subset(D
, domain
);
2565 isl_union_set_free(D
);
2566 isl_union_set_free(domain
);
2568 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
2569 test
= isl_union_map_apply_range(test
, dep
);
2570 test
= isl_union_map_apply_range(test
, schedule
);
2572 delta
= isl_union_map_deltas(test
);
2573 if (isl_union_set_n_set(delta
) == 0) {
2577 isl_union_set_free(delta
);
2579 delta_set
= isl_set_from_union_set(delta
);
2581 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2582 for (i
= 0; i
< tilable
; ++i
)
2583 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
2584 is_tilable
= isl_set_is_subset(delta_set
, slice
);
2585 isl_set_free(slice
);
2587 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2588 for (i
= 0; i
< parallel
; ++i
)
2589 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
2590 is_parallel
= isl_set_is_subset(delta_set
, slice
);
2591 isl_set_free(slice
);
2593 origin
= isl_set_universe(isl_set_get_space(delta_set
));
2594 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
2595 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2597 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2598 delta_set
= isl_set_lexmin(delta_set
);
2600 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2602 isl_set_free(origin
);
2603 isl_set_free(delta_set
);
2606 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2607 is_injection
< 0 || is_complete
< 0)
2610 isl_die(ctx
, isl_error_unknown
,
2611 "generated schedule incomplete", return -1);
2613 isl_die(ctx
, isl_error_unknown
,
2614 "generated schedule not injective on each statement",
2617 isl_die(ctx
, isl_error_unknown
,
2618 "negative dependences in generated schedule",
2621 isl_die(ctx
, isl_error_unknown
,
2622 "generated schedule not as tilable as expected",
2625 isl_die(ctx
, isl_error_unknown
,
2626 "generated schedule not as parallel as expected",
2632 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
2633 const char *domain
, const char *validity
, const char *proximity
)
2637 isl_union_map
*prox
;
2638 isl_schedule_constraints
*sc
;
2639 isl_schedule
*schedule
;
2640 isl_union_map
*sched
;
2642 dom
= isl_union_set_read_from_str(ctx
, domain
);
2643 dep
= isl_union_map_read_from_str(ctx
, validity
);
2644 prox
= isl_union_map_read_from_str(ctx
, proximity
);
2645 sc
= isl_schedule_constraints_on_domain(dom
);
2646 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
2647 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
2648 schedule
= isl_schedule_constraints_compute_schedule(sc
);
2649 sched
= isl_schedule_get_map(schedule
);
2650 isl_schedule_free(schedule
);
2655 /* Check that a schedule can be constructed on the given domain
2656 * with the given validity and proximity constraints.
2658 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
2659 const char *validity
, const char *proximity
)
2661 isl_union_map
*sched
;
2663 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
2667 isl_union_map_free(sched
);
2671 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
2672 const char *validity
, const char *proximity
, const char *expected_sched
)
2674 isl_union_map
*sched1
, *sched2
;
2677 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
2678 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
2680 equal
= isl_union_map_is_equal(sched1
, sched2
);
2681 isl_union_map_free(sched1
);
2682 isl_union_map_free(sched2
);
2687 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2693 /* Check that the schedule map is properly padded, even after being
2694 * reconstructed from the band forest.
2696 static int test_padded_schedule(isl_ctx
*ctx
)
2700 isl_union_map
*validity
, *proximity
;
2701 isl_schedule_constraints
*sc
;
2702 isl_schedule
*sched
;
2703 isl_union_map
*map1
, *map2
;
2704 isl_band_list
*list
;
2707 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2708 D
= isl_union_set_read_from_str(ctx
, str
);
2709 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
2710 proximity
= isl_union_map_copy(validity
);
2711 sc
= isl_schedule_constraints_on_domain(D
);
2712 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
2713 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
2714 sched
= isl_schedule_constraints_compute_schedule(sc
);
2715 map1
= isl_schedule_get_map(sched
);
2716 list
= isl_schedule_get_band_forest(sched
);
2717 isl_band_list_free(list
);
2718 map2
= isl_schedule_get_map(sched
);
2719 isl_schedule_free(sched
);
2720 equal
= isl_union_map_is_equal(map1
, map2
);
2721 isl_union_map_free(map1
);
2722 isl_union_map_free(map2
);
2727 isl_die(ctx
, isl_error_unknown
,
2728 "reconstructed schedule map not the same as original",
2734 /* Input for testing of schedule construction based on
2735 * conditional constraints.
2737 * domain is the iteration domain
2738 * flow are the flow dependences, which determine the validity and
2739 * proximity constraints
2740 * condition are the conditions on the conditional validity constraints
2741 * conditional_validity are the conditional validity constraints
2742 * outer_band_n is the expected number of members in the outer band
2747 const char *condition
;
2748 const char *conditional_validity
;
2750 } live_range_tests
[] = {
2751 /* Contrived example that illustrates that we need to keep
2752 * track of tagged condition dependences and
2753 * tagged conditional validity dependences
2754 * in isl_sched_edge separately.
2755 * In particular, the conditional validity constraints on A
2756 * cannot be satisfied,
2757 * but they can be ignored because there are no corresponding
2758 * condition constraints. However, we do have an additional
2759 * conditional validity constraint that maps to the same
2760 * dependence relation
2761 * as the condition constraint on B. If we did not make a distinction
2762 * between tagged condition and tagged conditional validity
2763 * dependences, then we
2764 * could end up treating this shared dependence as an condition
2765 * constraint on A, forcing a localization of the conditions,
2766 * which is impossible.
2768 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
2769 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
2770 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
2771 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2772 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2773 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
2776 /* TACO 2013 Fig. 7 */
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] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
2781 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
2782 "0 <= i < n and 0 <= j < n - 1 }",
2783 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
2784 "0 <= i < n and 0 <= j < j' < n;"
2785 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
2786 "0 <= i < i' < n and 0 <= j,j' < n;"
2787 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
2788 "0 <= i,j,j' < n and j < j' }",
2791 /* TACO 2013 Fig. 7, without tags */
2792 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2793 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2794 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2795 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2796 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2797 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
2798 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
2799 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
2802 /* TACO 2013 Fig. 12 */
2803 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
2804 "S3[i,3] : 0 <= i <= 1 }",
2805 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
2806 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
2807 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
2808 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
2809 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2810 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
2811 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2812 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
2813 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
2814 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
2815 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
2820 /* Test schedule construction based on conditional constraints.
2821 * In particular, check the number of members in the outer band
2822 * as an indication of whether tiling is possible or not.
2824 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
2827 isl_union_set
*domain
;
2828 isl_union_map
*condition
;
2829 isl_union_map
*flow
;
2830 isl_union_map
*validity
;
2831 isl_schedule_constraints
*sc
;
2832 isl_schedule
*schedule
;
2833 isl_band_list
*list
;
2837 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
2838 domain
= isl_union_set_read_from_str(ctx
,
2839 live_range_tests
[i
].domain
);
2840 flow
= isl_union_map_read_from_str(ctx
,
2841 live_range_tests
[i
].flow
);
2842 condition
= isl_union_map_read_from_str(ctx
,
2843 live_range_tests
[i
].condition
);
2844 validity
= isl_union_map_read_from_str(ctx
,
2845 live_range_tests
[i
].conditional_validity
);
2846 sc
= isl_schedule_constraints_on_domain(domain
);
2847 sc
= isl_schedule_constraints_set_validity(sc
,
2848 isl_union_map_copy(flow
));
2849 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
2850 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
2851 condition
, validity
);
2852 schedule
= isl_schedule_constraints_compute_schedule(sc
);
2853 list
= isl_schedule_get_band_forest(schedule
);
2854 band
= isl_band_list_get_band(list
, 0);
2855 n_member
= isl_band_n_member(band
);
2856 isl_band_free(band
);
2857 isl_band_list_free(list
);
2858 isl_schedule_free(schedule
);
2862 if (n_member
!= live_range_tests
[i
].outer_band_n
)
2863 isl_die(ctx
, isl_error_unknown
,
2864 "unexpected number of members in outer band",
2870 int test_schedule(isl_ctx
*ctx
)
2872 const char *D
, *W
, *R
, *V
, *P
, *S
;
2874 /* Handle resulting schedule with zero bands. */
2875 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2879 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2880 W
= "{ S1[t,i] -> a[t,i] }";
2881 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2882 "S1[t,i] -> a[t-1,i+1] }";
2883 S
= "{ S1[t,i] -> [t,i] }";
2884 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2887 /* Fig. 5 of CC2008 */
2888 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2890 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2891 "j >= 2 and j <= -1 + N }";
2892 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2893 "j >= 2 and j <= -1 + N; "
2894 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2895 "j >= 2 and j <= -1 + N }";
2896 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2897 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2900 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2901 W
= "{ S1[i] -> a[i] }";
2902 R
= "{ S2[i] -> a[i+1] }";
2903 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2904 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2907 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2908 W
= "{ S1[i] -> a[i] }";
2909 R
= "{ S2[i] -> a[9-i] }";
2910 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2911 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2914 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2915 W
= "{ S1[i] -> a[i] }";
2916 R
= "[N] -> { S2[i] -> a[N-1-i] }";
2917 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2918 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2921 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
2922 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
2923 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
2924 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
2925 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2928 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2929 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
2930 R
= "{ S2[i,j] -> a[i-1,j] }";
2931 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2932 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2935 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
2936 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
2937 R
= "{ S2[i,j] -> a[i,j-1] }";
2938 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
2939 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2942 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
2943 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
2944 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
2945 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
2946 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
2947 "S_0[] -> [0, 0, 0] }";
2948 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
2950 ctx
->opt
->schedule_parametric
= 0;
2951 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2953 ctx
->opt
->schedule_parametric
= 1;
2955 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
2956 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
2957 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
2958 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
2959 "S4[i] -> a[i,N] }";
2960 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
2961 "S4[i] -> [4,i,0] }";
2962 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2965 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
2966 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2968 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
2970 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
2972 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2973 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2976 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
2977 " S_2[t] : t >= 0 and t <= -1 + N; "
2978 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
2980 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
2981 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
2982 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
2983 "i >= 0 and i <= -1 + N }";
2984 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
2985 "i >= 0 and i <= -1 + N; "
2986 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
2987 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
2988 " S_0[t] -> [0, t, 0] }";
2990 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
2992 ctx
->opt
->schedule_parametric
= 0;
2993 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
2995 ctx
->opt
->schedule_parametric
= 1;
2997 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
2998 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
2999 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
3002 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3003 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3004 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3005 "j >= 0 and j <= -1 + N; "
3006 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3007 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3008 "j >= 0 and j <= -1 + N; "
3009 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3010 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3011 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3014 D
= "{ S_0[i] : i >= 0 }";
3015 W
= "{ S_0[i] -> a[i] : i >= 0 }";
3016 R
= "{ S_0[i] -> a[0] : i >= 0 }";
3017 S
= "{ S_0[i] -> [0, i, 0] }";
3018 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3021 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3022 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3023 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3024 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3025 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3028 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3029 "k <= -1 + n and k >= 0 }";
3030 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3031 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3032 "k <= -1 + n and k >= 0; "
3033 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3034 "k <= -1 + n and k >= 0; "
3035 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3036 "k <= -1 + n and k >= 0 }";
3037 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
3038 ctx
->opt
->schedule_outer_coincidence
= 1;
3039 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3041 ctx
->opt
->schedule_outer_coincidence
= 0;
3043 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
3044 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3045 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3046 "Stmt_for_body24[i0, i1, 1, 0]:"
3047 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3048 "Stmt_for_body7[i0, i1, i2]:"
3049 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3052 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
3053 "Stmt_for_body24[1, i1, i2, i3]:"
3054 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3056 "Stmt_for_body24[0, i1, i2, i3] -> "
3057 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3058 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3060 "Stmt_for_body24[0, i1, i2, i3] ->"
3061 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3062 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3063 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3064 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3065 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3066 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3067 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3068 "i1 <= 6 and i1 >= 0;"
3069 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3070 "Stmt_for_body7[i0, i1, i2] -> "
3071 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3072 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3073 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3074 "Stmt_for_body7[i0, i1, i2] -> "
3075 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3076 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3077 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3079 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3080 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3081 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3083 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3086 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3087 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3088 "j >= 1 and j <= 7;"
3089 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3090 "j >= 1 and j <= 8 }";
3092 S
= "{ S_0[i, j] -> [i + j, j] }";
3093 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3094 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3096 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3098 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3099 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3100 "j >= 0 and j <= -1 + i }";
3101 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3102 "i <= -1 + N and j >= 0;"
3103 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3106 S
= "{ S_0[i, j] -> [i, j] }";
3107 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3108 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3110 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3112 /* Test both algorithms on a case with only proximity dependences. */
3113 D
= "{ S[i,j] : 0 <= i <= 10 }";
3115 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3116 S
= "{ S[i, j] -> [j, i] }";
3117 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3118 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3120 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3121 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3124 D
= "{ A[a]; B[] }";
3126 P
= "{ A[a] -> B[] }";
3127 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3130 if (test_padded_schedule(ctx
) < 0)
3133 /* Check that check for progress is not confused by rational
3136 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3137 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3139 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3140 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3142 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3143 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3145 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3147 if (test_conditional_schedule_constraints(ctx
) < 0)
3153 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
3155 isl_union_map
*umap
;
3158 umap
= isl_union_map_read_from_str(ctx
, str
);
3159 test
= isl_union_map_plain_is_injective(umap
);
3160 isl_union_map_free(umap
);
3163 if (test
== injective
)
3166 isl_die(ctx
, isl_error_unknown
,
3167 "map not detected as injective", return -1);
3169 isl_die(ctx
, isl_error_unknown
,
3170 "map detected as injective", return -1);
3173 int test_injective(isl_ctx
*ctx
)
3177 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3179 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
3181 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
3183 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
3185 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3187 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3189 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3191 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3194 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3195 if (test_plain_injective(ctx
, str
, 1))
3197 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3198 if (test_plain_injective(ctx
, str
, 0))
3204 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
3212 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
3213 equal
= isl_aff_plain_is_equal(aff
, aff2
);
3219 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
3223 equal
= aff_plain_is_equal(aff
, str
);
3227 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
3228 "result not as expected", return -1);
3233 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3234 __isl_take isl_aff
*aff2
);
3236 ['+'] = { &isl_aff_add
},
3237 ['-'] = { &isl_aff_sub
},
3238 ['*'] = { &isl_aff_mul
},
3239 ['/'] = { &isl_aff_div
},
3247 } aff_bin_tests
[] = {
3248 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3249 "{ [i] -> [2i] }" },
3250 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3252 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3253 "{ [i] -> [2i] }" },
3254 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3255 "{ [i] -> [2i] }" },
3256 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
3257 "{ [i] -> [i/2] }" },
3258 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
3260 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3261 "{ [i] -> [NaN] }" },
3262 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3263 "{ [i] -> [NaN] }" },
3264 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3265 "{ [i] -> [NaN] }" },
3266 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3267 "{ [i] -> [NaN] }" },
3268 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
3269 "{ [i] -> [NaN] }" },
3270 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
3271 "{ [i] -> [NaN] }" },
3272 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3273 "{ [i] -> [NaN] }" },
3274 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3275 "{ [i] -> [NaN] }" },
3276 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3277 "{ [i] -> [NaN] }" },
3278 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3279 "{ [i] -> [NaN] }" },
3280 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
3281 "{ [i] -> [NaN] }" },
3282 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
3283 "{ [i] -> [NaN] }" },
3286 /* Perform some basic tests of binary operations on isl_aff objects.
3288 static int test_bin_aff(isl_ctx
*ctx
)
3291 isl_aff
*aff1
, *aff2
, *res
;
3292 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3293 __isl_take isl_aff
*aff2
);
3296 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
3297 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
3298 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
3299 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
3300 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
3301 aff1
= fn(aff1
, aff2
);
3302 if (isl_aff_is_nan(res
))
3303 ok
= isl_aff_is_nan(aff1
);
3305 ok
= isl_aff_plain_is_equal(aff1
, res
);
3311 isl_die(ctx
, isl_error_unknown
,
3312 "unexpected result", return -1);
3318 int test_aff(isl_ctx
*ctx
)
3323 isl_local_space
*ls
;
3327 if (test_bin_aff(ctx
) < 0)
3330 space
= isl_space_set_alloc(ctx
, 0, 1);
3331 ls
= isl_local_space_from_space(space
);
3332 aff
= isl_aff_zero_on_domain(ls
);
3334 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3335 aff
= isl_aff_scale_down_ui(aff
, 3);
3336 aff
= isl_aff_floor(aff
);
3337 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3338 aff
= isl_aff_scale_down_ui(aff
, 2);
3339 aff
= isl_aff_floor(aff
);
3340 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3343 set
= isl_set_read_from_str(ctx
, str
);
3344 aff
= isl_aff_gist(aff
, set
);
3346 aff
= isl_aff_add_constant_si(aff
, -16);
3347 zero
= isl_aff_plain_is_zero(aff
);
3353 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3355 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
3356 aff
= isl_aff_scale_down_ui(aff
, 64);
3357 aff
= isl_aff_floor(aff
);
3358 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
3366 int test_dim_max(isl_ctx
*ctx
)
3370 isl_set
*set1
, *set2
;
3375 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
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] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
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] -> { [i] : 0 <= i <= max(2N,N+6) }";
3390 set
= isl_set_read_from_str(ctx
, str
);
3391 pwaff
= isl_set_dim_max(set
, 0);
3392 set1
= isl_set_from_pw_aff(pwaff
);
3393 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3394 set2
= isl_set_read_from_str(ctx
, str
);
3395 equal
= isl_set_is_equal(set1
, set2
);
3401 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3403 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
3404 set
= isl_set_read_from_str(ctx
, str
);
3405 pwaff
= isl_set_dim_max(set
, 0);
3406 set1
= isl_set_from_pw_aff(pwaff
);
3407 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3408 set2
= isl_set_read_from_str(ctx
, str
);
3409 equal
= isl_set_is_equal(set1
, set2
);
3415 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3417 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
3418 "0 <= i < N and 0 <= j < M }";
3419 map
= isl_map_read_from_str(ctx
, str
);
3420 set
= isl_map_range(map
);
3422 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
3423 set1
= isl_set_from_pw_aff(pwaff
);
3424 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
3425 set2
= isl_set_read_from_str(ctx
, str
);
3426 equal
= isl_set_is_equal(set1
, set2
);
3430 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
3431 set1
= isl_set_from_pw_aff(pwaff
);
3432 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
3433 set2
= isl_set_read_from_str(ctx
, str
);
3434 if (equal
>= 0 && equal
)
3435 equal
= isl_set_is_equal(set1
, set2
);
3444 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3446 /* Check that solutions are properly merged. */
3447 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
3448 "c <= -1 + n - 4a - 2b and c >= -2b and "
3449 "4a >= -4 + n and c >= 0 }";
3450 set
= isl_set_read_from_str(ctx
, str
);
3451 pwaff
= isl_set_dim_min(set
, 2);
3452 set1
= isl_set_from_pw_aff(pwaff
);
3453 str
= "[n] -> { [(0)] : n >= 1 }";
3454 set2
= isl_set_read_from_str(ctx
, str
);
3455 equal
= isl_set_is_equal(set1
, set2
);
3462 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3464 /* Check that empty solution lie in the right space. */
3465 str
= "[n] -> { [t,a] : 1 = 0 }";
3466 set
= isl_set_read_from_str(ctx
, str
);
3467 pwaff
= isl_set_dim_max(set
, 0);
3468 set1
= isl_set_from_pw_aff(pwaff
);
3469 str
= "[n] -> { [t] : 1 = 0 }";
3470 set2
= isl_set_read_from_str(ctx
, str
);
3471 equal
= isl_set_is_equal(set1
, set2
);
3478 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3483 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
3485 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
3489 isl_pw_multi_aff
*pma2
;
3495 ctx
= isl_pw_multi_aff_get_ctx(pma
);
3496 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3497 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
3498 isl_pw_multi_aff_free(pma2
);
3503 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
3504 * represented by "str".
3506 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
3511 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
3515 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
3516 "result not as expected", return -1);
3520 /* Basic test for isl_pw_multi_aff_product.
3522 * Check that multiple pieces are properly handled.
3524 static int test_product_pma(isl_ctx
*ctx
)
3528 isl_pw_multi_aff
*pma1
, *pma2
;
3530 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
3531 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3532 str
= "{ C[] -> D[] }";
3533 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3534 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
3535 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
3536 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
3537 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
3538 isl_pw_multi_aff_free(pma1
);
3545 int test_product(isl_ctx
*ctx
)
3549 isl_union_set
*uset1
, *uset2
;
3553 set
= isl_set_read_from_str(ctx
, str
);
3554 set
= isl_set_product(set
, isl_set_copy(set
));
3555 ok
= isl_set_is_wrapping(set
);
3560 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3563 uset1
= isl_union_set_read_from_str(ctx
, str
);
3564 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
3565 str
= "{ [[] -> []] }";
3566 uset2
= isl_union_set_read_from_str(ctx
, str
);
3567 ok
= isl_union_set_is_equal(uset1
, uset2
);
3568 isl_union_set_free(uset1
);
3569 isl_union_set_free(uset2
);
3573 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3575 if (test_product_pma(ctx
) < 0)
3581 /* Check that two sets are not considered disjoint just because
3582 * they have a different set of (named) parameters.
3584 static int test_disjoint(isl_ctx
*ctx
)
3587 isl_set
*set
, *set2
;
3590 str
= "[n] -> { [[]->[]] }";
3591 set
= isl_set_read_from_str(ctx
, str
);
3592 str
= "{ [[]->[]] }";
3593 set2
= isl_set_read_from_str(ctx
, str
);
3594 disjoint
= isl_set_is_disjoint(set
, set2
);
3600 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3605 int test_equal(isl_ctx
*ctx
)
3608 isl_set
*set
, *set2
;
3612 set
= isl_set_read_from_str(ctx
, str
);
3614 set2
= isl_set_read_from_str(ctx
, str
);
3615 equal
= isl_set_is_equal(set
, set2
);
3621 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3626 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
3627 enum isl_dim_type type
, unsigned pos
, int fixed
)
3631 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
3638 isl_die(ctx
, isl_error_unknown
,
3639 "map not detected as fixed", return -1);
3641 isl_die(ctx
, isl_error_unknown
,
3642 "map detected as fixed", return -1);
3645 int test_fixed(isl_ctx
*ctx
)
3650 str
= "{ [i] -> [i] }";
3651 map
= isl_map_read_from_str(ctx
, str
);
3652 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
3654 str
= "{ [i] -> [1] }";
3655 map
= isl_map_read_from_str(ctx
, str
);
3656 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
3658 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
3659 map
= isl_map_read_from_str(ctx
, str
);
3660 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
3662 map
= isl_map_read_from_str(ctx
, str
);
3663 map
= isl_map_neg(map
);
3664 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
3670 struct isl_vertices_test_data
{
3673 const char *vertex
[2];
3674 } vertices_tests
[] = {
3675 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
3676 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
3677 { "{ A[t, i] : t = 14 and i = 1 }",
3678 1, { "{ A[14, 1] }" } },
3681 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
3683 static int find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
3685 struct isl_vertices_test_data
*data
= user
;
3688 isl_basic_set
*bset
;
3689 isl_pw_multi_aff
*pma
;
3693 ctx
= isl_vertex_get_ctx(vertex
);
3694 bset
= isl_vertex_get_domain(vertex
);
3695 ma
= isl_vertex_get_expr(vertex
);
3696 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
3698 for (i
= 0; i
< data
->n
; ++i
) {
3699 isl_pw_multi_aff
*pma_i
;
3701 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
3702 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
3703 isl_pw_multi_aff_free(pma_i
);
3705 if (equal
< 0 || equal
)
3709 isl_pw_multi_aff_free(pma
);
3710 isl_vertex_free(vertex
);
3715 return equal
? 0 : - 1;
3718 int test_vertices(isl_ctx
*ctx
)
3722 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
3723 isl_basic_set
*bset
;
3724 isl_vertices
*vertices
;
3728 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
3729 vertices
= isl_basic_set_compute_vertices(bset
);
3730 n
= isl_vertices_get_n_vertices(vertices
);
3731 if (vertices_tests
[i
].n
!= n
)
3733 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
3734 &vertices_tests
[i
]) < 0)
3736 isl_vertices_free(vertices
);
3737 isl_basic_set_free(bset
);
3742 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
3749 int test_union_pw(isl_ctx
*ctx
)
3753 isl_union_set
*uset
;
3754 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
3756 str
= "{ [x] -> x^2 }";
3757 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
3758 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
3759 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
3760 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
3761 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
3762 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
3763 isl_union_pw_qpolynomial_free(upwqp1
);
3764 isl_union_pw_qpolynomial_free(upwqp2
);
3768 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3773 int test_output(isl_ctx
*ctx
)
3781 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
3782 pa
= isl_pw_aff_read_from_str(ctx
, str
);
3784 p
= isl_printer_to_str(ctx
);
3785 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
3786 p
= isl_printer_print_pw_aff(p
, pa
);
3787 s
= isl_printer_get_str(p
);
3788 isl_printer_free(p
);
3789 isl_pw_aff_free(pa
);
3793 equal
= !strcmp(s
, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
3798 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3803 int test_sample(isl_ctx
*ctx
)
3806 isl_basic_set
*bset1
, *bset2
;
3809 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
3810 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
3811 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
3812 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
3813 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
3814 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
3815 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
3816 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
3817 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3818 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3819 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3820 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3821 "d - 1073741821e and "
3822 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3823 "3j >= 1 - a + b + 2e and "
3824 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3825 "3i <= 4 - a + 4b - e and "
3826 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3827 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3828 "c <= -1 + a and 3i >= -2 - a + 3e and "
3829 "1073741822e <= 1073741823 - a + 1073741822b + c and "
3830 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3831 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3832 "1073741823e >= 1 + 1073741823b - d and "
3833 "3i >= 1073741823b + c - 1073741823e - f and "
3834 "3i >= 1 + 2b + e + 3g }";
3835 bset1
= isl_basic_set_read_from_str(ctx
, str
);
3836 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
3837 empty
= isl_basic_set_is_empty(bset2
);
3838 subset
= isl_basic_set_is_subset(bset2
, bset1
);
3839 isl_basic_set_free(bset1
);
3840 isl_basic_set_free(bset2
);
3841 if (empty
< 0 || subset
< 0)
3844 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
3846 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
3851 int test_fixed_power(isl_ctx
*ctx
)
3859 str
= "{ [i] -> [i + 1] }";
3860 map
= isl_map_read_from_str(ctx
, str
);
3861 isl_int_set_si(exp
, 23);
3862 map
= isl_map_fixed_power(map
, exp
);
3863 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
3872 int test_slice(isl_ctx
*ctx
)
3878 str
= "{ [i] -> [j] }";
3879 map
= isl_map_read_from_str(ctx
, str
);
3880 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3881 equal
= map_check_equal(map
, "{ [i] -> [i] }");
3886 str
= "{ [i] -> [j] }";
3887 map
= isl_map_read_from_str(ctx
, str
);
3888 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3889 equal
= map_check_equal(map
, "{ [i] -> [j] }");
3894 str
= "{ [i] -> [j] }";
3895 map
= isl_map_read_from_str(ctx
, str
);
3896 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3897 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
3902 str
= "{ [i] -> [j] }";
3903 map
= isl_map_read_from_str(ctx
, str
);
3904 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3905 equal
= map_check_equal(map
, "{ [0] -> [j] }");
3910 str
= "{ [i] -> [j] }";
3911 map
= isl_map_read_from_str(ctx
, str
);
3912 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
3913 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
3918 str
= "{ [i] -> [j] }";
3919 map
= isl_map_read_from_str(ctx
, str
);
3920 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
3921 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
3929 int test_eliminate(isl_ctx
*ctx
)
3935 str
= "{ [i] -> [j] : i = 2j }";
3936 map
= isl_map_read_from_str(ctx
, str
);
3937 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
3938 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
3946 /* Check that isl_set_dim_residue_class detects that the values of j
3947 * in the set below are all odd and that it does not detect any spurious
3950 static int test_residue_class(isl_ctx
*ctx
)
3957 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
3958 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
3959 set
= isl_set_read_from_str(ctx
, str
);
3962 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
3964 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
3965 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
3974 int test_align_parameters(isl_ctx
*ctx
)
3978 isl_multi_aff
*ma1
, *ma2
;
3981 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
3982 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
3984 space
= isl_space_params_alloc(ctx
, 1);
3985 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
3986 ma1
= isl_multi_aff_align_params(ma1
, space
);
3988 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
3989 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
3991 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
3993 isl_multi_aff_free(ma1
);
3994 isl_multi_aff_free(ma2
);
3999 isl_die(ctx
, isl_error_unknown
,
4000 "result not as expected", return -1);
4005 static int test_list(isl_ctx
*ctx
)
4007 isl_id
*a
, *b
, *c
, *d
, *id
;
4011 a
= isl_id_alloc(ctx
, "a", NULL
);
4012 b
= isl_id_alloc(ctx
, "b", NULL
);
4013 c
= isl_id_alloc(ctx
, "c", NULL
);
4014 d
= isl_id_alloc(ctx
, "d", NULL
);
4016 list
= isl_id_list_alloc(ctx
, 4);
4017 list
= isl_id_list_add(list
, a
);
4018 list
= isl_id_list_add(list
, b
);
4019 list
= isl_id_list_add(list
, c
);
4020 list
= isl_id_list_add(list
, d
);
4021 list
= isl_id_list_drop(list
, 1, 1);
4023 if (isl_id_list_n_id(list
) != 3) {
4024 isl_id_list_free(list
);
4025 isl_die(ctx
, isl_error_unknown
,
4026 "unexpected number of elements in list", return -1);
4029 id
= isl_id_list_get_id(list
, 0);
4032 id
= isl_id_list_get_id(list
, 1);
4035 id
= isl_id_list_get_id(list
, 2);
4039 isl_id_list_free(list
);
4042 isl_die(ctx
, isl_error_unknown
,
4043 "unexpected elements in list", return -1);
4048 const char *set_conversion_tests
[] = {
4049 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4050 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4051 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4052 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4055 /* Check that converting from isl_set to isl_pw_multi_aff and back
4056 * to isl_set produces the original isl_set.
4058 static int test_set_conversion(isl_ctx
*ctx
)
4062 isl_set
*set1
, *set2
;
4063 isl_pw_multi_aff
*pma
;
4066 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
4067 str
= set_conversion_tests
[i
];
4068 set1
= isl_set_read_from_str(ctx
, str
);
4069 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
4070 set2
= isl_set_from_pw_multi_aff(pma
);
4071 equal
= isl_set_is_equal(set1
, set2
);
4078 isl_die(ctx
, isl_error_unknown
, "bad conversion",
4085 /* Check that converting from isl_map to isl_pw_multi_aff and back
4086 * to isl_map produces the original isl_map.
4088 static int test_map_conversion(isl_ctx
*ctx
)
4091 isl_map
*map1
, *map2
;
4092 isl_pw_multi_aff
*pma
;
4095 str
= "{ [a, b, c, d] -> s0[a, b, e, f] : "
4096 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4097 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4098 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4100 map1
= isl_map_read_from_str(ctx
, str
);
4101 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
4102 map2
= isl_map_from_pw_multi_aff(pma
);
4103 equal
= isl_map_is_equal(map1
, map2
);
4110 isl_die(ctx
, isl_error_unknown
, "bad conversion", return -1);
4115 static int test_conversion(isl_ctx
*ctx
)
4117 if (test_set_conversion(ctx
) < 0)
4119 if (test_map_conversion(ctx
) < 0)
4124 /* Check that isl_basic_map_curry does not modify input.
4126 static int test_curry(isl_ctx
*ctx
)
4129 isl_basic_map
*bmap1
, *bmap2
;
4132 str
= "{ [A[] -> B[]] -> C[] }";
4133 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
4134 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
4135 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
4136 isl_basic_map_free(bmap1
);
4137 isl_basic_map_free(bmap2
);
4142 isl_die(ctx
, isl_error_unknown
,
4143 "curried map should not be equal to original",
4153 } preimage_tests
[] = {
4154 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4155 "{ A[j,i] -> B[i,j] }",
4156 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4157 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4158 "{ A[a,b] -> B[a/2,b/6] }",
4159 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4160 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4161 "{ A[a,b] -> B[a/2,b/6] }",
4162 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4163 "exists i,j : a = 2 i and b = 6 j }" },
4164 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4165 "[n] -> { : 0 <= n <= 100 }" },
4166 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4167 "{ A[a] -> B[2a] }",
4168 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4169 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4170 "{ A[a] -> B[([a/2])] }",
4171 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4172 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4173 "{ A[a] -> B[a,a,a/3] }",
4174 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4175 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4176 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4179 static int test_preimage_basic_set(isl_ctx
*ctx
)
4182 isl_basic_set
*bset1
, *bset2
;
4186 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
4187 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
4188 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
4189 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
4190 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
4191 equal
= isl_basic_set_is_equal(bset1
, bset2
);
4192 isl_basic_set_free(bset1
);
4193 isl_basic_set_free(bset2
);
4197 isl_die(ctx
, isl_error_unknown
, "bad preimage",
4208 } preimage_domain_tests
[] = {
4209 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4210 "{ A[j,i] -> B[i,j] }",
4211 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4212 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4213 "{ A[i] -> B[i + 1] }",
4214 "{ A[i] -> C[i + 1] }" },
4215 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4216 "{ A[i] -> B[i + 1] }",
4217 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4218 { "{ B[i] -> C[([i/2])] }",
4219 "{ A[i] -> B[2i] }",
4220 "{ A[i] -> C[i] }" },
4221 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4222 "{ A[i] -> B[([i/5]), ([i/7])] }",
4223 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4224 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4225 "[N] -> { A[] -> B[([N/5])] }",
4226 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4227 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4228 "{ A[i] -> B[2i] }",
4229 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4230 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4231 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4232 "{ A[i] -> B[2i] }",
4233 "{ A[i] -> C[2i] }" },
4236 static int test_preimage_union_map(isl_ctx
*ctx
)
4239 isl_union_map
*umap1
, *umap2
;
4243 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
4244 umap1
= isl_union_map_read_from_str(ctx
,
4245 preimage_domain_tests
[i
].map
);
4246 ma
= isl_multi_aff_read_from_str(ctx
,
4247 preimage_domain_tests
[i
].ma
);
4248 umap2
= isl_union_map_read_from_str(ctx
,
4249 preimage_domain_tests
[i
].res
);
4250 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
4251 equal
= isl_union_map_is_equal(umap1
, umap2
);
4252 isl_union_map_free(umap1
);
4253 isl_union_map_free(umap2
);
4257 isl_die(ctx
, isl_error_unknown
, "bad preimage",
4264 static int test_preimage(isl_ctx
*ctx
)
4266 if (test_preimage_basic_set(ctx
) < 0)
4268 if (test_preimage_union_map(ctx
) < 0)
4278 } pullback_tests
[] = {
4279 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
4280 "{ A[a,b] -> C[b + 2a] }" },
4281 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
4282 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
4283 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
4284 "{ A[a] -> C[(a)/6] }" },
4285 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
4286 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
4287 "{ A[a] -> C[(2a)/3] }" },
4288 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
4289 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
4290 "{ A[i,j] -> C[i + j, i + j] }"},
4291 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
4292 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
4293 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
4296 static int test_pullback(isl_ctx
*ctx
)
4299 isl_multi_aff
*ma1
, *ma2
;
4303 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
4304 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
4305 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
4306 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
4307 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
4308 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
4309 isl_multi_aff_free(ma1
);
4310 isl_multi_aff_free(ma2
);
4314 isl_die(ctx
, isl_error_unknown
, "bad pullback",
4321 /* Check that negation is printed correctly.
4323 static int test_ast(isl_ctx
*ctx
)
4325 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
4329 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
4330 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
4331 expr
= isl_ast_expr_add(expr1
, expr2
);
4332 expr
= isl_ast_expr_neg(expr
);
4333 str
= isl_ast_expr_to_str(expr
);
4334 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
4336 isl_ast_expr_free(expr
);
4341 isl_die(ctx
, isl_error_unknown
,
4342 "isl_ast_expr printed incorrectly", return -1);
4344 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
4345 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
4346 expr
= isl_ast_expr_add(expr1
, expr2
);
4347 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
4348 expr
= isl_ast_expr_sub(expr3
, expr
);
4349 str
= isl_ast_expr_to_str(expr
);
4350 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
4352 isl_ast_expr_free(expr
);
4357 isl_die(ctx
, isl_error_unknown
,
4358 "isl_ast_expr printed incorrectly", return -1);
4363 /* Check that isl_ast_build_expr_from_set returns a valid expression
4364 * for an empty set. Note that isl_ast_build_expr_from_set getting
4365 * called on an empty set probably indicates a bug in the caller.
4367 static int test_ast_build(isl_ctx
*ctx
)
4370 isl_ast_build
*build
;
4373 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4374 build
= isl_ast_build_from_context(set
);
4376 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
4377 expr
= isl_ast_build_expr_from_set(build
, set
);
4379 isl_ast_expr_free(expr
);
4380 isl_ast_build_free(build
);
4388 /* Internal data structure for before_for and after_for callbacks.
4390 * depth is the current depth
4391 * before is the number of times before_for has been called
4392 * after is the number of times after_for has been called
4394 struct isl_test_codegen_data
{
4400 /* This function is called before each for loop in the AST generated
4401 * from test_ast_gen1.
4403 * Increment the number of calls and the depth.
4404 * Check that the space returned by isl_ast_build_get_schedule_space
4405 * matches the target space of the schedule returned by
4406 * isl_ast_build_get_schedule.
4407 * Return an isl_id that is checked by the corresponding call
4410 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
4413 struct isl_test_codegen_data
*data
= user
;
4416 isl_union_map
*schedule
;
4417 isl_union_set
*uset
;
4422 ctx
= isl_ast_build_get_ctx(build
);
4424 if (data
->before
>= 3)
4425 isl_die(ctx
, isl_error_unknown
,
4426 "unexpected number of for nodes", return NULL
);
4427 if (data
->depth
>= 2)
4428 isl_die(ctx
, isl_error_unknown
,
4429 "unexpected depth", return NULL
);
4431 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
4435 schedule
= isl_ast_build_get_schedule(build
);
4436 uset
= isl_union_map_range(schedule
);
4439 if (isl_union_set_n_set(uset
) != 1) {
4440 isl_union_set_free(uset
);
4441 isl_die(ctx
, isl_error_unknown
,
4442 "expecting single range space", return NULL
);
4445 space
= isl_ast_build_get_schedule_space(build
);
4446 set
= isl_union_set_extract_set(uset
, space
);
4447 isl_union_set_free(uset
);
4448 empty
= isl_set_is_empty(set
);
4454 isl_die(ctx
, isl_error_unknown
,
4455 "spaces don't match", return NULL
);
4457 return isl_id_alloc(ctx
, name
, NULL
);
4460 /* This function is called after each for loop in the AST generated
4461 * from test_ast_gen1.
4463 * Increment the number of calls and decrement the depth.
4464 * Check that the annotation attached to the node matches
4465 * the isl_id returned by the corresponding call to before_for.
4467 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
4468 __isl_keep isl_ast_build
*build
, void *user
)
4470 struct isl_test_codegen_data
*data
= user
;
4478 if (data
->after
> data
->before
)
4479 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
4480 "mismatch in number of for nodes",
4481 return isl_ast_node_free(node
));
4483 id
= isl_ast_node_get_annotation(node
);
4485 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
4486 "missing annotation", return isl_ast_node_free(node
));
4488 name
= isl_id_get_name(id
);
4489 valid
= name
&& atoi(name
+ 1) == data
->depth
;
4493 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
4494 "wrong annotation", return isl_ast_node_free(node
));
4499 /* Check that the before_each_for and after_each_for callbacks
4500 * are called for each for loop in the generated code,
4501 * that they are called in the right order and that the isl_id
4502 * returned from the before_each_for callback is attached to
4503 * the isl_ast_node passed to the corresponding after_each_for call.
4505 static int test_ast_gen1(isl_ctx
*ctx
)
4509 isl_union_map
*schedule
;
4510 isl_ast_build
*build
;
4512 struct isl_test_codegen_data data
;
4514 str
= "[N] -> { : N >= 10 }";
4515 set
= isl_set_read_from_str(ctx
, str
);
4516 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
4517 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
4518 schedule
= isl_union_map_read_from_str(ctx
, str
);
4523 build
= isl_ast_build_from_context(set
);
4524 build
= isl_ast_build_set_before_each_for(build
,
4525 &before_for
, &data
);
4526 build
= isl_ast_build_set_after_each_for(build
,
4528 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4529 isl_ast_build_free(build
);
4533 isl_ast_node_free(tree
);
4535 if (data
.before
!= 3 || data
.after
!= 3)
4536 isl_die(ctx
, isl_error_unknown
,
4537 "unexpected number of for nodes", return -1);
4542 /* Check that the AST generator handles domains that are integrally disjoint
4543 * but not ratinoally disjoint.
4545 static int test_ast_gen2(isl_ctx
*ctx
)
4549 isl_union_map
*schedule
;
4550 isl_union_map
*options
;
4551 isl_ast_build
*build
;
4554 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
4555 schedule
= isl_union_map_read_from_str(ctx
, str
);
4556 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4557 build
= isl_ast_build_from_context(set
);
4559 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
4560 options
= isl_union_map_read_from_str(ctx
, str
);
4561 build
= isl_ast_build_set_options(build
, options
);
4562 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4563 isl_ast_build_free(build
);
4566 isl_ast_node_free(tree
);
4571 /* Increment *user on each call.
4573 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
4574 __isl_keep isl_ast_build
*build
, void *user
)
4583 /* Test that unrolling tries to minimize the number of instances.
4584 * In particular, for the schedule given below, make sure it generates
4585 * 3 nodes (rather than 101).
4587 static int test_ast_gen3(isl_ctx
*ctx
)
4591 isl_union_map
*schedule
;
4592 isl_union_map
*options
;
4593 isl_ast_build
*build
;
4597 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
4598 schedule
= isl_union_map_read_from_str(ctx
, str
);
4599 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4601 str
= "{ [i] -> unroll[0] }";
4602 options
= isl_union_map_read_from_str(ctx
, str
);
4604 build
= isl_ast_build_from_context(set
);
4605 build
= isl_ast_build_set_options(build
, options
);
4606 build
= isl_ast_build_set_at_each_domain(build
,
4607 &count_domains
, &n_domain
);
4608 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4609 isl_ast_build_free(build
);
4613 isl_ast_node_free(tree
);
4616 isl_die(ctx
, isl_error_unknown
,
4617 "unexpected number of for nodes", return -1);
4622 /* Check that if the ast_build_exploit_nested_bounds options is set,
4623 * we do not get an outer if node in the generated AST,
4624 * while we do get such an outer if node if the options is not set.
4626 static int test_ast_gen4(isl_ctx
*ctx
)
4630 isl_union_map
*schedule
;
4631 isl_ast_build
*build
;
4633 enum isl_ast_node_type type
;
4636 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
4637 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
4639 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
4641 schedule
= isl_union_map_read_from_str(ctx
, str
);
4642 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4643 build
= isl_ast_build_from_context(set
);
4644 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4645 isl_ast_build_free(build
);
4649 type
= isl_ast_node_get_type(tree
);
4650 isl_ast_node_free(tree
);
4652 if (type
== isl_ast_node_if
)
4653 isl_die(ctx
, isl_error_unknown
,
4654 "not expecting if node", return -1);
4656 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
4658 schedule
= isl_union_map_read_from_str(ctx
, str
);
4659 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4660 build
= isl_ast_build_from_context(set
);
4661 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4662 isl_ast_build_free(build
);
4666 type
= isl_ast_node_get_type(tree
);
4667 isl_ast_node_free(tree
);
4669 if (type
!= isl_ast_node_if
)
4670 isl_die(ctx
, isl_error_unknown
,
4671 "expecting if node", return -1);
4673 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
4678 /* This function is called for each leaf in the AST generated
4679 * from test_ast_gen5.
4681 * We finalize the AST generation by extending the outer schedule
4682 * with a zero-dimensional schedule. If this results in any for loops,
4683 * then this means that we did not pass along enough information
4684 * about the outer schedule to the inner AST generation.
4686 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
4689 isl_union_map
*schedule
, *extra
;
4692 schedule
= isl_ast_build_get_schedule(build
);
4693 extra
= isl_union_map_copy(schedule
);
4694 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
4695 schedule
= isl_union_map_range_product(schedule
, extra
);
4696 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4697 isl_ast_build_free(build
);
4702 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
4703 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
4704 "code should not contain any for loop",
4705 return isl_ast_node_free(tree
));
4710 /* Check that we do not lose any information when going back and
4711 * forth between internal and external schedule.
4713 * In particular, we create an AST where we unroll the only
4714 * non-constant dimension in the schedule. We therefore do
4715 * not expect any for loops in the AST. However, older versions
4716 * of isl would not pass along enough information about the outer
4717 * schedule when performing an inner code generation from a create_leaf
4718 * callback, resulting in the inner code generation producing a for loop.
4720 static int test_ast_gen5(isl_ctx
*ctx
)
4724 isl_union_map
*schedule
, *options
;
4725 isl_ast_build
*build
;
4728 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
4729 schedule
= isl_union_map_read_from_str(ctx
, str
);
4731 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
4732 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
4733 options
= isl_union_map_read_from_str(ctx
, str
);
4735 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4736 build
= isl_ast_build_from_context(set
);
4737 build
= isl_ast_build_set_options(build
, options
);
4738 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
4739 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4740 isl_ast_build_free(build
);
4741 isl_ast_node_free(tree
);
4748 static int test_ast_gen(isl_ctx
*ctx
)
4750 if (test_ast_gen1(ctx
) < 0)
4752 if (test_ast_gen2(ctx
) < 0)
4754 if (test_ast_gen3(ctx
) < 0)
4756 if (test_ast_gen4(ctx
) < 0)
4758 if (test_ast_gen5(ctx
) < 0)
4763 /* Check if dropping output dimensions from an isl_pw_multi_aff
4766 static int test_pw_multi_aff(isl_ctx
*ctx
)
4769 isl_pw_multi_aff
*pma1
, *pma2
;
4772 str
= "{ [i,j] -> [i+j, 4i-j] }";
4773 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4774 str
= "{ [i,j] -> [4i-j] }";
4775 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4777 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
4779 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
4781 isl_pw_multi_aff_free(pma1
);
4782 isl_pw_multi_aff_free(pma2
);
4786 isl_die(ctx
, isl_error_unknown
,
4787 "expressions not equal", return -1);
4792 /* Check that we can properly parse multi piecewise affine expressions
4793 * where the piecewise affine expressions have different domains.
4795 static int test_multi_pw_aff(isl_ctx
*ctx
)
4798 isl_set
*dom
, *dom2
;
4799 isl_multi_pw_aff
*mpa1
, *mpa2
;
4804 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
4805 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
4806 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
4807 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
4808 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
4809 str
= "{ [i] -> [(i : i > 0), 2i] }";
4810 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
4812 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
4814 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
4815 dom
= isl_pw_aff_domain(pa
);
4816 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
4817 dom2
= isl_pw_aff_domain(pa
);
4818 equal_domain
= isl_set_is_equal(dom
, dom2
);
4822 isl_multi_pw_aff_free(mpa1
);
4823 isl_multi_pw_aff_free(mpa2
);
4828 isl_die(ctx
, isl_error_unknown
,
4829 "expressions not equal", return -1);
4831 if (equal_domain
< 0)
4834 isl_die(ctx
, isl_error_unknown
,
4835 "domains unexpectedly equal", return -1);
4840 /* This is a regression test for a bug where isl_basic_map_simplify
4841 * would end up in an infinite loop. In particular, we construct
4842 * an empty basic set that is not obviously empty.
4843 * isl_basic_set_is_empty marks the basic set as empty.
4844 * After projecting out i3, the variable can be dropped completely,
4845 * but isl_basic_map_simplify refrains from doing so if the basic set
4846 * is empty and would end up in an infinite loop if it didn't test
4847 * explicitly for empty basic maps in the outer loop.
4849 static int test_simplify(isl_ctx
*ctx
)
4852 isl_basic_set
*bset
;
4855 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
4856 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
4857 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
4859 bset
= isl_basic_set_read_from_str(ctx
, str
);
4860 empty
= isl_basic_set_is_empty(bset
);
4861 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
4862 isl_basic_set_free(bset
);
4866 isl_die(ctx
, isl_error_unknown
,
4867 "basic set should be empty", return -1);
4872 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
4873 * with gbr context would fail to disable the use of the shifted tableau
4874 * when transferring equalities for the input to the context, resulting
4875 * in invalid sample values.
4877 static int test_partial_lexmin(isl_ctx
*ctx
)
4880 isl_basic_set
*bset
;
4881 isl_basic_map
*bmap
;
4884 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
4885 bmap
= isl_basic_map_read_from_str(ctx
, str
);
4886 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
4887 bset
= isl_basic_set_read_from_str(ctx
, str
);
4888 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
4897 /* Check that the variable compression performed on the existentially
4898 * quantified variables inside isl_basic_set_compute_divs is not confused
4899 * by the implicit equalities among the parameters.
4901 static int test_compute_divs(isl_ctx
*ctx
)
4904 isl_basic_set
*bset
;
4907 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
4908 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
4909 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
4910 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
4911 bset
= isl_basic_set_read_from_str(ctx
, str
);
4912 set
= isl_basic_set_compute_divs(bset
);
4924 { "{ rat: [i] : 0 <= i <= 10 }",
4925 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
4926 { "{ rat: [i] : FALSE }",
4927 "{ rat: coefficients[[cst] -> [a]] }" },
4929 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
4936 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
4937 "{ rat: [i] : 0 <= i <= 10 }" },
4938 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
4940 { "{ rat: coefficients[[cst] -> [a]] }",
4941 "{ rat: [i] : FALSE }" },
4944 /* Test the basic functionality of isl_basic_set_coefficients and
4945 * isl_basic_set_solutions.
4947 static int test_dual(isl_ctx
*ctx
)
4951 for (i
= 0; i
< ARRAY_SIZE(coef_tests
); ++i
) {
4953 isl_basic_set
*bset1
, *bset2
;
4955 bset1
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].set
);
4956 bset2
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].dual
);
4957 bset1
= isl_basic_set_coefficients(bset1
);
4958 equal
= isl_basic_set_is_equal(bset1
, bset2
);
4959 isl_basic_set_free(bset1
);
4960 isl_basic_set_free(bset2
);
4964 isl_die(ctx
, isl_error_unknown
,
4965 "incorrect dual", return -1);
4968 for (i
= 0; i
< ARRAY_SIZE(sol_tests
); ++i
) {
4970 isl_basic_set
*bset1
, *bset2
;
4972 bset1
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].set
);
4973 bset2
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].dual
);
4974 bset1
= isl_basic_set_solutions(bset1
);
4975 equal
= isl_basic_set_is_equal(bset1
, bset2
);
4976 isl_basic_set_free(bset1
);
4977 isl_basic_set_free(bset2
);
4981 isl_die(ctx
, isl_error_unknown
,
4982 "incorrect dual", return -1);
4990 int (*fn
)(isl_ctx
*ctx
);
4992 { "dual", &test_dual
},
4993 { "dependence analysis", &test_flow
},
4994 { "val", &test_val
},
4995 { "compute divs", &test_compute_divs
},
4996 { "partial lexmin", &test_partial_lexmin
},
4997 { "simplify", &test_simplify
},
4998 { "curry", &test_curry
},
4999 { "piecewise multi affine expressions", &test_pw_multi_aff
},
5000 { "multi piecewise affine expressions", &test_multi_pw_aff
},
5001 { "conversion", &test_conversion
},
5002 { "list", &test_list
},
5003 { "align parameters", &test_align_parameters
},
5004 { "preimage", &test_preimage
},
5005 { "pullback", &test_pullback
},
5006 { "AST", &test_ast
},
5007 { "AST build", &test_ast_build
},
5008 { "AST generation", &test_ast_gen
},
5009 { "eliminate", &test_eliminate
},
5010 { "residue class", &test_residue_class
},
5011 { "div", &test_div
},
5012 { "slice", &test_slice
},
5013 { "fixed power", &test_fixed_power
},
5014 { "sample", &test_sample
},
5015 { "output", &test_output
},
5016 { "vertices", &test_vertices
},
5017 { "fixed", &test_fixed
},
5018 { "equal", &test_equal
},
5019 { "disjoint", &test_disjoint
},
5020 { "product", &test_product
},
5021 { "dim_max", &test_dim_max
},
5022 { "affine", &test_aff
},
5023 { "injective", &test_injective
},
5024 { "schedule", &test_schedule
},
5025 { "union_pw", &test_union_pw
},
5026 { "parse", &test_parse
},
5027 { "single-valued", &test_sv
},
5028 { "affine hull", &test_affine_hull
},
5029 { "coalesce", &test_coalesce
},
5030 { "factorize", &test_factorize
},
5031 { "subset", &test_subset
},
5032 { "subtract", &test_subtract
},
5033 { "lexmin", &test_lexmin
},
5034 { "min", &test_min
},
5035 { "gist", &test_gist
},
5036 { "piecewise quasi-polynomials", &test_pwqp
},
5042 struct isl_ctx
*ctx
;
5044 srcdir
= getenv("srcdir");
5047 ctx
= isl_ctx_alloc();
5048 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
5049 printf("%s\n", tests
[i
].name
);
5050 if (tests
[i
].fn(ctx
) < 0)
5056 test_split_periods(ctx
);
5058 test_bijective(ctx
);
5062 test_construction(ctx
);
5064 test_application(ctx
);
5065 test_convex_hull(ctx
);