2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
12 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
15 * B.P. 105 - 78153 Le Chesnay, France
21 #include <isl_ctx_private.h>
22 #include <isl_map_private.h>
23 #include <isl_aff_private.h>
26 #include <isl_constraint_private.h>
27 #include <isl/polynomial.h>
28 #include <isl/union_set.h>
29 #include <isl/union_map.h>
30 #include <isl_factorization.h>
31 #include <isl/schedule.h>
32 #include <isl/schedule_node.h>
33 #include <isl_options_private.h>
34 #include <isl/vertices.h>
35 #include <isl/ast_build.h>
38 #include <isl_ast_build_expr.h>
39 #include <isl/options.h>
41 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
45 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
48 char *pattern
= "%s/test_inputs/%s.%s";
50 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
52 filename
= isl_alloc_array(ctx
, char, length
);
57 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
62 void test_parse_map(isl_ctx
*ctx
, const char *str
)
66 map
= isl_map_read_from_str(ctx
, str
);
71 int test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
76 map
= isl_map_read_from_str(ctx
, str
);
77 map2
= isl_map_read_from_str(ctx
, str2
);
78 equal
= isl_map_is_equal(map
, map2
);
85 isl_die(ctx
, isl_error_unknown
, "maps not equal",
91 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
93 isl_pw_qpolynomial
*pwqp
;
95 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
97 isl_pw_qpolynomial_free(pwqp
);
100 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
104 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
106 isl_pw_aff_free(pwaff
);
109 /* Check that we can read an isl_multi_val from "str" without errors.
111 static int test_parse_multi_val(isl_ctx
*ctx
, const char *str
)
115 mv
= isl_multi_val_read_from_str(ctx
, str
);
116 isl_multi_val_free(mv
);
121 int test_parse(struct isl_ctx
*ctx
)
124 const char *str
, *str2
;
126 if (test_parse_multi_val(ctx
, "{ A[B[2] -> C[5, 7]] }") < 0)
128 if (test_parse_multi_val(ctx
, "[n] -> { [2] }") < 0)
130 if (test_parse_multi_val(ctx
, "{ A[4, infty, NaN, -1/2, 2/3] }") < 0)
133 str
= "{ [i] -> [-i] }";
134 map
= isl_map_read_from_str(ctx
, str
);
138 str
= "{ A[i] -> L[([i/3])] }";
139 map
= isl_map_read_from_str(ctx
, str
);
143 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
144 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
145 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
147 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
148 str2
= "{ [x, y] : 2y >= 6 - x }";
149 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
152 if (test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
153 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
155 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
156 if (test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }",
160 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
161 map
= isl_map_read_from_str(ctx
, str
);
162 str
= "{ [new, old] -> [o0, o1] : "
163 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
164 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
165 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
166 map2
= isl_map_read_from_str(ctx
, str
);
167 assert(isl_map_is_equal(map
, map2
));
171 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
172 map
= isl_map_read_from_str(ctx
, str
);
173 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
174 map2
= isl_map_read_from_str(ctx
, str
);
175 assert(isl_map_is_equal(map
, map2
));
179 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
180 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
181 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
184 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
185 str2
= "{ [i,j] -> [min(i,j)] }";
186 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
189 str
= "{ [i,j] : i != j }";
190 str2
= "{ [i,j] : i < j or i > j }";
191 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
194 str
= "{ [i,j] : (i+1)*2 >= j }";
195 str2
= "{ [i, j] : j <= 2 + 2i }";
196 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
199 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
200 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
201 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
204 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
205 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
206 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
209 str
= "{ [x] : x >= 0 }";
210 str2
= "{ [x] : x-0 >= 0 }";
211 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
214 str
= "{ [i] : ((i > 10)) }";
215 str2
= "{ [i] : i >= 11 }";
216 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
219 str
= "{ [i] -> [0] }";
220 str2
= "{ [i] -> [0 * i] }";
221 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
224 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
225 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
226 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
227 test_parse_pwqp(ctx
, "{ [x] -> ([(x)/2] * [(x)/3]) }");
229 if (test_parse_map_equal(ctx
, "{ [a] -> [b] : (not false) }",
230 "{ [a] -> [b] : true }") < 0)
233 if (test_parse_map_equal(ctx
, "{ [i] : i/2 <= 5 }",
234 "{ [i] : i <= 10 }") < 0)
237 if (test_parse_map_equal(ctx
, "{Sym=[n] [i] : i <= n }",
238 "[n] -> { [i] : i <= n }") < 0)
241 if (test_parse_map_equal(ctx
, "{ [*] }", "{ [a] }") < 0)
244 if (test_parse_map_equal(ctx
, "{ [i] : 2*floor(i/2) = i }",
245 "{ [i] : exists a : i = 2 a }") < 0)
248 if (test_parse_map_equal(ctx
, "{ [a] -> [b] : a = 5 implies b = 5 }",
249 "{ [a] -> [b] : a != 5 or b = 5 }") < 0)
252 if (test_parse_map_equal(ctx
, "{ [a] -> [a - 1 : a > 0] }",
253 "{ [a] -> [a - 1] : a > 0 }") < 0)
255 if (test_parse_map_equal(ctx
,
256 "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
257 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }") < 0)
259 if (test_parse_map_equal(ctx
,
260 "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
261 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
263 if (test_parse_map_equal(ctx
,
264 "{ [a] -> [(a * 2) : a >= 0; 0 : a < 0] }",
265 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
267 if (test_parse_map_equal(ctx
,
268 "{ [a] -> [(a * 2 : a >= 0); 0 : a < 0] }",
269 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
271 if (test_parse_map_equal(ctx
,
272 "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
273 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
279 static int test_read(isl_ctx
*ctx
)
283 isl_basic_set
*bset1
, *bset2
;
284 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
287 filename
= get_filename(ctx
, "set", "omega");
289 input
= fopen(filename
, "r");
292 bset1
= isl_basic_set_read_from_file(ctx
, input
);
293 bset2
= isl_basic_set_read_from_str(ctx
, str
);
295 equal
= isl_basic_set_is_equal(bset1
, bset2
);
297 isl_basic_set_free(bset1
);
298 isl_basic_set_free(bset2
);
306 isl_die(ctx
, isl_error_unknown
,
307 "read sets not equal", return -1);
312 static int test_bounded(isl_ctx
*ctx
)
317 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
318 bounded
= isl_set_is_bounded(set
);
324 isl_die(ctx
, isl_error_unknown
,
325 "set not considered bounded", return -1);
327 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
328 bounded
= isl_set_is_bounded(set
);
335 isl_die(ctx
, isl_error_unknown
,
336 "set considered bounded", return -1);
338 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
339 bounded
= isl_set_is_bounded(set
);
345 isl_die(ctx
, isl_error_unknown
,
346 "set considered bounded", return -1);
351 /* Construct the basic set { [i] : 5 <= i <= N } */
352 static int test_construction(isl_ctx
*ctx
)
362 dim
= isl_space_set_alloc(ctx
, 1, 1);
363 bset
= isl_basic_set_universe(isl_space_copy(dim
));
364 ls
= isl_local_space_from_space(dim
);
366 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
367 isl_int_set_si(v
, -1);
368 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
369 isl_int_set_si(v
, 1);
370 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
371 bset
= isl_basic_set_add_constraint(bset
, c
);
373 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
374 isl_int_set_si(v
, 1);
375 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
376 isl_int_set_si(v
, -5);
377 isl_constraint_set_constant(c
, v
);
378 bset
= isl_basic_set_add_constraint(bset
, c
);
380 isl_local_space_free(ls
);
381 isl_basic_set_free(bset
);
388 static int test_dim(isl_ctx
*ctx
)
391 isl_map
*map1
, *map2
;
394 map1
= isl_map_read_from_str(ctx
,
395 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
396 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
397 map2
= isl_map_read_from_str(ctx
,
398 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
399 equal
= isl_map_is_equal(map1
, map2
);
402 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
403 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
404 if (equal
>= 0 && equal
)
405 equal
= isl_map_is_equal(map1
, map2
);
413 isl_die(ctx
, isl_error_unknown
,
414 "unexpected result", return -1);
416 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
417 map1
= isl_map_read_from_str(ctx
, str
);
418 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
419 map2
= isl_map_read_from_str(ctx
, str
);
420 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
421 equal
= isl_map_is_equal(map1
, map2
);
428 isl_die(ctx
, isl_error_unknown
,
429 "unexpected result", return -1);
435 __isl_give isl_val
*(*op
)(__isl_take isl_val
*v
);
439 { &isl_val_neg
, "0", "0" },
440 { &isl_val_abs
, "0", "0" },
441 { &isl_val_2exp
, "0", "1" },
442 { &isl_val_floor
, "0", "0" },
443 { &isl_val_ceil
, "0", "0" },
444 { &isl_val_neg
, "1", "-1" },
445 { &isl_val_neg
, "-1", "1" },
446 { &isl_val_neg
, "1/2", "-1/2" },
447 { &isl_val_neg
, "-1/2", "1/2" },
448 { &isl_val_neg
, "infty", "-infty" },
449 { &isl_val_neg
, "-infty", "infty" },
450 { &isl_val_neg
, "NaN", "NaN" },
451 { &isl_val_abs
, "1", "1" },
452 { &isl_val_abs
, "-1", "1" },
453 { &isl_val_abs
, "1/2", "1/2" },
454 { &isl_val_abs
, "-1/2", "1/2" },
455 { &isl_val_abs
, "infty", "infty" },
456 { &isl_val_abs
, "-infty", "infty" },
457 { &isl_val_abs
, "NaN", "NaN" },
458 { &isl_val_floor
, "1", "1" },
459 { &isl_val_floor
, "-1", "-1" },
460 { &isl_val_floor
, "1/2", "0" },
461 { &isl_val_floor
, "-1/2", "-1" },
462 { &isl_val_floor
, "infty", "infty" },
463 { &isl_val_floor
, "-infty", "-infty" },
464 { &isl_val_floor
, "NaN", "NaN" },
465 { &isl_val_ceil
, "1", "1" },
466 { &isl_val_ceil
, "-1", "-1" },
467 { &isl_val_ceil
, "1/2", "1" },
468 { &isl_val_ceil
, "-1/2", "0" },
469 { &isl_val_ceil
, "infty", "infty" },
470 { &isl_val_ceil
, "-infty", "-infty" },
471 { &isl_val_ceil
, "NaN", "NaN" },
472 { &isl_val_2exp
, "-3", "1/8" },
473 { &isl_val_2exp
, "-1", "1/2" },
474 { &isl_val_2exp
, "1", "2" },
475 { &isl_val_2exp
, "2", "4" },
476 { &isl_val_2exp
, "3", "8" },
477 { &isl_val_inv
, "1", "1" },
478 { &isl_val_inv
, "2", "1/2" },
479 { &isl_val_inv
, "1/2", "2" },
480 { &isl_val_inv
, "-2", "-1/2" },
481 { &isl_val_inv
, "-1/2", "-2" },
482 { &isl_val_inv
, "0", "NaN" },
483 { &isl_val_inv
, "NaN", "NaN" },
484 { &isl_val_inv
, "infty", "0" },
485 { &isl_val_inv
, "-infty", "0" },
488 /* Perform some basic tests of unary operations on isl_val objects.
490 static int test_un_val(isl_ctx
*ctx
)
494 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v
);
497 for (i
= 0; i
< ARRAY_SIZE(val_un_tests
); ++i
) {
498 v
= isl_val_read_from_str(ctx
, val_un_tests
[i
].arg
);
499 res
= isl_val_read_from_str(ctx
, val_un_tests
[i
].res
);
500 fn
= val_un_tests
[i
].op
;
502 if (isl_val_is_nan(res
))
503 ok
= isl_val_is_nan(v
);
505 ok
= isl_val_eq(v
, res
);
511 isl_die(ctx
, isl_error_unknown
,
512 "unexpected result", return -1);
519 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
520 __isl_take isl_val
*v2
);
522 ['+'] = { &isl_val_add
},
523 ['-'] = { &isl_val_sub
},
524 ['*'] = { &isl_val_mul
},
525 ['/'] = { &isl_val_div
},
526 ['g'] = { &isl_val_gcd
},
527 ['m'] = { &isl_val_min
},
528 ['M'] = { &isl_val_max
},
536 } val_bin_tests
[] = {
537 { "0", '+', "0", "0" },
538 { "1", '+', "0", "1" },
539 { "1", '+', "1", "2" },
540 { "1", '-', "1", "0" },
541 { "1", '*', "1", "1" },
542 { "1", '/', "1", "1" },
543 { "2", '*', "3", "6" },
544 { "2", '*', "1/2", "1" },
545 { "2", '*', "1/3", "2/3" },
546 { "2/3", '*', "3/5", "2/5" },
547 { "2/3", '*', "7/5", "14/15" },
548 { "2", '/', "1/2", "4" },
549 { "-2", '/', "-1/2", "4" },
550 { "-2", '/', "1/2", "-4" },
551 { "2", '/', "-1/2", "-4" },
552 { "2", '/', "2", "1" },
553 { "2", '/', "3", "2/3" },
554 { "2/3", '/', "5/3", "2/5" },
555 { "2/3", '/', "5/7", "14/15" },
556 { "0", '/', "0", "NaN" },
557 { "42", '/', "0", "NaN" },
558 { "-42", '/', "0", "NaN" },
559 { "infty", '/', "0", "NaN" },
560 { "-infty", '/', "0", "NaN" },
561 { "NaN", '/', "0", "NaN" },
562 { "0", '/', "NaN", "NaN" },
563 { "42", '/', "NaN", "NaN" },
564 { "-42", '/', "NaN", "NaN" },
565 { "infty", '/', "NaN", "NaN" },
566 { "-infty", '/', "NaN", "NaN" },
567 { "NaN", '/', "NaN", "NaN" },
568 { "0", '/', "infty", "0" },
569 { "42", '/', "infty", "0" },
570 { "-42", '/', "infty", "0" },
571 { "infty", '/', "infty", "NaN" },
572 { "-infty", '/', "infty", "NaN" },
573 { "NaN", '/', "infty", "NaN" },
574 { "0", '/', "-infty", "0" },
575 { "42", '/', "-infty", "0" },
576 { "-42", '/', "-infty", "0" },
577 { "infty", '/', "-infty", "NaN" },
578 { "-infty", '/', "-infty", "NaN" },
579 { "NaN", '/', "-infty", "NaN" },
580 { "1", '-', "1/3", "2/3" },
581 { "1/3", '+', "1/2", "5/6" },
582 { "1/2", '+', "1/2", "1" },
583 { "3/4", '-', "1/4", "1/2" },
584 { "1/2", '-', "1/3", "1/6" },
585 { "infty", '+', "42", "infty" },
586 { "infty", '+', "infty", "infty" },
587 { "42", '+', "infty", "infty" },
588 { "infty", '-', "infty", "NaN" },
589 { "infty", '*', "infty", "infty" },
590 { "infty", '*', "-infty", "-infty" },
591 { "-infty", '*', "infty", "-infty" },
592 { "-infty", '*', "-infty", "infty" },
593 { "0", '*', "infty", "NaN" },
594 { "1", '*', "infty", "infty" },
595 { "infty", '*', "0", "NaN" },
596 { "infty", '*', "42", "infty" },
597 { "42", '-', "infty", "-infty" },
598 { "infty", '+', "-infty", "NaN" },
599 { "4", 'g', "6", "2" },
600 { "5", 'g', "6", "1" },
601 { "42", 'm', "3", "3" },
602 { "42", 'M', "3", "42" },
603 { "3", 'm', "42", "3" },
604 { "3", 'M', "42", "42" },
605 { "42", 'm', "infty", "42" },
606 { "42", 'M', "infty", "infty" },
607 { "42", 'm', "-infty", "-infty" },
608 { "42", 'M', "-infty", "42" },
609 { "42", 'm', "NaN", "NaN" },
610 { "42", 'M', "NaN", "NaN" },
611 { "infty", 'm', "-infty", "-infty" },
612 { "infty", 'M', "-infty", "infty" },
615 /* Perform some basic tests of binary operations on isl_val objects.
617 static int test_bin_val(isl_ctx
*ctx
)
620 isl_val
*v1
, *v2
, *res
;
621 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
622 __isl_take isl_val
*v2
);
625 for (i
= 0; i
< ARRAY_SIZE(val_bin_tests
); ++i
) {
626 v1
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg1
);
627 v2
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg2
);
628 res
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].res
);
629 fn
= val_bin_op
[val_bin_tests
[i
].op
].fn
;
631 if (isl_val_is_nan(res
))
632 ok
= isl_val_is_nan(v1
);
634 ok
= isl_val_eq(v1
, res
);
640 isl_die(ctx
, isl_error_unknown
,
641 "unexpected result", return -1);
647 /* Perform some basic tests on isl_val objects.
649 static int test_val(isl_ctx
*ctx
)
651 if (test_un_val(ctx
) < 0)
653 if (test_bin_val(ctx
) < 0)
658 static int test_div(isl_ctx
*ctx
)
667 struct isl_basic_set
*bset
;
668 struct isl_constraint
*c
;
673 dim
= isl_space_set_alloc(ctx
, 0, 3);
674 bset
= isl_basic_set_universe(isl_space_copy(dim
));
675 ls
= isl_local_space_from_space(dim
);
677 c
= isl_equality_alloc(isl_local_space_copy(ls
));
678 isl_int_set_si(v
, -1);
679 isl_constraint_set_constant(c
, v
);
680 isl_int_set_si(v
, 1);
681 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
682 isl_int_set_si(v
, 3);
683 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
684 bset
= isl_basic_set_add_constraint(bset
, c
);
686 c
= isl_equality_alloc(isl_local_space_copy(ls
));
687 isl_int_set_si(v
, 1);
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
, 2, v
);
693 bset
= isl_basic_set_add_constraint(bset
, c
);
695 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
697 assert(bset
&& bset
->n_div
== 1);
698 isl_local_space_free(ls
);
699 isl_basic_set_free(bset
);
702 dim
= isl_space_set_alloc(ctx
, 0, 3);
703 bset
= isl_basic_set_universe(isl_space_copy(dim
));
704 ls
= isl_local_space_from_space(dim
);
706 c
= isl_equality_alloc(isl_local_space_copy(ls
));
707 isl_int_set_si(v
, 1);
708 isl_constraint_set_constant(c
, v
);
709 isl_int_set_si(v
, -1);
710 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
711 isl_int_set_si(v
, 3);
712 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
713 bset
= isl_basic_set_add_constraint(bset
, c
);
715 c
= isl_equality_alloc(isl_local_space_copy(ls
));
716 isl_int_set_si(v
, -1);
717 isl_constraint_set_constant(c
, v
);
718 isl_int_set_si(v
, 1);
719 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
720 isl_int_set_si(v
, 3);
721 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
722 bset
= isl_basic_set_add_constraint(bset
, c
);
724 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
726 assert(bset
&& bset
->n_div
== 1);
727 isl_local_space_free(ls
);
728 isl_basic_set_free(bset
);
731 dim
= isl_space_set_alloc(ctx
, 0, 3);
732 bset
= isl_basic_set_universe(isl_space_copy(dim
));
733 ls
= isl_local_space_from_space(dim
);
735 c
= isl_equality_alloc(isl_local_space_copy(ls
));
736 isl_int_set_si(v
, 1);
737 isl_constraint_set_constant(c
, v
);
738 isl_int_set_si(v
, -1);
739 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
740 isl_int_set_si(v
, 3);
741 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
742 bset
= isl_basic_set_add_constraint(bset
, c
);
744 c
= isl_equality_alloc(isl_local_space_copy(ls
));
745 isl_int_set_si(v
, -3);
746 isl_constraint_set_constant(c
, v
);
747 isl_int_set_si(v
, 1);
748 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
749 isl_int_set_si(v
, 4);
750 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
751 bset
= isl_basic_set_add_constraint(bset
, c
);
753 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
755 assert(bset
&& bset
->n_div
== 1);
756 isl_local_space_free(ls
);
757 isl_basic_set_free(bset
);
760 dim
= isl_space_set_alloc(ctx
, 0, 3);
761 bset
= isl_basic_set_universe(isl_space_copy(dim
));
762 ls
= isl_local_space_from_space(dim
);
764 c
= isl_equality_alloc(isl_local_space_copy(ls
));
765 isl_int_set_si(v
, 2);
766 isl_constraint_set_constant(c
, v
);
767 isl_int_set_si(v
, -1);
768 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
769 isl_int_set_si(v
, 3);
770 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
771 bset
= isl_basic_set_add_constraint(bset
, c
);
773 c
= isl_equality_alloc(isl_local_space_copy(ls
));
774 isl_int_set_si(v
, -1);
775 isl_constraint_set_constant(c
, v
);
776 isl_int_set_si(v
, 1);
777 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
778 isl_int_set_si(v
, 6);
779 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
780 bset
= isl_basic_set_add_constraint(bset
, c
);
782 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
784 assert(isl_basic_set_is_empty(bset
));
785 isl_local_space_free(ls
);
786 isl_basic_set_free(bset
);
789 dim
= isl_space_set_alloc(ctx
, 0, 3);
790 bset
= isl_basic_set_universe(isl_space_copy(dim
));
791 ls
= isl_local_space_from_space(dim
);
793 c
= isl_equality_alloc(isl_local_space_copy(ls
));
794 isl_int_set_si(v
, -1);
795 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
796 isl_int_set_si(v
, 3);
797 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
798 bset
= isl_basic_set_add_constraint(bset
, c
);
800 c
= isl_equality_alloc(isl_local_space_copy(ls
));
801 isl_int_set_si(v
, 1);
802 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
803 isl_int_set_si(v
, -3);
804 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
805 bset
= isl_basic_set_add_constraint(bset
, c
);
807 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
809 assert(bset
&& bset
->n_div
== 0);
810 isl_basic_set_free(bset
);
811 isl_local_space_free(ls
);
814 dim
= isl_space_set_alloc(ctx
, 0, 3);
815 bset
= isl_basic_set_universe(isl_space_copy(dim
));
816 ls
= isl_local_space_from_space(dim
);
818 c
= isl_equality_alloc(isl_local_space_copy(ls
));
819 isl_int_set_si(v
, -1);
820 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
821 isl_int_set_si(v
, 6);
822 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
823 bset
= isl_basic_set_add_constraint(bset
, c
);
825 c
= isl_equality_alloc(isl_local_space_copy(ls
));
826 isl_int_set_si(v
, 1);
827 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
828 isl_int_set_si(v
, -3);
829 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
830 bset
= isl_basic_set_add_constraint(bset
, c
);
832 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
834 assert(bset
&& bset
->n_div
== 1);
835 isl_basic_set_free(bset
);
836 isl_local_space_free(ls
);
839 /* This test is a bit tricky. We set up an equality
841 * Normalization of divs creates _two_ divs
844 * Afterwards e0 is removed again because it has coefficient -1
845 * and we end up with the original equality and div again.
846 * Perhaps we can avoid the introduction of this temporary div.
848 dim
= isl_space_set_alloc(ctx
, 0, 4);
849 bset
= isl_basic_set_universe(isl_space_copy(dim
));
850 ls
= isl_local_space_from_space(dim
);
852 c
= isl_equality_alloc(isl_local_space_copy(ls
));
853 isl_int_set_si(v
, -1);
854 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
855 isl_int_set_si(v
, -3);
856 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
857 isl_int_set_si(v
, -3);
858 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
859 isl_int_set_si(v
, 6);
860 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
861 bset
= isl_basic_set_add_constraint(bset
, c
);
863 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
865 /* Test disabled for now */
867 assert(bset && bset->n_div == 1);
869 isl_local_space_free(ls
);
870 isl_basic_set_free(bset
);
873 dim
= isl_space_set_alloc(ctx
, 0, 5);
874 bset
= isl_basic_set_universe(isl_space_copy(dim
));
875 ls
= isl_local_space_from_space(dim
);
877 c
= isl_equality_alloc(isl_local_space_copy(ls
));
878 isl_int_set_si(v
, -1);
879 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
880 isl_int_set_si(v
, -3);
881 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
882 isl_int_set_si(v
, -3);
883 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
884 isl_int_set_si(v
, 6);
885 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
886 bset
= isl_basic_set_add_constraint(bset
, c
);
888 c
= isl_equality_alloc(isl_local_space_copy(ls
));
889 isl_int_set_si(v
, -1);
890 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
891 isl_int_set_si(v
, 1);
892 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
893 isl_int_set_si(v
, 1);
894 isl_constraint_set_constant(c
, v
);
895 bset
= isl_basic_set_add_constraint(bset
, c
);
897 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
899 /* Test disabled for now */
901 assert(bset && bset->n_div == 1);
903 isl_local_space_free(ls
);
904 isl_basic_set_free(bset
);
907 dim
= isl_space_set_alloc(ctx
, 0, 4);
908 bset
= isl_basic_set_universe(isl_space_copy(dim
));
909 ls
= isl_local_space_from_space(dim
);
911 c
= isl_equality_alloc(isl_local_space_copy(ls
));
912 isl_int_set_si(v
, 1);
913 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
914 isl_int_set_si(v
, -1);
915 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
916 isl_int_set_si(v
, -2);
917 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
918 bset
= isl_basic_set_add_constraint(bset
, c
);
920 c
= isl_equality_alloc(isl_local_space_copy(ls
));
921 isl_int_set_si(v
, -1);
922 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
923 isl_int_set_si(v
, 3);
924 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
925 isl_int_set_si(v
, 2);
926 isl_constraint_set_constant(c
, v
);
927 bset
= isl_basic_set_add_constraint(bset
, c
);
929 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
931 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
933 assert(!isl_basic_set_is_empty(bset
));
935 isl_local_space_free(ls
);
936 isl_basic_set_free(bset
);
939 dim
= isl_space_set_alloc(ctx
, 0, 3);
940 bset
= isl_basic_set_universe(isl_space_copy(dim
));
941 ls
= isl_local_space_from_space(dim
);
943 c
= isl_equality_alloc(isl_local_space_copy(ls
));
944 isl_int_set_si(v
, 1);
945 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
946 isl_int_set_si(v
, -2);
947 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
948 bset
= isl_basic_set_add_constraint(bset
, c
);
950 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
952 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
954 isl_local_space_free(ls
);
955 isl_basic_set_free(bset
);
959 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
960 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
961 set
= isl_set_read_from_str(ctx
, str
);
962 set
= isl_set_compute_divs(set
);
967 str
= "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
968 bset
= isl_basic_set_read_from_str(ctx
, str
);
969 n
= isl_basic_set_dim(bset
, isl_dim_div
);
970 isl_basic_set_free(bset
);
974 isl_die(ctx
, isl_error_unknown
,
975 "expecting no existentials", return -1);
977 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
978 set
= isl_set_read_from_str(ctx
, str
);
979 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
980 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
981 empty
= isl_set_is_empty(set
);
986 isl_die(ctx
, isl_error_unknown
,
987 "result not as accurate as expected", return -1);
992 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
996 struct isl_basic_set
*bset1
, *bset2
;
997 struct isl_basic_map
*bmap
;
999 filename
= get_filename(ctx
, name
, "omega");
1001 input
= fopen(filename
, "r");
1004 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1005 bmap
= isl_basic_map_read_from_file(ctx
, input
);
1007 bset1
= isl_basic_set_apply(bset1
, bmap
);
1009 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1011 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1013 isl_basic_set_free(bset1
);
1014 isl_basic_set_free(bset2
);
1020 static int test_application(isl_ctx
*ctx
)
1022 test_application_case(ctx
, "application");
1023 test_application_case(ctx
, "application2");
1028 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
1032 struct isl_basic_set
*bset1
, *bset2
;
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 bset1
= isl_basic_set_affine_hull(bset1
);
1044 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1046 isl_basic_set_free(bset1
);
1047 isl_basic_set_free(bset2
);
1053 int test_affine_hull(struct isl_ctx
*ctx
)
1057 isl_basic_set
*bset
, *bset2
;
1061 test_affine_hull_case(ctx
, "affine2");
1062 test_affine_hull_case(ctx
, "affine");
1063 test_affine_hull_case(ctx
, "affine3");
1065 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
1066 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
1067 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
1068 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
1069 set
= isl_set_read_from_str(ctx
, str
);
1070 bset
= isl_set_affine_hull(set
);
1071 n
= isl_basic_set_dim(bset
, isl_dim_div
);
1072 isl_basic_set_free(bset
);
1074 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
1077 /* Check that isl_map_affine_hull is not confused by
1078 * the reordering of divs in isl_map_align_divs.
1080 str
= "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1081 "32e0 = b and 32e1 = c); "
1082 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1083 set
= isl_set_read_from_str(ctx
, str
);
1084 bset
= isl_set_affine_hull(set
);
1085 isl_basic_set_free(bset
);
1089 str
= "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1090 "32e2 = 31 + 31e0 }";
1091 set
= isl_set_read_from_str(ctx
, str
);
1092 bset
= isl_set_affine_hull(set
);
1093 str
= "{ [a] : exists e : a = 32 e }";
1094 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1095 subset
= isl_basic_set_is_subset(bset
, bset2
);
1096 isl_basic_set_free(bset
);
1097 isl_basic_set_free(bset2
);
1101 isl_die(ctx
, isl_error_unknown
, "not as accurate as expected",
1107 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
1111 struct isl_basic_set
*bset1
, *bset2
;
1112 struct isl_set
*set
;
1114 filename
= get_filename(ctx
, name
, "polylib");
1116 input
= fopen(filename
, "r");
1119 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1120 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1122 set
= isl_basic_set_union(bset1
, bset2
);
1123 bset1
= isl_set_convex_hull(set
);
1125 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1127 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1129 isl_basic_set_free(bset1
);
1130 isl_basic_set_free(bset2
);
1139 } convex_hull_tests
[] = {
1140 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1141 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1142 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1143 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1144 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1145 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1146 "i2 <= 5 and i2 >= 4; "
1147 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1148 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1149 "i2 <= 5 + i0 and i2 >= i0 }" },
1150 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1151 "{ [x, y] : 1 = 0 }" },
1154 static int test_convex_hull_algo(isl_ctx
*ctx
, int convex
)
1157 int orig_convex
= ctx
->opt
->convex
;
1158 ctx
->opt
->convex
= convex
;
1160 test_convex_hull_case(ctx
, "convex0");
1161 test_convex_hull_case(ctx
, "convex1");
1162 test_convex_hull_case(ctx
, "convex2");
1163 test_convex_hull_case(ctx
, "convex3");
1164 test_convex_hull_case(ctx
, "convex4");
1165 test_convex_hull_case(ctx
, "convex5");
1166 test_convex_hull_case(ctx
, "convex6");
1167 test_convex_hull_case(ctx
, "convex7");
1168 test_convex_hull_case(ctx
, "convex8");
1169 test_convex_hull_case(ctx
, "convex9");
1170 test_convex_hull_case(ctx
, "convex10");
1171 test_convex_hull_case(ctx
, "convex11");
1172 test_convex_hull_case(ctx
, "convex12");
1173 test_convex_hull_case(ctx
, "convex13");
1174 test_convex_hull_case(ctx
, "convex14");
1175 test_convex_hull_case(ctx
, "convex15");
1177 for (i
= 0; i
< ARRAY_SIZE(convex_hull_tests
); ++i
) {
1178 isl_set
*set1
, *set2
;
1181 set1
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].set
);
1182 set2
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].hull
);
1183 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
1184 equal
= isl_set_is_equal(set1
, set2
);
1191 isl_die(ctx
, isl_error_unknown
,
1192 "unexpected convex hull", return -1);
1195 ctx
->opt
->convex
= orig_convex
;
1200 static int test_convex_hull(isl_ctx
*ctx
)
1202 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
) < 0)
1204 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
) < 0)
1209 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
1213 struct isl_basic_set
*bset1
, *bset2
;
1215 filename
= get_filename(ctx
, name
, "polylib");
1217 input
= fopen(filename
, "r");
1220 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1221 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1223 bset1
= isl_basic_set_gist(bset1
, bset2
);
1225 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1227 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1229 isl_basic_set_free(bset1
);
1230 isl_basic_set_free(bset2
);
1238 const char *context
;
1241 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1242 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1243 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1244 "{ [a, b, c] : a <= 15 }" },
1245 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1246 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1247 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1248 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1249 { "{ [m, n, a, b] : a <= 2147 + n }",
1250 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1251 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1252 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1254 "{ [m, n, ku, kl] }" },
1257 static int test_gist(struct isl_ctx
*ctx
)
1261 isl_basic_set
*bset1
, *bset2
;
1262 isl_map
*map1
, *map2
;
1265 for (i
= 0; i
< ARRAY_SIZE(gist_tests
); ++i
) {
1267 isl_set
*set1
, *set2
, *copy
;
1269 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1270 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].context
);
1271 copy
= isl_set_copy(set1
);
1272 set1
= isl_set_gist(set1
, set2
);
1273 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].gist
);
1274 equal
= isl_set_is_equal(set1
, set2
);
1277 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1278 equal_input
= isl_set_is_equal(set1
, copy
);
1281 if (equal
< 0 || equal_input
< 0)
1284 isl_die(ctx
, isl_error_unknown
,
1285 "incorrect gist result", return -1);
1287 isl_die(ctx
, isl_error_unknown
,
1288 "gist modified input", return -1);
1291 test_gist_case(ctx
, "gist1");
1293 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1294 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1295 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1296 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1297 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1298 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1299 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1300 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1301 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1302 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1303 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1304 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1305 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1306 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1307 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1308 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1309 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1310 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1311 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1312 bset1
= isl_basic_set_gist(bset1
, bset2
);
1313 assert(bset1
&& bset1
->n_div
== 0);
1314 isl_basic_set_free(bset1
);
1316 /* Check that the integer divisions of the second disjunct
1317 * do not spread to the first disjunct.
1319 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1320 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1321 "(exists (e0 = [(-1 + t1)/16], "
1322 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1323 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1324 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1325 "o0 <= 4294967295 and t1 <= -1)) }";
1326 map1
= isl_map_read_from_str(ctx
, str
);
1327 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1328 map2
= isl_map_read_from_str(ctx
, str
);
1329 map1
= isl_map_gist(map1
, map2
);
1333 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1334 isl_map_free(map1
); return -1);
1335 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1336 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1337 isl_map_free(map1
); return -1);
1343 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1345 isl_set
*set
, *set2
;
1349 set
= isl_set_read_from_str(ctx
, str
);
1350 set
= isl_set_coalesce(set
);
1351 set2
= isl_set_read_from_str(ctx
, str
);
1352 equal
= isl_set_is_equal(set
, set2
);
1353 one
= set
&& set
->n
== 1;
1360 isl_die(ctx
, isl_error_unknown
,
1361 "coalesced set not equal to input", return -1);
1362 if (check_one
&& !one
)
1363 isl_die(ctx
, isl_error_unknown
,
1364 "coalesced set should not be a union", return -1);
1369 /* Inputs for coalescing tests with unbounded wrapping.
1370 * "str" is a string representation of the input set.
1371 * "single_disjunct" is set if we expect the result to consist of
1372 * a single disjunct.
1375 int single_disjunct
;
1377 } coalesce_unbounded_tests
[] = {
1378 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1379 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1380 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1381 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1383 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1384 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1385 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1386 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1389 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1390 * option turned off.
1392 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1398 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1399 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1401 for (i
= 0; i
< ARRAY_SIZE(coalesce_unbounded_tests
); ++i
) {
1402 const char *str
= coalesce_unbounded_tests
[i
].str
;
1403 int check_one
= coalesce_unbounded_tests
[i
].single_disjunct
;
1404 if (test_coalesce_set(ctx
, str
, check_one
) >= 0)
1410 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1415 /* Inputs for coalescing tests.
1416 * "str" is a string representation of the input set.
1417 * "single_disjunct" is set if we expect the result to consist of
1418 * a single disjunct.
1421 int single_disjunct
;
1423 } coalesce_tests
[] = {
1424 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1425 "y >= x & x >= 2 & 5 >= y }" },
1426 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1427 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1428 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1429 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1430 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1431 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1432 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1433 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1434 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1435 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1436 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1437 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1438 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1439 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1440 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1441 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1442 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1443 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1444 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1445 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1446 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1447 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1448 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1449 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1450 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1451 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1452 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1453 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1454 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1455 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1456 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1457 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1458 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1459 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1460 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1461 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1462 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1463 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1464 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1465 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1466 "[o0, o1, o2, o3, o4, o5, o6]] : "
1467 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1468 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1469 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1470 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1471 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1472 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1473 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1474 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1475 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1476 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1477 "o6 >= i3 + i6 - o3 and M >= 0 and "
1478 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1479 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1480 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1481 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1482 "(o0 = 0 and M >= 2 and N >= 3) or "
1483 "(M = 0 and o0 = 0 and N >= 3) }" },
1484 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1485 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1486 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1487 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1488 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1489 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1490 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1491 "(y = 3 and x = 1) }" },
1492 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1493 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1494 "i1 <= M and i3 <= M and i4 <= M) or "
1495 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1496 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1497 "i4 <= -1 + M) }" },
1498 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1499 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1500 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1501 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1502 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1503 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1504 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1505 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1506 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1507 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1508 { 0, "{ [a, b] : exists e : 2e = a and "
1509 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1510 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1511 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1512 "j >= 1 and j' <= i + j - i' and i >= 1; "
1514 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1515 "[i,j] : exists a : j = 3a }" },
1516 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1517 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1519 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1520 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1521 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1522 "c <= 6 + 8a and a >= 3; "
1523 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1524 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1525 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1526 "[x,0] : 3 <= x <= 4 }" },
1527 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1528 "[x,0] : 4 <= x <= 5 }" },
1529 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1530 "[x,0] : 3 <= x <= 5 }" },
1531 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1532 "[x,0] : 3 <= x <= 4 }" },
1533 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1535 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1536 { 1, "{ [0,0]; [1,1] }" },
1537 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1538 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1540 "[k, 0, k] : k <= 6 and k >= 1 }" },
1541 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1542 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1543 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1544 { 1, "[n] -> { [1] : n >= 0;"
1545 "[x] : exists (e0 = floor((x)/2): x >= 2 and "
1546 "2e0 >= -1 + x and 2e0 <= x and 2e0 <= n) }" },
1547 { 1, "[n] -> { [x, y] : exists (e0 = floor((x)/2), e1 = floor((y)/3): "
1548 "3e1 = y and x >= 2 and 2e0 >= -1 + x and "
1549 "2e0 <= x and 2e0 <= n);"
1550 "[1, y] : exists (e0 = floor((y)/3): 3e0 = y and "
1552 { 1, "[t1] -> { [i0] : (exists (e0 = floor((63t1)/64): "
1553 "128e0 >= -134 + 127t1 and t1 >= 2 and "
1554 "64e0 <= 63t1 and 64e0 >= -63 + 63t1)) or "
1556 { 1, "{ [i, i] : exists (e0 = floor((1 + 2i)/3): 3e0 <= 2i and "
1557 "3e0 >= -1 + 2i and i <= 9 and i >= 1);"
1559 { 1, "{ [t1] : exists (e0 = floor((-11 + t1)/2): 2e0 = -11 + t1 and "
1560 "t1 >= 13 and t1 <= 16);"
1561 "[t1] : t1 <= 15 and t1 >= 12 }" },
1562 { 1, "{ [x,y] : x = 3y and 0 <= y <= 2; [-3,-1] }" },
1563 { 1, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-2] }" },
1564 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-2,-2] }" },
1565 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-1] }" },
1566 { 1, "{ [i] : exists j : i = 4 j and 0 <= i <= 100;"
1567 "[i] : exists j : 1 <= i <= 100 and i >= 4j + 1 and "
1569 { 1, "{ [c0] : (exists (e0 : c0 - 1 <= 3e0 <= c0)) or "
1570 "(exists (e0 : 3e0 = -2 + c0)) }" },
1571 { 0, "[n, b0, t0] -> "
1572 "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1573 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1574 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1575 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1576 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 >= 8 + n and "
1577 "3i4 <= -96 + 3t0 + i0 and 3i4 >= -95 - n + 3t0 + i0 and "
1578 "i8 >= -157 + i0 - 4i4 and i8 >= 0 and "
1579 "i8 <= -33 + i0 - 4i4 and 3i8 <= -91 + 4n - i0)) or "
1580 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1581 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1582 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1583 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 <= 7 + n and "
1584 "4i4 <= -3 + i0 and 3i4 <= -96 + 3t0 + i0 and "
1585 "3i4 >= -95 - n + 3t0 + i0 and i8 >= -157 + i0 - 4i4 and "
1586 "i8 >= 0 and i8 <= -4 + i0 - 3i4 and i8 <= -41 + i0));"
1587 "[i0, i1, i2, i3, 0, i5, i6, i7, i8, i9, i10, i11, i12] : "
1588 "(exists (e0 = floor((i8)/32): b0 = 0 and 32e0 = i8 and "
1589 "n <= 2147483647 and t0 <= 31 and t0 >= 0 and i0 >= 11 and "
1590 "i0 >= 96 - 3t0 and i0 <= 95 + n - 3t0 and i0 <= 7 + n and "
1591 "i8 >= -40 + i0 and i8 <= -10 + i0)) }" },
1592 { 0, "{ [i0, i1, i2] : "
1593 "(exists (e0, e1 = floor((i0)/32), e2 = floor((i1)/32): "
1594 "32e1 = i0 and 32e2 = i1 and i1 >= -31 + i0 and "
1595 "i1 <= 31 + i0 and i2 >= -30 + i0 and i2 >= -30 + i1 and "
1596 "32e0 >= -30 + i0 and 32e0 >= -30 + i1 and "
1597 "32e0 >= -31 + i2 and 32e0 <= 30 + i2 and 32e0 <= 31 + i1 and "
1598 "32e0 <= 31 + i0)) or "
1602 /* A specialized coalescing test case that would result
1603 * in a segmentation fault or a failed assertion in earlier versions of isl.
1605 static int test_coalesce_special(struct isl_ctx
*ctx
)
1608 isl_map
*map1
, *map2
;
1610 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1611 "[[S_L309_IN[] -> T11[]] -> ce_imag2[1, o1]] : "
1612 "(y = 201 and o1 <= 239 and o1 >= 212) or "
1613 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 198 and y >= 3 and "
1614 "o1 <= 239 and o1 >= 212)) or "
1615 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 201 and y >= 3 and "
1616 "o1 <= 241 and o1 >= 240));"
1617 "[S_L220_OUT[] -> T7[]] -> "
1618 "[[S_L309_IN[] -> T11[]] -> ce_imag2[0, o1]] : "
1619 "(y = 2 and o1 <= 241 and o1 >= 212) or "
1620 "(exists (e0 = [(-2 + y)/3]: 3e0 = -2 + y and y <= 200 and "
1621 "y >= 5 and o1 <= 241 and o1 >= 212)) }";
1622 map1
= isl_map_read_from_str(ctx
, str
);
1623 map1
= isl_map_align_divs(map1
);
1624 map1
= isl_map_coalesce(map1
);
1625 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1626 "[[S_L309_IN[] -> T11[]] -> ce_imag2[o0, o1]] : "
1627 "exists (e0 = [(-1 - y + o0)/3]: 3e0 = -1 - y + o0 and "
1628 "y <= 201 and o0 <= 2 and o1 >= 212 and o1 <= 241 and "
1629 "o0 >= 3 - y and o0 <= -2 + y and o0 >= 0) }";
1630 map2
= isl_map_read_from_str(ctx
, str
);
1631 map2
= isl_map_union(map2
, map1
);
1632 map2
= isl_map_align_divs(map2
);
1633 map2
= isl_map_coalesce(map2
);
1641 /* Test the functionality of isl_set_coalesce.
1642 * That is, check that the output is always equal to the input
1643 * and in some cases that the result consists of a single disjunct.
1645 static int test_coalesce(struct isl_ctx
*ctx
)
1649 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
1650 const char *str
= coalesce_tests
[i
].str
;
1651 int check_one
= coalesce_tests
[i
].single_disjunct
;
1652 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
1656 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1658 if (test_coalesce_special(ctx
) < 0)
1664 static int test_closure(isl_ctx
*ctx
)
1668 isl_map
*up
, *right
;
1669 isl_map
*map
, *map2
;
1672 /* COCOA example 1 */
1673 map
= isl_map_read_from_str(ctx
,
1674 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1675 "1 <= i and i < n and 1 <= j and j < n or "
1676 "i2 = i + 1 and j2 = j - 1 and "
1677 "1 <= i and i < n and 2 <= j and j <= n }");
1678 map
= isl_map_power(map
, &exact
);
1682 /* COCOA example 1 */
1683 map
= isl_map_read_from_str(ctx
,
1684 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1685 "1 <= i and i < n and 1 <= j and j < n or "
1686 "i2 = i + 1 and j2 = j - 1 and "
1687 "1 <= i and i < n and 2 <= j and j <= n }");
1688 map
= isl_map_transitive_closure(map
, &exact
);
1690 map2
= isl_map_read_from_str(ctx
,
1691 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1692 "1 <= i and i < n and 1 <= j and j <= n and "
1693 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1694 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1695 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1696 assert(isl_map_is_equal(map
, map2
));
1700 map
= isl_map_read_from_str(ctx
,
1701 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1702 " 0 <= y and y <= n }");
1703 map
= isl_map_transitive_closure(map
, &exact
);
1704 map2
= isl_map_read_from_str(ctx
,
1705 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1706 " 0 <= y and y <= n }");
1707 assert(isl_map_is_equal(map
, map2
));
1711 /* COCOA example 2 */
1712 map
= isl_map_read_from_str(ctx
,
1713 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1714 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1715 "i2 = i + 2 and j2 = j - 2 and "
1716 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1717 map
= isl_map_transitive_closure(map
, &exact
);
1719 map2
= isl_map_read_from_str(ctx
,
1720 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1721 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1722 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1723 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1724 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1725 assert(isl_map_is_equal(map
, map2
));
1729 /* COCOA Fig.2 left */
1730 map
= isl_map_read_from_str(ctx
,
1731 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1732 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1734 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1735 "j <= 2 i - 3 and j <= n - 2 or "
1736 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1737 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1738 map
= isl_map_transitive_closure(map
, &exact
);
1742 /* COCOA Fig.2 right */
1743 map
= isl_map_read_from_str(ctx
,
1744 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1745 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1747 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1748 "j <= 2 i - 4 and j <= n - 3 or "
1749 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1750 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1751 map
= isl_map_power(map
, &exact
);
1755 /* COCOA Fig.2 right */
1756 map
= isl_map_read_from_str(ctx
,
1757 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1758 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1760 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1761 "j <= 2 i - 4 and j <= n - 3 or "
1762 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1763 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1764 map
= isl_map_transitive_closure(map
, &exact
);
1766 map2
= isl_map_read_from_str(ctx
,
1767 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1768 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1769 "j <= n and 3 + i + 2 j <= 3 n and "
1770 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1771 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1772 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1773 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1774 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1775 assert(isl_map_is_equal(map
, map2
));
1779 /* COCOA Fig.1 right */
1780 dom
= isl_set_read_from_str(ctx
,
1781 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1782 "2 x - 3 y + 3 >= 0 }");
1783 right
= isl_map_read_from_str(ctx
,
1784 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1785 up
= isl_map_read_from_str(ctx
,
1786 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1787 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1788 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1789 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1790 up
= isl_map_intersect_range(up
, dom
);
1791 map
= isl_map_union(up
, right
);
1792 map
= isl_map_transitive_closure(map
, &exact
);
1794 map2
= isl_map_read_from_str(ctx
,
1795 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1796 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1797 assert(isl_map_is_equal(map
, map2
));
1801 /* COCOA Theorem 1 counter example */
1802 map
= isl_map_read_from_str(ctx
,
1803 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1804 "i2 = 1 and j2 = j or "
1805 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1806 map
= isl_map_transitive_closure(map
, &exact
);
1810 map
= isl_map_read_from_str(ctx
,
1811 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1812 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1813 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1814 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1815 map
= isl_map_transitive_closure(map
, &exact
);
1819 /* Kelly et al 1996, fig 12 */
1820 map
= isl_map_read_from_str(ctx
,
1821 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1822 "1 <= i,j,j+1 <= n or "
1823 "j = n and j2 = 1 and i2 = i + 1 and "
1824 "1 <= i,i+1 <= n }");
1825 map
= isl_map_transitive_closure(map
, &exact
);
1827 map2
= isl_map_read_from_str(ctx
,
1828 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1829 "1 <= i <= n and i = i2 or "
1830 "1 <= i < i2 <= n and 1 <= j <= n and "
1832 assert(isl_map_is_equal(map
, map2
));
1836 /* Omega's closure4 */
1837 map
= isl_map_read_from_str(ctx
,
1838 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1839 "1 <= x,y <= 10 or "
1840 "x2 = x + 1 and y2 = y and "
1841 "1 <= x <= 20 && 5 <= y <= 15 }");
1842 map
= isl_map_transitive_closure(map
, &exact
);
1846 map
= isl_map_read_from_str(ctx
,
1847 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1848 map
= isl_map_transitive_closure(map
, &exact
);
1850 map2
= isl_map_read_from_str(ctx
,
1851 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1852 assert(isl_map_is_equal(map
, map2
));
1856 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1857 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1858 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1859 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1860 map
= isl_map_read_from_str(ctx
, str
);
1861 map
= isl_map_transitive_closure(map
, &exact
);
1863 map2
= isl_map_read_from_str(ctx
, str
);
1864 assert(isl_map_is_equal(map
, map2
));
1868 str
= "{[0] -> [1]; [2] -> [3]}";
1869 map
= isl_map_read_from_str(ctx
, str
);
1870 map
= isl_map_transitive_closure(map
, &exact
);
1872 map2
= isl_map_read_from_str(ctx
, str
);
1873 assert(isl_map_is_equal(map
, map2
));
1877 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1878 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1879 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1880 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1881 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1882 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1883 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1884 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1885 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1886 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1887 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1888 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1889 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1890 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1891 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1892 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1893 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1894 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1895 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1896 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1897 map
= isl_map_read_from_str(ctx
, str
);
1898 map
= isl_map_transitive_closure(map
, NULL
);
1905 static int test_lex(struct isl_ctx
*ctx
)
1911 dim
= isl_space_set_alloc(ctx
, 0, 0);
1912 map
= isl_map_lex_le(dim
);
1913 empty
= isl_map_is_empty(map
);
1919 isl_die(ctx
, isl_error_unknown
,
1920 "expecting non-empty result", return -1);
1925 static int test_lexmin(struct isl_ctx
*ctx
)
1929 isl_basic_map
*bmap
;
1930 isl_map
*map
, *map2
;
1933 isl_pw_multi_aff
*pma
;
1935 str
= "[p0, p1] -> { [] -> [] : "
1936 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1937 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1938 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1939 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1940 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1941 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1942 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1943 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1944 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1945 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1946 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1947 map
= isl_map_read_from_str(ctx
, str
);
1948 map
= isl_map_lexmin(map
);
1951 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1952 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1953 set
= isl_set_read_from_str(ctx
, str
);
1954 set
= isl_set_lexmax(set
);
1955 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1956 set2
= isl_set_read_from_str(ctx
, str
);
1957 set
= isl_set_intersect(set
, set2
);
1958 assert(!isl_set_is_empty(set
));
1961 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1962 map
= isl_map_read_from_str(ctx
, str
);
1963 map
= isl_map_lexmin(map
);
1964 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1965 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1966 map2
= isl_map_read_from_str(ctx
, str
);
1967 assert(isl_map_is_equal(map
, map2
));
1971 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1972 map
= isl_map_read_from_str(ctx
, str
);
1973 map2
= isl_map_copy(map
);
1974 map
= isl_map_lexmin(map
);
1975 assert(isl_map_is_equal(map
, map2
));
1979 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1980 map
= isl_map_read_from_str(ctx
, str
);
1981 map
= isl_map_lexmin(map
);
1982 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1983 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1984 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1985 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1986 map2
= isl_map_read_from_str(ctx
, str
);
1987 assert(isl_map_is_equal(map
, map2
));
1991 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1992 " 8i' <= i and 8i' >= -7 + i }";
1993 bmap
= isl_basic_map_read_from_str(ctx
, str
);
1994 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
1995 map2
= isl_map_from_pw_multi_aff(pma
);
1996 map
= isl_map_from_basic_map(bmap
);
1997 assert(isl_map_is_equal(map
, map2
));
2001 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
2002 map
= isl_map_read_from_str(ctx
, str
);
2003 map
= isl_map_lexmin(map
);
2004 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
2005 map2
= isl_map_read_from_str(ctx
, str
);
2006 assert(isl_map_is_equal(map
, map2
));
2010 /* Check that empty pieces are properly combined. */
2011 str
= "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
2012 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
2013 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
2014 map
= isl_map_read_from_str(ctx
, str
);
2015 map
= isl_map_lexmin(map
);
2016 str
= "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
2017 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
2019 map2
= isl_map_read_from_str(ctx
, str
);
2020 assert(isl_map_is_equal(map
, map2
));
2024 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2025 " 8i' <= i and 8i' >= -7 + i }";
2026 set
= isl_set_read_from_str(ctx
, str
);
2027 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
2028 set2
= isl_set_from_pw_multi_aff(pma
);
2029 equal
= isl_set_is_equal(set
, set2
);
2035 isl_die(ctx
, isl_error_unknown
,
2036 "unexpected difference between set and "
2037 "piecewise affine expression", return -1);
2042 /* Check that isl_set_min_val and isl_set_max_val compute the correct
2043 * result on non-convex inputs.
2045 static int test_min(struct isl_ctx
*ctx
)
2052 set
= isl_set_read_from_str(ctx
, "{ [-1]; [1] }");
2053 aff
= isl_aff_read_from_str(ctx
, "{ [x] -> [x] }");
2054 val
= isl_set_min_val(set
, aff
);
2055 min_ok
= isl_val_is_negone(val
);
2057 val
= isl_set_max_val(set
, aff
);
2058 max_ok
= isl_val_is_one(val
);
2063 if (min_ok
< 0 || max_ok
< 0)
2066 isl_die(ctx
, isl_error_unknown
,
2067 "unexpected minimum", return -1);
2069 isl_die(ctx
, isl_error_unknown
,
2070 "unexpected maximum", return -1);
2080 static isl_stat
collect_must_may(__isl_take isl_map
*dep
, int must
,
2081 void *dep_user
, void *user
)
2083 struct must_may
*mm
= (struct must_may
*)user
;
2086 mm
->must
= isl_map_union(mm
->must
, dep
);
2088 mm
->may
= isl_map_union(mm
->may
, dep
);
2093 static int common_space(void *first
, void *second
)
2095 int depth
= *(int *)first
;
2099 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
2107 map2
= isl_map_read_from_str(map
->ctx
, str
);
2108 equal
= isl_map_is_equal(map
, map2
);
2114 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
2118 equal
= map_is_equal(map
, str
);
2122 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
2123 "result not as expected", return -1);
2127 static int test_dep(struct isl_ctx
*ctx
)
2132 isl_access_info
*ai
;
2139 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2140 map
= isl_map_read_from_str(ctx
, str
);
2141 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2143 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2144 map
= isl_map_read_from_str(ctx
, str
);
2145 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2147 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2148 map
= isl_map_read_from_str(ctx
, str
);
2149 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2151 flow
= isl_access_info_compute_flow(ai
);
2152 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2153 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2154 mm
.may
= isl_map_empty(dim
);
2156 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2158 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
2159 " [1,10,0] -> [2,5,0] }";
2160 assert(map_is_equal(mm
.must
, str
));
2161 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2162 assert(map_is_equal(mm
.may
, str
));
2164 isl_map_free(mm
.must
);
2165 isl_map_free(mm
.may
);
2166 isl_flow_free(flow
);
2169 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2170 map
= isl_map_read_from_str(ctx
, str
);
2171 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2173 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2174 map
= isl_map_read_from_str(ctx
, str
);
2175 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2177 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2178 map
= isl_map_read_from_str(ctx
, str
);
2179 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2181 flow
= isl_access_info_compute_flow(ai
);
2182 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2183 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2184 mm
.may
= isl_map_empty(dim
);
2186 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2188 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2189 assert(map_is_equal(mm
.must
, str
));
2190 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2191 assert(map_is_equal(mm
.may
, str
));
2193 isl_map_free(mm
.must
);
2194 isl_map_free(mm
.may
);
2195 isl_flow_free(flow
);
2198 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2199 map
= isl_map_read_from_str(ctx
, str
);
2200 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2202 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2203 map
= isl_map_read_from_str(ctx
, str
);
2204 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2206 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2207 map
= isl_map_read_from_str(ctx
, str
);
2208 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2210 flow
= isl_access_info_compute_flow(ai
);
2211 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2212 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2213 mm
.may
= isl_map_empty(dim
);
2215 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2217 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2218 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2219 assert(map_is_equal(mm
.may
, str
));
2220 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2221 assert(map_is_equal(mm
.must
, str
));
2223 isl_map_free(mm
.must
);
2224 isl_map_free(mm
.may
);
2225 isl_flow_free(flow
);
2228 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2229 map
= isl_map_read_from_str(ctx
, str
);
2230 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2232 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2233 map
= isl_map_read_from_str(ctx
, str
);
2234 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2236 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2237 map
= isl_map_read_from_str(ctx
, str
);
2238 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2240 flow
= isl_access_info_compute_flow(ai
);
2241 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2242 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2243 mm
.may
= isl_map_empty(dim
);
2245 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2247 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2248 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2249 assert(map_is_equal(mm
.may
, str
));
2250 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2251 assert(map_is_equal(mm
.must
, str
));
2253 isl_map_free(mm
.must
);
2254 isl_map_free(mm
.may
);
2255 isl_flow_free(flow
);
2258 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2259 map
= isl_map_read_from_str(ctx
, str
);
2260 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2262 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2263 map
= isl_map_read_from_str(ctx
, str
);
2264 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2266 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2267 map
= isl_map_read_from_str(ctx
, str
);
2268 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2270 flow
= isl_access_info_compute_flow(ai
);
2271 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2272 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2273 mm
.may
= isl_map_empty(dim
);
2275 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2277 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2278 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2279 assert(map_is_equal(mm
.may
, str
));
2280 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2281 assert(map_is_equal(mm
.must
, str
));
2283 isl_map_free(mm
.must
);
2284 isl_map_free(mm
.may
);
2285 isl_flow_free(flow
);
2290 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2291 map
= isl_map_read_from_str(ctx
, str
);
2292 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2294 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2295 map
= isl_map_read_from_str(ctx
, str
);
2296 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2298 flow
= isl_access_info_compute_flow(ai
);
2299 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2300 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2301 mm
.may
= isl_map_empty(dim
);
2303 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2305 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2306 assert(map_is_equal(mm
.must
, str
));
2307 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2308 assert(map_is_equal(mm
.may
, str
));
2310 isl_map_free(mm
.must
);
2311 isl_map_free(mm
.may
);
2312 isl_flow_free(flow
);
2317 /* Check that the dependence analysis proceeds without errors.
2318 * Earlier versions of isl would break down during the analysis
2319 * due to the use of the wrong spaces.
2321 static int test_flow(isl_ctx
*ctx
)
2324 isl_union_map
*access
, *schedule
;
2325 isl_union_map
*must_dep
, *may_dep
;
2328 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2329 access
= isl_union_map_read_from_str(ctx
, str
);
2330 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2331 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2332 "S2[] -> [1,0,0,0]; "
2333 "S3[] -> [-1,0,0,0] }";
2334 schedule
= isl_union_map_read_from_str(ctx
, str
);
2335 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2336 isl_union_map_copy(access
), schedule
,
2337 &must_dep
, &may_dep
, NULL
, NULL
);
2338 isl_union_map_free(may_dep
);
2339 isl_union_map_free(must_dep
);
2348 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2349 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2350 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2351 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2352 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2353 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2354 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2355 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2356 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2359 int test_sv(isl_ctx
*ctx
)
2361 isl_union_map
*umap
;
2365 for (i
= 0; i
< ARRAY_SIZE(sv_tests
); ++i
) {
2366 umap
= isl_union_map_read_from_str(ctx
, sv_tests
[i
].map
);
2367 sv
= isl_union_map_is_single_valued(umap
);
2368 isl_union_map_free(umap
);
2371 if (sv_tests
[i
].sv
&& !sv
)
2372 isl_die(ctx
, isl_error_internal
,
2373 "map not detected as single valued", return -1);
2374 if (!sv_tests
[i
].sv
&& sv
)
2375 isl_die(ctx
, isl_error_internal
,
2376 "map detected as single valued", return -1);
2385 } bijective_tests
[] = {
2386 { "[N,M]->{[i,j] -> [i]}", 0 },
2387 { "[N,M]->{[i,j] -> [i] : j=i}", 1 },
2388 { "[N,M]->{[i,j] -> [i] : j=0}", 1 },
2389 { "[N,M]->{[i,j] -> [i] : j=N}", 1 },
2390 { "[N,M]->{[i,j] -> [j,i]}", 1 },
2391 { "[N,M]->{[i,j] -> [i+j]}", 0 },
2392 { "[N,M]->{[i,j] -> []}", 0 },
2393 { "[N,M]->{[i,j] -> [i,j,N]}", 1 },
2394 { "[N,M]->{[i,j] -> [2i]}", 0 },
2395 { "[N,M]->{[i,j] -> [i,i]}", 0 },
2396 { "[N,M]->{[i,j] -> [2i,i]}", 0 },
2397 { "[N,M]->{[i,j] -> [2i,j]}", 1 },
2398 { "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1 },
2401 static int test_bijective(struct isl_ctx
*ctx
)
2407 for (i
= 0; i
< ARRAY_SIZE(bijective_tests
); ++i
) {
2408 map
= isl_map_read_from_str(ctx
, bijective_tests
[i
].str
);
2409 bijective
= isl_map_is_bijective(map
);
2413 if (bijective_tests
[i
].bijective
&& !bijective
)
2414 isl_die(ctx
, isl_error_internal
,
2415 "map not detected as bijective", return -1);
2416 if (!bijective_tests
[i
].bijective
&& bijective
)
2417 isl_die(ctx
, isl_error_internal
,
2418 "map detected as bijective", return -1);
2424 /* Inputs for isl_pw_qpolynomial_gist tests.
2425 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2431 } pwqp_gist_tests
[] = {
2432 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2433 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2434 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2435 "{ [i] -> -1/2 + 1/2 * i }" },
2436 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2439 static int test_pwqp(struct isl_ctx
*ctx
)
2444 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
2447 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2448 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2450 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
2453 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2454 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2456 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2458 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2460 isl_pw_qpolynomial_free(pwqp1
);
2462 for (i
= 0; i
< ARRAY_SIZE(pwqp_gist_tests
); ++i
) {
2463 str
= pwqp_gist_tests
[i
].pwqp
;
2464 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2465 str
= pwqp_gist_tests
[i
].set
;
2466 set
= isl_set_read_from_str(ctx
, str
);
2467 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2468 str
= pwqp_gist_tests
[i
].gist
;
2469 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2470 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2471 equal
= isl_pw_qpolynomial_is_zero(pwqp1
);
2472 isl_pw_qpolynomial_free(pwqp1
);
2477 isl_die(ctx
, isl_error_unknown
,
2478 "unexpected result", return -1);
2481 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
2482 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2483 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
2484 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2486 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2488 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2490 isl_pw_qpolynomial_free(pwqp1
);
2492 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
2493 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2494 str
= "{ [x] -> x }";
2495 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2497 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2499 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2501 isl_pw_qpolynomial_free(pwqp1
);
2503 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2504 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2505 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2506 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
2507 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2508 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2509 isl_pw_qpolynomial_free(pwqp1
);
2511 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2512 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2513 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2514 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2515 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
2516 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
2517 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2518 isl_pw_qpolynomial_free(pwqp1
);
2519 isl_pw_qpolynomial_free(pwqp2
);
2523 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2525 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2526 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2527 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2528 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2529 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
2531 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2532 isl_pw_qpolynomial_free(pwqp1
);
2533 isl_pw_qpolynomial_free(pwqp2
);
2537 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2542 static int test_split_periods(isl_ctx
*ctx
)
2545 isl_pw_qpolynomial
*pwqp
;
2547 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2548 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2549 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2550 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2552 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
2554 isl_pw_qpolynomial_free(pwqp
);
2562 static int test_union(isl_ctx
*ctx
)
2565 isl_union_set
*uset1
, *uset2
;
2566 isl_union_map
*umap1
, *umap2
;
2569 str
= "{ [i] : 0 <= i <= 1 }";
2570 uset1
= isl_union_set_read_from_str(ctx
, str
);
2571 str
= "{ [1] -> [0] }";
2572 umap1
= isl_union_map_read_from_str(ctx
, str
);
2574 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
2575 equal
= isl_union_map_is_equal(umap1
, umap2
);
2577 isl_union_map_free(umap1
);
2578 isl_union_map_free(umap2
);
2583 isl_die(ctx
, isl_error_unknown
, "union maps not equal",
2586 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2587 umap1
= isl_union_map_read_from_str(ctx
, str
);
2588 str
= "{ A[i]; B[i] }";
2589 uset1
= isl_union_set_read_from_str(ctx
, str
);
2591 uset2
= isl_union_map_domain(umap1
);
2593 equal
= isl_union_set_is_equal(uset1
, uset2
);
2595 isl_union_set_free(uset1
);
2596 isl_union_set_free(uset2
);
2601 isl_die(ctx
, isl_error_unknown
, "union sets not equal",
2607 /* Check that computing a bound of a non-zero polynomial over an unbounded
2608 * domain does not produce a rational value.
2609 * Ideally, we want the value to be infinity, but we accept NaN for now.
2610 * We certainly do not want to obtain the value zero.
2612 static int test_bound_unbounded_domain(isl_ctx
*ctx
)
2617 isl_pw_qpolynomial
*pwqp
;
2618 isl_pw_qpolynomial_fold
*pwf
;
2622 str
= "{ [m,n] -> -m * n }";
2623 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2624 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2625 dom
= isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf
));
2626 pnt
= isl_set_sample_point(dom
);
2627 v
= isl_pw_qpolynomial_fold_eval(pwf
, pnt
);
2628 is_rat
= isl_val_is_rat(v
);
2634 isl_die(ctx
, isl_error_unknown
,
2635 "unexpected rational value", return -1);
2640 static int test_bound(isl_ctx
*ctx
)
2644 isl_pw_qpolynomial
*pwqp
;
2645 isl_pw_qpolynomial_fold
*pwf
;
2647 if (test_bound_unbounded_domain(ctx
) < 0)
2650 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
2651 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2652 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2653 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
2654 isl_pw_qpolynomial_fold_free(pwf
);
2656 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
2659 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2660 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2661 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2662 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
2663 isl_pw_qpolynomial_fold_free(pwf
);
2665 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
2671 static int test_lift(isl_ctx
*ctx
)
2674 isl_basic_map
*bmap
;
2675 isl_basic_set
*bset
;
2677 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
2678 bset
= isl_basic_set_read_from_str(ctx
, str
);
2679 bset
= isl_basic_set_lift(bset
);
2680 bmap
= isl_basic_map_from_range(bset
);
2681 bset
= isl_basic_map_domain(bmap
);
2682 isl_basic_set_free(bset
);
2691 } subset_tests
[] = {
2693 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2694 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2695 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2697 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2698 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2699 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2700 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2701 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2702 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2703 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2704 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2705 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2706 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2707 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2708 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2709 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2710 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2711 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2712 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2713 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2714 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2715 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2716 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2717 "4e0 <= -57 + i0 + i1)) or "
2718 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2719 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2720 "4e0 >= -61 + i0 + i1)) or "
2721 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2724 static int test_subset(isl_ctx
*ctx
)
2727 isl_set
*set1
, *set2
;
2730 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
2731 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
2732 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
2733 subset
= isl_set_is_subset(set1
, set2
);
2738 if (subset
!= subset_tests
[i
].subset
)
2739 isl_die(ctx
, isl_error_unknown
,
2740 "incorrect subset result", return -1);
2747 const char *minuend
;
2748 const char *subtrahend
;
2749 const char *difference
;
2750 } subtract_domain_tests
[] = {
2751 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2752 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2753 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2756 static int test_subtract(isl_ctx
*ctx
)
2759 isl_union_map
*umap1
, *umap2
;
2760 isl_union_pw_multi_aff
*upma1
, *upma2
;
2761 isl_union_set
*uset
;
2764 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2765 umap1
= isl_union_map_read_from_str(ctx
,
2766 subtract_domain_tests
[i
].minuend
);
2767 uset
= isl_union_set_read_from_str(ctx
,
2768 subtract_domain_tests
[i
].subtrahend
);
2769 umap2
= isl_union_map_read_from_str(ctx
,
2770 subtract_domain_tests
[i
].difference
);
2771 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
2772 equal
= isl_union_map_is_equal(umap1
, umap2
);
2773 isl_union_map_free(umap1
);
2774 isl_union_map_free(umap2
);
2778 isl_die(ctx
, isl_error_unknown
,
2779 "incorrect subtract domain result", return -1);
2782 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2783 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
2784 subtract_domain_tests
[i
].minuend
);
2785 uset
= isl_union_set_read_from_str(ctx
,
2786 subtract_domain_tests
[i
].subtrahend
);
2787 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
2788 subtract_domain_tests
[i
].difference
);
2789 upma1
= isl_union_pw_multi_aff_subtract_domain(upma1
, uset
);
2790 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
2791 isl_union_pw_multi_aff_free(upma1
);
2792 isl_union_pw_multi_aff_free(upma2
);
2796 isl_die(ctx
, isl_error_unknown
,
2797 "incorrect subtract domain result", return -1);
2803 int test_factorize(isl_ctx
*ctx
)
2806 isl_basic_set
*bset
;
2809 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2810 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2811 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2812 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2813 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2814 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2815 "3i5 >= -2i0 - i2 + 3i4 }";
2816 bset
= isl_basic_set_read_from_str(ctx
, str
);
2817 f
= isl_basic_set_factorizer(bset
);
2818 isl_basic_set_free(bset
);
2819 isl_factorizer_free(f
);
2821 isl_die(ctx
, isl_error_unknown
,
2822 "failed to construct factorizer", return -1);
2824 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2825 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2826 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2827 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2828 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2829 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2830 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2831 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2832 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2833 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2834 bset
= isl_basic_set_read_from_str(ctx
, str
);
2835 f
= isl_basic_set_factorizer(bset
);
2836 isl_basic_set_free(bset
);
2837 isl_factorizer_free(f
);
2839 isl_die(ctx
, isl_error_unknown
,
2840 "failed to construct factorizer", return -1);
2845 static isl_stat
check_injective(__isl_take isl_map
*map
, void *user
)
2847 int *injective
= user
;
2849 *injective
= isl_map_is_injective(map
);
2852 if (*injective
< 0 || !*injective
)
2853 return isl_stat_error
;
2858 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
2859 const char *r
, const char *s
, int tilable
, int parallel
)
2863 isl_union_map
*W
, *R
, *S
;
2864 isl_union_map
*empty
;
2865 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
2866 isl_union_map
*validity
, *proximity
, *coincidence
;
2867 isl_union_map
*schedule
;
2868 isl_union_map
*test
;
2869 isl_union_set
*delta
;
2870 isl_union_set
*domain
;
2874 isl_schedule_constraints
*sc
;
2875 isl_schedule
*sched
;
2876 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
2878 D
= isl_union_set_read_from_str(ctx
, d
);
2879 W
= isl_union_map_read_from_str(ctx
, w
);
2880 R
= isl_union_map_read_from_str(ctx
, r
);
2881 S
= isl_union_map_read_from_str(ctx
, s
);
2883 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
2884 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
2886 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
2887 isl_union_map_compute_flow(isl_union_map_copy(R
),
2888 isl_union_map_copy(W
), empty
,
2889 isl_union_map_copy(S
),
2890 &dep_raw
, NULL
, NULL
, NULL
);
2891 isl_union_map_compute_flow(isl_union_map_copy(W
),
2892 isl_union_map_copy(W
),
2893 isl_union_map_copy(R
),
2894 isl_union_map_copy(S
),
2895 &dep_waw
, &dep_war
, NULL
, NULL
);
2897 dep
= isl_union_map_union(dep_waw
, dep_war
);
2898 dep
= isl_union_map_union(dep
, dep_raw
);
2899 validity
= isl_union_map_copy(dep
);
2900 coincidence
= isl_union_map_copy(dep
);
2901 proximity
= isl_union_map_copy(dep
);
2903 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
2904 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
2905 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
2906 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
2907 sched
= isl_schedule_constraints_compute_schedule(sc
);
2908 schedule
= isl_schedule_get_map(sched
);
2909 isl_schedule_free(sched
);
2910 isl_union_map_free(W
);
2911 isl_union_map_free(R
);
2912 isl_union_map_free(S
);
2915 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
2917 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
2918 is_complete
= isl_union_set_is_subset(D
, domain
);
2919 isl_union_set_free(D
);
2920 isl_union_set_free(domain
);
2922 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
2923 test
= isl_union_map_apply_range(test
, dep
);
2924 test
= isl_union_map_apply_range(test
, schedule
);
2926 delta
= isl_union_map_deltas(test
);
2927 if (isl_union_set_n_set(delta
) == 0) {
2931 isl_union_set_free(delta
);
2933 delta_set
= isl_set_from_union_set(delta
);
2935 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2936 for (i
= 0; i
< tilable
; ++i
)
2937 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
2938 is_tilable
= isl_set_is_subset(delta_set
, slice
);
2939 isl_set_free(slice
);
2941 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2942 for (i
= 0; i
< parallel
; ++i
)
2943 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
2944 is_parallel
= isl_set_is_subset(delta_set
, slice
);
2945 isl_set_free(slice
);
2947 origin
= isl_set_universe(isl_set_get_space(delta_set
));
2948 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
2949 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2951 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2952 delta_set
= isl_set_lexmin(delta_set
);
2954 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2956 isl_set_free(origin
);
2957 isl_set_free(delta_set
);
2960 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2961 is_injection
< 0 || is_complete
< 0)
2964 isl_die(ctx
, isl_error_unknown
,
2965 "generated schedule incomplete", return -1);
2967 isl_die(ctx
, isl_error_unknown
,
2968 "generated schedule not injective on each statement",
2971 isl_die(ctx
, isl_error_unknown
,
2972 "negative dependences in generated schedule",
2975 isl_die(ctx
, isl_error_unknown
,
2976 "generated schedule not as tilable as expected",
2979 isl_die(ctx
, isl_error_unknown
,
2980 "generated schedule not as parallel as expected",
2986 /* Compute a schedule for the given instance set, validity constraints,
2987 * proximity constraints and context and return a corresponding union map
2990 static __isl_give isl_union_map
*compute_schedule_with_context(isl_ctx
*ctx
,
2991 const char *domain
, const char *validity
, const char *proximity
,
2992 const char *context
)
2997 isl_union_map
*prox
;
2998 isl_schedule_constraints
*sc
;
2999 isl_schedule
*schedule
;
3000 isl_union_map
*sched
;
3002 con
= isl_set_read_from_str(ctx
, context
);
3003 dom
= isl_union_set_read_from_str(ctx
, domain
);
3004 dep
= isl_union_map_read_from_str(ctx
, validity
);
3005 prox
= isl_union_map_read_from_str(ctx
, proximity
);
3006 sc
= isl_schedule_constraints_on_domain(dom
);
3007 sc
= isl_schedule_constraints_set_context(sc
, con
);
3008 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
3009 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
3010 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3011 sched
= isl_schedule_get_map(schedule
);
3012 isl_schedule_free(schedule
);
3017 /* Compute a schedule for the given instance set, validity constraints and
3018 * proximity constraints and return a corresponding union map representation.
3020 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
3021 const char *domain
, const char *validity
, const char *proximity
)
3023 return compute_schedule_with_context(ctx
, domain
, validity
, proximity
,
3027 /* Check that a schedule can be constructed on the given domain
3028 * with the given validity and proximity constraints.
3030 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
3031 const char *validity
, const char *proximity
)
3033 isl_union_map
*sched
;
3035 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
3039 isl_union_map_free(sched
);
3043 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
3044 const char *validity
, const char *proximity
, const char *expected_sched
)
3046 isl_union_map
*sched1
, *sched2
;
3049 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
3050 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
3052 equal
= isl_union_map_is_equal(sched1
, sched2
);
3053 isl_union_map_free(sched1
);
3054 isl_union_map_free(sched2
);
3059 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
3065 /* Check that the schedule map is properly padded, even after being
3066 * reconstructed from the band forest.
3068 static int test_padded_schedule(isl_ctx
*ctx
)
3072 isl_union_map
*validity
, *proximity
;
3073 isl_schedule_constraints
*sc
;
3074 isl_schedule
*sched
;
3075 isl_union_map
*map1
, *map2
;
3076 isl_band_list
*list
;
3079 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
3080 D
= isl_union_set_read_from_str(ctx
, str
);
3081 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
3082 proximity
= isl_union_map_copy(validity
);
3083 sc
= isl_schedule_constraints_on_domain(D
);
3084 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3085 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3086 sched
= isl_schedule_constraints_compute_schedule(sc
);
3087 map1
= isl_schedule_get_map(sched
);
3088 list
= isl_schedule_get_band_forest(sched
);
3089 isl_band_list_free(list
);
3090 map2
= isl_schedule_get_map(sched
);
3091 isl_schedule_free(sched
);
3092 equal
= isl_union_map_is_equal(map1
, map2
);
3093 isl_union_map_free(map1
);
3094 isl_union_map_free(map2
);
3099 isl_die(ctx
, isl_error_unknown
,
3100 "reconstructed schedule map not the same as original",
3106 /* Check that conditional validity constraints are also taken into
3107 * account across bands.
3108 * In particular, try to make sure that live ranges D[1,0]->C[2,1] and
3109 * D[2,0]->C[3,0] are not local in the outer band of the generated schedule
3110 * and then check that the adjacent order constraint C[2,1]->D[2,0]
3111 * is enforced by the rest of the schedule.
3113 static int test_special_conditional_schedule_constraints(isl_ctx
*ctx
)
3116 isl_union_set
*domain
;
3117 isl_union_map
*validity
, *proximity
, *condition
;
3118 isl_union_map
*sink
, *source
, *dep
;
3119 isl_schedule_constraints
*sc
;
3120 isl_schedule
*schedule
;
3121 isl_union_access_info
*access
;
3122 isl_union_flow
*flow
;
3125 str
= "[n] -> { C[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3126 "A[k] : k >= 1 and k <= -1 + n; "
3127 "B[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3128 "D[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k }";
3129 domain
= isl_union_set_read_from_str(ctx
, str
);
3130 sc
= isl_schedule_constraints_on_domain(domain
);
3131 str
= "[n] -> { D[k, i] -> C[1 + k, k - i] : "
3132 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3133 "D[k, i] -> C[1 + k, i] : "
3134 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3135 "D[k, 0] -> C[1 + k, k] : k >= 1 and k <= -2 + n; "
3136 "D[k, 0] -> C[1 + k, 0] : k >= 1 and k <= -2 + n }";
3137 validity
= isl_union_map_read_from_str(ctx
, str
);
3138 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3139 str
= "[n] -> { C[k, i] -> D[k, i] : "
3140 "0 <= i <= -1 + k and k <= -1 + n }";
3141 proximity
= isl_union_map_read_from_str(ctx
, str
);
3142 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3143 str
= "[n] -> { [D[k, i] -> a[]] -> [C[1 + k, k - i] -> b[]] : "
3144 "i <= -1 + k and i >= 1 and k <= -2 + n; "
3145 "[B[k, i] -> c[]] -> [B[k, 1 + i] -> c[]] : "
3146 "k <= -1 + n and i >= 0 and i <= -2 + k }";
3147 condition
= isl_union_map_read_from_str(ctx
, str
);
3148 str
= "[n] -> { [B[k, i] -> e[]] -> [D[k, i] -> a[]] : "
3149 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3150 "[C[k, i] -> b[]] -> [D[k', -1 + k - i] -> a[]] : "
3151 "i >= 0 and i <= -1 + k and k <= -1 + n and "
3152 "k' <= -1 + n and k' >= k - i and k' >= 1 + k; "
3153 "[C[k, i] -> b[]] -> [D[k, -1 + k - i] -> a[]] : "
3154 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3155 "[B[k, i] -> c[]] -> [A[k'] -> d[]] : "
3156 "k <= -1 + n and i >= 0 and i <= -1 + k and "
3157 "k' >= 1 and k' <= -1 + n and k' >= 1 + k }";
3158 validity
= isl_union_map_read_from_str(ctx
, str
);
3159 sc
= isl_schedule_constraints_set_conditional_validity(sc
, condition
,
3161 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3162 str
= "{ D[2,0] -> [] }";
3163 sink
= isl_union_map_read_from_str(ctx
, str
);
3164 access
= isl_union_access_info_from_sink(sink
);
3165 str
= "{ C[2,1] -> [] }";
3166 source
= isl_union_map_read_from_str(ctx
, str
);
3167 access
= isl_union_access_info_set_must_source(access
, source
);
3168 access
= isl_union_access_info_set_schedule(access
, schedule
);
3169 flow
= isl_union_access_info_compute_flow(access
);
3170 dep
= isl_union_flow_get_must_dependence(flow
);
3171 isl_union_flow_free(flow
);
3172 empty
= isl_union_map_is_empty(dep
);
3173 isl_union_map_free(dep
);
3178 isl_die(ctx
, isl_error_unknown
,
3179 "conditional validity not respected", return -1);
3184 /* Input for testing of schedule construction based on
3185 * conditional constraints.
3187 * domain is the iteration domain
3188 * flow are the flow dependences, which determine the validity and
3189 * proximity constraints
3190 * condition are the conditions on the conditional validity constraints
3191 * conditional_validity are the conditional validity constraints
3192 * outer_band_n is the expected number of members in the outer band
3197 const char *condition
;
3198 const char *conditional_validity
;
3200 } live_range_tests
[] = {
3201 /* Contrived example that illustrates that we need to keep
3202 * track of tagged condition dependences and
3203 * tagged conditional validity dependences
3204 * in isl_sched_edge separately.
3205 * In particular, the conditional validity constraints on A
3206 * cannot be satisfied,
3207 * but they can be ignored because there are no corresponding
3208 * condition constraints. However, we do have an additional
3209 * conditional validity constraint that maps to the same
3210 * dependence relation
3211 * as the condition constraint on B. If we did not make a distinction
3212 * between tagged condition and tagged conditional validity
3213 * dependences, then we
3214 * could end up treating this shared dependence as an condition
3215 * constraint on A, forcing a localization of the conditions,
3216 * which is impossible.
3218 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
3219 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
3220 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
3221 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3222 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3223 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
3226 /* TACO 2013 Fig. 7 */
3227 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3228 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3229 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3230 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
3231 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
3232 "0 <= i < n and 0 <= j < n - 1 }",
3233 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
3234 "0 <= i < n and 0 <= j < j' < n;"
3235 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
3236 "0 <= i < i' < n and 0 <= j,j' < n;"
3237 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
3238 "0 <= i,j,j' < n and j < j' }",
3241 /* TACO 2013 Fig. 7, without tags */
3242 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3243 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3244 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3245 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3246 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3247 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
3248 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
3249 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
3252 /* TACO 2013 Fig. 12 */
3253 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
3254 "S3[i,3] : 0 <= i <= 1 }",
3255 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
3256 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
3257 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
3258 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
3259 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3260 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
3261 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3262 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
3263 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
3264 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
3265 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
3270 /* Test schedule construction based on conditional constraints.
3271 * In particular, check the number of members in the outer band node
3272 * as an indication of whether tiling is possible or not.
3274 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
3277 isl_union_set
*domain
;
3278 isl_union_map
*condition
;
3279 isl_union_map
*flow
;
3280 isl_union_map
*validity
;
3281 isl_schedule_constraints
*sc
;
3282 isl_schedule
*schedule
;
3283 isl_schedule_node
*node
;
3286 if (test_special_conditional_schedule_constraints(ctx
) < 0)
3289 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
3290 domain
= isl_union_set_read_from_str(ctx
,
3291 live_range_tests
[i
].domain
);
3292 flow
= isl_union_map_read_from_str(ctx
,
3293 live_range_tests
[i
].flow
);
3294 condition
= isl_union_map_read_from_str(ctx
,
3295 live_range_tests
[i
].condition
);
3296 validity
= isl_union_map_read_from_str(ctx
,
3297 live_range_tests
[i
].conditional_validity
);
3298 sc
= isl_schedule_constraints_on_domain(domain
);
3299 sc
= isl_schedule_constraints_set_validity(sc
,
3300 isl_union_map_copy(flow
));
3301 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
3302 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
3303 condition
, validity
);
3304 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3305 node
= isl_schedule_get_root(schedule
);
3307 isl_schedule_node_get_type(node
) != isl_schedule_node_band
)
3308 node
= isl_schedule_node_first_child(node
);
3309 n_member
= isl_schedule_node_band_n_member(node
);
3310 isl_schedule_node_free(node
);
3311 isl_schedule_free(schedule
);
3315 if (n_member
!= live_range_tests
[i
].outer_band_n
)
3316 isl_die(ctx
, isl_error_unknown
,
3317 "unexpected number of members in outer band",
3323 /* Check that the schedule computed for the given instance set and
3324 * dependence relation strongly satisfies the dependences.
3325 * In particular, check that no instance is scheduled before
3326 * or together with an instance on which it depends.
3327 * Earlier versions of isl would produce a schedule that
3328 * only weakly satisfies the dependences.
3330 static int test_strongly_satisfying_schedule(isl_ctx
*ctx
)
3332 const char *domain
, *dep
;
3333 isl_union_map
*D
, *schedule
;
3337 domain
= "{ B[i0, i1] : 0 <= i0 <= 1 and 0 <= i1 <= 11; "
3338 "A[i0] : 0 <= i0 <= 1 }";
3339 dep
= "{ B[i0, i1] -> B[i0, 1 + i1] : 0 <= i0 <= 1 and 0 <= i1 <= 10; "
3340 "B[0, 11] -> A[1]; A[i0] -> B[i0, 0] : 0 <= i0 <= 1 }";
3341 schedule
= compute_schedule(ctx
, domain
, dep
, dep
);
3342 D
= isl_union_map_read_from_str(ctx
, dep
);
3343 D
= isl_union_map_apply_domain(D
, isl_union_map_copy(schedule
));
3344 D
= isl_union_map_apply_range(D
, schedule
);
3345 map
= isl_map_from_union_map(D
);
3346 ge
= isl_map_lex_ge(isl_space_domain(isl_map_get_space(map
)));
3347 map
= isl_map_intersect(map
, ge
);
3348 empty
= isl_map_is_empty(map
);
3354 isl_die(ctx
, isl_error_unknown
,
3355 "dependences not strongly satisfied", return -1);
3360 /* Compute a schedule for input where the instance set constraints
3361 * conflict with the context constraints.
3362 * Earlier versions of isl did not properly handle this situation.
3364 static int test_conflicting_context_schedule(isl_ctx
*ctx
)
3366 isl_union_map
*schedule
;
3367 const char *domain
, *context
;
3369 domain
= "[n] -> { A[] : n >= 0 }";
3370 context
= "[n] -> { : n < 0 }";
3371 schedule
= compute_schedule_with_context(ctx
,
3372 domain
, "{}", "{}", context
);
3373 isl_union_map_free(schedule
);
3381 int test_schedule(isl_ctx
*ctx
)
3383 const char *D
, *W
, *R
, *V
, *P
, *S
;
3385 /* Handle resulting schedule with zero bands. */
3386 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
3390 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
3391 W
= "{ S1[t,i] -> a[t,i] }";
3392 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
3393 "S1[t,i] -> a[t-1,i+1] }";
3394 S
= "{ S1[t,i] -> [t,i] }";
3395 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3398 /* Fig. 5 of CC2008 */
3399 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
3401 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
3402 "j >= 2 and j <= -1 + N }";
3403 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
3404 "j >= 2 and j <= -1 + N; "
3405 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
3406 "j >= 2 and j <= -1 + N }";
3407 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3408 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3411 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
3412 W
= "{ S1[i] -> a[i] }";
3413 R
= "{ S2[i] -> a[i+1] }";
3414 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3415 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3418 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
3419 W
= "{ S1[i] -> a[i] }";
3420 R
= "{ S2[i] -> a[9-i] }";
3421 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3422 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3425 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
3426 W
= "{ S1[i] -> a[i] }";
3427 R
= "[N] -> { S2[i] -> a[N-1-i] }";
3428 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3429 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3432 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
3433 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
3434 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
3435 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
3436 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3439 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3440 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
3441 R
= "{ S2[i,j] -> a[i-1,j] }";
3442 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3443 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3446 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3447 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
3448 R
= "{ S2[i,j] -> a[i,j-1] }";
3449 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3450 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3453 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
3454 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
3455 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
3456 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
3457 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
3458 "S_0[] -> [0, 0, 0] }";
3459 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
3461 ctx
->opt
->schedule_parametric
= 0;
3462 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3464 ctx
->opt
->schedule_parametric
= 1;
3466 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
3467 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
3468 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
3469 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
3470 "S4[i] -> a[i,N] }";
3471 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
3472 "S4[i] -> [4,i,0] }";
3473 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3476 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
3477 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3479 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3481 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
3483 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3484 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3487 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
3488 " S_2[t] : t >= 0 and t <= -1 + N; "
3489 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
3491 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
3492 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
3493 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
3494 "i >= 0 and i <= -1 + N }";
3495 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
3496 "i >= 0 and i <= -1 + N; "
3497 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
3498 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
3499 " S_0[t] -> [0, t, 0] }";
3501 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3503 ctx
->opt
->schedule_parametric
= 0;
3504 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3506 ctx
->opt
->schedule_parametric
= 1;
3508 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
3509 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
3510 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
3513 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3514 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3515 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3516 "j >= 0 and j <= -1 + N; "
3517 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3518 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3519 "j >= 0 and j <= -1 + N; "
3520 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3521 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3522 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3525 D
= "{ S_0[i] : i >= 0 }";
3526 W
= "{ S_0[i] -> a[i] : i >= 0 }";
3527 R
= "{ S_0[i] -> a[0] : i >= 0 }";
3528 S
= "{ S_0[i] -> [0, i, 0] }";
3529 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3532 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3533 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3534 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3535 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3536 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3539 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3540 "k <= -1 + n and k >= 0 }";
3541 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3542 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3543 "k <= -1 + n and k >= 0; "
3544 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3545 "k <= -1 + n and k >= 0; "
3546 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3547 "k <= -1 + n and k >= 0 }";
3548 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
3549 ctx
->opt
->schedule_outer_coincidence
= 1;
3550 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3552 ctx
->opt
->schedule_outer_coincidence
= 0;
3554 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
3555 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3556 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3557 "Stmt_for_body24[i0, i1, 1, 0]:"
3558 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3559 "Stmt_for_body7[i0, i1, i2]:"
3560 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3563 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
3564 "Stmt_for_body24[1, i1, i2, i3]:"
3565 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3567 "Stmt_for_body24[0, i1, i2, i3] -> "
3568 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3569 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3571 "Stmt_for_body24[0, i1, i2, i3] ->"
3572 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3573 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3574 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3575 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3576 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3577 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3578 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3579 "i1 <= 6 and i1 >= 0;"
3580 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3581 "Stmt_for_body7[i0, i1, i2] -> "
3582 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3583 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3584 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3585 "Stmt_for_body7[i0, i1, i2] -> "
3586 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3587 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3588 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3590 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3591 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3592 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3594 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3597 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3598 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3599 "j >= 1 and j <= 7;"
3600 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3601 "j >= 1 and j <= 8 }";
3603 S
= "{ S_0[i, j] -> [i + j, j] }";
3604 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3605 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3607 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3609 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3610 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3611 "j >= 0 and j <= -1 + i }";
3612 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3613 "i <= -1 + N and j >= 0;"
3614 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3617 S
= "{ S_0[i, j] -> [i, j] }";
3618 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3619 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3621 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3623 /* Test both algorithms on a case with only proximity dependences. */
3624 D
= "{ S[i,j] : 0 <= i <= 10 }";
3626 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3627 S
= "{ S[i, j] -> [j, i] }";
3628 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3629 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3631 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3632 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3635 D
= "{ A[a]; B[] }";
3637 P
= "{ A[a] -> B[] }";
3638 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3641 if (test_padded_schedule(ctx
) < 0)
3644 /* Check that check for progress is not confused by rational
3647 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3648 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3650 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3651 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3653 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3654 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3656 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3658 /* Check that we allow schedule rows that are only non-trivial
3659 * on some full-dimensional domains.
3661 D
= "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
3662 V
= "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
3663 "S1[j] -> S2[1] : 0 <= j <= 1 }";
3665 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3666 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3668 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3670 if (test_conditional_schedule_constraints(ctx
) < 0)
3673 if (test_strongly_satisfying_schedule(ctx
) < 0)
3676 if (test_conflicting_context_schedule(ctx
) < 0)
3682 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
3684 isl_union_map
*umap
;
3687 umap
= isl_union_map_read_from_str(ctx
, str
);
3688 test
= isl_union_map_plain_is_injective(umap
);
3689 isl_union_map_free(umap
);
3692 if (test
== injective
)
3695 isl_die(ctx
, isl_error_unknown
,
3696 "map not detected as injective", return -1);
3698 isl_die(ctx
, isl_error_unknown
,
3699 "map detected as injective", return -1);
3702 int test_injective(isl_ctx
*ctx
)
3706 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3708 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
3710 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
3712 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
3714 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3716 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3718 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3720 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3723 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3724 if (test_plain_injective(ctx
, str
, 1))
3726 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3727 if (test_plain_injective(ctx
, str
, 0))
3733 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
3741 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
3742 equal
= isl_aff_plain_is_equal(aff
, aff2
);
3748 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
3752 equal
= aff_plain_is_equal(aff
, str
);
3756 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
3757 "result not as expected", return -1);
3762 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3763 __isl_take isl_aff
*aff2
);
3765 ['+'] = { &isl_aff_add
},
3766 ['-'] = { &isl_aff_sub
},
3767 ['*'] = { &isl_aff_mul
},
3768 ['/'] = { &isl_aff_div
},
3776 } aff_bin_tests
[] = {
3777 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3778 "{ [i] -> [2i] }" },
3779 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3781 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3782 "{ [i] -> [2i] }" },
3783 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3784 "{ [i] -> [2i] }" },
3785 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
3786 "{ [i] -> [i/2] }" },
3787 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
3789 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3790 "{ [i] -> [NaN] }" },
3791 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3792 "{ [i] -> [NaN] }" },
3793 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3794 "{ [i] -> [NaN] }" },
3795 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3796 "{ [i] -> [NaN] }" },
3797 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
3798 "{ [i] -> [NaN] }" },
3799 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
3800 "{ [i] -> [NaN] }" },
3801 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3802 "{ [i] -> [NaN] }" },
3803 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3804 "{ [i] -> [NaN] }" },
3805 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3806 "{ [i] -> [NaN] }" },
3807 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3808 "{ [i] -> [NaN] }" },
3809 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
3810 "{ [i] -> [NaN] }" },
3811 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
3812 "{ [i] -> [NaN] }" },
3815 /* Perform some basic tests of binary operations on isl_aff objects.
3817 static int test_bin_aff(isl_ctx
*ctx
)
3820 isl_aff
*aff1
, *aff2
, *res
;
3821 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3822 __isl_take isl_aff
*aff2
);
3825 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
3826 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
3827 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
3828 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
3829 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
3830 aff1
= fn(aff1
, aff2
);
3831 if (isl_aff_is_nan(res
))
3832 ok
= isl_aff_is_nan(aff1
);
3834 ok
= isl_aff_plain_is_equal(aff1
, res
);
3840 isl_die(ctx
, isl_error_unknown
,
3841 "unexpected result", return -1);
3848 __isl_give isl_union_pw_multi_aff
*(*fn
)(
3849 __isl_take isl_union_pw_multi_aff
*upma1
,
3850 __isl_take isl_union_pw_multi_aff
*upma2
);
3854 } upma_bin_tests
[] = {
3855 { &isl_union_pw_multi_aff_add
, "{ A[] -> [0]; B[0] -> [1] }",
3856 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
3857 { &isl_union_pw_multi_aff_union_add
, "{ A[] -> [0]; B[0] -> [1] }",
3858 "{ B[x] -> [2] : x >= 0 }",
3859 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
3862 /* Perform some basic tests of binary operations on
3863 * isl_union_pw_multi_aff objects.
3865 static int test_bin_upma(isl_ctx
*ctx
)
3868 isl_union_pw_multi_aff
*upma1
, *upma2
, *res
;
3871 for (i
= 0; i
< ARRAY_SIZE(upma_bin_tests
); ++i
) {
3872 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
3873 upma_bin_tests
[i
].arg1
);
3874 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
3875 upma_bin_tests
[i
].arg2
);
3876 res
= isl_union_pw_multi_aff_read_from_str(ctx
,
3877 upma_bin_tests
[i
].res
);
3878 upma1
= upma_bin_tests
[i
].fn(upma1
, upma2
);
3879 ok
= isl_union_pw_multi_aff_plain_is_equal(upma1
, res
);
3880 isl_union_pw_multi_aff_free(upma1
);
3881 isl_union_pw_multi_aff_free(res
);
3885 isl_die(ctx
, isl_error_unknown
,
3886 "unexpected result", return -1);
3892 int test_aff(isl_ctx
*ctx
)
3897 isl_local_space
*ls
;
3901 if (test_bin_aff(ctx
) < 0)
3903 if (test_bin_upma(ctx
) < 0)
3906 space
= isl_space_set_alloc(ctx
, 0, 1);
3907 ls
= isl_local_space_from_space(space
);
3908 aff
= isl_aff_zero_on_domain(ls
);
3910 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3911 aff
= isl_aff_scale_down_ui(aff
, 3);
3912 aff
= isl_aff_floor(aff
);
3913 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3914 aff
= isl_aff_scale_down_ui(aff
, 2);
3915 aff
= isl_aff_floor(aff
);
3916 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3919 set
= isl_set_read_from_str(ctx
, str
);
3920 aff
= isl_aff_gist(aff
, set
);
3922 aff
= isl_aff_add_constant_si(aff
, -16);
3923 zero
= isl_aff_plain_is_zero(aff
);
3929 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3931 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
3932 aff
= isl_aff_scale_down_ui(aff
, 64);
3933 aff
= isl_aff_floor(aff
);
3934 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
3942 int test_dim_max(isl_ctx
*ctx
)
3946 isl_set
*set1
, *set2
;
3951 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
3952 set
= isl_set_read_from_str(ctx
, str
);
3953 pwaff
= isl_set_dim_max(set
, 0);
3954 set1
= isl_set_from_pw_aff(pwaff
);
3955 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
3956 set2
= isl_set_read_from_str(ctx
, str
);
3957 equal
= isl_set_is_equal(set1
, set2
);
3963 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3965 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
3966 set
= isl_set_read_from_str(ctx
, str
);
3967 pwaff
= isl_set_dim_max(set
, 0);
3968 set1
= isl_set_from_pw_aff(pwaff
);
3969 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3970 set2
= isl_set_read_from_str(ctx
, str
);
3971 equal
= isl_set_is_equal(set1
, set2
);
3977 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3979 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
3980 set
= isl_set_read_from_str(ctx
, str
);
3981 pwaff
= isl_set_dim_max(set
, 0);
3982 set1
= isl_set_from_pw_aff(pwaff
);
3983 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3984 set2
= isl_set_read_from_str(ctx
, str
);
3985 equal
= isl_set_is_equal(set1
, set2
);
3991 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3993 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
3994 "0 <= i < N and 0 <= j < M }";
3995 map
= isl_map_read_from_str(ctx
, str
);
3996 set
= isl_map_range(map
);
3998 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
3999 set1
= isl_set_from_pw_aff(pwaff
);
4000 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
4001 set2
= isl_set_read_from_str(ctx
, str
);
4002 equal
= isl_set_is_equal(set1
, set2
);
4006 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
4007 set1
= isl_set_from_pw_aff(pwaff
);
4008 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
4009 set2
= isl_set_read_from_str(ctx
, str
);
4010 if (equal
>= 0 && equal
)
4011 equal
= isl_set_is_equal(set1
, set2
);
4020 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4022 /* Check that solutions are properly merged. */
4023 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
4024 "c <= -1 + n - 4a - 2b and c >= -2b and "
4025 "4a >= -4 + n and c >= 0 }";
4026 set
= isl_set_read_from_str(ctx
, str
);
4027 pwaff
= isl_set_dim_min(set
, 2);
4028 set1
= isl_set_from_pw_aff(pwaff
);
4029 str
= "[n] -> { [(0)] : n >= 1 }";
4030 set2
= isl_set_read_from_str(ctx
, str
);
4031 equal
= isl_set_is_equal(set1
, set2
);
4038 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4040 /* Check that empty solution lie in the right space. */
4041 str
= "[n] -> { [t,a] : 1 = 0 }";
4042 set
= isl_set_read_from_str(ctx
, str
);
4043 pwaff
= isl_set_dim_max(set
, 0);
4044 set1
= isl_set_from_pw_aff(pwaff
);
4045 str
= "[n] -> { [t] : 1 = 0 }";
4046 set2
= isl_set_read_from_str(ctx
, str
);
4047 equal
= isl_set_is_equal(set1
, set2
);
4054 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4059 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
4061 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
4065 isl_pw_multi_aff
*pma2
;
4071 ctx
= isl_pw_multi_aff_get_ctx(pma
);
4072 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4073 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
4074 isl_pw_multi_aff_free(pma2
);
4079 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
4080 * represented by "str".
4082 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
4087 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
4091 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
4092 "result not as expected", return -1);
4096 /* Basic test for isl_pw_multi_aff_product.
4098 * Check that multiple pieces are properly handled.
4100 static int test_product_pma(isl_ctx
*ctx
)
4104 isl_pw_multi_aff
*pma1
, *pma2
;
4106 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
4107 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4108 str
= "{ C[] -> D[] }";
4109 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4110 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
4111 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
4112 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
4113 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
4114 isl_pw_multi_aff_free(pma1
);
4121 int test_product(isl_ctx
*ctx
)
4125 isl_union_set
*uset1
, *uset2
;
4129 set
= isl_set_read_from_str(ctx
, str
);
4130 set
= isl_set_product(set
, isl_set_copy(set
));
4131 ok
= isl_set_is_wrapping(set
);
4136 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4139 uset1
= isl_union_set_read_from_str(ctx
, str
);
4140 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
4141 str
= "{ [[] -> []] }";
4142 uset2
= isl_union_set_read_from_str(ctx
, str
);
4143 ok
= isl_union_set_is_equal(uset1
, uset2
);
4144 isl_union_set_free(uset1
);
4145 isl_union_set_free(uset2
);
4149 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4151 if (test_product_pma(ctx
) < 0)
4157 /* Check that two sets are not considered disjoint just because
4158 * they have a different set of (named) parameters.
4160 static int test_disjoint(isl_ctx
*ctx
)
4163 isl_set
*set
, *set2
;
4166 str
= "[n] -> { [[]->[]] }";
4167 set
= isl_set_read_from_str(ctx
, str
);
4168 str
= "{ [[]->[]] }";
4169 set2
= isl_set_read_from_str(ctx
, str
);
4170 disjoint
= isl_set_is_disjoint(set
, set2
);
4176 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4181 int test_equal(isl_ctx
*ctx
)
4184 isl_set
*set
, *set2
;
4188 set
= isl_set_read_from_str(ctx
, str
);
4190 set2
= isl_set_read_from_str(ctx
, str
);
4191 equal
= isl_set_is_equal(set
, set2
);
4197 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4202 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
4203 enum isl_dim_type type
, unsigned pos
, int fixed
)
4207 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
4214 isl_die(ctx
, isl_error_unknown
,
4215 "map not detected as fixed", return -1);
4217 isl_die(ctx
, isl_error_unknown
,
4218 "map detected as fixed", return -1);
4221 int test_fixed(isl_ctx
*ctx
)
4226 str
= "{ [i] -> [i] }";
4227 map
= isl_map_read_from_str(ctx
, str
);
4228 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
4230 str
= "{ [i] -> [1] }";
4231 map
= isl_map_read_from_str(ctx
, str
);
4232 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4234 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
4235 map
= isl_map_read_from_str(ctx
, str
);
4236 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4238 map
= isl_map_read_from_str(ctx
, str
);
4239 map
= isl_map_neg(map
);
4240 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4246 struct isl_vertices_test_data
{
4249 const char *vertex
[2];
4250 } vertices_tests
[] = {
4251 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
4252 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
4253 { "{ A[t, i] : t = 14 and i = 1 }",
4254 1, { "{ A[14, 1] }" } },
4257 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
4259 static isl_stat
find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
4261 struct isl_vertices_test_data
*data
= user
;
4264 isl_basic_set
*bset
;
4265 isl_pw_multi_aff
*pma
;
4269 ctx
= isl_vertex_get_ctx(vertex
);
4270 bset
= isl_vertex_get_domain(vertex
);
4271 ma
= isl_vertex_get_expr(vertex
);
4272 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
4274 for (i
= 0; i
< data
->n
; ++i
) {
4275 isl_pw_multi_aff
*pma_i
;
4277 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
4278 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
4279 isl_pw_multi_aff_free(pma_i
);
4281 if (equal
< 0 || equal
)
4285 isl_pw_multi_aff_free(pma
);
4286 isl_vertex_free(vertex
);
4289 return isl_stat_error
;
4291 return equal
? isl_stat_ok
: isl_stat_error
;
4294 int test_vertices(isl_ctx
*ctx
)
4298 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
4299 isl_basic_set
*bset
;
4300 isl_vertices
*vertices
;
4304 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
4305 vertices
= isl_basic_set_compute_vertices(bset
);
4306 n
= isl_vertices_get_n_vertices(vertices
);
4307 if (vertices_tests
[i
].n
!= n
)
4309 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
4310 &vertices_tests
[i
]) < 0)
4312 isl_vertices_free(vertices
);
4313 isl_basic_set_free(bset
);
4318 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
4325 int test_union_pw(isl_ctx
*ctx
)
4329 isl_union_set
*uset
;
4330 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
4332 str
= "{ [x] -> x^2 }";
4333 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
4334 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
4335 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
4336 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
4337 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
4338 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
4339 isl_union_pw_qpolynomial_free(upwqp1
);
4340 isl_union_pw_qpolynomial_free(upwqp2
);
4344 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4349 int test_output(isl_ctx
*ctx
)
4357 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
4358 pa
= isl_pw_aff_read_from_str(ctx
, str
);
4360 p
= isl_printer_to_str(ctx
);
4361 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
4362 p
= isl_printer_print_pw_aff(p
, pa
);
4363 s
= isl_printer_get_str(p
);
4364 isl_printer_free(p
);
4365 isl_pw_aff_free(pa
);
4369 equal
= !strcmp(s
, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
4374 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4379 int test_sample(isl_ctx
*ctx
)
4382 isl_basic_set
*bset1
, *bset2
;
4385 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
4386 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
4387 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
4388 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
4389 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
4390 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
4391 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
4392 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
4393 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
4394 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
4395 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
4396 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
4397 "d - 1073741821e and "
4398 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
4399 "3j >= 1 - a + b + 2e and "
4400 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
4401 "3i <= 4 - a + 4b - e and "
4402 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
4403 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
4404 "c <= -1 + a and 3i >= -2 - a + 3e and "
4405 "1073741822e <= 1073741823 - a + 1073741822b + c and "
4406 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
4407 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
4408 "1073741823e >= 1 + 1073741823b - d and "
4409 "3i >= 1073741823b + c - 1073741823e - f and "
4410 "3i >= 1 + 2b + e + 3g }";
4411 bset1
= isl_basic_set_read_from_str(ctx
, str
);
4412 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
4413 empty
= isl_basic_set_is_empty(bset2
);
4414 subset
= isl_basic_set_is_subset(bset2
, bset1
);
4415 isl_basic_set_free(bset1
);
4416 isl_basic_set_free(bset2
);
4417 if (empty
< 0 || subset
< 0)
4420 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
4422 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
4427 int test_fixed_power(isl_ctx
*ctx
)
4435 str
= "{ [i] -> [i + 1] }";
4436 map
= isl_map_read_from_str(ctx
, str
);
4437 isl_int_set_si(exp
, 23);
4438 map
= isl_map_fixed_power(map
, exp
);
4439 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
4448 int test_slice(isl_ctx
*ctx
)
4454 str
= "{ [i] -> [j] }";
4455 map
= isl_map_read_from_str(ctx
, str
);
4456 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4457 equal
= map_check_equal(map
, "{ [i] -> [i] }");
4462 str
= "{ [i] -> [j] }";
4463 map
= isl_map_read_from_str(ctx
, str
);
4464 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4465 equal
= map_check_equal(map
, "{ [i] -> [j] }");
4470 str
= "{ [i] -> [j] }";
4471 map
= isl_map_read_from_str(ctx
, str
);
4472 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4473 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
4478 str
= "{ [i] -> [j] }";
4479 map
= isl_map_read_from_str(ctx
, str
);
4480 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4481 equal
= map_check_equal(map
, "{ [0] -> [j] }");
4486 str
= "{ [i] -> [j] }";
4487 map
= isl_map_read_from_str(ctx
, str
);
4488 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4489 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
4494 str
= "{ [i] -> [j] }";
4495 map
= isl_map_read_from_str(ctx
, str
);
4496 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4497 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
4505 int test_eliminate(isl_ctx
*ctx
)
4511 str
= "{ [i] -> [j] : i = 2j }";
4512 map
= isl_map_read_from_str(ctx
, str
);
4513 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
4514 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
4522 /* Check that isl_set_dim_residue_class detects that the values of j
4523 * in the set below are all odd and that it does not detect any spurious
4526 static int test_residue_class(isl_ctx
*ctx
)
4533 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
4534 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
4535 set
= isl_set_read_from_str(ctx
, str
);
4538 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
4540 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
4541 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
4550 int test_align_parameters(isl_ctx
*ctx
)
4554 isl_multi_aff
*ma1
, *ma2
;
4557 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
4558 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
4560 space
= isl_space_params_alloc(ctx
, 1);
4561 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
4562 ma1
= isl_multi_aff_align_params(ma1
, space
);
4564 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
4565 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
4567 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
4569 isl_multi_aff_free(ma1
);
4570 isl_multi_aff_free(ma2
);
4575 isl_die(ctx
, isl_error_unknown
,
4576 "result not as expected", return -1);
4581 static int test_list(isl_ctx
*ctx
)
4583 isl_id
*a
, *b
, *c
, *d
, *id
;
4587 a
= isl_id_alloc(ctx
, "a", NULL
);
4588 b
= isl_id_alloc(ctx
, "b", NULL
);
4589 c
= isl_id_alloc(ctx
, "c", NULL
);
4590 d
= isl_id_alloc(ctx
, "d", NULL
);
4592 list
= isl_id_list_alloc(ctx
, 4);
4593 list
= isl_id_list_add(list
, a
);
4594 list
= isl_id_list_add(list
, b
);
4595 list
= isl_id_list_add(list
, c
);
4596 list
= isl_id_list_add(list
, d
);
4597 list
= isl_id_list_drop(list
, 1, 1);
4599 if (isl_id_list_n_id(list
) != 3) {
4600 isl_id_list_free(list
);
4601 isl_die(ctx
, isl_error_unknown
,
4602 "unexpected number of elements in list", return -1);
4605 id
= isl_id_list_get_id(list
, 0);
4608 id
= isl_id_list_get_id(list
, 1);
4611 id
= isl_id_list_get_id(list
, 2);
4615 isl_id_list_free(list
);
4618 isl_die(ctx
, isl_error_unknown
,
4619 "unexpected elements in list", return -1);
4624 const char *set_conversion_tests
[] = {
4625 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4626 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4627 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4628 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4629 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
4632 /* Check that converting from isl_set to isl_pw_multi_aff and back
4633 * to isl_set produces the original isl_set.
4635 static int test_set_conversion(isl_ctx
*ctx
)
4639 isl_set
*set1
, *set2
;
4640 isl_pw_multi_aff
*pma
;
4643 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
4644 str
= set_conversion_tests
[i
];
4645 set1
= isl_set_read_from_str(ctx
, str
);
4646 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
4647 set2
= isl_set_from_pw_multi_aff(pma
);
4648 equal
= isl_set_is_equal(set1
, set2
);
4655 isl_die(ctx
, isl_error_unknown
, "bad conversion",
4662 /* Check that converting from isl_map to isl_pw_multi_aff and back
4663 * to isl_map produces the original isl_map.
4665 static int test_map_conversion(isl_ctx
*ctx
)
4668 isl_map
*map1
, *map2
;
4669 isl_pw_multi_aff
*pma
;
4672 str
= "{ [a, b, c, d] -> s0[a, b, e, f] : "
4673 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4674 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4675 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4677 map1
= isl_map_read_from_str(ctx
, str
);
4678 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
4679 map2
= isl_map_from_pw_multi_aff(pma
);
4680 equal
= isl_map_is_equal(map1
, map2
);
4687 isl_die(ctx
, isl_error_unknown
, "bad conversion", return -1);
4692 static int test_conversion(isl_ctx
*ctx
)
4694 if (test_set_conversion(ctx
) < 0)
4696 if (test_map_conversion(ctx
) < 0)
4701 /* Check that isl_basic_map_curry does not modify input.
4703 static int test_curry(isl_ctx
*ctx
)
4706 isl_basic_map
*bmap1
, *bmap2
;
4709 str
= "{ [A[] -> B[]] -> C[] }";
4710 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
4711 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
4712 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
4713 isl_basic_map_free(bmap1
);
4714 isl_basic_map_free(bmap2
);
4719 isl_die(ctx
, isl_error_unknown
,
4720 "curried map should not be equal to original",
4730 } preimage_tests
[] = {
4731 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4732 "{ A[j,i] -> B[i,j] }",
4733 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4734 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4735 "{ A[a,b] -> B[a/2,b/6] }",
4736 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4737 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4738 "{ A[a,b] -> B[a/2,b/6] }",
4739 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4740 "exists i,j : a = 2 i and b = 6 j }" },
4741 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4742 "[n] -> { : 0 <= n <= 100 }" },
4743 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4744 "{ A[a] -> B[2a] }",
4745 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4746 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4747 "{ A[a] -> B[([a/2])] }",
4748 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4749 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4750 "{ A[a] -> B[a,a,a/3] }",
4751 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4752 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4753 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4756 static int test_preimage_basic_set(isl_ctx
*ctx
)
4759 isl_basic_set
*bset1
, *bset2
;
4763 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
4764 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
4765 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
4766 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
4767 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
4768 equal
= isl_basic_set_is_equal(bset1
, bset2
);
4769 isl_basic_set_free(bset1
);
4770 isl_basic_set_free(bset2
);
4774 isl_die(ctx
, isl_error_unknown
, "bad preimage",
4785 } preimage_domain_tests
[] = {
4786 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4787 "{ A[j,i] -> B[i,j] }",
4788 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4789 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4790 "{ A[i] -> B[i + 1] }",
4791 "{ A[i] -> C[i + 1] }" },
4792 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4793 "{ A[i] -> B[i + 1] }",
4794 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4795 { "{ B[i] -> C[([i/2])] }",
4796 "{ A[i] -> B[2i] }",
4797 "{ A[i] -> C[i] }" },
4798 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4799 "{ A[i] -> B[([i/5]), ([i/7])] }",
4800 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4801 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4802 "[N] -> { A[] -> B[([N/5])] }",
4803 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4804 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4805 "{ A[i] -> B[2i] }",
4806 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4807 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4808 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4809 "{ A[i] -> B[2i] }",
4810 "{ A[i] -> C[2i] }" },
4813 static int test_preimage_union_map(isl_ctx
*ctx
)
4816 isl_union_map
*umap1
, *umap2
;
4820 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
4821 umap1
= isl_union_map_read_from_str(ctx
,
4822 preimage_domain_tests
[i
].map
);
4823 ma
= isl_multi_aff_read_from_str(ctx
,
4824 preimage_domain_tests
[i
].ma
);
4825 umap2
= isl_union_map_read_from_str(ctx
,
4826 preimage_domain_tests
[i
].res
);
4827 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
4828 equal
= isl_union_map_is_equal(umap1
, umap2
);
4829 isl_union_map_free(umap1
);
4830 isl_union_map_free(umap2
);
4834 isl_die(ctx
, isl_error_unknown
, "bad preimage",
4841 static int test_preimage(isl_ctx
*ctx
)
4843 if (test_preimage_basic_set(ctx
) < 0)
4845 if (test_preimage_union_map(ctx
) < 0)
4855 } pullback_tests
[] = {
4856 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
4857 "{ A[a,b] -> C[b + 2a] }" },
4858 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
4859 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
4860 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
4861 "{ A[a] -> C[(a)/6] }" },
4862 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
4863 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
4864 "{ A[a] -> C[(2a)/3] }" },
4865 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
4866 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
4867 "{ A[i,j] -> C[i + j, i + j] }"},
4868 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
4869 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
4870 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
4871 { "{ [i, j] -> [floor((i)/4) + floor((2*i+j)/5)] }",
4872 "{ [i, j] -> [floor((i)/3), j] }",
4873 "{ [i, j] -> [(floor((i)/12) + floor((j + 2*floor((i)/3))/5))] }" },
4876 static int test_pullback(isl_ctx
*ctx
)
4879 isl_multi_aff
*ma1
, *ma2
;
4883 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
4884 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
4885 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
4886 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
4887 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
4888 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
4889 isl_multi_aff_free(ma1
);
4890 isl_multi_aff_free(ma2
);
4894 isl_die(ctx
, isl_error_unknown
, "bad pullback",
4901 /* Check that negation is printed correctly and that equal expressions
4902 * are correctly identified.
4904 static int test_ast(isl_ctx
*ctx
)
4906 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
4910 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
4911 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
4912 expr
= isl_ast_expr_add(expr1
, expr2
);
4913 expr2
= isl_ast_expr_copy(expr
);
4914 expr
= isl_ast_expr_neg(expr
);
4915 expr2
= isl_ast_expr_neg(expr2
);
4916 equal
= isl_ast_expr_is_equal(expr
, expr2
);
4917 str
= isl_ast_expr_to_str(expr
);
4918 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
4920 isl_ast_expr_free(expr
);
4921 isl_ast_expr_free(expr2
);
4923 if (ok
< 0 || equal
< 0)
4926 isl_die(ctx
, isl_error_unknown
,
4927 "equal expressions not considered equal", return -1);
4929 isl_die(ctx
, isl_error_unknown
,
4930 "isl_ast_expr printed incorrectly", return -1);
4932 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
4933 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
4934 expr
= isl_ast_expr_add(expr1
, expr2
);
4935 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
4936 expr
= isl_ast_expr_sub(expr3
, expr
);
4937 str
= isl_ast_expr_to_str(expr
);
4938 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
4940 isl_ast_expr_free(expr
);
4945 isl_die(ctx
, isl_error_unknown
,
4946 "isl_ast_expr printed incorrectly", return -1);
4951 /* Check that isl_ast_build_expr_from_set returns a valid expression
4952 * for an empty set. Note that isl_ast_build_expr_from_set getting
4953 * called on an empty set probably indicates a bug in the caller.
4955 static int test_ast_build(isl_ctx
*ctx
)
4958 isl_ast_build
*build
;
4961 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4962 build
= isl_ast_build_from_context(set
);
4964 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
4965 expr
= isl_ast_build_expr_from_set(build
, set
);
4967 isl_ast_expr_free(expr
);
4968 isl_ast_build_free(build
);
4976 /* Internal data structure for before_for and after_for callbacks.
4978 * depth is the current depth
4979 * before is the number of times before_for has been called
4980 * after is the number of times after_for has been called
4982 struct isl_test_codegen_data
{
4988 /* This function is called before each for loop in the AST generated
4989 * from test_ast_gen1.
4991 * Increment the number of calls and the depth.
4992 * Check that the space returned by isl_ast_build_get_schedule_space
4993 * matches the target space of the schedule returned by
4994 * isl_ast_build_get_schedule.
4995 * Return an isl_id that is checked by the corresponding call
4998 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
5001 struct isl_test_codegen_data
*data
= user
;
5004 isl_union_map
*schedule
;
5005 isl_union_set
*uset
;
5010 ctx
= isl_ast_build_get_ctx(build
);
5012 if (data
->before
>= 3)
5013 isl_die(ctx
, isl_error_unknown
,
5014 "unexpected number of for nodes", return NULL
);
5015 if (data
->depth
>= 2)
5016 isl_die(ctx
, isl_error_unknown
,
5017 "unexpected depth", return NULL
);
5019 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
5023 schedule
= isl_ast_build_get_schedule(build
);
5024 uset
= isl_union_map_range(schedule
);
5027 if (isl_union_set_n_set(uset
) != 1) {
5028 isl_union_set_free(uset
);
5029 isl_die(ctx
, isl_error_unknown
,
5030 "expecting single range space", return NULL
);
5033 space
= isl_ast_build_get_schedule_space(build
);
5034 set
= isl_union_set_extract_set(uset
, space
);
5035 isl_union_set_free(uset
);
5036 empty
= isl_set_is_empty(set
);
5042 isl_die(ctx
, isl_error_unknown
,
5043 "spaces don't match", return NULL
);
5045 return isl_id_alloc(ctx
, name
, NULL
);
5048 /* This function is called after each for loop in the AST generated
5049 * from test_ast_gen1.
5051 * Increment the number of calls and decrement the depth.
5052 * Check that the annotation attached to the node matches
5053 * the isl_id returned by the corresponding call to before_for.
5055 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
5056 __isl_keep isl_ast_build
*build
, void *user
)
5058 struct isl_test_codegen_data
*data
= user
;
5066 if (data
->after
> data
->before
)
5067 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5068 "mismatch in number of for nodes",
5069 return isl_ast_node_free(node
));
5071 id
= isl_ast_node_get_annotation(node
);
5073 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5074 "missing annotation", return isl_ast_node_free(node
));
5076 name
= isl_id_get_name(id
);
5077 valid
= name
&& atoi(name
+ 1) == data
->depth
;
5081 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5082 "wrong annotation", return isl_ast_node_free(node
));
5087 /* Check that the before_each_for and after_each_for callbacks
5088 * are called for each for loop in the generated code,
5089 * that they are called in the right order and that the isl_id
5090 * returned from the before_each_for callback is attached to
5091 * the isl_ast_node passed to the corresponding after_each_for call.
5093 static int test_ast_gen1(isl_ctx
*ctx
)
5097 isl_union_map
*schedule
;
5098 isl_ast_build
*build
;
5100 struct isl_test_codegen_data data
;
5102 str
= "[N] -> { : N >= 10 }";
5103 set
= isl_set_read_from_str(ctx
, str
);
5104 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
5105 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
5106 schedule
= isl_union_map_read_from_str(ctx
, str
);
5111 build
= isl_ast_build_from_context(set
);
5112 build
= isl_ast_build_set_before_each_for(build
,
5113 &before_for
, &data
);
5114 build
= isl_ast_build_set_after_each_for(build
,
5116 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5117 isl_ast_build_free(build
);
5121 isl_ast_node_free(tree
);
5123 if (data
.before
!= 3 || data
.after
!= 3)
5124 isl_die(ctx
, isl_error_unknown
,
5125 "unexpected number of for nodes", return -1);
5130 /* Check that the AST generator handles domains that are integrally disjoint
5131 * but not ratinoally disjoint.
5133 static int test_ast_gen2(isl_ctx
*ctx
)
5137 isl_union_map
*schedule
;
5138 isl_union_map
*options
;
5139 isl_ast_build
*build
;
5142 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
5143 schedule
= isl_union_map_read_from_str(ctx
, str
);
5144 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5145 build
= isl_ast_build_from_context(set
);
5147 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
5148 options
= isl_union_map_read_from_str(ctx
, str
);
5149 build
= isl_ast_build_set_options(build
, options
);
5150 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5151 isl_ast_build_free(build
);
5154 isl_ast_node_free(tree
);
5159 /* Increment *user on each call.
5161 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
5162 __isl_keep isl_ast_build
*build
, void *user
)
5171 /* Test that unrolling tries to minimize the number of instances.
5172 * In particular, for the schedule given below, make sure it generates
5173 * 3 nodes (rather than 101).
5175 static int test_ast_gen3(isl_ctx
*ctx
)
5179 isl_union_map
*schedule
;
5180 isl_union_map
*options
;
5181 isl_ast_build
*build
;
5185 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
5186 schedule
= isl_union_map_read_from_str(ctx
, str
);
5187 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5189 str
= "{ [i] -> unroll[0] }";
5190 options
= isl_union_map_read_from_str(ctx
, str
);
5192 build
= isl_ast_build_from_context(set
);
5193 build
= isl_ast_build_set_options(build
, options
);
5194 build
= isl_ast_build_set_at_each_domain(build
,
5195 &count_domains
, &n_domain
);
5196 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5197 isl_ast_build_free(build
);
5201 isl_ast_node_free(tree
);
5204 isl_die(ctx
, isl_error_unknown
,
5205 "unexpected number of for nodes", return -1);
5210 /* Check that if the ast_build_exploit_nested_bounds options is set,
5211 * we do not get an outer if node in the generated AST,
5212 * while we do get such an outer if node if the options is not set.
5214 static int test_ast_gen4(isl_ctx
*ctx
)
5218 isl_union_map
*schedule
;
5219 isl_ast_build
*build
;
5221 enum isl_ast_node_type type
;
5224 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
5225 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
5227 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
5229 schedule
= isl_union_map_read_from_str(ctx
, str
);
5230 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5231 build
= isl_ast_build_from_context(set
);
5232 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5233 isl_ast_build_free(build
);
5237 type
= isl_ast_node_get_type(tree
);
5238 isl_ast_node_free(tree
);
5240 if (type
== isl_ast_node_if
)
5241 isl_die(ctx
, isl_error_unknown
,
5242 "not expecting if node", return -1);
5244 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
5246 schedule
= isl_union_map_read_from_str(ctx
, str
);
5247 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5248 build
= isl_ast_build_from_context(set
);
5249 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5250 isl_ast_build_free(build
);
5254 type
= isl_ast_node_get_type(tree
);
5255 isl_ast_node_free(tree
);
5257 if (type
!= isl_ast_node_if
)
5258 isl_die(ctx
, isl_error_unknown
,
5259 "expecting if node", return -1);
5261 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
5266 /* This function is called for each leaf in the AST generated
5267 * from test_ast_gen5.
5269 * We finalize the AST generation by extending the outer schedule
5270 * with a zero-dimensional schedule. If this results in any for loops,
5271 * then this means that we did not pass along enough information
5272 * about the outer schedule to the inner AST generation.
5274 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
5277 isl_union_map
*schedule
, *extra
;
5280 schedule
= isl_ast_build_get_schedule(build
);
5281 extra
= isl_union_map_copy(schedule
);
5282 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
5283 schedule
= isl_union_map_range_product(schedule
, extra
);
5284 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5285 isl_ast_build_free(build
);
5290 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
5291 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
5292 "code should not contain any for loop",
5293 return isl_ast_node_free(tree
));
5298 /* Check that we do not lose any information when going back and
5299 * forth between internal and external schedule.
5301 * In particular, we create an AST where we unroll the only
5302 * non-constant dimension in the schedule. We therefore do
5303 * not expect any for loops in the AST. However, older versions
5304 * of isl would not pass along enough information about the outer
5305 * schedule when performing an inner code generation from a create_leaf
5306 * callback, resulting in the inner code generation producing a for loop.
5308 static int test_ast_gen5(isl_ctx
*ctx
)
5312 isl_union_map
*schedule
, *options
;
5313 isl_ast_build
*build
;
5316 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
5317 schedule
= isl_union_map_read_from_str(ctx
, str
);
5319 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
5320 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
5321 options
= isl_union_map_read_from_str(ctx
, str
);
5323 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5324 build
= isl_ast_build_from_context(set
);
5325 build
= isl_ast_build_set_options(build
, options
);
5326 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
5327 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5328 isl_ast_build_free(build
);
5329 isl_ast_node_free(tree
);
5336 static int test_ast_gen(isl_ctx
*ctx
)
5338 if (test_ast_gen1(ctx
) < 0)
5340 if (test_ast_gen2(ctx
) < 0)
5342 if (test_ast_gen3(ctx
) < 0)
5344 if (test_ast_gen4(ctx
) < 0)
5346 if (test_ast_gen5(ctx
) < 0)
5351 /* Check if dropping output dimensions from an isl_pw_multi_aff
5354 static int test_pw_multi_aff(isl_ctx
*ctx
)
5357 isl_pw_multi_aff
*pma1
, *pma2
;
5360 str
= "{ [i,j] -> [i+j, 4i-j] }";
5361 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5362 str
= "{ [i,j] -> [4i-j] }";
5363 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5365 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
5367 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
5369 isl_pw_multi_aff_free(pma1
);
5370 isl_pw_multi_aff_free(pma2
);
5374 isl_die(ctx
, isl_error_unknown
,
5375 "expressions not equal", return -1);
5380 /* Check that we can properly parse multi piecewise affine expressions
5381 * where the piecewise affine expressions have different domains.
5383 static int test_multi_pw_aff(isl_ctx
*ctx
)
5386 isl_set
*dom
, *dom2
;
5387 isl_multi_pw_aff
*mpa1
, *mpa2
;
5392 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
5393 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
5394 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
5395 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
5396 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
5397 str
= "{ [i] -> [(i : i > 0), 2i] }";
5398 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
5400 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
5402 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
5403 dom
= isl_pw_aff_domain(pa
);
5404 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
5405 dom2
= isl_pw_aff_domain(pa
);
5406 equal_domain
= isl_set_is_equal(dom
, dom2
);
5410 isl_multi_pw_aff_free(mpa1
);
5411 isl_multi_pw_aff_free(mpa2
);
5416 isl_die(ctx
, isl_error_unknown
,
5417 "expressions not equal", return -1);
5419 if (equal_domain
< 0)
5422 isl_die(ctx
, isl_error_unknown
,
5423 "domains unexpectedly equal", return -1);
5428 /* This is a regression test for a bug where isl_basic_map_simplify
5429 * would end up in an infinite loop. In particular, we construct
5430 * an empty basic set that is not obviously empty.
5431 * isl_basic_set_is_empty marks the basic set as empty.
5432 * After projecting out i3, the variable can be dropped completely,
5433 * but isl_basic_map_simplify refrains from doing so if the basic set
5434 * is empty and would end up in an infinite loop if it didn't test
5435 * explicitly for empty basic maps in the outer loop.
5437 static int test_simplify(isl_ctx
*ctx
)
5440 isl_basic_set
*bset
;
5443 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
5444 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
5445 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
5447 bset
= isl_basic_set_read_from_str(ctx
, str
);
5448 empty
= isl_basic_set_is_empty(bset
);
5449 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
5450 isl_basic_set_free(bset
);
5454 isl_die(ctx
, isl_error_unknown
,
5455 "basic set should be empty", return -1);
5460 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
5461 * with gbr context would fail to disable the use of the shifted tableau
5462 * when transferring equalities for the input to the context, resulting
5463 * in invalid sample values.
5465 static int test_partial_lexmin(isl_ctx
*ctx
)
5468 isl_basic_set
*bset
;
5469 isl_basic_map
*bmap
;
5472 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
5473 bmap
= isl_basic_map_read_from_str(ctx
, str
);
5474 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
5475 bset
= isl_basic_set_read_from_str(ctx
, str
);
5476 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
5485 /* Check that the variable compression performed on the existentially
5486 * quantified variables inside isl_basic_set_compute_divs is not confused
5487 * by the implicit equalities among the parameters.
5489 static int test_compute_divs(isl_ctx
*ctx
)
5492 isl_basic_set
*bset
;
5495 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
5496 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
5497 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
5498 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
5499 bset
= isl_basic_set_read_from_str(ctx
, str
);
5500 set
= isl_basic_set_compute_divs(bset
);
5508 /* Check that the reaching domain elements and the prefix schedule
5509 * at a leaf node are the same before and after grouping.
5511 static int test_schedule_tree_group_1(isl_ctx
*ctx
)
5516 isl_union_set
*uset
;
5517 isl_multi_union_pw_aff
*mupa
;
5518 isl_union_pw_multi_aff
*upma1
, *upma2
;
5519 isl_union_set
*domain1
, *domain2
;
5520 isl_union_map
*umap1
, *umap2
;
5521 isl_schedule_node
*node
;
5523 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10 }";
5524 uset
= isl_union_set_read_from_str(ctx
, str
);
5525 node
= isl_schedule_node_from_domain(uset
);
5526 node
= isl_schedule_node_child(node
, 0);
5527 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [9 - i] }]";
5528 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5529 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5530 node
= isl_schedule_node_child(node
, 0);
5531 str
= "[{ S1[i,j] -> [j]; S2[i,j] -> [j] }]";
5532 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5533 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5534 node
= isl_schedule_node_child(node
, 0);
5535 umap1
= isl_schedule_node_get_prefix_schedule_union_map(node
);
5536 upma1
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
5537 domain1
= isl_schedule_node_get_domain(node
);
5538 id
= isl_id_alloc(ctx
, "group", NULL
);
5539 node
= isl_schedule_node_parent(node
);
5540 node
= isl_schedule_node_group(node
, id
);
5541 node
= isl_schedule_node_child(node
, 0);
5542 umap2
= isl_schedule_node_get_prefix_schedule_union_map(node
);
5543 upma2
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
5544 domain2
= isl_schedule_node_get_domain(node
);
5545 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
5546 if (equal
>= 0 && equal
)
5547 equal
= isl_union_set_is_equal(domain1
, domain2
);
5548 if (equal
>= 0 && equal
)
5549 equal
= isl_union_map_is_equal(umap1
, umap2
);
5550 isl_union_map_free(umap1
);
5551 isl_union_map_free(umap2
);
5552 isl_union_set_free(domain1
);
5553 isl_union_set_free(domain2
);
5554 isl_union_pw_multi_aff_free(upma1
);
5555 isl_union_pw_multi_aff_free(upma2
);
5556 isl_schedule_node_free(node
);
5561 isl_die(ctx
, isl_error_unknown
,
5562 "expressions not equal", return -1);
5567 /* Check that we can have nested groupings and that the union map
5568 * schedule representation is the same before and after the grouping.
5569 * Note that after the grouping, the union map representation contains
5570 * the domain constraints from the ranges of the expansion nodes,
5571 * while they are missing from the union map representation of
5572 * the tree without expansion nodes.
5574 * Also check that the global expansion is as expected.
5576 static int test_schedule_tree_group_2(isl_ctx
*ctx
)
5578 int equal
, equal_expansion
;
5581 isl_union_set
*uset
;
5582 isl_union_map
*umap1
, *umap2
;
5583 isl_union_map
*expansion1
, *expansion2
;
5584 isl_union_set_list
*filters
;
5585 isl_multi_union_pw_aff
*mupa
;
5586 isl_schedule
*schedule
;
5587 isl_schedule_node
*node
;
5589 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10; "
5590 "S3[i,j] : 0 <= i,j < 10 }";
5591 uset
= isl_union_set_read_from_str(ctx
, str
);
5592 node
= isl_schedule_node_from_domain(uset
);
5593 node
= isl_schedule_node_child(node
, 0);
5594 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [i]; S3[i,j] -> [i] }]";
5595 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5596 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5597 node
= isl_schedule_node_child(node
, 0);
5598 str
= "{ S1[i,j] }";
5599 uset
= isl_union_set_read_from_str(ctx
, str
);
5600 filters
= isl_union_set_list_from_union_set(uset
);
5601 str
= "{ S2[i,j]; S3[i,j] }";
5602 uset
= isl_union_set_read_from_str(ctx
, str
);
5603 filters
= isl_union_set_list_add(filters
, uset
);
5604 node
= isl_schedule_node_insert_sequence(node
, filters
);
5605 node
= isl_schedule_node_child(node
, 1);
5606 node
= isl_schedule_node_child(node
, 0);
5607 str
= "{ S2[i,j] }";
5608 uset
= isl_union_set_read_from_str(ctx
, str
);
5609 filters
= isl_union_set_list_from_union_set(uset
);
5610 str
= "{ S3[i,j] }";
5611 uset
= isl_union_set_read_from_str(ctx
, str
);
5612 filters
= isl_union_set_list_add(filters
, uset
);
5613 node
= isl_schedule_node_insert_sequence(node
, filters
);
5615 schedule
= isl_schedule_node_get_schedule(node
);
5616 umap1
= isl_schedule_get_map(schedule
);
5617 uset
= isl_schedule_get_domain(schedule
);
5618 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
5619 isl_schedule_free(schedule
);
5621 node
= isl_schedule_node_parent(node
);
5622 node
= isl_schedule_node_parent(node
);
5623 id
= isl_id_alloc(ctx
, "group1", NULL
);
5624 node
= isl_schedule_node_group(node
, id
);
5625 node
= isl_schedule_node_child(node
, 1);
5626 node
= isl_schedule_node_child(node
, 0);
5627 id
= isl_id_alloc(ctx
, "group2", NULL
);
5628 node
= isl_schedule_node_group(node
, id
);
5630 schedule
= isl_schedule_node_get_schedule(node
);
5631 umap2
= isl_schedule_get_map(schedule
);
5632 isl_schedule_free(schedule
);
5634 node
= isl_schedule_node_root(node
);
5635 node
= isl_schedule_node_child(node
, 0);
5636 expansion1
= isl_schedule_node_get_subtree_expansion(node
);
5637 isl_schedule_node_free(node
);
5639 str
= "{ group1[i] -> S1[i,j] : 0 <= i,j < 10; "
5640 "group1[i] -> S2[i,j] : 0 <= i,j < 10; "
5641 "group1[i] -> S3[i,j] : 0 <= i,j < 10 }";
5643 expansion2
= isl_union_map_read_from_str(ctx
, str
);
5645 equal
= isl_union_map_is_equal(umap1
, umap2
);
5646 equal_expansion
= isl_union_map_is_equal(expansion1
, expansion2
);
5648 isl_union_map_free(umap1
);
5649 isl_union_map_free(umap2
);
5650 isl_union_map_free(expansion1
);
5651 isl_union_map_free(expansion2
);
5653 if (equal
< 0 || equal_expansion
< 0)
5656 isl_die(ctx
, isl_error_unknown
,
5657 "expressions not equal", return -1);
5658 if (!equal_expansion
)
5659 isl_die(ctx
, isl_error_unknown
,
5660 "unexpected expansion", return -1);
5665 /* Some tests for the isl_schedule_node_group function.
5667 static int test_schedule_tree_group(isl_ctx
*ctx
)
5669 if (test_schedule_tree_group_1(ctx
) < 0)
5671 if (test_schedule_tree_group_2(ctx
) < 0)
5680 { "{ rat: [i] : 0 <= i <= 10 }",
5681 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
5682 { "{ rat: [i] : FALSE }",
5683 "{ rat: coefficients[[cst] -> [a]] }" },
5685 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
5692 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
5693 "{ rat: [i] : 0 <= i <= 10 }" },
5694 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
5696 { "{ rat: coefficients[[cst] -> [a]] }",
5697 "{ rat: [i] : FALSE }" },
5700 /* Test the basic functionality of isl_basic_set_coefficients and
5701 * isl_basic_set_solutions.
5703 static int test_dual(isl_ctx
*ctx
)
5707 for (i
= 0; i
< ARRAY_SIZE(coef_tests
); ++i
) {
5709 isl_basic_set
*bset1
, *bset2
;
5711 bset1
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].set
);
5712 bset2
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].dual
);
5713 bset1
= isl_basic_set_coefficients(bset1
);
5714 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5715 isl_basic_set_free(bset1
);
5716 isl_basic_set_free(bset2
);
5720 isl_die(ctx
, isl_error_unknown
,
5721 "incorrect dual", return -1);
5724 for (i
= 0; i
< ARRAY_SIZE(sol_tests
); ++i
) {
5726 isl_basic_set
*bset1
, *bset2
;
5728 bset1
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].set
);
5729 bset2
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].dual
);
5730 bset1
= isl_basic_set_solutions(bset1
);
5731 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5732 isl_basic_set_free(bset1
);
5733 isl_basic_set_free(bset2
);
5737 isl_die(ctx
, isl_error_unknown
,
5738 "incorrect dual", return -1);
5748 const char *schedule
;
5753 { 0, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
5754 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5756 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
5757 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5759 { 1, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
5760 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5762 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
5763 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5765 { 0, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
5766 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5768 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
5769 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
5771 { 1, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
5772 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5774 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
5775 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
5779 /* Basic tiling tests. Create a schedule tree with a domain and a band node,
5780 * tile the band and then check if the tile and point bands have the
5781 * expected partial schedule.
5783 static int test_tile(isl_ctx
*ctx
)
5789 scale
= isl_options_get_tile_scale_tile_loops(ctx
);
5790 shift
= isl_options_get_tile_shift_point_loops(ctx
);
5792 for (i
= 0; i
< ARRAY_SIZE(tile_tests
); ++i
) {
5796 isl_union_set
*domain
;
5797 isl_multi_union_pw_aff
*mupa
, *mupa2
;
5798 isl_schedule_node
*node
;
5799 isl_multi_val
*sizes
;
5801 opt
= tile_tests
[i
].scale_tile
;
5802 isl_options_set_tile_scale_tile_loops(ctx
, opt
);
5803 opt
= tile_tests
[i
].shift_point
;
5804 isl_options_set_tile_shift_point_loops(ctx
, opt
);
5806 str
= tile_tests
[i
].domain
;
5807 domain
= isl_union_set_read_from_str(ctx
, str
);
5808 node
= isl_schedule_node_from_domain(domain
);
5809 node
= isl_schedule_node_child(node
, 0);
5810 str
= tile_tests
[i
].schedule
;
5811 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5812 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5813 str
= tile_tests
[i
].sizes
;
5814 sizes
= isl_multi_val_read_from_str(ctx
, str
);
5815 node
= isl_schedule_node_band_tile(node
, sizes
);
5817 str
= tile_tests
[i
].tile
;
5818 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5819 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
5820 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
, mupa2
);
5821 isl_multi_union_pw_aff_free(mupa
);
5822 isl_multi_union_pw_aff_free(mupa2
);
5824 node
= isl_schedule_node_child(node
, 0);
5826 str
= tile_tests
[i
].point
;
5827 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5828 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
5829 if (equal
>= 0 && equal
)
5830 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
,
5832 isl_multi_union_pw_aff_free(mupa
);
5833 isl_multi_union_pw_aff_free(mupa2
);
5835 isl_schedule_node_free(node
);
5840 isl_die(ctx
, isl_error_unknown
,
5841 "unexpected result", return -1);
5844 isl_options_set_tile_scale_tile_loops(ctx
, scale
);
5845 isl_options_set_tile_shift_point_loops(ctx
, shift
);
5852 int (*fn
)(isl_ctx
*ctx
);
5854 { "dual", &test_dual
},
5855 { "dependence analysis", &test_flow
},
5856 { "val", &test_val
},
5857 { "compute divs", &test_compute_divs
},
5858 { "partial lexmin", &test_partial_lexmin
},
5859 { "simplify", &test_simplify
},
5860 { "curry", &test_curry
},
5861 { "piecewise multi affine expressions", &test_pw_multi_aff
},
5862 { "multi piecewise affine expressions", &test_multi_pw_aff
},
5863 { "conversion", &test_conversion
},
5864 { "list", &test_list
},
5865 { "align parameters", &test_align_parameters
},
5866 { "preimage", &test_preimage
},
5867 { "pullback", &test_pullback
},
5868 { "AST", &test_ast
},
5869 { "AST build", &test_ast_build
},
5870 { "AST generation", &test_ast_gen
},
5871 { "eliminate", &test_eliminate
},
5872 { "residue class", &test_residue_class
},
5873 { "div", &test_div
},
5874 { "slice", &test_slice
},
5875 { "fixed power", &test_fixed_power
},
5876 { "sample", &test_sample
},
5877 { "output", &test_output
},
5878 { "vertices", &test_vertices
},
5879 { "fixed", &test_fixed
},
5880 { "equal", &test_equal
},
5881 { "disjoint", &test_disjoint
},
5882 { "product", &test_product
},
5883 { "dim_max", &test_dim_max
},
5884 { "affine", &test_aff
},
5885 { "injective", &test_injective
},
5886 { "schedule", &test_schedule
},
5887 { "schedule tree grouping", &test_schedule_tree_group
},
5888 { "tile", &test_tile
},
5889 { "union_pw", &test_union_pw
},
5890 { "parse", &test_parse
},
5891 { "single-valued", &test_sv
},
5892 { "affine hull", &test_affine_hull
},
5893 { "coalesce", &test_coalesce
},
5894 { "factorize", &test_factorize
},
5895 { "subset", &test_subset
},
5896 { "subtract", &test_subtract
},
5897 { "lexmin", &test_lexmin
},
5898 { "min", &test_min
},
5899 { "gist", &test_gist
},
5900 { "piecewise quasi-polynomials", &test_pwqp
},
5901 { "lift", &test_lift
},
5902 { "bound", &test_bound
},
5903 { "union", &test_union
},
5904 { "split periods", &test_split_periods
},
5905 { "lexicographic order", &test_lex
},
5906 { "bijectivity", &test_bijective
},
5907 { "dataflow analysis", &test_dep
},
5908 { "reading", &test_read
},
5909 { "bounded", &test_bounded
},
5910 { "construction", &test_construction
},
5911 { "dimension manipulation", &test_dim
},
5912 { "map application", &test_application
},
5913 { "convex hull", &test_convex_hull
},
5914 { "transitive closure", &test_closure
},
5917 int main(int argc
, char **argv
)
5920 struct isl_ctx
*ctx
;
5921 struct isl_options
*options
;
5923 srcdir
= getenv("srcdir");
5926 options
= isl_options_new_with_defaults();
5928 argc
= isl_options_parse(options
, argc
, argv
, ISL_ARG_ALL
);
5930 ctx
= isl_ctx_alloc_with_options(&isl_options_args
, options
);
5931 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
5932 printf("%s\n", tests
[i
].name
);
5933 if (tests
[i
].fn(ctx
) < 0)