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>
24 #include <isl_space_private.h>
27 #include <isl_constraint_private.h>
28 #include <isl/polynomial.h>
29 #include <isl/union_set.h>
30 #include <isl/union_map.h>
31 #include <isl_factorization.h>
32 #include <isl/schedule.h>
33 #include <isl/schedule_node.h>
34 #include <isl_options_private.h>
35 #include <isl/vertices.h>
36 #include <isl/ast_build.h>
39 #include <isl_ast_build_expr.h>
40 #include <isl/options.h>
42 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
46 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
49 char *pattern
= "%s/test_inputs/%s.%s";
51 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
53 filename
= isl_alloc_array(ctx
, char, length
);
58 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
63 void test_parse_map(isl_ctx
*ctx
, const char *str
)
67 map
= isl_map_read_from_str(ctx
, str
);
72 int test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
77 map
= isl_map_read_from_str(ctx
, str
);
78 map2
= isl_map_read_from_str(ctx
, str2
);
79 equal
= isl_map_is_equal(map
, map2
);
86 isl_die(ctx
, isl_error_unknown
, "maps not equal",
92 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
94 isl_pw_qpolynomial
*pwqp
;
96 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
98 isl_pw_qpolynomial_free(pwqp
);
101 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
105 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
107 isl_pw_aff_free(pwaff
);
110 /* Check that we can read an isl_multi_val from "str" without errors.
112 static int test_parse_multi_val(isl_ctx
*ctx
, const char *str
)
116 mv
= isl_multi_val_read_from_str(ctx
, str
);
117 isl_multi_val_free(mv
);
122 int test_parse(struct isl_ctx
*ctx
)
125 const char *str
, *str2
;
127 if (test_parse_multi_val(ctx
, "{ A[B[2] -> C[5, 7]] }") < 0)
129 if (test_parse_multi_val(ctx
, "[n] -> { [2] }") < 0)
131 if (test_parse_multi_val(ctx
, "{ A[4, infty, NaN, -1/2, 2/3] }") < 0)
134 str
= "{ [i] -> [-i] }";
135 map
= isl_map_read_from_str(ctx
, str
);
139 str
= "{ A[i] -> L[([i/3])] }";
140 map
= isl_map_read_from_str(ctx
, str
);
144 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
145 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
146 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
148 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
149 str2
= "{ [x, y] : 2y >= 6 - x }";
150 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
153 if (test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
154 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
156 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
157 if (test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }",
161 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
162 map
= isl_map_read_from_str(ctx
, str
);
163 str
= "{ [new, old] -> [o0, o1] : "
164 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
165 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
166 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
167 map2
= isl_map_read_from_str(ctx
, str
);
168 assert(isl_map_is_equal(map
, map2
));
172 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
173 map
= isl_map_read_from_str(ctx
, str
);
174 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
175 map2
= isl_map_read_from_str(ctx
, str
);
176 assert(isl_map_is_equal(map
, map2
));
180 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
181 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
182 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
185 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
186 str2
= "{ [i,j] -> [min(i,j)] }";
187 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
190 str
= "{ [i,j] : i != j }";
191 str2
= "{ [i,j] : i < j or i > j }";
192 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
195 str
= "{ [i,j] : (i+1)*2 >= j }";
196 str2
= "{ [i, j] : j <= 2 + 2i }";
197 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
200 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
201 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
202 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
205 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
206 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
207 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
210 str
= "{ [x] : x >= 0 }";
211 str2
= "{ [x] : x-0 >= 0 }";
212 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
215 str
= "{ [i] : ((i > 10)) }";
216 str2
= "{ [i] : i >= 11 }";
217 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
220 str
= "{ [i] -> [0] }";
221 str2
= "{ [i] -> [0 * i] }";
222 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
225 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
226 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
227 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
228 test_parse_pwqp(ctx
, "{ [x] -> ([(x)/2] * [(x)/3]) }");
230 if (test_parse_map_equal(ctx
, "{ [a] -> [b] : (not false) }",
231 "{ [a] -> [b] : true }") < 0)
234 if (test_parse_map_equal(ctx
, "{ [i] : i/2 <= 5 }",
235 "{ [i] : i <= 10 }") < 0)
238 if (test_parse_map_equal(ctx
, "{Sym=[n] [i] : i <= n }",
239 "[n] -> { [i] : i <= n }") < 0)
242 if (test_parse_map_equal(ctx
, "{ [*] }", "{ [a] }") < 0)
245 if (test_parse_map_equal(ctx
, "{ [i] : 2*floor(i/2) = i }",
246 "{ [i] : exists a : i = 2 a }") < 0)
249 if (test_parse_map_equal(ctx
, "{ [a] -> [b] : a = 5 implies b = 5 }",
250 "{ [a] -> [b] : a != 5 or b = 5 }") < 0)
253 if (test_parse_map_equal(ctx
, "{ [a] -> [a - 1 : a > 0] }",
254 "{ [a] -> [a - 1] : a > 0 }") < 0)
256 if (test_parse_map_equal(ctx
,
257 "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
258 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }") < 0)
260 if (test_parse_map_equal(ctx
,
261 "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
262 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
264 if (test_parse_map_equal(ctx
,
265 "{ [a] -> [(a * 2) : a >= 0; 0 : a < 0] }",
266 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
268 if (test_parse_map_equal(ctx
,
269 "{ [a] -> [(a * 2 : a >= 0); 0 : a < 0] }",
270 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
272 if (test_parse_map_equal(ctx
,
273 "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
274 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
280 static int test_read(isl_ctx
*ctx
)
284 isl_basic_set
*bset1
, *bset2
;
285 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
288 filename
= get_filename(ctx
, "set", "omega");
290 input
= fopen(filename
, "r");
293 bset1
= isl_basic_set_read_from_file(ctx
, input
);
294 bset2
= isl_basic_set_read_from_str(ctx
, str
);
296 equal
= isl_basic_set_is_equal(bset1
, bset2
);
298 isl_basic_set_free(bset1
);
299 isl_basic_set_free(bset2
);
307 isl_die(ctx
, isl_error_unknown
,
308 "read sets not equal", return -1);
313 static int test_bounded(isl_ctx
*ctx
)
318 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
319 bounded
= isl_set_is_bounded(set
);
325 isl_die(ctx
, isl_error_unknown
,
326 "set not considered bounded", return -1);
328 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
329 bounded
= isl_set_is_bounded(set
);
336 isl_die(ctx
, isl_error_unknown
,
337 "set considered bounded", return -1);
339 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
340 bounded
= isl_set_is_bounded(set
);
346 isl_die(ctx
, isl_error_unknown
,
347 "set considered bounded", return -1);
352 /* Construct the basic set { [i] : 5 <= i <= N } */
353 static int test_construction(isl_ctx
*ctx
)
363 dim
= isl_space_set_alloc(ctx
, 1, 1);
364 bset
= isl_basic_set_universe(isl_space_copy(dim
));
365 ls
= isl_local_space_from_space(dim
);
367 c
= isl_constraint_alloc_inequality(isl_local_space_copy(ls
));
368 isl_int_set_si(v
, -1);
369 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
370 isl_int_set_si(v
, 1);
371 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
372 bset
= isl_basic_set_add_constraint(bset
, c
);
374 c
= isl_constraint_alloc_inequality(isl_local_space_copy(ls
));
375 isl_int_set_si(v
, 1);
376 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
377 isl_int_set_si(v
, -5);
378 isl_constraint_set_constant(c
, v
);
379 bset
= isl_basic_set_add_constraint(bset
, c
);
381 isl_local_space_free(ls
);
382 isl_basic_set_free(bset
);
389 static int test_dim(isl_ctx
*ctx
)
392 isl_map
*map1
, *map2
;
395 map1
= isl_map_read_from_str(ctx
,
396 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
397 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
398 map2
= isl_map_read_from_str(ctx
,
399 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
400 equal
= isl_map_is_equal(map1
, map2
);
403 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
404 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
405 if (equal
>= 0 && equal
)
406 equal
= isl_map_is_equal(map1
, map2
);
414 isl_die(ctx
, isl_error_unknown
,
415 "unexpected result", return -1);
417 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
418 map1
= isl_map_read_from_str(ctx
, str
);
419 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
420 map2
= isl_map_read_from_str(ctx
, str
);
421 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
422 equal
= isl_map_is_equal(map1
, map2
);
429 isl_die(ctx
, isl_error_unknown
,
430 "unexpected result", return -1);
436 __isl_give isl_val
*(*op
)(__isl_take isl_val
*v
);
440 { &isl_val_neg
, "0", "0" },
441 { &isl_val_abs
, "0", "0" },
442 { &isl_val_2exp
, "0", "1" },
443 { &isl_val_floor
, "0", "0" },
444 { &isl_val_ceil
, "0", "0" },
445 { &isl_val_neg
, "1", "-1" },
446 { &isl_val_neg
, "-1", "1" },
447 { &isl_val_neg
, "1/2", "-1/2" },
448 { &isl_val_neg
, "-1/2", "1/2" },
449 { &isl_val_neg
, "infty", "-infty" },
450 { &isl_val_neg
, "-infty", "infty" },
451 { &isl_val_neg
, "NaN", "NaN" },
452 { &isl_val_abs
, "1", "1" },
453 { &isl_val_abs
, "-1", "1" },
454 { &isl_val_abs
, "1/2", "1/2" },
455 { &isl_val_abs
, "-1/2", "1/2" },
456 { &isl_val_abs
, "infty", "infty" },
457 { &isl_val_abs
, "-infty", "infty" },
458 { &isl_val_abs
, "NaN", "NaN" },
459 { &isl_val_floor
, "1", "1" },
460 { &isl_val_floor
, "-1", "-1" },
461 { &isl_val_floor
, "1/2", "0" },
462 { &isl_val_floor
, "-1/2", "-1" },
463 { &isl_val_floor
, "infty", "infty" },
464 { &isl_val_floor
, "-infty", "-infty" },
465 { &isl_val_floor
, "NaN", "NaN" },
466 { &isl_val_ceil
, "1", "1" },
467 { &isl_val_ceil
, "-1", "-1" },
468 { &isl_val_ceil
, "1/2", "1" },
469 { &isl_val_ceil
, "-1/2", "0" },
470 { &isl_val_ceil
, "infty", "infty" },
471 { &isl_val_ceil
, "-infty", "-infty" },
472 { &isl_val_ceil
, "NaN", "NaN" },
473 { &isl_val_2exp
, "-3", "1/8" },
474 { &isl_val_2exp
, "-1", "1/2" },
475 { &isl_val_2exp
, "1", "2" },
476 { &isl_val_2exp
, "2", "4" },
477 { &isl_val_2exp
, "3", "8" },
478 { &isl_val_inv
, "1", "1" },
479 { &isl_val_inv
, "2", "1/2" },
480 { &isl_val_inv
, "1/2", "2" },
481 { &isl_val_inv
, "-2", "-1/2" },
482 { &isl_val_inv
, "-1/2", "-2" },
483 { &isl_val_inv
, "0", "NaN" },
484 { &isl_val_inv
, "NaN", "NaN" },
485 { &isl_val_inv
, "infty", "0" },
486 { &isl_val_inv
, "-infty", "0" },
489 /* Perform some basic tests of unary operations on isl_val objects.
491 static int test_un_val(isl_ctx
*ctx
)
495 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v
);
498 for (i
= 0; i
< ARRAY_SIZE(val_un_tests
); ++i
) {
499 v
= isl_val_read_from_str(ctx
, val_un_tests
[i
].arg
);
500 res
= isl_val_read_from_str(ctx
, val_un_tests
[i
].res
);
501 fn
= val_un_tests
[i
].op
;
503 if (isl_val_is_nan(res
))
504 ok
= isl_val_is_nan(v
);
506 ok
= isl_val_eq(v
, res
);
512 isl_die(ctx
, isl_error_unknown
,
513 "unexpected result", return -1);
520 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
521 __isl_take isl_val
*v2
);
523 ['+'] = { &isl_val_add
},
524 ['-'] = { &isl_val_sub
},
525 ['*'] = { &isl_val_mul
},
526 ['/'] = { &isl_val_div
},
527 ['g'] = { &isl_val_gcd
},
528 ['m'] = { &isl_val_min
},
529 ['M'] = { &isl_val_max
},
537 } val_bin_tests
[] = {
538 { "0", '+', "0", "0" },
539 { "1", '+', "0", "1" },
540 { "1", '+', "1", "2" },
541 { "1", '-', "1", "0" },
542 { "1", '*', "1", "1" },
543 { "1", '/', "1", "1" },
544 { "2", '*', "3", "6" },
545 { "2", '*', "1/2", "1" },
546 { "2", '*', "1/3", "2/3" },
547 { "2/3", '*', "3/5", "2/5" },
548 { "2/3", '*', "7/5", "14/15" },
549 { "2", '/', "1/2", "4" },
550 { "-2", '/', "-1/2", "4" },
551 { "-2", '/', "1/2", "-4" },
552 { "2", '/', "-1/2", "-4" },
553 { "2", '/', "2", "1" },
554 { "2", '/', "3", "2/3" },
555 { "2/3", '/', "5/3", "2/5" },
556 { "2/3", '/', "5/7", "14/15" },
557 { "0", '/', "0", "NaN" },
558 { "42", '/', "0", "NaN" },
559 { "-42", '/', "0", "NaN" },
560 { "infty", '/', "0", "NaN" },
561 { "-infty", '/', "0", "NaN" },
562 { "NaN", '/', "0", "NaN" },
563 { "0", '/', "NaN", "NaN" },
564 { "42", '/', "NaN", "NaN" },
565 { "-42", '/', "NaN", "NaN" },
566 { "infty", '/', "NaN", "NaN" },
567 { "-infty", '/', "NaN", "NaN" },
568 { "NaN", '/', "NaN", "NaN" },
569 { "0", '/', "infty", "0" },
570 { "42", '/', "infty", "0" },
571 { "-42", '/', "infty", "0" },
572 { "infty", '/', "infty", "NaN" },
573 { "-infty", '/', "infty", "NaN" },
574 { "NaN", '/', "infty", "NaN" },
575 { "0", '/', "-infty", "0" },
576 { "42", '/', "-infty", "0" },
577 { "-42", '/', "-infty", "0" },
578 { "infty", '/', "-infty", "NaN" },
579 { "-infty", '/', "-infty", "NaN" },
580 { "NaN", '/', "-infty", "NaN" },
581 { "1", '-', "1/3", "2/3" },
582 { "1/3", '+', "1/2", "5/6" },
583 { "1/2", '+', "1/2", "1" },
584 { "3/4", '-', "1/4", "1/2" },
585 { "1/2", '-', "1/3", "1/6" },
586 { "infty", '+', "42", "infty" },
587 { "infty", '+', "infty", "infty" },
588 { "42", '+', "infty", "infty" },
589 { "infty", '-', "infty", "NaN" },
590 { "infty", '*', "infty", "infty" },
591 { "infty", '*', "-infty", "-infty" },
592 { "-infty", '*', "infty", "-infty" },
593 { "-infty", '*', "-infty", "infty" },
594 { "0", '*', "infty", "NaN" },
595 { "1", '*', "infty", "infty" },
596 { "infty", '*', "0", "NaN" },
597 { "infty", '*', "42", "infty" },
598 { "42", '-', "infty", "-infty" },
599 { "infty", '+', "-infty", "NaN" },
600 { "4", 'g', "6", "2" },
601 { "5", 'g', "6", "1" },
602 { "42", 'm', "3", "3" },
603 { "42", 'M', "3", "42" },
604 { "3", 'm', "42", "3" },
605 { "3", 'M', "42", "42" },
606 { "42", 'm', "infty", "42" },
607 { "42", 'M', "infty", "infty" },
608 { "42", 'm', "-infty", "-infty" },
609 { "42", 'M', "-infty", "42" },
610 { "42", 'm', "NaN", "NaN" },
611 { "42", 'M', "NaN", "NaN" },
612 { "infty", 'm', "-infty", "-infty" },
613 { "infty", 'M', "-infty", "infty" },
616 /* Perform some basic tests of binary operations on isl_val objects.
618 static int test_bin_val(isl_ctx
*ctx
)
621 isl_val
*v1
, *v2
, *res
;
622 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
623 __isl_take isl_val
*v2
);
626 for (i
= 0; i
< ARRAY_SIZE(val_bin_tests
); ++i
) {
627 v1
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg1
);
628 v2
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg2
);
629 res
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].res
);
630 fn
= val_bin_op
[val_bin_tests
[i
].op
].fn
;
632 if (isl_val_is_nan(res
))
633 ok
= isl_val_is_nan(v1
);
635 ok
= isl_val_eq(v1
, res
);
641 isl_die(ctx
, isl_error_unknown
,
642 "unexpected result", return -1);
648 /* Perform some basic tests on isl_val objects.
650 static int test_val(isl_ctx
*ctx
)
652 if (test_un_val(ctx
) < 0)
654 if (test_bin_val(ctx
) < 0)
659 static int test_div(isl_ctx
*ctx
)
668 struct isl_basic_set
*bset
;
669 struct isl_constraint
*c
;
674 dim
= isl_space_set_alloc(ctx
, 0, 3);
675 bset
= isl_basic_set_universe(isl_space_copy(dim
));
676 ls
= isl_local_space_from_space(dim
);
678 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
679 isl_int_set_si(v
, -1);
680 isl_constraint_set_constant(c
, v
);
681 isl_int_set_si(v
, 1);
682 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
683 isl_int_set_si(v
, 3);
684 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
685 bset
= isl_basic_set_add_constraint(bset
, c
);
687 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
688 isl_int_set_si(v
, 1);
689 isl_constraint_set_constant(c
, v
);
690 isl_int_set_si(v
, -1);
691 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
692 isl_int_set_si(v
, 3);
693 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
694 bset
= isl_basic_set_add_constraint(bset
, c
);
696 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
698 assert(bset
&& bset
->n_div
== 1);
699 isl_local_space_free(ls
);
700 isl_basic_set_free(bset
);
703 dim
= isl_space_set_alloc(ctx
, 0, 3);
704 bset
= isl_basic_set_universe(isl_space_copy(dim
));
705 ls
= isl_local_space_from_space(dim
);
707 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
708 isl_int_set_si(v
, 1);
709 isl_constraint_set_constant(c
, v
);
710 isl_int_set_si(v
, -1);
711 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
712 isl_int_set_si(v
, 3);
713 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
714 bset
= isl_basic_set_add_constraint(bset
, c
);
716 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
717 isl_int_set_si(v
, -1);
718 isl_constraint_set_constant(c
, v
);
719 isl_int_set_si(v
, 1);
720 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
721 isl_int_set_si(v
, 3);
722 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
723 bset
= isl_basic_set_add_constraint(bset
, c
);
725 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
727 assert(bset
&& bset
->n_div
== 1);
728 isl_local_space_free(ls
);
729 isl_basic_set_free(bset
);
732 dim
= isl_space_set_alloc(ctx
, 0, 3);
733 bset
= isl_basic_set_universe(isl_space_copy(dim
));
734 ls
= isl_local_space_from_space(dim
);
736 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
737 isl_int_set_si(v
, 1);
738 isl_constraint_set_constant(c
, v
);
739 isl_int_set_si(v
, -1);
740 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
741 isl_int_set_si(v
, 3);
742 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
743 bset
= isl_basic_set_add_constraint(bset
, c
);
745 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
746 isl_int_set_si(v
, -3);
747 isl_constraint_set_constant(c
, v
);
748 isl_int_set_si(v
, 1);
749 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
750 isl_int_set_si(v
, 4);
751 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
752 bset
= isl_basic_set_add_constraint(bset
, c
);
754 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
756 assert(bset
&& bset
->n_div
== 1);
757 isl_local_space_free(ls
);
758 isl_basic_set_free(bset
);
761 dim
= isl_space_set_alloc(ctx
, 0, 3);
762 bset
= isl_basic_set_universe(isl_space_copy(dim
));
763 ls
= isl_local_space_from_space(dim
);
765 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
766 isl_int_set_si(v
, 2);
767 isl_constraint_set_constant(c
, v
);
768 isl_int_set_si(v
, -1);
769 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
770 isl_int_set_si(v
, 3);
771 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
772 bset
= isl_basic_set_add_constraint(bset
, c
);
774 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
775 isl_int_set_si(v
, -1);
776 isl_constraint_set_constant(c
, v
);
777 isl_int_set_si(v
, 1);
778 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
779 isl_int_set_si(v
, 6);
780 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
781 bset
= isl_basic_set_add_constraint(bset
, c
);
783 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
785 assert(isl_basic_set_is_empty(bset
));
786 isl_local_space_free(ls
);
787 isl_basic_set_free(bset
);
790 dim
= isl_space_set_alloc(ctx
, 0, 3);
791 bset
= isl_basic_set_universe(isl_space_copy(dim
));
792 ls
= isl_local_space_from_space(dim
);
794 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
795 isl_int_set_si(v
, -1);
796 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
797 isl_int_set_si(v
, 3);
798 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
799 bset
= isl_basic_set_add_constraint(bset
, c
);
801 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
802 isl_int_set_si(v
, 1);
803 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
804 isl_int_set_si(v
, -3);
805 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
806 bset
= isl_basic_set_add_constraint(bset
, c
);
808 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
810 assert(bset
&& bset
->n_div
== 0);
811 isl_basic_set_free(bset
);
812 isl_local_space_free(ls
);
815 dim
= isl_space_set_alloc(ctx
, 0, 3);
816 bset
= isl_basic_set_universe(isl_space_copy(dim
));
817 ls
= isl_local_space_from_space(dim
);
819 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
820 isl_int_set_si(v
, -1);
821 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
822 isl_int_set_si(v
, 6);
823 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
824 bset
= isl_basic_set_add_constraint(bset
, c
);
826 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
827 isl_int_set_si(v
, 1);
828 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
829 isl_int_set_si(v
, -3);
830 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
831 bset
= isl_basic_set_add_constraint(bset
, c
);
833 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
835 assert(bset
&& bset
->n_div
== 1);
836 isl_basic_set_free(bset
);
837 isl_local_space_free(ls
);
840 /* This test is a bit tricky. We set up an equality
842 * Normalization of divs creates _two_ divs
845 * Afterwards e0 is removed again because it has coefficient -1
846 * and we end up with the original equality and div again.
847 * Perhaps we can avoid the introduction of this temporary div.
849 dim
= isl_space_set_alloc(ctx
, 0, 4);
850 bset
= isl_basic_set_universe(isl_space_copy(dim
));
851 ls
= isl_local_space_from_space(dim
);
853 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
854 isl_int_set_si(v
, -1);
855 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
856 isl_int_set_si(v
, -3);
857 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
858 isl_int_set_si(v
, -3);
859 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
860 isl_int_set_si(v
, 6);
861 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
862 bset
= isl_basic_set_add_constraint(bset
, c
);
864 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
866 /* Test disabled for now */
868 assert(bset && bset->n_div == 1);
870 isl_local_space_free(ls
);
871 isl_basic_set_free(bset
);
874 dim
= isl_space_set_alloc(ctx
, 0, 5);
875 bset
= isl_basic_set_universe(isl_space_copy(dim
));
876 ls
= isl_local_space_from_space(dim
);
878 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
879 isl_int_set_si(v
, -1);
880 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
881 isl_int_set_si(v
, -3);
882 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
883 isl_int_set_si(v
, -3);
884 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
885 isl_int_set_si(v
, 6);
886 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
887 bset
= isl_basic_set_add_constraint(bset
, c
);
889 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
890 isl_int_set_si(v
, -1);
891 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
892 isl_int_set_si(v
, 1);
893 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
894 isl_int_set_si(v
, 1);
895 isl_constraint_set_constant(c
, v
);
896 bset
= isl_basic_set_add_constraint(bset
, c
);
898 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
900 /* Test disabled for now */
902 assert(bset && bset->n_div == 1);
904 isl_local_space_free(ls
);
905 isl_basic_set_free(bset
);
908 dim
= isl_space_set_alloc(ctx
, 0, 4);
909 bset
= isl_basic_set_universe(isl_space_copy(dim
));
910 ls
= isl_local_space_from_space(dim
);
912 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
913 isl_int_set_si(v
, 1);
914 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
915 isl_int_set_si(v
, -1);
916 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
917 isl_int_set_si(v
, -2);
918 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
919 bset
= isl_basic_set_add_constraint(bset
, c
);
921 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
922 isl_int_set_si(v
, -1);
923 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
924 isl_int_set_si(v
, 3);
925 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
926 isl_int_set_si(v
, 2);
927 isl_constraint_set_constant(c
, v
);
928 bset
= isl_basic_set_add_constraint(bset
, c
);
930 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
932 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
934 assert(!isl_basic_set_is_empty(bset
));
936 isl_local_space_free(ls
);
937 isl_basic_set_free(bset
);
940 dim
= isl_space_set_alloc(ctx
, 0, 3);
941 bset
= isl_basic_set_universe(isl_space_copy(dim
));
942 ls
= isl_local_space_from_space(dim
);
944 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
945 isl_int_set_si(v
, 1);
946 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
947 isl_int_set_si(v
, -2);
948 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
949 bset
= isl_basic_set_add_constraint(bset
, c
);
951 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
953 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
955 isl_local_space_free(ls
);
956 isl_basic_set_free(bset
);
960 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
961 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
962 set
= isl_set_read_from_str(ctx
, str
);
963 set
= isl_set_compute_divs(set
);
968 str
= "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
969 bset
= isl_basic_set_read_from_str(ctx
, str
);
970 n
= isl_basic_set_dim(bset
, isl_dim_div
);
971 isl_basic_set_free(bset
);
975 isl_die(ctx
, isl_error_unknown
,
976 "expecting no existentials", return -1);
978 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
979 set
= isl_set_read_from_str(ctx
, str
);
980 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
981 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
982 empty
= isl_set_is_empty(set
);
987 isl_die(ctx
, isl_error_unknown
,
988 "result not as accurate as expected", return -1);
993 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
997 struct isl_basic_set
*bset1
, *bset2
;
998 struct isl_basic_map
*bmap
;
1000 filename
= get_filename(ctx
, name
, "omega");
1002 input
= fopen(filename
, "r");
1005 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1006 bmap
= isl_basic_map_read_from_file(ctx
, input
);
1008 bset1
= isl_basic_set_apply(bset1
, bmap
);
1010 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1012 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1014 isl_basic_set_free(bset1
);
1015 isl_basic_set_free(bset2
);
1021 static int test_application(isl_ctx
*ctx
)
1023 test_application_case(ctx
, "application");
1024 test_application_case(ctx
, "application2");
1029 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
1033 struct isl_basic_set
*bset1
, *bset2
;
1035 filename
= get_filename(ctx
, name
, "polylib");
1037 input
= fopen(filename
, "r");
1040 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1041 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1043 bset1
= isl_basic_set_affine_hull(bset1
);
1045 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1047 isl_basic_set_free(bset1
);
1048 isl_basic_set_free(bset2
);
1054 int test_affine_hull(struct isl_ctx
*ctx
)
1058 isl_basic_set
*bset
, *bset2
;
1062 test_affine_hull_case(ctx
, "affine2");
1063 test_affine_hull_case(ctx
, "affine");
1064 test_affine_hull_case(ctx
, "affine3");
1066 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
1067 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
1068 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
1069 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
1070 set
= isl_set_read_from_str(ctx
, str
);
1071 bset
= isl_set_affine_hull(set
);
1072 n
= isl_basic_set_dim(bset
, isl_dim_div
);
1073 isl_basic_set_free(bset
);
1075 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
1078 /* Check that isl_map_affine_hull is not confused by
1079 * the reordering of divs in isl_map_align_divs.
1081 str
= "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1082 "32e0 = b and 32e1 = c); "
1083 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1084 set
= isl_set_read_from_str(ctx
, str
);
1085 bset
= isl_set_affine_hull(set
);
1086 isl_basic_set_free(bset
);
1090 str
= "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1091 "32e2 = 31 + 31e0 }";
1092 set
= isl_set_read_from_str(ctx
, str
);
1093 bset
= isl_set_affine_hull(set
);
1094 str
= "{ [a] : exists e : a = 32 e }";
1095 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1096 subset
= isl_basic_set_is_subset(bset
, bset2
);
1097 isl_basic_set_free(bset
);
1098 isl_basic_set_free(bset2
);
1102 isl_die(ctx
, isl_error_unknown
, "not as accurate as expected",
1108 static int test_simple_hull(struct isl_ctx
*ctx
)
1112 isl_basic_set
*bset
;
1115 str
= "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x;"
1116 "[y, x] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }";
1117 set
= isl_set_read_from_str(ctx
, str
);
1118 bset
= isl_set_simple_hull(set
);
1119 is_empty
= isl_basic_set_is_empty(bset
);
1120 isl_basic_set_free(bset
);
1122 if (is_empty
== isl_bool_error
)
1125 if (is_empty
== isl_bool_false
)
1126 isl_die(ctx
, isl_error_unknown
, "Empty set should be detected",
1132 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
1136 struct isl_basic_set
*bset1
, *bset2
;
1137 struct isl_set
*set
;
1139 filename
= get_filename(ctx
, name
, "polylib");
1141 input
= fopen(filename
, "r");
1144 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1145 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1147 set
= isl_basic_set_union(bset1
, bset2
);
1148 bset1
= isl_set_convex_hull(set
);
1150 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1152 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1154 isl_basic_set_free(bset1
);
1155 isl_basic_set_free(bset2
);
1164 } convex_hull_tests
[] = {
1165 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1166 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1167 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1168 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1169 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1170 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1171 "i2 <= 5 and i2 >= 4; "
1172 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1173 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1174 "i2 <= 5 + i0 and i2 >= i0 }" },
1175 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1176 "{ [x, y] : 1 = 0 }" },
1179 static int test_convex_hull_algo(isl_ctx
*ctx
, int convex
)
1182 int orig_convex
= ctx
->opt
->convex
;
1183 ctx
->opt
->convex
= convex
;
1185 test_convex_hull_case(ctx
, "convex0");
1186 test_convex_hull_case(ctx
, "convex1");
1187 test_convex_hull_case(ctx
, "convex2");
1188 test_convex_hull_case(ctx
, "convex3");
1189 test_convex_hull_case(ctx
, "convex4");
1190 test_convex_hull_case(ctx
, "convex5");
1191 test_convex_hull_case(ctx
, "convex6");
1192 test_convex_hull_case(ctx
, "convex7");
1193 test_convex_hull_case(ctx
, "convex8");
1194 test_convex_hull_case(ctx
, "convex9");
1195 test_convex_hull_case(ctx
, "convex10");
1196 test_convex_hull_case(ctx
, "convex11");
1197 test_convex_hull_case(ctx
, "convex12");
1198 test_convex_hull_case(ctx
, "convex13");
1199 test_convex_hull_case(ctx
, "convex14");
1200 test_convex_hull_case(ctx
, "convex15");
1202 for (i
= 0; i
< ARRAY_SIZE(convex_hull_tests
); ++i
) {
1203 isl_set
*set1
, *set2
;
1206 set1
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].set
);
1207 set2
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].hull
);
1208 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
1209 equal
= isl_set_is_equal(set1
, set2
);
1216 isl_die(ctx
, isl_error_unknown
,
1217 "unexpected convex hull", return -1);
1220 ctx
->opt
->convex
= orig_convex
;
1225 static int test_convex_hull(isl_ctx
*ctx
)
1227 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
) < 0)
1229 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
) < 0)
1234 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
1238 struct isl_basic_set
*bset1
, *bset2
;
1240 filename
= get_filename(ctx
, name
, "polylib");
1242 input
= fopen(filename
, "r");
1245 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1246 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1248 bset1
= isl_basic_set_gist(bset1
, bset2
);
1250 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1252 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1254 isl_basic_set_free(bset1
);
1255 isl_basic_set_free(bset2
);
1263 const char *context
;
1266 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1267 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1268 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1269 "{ [a, b, c] : a <= 15 }" },
1270 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1271 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1272 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1273 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1274 { "{ [m, n, a, b] : a <= 2147 + n }",
1275 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1276 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1277 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1279 "{ [m, n, ku, kl] }" },
1280 { "{ [a, a, b] : a >= 10 }",
1281 "{ [a, b, c] : c >= a and c <= b and c >= 2 }",
1282 "{ [a, a, b] : a >= 10 }" },
1283 { "{ [i, j] : i >= 0 and i + j >= 0 }", "{ [i, j] : i <= 0 }",
1284 "{ [0, j] : j >= 0 }" },
1285 /* Check that no constraints on i6 are introduced in the gist */
1286 { "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1287 "20e0 <= 1530 - 4t1 - 5i4 and 20e0 >= 1511 - 4t1 - 5i4 and "
1288 "5e0 <= 381 - t1 and i4 <= 1) }",
1289 "[t1] -> { [i4, i6] : exists (e0 = floor((-t1 + i6)/5): "
1290 "5e0 = -t1 + i6 and i6 <= 6 and i6 >= 3) }",
1291 "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1292 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 <= 1530 - 4t1 - 5i4 and "
1293 "20e0 >= 1511 - 4t1 - 5i4) }" },
1296 static int test_gist(struct isl_ctx
*ctx
)
1300 isl_basic_set
*bset1
, *bset2
;
1301 isl_map
*map1
, *map2
;
1304 for (i
= 0; i
< ARRAY_SIZE(gist_tests
); ++i
) {
1306 isl_set
*set1
, *set2
, *copy
;
1308 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1309 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].context
);
1310 copy
= isl_set_copy(set1
);
1311 set1
= isl_set_gist(set1
, set2
);
1312 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].gist
);
1313 equal
= isl_set_is_equal(set1
, set2
);
1316 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1317 equal_input
= isl_set_is_equal(set1
, copy
);
1320 if (equal
< 0 || equal_input
< 0)
1323 isl_die(ctx
, isl_error_unknown
,
1324 "incorrect gist result", return -1);
1326 isl_die(ctx
, isl_error_unknown
,
1327 "gist modified input", return -1);
1330 test_gist_case(ctx
, "gist1");
1332 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1333 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1334 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1335 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1336 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1337 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1338 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1339 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1340 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1341 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1342 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1343 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1344 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1345 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1346 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1347 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1348 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1349 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1350 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1351 bset1
= isl_basic_set_gist(bset1
, bset2
);
1352 assert(bset1
&& bset1
->n_div
== 0);
1353 isl_basic_set_free(bset1
);
1355 /* Check that the integer divisions of the second disjunct
1356 * do not spread to the first disjunct.
1358 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1359 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1360 "(exists (e0 = [(-1 + t1)/16], "
1361 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1362 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1363 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1364 "o0 <= 4294967295 and t1 <= -1)) }";
1365 map1
= isl_map_read_from_str(ctx
, str
);
1366 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1367 map2
= isl_map_read_from_str(ctx
, str
);
1368 map1
= isl_map_gist(map1
, map2
);
1372 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1373 isl_map_free(map1
); return -1);
1374 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1375 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1376 isl_map_free(map1
); return -1);
1382 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1384 isl_set
*set
, *set2
;
1388 set
= isl_set_read_from_str(ctx
, str
);
1389 set
= isl_set_coalesce(set
);
1390 set2
= isl_set_read_from_str(ctx
, str
);
1391 equal
= isl_set_is_equal(set
, set2
);
1392 one
= set
&& set
->n
== 1;
1399 isl_die(ctx
, isl_error_unknown
,
1400 "coalesced set not equal to input", return -1);
1401 if (check_one
&& !one
)
1402 isl_die(ctx
, isl_error_unknown
,
1403 "coalesced set should not be a union", return -1);
1408 /* Inputs for coalescing tests with unbounded wrapping.
1409 * "str" is a string representation of the input set.
1410 * "single_disjunct" is set if we expect the result to consist of
1411 * a single disjunct.
1414 int single_disjunct
;
1416 } coalesce_unbounded_tests
[] = {
1417 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1418 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1419 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1420 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1422 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1423 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1424 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1425 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1428 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1429 * option turned off.
1431 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1437 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1438 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1440 for (i
= 0; i
< ARRAY_SIZE(coalesce_unbounded_tests
); ++i
) {
1441 const char *str
= coalesce_unbounded_tests
[i
].str
;
1442 int check_one
= coalesce_unbounded_tests
[i
].single_disjunct
;
1443 if (test_coalesce_set(ctx
, str
, check_one
) >= 0)
1449 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1454 /* Inputs for coalescing tests.
1455 * "str" is a string representation of the input set.
1456 * "single_disjunct" is set if we expect the result to consist of
1457 * a single disjunct.
1460 int single_disjunct
;
1462 } coalesce_tests
[] = {
1463 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1464 "y >= x & x >= 2 & 5 >= y }" },
1465 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1466 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1467 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1468 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1469 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1470 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1471 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1472 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1473 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1474 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1475 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1476 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1477 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1478 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1479 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1480 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1481 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1482 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1483 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1484 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1485 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1486 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1487 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1488 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1489 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1490 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1491 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1492 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1493 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1494 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1495 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1496 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1497 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1498 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1499 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1500 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1501 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1502 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1503 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1504 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1505 "[o0, o1, o2, o3, o4, o5, o6]] : "
1506 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1507 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1508 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1509 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1510 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1511 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1512 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1513 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1514 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1515 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1516 "o6 >= i3 + i6 - o3 and M >= 0 and "
1517 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1518 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1519 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1520 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1521 "(o0 = 0 and M >= 2 and N >= 3) or "
1522 "(M = 0 and o0 = 0 and N >= 3) }" },
1523 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1524 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1525 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1526 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1527 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1528 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1529 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1530 "(y = 3 and x = 1) }" },
1531 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1532 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1533 "i1 <= M and i3 <= M and i4 <= M) or "
1534 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1535 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1536 "i4 <= -1 + M) }" },
1537 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1538 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1539 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1540 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1541 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1542 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1543 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1544 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1545 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1546 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1547 { 0, "{ [a, b] : exists e : 2e = a and "
1548 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1549 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1550 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1551 "j >= 1 and j' <= i + j - i' and i >= 1; "
1553 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1554 "[i,j] : exists a : j = 3a }" },
1555 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1556 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1558 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1559 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1560 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1561 "c <= 6 + 8a and a >= 3; "
1562 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1563 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1564 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1565 "[x,0] : 3 <= x <= 4 }" },
1566 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1567 "[x,0] : 4 <= x <= 5 }" },
1568 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1569 "[x,0] : 3 <= x <= 5 }" },
1570 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1571 "[x,0] : 3 <= x <= 4 }" },
1572 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1574 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1575 { 1, "{ [0,0]; [1,1] }" },
1576 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1577 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1579 "[k, 0, k] : k <= 6 and k >= 1 }" },
1580 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1581 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1582 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1583 { 1, "[n] -> { [1] : n >= 0;"
1584 "[x] : exists (e0 = floor((x)/2): x >= 2 and "
1585 "2e0 >= -1 + x and 2e0 <= x and 2e0 <= n) }" },
1586 { 1, "[n] -> { [x, y] : exists (e0 = floor((x)/2), e1 = floor((y)/3): "
1587 "3e1 = y and x >= 2 and 2e0 >= -1 + x and "
1588 "2e0 <= x and 2e0 <= n);"
1589 "[1, y] : exists (e0 = floor((y)/3): 3e0 = y and "
1591 { 1, "[t1] -> { [i0] : (exists (e0 = floor((63t1)/64): "
1592 "128e0 >= -134 + 127t1 and t1 >= 2 and "
1593 "64e0 <= 63t1 and 64e0 >= -63 + 63t1)) or "
1595 { 1, "{ [i, i] : exists (e0 = floor((1 + 2i)/3): 3e0 <= 2i and "
1596 "3e0 >= -1 + 2i and i <= 9 and i >= 1);"
1598 { 1, "{ [t1] : exists (e0 = floor((-11 + t1)/2): 2e0 = -11 + t1 and "
1599 "t1 >= 13 and t1 <= 16);"
1600 "[t1] : t1 <= 15 and t1 >= 12 }" },
1601 { 1, "{ [x,y] : x = 3y and 0 <= y <= 2; [-3,-1] }" },
1602 { 1, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-2] }" },
1603 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-2,-2] }" },
1604 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-1] }" },
1605 { 1, "{ [i] : exists j : i = 4 j and 0 <= i <= 100;"
1606 "[i] : exists j : 1 <= i <= 100 and i >= 4j + 1 and "
1608 { 1, "{ [c0] : (exists (e0 : c0 - 1 <= 3e0 <= c0)) or "
1609 "(exists (e0 : 3e0 = -2 + c0)) }" },
1610 { 0, "[n, b0, t0] -> "
1611 "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1612 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1613 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1614 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1615 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 >= 8 + n and "
1616 "3i4 <= -96 + 3t0 + i0 and 3i4 >= -95 - n + 3t0 + i0 and "
1617 "i8 >= -157 + i0 - 4i4 and i8 >= 0 and "
1618 "i8 <= -33 + i0 - 4i4 and 3i8 <= -91 + 4n - i0)) or "
1619 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1620 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1621 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1622 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 <= 7 + n and "
1623 "4i4 <= -3 + i0 and 3i4 <= -96 + 3t0 + i0 and "
1624 "3i4 >= -95 - n + 3t0 + i0 and i8 >= -157 + i0 - 4i4 and "
1625 "i8 >= 0 and i8 <= -4 + i0 - 3i4 and i8 <= -41 + i0));"
1626 "[i0, i1, i2, i3, 0, i5, i6, i7, i8, i9, i10, i11, i12] : "
1627 "(exists (e0 = floor((i8)/32): b0 = 0 and 32e0 = i8 and "
1628 "n <= 2147483647 and t0 <= 31 and t0 >= 0 and i0 >= 11 and "
1629 "i0 >= 96 - 3t0 and i0 <= 95 + n - 3t0 and i0 <= 7 + n and "
1630 "i8 >= -40 + i0 and i8 <= -10 + i0)) }" },
1631 { 0, "{ [i0, i1, i2] : "
1632 "(exists (e0, e1 = floor((i0)/32), e2 = floor((i1)/32): "
1633 "32e1 = i0 and 32e2 = i1 and i1 >= -31 + i0 and "
1634 "i1 <= 31 + i0 and i2 >= -30 + i0 and i2 >= -30 + i1 and "
1635 "32e0 >= -30 + i0 and 32e0 >= -30 + i1 and "
1636 "32e0 >= -31 + i2 and 32e0 <= 30 + i2 and 32e0 <= 31 + i1 and "
1637 "32e0 <= 31 + i0)) or "
1639 { 1, "{ [a, b, c] : 2b = 1 + a and 2c = 2 + a; [0, 0, 0] }" },
1642 /* A specialized coalescing test case that would result
1643 * in a segmentation fault or a failed assertion in earlier versions of isl.
1645 static int test_coalesce_special(struct isl_ctx
*ctx
)
1648 isl_map
*map1
, *map2
;
1650 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1651 "[[S_L309_IN[] -> T11[]] -> ce_imag2[1, o1]] : "
1652 "(y = 201 and o1 <= 239 and o1 >= 212) or "
1653 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 198 and y >= 3 and "
1654 "o1 <= 239 and o1 >= 212)) or "
1655 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 201 and y >= 3 and "
1656 "o1 <= 241 and o1 >= 240));"
1657 "[S_L220_OUT[] -> T7[]] -> "
1658 "[[S_L309_IN[] -> T11[]] -> ce_imag2[0, o1]] : "
1659 "(y = 2 and o1 <= 241 and o1 >= 212) or "
1660 "(exists (e0 = [(-2 + y)/3]: 3e0 = -2 + y and y <= 200 and "
1661 "y >= 5 and o1 <= 241 and o1 >= 212)) }";
1662 map1
= isl_map_read_from_str(ctx
, str
);
1663 map1
= isl_map_align_divs(map1
);
1664 map1
= isl_map_coalesce(map1
);
1665 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1666 "[[S_L309_IN[] -> T11[]] -> ce_imag2[o0, o1]] : "
1667 "exists (e0 = [(-1 - y + o0)/3]: 3e0 = -1 - y + o0 and "
1668 "y <= 201 and o0 <= 2 and o1 >= 212 and o1 <= 241 and "
1669 "o0 >= 3 - y and o0 <= -2 + y and o0 >= 0) }";
1670 map2
= isl_map_read_from_str(ctx
, str
);
1671 map2
= isl_map_union(map2
, map1
);
1672 map2
= isl_map_align_divs(map2
);
1673 map2
= isl_map_coalesce(map2
);
1681 /* Test the functionality of isl_set_coalesce.
1682 * That is, check that the output is always equal to the input
1683 * and in some cases that the result consists of a single disjunct.
1685 static int test_coalesce(struct isl_ctx
*ctx
)
1689 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
1690 const char *str
= coalesce_tests
[i
].str
;
1691 int check_one
= coalesce_tests
[i
].single_disjunct
;
1692 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
1696 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1698 if (test_coalesce_special(ctx
) < 0)
1704 static int test_closure(isl_ctx
*ctx
)
1708 isl_map
*up
, *right
;
1709 isl_map
*map
, *map2
;
1712 /* COCOA example 1 */
1713 map
= isl_map_read_from_str(ctx
,
1714 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1715 "1 <= i and i < n and 1 <= j and j < n or "
1716 "i2 = i + 1 and j2 = j - 1 and "
1717 "1 <= i and i < n and 2 <= j and j <= n }");
1718 map
= isl_map_power(map
, &exact
);
1722 /* COCOA example 1 */
1723 map
= isl_map_read_from_str(ctx
,
1724 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1725 "1 <= i and i < n and 1 <= j and j < n or "
1726 "i2 = i + 1 and j2 = j - 1 and "
1727 "1 <= i and i < n and 2 <= j and j <= n }");
1728 map
= isl_map_transitive_closure(map
, &exact
);
1730 map2
= isl_map_read_from_str(ctx
,
1731 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1732 "1 <= i and i < n and 1 <= j and j <= n and "
1733 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1734 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1735 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1736 assert(isl_map_is_equal(map
, map2
));
1740 map
= isl_map_read_from_str(ctx
,
1741 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1742 " 0 <= y and y <= n }");
1743 map
= isl_map_transitive_closure(map
, &exact
);
1744 map2
= isl_map_read_from_str(ctx
,
1745 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1746 " 0 <= y and y <= n }");
1747 assert(isl_map_is_equal(map
, map2
));
1751 /* COCOA example 2 */
1752 map
= isl_map_read_from_str(ctx
,
1753 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1754 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1755 "i2 = i + 2 and j2 = j - 2 and "
1756 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1757 map
= isl_map_transitive_closure(map
, &exact
);
1759 map2
= isl_map_read_from_str(ctx
,
1760 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1761 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1762 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1763 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1764 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1765 assert(isl_map_is_equal(map
, map2
));
1769 /* COCOA Fig.2 left */
1770 map
= isl_map_read_from_str(ctx
,
1771 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1772 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1774 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1775 "j <= 2 i - 3 and j <= n - 2 or "
1776 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1777 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1778 map
= isl_map_transitive_closure(map
, &exact
);
1782 /* COCOA Fig.2 right */
1783 map
= isl_map_read_from_str(ctx
,
1784 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1785 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1787 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1788 "j <= 2 i - 4 and j <= n - 3 or "
1789 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1790 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1791 map
= isl_map_power(map
, &exact
);
1795 /* COCOA Fig.2 right */
1796 map
= isl_map_read_from_str(ctx
,
1797 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1798 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1800 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1801 "j <= 2 i - 4 and j <= n - 3 or "
1802 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1803 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1804 map
= isl_map_transitive_closure(map
, &exact
);
1806 map2
= isl_map_read_from_str(ctx
,
1807 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1808 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1809 "j <= n and 3 + i + 2 j <= 3 n and "
1810 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1811 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1812 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1813 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1814 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1815 assert(isl_map_is_equal(map
, map2
));
1819 /* COCOA Fig.1 right */
1820 dom
= isl_set_read_from_str(ctx
,
1821 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1822 "2 x - 3 y + 3 >= 0 }");
1823 right
= isl_map_read_from_str(ctx
,
1824 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1825 up
= isl_map_read_from_str(ctx
,
1826 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1827 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1828 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1829 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1830 up
= isl_map_intersect_range(up
, dom
);
1831 map
= isl_map_union(up
, right
);
1832 map
= isl_map_transitive_closure(map
, &exact
);
1834 map2
= isl_map_read_from_str(ctx
,
1835 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1836 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1837 assert(isl_map_is_equal(map
, map2
));
1841 /* COCOA Theorem 1 counter example */
1842 map
= isl_map_read_from_str(ctx
,
1843 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1844 "i2 = 1 and j2 = j or "
1845 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1846 map
= isl_map_transitive_closure(map
, &exact
);
1850 map
= isl_map_read_from_str(ctx
,
1851 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1852 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1853 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1854 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1855 map
= isl_map_transitive_closure(map
, &exact
);
1859 /* Kelly et al 1996, fig 12 */
1860 map
= isl_map_read_from_str(ctx
,
1861 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1862 "1 <= i,j,j+1 <= n or "
1863 "j = n and j2 = 1 and i2 = i + 1 and "
1864 "1 <= i,i+1 <= n }");
1865 map
= isl_map_transitive_closure(map
, &exact
);
1867 map2
= isl_map_read_from_str(ctx
,
1868 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1869 "1 <= i <= n and i = i2 or "
1870 "1 <= i < i2 <= n and 1 <= j <= n and "
1872 assert(isl_map_is_equal(map
, map2
));
1876 /* Omega's closure4 */
1877 map
= isl_map_read_from_str(ctx
,
1878 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1879 "1 <= x,y <= 10 or "
1880 "x2 = x + 1 and y2 = y and "
1881 "1 <= x <= 20 && 5 <= y <= 15 }");
1882 map
= isl_map_transitive_closure(map
, &exact
);
1886 map
= isl_map_read_from_str(ctx
,
1887 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1888 map
= isl_map_transitive_closure(map
, &exact
);
1890 map2
= isl_map_read_from_str(ctx
,
1891 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1892 assert(isl_map_is_equal(map
, map2
));
1896 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1897 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1898 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1899 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1900 map
= isl_map_read_from_str(ctx
, str
);
1901 map
= isl_map_transitive_closure(map
, &exact
);
1903 map2
= isl_map_read_from_str(ctx
, str
);
1904 assert(isl_map_is_equal(map
, map2
));
1908 str
= "{[0] -> [1]; [2] -> [3]}";
1909 map
= isl_map_read_from_str(ctx
, str
);
1910 map
= isl_map_transitive_closure(map
, &exact
);
1912 map2
= isl_map_read_from_str(ctx
, str
);
1913 assert(isl_map_is_equal(map
, map2
));
1917 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1918 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1919 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1920 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1921 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1922 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1923 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1924 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1925 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1926 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1927 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1928 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1929 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1930 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1931 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1932 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1933 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1934 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1935 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1936 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1937 map
= isl_map_read_from_str(ctx
, str
);
1938 map
= isl_map_transitive_closure(map
, NULL
);
1945 static int test_lex(struct isl_ctx
*ctx
)
1951 dim
= isl_space_set_alloc(ctx
, 0, 0);
1952 map
= isl_map_lex_le(dim
);
1953 empty
= isl_map_is_empty(map
);
1959 isl_die(ctx
, isl_error_unknown
,
1960 "expecting non-empty result", return -1);
1965 static int test_lexmin(struct isl_ctx
*ctx
)
1969 isl_basic_map
*bmap
;
1970 isl_map
*map
, *map2
;
1973 isl_pw_multi_aff
*pma
;
1975 str
= "[p0, p1] -> { [] -> [] : "
1976 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1977 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1978 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1979 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1980 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1981 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1982 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1983 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1984 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1985 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1986 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1987 map
= isl_map_read_from_str(ctx
, str
);
1988 map
= isl_map_lexmin(map
);
1991 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1992 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1993 set
= isl_set_read_from_str(ctx
, str
);
1994 set
= isl_set_lexmax(set
);
1995 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1996 set2
= isl_set_read_from_str(ctx
, str
);
1997 set
= isl_set_intersect(set
, set2
);
1998 assert(!isl_set_is_empty(set
));
2001 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
2002 map
= isl_map_read_from_str(ctx
, str
);
2003 map
= isl_map_lexmin(map
);
2004 str
= "{ [x] -> [5] : 6 <= x <= 8; "
2005 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
2006 map2
= isl_map_read_from_str(ctx
, str
);
2007 assert(isl_map_is_equal(map
, map2
));
2011 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
2012 map
= isl_map_read_from_str(ctx
, str
);
2013 map2
= isl_map_copy(map
);
2014 map
= isl_map_lexmin(map
);
2015 assert(isl_map_is_equal(map
, map2
));
2019 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
2020 map
= isl_map_read_from_str(ctx
, str
);
2021 map
= isl_map_lexmin(map
);
2022 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
2023 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
2024 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
2025 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
2026 map2
= isl_map_read_from_str(ctx
, str
);
2027 assert(isl_map_is_equal(map
, map2
));
2031 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2032 " 8i' <= i and 8i' >= -7 + i }";
2033 bmap
= isl_basic_map_read_from_str(ctx
, str
);
2034 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
2035 map2
= isl_map_from_pw_multi_aff(pma
);
2036 map
= isl_map_from_basic_map(bmap
);
2037 assert(isl_map_is_equal(map
, map2
));
2041 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
2042 map
= isl_map_read_from_str(ctx
, str
);
2043 map
= isl_map_lexmin(map
);
2044 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
2045 map2
= isl_map_read_from_str(ctx
, str
);
2046 assert(isl_map_is_equal(map
, map2
));
2050 /* Check that empty pieces are properly combined. */
2051 str
= "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
2052 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
2053 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
2054 map
= isl_map_read_from_str(ctx
, str
);
2055 map
= isl_map_lexmin(map
);
2056 str
= "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
2057 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
2059 map2
= isl_map_read_from_str(ctx
, str
);
2060 assert(isl_map_is_equal(map
, map2
));
2064 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2065 " 8i' <= i and 8i' >= -7 + i }";
2066 set
= isl_set_read_from_str(ctx
, str
);
2067 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
2068 set2
= isl_set_from_pw_multi_aff(pma
);
2069 equal
= isl_set_is_equal(set
, set2
);
2075 isl_die(ctx
, isl_error_unknown
,
2076 "unexpected difference between set and "
2077 "piecewise affine expression", return -1);
2082 /* Check that isl_set_min_val and isl_set_max_val compute the correct
2083 * result on non-convex inputs.
2085 static int test_min(struct isl_ctx
*ctx
)
2092 set
= isl_set_read_from_str(ctx
, "{ [-1]; [1] }");
2093 aff
= isl_aff_read_from_str(ctx
, "{ [x] -> [x] }");
2094 val
= isl_set_min_val(set
, aff
);
2095 min_ok
= isl_val_is_negone(val
);
2097 val
= isl_set_max_val(set
, aff
);
2098 max_ok
= isl_val_is_one(val
);
2103 if (min_ok
< 0 || max_ok
< 0)
2106 isl_die(ctx
, isl_error_unknown
,
2107 "unexpected minimum", return -1);
2109 isl_die(ctx
, isl_error_unknown
,
2110 "unexpected maximum", return -1);
2120 static isl_stat
collect_must_may(__isl_take isl_map
*dep
, int must
,
2121 void *dep_user
, void *user
)
2123 struct must_may
*mm
= (struct must_may
*)user
;
2126 mm
->must
= isl_map_union(mm
->must
, dep
);
2128 mm
->may
= isl_map_union(mm
->may
, dep
);
2133 static int common_space(void *first
, void *second
)
2135 int depth
= *(int *)first
;
2139 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
2147 map2
= isl_map_read_from_str(map
->ctx
, str
);
2148 equal
= isl_map_is_equal(map
, map2
);
2154 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
2158 equal
= map_is_equal(map
, str
);
2162 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
2163 "result not as expected", return -1);
2167 static int test_dep(struct isl_ctx
*ctx
)
2172 isl_access_info
*ai
;
2179 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2180 map
= isl_map_read_from_str(ctx
, str
);
2181 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2183 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2184 map
= isl_map_read_from_str(ctx
, str
);
2185 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2187 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2188 map
= isl_map_read_from_str(ctx
, str
);
2189 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2191 flow
= isl_access_info_compute_flow(ai
);
2192 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2193 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2194 mm
.may
= isl_map_empty(dim
);
2196 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2198 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
2199 " [1,10,0] -> [2,5,0] }";
2200 assert(map_is_equal(mm
.must
, str
));
2201 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2202 assert(map_is_equal(mm
.may
, str
));
2204 isl_map_free(mm
.must
);
2205 isl_map_free(mm
.may
);
2206 isl_flow_free(flow
);
2209 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2210 map
= isl_map_read_from_str(ctx
, str
);
2211 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2213 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2214 map
= isl_map_read_from_str(ctx
, str
);
2215 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2217 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2218 map
= isl_map_read_from_str(ctx
, str
);
2219 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2221 flow
= isl_access_info_compute_flow(ai
);
2222 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2223 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2224 mm
.may
= isl_map_empty(dim
);
2226 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2228 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2229 assert(map_is_equal(mm
.must
, str
));
2230 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2231 assert(map_is_equal(mm
.may
, str
));
2233 isl_map_free(mm
.must
);
2234 isl_map_free(mm
.may
);
2235 isl_flow_free(flow
);
2238 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2239 map
= isl_map_read_from_str(ctx
, str
);
2240 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2242 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2243 map
= isl_map_read_from_str(ctx
, str
);
2244 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2246 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2247 map
= isl_map_read_from_str(ctx
, str
);
2248 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2250 flow
= isl_access_info_compute_flow(ai
);
2251 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2252 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2253 mm
.may
= isl_map_empty(dim
);
2255 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2257 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2258 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2259 assert(map_is_equal(mm
.may
, str
));
2260 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2261 assert(map_is_equal(mm
.must
, str
));
2263 isl_map_free(mm
.must
);
2264 isl_map_free(mm
.may
);
2265 isl_flow_free(flow
);
2268 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2269 map
= isl_map_read_from_str(ctx
, str
);
2270 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2272 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2273 map
= isl_map_read_from_str(ctx
, str
);
2274 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2276 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2277 map
= isl_map_read_from_str(ctx
, str
);
2278 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2280 flow
= isl_access_info_compute_flow(ai
);
2281 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2282 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2283 mm
.may
= isl_map_empty(dim
);
2285 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2287 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2288 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2289 assert(map_is_equal(mm
.may
, str
));
2290 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2291 assert(map_is_equal(mm
.must
, str
));
2293 isl_map_free(mm
.must
);
2294 isl_map_free(mm
.may
);
2295 isl_flow_free(flow
);
2298 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2299 map
= isl_map_read_from_str(ctx
, str
);
2300 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2302 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2303 map
= isl_map_read_from_str(ctx
, str
);
2304 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2306 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2307 map
= isl_map_read_from_str(ctx
, str
);
2308 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2310 flow
= isl_access_info_compute_flow(ai
);
2311 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2312 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2313 mm
.may
= isl_map_empty(dim
);
2315 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2317 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2318 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2319 assert(map_is_equal(mm
.may
, str
));
2320 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2321 assert(map_is_equal(mm
.must
, str
));
2323 isl_map_free(mm
.must
);
2324 isl_map_free(mm
.may
);
2325 isl_flow_free(flow
);
2330 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2331 map
= isl_map_read_from_str(ctx
, str
);
2332 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2334 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2335 map
= isl_map_read_from_str(ctx
, str
);
2336 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2338 flow
= isl_access_info_compute_flow(ai
);
2339 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2340 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2341 mm
.may
= isl_map_empty(dim
);
2343 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2345 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2346 assert(map_is_equal(mm
.must
, str
));
2347 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2348 assert(map_is_equal(mm
.may
, str
));
2350 isl_map_free(mm
.must
);
2351 isl_map_free(mm
.may
);
2352 isl_flow_free(flow
);
2357 /* Check that the dependence analysis proceeds without errors.
2358 * Earlier versions of isl would break down during the analysis
2359 * due to the use of the wrong spaces.
2361 static int test_flow(isl_ctx
*ctx
)
2364 isl_union_map
*access
, *schedule
;
2365 isl_union_map
*must_dep
, *may_dep
;
2368 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2369 access
= isl_union_map_read_from_str(ctx
, str
);
2370 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2371 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2372 "S2[] -> [1,0,0,0]; "
2373 "S3[] -> [-1,0,0,0] }";
2374 schedule
= isl_union_map_read_from_str(ctx
, str
);
2375 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2376 isl_union_map_copy(access
), schedule
,
2377 &must_dep
, &may_dep
, NULL
, NULL
);
2378 isl_union_map_free(may_dep
);
2379 isl_union_map_free(must_dep
);
2388 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2389 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2390 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2391 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2392 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2393 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2394 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2395 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2396 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2399 int test_sv(isl_ctx
*ctx
)
2401 isl_union_map
*umap
;
2405 for (i
= 0; i
< ARRAY_SIZE(sv_tests
); ++i
) {
2406 umap
= isl_union_map_read_from_str(ctx
, sv_tests
[i
].map
);
2407 sv
= isl_union_map_is_single_valued(umap
);
2408 isl_union_map_free(umap
);
2411 if (sv_tests
[i
].sv
&& !sv
)
2412 isl_die(ctx
, isl_error_internal
,
2413 "map not detected as single valued", return -1);
2414 if (!sv_tests
[i
].sv
&& sv
)
2415 isl_die(ctx
, isl_error_internal
,
2416 "map detected as single valued", return -1);
2425 } bijective_tests
[] = {
2426 { "[N,M]->{[i,j] -> [i]}", 0 },
2427 { "[N,M]->{[i,j] -> [i] : j=i}", 1 },
2428 { "[N,M]->{[i,j] -> [i] : j=0}", 1 },
2429 { "[N,M]->{[i,j] -> [i] : j=N}", 1 },
2430 { "[N,M]->{[i,j] -> [j,i]}", 1 },
2431 { "[N,M]->{[i,j] -> [i+j]}", 0 },
2432 { "[N,M]->{[i,j] -> []}", 0 },
2433 { "[N,M]->{[i,j] -> [i,j,N]}", 1 },
2434 { "[N,M]->{[i,j] -> [2i]}", 0 },
2435 { "[N,M]->{[i,j] -> [i,i]}", 0 },
2436 { "[N,M]->{[i,j] -> [2i,i]}", 0 },
2437 { "[N,M]->{[i,j] -> [2i,j]}", 1 },
2438 { "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1 },
2441 static int test_bijective(struct isl_ctx
*ctx
)
2447 for (i
= 0; i
< ARRAY_SIZE(bijective_tests
); ++i
) {
2448 map
= isl_map_read_from_str(ctx
, bijective_tests
[i
].str
);
2449 bijective
= isl_map_is_bijective(map
);
2453 if (bijective_tests
[i
].bijective
&& !bijective
)
2454 isl_die(ctx
, isl_error_internal
,
2455 "map not detected as bijective", return -1);
2456 if (!bijective_tests
[i
].bijective
&& bijective
)
2457 isl_die(ctx
, isl_error_internal
,
2458 "map detected as bijective", return -1);
2464 /* Inputs for isl_pw_qpolynomial_gist tests.
2465 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2471 } pwqp_gist_tests
[] = {
2472 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2473 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2474 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2475 "{ [i] -> -1/2 + 1/2 * i }" },
2476 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2479 static int test_pwqp(struct isl_ctx
*ctx
)
2484 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
2487 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2488 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2490 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
2493 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2494 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2496 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2498 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2500 isl_pw_qpolynomial_free(pwqp1
);
2502 for (i
= 0; i
< ARRAY_SIZE(pwqp_gist_tests
); ++i
) {
2503 str
= pwqp_gist_tests
[i
].pwqp
;
2504 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2505 str
= pwqp_gist_tests
[i
].set
;
2506 set
= isl_set_read_from_str(ctx
, str
);
2507 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2508 str
= pwqp_gist_tests
[i
].gist
;
2509 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2510 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2511 equal
= isl_pw_qpolynomial_is_zero(pwqp1
);
2512 isl_pw_qpolynomial_free(pwqp1
);
2517 isl_die(ctx
, isl_error_unknown
,
2518 "unexpected result", return -1);
2521 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
2522 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2523 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
2524 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2526 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2528 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2530 isl_pw_qpolynomial_free(pwqp1
);
2532 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
2533 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2534 str
= "{ [x] -> x }";
2535 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2537 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2539 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2541 isl_pw_qpolynomial_free(pwqp1
);
2543 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2544 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2545 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2546 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
2547 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2548 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2549 isl_pw_qpolynomial_free(pwqp1
);
2551 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2552 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2553 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2554 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2555 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
2556 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
2557 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2558 isl_pw_qpolynomial_free(pwqp1
);
2559 isl_pw_qpolynomial_free(pwqp2
);
2563 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2565 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2566 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2567 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2568 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2569 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
2571 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2572 isl_pw_qpolynomial_free(pwqp1
);
2573 isl_pw_qpolynomial_free(pwqp2
);
2577 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2582 static int test_split_periods(isl_ctx
*ctx
)
2585 isl_pw_qpolynomial
*pwqp
;
2587 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2588 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2589 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2590 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2592 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
2594 isl_pw_qpolynomial_free(pwqp
);
2602 static int test_union(isl_ctx
*ctx
)
2605 isl_union_set
*uset1
, *uset2
;
2606 isl_union_map
*umap1
, *umap2
;
2609 str
= "{ [i] : 0 <= i <= 1 }";
2610 uset1
= isl_union_set_read_from_str(ctx
, str
);
2611 str
= "{ [1] -> [0] }";
2612 umap1
= isl_union_map_read_from_str(ctx
, str
);
2614 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
2615 equal
= isl_union_map_is_equal(umap1
, umap2
);
2617 isl_union_map_free(umap1
);
2618 isl_union_map_free(umap2
);
2623 isl_die(ctx
, isl_error_unknown
, "union maps not equal",
2626 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2627 umap1
= isl_union_map_read_from_str(ctx
, str
);
2628 str
= "{ A[i]; B[i] }";
2629 uset1
= isl_union_set_read_from_str(ctx
, str
);
2631 uset2
= isl_union_map_domain(umap1
);
2633 equal
= isl_union_set_is_equal(uset1
, uset2
);
2635 isl_union_set_free(uset1
);
2636 isl_union_set_free(uset2
);
2641 isl_die(ctx
, isl_error_unknown
, "union sets not equal",
2647 /* Check that computing a bound of a non-zero polynomial over an unbounded
2648 * domain does not produce a rational value.
2649 * In particular, check that the upper bound is infinity.
2651 static int test_bound_unbounded_domain(isl_ctx
*ctx
)
2654 isl_pw_qpolynomial
*pwqp
;
2655 isl_pw_qpolynomial_fold
*pwf
, *pwf2
;
2658 str
= "{ [m,n] -> -m * n }";
2659 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2660 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2662 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2663 pwf2
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2664 equal
= isl_pw_qpolynomial_fold_plain_is_equal(pwf
, pwf2
);
2665 isl_pw_qpolynomial_fold_free(pwf
);
2666 isl_pw_qpolynomial_fold_free(pwf2
);
2671 isl_die(ctx
, isl_error_unknown
,
2672 "expecting infinite polynomial bound", return -1);
2677 static int test_bound(isl_ctx
*ctx
)
2681 isl_pw_qpolynomial
*pwqp
;
2682 isl_pw_qpolynomial_fold
*pwf
;
2684 if (test_bound_unbounded_domain(ctx
) < 0)
2687 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
2688 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2689 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2690 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
2691 isl_pw_qpolynomial_fold_free(pwf
);
2693 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
2696 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2697 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2698 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2699 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
2700 isl_pw_qpolynomial_fold_free(pwf
);
2702 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
2708 static int test_lift(isl_ctx
*ctx
)
2711 isl_basic_map
*bmap
;
2712 isl_basic_set
*bset
;
2714 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
2715 bset
= isl_basic_set_read_from_str(ctx
, str
);
2716 bset
= isl_basic_set_lift(bset
);
2717 bmap
= isl_basic_map_from_range(bset
);
2718 bset
= isl_basic_map_domain(bmap
);
2719 isl_basic_set_free(bset
);
2728 } subset_tests
[] = {
2730 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2731 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2732 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2734 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2735 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2736 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2737 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2738 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2739 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2740 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2741 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2742 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2743 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2744 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2745 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2746 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2747 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2748 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2749 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2750 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2751 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2752 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2753 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2754 "4e0 <= -57 + i0 + i1)) or "
2755 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2756 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2757 "4e0 >= -61 + i0 + i1)) or "
2758 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2761 static int test_subset(isl_ctx
*ctx
)
2764 isl_set
*set1
, *set2
;
2767 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
2768 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
2769 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
2770 subset
= isl_set_is_subset(set1
, set2
);
2775 if (subset
!= subset_tests
[i
].subset
)
2776 isl_die(ctx
, isl_error_unknown
,
2777 "incorrect subset result", return -1);
2784 const char *minuend
;
2785 const char *subtrahend
;
2786 const char *difference
;
2787 } subtract_domain_tests
[] = {
2788 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2789 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2790 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2793 static int test_subtract(isl_ctx
*ctx
)
2796 isl_union_map
*umap1
, *umap2
;
2797 isl_union_pw_multi_aff
*upma1
, *upma2
;
2798 isl_union_set
*uset
;
2801 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2802 umap1
= isl_union_map_read_from_str(ctx
,
2803 subtract_domain_tests
[i
].minuend
);
2804 uset
= isl_union_set_read_from_str(ctx
,
2805 subtract_domain_tests
[i
].subtrahend
);
2806 umap2
= isl_union_map_read_from_str(ctx
,
2807 subtract_domain_tests
[i
].difference
);
2808 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
2809 equal
= isl_union_map_is_equal(umap1
, umap2
);
2810 isl_union_map_free(umap1
);
2811 isl_union_map_free(umap2
);
2815 isl_die(ctx
, isl_error_unknown
,
2816 "incorrect subtract domain result", return -1);
2819 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2820 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
2821 subtract_domain_tests
[i
].minuend
);
2822 uset
= isl_union_set_read_from_str(ctx
,
2823 subtract_domain_tests
[i
].subtrahend
);
2824 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
2825 subtract_domain_tests
[i
].difference
);
2826 upma1
= isl_union_pw_multi_aff_subtract_domain(upma1
, uset
);
2827 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
2828 isl_union_pw_multi_aff_free(upma1
);
2829 isl_union_pw_multi_aff_free(upma2
);
2833 isl_die(ctx
, isl_error_unknown
,
2834 "incorrect subtract domain result", return -1);
2840 int test_factorize(isl_ctx
*ctx
)
2843 isl_basic_set
*bset
;
2846 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2847 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2848 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2849 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2850 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2851 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2852 "3i5 >= -2i0 - i2 + 3i4 }";
2853 bset
= isl_basic_set_read_from_str(ctx
, str
);
2854 f
= isl_basic_set_factorizer(bset
);
2855 isl_basic_set_free(bset
);
2856 isl_factorizer_free(f
);
2858 isl_die(ctx
, isl_error_unknown
,
2859 "failed to construct factorizer", return -1);
2861 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2862 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2863 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2864 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2865 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2866 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2867 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2868 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2869 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2870 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2871 bset
= isl_basic_set_read_from_str(ctx
, str
);
2872 f
= isl_basic_set_factorizer(bset
);
2873 isl_basic_set_free(bset
);
2874 isl_factorizer_free(f
);
2876 isl_die(ctx
, isl_error_unknown
,
2877 "failed to construct factorizer", return -1);
2882 static isl_stat
check_injective(__isl_take isl_map
*map
, void *user
)
2884 int *injective
= user
;
2886 *injective
= isl_map_is_injective(map
);
2889 if (*injective
< 0 || !*injective
)
2890 return isl_stat_error
;
2895 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
2896 const char *r
, const char *s
, int tilable
, int parallel
)
2900 isl_union_map
*W
, *R
, *S
;
2901 isl_union_map
*empty
;
2902 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
2903 isl_union_map
*validity
, *proximity
, *coincidence
;
2904 isl_union_map
*schedule
;
2905 isl_union_map
*test
;
2906 isl_union_set
*delta
;
2907 isl_union_set
*domain
;
2911 isl_schedule_constraints
*sc
;
2912 isl_schedule
*sched
;
2913 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
2915 D
= isl_union_set_read_from_str(ctx
, d
);
2916 W
= isl_union_map_read_from_str(ctx
, w
);
2917 R
= isl_union_map_read_from_str(ctx
, r
);
2918 S
= isl_union_map_read_from_str(ctx
, s
);
2920 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
2921 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
2923 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
2924 isl_union_map_compute_flow(isl_union_map_copy(R
),
2925 isl_union_map_copy(W
), empty
,
2926 isl_union_map_copy(S
),
2927 &dep_raw
, NULL
, NULL
, NULL
);
2928 isl_union_map_compute_flow(isl_union_map_copy(W
),
2929 isl_union_map_copy(W
),
2930 isl_union_map_copy(R
),
2931 isl_union_map_copy(S
),
2932 &dep_waw
, &dep_war
, NULL
, NULL
);
2934 dep
= isl_union_map_union(dep_waw
, dep_war
);
2935 dep
= isl_union_map_union(dep
, dep_raw
);
2936 validity
= isl_union_map_copy(dep
);
2937 coincidence
= isl_union_map_copy(dep
);
2938 proximity
= isl_union_map_copy(dep
);
2940 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
2941 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
2942 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
2943 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
2944 sched
= isl_schedule_constraints_compute_schedule(sc
);
2945 schedule
= isl_schedule_get_map(sched
);
2946 isl_schedule_free(sched
);
2947 isl_union_map_free(W
);
2948 isl_union_map_free(R
);
2949 isl_union_map_free(S
);
2952 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
2954 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
2955 is_complete
= isl_union_set_is_subset(D
, domain
);
2956 isl_union_set_free(D
);
2957 isl_union_set_free(domain
);
2959 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
2960 test
= isl_union_map_apply_range(test
, dep
);
2961 test
= isl_union_map_apply_range(test
, schedule
);
2963 delta
= isl_union_map_deltas(test
);
2964 if (isl_union_set_n_set(delta
) == 0) {
2968 isl_union_set_free(delta
);
2970 delta_set
= isl_set_from_union_set(delta
);
2972 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2973 for (i
= 0; i
< tilable
; ++i
)
2974 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
2975 is_tilable
= isl_set_is_subset(delta_set
, slice
);
2976 isl_set_free(slice
);
2978 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2979 for (i
= 0; i
< parallel
; ++i
)
2980 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
2981 is_parallel
= isl_set_is_subset(delta_set
, slice
);
2982 isl_set_free(slice
);
2984 origin
= isl_set_universe(isl_set_get_space(delta_set
));
2985 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
2986 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2988 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2989 delta_set
= isl_set_lexmin(delta_set
);
2991 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2993 isl_set_free(origin
);
2994 isl_set_free(delta_set
);
2997 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2998 is_injection
< 0 || is_complete
< 0)
3001 isl_die(ctx
, isl_error_unknown
,
3002 "generated schedule incomplete", return -1);
3004 isl_die(ctx
, isl_error_unknown
,
3005 "generated schedule not injective on each statement",
3008 isl_die(ctx
, isl_error_unknown
,
3009 "negative dependences in generated schedule",
3012 isl_die(ctx
, isl_error_unknown
,
3013 "generated schedule not as tilable as expected",
3016 isl_die(ctx
, isl_error_unknown
,
3017 "generated schedule not as parallel as expected",
3023 /* Compute a schedule for the given instance set, validity constraints,
3024 * proximity constraints and context and return a corresponding union map
3027 static __isl_give isl_union_map
*compute_schedule_with_context(isl_ctx
*ctx
,
3028 const char *domain
, const char *validity
, const char *proximity
,
3029 const char *context
)
3034 isl_union_map
*prox
;
3035 isl_schedule_constraints
*sc
;
3036 isl_schedule
*schedule
;
3037 isl_union_map
*sched
;
3039 con
= isl_set_read_from_str(ctx
, context
);
3040 dom
= isl_union_set_read_from_str(ctx
, domain
);
3041 dep
= isl_union_map_read_from_str(ctx
, validity
);
3042 prox
= isl_union_map_read_from_str(ctx
, proximity
);
3043 sc
= isl_schedule_constraints_on_domain(dom
);
3044 sc
= isl_schedule_constraints_set_context(sc
, con
);
3045 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
3046 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
3047 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3048 sched
= isl_schedule_get_map(schedule
);
3049 isl_schedule_free(schedule
);
3054 /* Compute a schedule for the given instance set, validity constraints and
3055 * proximity constraints and return a corresponding union map representation.
3057 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
3058 const char *domain
, const char *validity
, const char *proximity
)
3060 return compute_schedule_with_context(ctx
, domain
, validity
, proximity
,
3064 /* Check that a schedule can be constructed on the given domain
3065 * with the given validity and proximity constraints.
3067 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
3068 const char *validity
, const char *proximity
)
3070 isl_union_map
*sched
;
3072 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
3076 isl_union_map_free(sched
);
3080 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
3081 const char *validity
, const char *proximity
, const char *expected_sched
)
3083 isl_union_map
*sched1
, *sched2
;
3086 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
3087 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
3089 equal
= isl_union_map_is_equal(sched1
, sched2
);
3090 isl_union_map_free(sched1
);
3091 isl_union_map_free(sched2
);
3096 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
3102 /* Check that the schedule map is properly padded, even after being
3103 * reconstructed from the band forest.
3105 static int test_padded_schedule(isl_ctx
*ctx
)
3109 isl_union_map
*validity
, *proximity
;
3110 isl_schedule_constraints
*sc
;
3111 isl_schedule
*sched
;
3112 isl_union_map
*map1
, *map2
;
3113 isl_band_list
*list
;
3116 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
3117 D
= isl_union_set_read_from_str(ctx
, str
);
3118 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
3119 proximity
= isl_union_map_copy(validity
);
3120 sc
= isl_schedule_constraints_on_domain(D
);
3121 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3122 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3123 sched
= isl_schedule_constraints_compute_schedule(sc
);
3124 map1
= isl_schedule_get_map(sched
);
3125 list
= isl_schedule_get_band_forest(sched
);
3126 isl_band_list_free(list
);
3127 map2
= isl_schedule_get_map(sched
);
3128 isl_schedule_free(sched
);
3129 equal
= isl_union_map_is_equal(map1
, map2
);
3130 isl_union_map_free(map1
);
3131 isl_union_map_free(map2
);
3136 isl_die(ctx
, isl_error_unknown
,
3137 "reconstructed schedule map not the same as original",
3143 /* Check that conditional validity constraints are also taken into
3144 * account across bands.
3145 * In particular, try to make sure that live ranges D[1,0]->C[2,1] and
3146 * D[2,0]->C[3,0] are not local in the outer band of the generated schedule
3147 * and then check that the adjacent order constraint C[2,1]->D[2,0]
3148 * is enforced by the rest of the schedule.
3150 static int test_special_conditional_schedule_constraints(isl_ctx
*ctx
)
3153 isl_union_set
*domain
;
3154 isl_union_map
*validity
, *proximity
, *condition
;
3155 isl_union_map
*sink
, *source
, *dep
;
3156 isl_schedule_constraints
*sc
;
3157 isl_schedule
*schedule
;
3158 isl_union_access_info
*access
;
3159 isl_union_flow
*flow
;
3162 str
= "[n] -> { C[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3163 "A[k] : k >= 1 and k <= -1 + n; "
3164 "B[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3165 "D[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k }";
3166 domain
= isl_union_set_read_from_str(ctx
, str
);
3167 sc
= isl_schedule_constraints_on_domain(domain
);
3168 str
= "[n] -> { D[k, i] -> C[1 + k, k - i] : "
3169 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3170 "D[k, i] -> C[1 + k, i] : "
3171 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3172 "D[k, 0] -> C[1 + k, k] : k >= 1 and k <= -2 + n; "
3173 "D[k, 0] -> C[1 + k, 0] : k >= 1 and k <= -2 + n }";
3174 validity
= isl_union_map_read_from_str(ctx
, str
);
3175 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3176 str
= "[n] -> { C[k, i] -> D[k, i] : "
3177 "0 <= i <= -1 + k and k <= -1 + n }";
3178 proximity
= isl_union_map_read_from_str(ctx
, str
);
3179 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3180 str
= "[n] -> { [D[k, i] -> a[]] -> [C[1 + k, k - i] -> b[]] : "
3181 "i <= -1 + k and i >= 1 and k <= -2 + n; "
3182 "[B[k, i] -> c[]] -> [B[k, 1 + i] -> c[]] : "
3183 "k <= -1 + n and i >= 0 and i <= -2 + k }";
3184 condition
= isl_union_map_read_from_str(ctx
, str
);
3185 str
= "[n] -> { [B[k, i] -> e[]] -> [D[k, i] -> a[]] : "
3186 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3187 "[C[k, i] -> b[]] -> [D[k', -1 + k - i] -> a[]] : "
3188 "i >= 0 and i <= -1 + k and k <= -1 + n and "
3189 "k' <= -1 + n and k' >= k - i and k' >= 1 + k; "
3190 "[C[k, i] -> b[]] -> [D[k, -1 + k - i] -> a[]] : "
3191 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3192 "[B[k, i] -> c[]] -> [A[k'] -> d[]] : "
3193 "k <= -1 + n and i >= 0 and i <= -1 + k and "
3194 "k' >= 1 and k' <= -1 + n and k' >= 1 + k }";
3195 validity
= isl_union_map_read_from_str(ctx
, str
);
3196 sc
= isl_schedule_constraints_set_conditional_validity(sc
, condition
,
3198 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3199 str
= "{ D[2,0] -> [] }";
3200 sink
= isl_union_map_read_from_str(ctx
, str
);
3201 access
= isl_union_access_info_from_sink(sink
);
3202 str
= "{ C[2,1] -> [] }";
3203 source
= isl_union_map_read_from_str(ctx
, str
);
3204 access
= isl_union_access_info_set_must_source(access
, source
);
3205 access
= isl_union_access_info_set_schedule(access
, schedule
);
3206 flow
= isl_union_access_info_compute_flow(access
);
3207 dep
= isl_union_flow_get_must_dependence(flow
);
3208 isl_union_flow_free(flow
);
3209 empty
= isl_union_map_is_empty(dep
);
3210 isl_union_map_free(dep
);
3215 isl_die(ctx
, isl_error_unknown
,
3216 "conditional validity not respected", return -1);
3221 /* Input for testing of schedule construction based on
3222 * conditional constraints.
3224 * domain is the iteration domain
3225 * flow are the flow dependences, which determine the validity and
3226 * proximity constraints
3227 * condition are the conditions on the conditional validity constraints
3228 * conditional_validity are the conditional validity constraints
3229 * outer_band_n is the expected number of members in the outer band
3234 const char *condition
;
3235 const char *conditional_validity
;
3237 } live_range_tests
[] = {
3238 /* Contrived example that illustrates that we need to keep
3239 * track of tagged condition dependences and
3240 * tagged conditional validity dependences
3241 * in isl_sched_edge separately.
3242 * In particular, the conditional validity constraints on A
3243 * cannot be satisfied,
3244 * but they can be ignored because there are no corresponding
3245 * condition constraints. However, we do have an additional
3246 * conditional validity constraint that maps to the same
3247 * dependence relation
3248 * as the condition constraint on B. If we did not make a distinction
3249 * between tagged condition and tagged conditional validity
3250 * dependences, then we
3251 * could end up treating this shared dependence as an condition
3252 * constraint on A, forcing a localization of the conditions,
3253 * which is impossible.
3255 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
3256 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
3257 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
3258 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3259 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3260 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
3263 /* TACO 2013 Fig. 7 */
3264 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3265 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3266 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3267 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
3268 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
3269 "0 <= i < n and 0 <= j < n - 1 }",
3270 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
3271 "0 <= i < n and 0 <= j < j' < n;"
3272 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
3273 "0 <= i < i' < n and 0 <= j,j' < n;"
3274 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
3275 "0 <= i,j,j' < n and j < j' }",
3278 /* TACO 2013 Fig. 7, without tags */
3279 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3280 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3281 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3282 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3283 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3284 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
3285 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
3286 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
3289 /* TACO 2013 Fig. 12 */
3290 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
3291 "S3[i,3] : 0 <= i <= 1 }",
3292 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
3293 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
3294 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
3295 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
3296 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3297 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
3298 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3299 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
3300 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
3301 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
3302 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
3307 /* Test schedule construction based on conditional constraints.
3308 * In particular, check the number of members in the outer band node
3309 * as an indication of whether tiling is possible or not.
3311 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
3314 isl_union_set
*domain
;
3315 isl_union_map
*condition
;
3316 isl_union_map
*flow
;
3317 isl_union_map
*validity
;
3318 isl_schedule_constraints
*sc
;
3319 isl_schedule
*schedule
;
3320 isl_schedule_node
*node
;
3323 if (test_special_conditional_schedule_constraints(ctx
) < 0)
3326 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
3327 domain
= isl_union_set_read_from_str(ctx
,
3328 live_range_tests
[i
].domain
);
3329 flow
= isl_union_map_read_from_str(ctx
,
3330 live_range_tests
[i
].flow
);
3331 condition
= isl_union_map_read_from_str(ctx
,
3332 live_range_tests
[i
].condition
);
3333 validity
= isl_union_map_read_from_str(ctx
,
3334 live_range_tests
[i
].conditional_validity
);
3335 sc
= isl_schedule_constraints_on_domain(domain
);
3336 sc
= isl_schedule_constraints_set_validity(sc
,
3337 isl_union_map_copy(flow
));
3338 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
3339 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
3340 condition
, validity
);
3341 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3342 node
= isl_schedule_get_root(schedule
);
3344 isl_schedule_node_get_type(node
) != isl_schedule_node_band
)
3345 node
= isl_schedule_node_first_child(node
);
3346 n_member
= isl_schedule_node_band_n_member(node
);
3347 isl_schedule_node_free(node
);
3348 isl_schedule_free(schedule
);
3352 if (n_member
!= live_range_tests
[i
].outer_band_n
)
3353 isl_die(ctx
, isl_error_unknown
,
3354 "unexpected number of members in outer band",
3360 /* Check that the schedule computed for the given instance set and
3361 * dependence relation strongly satisfies the dependences.
3362 * In particular, check that no instance is scheduled before
3363 * or together with an instance on which it depends.
3364 * Earlier versions of isl would produce a schedule that
3365 * only weakly satisfies the dependences.
3367 static int test_strongly_satisfying_schedule(isl_ctx
*ctx
)
3369 const char *domain
, *dep
;
3370 isl_union_map
*D
, *schedule
;
3374 domain
= "{ B[i0, i1] : 0 <= i0 <= 1 and 0 <= i1 <= 11; "
3375 "A[i0] : 0 <= i0 <= 1 }";
3376 dep
= "{ B[i0, i1] -> B[i0, 1 + i1] : 0 <= i0 <= 1 and 0 <= i1 <= 10; "
3377 "B[0, 11] -> A[1]; A[i0] -> B[i0, 0] : 0 <= i0 <= 1 }";
3378 schedule
= compute_schedule(ctx
, domain
, dep
, dep
);
3379 D
= isl_union_map_read_from_str(ctx
, dep
);
3380 D
= isl_union_map_apply_domain(D
, isl_union_map_copy(schedule
));
3381 D
= isl_union_map_apply_range(D
, schedule
);
3382 map
= isl_map_from_union_map(D
);
3383 ge
= isl_map_lex_ge(isl_space_domain(isl_map_get_space(map
)));
3384 map
= isl_map_intersect(map
, ge
);
3385 empty
= isl_map_is_empty(map
);
3391 isl_die(ctx
, isl_error_unknown
,
3392 "dependences not strongly satisfied", return -1);
3397 /* Compute a schedule for input where the instance set constraints
3398 * conflict with the context constraints.
3399 * Earlier versions of isl did not properly handle this situation.
3401 static int test_conflicting_context_schedule(isl_ctx
*ctx
)
3403 isl_union_map
*schedule
;
3404 const char *domain
, *context
;
3406 domain
= "[n] -> { A[] : n >= 0 }";
3407 context
= "[n] -> { : n < 0 }";
3408 schedule
= compute_schedule_with_context(ctx
,
3409 domain
, "{}", "{}", context
);
3410 isl_union_map_free(schedule
);
3418 /* Check that the dependence carrying step is not confused by
3419 * a bound on the coefficient size.
3420 * In particular, force the scheduler to move to a dependence carrying
3421 * step by demanding outer coincidence and bound the size of
3422 * the coefficients. Earlier versions of isl would take this
3423 * bound into account while carrying dependences, breaking
3424 * fundamental assumptions.
3426 static int test_bounded_coefficients_schedule(isl_ctx
*ctx
)
3428 const char *domain
, *dep
;
3431 isl_schedule_constraints
*sc
;
3432 isl_schedule
*schedule
;
3434 domain
= "{ C[i0, i1] : 2 <= i0 <= 3999 and 0 <= i1 <= -1 + i0 }";
3435 dep
= "{ C[i0, i1] -> C[i0, 1 + i1] : i0 <= 3999 and i1 >= 0 and "
3437 "C[i0, -1 + i0] -> C[1 + i0, 0] : i0 <= 3998 and i0 >= 1 }";
3438 I
= isl_union_set_read_from_str(ctx
, domain
);
3439 D
= isl_union_map_read_from_str(ctx
, dep
);
3440 sc
= isl_schedule_constraints_on_domain(I
);
3441 sc
= isl_schedule_constraints_set_validity(sc
, isl_union_map_copy(D
));
3442 sc
= isl_schedule_constraints_set_coincidence(sc
, D
);
3443 isl_options_set_schedule_outer_coincidence(ctx
, 1);
3444 isl_options_set_schedule_max_coefficient(ctx
, 20);
3445 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3446 isl_options_set_schedule_max_coefficient(ctx
, -1);
3447 isl_options_set_schedule_outer_coincidence(ctx
, 0);
3448 isl_schedule_free(schedule
);
3456 int test_schedule(isl_ctx
*ctx
)
3458 const char *D
, *W
, *R
, *V
, *P
, *S
;
3460 /* Handle resulting schedule with zero bands. */
3461 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
3465 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
3466 W
= "{ S1[t,i] -> a[t,i] }";
3467 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
3468 "S1[t,i] -> a[t-1,i+1] }";
3469 S
= "{ S1[t,i] -> [t,i] }";
3470 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3473 /* Fig. 5 of CC2008 */
3474 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
3476 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
3477 "j >= 2 and j <= -1 + N }";
3478 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
3479 "j >= 2 and j <= -1 + N; "
3480 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
3481 "j >= 2 and j <= -1 + N }";
3482 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3483 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3486 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
3487 W
= "{ S1[i] -> a[i] }";
3488 R
= "{ S2[i] -> a[i+1] }";
3489 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3490 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3493 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
3494 W
= "{ S1[i] -> a[i] }";
3495 R
= "{ S2[i] -> a[9-i] }";
3496 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3497 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3500 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
3501 W
= "{ S1[i] -> a[i] }";
3502 R
= "[N] -> { S2[i] -> a[N-1-i] }";
3503 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3504 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3507 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
3508 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
3509 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
3510 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
3511 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3514 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3515 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
3516 R
= "{ S2[i,j] -> a[i-1,j] }";
3517 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3518 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3521 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3522 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
3523 R
= "{ S2[i,j] -> a[i,j-1] }";
3524 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3525 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3528 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
3529 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
3530 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
3531 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
3532 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
3533 "S_0[] -> [0, 0, 0] }";
3534 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
3536 ctx
->opt
->schedule_parametric
= 0;
3537 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3539 ctx
->opt
->schedule_parametric
= 1;
3541 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
3542 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
3543 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
3544 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
3545 "S4[i] -> a[i,N] }";
3546 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
3547 "S4[i] -> [4,i,0] }";
3548 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3551 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
3552 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3554 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3556 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
3558 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3559 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3562 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
3563 " S_2[t] : t >= 0 and t <= -1 + N; "
3564 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
3566 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
3567 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
3568 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
3569 "i >= 0 and i <= -1 + N }";
3570 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
3571 "i >= 0 and i <= -1 + N; "
3572 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
3573 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
3574 " S_0[t] -> [0, t, 0] }";
3576 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3578 ctx
->opt
->schedule_parametric
= 0;
3579 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3581 ctx
->opt
->schedule_parametric
= 1;
3583 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
3584 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
3585 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
3588 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3589 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3590 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3591 "j >= 0 and j <= -1 + N; "
3592 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3593 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3594 "j >= 0 and j <= -1 + N; "
3595 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3596 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3597 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3600 D
= "{ S_0[i] : i >= 0 }";
3601 W
= "{ S_0[i] -> a[i] : i >= 0 }";
3602 R
= "{ S_0[i] -> a[0] : i >= 0 }";
3603 S
= "{ S_0[i] -> [0, i, 0] }";
3604 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3607 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3608 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3609 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3610 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3611 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3614 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3615 "k <= -1 + n and k >= 0 }";
3616 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3617 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3618 "k <= -1 + n and k >= 0; "
3619 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3620 "k <= -1 + n and k >= 0; "
3621 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3622 "k <= -1 + n and k >= 0 }";
3623 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
3624 ctx
->opt
->schedule_outer_coincidence
= 1;
3625 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3627 ctx
->opt
->schedule_outer_coincidence
= 0;
3629 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
3630 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3631 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3632 "Stmt_for_body24[i0, i1, 1, 0]:"
3633 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3634 "Stmt_for_body7[i0, i1, i2]:"
3635 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3638 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
3639 "Stmt_for_body24[1, i1, i2, i3]:"
3640 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3642 "Stmt_for_body24[0, i1, i2, i3] -> "
3643 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3644 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3646 "Stmt_for_body24[0, i1, i2, i3] ->"
3647 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3648 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3649 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3650 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3651 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3652 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3653 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3654 "i1 <= 6 and i1 >= 0;"
3655 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3656 "Stmt_for_body7[i0, i1, i2] -> "
3657 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3658 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3659 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3660 "Stmt_for_body7[i0, i1, i2] -> "
3661 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3662 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3663 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3665 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3666 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3667 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3669 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3672 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3673 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3674 "j >= 1 and j <= 7;"
3675 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3676 "j >= 1 and j <= 8 }";
3678 S
= "{ S_0[i, j] -> [i + j, j] }";
3679 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3680 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3682 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3684 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3685 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3686 "j >= 0 and j <= -1 + i }";
3687 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3688 "i <= -1 + N and j >= 0;"
3689 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3692 S
= "{ S_0[i, j] -> [i, j] }";
3693 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3694 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3696 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3698 /* Test both algorithms on a case with only proximity dependences. */
3699 D
= "{ S[i,j] : 0 <= i <= 10 }";
3701 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3702 S
= "{ S[i, j] -> [j, i] }";
3703 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3704 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3706 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3707 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3710 D
= "{ A[a]; B[] }";
3712 P
= "{ A[a] -> B[] }";
3713 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3716 if (test_padded_schedule(ctx
) < 0)
3719 /* Check that check for progress is not confused by rational
3722 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3723 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3725 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3726 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3728 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3729 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3731 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3733 /* Check that we allow schedule rows that are only non-trivial
3734 * on some full-dimensional domains.
3736 D
= "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
3737 V
= "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
3738 "S1[j] -> S2[1] : 0 <= j <= 1 }";
3740 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3741 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3743 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3745 if (test_conditional_schedule_constraints(ctx
) < 0)
3748 if (test_strongly_satisfying_schedule(ctx
) < 0)
3751 if (test_conflicting_context_schedule(ctx
) < 0)
3754 if (test_bounded_coefficients_schedule(ctx
) < 0)
3760 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
3762 isl_union_map
*umap
;
3765 umap
= isl_union_map_read_from_str(ctx
, str
);
3766 test
= isl_union_map_plain_is_injective(umap
);
3767 isl_union_map_free(umap
);
3770 if (test
== injective
)
3773 isl_die(ctx
, isl_error_unknown
,
3774 "map not detected as injective", return -1);
3776 isl_die(ctx
, isl_error_unknown
,
3777 "map detected as injective", return -1);
3780 int test_injective(isl_ctx
*ctx
)
3784 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3786 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
3788 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
3790 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
3792 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3794 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3796 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3798 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3801 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3802 if (test_plain_injective(ctx
, str
, 1))
3804 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3805 if (test_plain_injective(ctx
, str
, 0))
3811 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
3819 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
3820 equal
= isl_aff_plain_is_equal(aff
, aff2
);
3826 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
3830 equal
= aff_plain_is_equal(aff
, str
);
3834 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
3835 "result not as expected", return -1);
3840 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3841 __isl_take isl_aff
*aff2
);
3843 ['+'] = { &isl_aff_add
},
3844 ['-'] = { &isl_aff_sub
},
3845 ['*'] = { &isl_aff_mul
},
3846 ['/'] = { &isl_aff_div
},
3854 } aff_bin_tests
[] = {
3855 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3856 "{ [i] -> [2i] }" },
3857 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3859 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3860 "{ [i] -> [2i] }" },
3861 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3862 "{ [i] -> [2i] }" },
3863 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
3864 "{ [i] -> [i/2] }" },
3865 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
3867 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3868 "{ [i] -> [NaN] }" },
3869 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3870 "{ [i] -> [NaN] }" },
3871 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3872 "{ [i] -> [NaN] }" },
3873 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3874 "{ [i] -> [NaN] }" },
3875 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
3876 "{ [i] -> [NaN] }" },
3877 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
3878 "{ [i] -> [NaN] }" },
3879 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3880 "{ [i] -> [NaN] }" },
3881 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3882 "{ [i] -> [NaN] }" },
3883 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3884 "{ [i] -> [NaN] }" },
3885 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3886 "{ [i] -> [NaN] }" },
3887 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
3888 "{ [i] -> [NaN] }" },
3889 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
3890 "{ [i] -> [NaN] }" },
3893 /* Perform some basic tests of binary operations on isl_aff objects.
3895 static int test_bin_aff(isl_ctx
*ctx
)
3898 isl_aff
*aff1
, *aff2
, *res
;
3899 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3900 __isl_take isl_aff
*aff2
);
3903 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
3904 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
3905 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
3906 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
3907 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
3908 aff1
= fn(aff1
, aff2
);
3909 if (isl_aff_is_nan(res
))
3910 ok
= isl_aff_is_nan(aff1
);
3912 ok
= isl_aff_plain_is_equal(aff1
, res
);
3918 isl_die(ctx
, isl_error_unknown
,
3919 "unexpected result", return -1);
3926 __isl_give isl_union_pw_multi_aff
*(*fn
)(
3927 __isl_take isl_union_pw_multi_aff
*upma1
,
3928 __isl_take isl_union_pw_multi_aff
*upma2
);
3932 } upma_bin_tests
[] = {
3933 { &isl_union_pw_multi_aff_add
, "{ A[] -> [0]; B[0] -> [1] }",
3934 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
3935 { &isl_union_pw_multi_aff_union_add
, "{ A[] -> [0]; B[0] -> [1] }",
3936 "{ B[x] -> [2] : x >= 0 }",
3937 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
3938 { &isl_union_pw_multi_aff_pullback_union_pw_multi_aff
,
3939 "{ A[] -> B[0]; C[x] -> B[1] : x < 10; C[y] -> B[2] : y >= 10 }",
3940 "{ D[i] -> A[] : i < 0; D[i] -> C[i + 5] : i >= 0 }",
3941 "{ D[i] -> B[0] : i < 0; D[i] -> B[1] : 0 <= i < 5; "
3942 "D[i] -> B[2] : i >= 5 }" },
3943 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
3944 "{ B[x] -> C[2] : x > 0 }",
3945 "{ B[x] -> A[1] : x <= 0; B[x] -> C[2] : x > 0 }" },
3946 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
3947 "{ B[x] -> A[2] : x >= 0 }",
3948 "{ B[x] -> A[1] : x < 0; B[x] -> A[2] : x > 0; B[0] -> A[3] }" },
3951 /* Perform some basic tests of binary operations on
3952 * isl_union_pw_multi_aff objects.
3954 static int test_bin_upma(isl_ctx
*ctx
)
3957 isl_union_pw_multi_aff
*upma1
, *upma2
, *res
;
3960 for (i
= 0; i
< ARRAY_SIZE(upma_bin_tests
); ++i
) {
3961 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
3962 upma_bin_tests
[i
].arg1
);
3963 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
3964 upma_bin_tests
[i
].arg2
);
3965 res
= isl_union_pw_multi_aff_read_from_str(ctx
,
3966 upma_bin_tests
[i
].res
);
3967 upma1
= upma_bin_tests
[i
].fn(upma1
, upma2
);
3968 ok
= isl_union_pw_multi_aff_plain_is_equal(upma1
, res
);
3969 isl_union_pw_multi_aff_free(upma1
);
3970 isl_union_pw_multi_aff_free(res
);
3974 isl_die(ctx
, isl_error_unknown
,
3975 "unexpected result", return -1);
3982 __isl_give isl_union_pw_multi_aff
*(*fn
)(
3983 __isl_take isl_union_pw_multi_aff
*upma1
,
3984 __isl_take isl_union_pw_multi_aff
*upma2
);
3987 } upma_bin_fail_tests
[] = {
3988 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
3989 "{ B[x] -> C[2] : x >= 0 }" },
3992 /* Perform some basic tests of binary operations on
3993 * isl_union_pw_multi_aff objects that are expected to fail.
3995 static int test_bin_upma_fail(isl_ctx
*ctx
)
3998 isl_union_pw_multi_aff
*upma1
, *upma2
;
4001 on_error
= isl_options_get_on_error(ctx
);
4002 isl_options_set_on_error(ctx
, ISL_ON_ERROR_CONTINUE
);
4003 n
= ARRAY_SIZE(upma_bin_fail_tests
);
4004 for (i
= 0; i
< n
; ++i
) {
4005 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4006 upma_bin_fail_tests
[i
].arg1
);
4007 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4008 upma_bin_fail_tests
[i
].arg2
);
4009 upma1
= upma_bin_fail_tests
[i
].fn(upma1
, upma2
);
4010 isl_union_pw_multi_aff_free(upma1
);
4014 isl_options_set_on_error(ctx
, on_error
);
4016 isl_die(ctx
, isl_error_unknown
,
4017 "operation not expected to succeed", return -1);
4022 int test_aff(isl_ctx
*ctx
)
4027 isl_local_space
*ls
;
4031 if (test_bin_aff(ctx
) < 0)
4033 if (test_bin_upma(ctx
) < 0)
4035 if (test_bin_upma_fail(ctx
) < 0)
4038 space
= isl_space_set_alloc(ctx
, 0, 1);
4039 ls
= isl_local_space_from_space(space
);
4040 aff
= isl_aff_zero_on_domain(ls
);
4042 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4043 aff
= isl_aff_scale_down_ui(aff
, 3);
4044 aff
= isl_aff_floor(aff
);
4045 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4046 aff
= isl_aff_scale_down_ui(aff
, 2);
4047 aff
= isl_aff_floor(aff
);
4048 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4051 set
= isl_set_read_from_str(ctx
, str
);
4052 aff
= isl_aff_gist(aff
, set
);
4054 aff
= isl_aff_add_constant_si(aff
, -16);
4055 zero
= isl_aff_plain_is_zero(aff
);
4061 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4063 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
4064 aff
= isl_aff_scale_down_ui(aff
, 64);
4065 aff
= isl_aff_floor(aff
);
4066 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
4074 int test_dim_max(isl_ctx
*ctx
)
4078 isl_set
*set1
, *set2
;
4083 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
4084 set
= isl_set_read_from_str(ctx
, str
);
4085 pwaff
= isl_set_dim_max(set
, 0);
4086 set1
= isl_set_from_pw_aff(pwaff
);
4087 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
4088 set2
= isl_set_read_from_str(ctx
, str
);
4089 equal
= isl_set_is_equal(set1
, set2
);
4095 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4097 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
4098 set
= isl_set_read_from_str(ctx
, str
);
4099 pwaff
= isl_set_dim_max(set
, 0);
4100 set1
= isl_set_from_pw_aff(pwaff
);
4101 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4102 set2
= isl_set_read_from_str(ctx
, str
);
4103 equal
= isl_set_is_equal(set1
, set2
);
4109 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4111 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
4112 set
= isl_set_read_from_str(ctx
, str
);
4113 pwaff
= isl_set_dim_max(set
, 0);
4114 set1
= isl_set_from_pw_aff(pwaff
);
4115 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4116 set2
= isl_set_read_from_str(ctx
, str
);
4117 equal
= isl_set_is_equal(set1
, set2
);
4123 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4125 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
4126 "0 <= i < N and 0 <= j < M }";
4127 map
= isl_map_read_from_str(ctx
, str
);
4128 set
= isl_map_range(map
);
4130 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
4131 set1
= isl_set_from_pw_aff(pwaff
);
4132 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
4133 set2
= isl_set_read_from_str(ctx
, str
);
4134 equal
= isl_set_is_equal(set1
, set2
);
4138 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
4139 set1
= isl_set_from_pw_aff(pwaff
);
4140 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
4141 set2
= isl_set_read_from_str(ctx
, str
);
4142 if (equal
>= 0 && equal
)
4143 equal
= isl_set_is_equal(set1
, set2
);
4152 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4154 /* Check that solutions are properly merged. */
4155 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
4156 "c <= -1 + n - 4a - 2b and c >= -2b and "
4157 "4a >= -4 + n and c >= 0 }";
4158 set
= isl_set_read_from_str(ctx
, str
);
4159 pwaff
= isl_set_dim_min(set
, 2);
4160 set1
= isl_set_from_pw_aff(pwaff
);
4161 str
= "[n] -> { [(0)] : n >= 1 }";
4162 set2
= isl_set_read_from_str(ctx
, str
);
4163 equal
= isl_set_is_equal(set1
, set2
);
4170 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4172 /* Check that empty solution lie in the right space. */
4173 str
= "[n] -> { [t,a] : 1 = 0 }";
4174 set
= isl_set_read_from_str(ctx
, str
);
4175 pwaff
= isl_set_dim_max(set
, 0);
4176 set1
= isl_set_from_pw_aff(pwaff
);
4177 str
= "[n] -> { [t] : 1 = 0 }";
4178 set2
= isl_set_read_from_str(ctx
, str
);
4179 equal
= isl_set_is_equal(set1
, set2
);
4186 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4191 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
4193 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
4197 isl_pw_multi_aff
*pma2
;
4203 ctx
= isl_pw_multi_aff_get_ctx(pma
);
4204 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4205 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
4206 isl_pw_multi_aff_free(pma2
);
4211 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
4212 * represented by "str".
4214 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
4219 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
4223 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
4224 "result not as expected", return -1);
4228 /* Basic test for isl_pw_multi_aff_product.
4230 * Check that multiple pieces are properly handled.
4232 static int test_product_pma(isl_ctx
*ctx
)
4236 isl_pw_multi_aff
*pma1
, *pma2
;
4238 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
4239 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4240 str
= "{ C[] -> D[] }";
4241 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4242 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
4243 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
4244 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
4245 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
4246 isl_pw_multi_aff_free(pma1
);
4253 int test_product(isl_ctx
*ctx
)
4257 isl_union_set
*uset1
, *uset2
;
4261 set
= isl_set_read_from_str(ctx
, str
);
4262 set
= isl_set_product(set
, isl_set_copy(set
));
4263 ok
= isl_set_is_wrapping(set
);
4268 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4271 uset1
= isl_union_set_read_from_str(ctx
, str
);
4272 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
4273 str
= "{ [[] -> []] }";
4274 uset2
= isl_union_set_read_from_str(ctx
, str
);
4275 ok
= isl_union_set_is_equal(uset1
, uset2
);
4276 isl_union_set_free(uset1
);
4277 isl_union_set_free(uset2
);
4281 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4283 if (test_product_pma(ctx
) < 0)
4289 /* Check that two sets are not considered disjoint just because
4290 * they have a different set of (named) parameters.
4292 static int test_disjoint(isl_ctx
*ctx
)
4295 isl_set
*set
, *set2
;
4298 str
= "[n] -> { [[]->[]] }";
4299 set
= isl_set_read_from_str(ctx
, str
);
4300 str
= "{ [[]->[]] }";
4301 set2
= isl_set_read_from_str(ctx
, str
);
4302 disjoint
= isl_set_is_disjoint(set
, set2
);
4308 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4313 int test_equal(isl_ctx
*ctx
)
4316 isl_set
*set
, *set2
;
4320 set
= isl_set_read_from_str(ctx
, str
);
4322 set2
= isl_set_read_from_str(ctx
, str
);
4323 equal
= isl_set_is_equal(set
, set2
);
4329 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4334 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
4335 enum isl_dim_type type
, unsigned pos
, int fixed
)
4339 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
4346 isl_die(ctx
, isl_error_unknown
,
4347 "map not detected as fixed", return -1);
4349 isl_die(ctx
, isl_error_unknown
,
4350 "map detected as fixed", return -1);
4353 int test_fixed(isl_ctx
*ctx
)
4358 str
= "{ [i] -> [i] }";
4359 map
= isl_map_read_from_str(ctx
, str
);
4360 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
4362 str
= "{ [i] -> [1] }";
4363 map
= isl_map_read_from_str(ctx
, str
);
4364 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4366 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
4367 map
= isl_map_read_from_str(ctx
, str
);
4368 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4370 map
= isl_map_read_from_str(ctx
, str
);
4371 map
= isl_map_neg(map
);
4372 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4378 struct isl_vertices_test_data
{
4381 const char *vertex
[2];
4382 } vertices_tests
[] = {
4383 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
4384 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
4385 { "{ A[t, i] : t = 14 and i = 1 }",
4386 1, { "{ A[14, 1] }" } },
4389 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
4391 static isl_stat
find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
4393 struct isl_vertices_test_data
*data
= user
;
4396 isl_basic_set
*bset
;
4397 isl_pw_multi_aff
*pma
;
4401 ctx
= isl_vertex_get_ctx(vertex
);
4402 bset
= isl_vertex_get_domain(vertex
);
4403 ma
= isl_vertex_get_expr(vertex
);
4404 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
4406 for (i
= 0; i
< data
->n
; ++i
) {
4407 isl_pw_multi_aff
*pma_i
;
4409 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
4410 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
4411 isl_pw_multi_aff_free(pma_i
);
4413 if (equal
< 0 || equal
)
4417 isl_pw_multi_aff_free(pma
);
4418 isl_vertex_free(vertex
);
4421 return isl_stat_error
;
4423 return equal
? isl_stat_ok
: isl_stat_error
;
4426 int test_vertices(isl_ctx
*ctx
)
4430 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
4431 isl_basic_set
*bset
;
4432 isl_vertices
*vertices
;
4436 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
4437 vertices
= isl_basic_set_compute_vertices(bset
);
4438 n
= isl_vertices_get_n_vertices(vertices
);
4439 if (vertices_tests
[i
].n
!= n
)
4441 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
4442 &vertices_tests
[i
]) < 0)
4444 isl_vertices_free(vertices
);
4445 isl_basic_set_free(bset
);
4450 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
4457 int test_union_pw(isl_ctx
*ctx
)
4461 isl_union_set
*uset
;
4462 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
4464 str
= "{ [x] -> x^2 }";
4465 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
4466 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
4467 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
4468 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
4469 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
4470 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
4471 isl_union_pw_qpolynomial_free(upwqp1
);
4472 isl_union_pw_qpolynomial_free(upwqp2
);
4476 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4481 /* Test that isl_union_pw_qpolynomial_eval picks up the function
4482 * defined over the correct domain space.
4484 static int test_eval(isl_ctx
*ctx
)
4489 isl_union_pw_qpolynomial
*upwqp
;
4493 str
= "{ A[x] -> x^2; B[x] -> -x^2 }";
4494 upwqp
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
4496 set
= isl_set_read_from_str(ctx
, str
);
4497 pnt
= isl_set_sample_point(set
);
4498 v
= isl_union_pw_qpolynomial_eval(upwqp
, pnt
);
4499 cmp
= isl_val_cmp_si(v
, 36);
4505 isl_die(ctx
, isl_error_unknown
, "unexpected value", return -1);
4510 int test_output(isl_ctx
*ctx
)
4518 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
4519 pa
= isl_pw_aff_read_from_str(ctx
, str
);
4521 p
= isl_printer_to_str(ctx
);
4522 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
4523 p
= isl_printer_print_pw_aff(p
, pa
);
4524 s
= isl_printer_get_str(p
);
4525 isl_printer_free(p
);
4526 isl_pw_aff_free(pa
);
4530 equal
= !strcmp(s
, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
4535 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4540 int test_sample(isl_ctx
*ctx
)
4543 isl_basic_set
*bset1
, *bset2
;
4546 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
4547 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
4548 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
4549 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
4550 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
4551 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
4552 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
4553 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
4554 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
4555 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
4556 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
4557 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
4558 "d - 1073741821e and "
4559 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
4560 "3j >= 1 - a + b + 2e and "
4561 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
4562 "3i <= 4 - a + 4b - e and "
4563 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
4564 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
4565 "c <= -1 + a and 3i >= -2 - a + 3e and "
4566 "1073741822e <= 1073741823 - a + 1073741822b + c and "
4567 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
4568 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
4569 "1073741823e >= 1 + 1073741823b - d and "
4570 "3i >= 1073741823b + c - 1073741823e - f and "
4571 "3i >= 1 + 2b + e + 3g }";
4572 bset1
= isl_basic_set_read_from_str(ctx
, str
);
4573 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
4574 empty
= isl_basic_set_is_empty(bset2
);
4575 subset
= isl_basic_set_is_subset(bset2
, bset1
);
4576 isl_basic_set_free(bset1
);
4577 isl_basic_set_free(bset2
);
4578 if (empty
< 0 || subset
< 0)
4581 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
4583 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
4588 int test_fixed_power(isl_ctx
*ctx
)
4596 str
= "{ [i] -> [i + 1] }";
4597 map
= isl_map_read_from_str(ctx
, str
);
4598 isl_int_set_si(exp
, 23);
4599 map
= isl_map_fixed_power(map
, exp
);
4600 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
4609 int test_slice(isl_ctx
*ctx
)
4615 str
= "{ [i] -> [j] }";
4616 map
= isl_map_read_from_str(ctx
, str
);
4617 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4618 equal
= map_check_equal(map
, "{ [i] -> [i] }");
4623 str
= "{ [i] -> [j] }";
4624 map
= isl_map_read_from_str(ctx
, str
);
4625 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4626 equal
= map_check_equal(map
, "{ [i] -> [j] }");
4631 str
= "{ [i] -> [j] }";
4632 map
= isl_map_read_from_str(ctx
, str
);
4633 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4634 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
4639 str
= "{ [i] -> [j] }";
4640 map
= isl_map_read_from_str(ctx
, str
);
4641 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4642 equal
= map_check_equal(map
, "{ [0] -> [j] }");
4647 str
= "{ [i] -> [j] }";
4648 map
= isl_map_read_from_str(ctx
, str
);
4649 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4650 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
4655 str
= "{ [i] -> [j] }";
4656 map
= isl_map_read_from_str(ctx
, str
);
4657 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4658 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
4666 int test_eliminate(isl_ctx
*ctx
)
4672 str
= "{ [i] -> [j] : i = 2j }";
4673 map
= isl_map_read_from_str(ctx
, str
);
4674 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
4675 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
4683 /* Check that isl_set_dim_residue_class detects that the values of j
4684 * in the set below are all odd and that it does not detect any spurious
4687 static int test_residue_class(isl_ctx
*ctx
)
4694 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
4695 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
4696 set
= isl_set_read_from_str(ctx
, str
);
4699 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
4701 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
4702 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
4711 int test_align_parameters(isl_ctx
*ctx
)
4715 isl_multi_aff
*ma1
, *ma2
;
4718 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
4719 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
4721 space
= isl_space_params_alloc(ctx
, 1);
4722 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
4723 ma1
= isl_multi_aff_align_params(ma1
, space
);
4725 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
4726 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
4728 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
4730 isl_multi_aff_free(ma1
);
4731 isl_multi_aff_free(ma2
);
4736 isl_die(ctx
, isl_error_unknown
,
4737 "result not as expected", return -1);
4742 static int test_list(isl_ctx
*ctx
)
4744 isl_id
*a
, *b
, *c
, *d
, *id
;
4748 a
= isl_id_alloc(ctx
, "a", NULL
);
4749 b
= isl_id_alloc(ctx
, "b", NULL
);
4750 c
= isl_id_alloc(ctx
, "c", NULL
);
4751 d
= isl_id_alloc(ctx
, "d", NULL
);
4753 list
= isl_id_list_alloc(ctx
, 4);
4754 list
= isl_id_list_add(list
, a
);
4755 list
= isl_id_list_add(list
, b
);
4756 list
= isl_id_list_add(list
, c
);
4757 list
= isl_id_list_add(list
, d
);
4758 list
= isl_id_list_drop(list
, 1, 1);
4760 if (isl_id_list_n_id(list
) != 3) {
4761 isl_id_list_free(list
);
4762 isl_die(ctx
, isl_error_unknown
,
4763 "unexpected number of elements in list", return -1);
4766 id
= isl_id_list_get_id(list
, 0);
4769 id
= isl_id_list_get_id(list
, 1);
4772 id
= isl_id_list_get_id(list
, 2);
4776 isl_id_list_free(list
);
4779 isl_die(ctx
, isl_error_unknown
,
4780 "unexpected elements in list", return -1);
4785 const char *set_conversion_tests
[] = {
4786 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4787 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4788 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4789 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4790 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
4793 /* Check that converting from isl_set to isl_pw_multi_aff and back
4794 * to isl_set produces the original isl_set.
4796 static int test_set_conversion(isl_ctx
*ctx
)
4800 isl_set
*set1
, *set2
;
4801 isl_pw_multi_aff
*pma
;
4804 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
4805 str
= set_conversion_tests
[i
];
4806 set1
= isl_set_read_from_str(ctx
, str
);
4807 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
4808 set2
= isl_set_from_pw_multi_aff(pma
);
4809 equal
= isl_set_is_equal(set1
, set2
);
4816 isl_die(ctx
, isl_error_unknown
, "bad conversion",
4823 /* Check that converting from isl_map to isl_pw_multi_aff and back
4824 * to isl_map produces the original isl_map.
4826 static int test_map_conversion(isl_ctx
*ctx
)
4829 isl_map
*map1
, *map2
;
4830 isl_pw_multi_aff
*pma
;
4833 str
= "{ [a, b, c, d] -> s0[a, b, e, f] : "
4834 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4835 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4836 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4838 map1
= isl_map_read_from_str(ctx
, str
);
4839 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
4840 map2
= isl_map_from_pw_multi_aff(pma
);
4841 equal
= isl_map_is_equal(map1
, map2
);
4848 isl_die(ctx
, isl_error_unknown
, "bad conversion", return -1);
4853 static int test_conversion(isl_ctx
*ctx
)
4855 if (test_set_conversion(ctx
) < 0)
4857 if (test_map_conversion(ctx
) < 0)
4862 /* Check that isl_basic_map_curry does not modify input.
4864 static int test_curry(isl_ctx
*ctx
)
4867 isl_basic_map
*bmap1
, *bmap2
;
4870 str
= "{ [A[] -> B[]] -> C[] }";
4871 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
4872 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
4873 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
4874 isl_basic_map_free(bmap1
);
4875 isl_basic_map_free(bmap2
);
4880 isl_die(ctx
, isl_error_unknown
,
4881 "curried map should not be equal to original",
4891 } preimage_tests
[] = {
4892 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4893 "{ A[j,i] -> B[i,j] }",
4894 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4895 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4896 "{ A[a,b] -> B[a/2,b/6] }",
4897 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4898 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4899 "{ A[a,b] -> B[a/2,b/6] }",
4900 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4901 "exists i,j : a = 2 i and b = 6 j }" },
4902 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4903 "[n] -> { : 0 <= n <= 100 }" },
4904 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4905 "{ A[a] -> B[2a] }",
4906 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4907 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4908 "{ A[a] -> B[([a/2])] }",
4909 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4910 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4911 "{ A[a] -> B[a,a,a/3] }",
4912 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4913 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4914 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4917 static int test_preimage_basic_set(isl_ctx
*ctx
)
4920 isl_basic_set
*bset1
, *bset2
;
4924 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
4925 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
4926 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
4927 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
4928 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
4929 equal
= isl_basic_set_is_equal(bset1
, bset2
);
4930 isl_basic_set_free(bset1
);
4931 isl_basic_set_free(bset2
);
4935 isl_die(ctx
, isl_error_unknown
, "bad preimage",
4946 } preimage_domain_tests
[] = {
4947 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4948 "{ A[j,i] -> B[i,j] }",
4949 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4950 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4951 "{ A[i] -> B[i + 1] }",
4952 "{ A[i] -> C[i + 1] }" },
4953 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4954 "{ A[i] -> B[i + 1] }",
4955 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4956 { "{ B[i] -> C[([i/2])] }",
4957 "{ A[i] -> B[2i] }",
4958 "{ A[i] -> C[i] }" },
4959 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4960 "{ A[i] -> B[([i/5]), ([i/7])] }",
4961 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4962 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4963 "[N] -> { A[] -> B[([N/5])] }",
4964 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4965 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4966 "{ A[i] -> B[2i] }",
4967 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4968 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4969 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4970 "{ A[i] -> B[2i] }",
4971 "{ A[i] -> C[2i] }" },
4974 static int test_preimage_union_map(isl_ctx
*ctx
)
4977 isl_union_map
*umap1
, *umap2
;
4981 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
4982 umap1
= isl_union_map_read_from_str(ctx
,
4983 preimage_domain_tests
[i
].map
);
4984 ma
= isl_multi_aff_read_from_str(ctx
,
4985 preimage_domain_tests
[i
].ma
);
4986 umap2
= isl_union_map_read_from_str(ctx
,
4987 preimage_domain_tests
[i
].res
);
4988 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
4989 equal
= isl_union_map_is_equal(umap1
, umap2
);
4990 isl_union_map_free(umap1
);
4991 isl_union_map_free(umap2
);
4995 isl_die(ctx
, isl_error_unknown
, "bad preimage",
5002 static int test_preimage(isl_ctx
*ctx
)
5004 if (test_preimage_basic_set(ctx
) < 0)
5006 if (test_preimage_union_map(ctx
) < 0)
5016 } pullback_tests
[] = {
5017 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
5018 "{ A[a,b] -> C[b + 2a] }" },
5019 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
5020 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
5021 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
5022 "{ A[a] -> C[(a)/6] }" },
5023 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
5024 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
5025 "{ A[a] -> C[(2a)/3] }" },
5026 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
5027 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
5028 "{ A[i,j] -> C[i + j, i + j] }"},
5029 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
5030 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
5031 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
5032 { "{ [i, j] -> [floor((i)/4) + floor((2*i+j)/5)] }",
5033 "{ [i, j] -> [floor((i)/3), j] }",
5034 "{ [i, j] -> [(floor((i)/12) + floor((j + 2*floor((i)/3))/5))] }" },
5037 static int test_pullback(isl_ctx
*ctx
)
5040 isl_multi_aff
*ma1
, *ma2
;
5044 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
5045 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
5046 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
5047 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
5048 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
5049 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
5050 isl_multi_aff_free(ma1
);
5051 isl_multi_aff_free(ma2
);
5055 isl_die(ctx
, isl_error_unknown
, "bad pullback",
5062 /* Check that negation is printed correctly and that equal expressions
5063 * are correctly identified.
5065 static int test_ast(isl_ctx
*ctx
)
5067 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
5071 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
5072 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
5073 expr
= isl_ast_expr_add(expr1
, expr2
);
5074 expr2
= isl_ast_expr_copy(expr
);
5075 expr
= isl_ast_expr_neg(expr
);
5076 expr2
= isl_ast_expr_neg(expr2
);
5077 equal
= isl_ast_expr_is_equal(expr
, expr2
);
5078 str
= isl_ast_expr_to_str(expr
);
5079 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
5081 isl_ast_expr_free(expr
);
5082 isl_ast_expr_free(expr2
);
5084 if (ok
< 0 || equal
< 0)
5087 isl_die(ctx
, isl_error_unknown
,
5088 "equal expressions not considered equal", return -1);
5090 isl_die(ctx
, isl_error_unknown
,
5091 "isl_ast_expr printed incorrectly", return -1);
5093 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
5094 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
5095 expr
= isl_ast_expr_add(expr1
, expr2
);
5096 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
5097 expr
= isl_ast_expr_sub(expr3
, expr
);
5098 str
= isl_ast_expr_to_str(expr
);
5099 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
5101 isl_ast_expr_free(expr
);
5106 isl_die(ctx
, isl_error_unknown
,
5107 "isl_ast_expr printed incorrectly", return -1);
5112 /* Check that isl_ast_build_expr_from_set returns a valid expression
5113 * for an empty set. Note that isl_ast_build_expr_from_set getting
5114 * called on an empty set probably indicates a bug in the caller.
5116 static int test_ast_build(isl_ctx
*ctx
)
5119 isl_ast_build
*build
;
5122 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5123 build
= isl_ast_build_from_context(set
);
5125 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
5126 expr
= isl_ast_build_expr_from_set(build
, set
);
5128 isl_ast_expr_free(expr
);
5129 isl_ast_build_free(build
);
5137 /* Internal data structure for before_for and after_for callbacks.
5139 * depth is the current depth
5140 * before is the number of times before_for has been called
5141 * after is the number of times after_for has been called
5143 struct isl_test_codegen_data
{
5149 /* This function is called before each for loop in the AST generated
5150 * from test_ast_gen1.
5152 * Increment the number of calls and the depth.
5153 * Check that the space returned by isl_ast_build_get_schedule_space
5154 * matches the target space of the schedule returned by
5155 * isl_ast_build_get_schedule.
5156 * Return an isl_id that is checked by the corresponding call
5159 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
5162 struct isl_test_codegen_data
*data
= user
;
5165 isl_union_map
*schedule
;
5166 isl_union_set
*uset
;
5171 ctx
= isl_ast_build_get_ctx(build
);
5173 if (data
->before
>= 3)
5174 isl_die(ctx
, isl_error_unknown
,
5175 "unexpected number of for nodes", return NULL
);
5176 if (data
->depth
>= 2)
5177 isl_die(ctx
, isl_error_unknown
,
5178 "unexpected depth", return NULL
);
5180 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
5184 schedule
= isl_ast_build_get_schedule(build
);
5185 uset
= isl_union_map_range(schedule
);
5188 if (isl_union_set_n_set(uset
) != 1) {
5189 isl_union_set_free(uset
);
5190 isl_die(ctx
, isl_error_unknown
,
5191 "expecting single range space", return NULL
);
5194 space
= isl_ast_build_get_schedule_space(build
);
5195 set
= isl_union_set_extract_set(uset
, space
);
5196 isl_union_set_free(uset
);
5197 empty
= isl_set_is_empty(set
);
5203 isl_die(ctx
, isl_error_unknown
,
5204 "spaces don't match", return NULL
);
5206 return isl_id_alloc(ctx
, name
, NULL
);
5209 /* This function is called after each for loop in the AST generated
5210 * from test_ast_gen1.
5212 * Increment the number of calls and decrement the depth.
5213 * Check that the annotation attached to the node matches
5214 * the isl_id returned by the corresponding call to before_for.
5216 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
5217 __isl_keep isl_ast_build
*build
, void *user
)
5219 struct isl_test_codegen_data
*data
= user
;
5227 if (data
->after
> data
->before
)
5228 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5229 "mismatch in number of for nodes",
5230 return isl_ast_node_free(node
));
5232 id
= isl_ast_node_get_annotation(node
);
5234 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5235 "missing annotation", return isl_ast_node_free(node
));
5237 name
= isl_id_get_name(id
);
5238 valid
= name
&& atoi(name
+ 1) == data
->depth
;
5242 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5243 "wrong annotation", return isl_ast_node_free(node
));
5248 /* Check that the before_each_for and after_each_for callbacks
5249 * are called for each for loop in the generated code,
5250 * that they are called in the right order and that the isl_id
5251 * returned from the before_each_for callback is attached to
5252 * the isl_ast_node passed to the corresponding after_each_for call.
5254 static int test_ast_gen1(isl_ctx
*ctx
)
5258 isl_union_map
*schedule
;
5259 isl_ast_build
*build
;
5261 struct isl_test_codegen_data data
;
5263 str
= "[N] -> { : N >= 10 }";
5264 set
= isl_set_read_from_str(ctx
, str
);
5265 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
5266 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
5267 schedule
= isl_union_map_read_from_str(ctx
, str
);
5272 build
= isl_ast_build_from_context(set
);
5273 build
= isl_ast_build_set_before_each_for(build
,
5274 &before_for
, &data
);
5275 build
= isl_ast_build_set_after_each_for(build
,
5277 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5278 isl_ast_build_free(build
);
5282 isl_ast_node_free(tree
);
5284 if (data
.before
!= 3 || data
.after
!= 3)
5285 isl_die(ctx
, isl_error_unknown
,
5286 "unexpected number of for nodes", return -1);
5291 /* Check that the AST generator handles domains that are integrally disjoint
5292 * but not rationally disjoint.
5294 static int test_ast_gen2(isl_ctx
*ctx
)
5298 isl_union_map
*schedule
;
5299 isl_union_map
*options
;
5300 isl_ast_build
*build
;
5303 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
5304 schedule
= isl_union_map_read_from_str(ctx
, str
);
5305 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5306 build
= isl_ast_build_from_context(set
);
5308 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
5309 options
= isl_union_map_read_from_str(ctx
, str
);
5310 build
= isl_ast_build_set_options(build
, options
);
5311 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5312 isl_ast_build_free(build
);
5315 isl_ast_node_free(tree
);
5320 /* Increment *user on each call.
5322 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
5323 __isl_keep isl_ast_build
*build
, void *user
)
5332 /* Test that unrolling tries to minimize the number of instances.
5333 * In particular, for the schedule given below, make sure it generates
5334 * 3 nodes (rather than 101).
5336 static int test_ast_gen3(isl_ctx
*ctx
)
5340 isl_union_map
*schedule
;
5341 isl_union_map
*options
;
5342 isl_ast_build
*build
;
5346 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
5347 schedule
= isl_union_map_read_from_str(ctx
, str
);
5348 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5350 str
= "{ [i] -> unroll[0] }";
5351 options
= isl_union_map_read_from_str(ctx
, str
);
5353 build
= isl_ast_build_from_context(set
);
5354 build
= isl_ast_build_set_options(build
, options
);
5355 build
= isl_ast_build_set_at_each_domain(build
,
5356 &count_domains
, &n_domain
);
5357 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5358 isl_ast_build_free(build
);
5362 isl_ast_node_free(tree
);
5365 isl_die(ctx
, isl_error_unknown
,
5366 "unexpected number of for nodes", return -1);
5371 /* Check that if the ast_build_exploit_nested_bounds options is set,
5372 * we do not get an outer if node in the generated AST,
5373 * while we do get such an outer if node if the options is not set.
5375 static int test_ast_gen4(isl_ctx
*ctx
)
5379 isl_union_map
*schedule
;
5380 isl_ast_build
*build
;
5382 enum isl_ast_node_type type
;
5385 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
5386 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
5388 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
5390 schedule
= isl_union_map_read_from_str(ctx
, str
);
5391 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5392 build
= isl_ast_build_from_context(set
);
5393 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5394 isl_ast_build_free(build
);
5398 type
= isl_ast_node_get_type(tree
);
5399 isl_ast_node_free(tree
);
5401 if (type
== isl_ast_node_if
)
5402 isl_die(ctx
, isl_error_unknown
,
5403 "not expecting if node", return -1);
5405 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
5407 schedule
= isl_union_map_read_from_str(ctx
, str
);
5408 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5409 build
= isl_ast_build_from_context(set
);
5410 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5411 isl_ast_build_free(build
);
5415 type
= isl_ast_node_get_type(tree
);
5416 isl_ast_node_free(tree
);
5418 if (type
!= isl_ast_node_if
)
5419 isl_die(ctx
, isl_error_unknown
,
5420 "expecting if node", return -1);
5422 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
5427 /* This function is called for each leaf in the AST generated
5428 * from test_ast_gen5.
5430 * We finalize the AST generation by extending the outer schedule
5431 * with a zero-dimensional schedule. If this results in any for loops,
5432 * then this means that we did not pass along enough information
5433 * about the outer schedule to the inner AST generation.
5435 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
5438 isl_union_map
*schedule
, *extra
;
5441 schedule
= isl_ast_build_get_schedule(build
);
5442 extra
= isl_union_map_copy(schedule
);
5443 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
5444 schedule
= isl_union_map_range_product(schedule
, extra
);
5445 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5446 isl_ast_build_free(build
);
5451 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
5452 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
5453 "code should not contain any for loop",
5454 return isl_ast_node_free(tree
));
5459 /* Check that we do not lose any information when going back and
5460 * forth between internal and external schedule.
5462 * In particular, we create an AST where we unroll the only
5463 * non-constant dimension in the schedule. We therefore do
5464 * not expect any for loops in the AST. However, older versions
5465 * of isl would not pass along enough information about the outer
5466 * schedule when performing an inner code generation from a create_leaf
5467 * callback, resulting in the inner code generation producing a for loop.
5469 static int test_ast_gen5(isl_ctx
*ctx
)
5473 isl_union_map
*schedule
, *options
;
5474 isl_ast_build
*build
;
5477 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
5478 schedule
= isl_union_map_read_from_str(ctx
, str
);
5480 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
5481 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
5482 options
= isl_union_map_read_from_str(ctx
, str
);
5484 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5485 build
= isl_ast_build_from_context(set
);
5486 build
= isl_ast_build_set_options(build
, options
);
5487 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
5488 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5489 isl_ast_build_free(build
);
5490 isl_ast_node_free(tree
);
5497 static int test_ast_gen(isl_ctx
*ctx
)
5499 if (test_ast_gen1(ctx
) < 0)
5501 if (test_ast_gen2(ctx
) < 0)
5503 if (test_ast_gen3(ctx
) < 0)
5505 if (test_ast_gen4(ctx
) < 0)
5507 if (test_ast_gen5(ctx
) < 0)
5512 /* Check if dropping output dimensions from an isl_pw_multi_aff
5515 static int test_pw_multi_aff(isl_ctx
*ctx
)
5518 isl_pw_multi_aff
*pma1
, *pma2
;
5521 str
= "{ [i,j] -> [i+j, 4i-j] }";
5522 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5523 str
= "{ [i,j] -> [4i-j] }";
5524 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5526 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
5528 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
5530 isl_pw_multi_aff_free(pma1
);
5531 isl_pw_multi_aff_free(pma2
);
5535 isl_die(ctx
, isl_error_unknown
,
5536 "expressions not equal", return -1);
5541 /* Check that we can properly parse multi piecewise affine expressions
5542 * where the piecewise affine expressions have different domains.
5544 static int test_multi_pw_aff(isl_ctx
*ctx
)
5547 isl_set
*dom
, *dom2
;
5548 isl_multi_pw_aff
*mpa1
, *mpa2
;
5553 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
5554 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
5555 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
5556 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
5557 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
5558 str
= "{ [i] -> [(i : i > 0), 2i] }";
5559 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
5561 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
5563 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
5564 dom
= isl_pw_aff_domain(pa
);
5565 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
5566 dom2
= isl_pw_aff_domain(pa
);
5567 equal_domain
= isl_set_is_equal(dom
, dom2
);
5571 isl_multi_pw_aff_free(mpa1
);
5572 isl_multi_pw_aff_free(mpa2
);
5577 isl_die(ctx
, isl_error_unknown
,
5578 "expressions not equal", return -1);
5580 if (equal_domain
< 0)
5583 isl_die(ctx
, isl_error_unknown
,
5584 "domains unexpectedly equal", return -1);
5589 /* This is a regression test for a bug where isl_basic_map_simplify
5590 * would end up in an infinite loop. In particular, we construct
5591 * an empty basic set that is not obviously empty.
5592 * isl_basic_set_is_empty marks the basic set as empty.
5593 * After projecting out i3, the variable can be dropped completely,
5594 * but isl_basic_map_simplify refrains from doing so if the basic set
5595 * is empty and would end up in an infinite loop if it didn't test
5596 * explicitly for empty basic maps in the outer loop.
5598 static int test_simplify(isl_ctx
*ctx
)
5601 isl_basic_set
*bset
;
5604 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
5605 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
5606 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
5608 bset
= isl_basic_set_read_from_str(ctx
, str
);
5609 empty
= isl_basic_set_is_empty(bset
);
5610 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
5611 isl_basic_set_free(bset
);
5615 isl_die(ctx
, isl_error_unknown
,
5616 "basic set should be empty", return -1);
5621 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
5622 * with gbr context would fail to disable the use of the shifted tableau
5623 * when transferring equalities for the input to the context, resulting
5624 * in invalid sample values.
5626 static int test_partial_lexmin(isl_ctx
*ctx
)
5629 isl_basic_set
*bset
;
5630 isl_basic_map
*bmap
;
5633 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
5634 bmap
= isl_basic_map_read_from_str(ctx
, str
);
5635 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
5636 bset
= isl_basic_set_read_from_str(ctx
, str
);
5637 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
5646 /* Check that the variable compression performed on the existentially
5647 * quantified variables inside isl_basic_set_compute_divs is not confused
5648 * by the implicit equalities among the parameters.
5650 static int test_compute_divs(isl_ctx
*ctx
)
5653 isl_basic_set
*bset
;
5656 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
5657 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
5658 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
5659 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
5660 bset
= isl_basic_set_read_from_str(ctx
, str
);
5661 set
= isl_basic_set_compute_divs(bset
);
5669 /* Check that the reaching domain elements and the prefix schedule
5670 * at a leaf node are the same before and after grouping.
5672 static int test_schedule_tree_group_1(isl_ctx
*ctx
)
5677 isl_union_set
*uset
;
5678 isl_multi_union_pw_aff
*mupa
;
5679 isl_union_pw_multi_aff
*upma1
, *upma2
;
5680 isl_union_set
*domain1
, *domain2
;
5681 isl_union_map
*umap1
, *umap2
;
5682 isl_schedule_node
*node
;
5684 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10 }";
5685 uset
= isl_union_set_read_from_str(ctx
, str
);
5686 node
= isl_schedule_node_from_domain(uset
);
5687 node
= isl_schedule_node_child(node
, 0);
5688 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [9 - i] }]";
5689 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5690 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5691 node
= isl_schedule_node_child(node
, 0);
5692 str
= "[{ S1[i,j] -> [j]; S2[i,j] -> [j] }]";
5693 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5694 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5695 node
= isl_schedule_node_child(node
, 0);
5696 umap1
= isl_schedule_node_get_prefix_schedule_union_map(node
);
5697 upma1
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
5698 domain1
= isl_schedule_node_get_domain(node
);
5699 id
= isl_id_alloc(ctx
, "group", NULL
);
5700 node
= isl_schedule_node_parent(node
);
5701 node
= isl_schedule_node_group(node
, id
);
5702 node
= isl_schedule_node_child(node
, 0);
5703 umap2
= isl_schedule_node_get_prefix_schedule_union_map(node
);
5704 upma2
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
5705 domain2
= isl_schedule_node_get_domain(node
);
5706 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
5707 if (equal
>= 0 && equal
)
5708 equal
= isl_union_set_is_equal(domain1
, domain2
);
5709 if (equal
>= 0 && equal
)
5710 equal
= isl_union_map_is_equal(umap1
, umap2
);
5711 isl_union_map_free(umap1
);
5712 isl_union_map_free(umap2
);
5713 isl_union_set_free(domain1
);
5714 isl_union_set_free(domain2
);
5715 isl_union_pw_multi_aff_free(upma1
);
5716 isl_union_pw_multi_aff_free(upma2
);
5717 isl_schedule_node_free(node
);
5722 isl_die(ctx
, isl_error_unknown
,
5723 "expressions not equal", return -1);
5728 /* Check that we can have nested groupings and that the union map
5729 * schedule representation is the same before and after the grouping.
5730 * Note that after the grouping, the union map representation contains
5731 * the domain constraints from the ranges of the expansion nodes,
5732 * while they are missing from the union map representation of
5733 * the tree without expansion nodes.
5735 * Also check that the global expansion is as expected.
5737 static int test_schedule_tree_group_2(isl_ctx
*ctx
)
5739 int equal
, equal_expansion
;
5742 isl_union_set
*uset
;
5743 isl_union_map
*umap1
, *umap2
;
5744 isl_union_map
*expansion1
, *expansion2
;
5745 isl_union_set_list
*filters
;
5746 isl_multi_union_pw_aff
*mupa
;
5747 isl_schedule
*schedule
;
5748 isl_schedule_node
*node
;
5750 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10; "
5751 "S3[i,j] : 0 <= i,j < 10 }";
5752 uset
= isl_union_set_read_from_str(ctx
, str
);
5753 node
= isl_schedule_node_from_domain(uset
);
5754 node
= isl_schedule_node_child(node
, 0);
5755 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [i]; S3[i,j] -> [i] }]";
5756 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5757 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5758 node
= isl_schedule_node_child(node
, 0);
5759 str
= "{ S1[i,j] }";
5760 uset
= isl_union_set_read_from_str(ctx
, str
);
5761 filters
= isl_union_set_list_from_union_set(uset
);
5762 str
= "{ S2[i,j]; S3[i,j] }";
5763 uset
= isl_union_set_read_from_str(ctx
, str
);
5764 filters
= isl_union_set_list_add(filters
, uset
);
5765 node
= isl_schedule_node_insert_sequence(node
, filters
);
5766 node
= isl_schedule_node_child(node
, 1);
5767 node
= isl_schedule_node_child(node
, 0);
5768 str
= "{ S2[i,j] }";
5769 uset
= isl_union_set_read_from_str(ctx
, str
);
5770 filters
= isl_union_set_list_from_union_set(uset
);
5771 str
= "{ S3[i,j] }";
5772 uset
= isl_union_set_read_from_str(ctx
, str
);
5773 filters
= isl_union_set_list_add(filters
, uset
);
5774 node
= isl_schedule_node_insert_sequence(node
, filters
);
5776 schedule
= isl_schedule_node_get_schedule(node
);
5777 umap1
= isl_schedule_get_map(schedule
);
5778 uset
= isl_schedule_get_domain(schedule
);
5779 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
5780 isl_schedule_free(schedule
);
5782 node
= isl_schedule_node_parent(node
);
5783 node
= isl_schedule_node_parent(node
);
5784 id
= isl_id_alloc(ctx
, "group1", NULL
);
5785 node
= isl_schedule_node_group(node
, id
);
5786 node
= isl_schedule_node_child(node
, 1);
5787 node
= isl_schedule_node_child(node
, 0);
5788 id
= isl_id_alloc(ctx
, "group2", NULL
);
5789 node
= isl_schedule_node_group(node
, id
);
5791 schedule
= isl_schedule_node_get_schedule(node
);
5792 umap2
= isl_schedule_get_map(schedule
);
5793 isl_schedule_free(schedule
);
5795 node
= isl_schedule_node_root(node
);
5796 node
= isl_schedule_node_child(node
, 0);
5797 expansion1
= isl_schedule_node_get_subtree_expansion(node
);
5798 isl_schedule_node_free(node
);
5800 str
= "{ group1[i] -> S1[i,j] : 0 <= i,j < 10; "
5801 "group1[i] -> S2[i,j] : 0 <= i,j < 10; "
5802 "group1[i] -> S3[i,j] : 0 <= i,j < 10 }";
5804 expansion2
= isl_union_map_read_from_str(ctx
, str
);
5806 equal
= isl_union_map_is_equal(umap1
, umap2
);
5807 equal_expansion
= isl_union_map_is_equal(expansion1
, expansion2
);
5809 isl_union_map_free(umap1
);
5810 isl_union_map_free(umap2
);
5811 isl_union_map_free(expansion1
);
5812 isl_union_map_free(expansion2
);
5814 if (equal
< 0 || equal_expansion
< 0)
5817 isl_die(ctx
, isl_error_unknown
,
5818 "expressions not equal", return -1);
5819 if (!equal_expansion
)
5820 isl_die(ctx
, isl_error_unknown
,
5821 "unexpected expansion", return -1);
5826 /* Some tests for the isl_schedule_node_group function.
5828 static int test_schedule_tree_group(isl_ctx
*ctx
)
5830 if (test_schedule_tree_group_1(ctx
) < 0)
5832 if (test_schedule_tree_group_2(ctx
) < 0)
5841 { "{ rat: [i] : 0 <= i <= 10 }",
5842 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
5843 { "{ rat: [i] : FALSE }",
5844 "{ rat: coefficients[[cst] -> [a]] }" },
5846 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
5853 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
5854 "{ rat: [i] : 0 <= i <= 10 }" },
5855 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
5857 { "{ rat: coefficients[[cst] -> [a]] }",
5858 "{ rat: [i] : FALSE }" },
5861 /* Test the basic functionality of isl_basic_set_coefficients and
5862 * isl_basic_set_solutions.
5864 static int test_dual(isl_ctx
*ctx
)
5868 for (i
= 0; i
< ARRAY_SIZE(coef_tests
); ++i
) {
5870 isl_basic_set
*bset1
, *bset2
;
5872 bset1
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].set
);
5873 bset2
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].dual
);
5874 bset1
= isl_basic_set_coefficients(bset1
);
5875 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5876 isl_basic_set_free(bset1
);
5877 isl_basic_set_free(bset2
);
5881 isl_die(ctx
, isl_error_unknown
,
5882 "incorrect dual", return -1);
5885 for (i
= 0; i
< ARRAY_SIZE(sol_tests
); ++i
) {
5887 isl_basic_set
*bset1
, *bset2
;
5889 bset1
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].set
);
5890 bset2
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].dual
);
5891 bset1
= isl_basic_set_solutions(bset1
);
5892 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5893 isl_basic_set_free(bset1
);
5894 isl_basic_set_free(bset2
);
5898 isl_die(ctx
, isl_error_unknown
,
5899 "incorrect dual", return -1);
5909 const char *schedule
;
5914 { 0, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
5915 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5917 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
5918 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5920 { 1, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
5921 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5923 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
5924 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5926 { 0, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
5927 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5929 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
5930 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
5932 { 1, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
5933 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5935 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
5936 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
5940 /* Basic tiling tests. Create a schedule tree with a domain and a band node,
5941 * tile the band and then check if the tile and point bands have the
5942 * expected partial schedule.
5944 static int test_tile(isl_ctx
*ctx
)
5950 scale
= isl_options_get_tile_scale_tile_loops(ctx
);
5951 shift
= isl_options_get_tile_shift_point_loops(ctx
);
5953 for (i
= 0; i
< ARRAY_SIZE(tile_tests
); ++i
) {
5957 isl_union_set
*domain
;
5958 isl_multi_union_pw_aff
*mupa
, *mupa2
;
5959 isl_schedule_node
*node
;
5960 isl_multi_val
*sizes
;
5962 opt
= tile_tests
[i
].scale_tile
;
5963 isl_options_set_tile_scale_tile_loops(ctx
, opt
);
5964 opt
= tile_tests
[i
].shift_point
;
5965 isl_options_set_tile_shift_point_loops(ctx
, opt
);
5967 str
= tile_tests
[i
].domain
;
5968 domain
= isl_union_set_read_from_str(ctx
, str
);
5969 node
= isl_schedule_node_from_domain(domain
);
5970 node
= isl_schedule_node_child(node
, 0);
5971 str
= tile_tests
[i
].schedule
;
5972 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5973 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5974 str
= tile_tests
[i
].sizes
;
5975 sizes
= isl_multi_val_read_from_str(ctx
, str
);
5976 node
= isl_schedule_node_band_tile(node
, sizes
);
5978 str
= tile_tests
[i
].tile
;
5979 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5980 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
5981 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
, mupa2
);
5982 isl_multi_union_pw_aff_free(mupa
);
5983 isl_multi_union_pw_aff_free(mupa2
);
5985 node
= isl_schedule_node_child(node
, 0);
5987 str
= tile_tests
[i
].point
;
5988 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5989 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
5990 if (equal
>= 0 && equal
)
5991 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
,
5993 isl_multi_union_pw_aff_free(mupa
);
5994 isl_multi_union_pw_aff_free(mupa2
);
5996 isl_schedule_node_free(node
);
6001 isl_die(ctx
, isl_error_unknown
,
6002 "unexpected result", return -1);
6005 isl_options_set_tile_scale_tile_loops(ctx
, scale
);
6006 isl_options_set_tile_shift_point_loops(ctx
, shift
);
6011 /* Check that the domain hash of a space is equal to the hash
6012 * of the domain of the space.
6014 static int test_domain_hash(isl_ctx
*ctx
)
6018 uint32_t hash1
, hash2
;
6020 map
= isl_map_read_from_str(ctx
, "[n] -> { A[B[x] -> C[]] -> D[] }");
6021 space
= isl_map_get_space(map
);
6023 hash1
= isl_space_get_domain_hash(space
);
6024 space
= isl_space_domain(space
);
6025 hash2
= isl_space_get_hash(space
);
6026 isl_space_free(space
);
6031 isl_die(ctx
, isl_error_unknown
,
6032 "domain hash not equal to hash of domain", return -1);
6039 int (*fn
)(isl_ctx
*ctx
);
6041 { "domain hash", &test_domain_hash
},
6042 { "dual", &test_dual
},
6043 { "dependence analysis", &test_flow
},
6044 { "val", &test_val
},
6045 { "compute divs", &test_compute_divs
},
6046 { "partial lexmin", &test_partial_lexmin
},
6047 { "simplify", &test_simplify
},
6048 { "curry", &test_curry
},
6049 { "piecewise multi affine expressions", &test_pw_multi_aff
},
6050 { "multi piecewise affine expressions", &test_multi_pw_aff
},
6051 { "conversion", &test_conversion
},
6052 { "list", &test_list
},
6053 { "align parameters", &test_align_parameters
},
6054 { "preimage", &test_preimage
},
6055 { "pullback", &test_pullback
},
6056 { "AST", &test_ast
},
6057 { "AST build", &test_ast_build
},
6058 { "AST generation", &test_ast_gen
},
6059 { "eliminate", &test_eliminate
},
6060 { "residue class", &test_residue_class
},
6061 { "div", &test_div
},
6062 { "slice", &test_slice
},
6063 { "fixed power", &test_fixed_power
},
6064 { "sample", &test_sample
},
6065 { "output", &test_output
},
6066 { "vertices", &test_vertices
},
6067 { "fixed", &test_fixed
},
6068 { "equal", &test_equal
},
6069 { "disjoint", &test_disjoint
},
6070 { "product", &test_product
},
6071 { "dim_max", &test_dim_max
},
6072 { "affine", &test_aff
},
6073 { "injective", &test_injective
},
6074 { "schedule", &test_schedule
},
6075 { "schedule tree grouping", &test_schedule_tree_group
},
6076 { "tile", &test_tile
},
6077 { "union_pw", &test_union_pw
},
6078 { "eval", &test_eval
},
6079 { "parse", &test_parse
},
6080 { "single-valued", &test_sv
},
6081 { "affine hull", &test_affine_hull
},
6082 { "simple_hull", &test_simple_hull
},
6083 { "coalesce", &test_coalesce
},
6084 { "factorize", &test_factorize
},
6085 { "subset", &test_subset
},
6086 { "subtract", &test_subtract
},
6087 { "lexmin", &test_lexmin
},
6088 { "min", &test_min
},
6089 { "gist", &test_gist
},
6090 { "piecewise quasi-polynomials", &test_pwqp
},
6091 { "lift", &test_lift
},
6092 { "bound", &test_bound
},
6093 { "union", &test_union
},
6094 { "split periods", &test_split_periods
},
6095 { "lexicographic order", &test_lex
},
6096 { "bijectivity", &test_bijective
},
6097 { "dataflow analysis", &test_dep
},
6098 { "reading", &test_read
},
6099 { "bounded", &test_bounded
},
6100 { "construction", &test_construction
},
6101 { "dimension manipulation", &test_dim
},
6102 { "map application", &test_application
},
6103 { "convex hull", &test_convex_hull
},
6104 { "transitive closure", &test_closure
},
6107 int main(int argc
, char **argv
)
6110 struct isl_ctx
*ctx
;
6111 struct isl_options
*options
;
6113 srcdir
= getenv("srcdir");
6116 options
= isl_options_new_with_defaults();
6118 argc
= isl_options_parse(options
, argc
, argv
, ISL_ARG_ALL
);
6120 ctx
= isl_ctx_alloc_with_options(&isl_options_args
, options
);
6121 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
6122 printf("%s\n", tests
[i
].name
);
6123 if (tests
[i
].fn(ctx
) < 0)