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) }" },
1294 /* Check that no constraints on i6 are introduced in the gist */
1295 { "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((1 + i4)/2), "
1296 "e1 = floor((1530 - 4t1 - 5i4)/20), "
1297 "e2 = floor((-4t1 - 5i4 + 10*floor((1 + i4)/2))/20), "
1298 "e3 = floor((-1 + i4)/2): t2 = 0 and 2e3 = -1 + i4 and "
1299 "20e2 >= -19 - 4t1 - 5i4 + 10e0 and 5e2 <= 1 - t1 and "
1300 "2e0 <= 1 + i4 and 2e0 >= i4 and "
1301 "20e1 <= 1530 - 4t1 - 5i4 and "
1302 "20e1 >= 1511 - 4t1 - 5i4 and i4 <= 1 and "
1303 "5e1 <= 381 - t1 and 20e2 <= -4t1 - 5i4 + 10e0) }",
1304 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((-17 + i4)/2), "
1305 "e1 = floor((-t1 + i6)/5): 5e1 = -t1 + i6 and "
1306 "2e0 <= -17 + i4 and 2e0 >= -18 + i4 and "
1307 "10e0 <= -91 + 5i4 + 4i6 and "
1308 "10e0 >= -105 + 5i4 + 4i6) }",
1309 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((381 - t1)/5), "
1310 "e1 = floor((-1 + i4)/2): t2 = 0 and 2e1 = -1 + i4 and "
1311 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 >= 1511 - 4t1 - 5i4) }" },
1314 static int test_gist(struct isl_ctx
*ctx
)
1318 isl_basic_set
*bset1
, *bset2
;
1319 isl_map
*map1
, *map2
;
1322 for (i
= 0; i
< ARRAY_SIZE(gist_tests
); ++i
) {
1324 isl_set
*set1
, *set2
, *copy
;
1326 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1327 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].context
);
1328 copy
= isl_set_copy(set1
);
1329 set1
= isl_set_gist(set1
, set2
);
1330 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].gist
);
1331 equal
= isl_set_is_equal(set1
, set2
);
1334 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1335 equal_input
= isl_set_is_equal(set1
, copy
);
1338 if (equal
< 0 || equal_input
< 0)
1341 isl_die(ctx
, isl_error_unknown
,
1342 "incorrect gist result", return -1);
1344 isl_die(ctx
, isl_error_unknown
,
1345 "gist modified input", return -1);
1348 test_gist_case(ctx
, "gist1");
1350 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1351 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1352 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1353 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1354 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1355 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1356 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1357 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1358 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1359 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1360 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1361 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1362 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1363 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1364 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1365 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1366 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1367 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1368 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1369 bset1
= isl_basic_set_gist(bset1
, bset2
);
1370 assert(bset1
&& bset1
->n_div
== 0);
1371 isl_basic_set_free(bset1
);
1373 /* Check that the integer divisions of the second disjunct
1374 * do not spread to the first disjunct.
1376 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1377 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1378 "(exists (e0 = [(-1 + t1)/16], "
1379 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1380 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1381 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1382 "o0 <= 4294967295 and t1 <= -1)) }";
1383 map1
= isl_map_read_from_str(ctx
, str
);
1384 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1385 map2
= isl_map_read_from_str(ctx
, str
);
1386 map1
= isl_map_gist(map1
, map2
);
1390 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1391 isl_map_free(map1
); return -1);
1392 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1393 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1394 isl_map_free(map1
); return -1);
1400 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1402 isl_set
*set
, *set2
;
1406 set
= isl_set_read_from_str(ctx
, str
);
1407 set
= isl_set_coalesce(set
);
1408 set2
= isl_set_read_from_str(ctx
, str
);
1409 equal
= isl_set_is_equal(set
, set2
);
1410 one
= set
&& set
->n
== 1;
1417 isl_die(ctx
, isl_error_unknown
,
1418 "coalesced set not equal to input", return -1);
1419 if (check_one
&& !one
)
1420 isl_die(ctx
, isl_error_unknown
,
1421 "coalesced set should not be a union", return -1);
1426 /* Inputs for coalescing tests with unbounded wrapping.
1427 * "str" is a string representation of the input set.
1428 * "single_disjunct" is set if we expect the result to consist of
1429 * a single disjunct.
1432 int single_disjunct
;
1434 } coalesce_unbounded_tests
[] = {
1435 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1436 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1437 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1438 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1440 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1441 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1442 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1443 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1446 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1447 * option turned off.
1449 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1455 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1456 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1458 for (i
= 0; i
< ARRAY_SIZE(coalesce_unbounded_tests
); ++i
) {
1459 const char *str
= coalesce_unbounded_tests
[i
].str
;
1460 int check_one
= coalesce_unbounded_tests
[i
].single_disjunct
;
1461 if (test_coalesce_set(ctx
, str
, check_one
) >= 0)
1467 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1472 /* Inputs for coalescing tests.
1473 * "str" is a string representation of the input set.
1474 * "single_disjunct" is set if we expect the result to consist of
1475 * a single disjunct.
1478 int single_disjunct
;
1480 } coalesce_tests
[] = {
1481 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1482 "y >= x & x >= 2 & 5 >= y }" },
1483 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1484 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1485 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1486 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1487 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1488 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1489 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1490 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1491 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1492 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1493 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1494 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1495 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1496 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1497 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1498 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1499 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1500 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1501 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1502 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1503 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1504 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1505 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1506 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1507 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1508 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1509 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1510 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1511 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1512 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1513 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1514 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1515 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1516 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1517 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1518 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1519 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1520 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1521 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1522 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1523 "[o0, o1, o2, o3, o4, o5, o6]] : "
1524 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1525 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1526 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1527 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1528 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1529 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1530 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1531 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1532 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1533 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1534 "o6 >= i3 + i6 - o3 and M >= 0 and "
1535 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1536 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1537 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1538 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1539 "(o0 = 0 and M >= 2 and N >= 3) or "
1540 "(M = 0 and o0 = 0 and N >= 3) }" },
1541 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1542 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1543 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1544 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1545 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1546 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1547 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1548 "(y = 3 and x = 1) }" },
1549 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1550 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1551 "i1 <= M and i3 <= M and i4 <= M) or "
1552 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1553 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1554 "i4 <= -1 + M) }" },
1555 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1556 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1557 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1558 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1559 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1560 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1561 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1562 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1563 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1564 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1565 { 0, "{ [a, b] : exists e : 2e = a and "
1566 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1567 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1568 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1569 "j >= 1 and j' <= i + j - i' and i >= 1; "
1571 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1572 "[i,j] : exists a : j = 3a }" },
1573 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1574 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1576 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1577 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1578 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1579 "c <= 6 + 8a and a >= 3; "
1580 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1581 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1582 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1583 "[x,0] : 3 <= x <= 4 }" },
1584 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1585 "[x,0] : 4 <= x <= 5 }" },
1586 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1587 "[x,0] : 3 <= x <= 5 }" },
1588 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1589 "[x,0] : 3 <= x <= 4 }" },
1590 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1592 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1593 { 1, "{ [0,0]; [1,1] }" },
1594 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1595 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1597 "[k, 0, k] : k <= 6 and k >= 1 }" },
1598 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1599 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1600 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1601 { 1, "[n] -> { [1] : n >= 0;"
1602 "[x] : exists (e0 = floor((x)/2): x >= 2 and "
1603 "2e0 >= -1 + x and 2e0 <= x and 2e0 <= n) }" },
1604 { 1, "[n] -> { [x, y] : exists (e0 = floor((x)/2), e1 = floor((y)/3): "
1605 "3e1 = y and x >= 2 and 2e0 >= -1 + x and "
1606 "2e0 <= x and 2e0 <= n);"
1607 "[1, y] : exists (e0 = floor((y)/3): 3e0 = y and "
1609 { 1, "[t1] -> { [i0] : (exists (e0 = floor((63t1)/64): "
1610 "128e0 >= -134 + 127t1 and t1 >= 2 and "
1611 "64e0 <= 63t1 and 64e0 >= -63 + 63t1)) or "
1613 { 1, "{ [i, i] : exists (e0 = floor((1 + 2i)/3): 3e0 <= 2i and "
1614 "3e0 >= -1 + 2i and i <= 9 and i >= 1);"
1616 { 1, "{ [t1] : exists (e0 = floor((-11 + t1)/2): 2e0 = -11 + t1 and "
1617 "t1 >= 13 and t1 <= 16);"
1618 "[t1] : t1 <= 15 and t1 >= 12 }" },
1619 { 1, "{ [x,y] : x = 3y and 0 <= y <= 2; [-3,-1] }" },
1620 { 1, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-2] }" },
1621 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-2,-2] }" },
1622 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-1] }" },
1623 { 1, "{ [i] : exists j : i = 4 j and 0 <= i <= 100;"
1624 "[i] : exists j : 1 <= i <= 100 and i >= 4j + 1 and "
1626 { 1, "{ [c0] : (exists (e0 : c0 - 1 <= 3e0 <= c0)) or "
1627 "(exists (e0 : 3e0 = -2 + c0)) }" },
1628 { 0, "[n, b0, t0] -> "
1629 "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1630 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1631 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1632 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1633 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 >= 8 + n and "
1634 "3i4 <= -96 + 3t0 + i0 and 3i4 >= -95 - n + 3t0 + i0 and "
1635 "i8 >= -157 + i0 - 4i4 and i8 >= 0 and "
1636 "i8 <= -33 + i0 - 4i4 and 3i8 <= -91 + 4n - i0)) or "
1637 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1638 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1639 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1640 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 <= 7 + n and "
1641 "4i4 <= -3 + i0 and 3i4 <= -96 + 3t0 + i0 and "
1642 "3i4 >= -95 - n + 3t0 + i0 and i8 >= -157 + i0 - 4i4 and "
1643 "i8 >= 0 and i8 <= -4 + i0 - 3i4 and i8 <= -41 + i0));"
1644 "[i0, i1, i2, i3, 0, i5, i6, i7, i8, i9, i10, i11, i12] : "
1645 "(exists (e0 = floor((i8)/32): b0 = 0 and 32e0 = i8 and "
1646 "n <= 2147483647 and t0 <= 31 and t0 >= 0 and i0 >= 11 and "
1647 "i0 >= 96 - 3t0 and i0 <= 95 + n - 3t0 and i0 <= 7 + n and "
1648 "i8 >= -40 + i0 and i8 <= -10 + i0)) }" },
1649 { 0, "{ [i0, i1, i2] : "
1650 "(exists (e0, e1 = floor((i0)/32), e2 = floor((i1)/32): "
1651 "32e1 = i0 and 32e2 = i1 and i1 >= -31 + i0 and "
1652 "i1 <= 31 + i0 and i2 >= -30 + i0 and i2 >= -30 + i1 and "
1653 "32e0 >= -30 + i0 and 32e0 >= -30 + i1 and "
1654 "32e0 >= -31 + i2 and 32e0 <= 30 + i2 and 32e0 <= 31 + i1 and "
1655 "32e0 <= 31 + i0)) or "
1657 { 1, "{ [a, b, c] : 2b = 1 + a and 2c = 2 + a; [0, 0, 0] }" },
1660 /* A specialized coalescing test case that would result
1661 * in a segmentation fault or a failed assertion in earlier versions of isl.
1663 static int test_coalesce_special(struct isl_ctx
*ctx
)
1666 isl_map
*map1
, *map2
;
1668 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1669 "[[S_L309_IN[] -> T11[]] -> ce_imag2[1, o1]] : "
1670 "(y = 201 and o1 <= 239 and o1 >= 212) or "
1671 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 198 and y >= 3 and "
1672 "o1 <= 239 and o1 >= 212)) or "
1673 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 201 and y >= 3 and "
1674 "o1 <= 241 and o1 >= 240));"
1675 "[S_L220_OUT[] -> T7[]] -> "
1676 "[[S_L309_IN[] -> T11[]] -> ce_imag2[0, o1]] : "
1677 "(y = 2 and o1 <= 241 and o1 >= 212) or "
1678 "(exists (e0 = [(-2 + y)/3]: 3e0 = -2 + y and y <= 200 and "
1679 "y >= 5 and o1 <= 241 and o1 >= 212)) }";
1680 map1
= isl_map_read_from_str(ctx
, str
);
1681 map1
= isl_map_align_divs(map1
);
1682 map1
= isl_map_coalesce(map1
);
1683 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1684 "[[S_L309_IN[] -> T11[]] -> ce_imag2[o0, o1]] : "
1685 "exists (e0 = [(-1 - y + o0)/3]: 3e0 = -1 - y + o0 and "
1686 "y <= 201 and o0 <= 2 and o1 >= 212 and o1 <= 241 and "
1687 "o0 >= 3 - y and o0 <= -2 + y and o0 >= 0) }";
1688 map2
= isl_map_read_from_str(ctx
, str
);
1689 map2
= isl_map_union(map2
, map1
);
1690 map2
= isl_map_align_divs(map2
);
1691 map2
= isl_map_coalesce(map2
);
1699 /* Test the functionality of isl_set_coalesce.
1700 * That is, check that the output is always equal to the input
1701 * and in some cases that the result consists of a single disjunct.
1703 static int test_coalesce(struct isl_ctx
*ctx
)
1707 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
1708 const char *str
= coalesce_tests
[i
].str
;
1709 int check_one
= coalesce_tests
[i
].single_disjunct
;
1710 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
1714 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1716 if (test_coalesce_special(ctx
) < 0)
1722 static int test_closure(isl_ctx
*ctx
)
1726 isl_map
*up
, *right
;
1727 isl_map
*map
, *map2
;
1730 /* COCOA example 1 */
1731 map
= isl_map_read_from_str(ctx
,
1732 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1733 "1 <= i and i < n and 1 <= j and j < n or "
1734 "i2 = i + 1 and j2 = j - 1 and "
1735 "1 <= i and i < n and 2 <= j and j <= n }");
1736 map
= isl_map_power(map
, &exact
);
1740 /* COCOA example 1 */
1741 map
= isl_map_read_from_str(ctx
,
1742 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1743 "1 <= i and i < n and 1 <= j and j < n or "
1744 "i2 = i + 1 and j2 = j - 1 and "
1745 "1 <= i and i < n and 2 <= j and j <= n }");
1746 map
= isl_map_transitive_closure(map
, &exact
);
1748 map2
= isl_map_read_from_str(ctx
,
1749 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1750 "1 <= i and i < n and 1 <= j and j <= n and "
1751 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1752 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1753 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1754 assert(isl_map_is_equal(map
, map2
));
1758 map
= isl_map_read_from_str(ctx
,
1759 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1760 " 0 <= y and y <= n }");
1761 map
= isl_map_transitive_closure(map
, &exact
);
1762 map2
= isl_map_read_from_str(ctx
,
1763 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1764 " 0 <= y and y <= n }");
1765 assert(isl_map_is_equal(map
, map2
));
1769 /* COCOA example 2 */
1770 map
= isl_map_read_from_str(ctx
,
1771 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1772 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1773 "i2 = i + 2 and j2 = j - 2 and "
1774 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1775 map
= isl_map_transitive_closure(map
, &exact
);
1777 map2
= isl_map_read_from_str(ctx
,
1778 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1779 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1780 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1781 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1782 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1783 assert(isl_map_is_equal(map
, map2
));
1787 /* COCOA Fig.2 left */
1788 map
= isl_map_read_from_str(ctx
,
1789 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1790 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1792 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1793 "j <= 2 i - 3 and j <= n - 2 or "
1794 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1795 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1796 map
= isl_map_transitive_closure(map
, &exact
);
1800 /* COCOA Fig.2 right */
1801 map
= isl_map_read_from_str(ctx
,
1802 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1803 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1805 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1806 "j <= 2 i - 4 and j <= n - 3 or "
1807 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1808 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1809 map
= isl_map_power(map
, &exact
);
1813 /* COCOA Fig.2 right */
1814 map
= isl_map_read_from_str(ctx
,
1815 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1816 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1818 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1819 "j <= 2 i - 4 and j <= n - 3 or "
1820 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1821 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1822 map
= isl_map_transitive_closure(map
, &exact
);
1824 map2
= isl_map_read_from_str(ctx
,
1825 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1826 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1827 "j <= n and 3 + i + 2 j <= 3 n and "
1828 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1829 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1830 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1831 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1832 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1833 assert(isl_map_is_equal(map
, map2
));
1837 /* COCOA Fig.1 right */
1838 dom
= isl_set_read_from_str(ctx
,
1839 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1840 "2 x - 3 y + 3 >= 0 }");
1841 right
= isl_map_read_from_str(ctx
,
1842 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1843 up
= isl_map_read_from_str(ctx
,
1844 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1845 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1846 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1847 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1848 up
= isl_map_intersect_range(up
, dom
);
1849 map
= isl_map_union(up
, right
);
1850 map
= isl_map_transitive_closure(map
, &exact
);
1852 map2
= isl_map_read_from_str(ctx
,
1853 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1854 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1855 assert(isl_map_is_equal(map
, map2
));
1859 /* COCOA Theorem 1 counter example */
1860 map
= isl_map_read_from_str(ctx
,
1861 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1862 "i2 = 1 and j2 = j or "
1863 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1864 map
= isl_map_transitive_closure(map
, &exact
);
1868 map
= isl_map_read_from_str(ctx
,
1869 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1870 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1871 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1872 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1873 map
= isl_map_transitive_closure(map
, &exact
);
1877 /* Kelly et al 1996, fig 12 */
1878 map
= isl_map_read_from_str(ctx
,
1879 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1880 "1 <= i,j,j+1 <= n or "
1881 "j = n and j2 = 1 and i2 = i + 1 and "
1882 "1 <= i,i+1 <= n }");
1883 map
= isl_map_transitive_closure(map
, &exact
);
1885 map2
= isl_map_read_from_str(ctx
,
1886 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1887 "1 <= i <= n and i = i2 or "
1888 "1 <= i < i2 <= n and 1 <= j <= n and "
1890 assert(isl_map_is_equal(map
, map2
));
1894 /* Omega's closure4 */
1895 map
= isl_map_read_from_str(ctx
,
1896 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1897 "1 <= x,y <= 10 or "
1898 "x2 = x + 1 and y2 = y and "
1899 "1 <= x <= 20 && 5 <= y <= 15 }");
1900 map
= isl_map_transitive_closure(map
, &exact
);
1904 map
= isl_map_read_from_str(ctx
,
1905 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1906 map
= isl_map_transitive_closure(map
, &exact
);
1908 map2
= isl_map_read_from_str(ctx
,
1909 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1910 assert(isl_map_is_equal(map
, map2
));
1914 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1915 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1916 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1917 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1918 map
= isl_map_read_from_str(ctx
, str
);
1919 map
= isl_map_transitive_closure(map
, &exact
);
1921 map2
= isl_map_read_from_str(ctx
, str
);
1922 assert(isl_map_is_equal(map
, map2
));
1926 str
= "{[0] -> [1]; [2] -> [3]}";
1927 map
= isl_map_read_from_str(ctx
, str
);
1928 map
= isl_map_transitive_closure(map
, &exact
);
1930 map2
= isl_map_read_from_str(ctx
, str
);
1931 assert(isl_map_is_equal(map
, map2
));
1935 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1936 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1937 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1938 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1939 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1940 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1941 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1942 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1943 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1944 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1945 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1946 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1947 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1948 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1949 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1950 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1951 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1952 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1953 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1954 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1955 map
= isl_map_read_from_str(ctx
, str
);
1956 map
= isl_map_transitive_closure(map
, NULL
);
1963 static int test_lex(struct isl_ctx
*ctx
)
1969 dim
= isl_space_set_alloc(ctx
, 0, 0);
1970 map
= isl_map_lex_le(dim
);
1971 empty
= isl_map_is_empty(map
);
1977 isl_die(ctx
, isl_error_unknown
,
1978 "expecting non-empty result", return -1);
1983 static int test_lexmin(struct isl_ctx
*ctx
)
1987 isl_basic_map
*bmap
;
1988 isl_map
*map
, *map2
;
1991 isl_pw_multi_aff
*pma
;
1993 str
= "[p0, p1] -> { [] -> [] : "
1994 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1995 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1996 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1997 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1998 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1999 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
2000 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
2001 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
2002 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
2003 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
2004 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
2005 map
= isl_map_read_from_str(ctx
, str
);
2006 map
= isl_map_lexmin(map
);
2009 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
2010 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
2011 set
= isl_set_read_from_str(ctx
, str
);
2012 set
= isl_set_lexmax(set
);
2013 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
2014 set2
= isl_set_read_from_str(ctx
, str
);
2015 set
= isl_set_intersect(set
, set2
);
2016 assert(!isl_set_is_empty(set
));
2019 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
2020 map
= isl_map_read_from_str(ctx
, str
);
2021 map
= isl_map_lexmin(map
);
2022 str
= "{ [x] -> [5] : 6 <= x <= 8; "
2023 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
2024 map2
= isl_map_read_from_str(ctx
, str
);
2025 assert(isl_map_is_equal(map
, map2
));
2029 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
2030 map
= isl_map_read_from_str(ctx
, str
);
2031 map2
= isl_map_copy(map
);
2032 map
= isl_map_lexmin(map
);
2033 assert(isl_map_is_equal(map
, map2
));
2037 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
2038 map
= isl_map_read_from_str(ctx
, str
);
2039 map
= isl_map_lexmin(map
);
2040 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
2041 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
2042 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
2043 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
2044 map2
= isl_map_read_from_str(ctx
, str
);
2045 assert(isl_map_is_equal(map
, map2
));
2049 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2050 " 8i' <= i and 8i' >= -7 + i }";
2051 bmap
= isl_basic_map_read_from_str(ctx
, str
);
2052 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
2053 map2
= isl_map_from_pw_multi_aff(pma
);
2054 map
= isl_map_from_basic_map(bmap
);
2055 assert(isl_map_is_equal(map
, map2
));
2059 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
2060 map
= isl_map_read_from_str(ctx
, str
);
2061 map
= isl_map_lexmin(map
);
2062 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
2063 map2
= isl_map_read_from_str(ctx
, str
);
2064 assert(isl_map_is_equal(map
, map2
));
2068 /* Check that empty pieces are properly combined. */
2069 str
= "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
2070 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
2071 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
2072 map
= isl_map_read_from_str(ctx
, str
);
2073 map
= isl_map_lexmin(map
);
2074 str
= "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
2075 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
2077 map2
= isl_map_read_from_str(ctx
, str
);
2078 assert(isl_map_is_equal(map
, map2
));
2082 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2083 " 8i' <= i and 8i' >= -7 + i }";
2084 set
= isl_set_read_from_str(ctx
, str
);
2085 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
2086 set2
= isl_set_from_pw_multi_aff(pma
);
2087 equal
= isl_set_is_equal(set
, set2
);
2093 isl_die(ctx
, isl_error_unknown
,
2094 "unexpected difference between set and "
2095 "piecewise affine expression", return -1);
2100 /* Check that isl_set_min_val and isl_set_max_val compute the correct
2101 * result on non-convex inputs.
2103 static int test_min(struct isl_ctx
*ctx
)
2110 set
= isl_set_read_from_str(ctx
, "{ [-1]; [1] }");
2111 aff
= isl_aff_read_from_str(ctx
, "{ [x] -> [x] }");
2112 val
= isl_set_min_val(set
, aff
);
2113 min_ok
= isl_val_is_negone(val
);
2115 val
= isl_set_max_val(set
, aff
);
2116 max_ok
= isl_val_is_one(val
);
2121 if (min_ok
< 0 || max_ok
< 0)
2124 isl_die(ctx
, isl_error_unknown
,
2125 "unexpected minimum", return -1);
2127 isl_die(ctx
, isl_error_unknown
,
2128 "unexpected maximum", return -1);
2138 static isl_stat
collect_must_may(__isl_take isl_map
*dep
, int must
,
2139 void *dep_user
, void *user
)
2141 struct must_may
*mm
= (struct must_may
*)user
;
2144 mm
->must
= isl_map_union(mm
->must
, dep
);
2146 mm
->may
= isl_map_union(mm
->may
, dep
);
2151 static int common_space(void *first
, void *second
)
2153 int depth
= *(int *)first
;
2157 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
2165 map2
= isl_map_read_from_str(map
->ctx
, str
);
2166 equal
= isl_map_is_equal(map
, map2
);
2172 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
2176 equal
= map_is_equal(map
, str
);
2180 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
2181 "result not as expected", return -1);
2185 static int test_dep(struct isl_ctx
*ctx
)
2190 isl_access_info
*ai
;
2197 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2198 map
= isl_map_read_from_str(ctx
, str
);
2199 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2201 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2202 map
= isl_map_read_from_str(ctx
, str
);
2203 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2205 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2206 map
= isl_map_read_from_str(ctx
, str
);
2207 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2209 flow
= isl_access_info_compute_flow(ai
);
2210 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2211 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2212 mm
.may
= isl_map_empty(dim
);
2214 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2216 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
2217 " [1,10,0] -> [2,5,0] }";
2218 assert(map_is_equal(mm
.must
, str
));
2219 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2220 assert(map_is_equal(mm
.may
, str
));
2222 isl_map_free(mm
.must
);
2223 isl_map_free(mm
.may
);
2224 isl_flow_free(flow
);
2227 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2228 map
= isl_map_read_from_str(ctx
, str
);
2229 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2231 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2232 map
= isl_map_read_from_str(ctx
, str
);
2233 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2235 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2236 map
= isl_map_read_from_str(ctx
, str
);
2237 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2239 flow
= isl_access_info_compute_flow(ai
);
2240 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2241 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2242 mm
.may
= isl_map_empty(dim
);
2244 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2246 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2247 assert(map_is_equal(mm
.must
, str
));
2248 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2249 assert(map_is_equal(mm
.may
, str
));
2251 isl_map_free(mm
.must
);
2252 isl_map_free(mm
.may
);
2253 isl_flow_free(flow
);
2256 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2257 map
= isl_map_read_from_str(ctx
, str
);
2258 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2260 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2261 map
= isl_map_read_from_str(ctx
, str
);
2262 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2264 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2265 map
= isl_map_read_from_str(ctx
, str
);
2266 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2268 flow
= isl_access_info_compute_flow(ai
);
2269 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2270 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2271 mm
.may
= isl_map_empty(dim
);
2273 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2275 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2276 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2277 assert(map_is_equal(mm
.may
, str
));
2278 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2279 assert(map_is_equal(mm
.must
, str
));
2281 isl_map_free(mm
.must
);
2282 isl_map_free(mm
.may
);
2283 isl_flow_free(flow
);
2286 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2287 map
= isl_map_read_from_str(ctx
, str
);
2288 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2290 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2291 map
= isl_map_read_from_str(ctx
, str
);
2292 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2294 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2295 map
= isl_map_read_from_str(ctx
, str
);
2296 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2298 flow
= isl_access_info_compute_flow(ai
);
2299 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2300 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2301 mm
.may
= isl_map_empty(dim
);
2303 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2305 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2306 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2307 assert(map_is_equal(mm
.may
, str
));
2308 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2309 assert(map_is_equal(mm
.must
, str
));
2311 isl_map_free(mm
.must
);
2312 isl_map_free(mm
.may
);
2313 isl_flow_free(flow
);
2316 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2317 map
= isl_map_read_from_str(ctx
, str
);
2318 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2320 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2321 map
= isl_map_read_from_str(ctx
, str
);
2322 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2324 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2325 map
= isl_map_read_from_str(ctx
, str
);
2326 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2328 flow
= isl_access_info_compute_flow(ai
);
2329 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2330 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2331 mm
.may
= isl_map_empty(dim
);
2333 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2335 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2336 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2337 assert(map_is_equal(mm
.may
, str
));
2338 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2339 assert(map_is_equal(mm
.must
, str
));
2341 isl_map_free(mm
.must
);
2342 isl_map_free(mm
.may
);
2343 isl_flow_free(flow
);
2348 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2349 map
= isl_map_read_from_str(ctx
, str
);
2350 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2352 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2353 map
= isl_map_read_from_str(ctx
, str
);
2354 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2356 flow
= isl_access_info_compute_flow(ai
);
2357 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2358 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2359 mm
.may
= isl_map_empty(dim
);
2361 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2363 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2364 assert(map_is_equal(mm
.must
, str
));
2365 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2366 assert(map_is_equal(mm
.may
, str
));
2368 isl_map_free(mm
.must
);
2369 isl_map_free(mm
.may
);
2370 isl_flow_free(flow
);
2375 /* Check that the dependence analysis proceeds without errors.
2376 * Earlier versions of isl would break down during the analysis
2377 * due to the use of the wrong spaces.
2379 static int test_flow(isl_ctx
*ctx
)
2382 isl_union_map
*access
, *schedule
;
2383 isl_union_map
*must_dep
, *may_dep
;
2386 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2387 access
= isl_union_map_read_from_str(ctx
, str
);
2388 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2389 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2390 "S2[] -> [1,0,0,0]; "
2391 "S3[] -> [-1,0,0,0] }";
2392 schedule
= isl_union_map_read_from_str(ctx
, str
);
2393 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2394 isl_union_map_copy(access
), schedule
,
2395 &must_dep
, &may_dep
, NULL
, NULL
);
2396 isl_union_map_free(may_dep
);
2397 isl_union_map_free(must_dep
);
2406 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2407 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2408 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2409 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2410 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2411 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2412 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2413 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2414 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2417 int test_sv(isl_ctx
*ctx
)
2419 isl_union_map
*umap
;
2423 for (i
= 0; i
< ARRAY_SIZE(sv_tests
); ++i
) {
2424 umap
= isl_union_map_read_from_str(ctx
, sv_tests
[i
].map
);
2425 sv
= isl_union_map_is_single_valued(umap
);
2426 isl_union_map_free(umap
);
2429 if (sv_tests
[i
].sv
&& !sv
)
2430 isl_die(ctx
, isl_error_internal
,
2431 "map not detected as single valued", return -1);
2432 if (!sv_tests
[i
].sv
&& sv
)
2433 isl_die(ctx
, isl_error_internal
,
2434 "map detected as single valued", return -1);
2443 } bijective_tests
[] = {
2444 { "[N,M]->{[i,j] -> [i]}", 0 },
2445 { "[N,M]->{[i,j] -> [i] : j=i}", 1 },
2446 { "[N,M]->{[i,j] -> [i] : j=0}", 1 },
2447 { "[N,M]->{[i,j] -> [i] : j=N}", 1 },
2448 { "[N,M]->{[i,j] -> [j,i]}", 1 },
2449 { "[N,M]->{[i,j] -> [i+j]}", 0 },
2450 { "[N,M]->{[i,j] -> []}", 0 },
2451 { "[N,M]->{[i,j] -> [i,j,N]}", 1 },
2452 { "[N,M]->{[i,j] -> [2i]}", 0 },
2453 { "[N,M]->{[i,j] -> [i,i]}", 0 },
2454 { "[N,M]->{[i,j] -> [2i,i]}", 0 },
2455 { "[N,M]->{[i,j] -> [2i,j]}", 1 },
2456 { "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1 },
2459 static int test_bijective(struct isl_ctx
*ctx
)
2465 for (i
= 0; i
< ARRAY_SIZE(bijective_tests
); ++i
) {
2466 map
= isl_map_read_from_str(ctx
, bijective_tests
[i
].str
);
2467 bijective
= isl_map_is_bijective(map
);
2471 if (bijective_tests
[i
].bijective
&& !bijective
)
2472 isl_die(ctx
, isl_error_internal
,
2473 "map not detected as bijective", return -1);
2474 if (!bijective_tests
[i
].bijective
&& bijective
)
2475 isl_die(ctx
, isl_error_internal
,
2476 "map detected as bijective", return -1);
2482 /* Inputs for isl_pw_qpolynomial_gist tests.
2483 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2489 } pwqp_gist_tests
[] = {
2490 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2491 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2492 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2493 "{ [i] -> -1/2 + 1/2 * i }" },
2494 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2497 static int test_pwqp(struct isl_ctx
*ctx
)
2502 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
2505 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2506 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2508 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
2511 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2512 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2514 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2516 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2518 isl_pw_qpolynomial_free(pwqp1
);
2520 for (i
= 0; i
< ARRAY_SIZE(pwqp_gist_tests
); ++i
) {
2521 str
= pwqp_gist_tests
[i
].pwqp
;
2522 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2523 str
= pwqp_gist_tests
[i
].set
;
2524 set
= isl_set_read_from_str(ctx
, str
);
2525 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2526 str
= pwqp_gist_tests
[i
].gist
;
2527 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2528 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2529 equal
= isl_pw_qpolynomial_is_zero(pwqp1
);
2530 isl_pw_qpolynomial_free(pwqp1
);
2535 isl_die(ctx
, isl_error_unknown
,
2536 "unexpected result", return -1);
2539 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
2540 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2541 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
2542 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2544 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2546 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2548 isl_pw_qpolynomial_free(pwqp1
);
2550 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
2551 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2552 str
= "{ [x] -> x }";
2553 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2555 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2557 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2559 isl_pw_qpolynomial_free(pwqp1
);
2561 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2562 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2563 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2564 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
2565 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2566 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2567 isl_pw_qpolynomial_free(pwqp1
);
2569 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2570 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2571 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2572 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2573 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
2574 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
2575 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2576 isl_pw_qpolynomial_free(pwqp1
);
2577 isl_pw_qpolynomial_free(pwqp2
);
2581 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2583 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2584 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2585 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2586 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2587 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
2589 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2590 isl_pw_qpolynomial_free(pwqp1
);
2591 isl_pw_qpolynomial_free(pwqp2
);
2595 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2600 static int test_split_periods(isl_ctx
*ctx
)
2603 isl_pw_qpolynomial
*pwqp
;
2605 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2606 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2607 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2608 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2610 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
2612 isl_pw_qpolynomial_free(pwqp
);
2620 static int test_union(isl_ctx
*ctx
)
2623 isl_union_set
*uset1
, *uset2
;
2624 isl_union_map
*umap1
, *umap2
;
2627 str
= "{ [i] : 0 <= i <= 1 }";
2628 uset1
= isl_union_set_read_from_str(ctx
, str
);
2629 str
= "{ [1] -> [0] }";
2630 umap1
= isl_union_map_read_from_str(ctx
, str
);
2632 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
2633 equal
= isl_union_map_is_equal(umap1
, umap2
);
2635 isl_union_map_free(umap1
);
2636 isl_union_map_free(umap2
);
2641 isl_die(ctx
, isl_error_unknown
, "union maps not equal",
2644 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2645 umap1
= isl_union_map_read_from_str(ctx
, str
);
2646 str
= "{ A[i]; B[i] }";
2647 uset1
= isl_union_set_read_from_str(ctx
, str
);
2649 uset2
= isl_union_map_domain(umap1
);
2651 equal
= isl_union_set_is_equal(uset1
, uset2
);
2653 isl_union_set_free(uset1
);
2654 isl_union_set_free(uset2
);
2659 isl_die(ctx
, isl_error_unknown
, "union sets not equal",
2665 /* Check that computing a bound of a non-zero polynomial over an unbounded
2666 * domain does not produce a rational value.
2667 * In particular, check that the upper bound is infinity.
2669 static int test_bound_unbounded_domain(isl_ctx
*ctx
)
2672 isl_pw_qpolynomial
*pwqp
;
2673 isl_pw_qpolynomial_fold
*pwf
, *pwf2
;
2676 str
= "{ [m,n] -> -m * n }";
2677 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2678 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2680 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2681 pwf2
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2682 equal
= isl_pw_qpolynomial_fold_plain_is_equal(pwf
, pwf2
);
2683 isl_pw_qpolynomial_fold_free(pwf
);
2684 isl_pw_qpolynomial_fold_free(pwf2
);
2689 isl_die(ctx
, isl_error_unknown
,
2690 "expecting infinite polynomial bound", return -1);
2695 static int test_bound(isl_ctx
*ctx
)
2699 isl_pw_qpolynomial
*pwqp
;
2700 isl_pw_qpolynomial_fold
*pwf
;
2702 if (test_bound_unbounded_domain(ctx
) < 0)
2705 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
2706 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2707 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2708 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
2709 isl_pw_qpolynomial_fold_free(pwf
);
2711 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
2714 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2715 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2716 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2717 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
2718 isl_pw_qpolynomial_fold_free(pwf
);
2720 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
2726 static int test_lift(isl_ctx
*ctx
)
2729 isl_basic_map
*bmap
;
2730 isl_basic_set
*bset
;
2732 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
2733 bset
= isl_basic_set_read_from_str(ctx
, str
);
2734 bset
= isl_basic_set_lift(bset
);
2735 bmap
= isl_basic_map_from_range(bset
);
2736 bset
= isl_basic_map_domain(bmap
);
2737 isl_basic_set_free(bset
);
2746 } subset_tests
[] = {
2748 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2749 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2750 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2752 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2753 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2754 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2755 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2756 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2757 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2758 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2759 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2760 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2761 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2762 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2763 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2764 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2765 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2766 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2767 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2768 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2769 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2770 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2771 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2772 "4e0 <= -57 + i0 + i1)) or "
2773 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2774 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2775 "4e0 >= -61 + i0 + i1)) or "
2776 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2779 static int test_subset(isl_ctx
*ctx
)
2782 isl_set
*set1
, *set2
;
2785 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
2786 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
2787 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
2788 subset
= isl_set_is_subset(set1
, set2
);
2793 if (subset
!= subset_tests
[i
].subset
)
2794 isl_die(ctx
, isl_error_unknown
,
2795 "incorrect subset result", return -1);
2802 const char *minuend
;
2803 const char *subtrahend
;
2804 const char *difference
;
2805 } subtract_domain_tests
[] = {
2806 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2807 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2808 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2811 static int test_subtract(isl_ctx
*ctx
)
2814 isl_union_map
*umap1
, *umap2
;
2815 isl_union_pw_multi_aff
*upma1
, *upma2
;
2816 isl_union_set
*uset
;
2819 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2820 umap1
= isl_union_map_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 umap2
= isl_union_map_read_from_str(ctx
,
2825 subtract_domain_tests
[i
].difference
);
2826 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
2827 equal
= isl_union_map_is_equal(umap1
, umap2
);
2828 isl_union_map_free(umap1
);
2829 isl_union_map_free(umap2
);
2833 isl_die(ctx
, isl_error_unknown
,
2834 "incorrect subtract domain result", return -1);
2837 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2838 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
2839 subtract_domain_tests
[i
].minuend
);
2840 uset
= isl_union_set_read_from_str(ctx
,
2841 subtract_domain_tests
[i
].subtrahend
);
2842 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
2843 subtract_domain_tests
[i
].difference
);
2844 upma1
= isl_union_pw_multi_aff_subtract_domain(upma1
, uset
);
2845 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
2846 isl_union_pw_multi_aff_free(upma1
);
2847 isl_union_pw_multi_aff_free(upma2
);
2851 isl_die(ctx
, isl_error_unknown
,
2852 "incorrect subtract domain result", return -1);
2858 int test_factorize(isl_ctx
*ctx
)
2861 isl_basic_set
*bset
;
2864 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2865 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2866 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2867 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2868 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2869 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2870 "3i5 >= -2i0 - i2 + 3i4 }";
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);
2879 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2880 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2881 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2882 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2883 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2884 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2885 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2886 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2887 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2888 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2889 bset
= isl_basic_set_read_from_str(ctx
, str
);
2890 f
= isl_basic_set_factorizer(bset
);
2891 isl_basic_set_free(bset
);
2892 isl_factorizer_free(f
);
2894 isl_die(ctx
, isl_error_unknown
,
2895 "failed to construct factorizer", return -1);
2900 static isl_stat
check_injective(__isl_take isl_map
*map
, void *user
)
2902 int *injective
= user
;
2904 *injective
= isl_map_is_injective(map
);
2907 if (*injective
< 0 || !*injective
)
2908 return isl_stat_error
;
2913 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
2914 const char *r
, const char *s
, int tilable
, int parallel
)
2918 isl_union_map
*W
, *R
, *S
;
2919 isl_union_map
*empty
;
2920 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
2921 isl_union_map
*validity
, *proximity
, *coincidence
;
2922 isl_union_map
*schedule
;
2923 isl_union_map
*test
;
2924 isl_union_set
*delta
;
2925 isl_union_set
*domain
;
2929 isl_schedule_constraints
*sc
;
2930 isl_schedule
*sched
;
2931 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
2933 D
= isl_union_set_read_from_str(ctx
, d
);
2934 W
= isl_union_map_read_from_str(ctx
, w
);
2935 R
= isl_union_map_read_from_str(ctx
, r
);
2936 S
= isl_union_map_read_from_str(ctx
, s
);
2938 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
2939 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
2941 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
2942 isl_union_map_compute_flow(isl_union_map_copy(R
),
2943 isl_union_map_copy(W
), empty
,
2944 isl_union_map_copy(S
),
2945 &dep_raw
, NULL
, NULL
, NULL
);
2946 isl_union_map_compute_flow(isl_union_map_copy(W
),
2947 isl_union_map_copy(W
),
2948 isl_union_map_copy(R
),
2949 isl_union_map_copy(S
),
2950 &dep_waw
, &dep_war
, NULL
, NULL
);
2952 dep
= isl_union_map_union(dep_waw
, dep_war
);
2953 dep
= isl_union_map_union(dep
, dep_raw
);
2954 validity
= isl_union_map_copy(dep
);
2955 coincidence
= isl_union_map_copy(dep
);
2956 proximity
= isl_union_map_copy(dep
);
2958 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
2959 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
2960 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
2961 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
2962 sched
= isl_schedule_constraints_compute_schedule(sc
);
2963 schedule
= isl_schedule_get_map(sched
);
2964 isl_schedule_free(sched
);
2965 isl_union_map_free(W
);
2966 isl_union_map_free(R
);
2967 isl_union_map_free(S
);
2970 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
2972 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
2973 is_complete
= isl_union_set_is_subset(D
, domain
);
2974 isl_union_set_free(D
);
2975 isl_union_set_free(domain
);
2977 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
2978 test
= isl_union_map_apply_range(test
, dep
);
2979 test
= isl_union_map_apply_range(test
, schedule
);
2981 delta
= isl_union_map_deltas(test
);
2982 if (isl_union_set_n_set(delta
) == 0) {
2986 isl_union_set_free(delta
);
2988 delta_set
= isl_set_from_union_set(delta
);
2990 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2991 for (i
= 0; i
< tilable
; ++i
)
2992 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
2993 is_tilable
= isl_set_is_subset(delta_set
, slice
);
2994 isl_set_free(slice
);
2996 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2997 for (i
= 0; i
< parallel
; ++i
)
2998 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
2999 is_parallel
= isl_set_is_subset(delta_set
, slice
);
3000 isl_set_free(slice
);
3002 origin
= isl_set_universe(isl_set_get_space(delta_set
));
3003 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
3004 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
3006 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
3007 delta_set
= isl_set_lexmin(delta_set
);
3009 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
3011 isl_set_free(origin
);
3012 isl_set_free(delta_set
);
3015 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
3016 is_injection
< 0 || is_complete
< 0)
3019 isl_die(ctx
, isl_error_unknown
,
3020 "generated schedule incomplete", return -1);
3022 isl_die(ctx
, isl_error_unknown
,
3023 "generated schedule not injective on each statement",
3026 isl_die(ctx
, isl_error_unknown
,
3027 "negative dependences in generated schedule",
3030 isl_die(ctx
, isl_error_unknown
,
3031 "generated schedule not as tilable as expected",
3034 isl_die(ctx
, isl_error_unknown
,
3035 "generated schedule not as parallel as expected",
3041 /* Compute a schedule for the given instance set, validity constraints,
3042 * proximity constraints and context and return a corresponding union map
3045 static __isl_give isl_union_map
*compute_schedule_with_context(isl_ctx
*ctx
,
3046 const char *domain
, const char *validity
, const char *proximity
,
3047 const char *context
)
3052 isl_union_map
*prox
;
3053 isl_schedule_constraints
*sc
;
3054 isl_schedule
*schedule
;
3055 isl_union_map
*sched
;
3057 con
= isl_set_read_from_str(ctx
, context
);
3058 dom
= isl_union_set_read_from_str(ctx
, domain
);
3059 dep
= isl_union_map_read_from_str(ctx
, validity
);
3060 prox
= isl_union_map_read_from_str(ctx
, proximity
);
3061 sc
= isl_schedule_constraints_on_domain(dom
);
3062 sc
= isl_schedule_constraints_set_context(sc
, con
);
3063 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
3064 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
3065 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3066 sched
= isl_schedule_get_map(schedule
);
3067 isl_schedule_free(schedule
);
3072 /* Compute a schedule for the given instance set, validity constraints and
3073 * proximity constraints and return a corresponding union map representation.
3075 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
3076 const char *domain
, const char *validity
, const char *proximity
)
3078 return compute_schedule_with_context(ctx
, domain
, validity
, proximity
,
3082 /* Check that a schedule can be constructed on the given domain
3083 * with the given validity and proximity constraints.
3085 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
3086 const char *validity
, const char *proximity
)
3088 isl_union_map
*sched
;
3090 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
3094 isl_union_map_free(sched
);
3098 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
3099 const char *validity
, const char *proximity
, const char *expected_sched
)
3101 isl_union_map
*sched1
, *sched2
;
3104 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
3105 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
3107 equal
= isl_union_map_is_equal(sched1
, sched2
);
3108 isl_union_map_free(sched1
);
3109 isl_union_map_free(sched2
);
3114 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
3120 /* Check that the schedule map is properly padded, even after being
3121 * reconstructed from the band forest.
3123 static int test_padded_schedule(isl_ctx
*ctx
)
3127 isl_union_map
*validity
, *proximity
;
3128 isl_schedule_constraints
*sc
;
3129 isl_schedule
*sched
;
3130 isl_union_map
*map1
, *map2
;
3131 isl_band_list
*list
;
3134 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
3135 D
= isl_union_set_read_from_str(ctx
, str
);
3136 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
3137 proximity
= isl_union_map_copy(validity
);
3138 sc
= isl_schedule_constraints_on_domain(D
);
3139 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3140 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3141 sched
= isl_schedule_constraints_compute_schedule(sc
);
3142 map1
= isl_schedule_get_map(sched
);
3143 list
= isl_schedule_get_band_forest(sched
);
3144 isl_band_list_free(list
);
3145 map2
= isl_schedule_get_map(sched
);
3146 isl_schedule_free(sched
);
3147 equal
= isl_union_map_is_equal(map1
, map2
);
3148 isl_union_map_free(map1
);
3149 isl_union_map_free(map2
);
3154 isl_die(ctx
, isl_error_unknown
,
3155 "reconstructed schedule map not the same as original",
3161 /* Check that conditional validity constraints are also taken into
3162 * account across bands.
3163 * In particular, try to make sure that live ranges D[1,0]->C[2,1] and
3164 * D[2,0]->C[3,0] are not local in the outer band of the generated schedule
3165 * and then check that the adjacent order constraint C[2,1]->D[2,0]
3166 * is enforced by the rest of the schedule.
3168 static int test_special_conditional_schedule_constraints(isl_ctx
*ctx
)
3171 isl_union_set
*domain
;
3172 isl_union_map
*validity
, *proximity
, *condition
;
3173 isl_union_map
*sink
, *source
, *dep
;
3174 isl_schedule_constraints
*sc
;
3175 isl_schedule
*schedule
;
3176 isl_union_access_info
*access
;
3177 isl_union_flow
*flow
;
3180 str
= "[n] -> { C[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3181 "A[k] : k >= 1 and k <= -1 + n; "
3182 "B[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3183 "D[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k }";
3184 domain
= isl_union_set_read_from_str(ctx
, str
);
3185 sc
= isl_schedule_constraints_on_domain(domain
);
3186 str
= "[n] -> { D[k, i] -> C[1 + k, k - i] : "
3187 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3188 "D[k, i] -> C[1 + k, i] : "
3189 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3190 "D[k, 0] -> C[1 + k, k] : k >= 1 and k <= -2 + n; "
3191 "D[k, 0] -> C[1 + k, 0] : k >= 1 and k <= -2 + n }";
3192 validity
= isl_union_map_read_from_str(ctx
, str
);
3193 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3194 str
= "[n] -> { C[k, i] -> D[k, i] : "
3195 "0 <= i <= -1 + k and k <= -1 + n }";
3196 proximity
= isl_union_map_read_from_str(ctx
, str
);
3197 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3198 str
= "[n] -> { [D[k, i] -> a[]] -> [C[1 + k, k - i] -> b[]] : "
3199 "i <= -1 + k and i >= 1 and k <= -2 + n; "
3200 "[B[k, i] -> c[]] -> [B[k, 1 + i] -> c[]] : "
3201 "k <= -1 + n and i >= 0 and i <= -2 + k }";
3202 condition
= isl_union_map_read_from_str(ctx
, str
);
3203 str
= "[n] -> { [B[k, i] -> e[]] -> [D[k, i] -> a[]] : "
3204 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3205 "[C[k, i] -> b[]] -> [D[k', -1 + k - i] -> a[]] : "
3206 "i >= 0 and i <= -1 + k and k <= -1 + n and "
3207 "k' <= -1 + n and k' >= k - i and k' >= 1 + k; "
3208 "[C[k, i] -> b[]] -> [D[k, -1 + k - i] -> a[]] : "
3209 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3210 "[B[k, i] -> c[]] -> [A[k'] -> d[]] : "
3211 "k <= -1 + n and i >= 0 and i <= -1 + k and "
3212 "k' >= 1 and k' <= -1 + n and k' >= 1 + k }";
3213 validity
= isl_union_map_read_from_str(ctx
, str
);
3214 sc
= isl_schedule_constraints_set_conditional_validity(sc
, condition
,
3216 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3217 str
= "{ D[2,0] -> [] }";
3218 sink
= isl_union_map_read_from_str(ctx
, str
);
3219 access
= isl_union_access_info_from_sink(sink
);
3220 str
= "{ C[2,1] -> [] }";
3221 source
= isl_union_map_read_from_str(ctx
, str
);
3222 access
= isl_union_access_info_set_must_source(access
, source
);
3223 access
= isl_union_access_info_set_schedule(access
, schedule
);
3224 flow
= isl_union_access_info_compute_flow(access
);
3225 dep
= isl_union_flow_get_must_dependence(flow
);
3226 isl_union_flow_free(flow
);
3227 empty
= isl_union_map_is_empty(dep
);
3228 isl_union_map_free(dep
);
3233 isl_die(ctx
, isl_error_unknown
,
3234 "conditional validity not respected", return -1);
3239 /* Input for testing of schedule construction based on
3240 * conditional constraints.
3242 * domain is the iteration domain
3243 * flow are the flow dependences, which determine the validity and
3244 * proximity constraints
3245 * condition are the conditions on the conditional validity constraints
3246 * conditional_validity are the conditional validity constraints
3247 * outer_band_n is the expected number of members in the outer band
3252 const char *condition
;
3253 const char *conditional_validity
;
3255 } live_range_tests
[] = {
3256 /* Contrived example that illustrates that we need to keep
3257 * track of tagged condition dependences and
3258 * tagged conditional validity dependences
3259 * in isl_sched_edge separately.
3260 * In particular, the conditional validity constraints on A
3261 * cannot be satisfied,
3262 * but they can be ignored because there are no corresponding
3263 * condition constraints. However, we do have an additional
3264 * conditional validity constraint that maps to the same
3265 * dependence relation
3266 * as the condition constraint on B. If we did not make a distinction
3267 * between tagged condition and tagged conditional validity
3268 * dependences, then we
3269 * could end up treating this shared dependence as an condition
3270 * constraint on A, forcing a localization of the conditions,
3271 * which is impossible.
3273 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
3274 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
3275 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
3276 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3277 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3278 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
3281 /* TACO 2013 Fig. 7 */
3282 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3283 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3284 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3285 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
3286 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
3287 "0 <= i < n and 0 <= j < n - 1 }",
3288 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
3289 "0 <= i < n and 0 <= j < j' < n;"
3290 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
3291 "0 <= i < i' < n and 0 <= j,j' < n;"
3292 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
3293 "0 <= i,j,j' < n and j < j' }",
3296 /* TACO 2013 Fig. 7, without tags */
3297 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3298 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3299 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3300 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3301 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3302 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
3303 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
3304 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
3307 /* TACO 2013 Fig. 12 */
3308 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
3309 "S3[i,3] : 0 <= i <= 1 }",
3310 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
3311 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
3312 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
3313 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
3314 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3315 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
3316 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3317 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
3318 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
3319 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
3320 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
3325 /* Test schedule construction based on conditional constraints.
3326 * In particular, check the number of members in the outer band node
3327 * as an indication of whether tiling is possible or not.
3329 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
3332 isl_union_set
*domain
;
3333 isl_union_map
*condition
;
3334 isl_union_map
*flow
;
3335 isl_union_map
*validity
;
3336 isl_schedule_constraints
*sc
;
3337 isl_schedule
*schedule
;
3338 isl_schedule_node
*node
;
3341 if (test_special_conditional_schedule_constraints(ctx
) < 0)
3344 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
3345 domain
= isl_union_set_read_from_str(ctx
,
3346 live_range_tests
[i
].domain
);
3347 flow
= isl_union_map_read_from_str(ctx
,
3348 live_range_tests
[i
].flow
);
3349 condition
= isl_union_map_read_from_str(ctx
,
3350 live_range_tests
[i
].condition
);
3351 validity
= isl_union_map_read_from_str(ctx
,
3352 live_range_tests
[i
].conditional_validity
);
3353 sc
= isl_schedule_constraints_on_domain(domain
);
3354 sc
= isl_schedule_constraints_set_validity(sc
,
3355 isl_union_map_copy(flow
));
3356 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
3357 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
3358 condition
, validity
);
3359 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3360 node
= isl_schedule_get_root(schedule
);
3362 isl_schedule_node_get_type(node
) != isl_schedule_node_band
)
3363 node
= isl_schedule_node_first_child(node
);
3364 n_member
= isl_schedule_node_band_n_member(node
);
3365 isl_schedule_node_free(node
);
3366 isl_schedule_free(schedule
);
3370 if (n_member
!= live_range_tests
[i
].outer_band_n
)
3371 isl_die(ctx
, isl_error_unknown
,
3372 "unexpected number of members in outer band",
3378 /* Check that the schedule computed for the given instance set and
3379 * dependence relation strongly satisfies the dependences.
3380 * In particular, check that no instance is scheduled before
3381 * or together with an instance on which it depends.
3382 * Earlier versions of isl would produce a schedule that
3383 * only weakly satisfies the dependences.
3385 static int test_strongly_satisfying_schedule(isl_ctx
*ctx
)
3387 const char *domain
, *dep
;
3388 isl_union_map
*D
, *schedule
;
3392 domain
= "{ B[i0, i1] : 0 <= i0 <= 1 and 0 <= i1 <= 11; "
3393 "A[i0] : 0 <= i0 <= 1 }";
3394 dep
= "{ B[i0, i1] -> B[i0, 1 + i1] : 0 <= i0 <= 1 and 0 <= i1 <= 10; "
3395 "B[0, 11] -> A[1]; A[i0] -> B[i0, 0] : 0 <= i0 <= 1 }";
3396 schedule
= compute_schedule(ctx
, domain
, dep
, dep
);
3397 D
= isl_union_map_read_from_str(ctx
, dep
);
3398 D
= isl_union_map_apply_domain(D
, isl_union_map_copy(schedule
));
3399 D
= isl_union_map_apply_range(D
, schedule
);
3400 map
= isl_map_from_union_map(D
);
3401 ge
= isl_map_lex_ge(isl_space_domain(isl_map_get_space(map
)));
3402 map
= isl_map_intersect(map
, ge
);
3403 empty
= isl_map_is_empty(map
);
3409 isl_die(ctx
, isl_error_unknown
,
3410 "dependences not strongly satisfied", return -1);
3415 /* Compute a schedule for input where the instance set constraints
3416 * conflict with the context constraints.
3417 * Earlier versions of isl did not properly handle this situation.
3419 static int test_conflicting_context_schedule(isl_ctx
*ctx
)
3421 isl_union_map
*schedule
;
3422 const char *domain
, *context
;
3424 domain
= "[n] -> { A[] : n >= 0 }";
3425 context
= "[n] -> { : n < 0 }";
3426 schedule
= compute_schedule_with_context(ctx
,
3427 domain
, "{}", "{}", context
);
3428 isl_union_map_free(schedule
);
3436 /* Check that the dependence carrying step is not confused by
3437 * a bound on the coefficient size.
3438 * In particular, force the scheduler to move to a dependence carrying
3439 * step by demanding outer coincidence and bound the size of
3440 * the coefficients. Earlier versions of isl would take this
3441 * bound into account while carrying dependences, breaking
3442 * fundamental assumptions.
3444 static int test_bounded_coefficients_schedule(isl_ctx
*ctx
)
3446 const char *domain
, *dep
;
3449 isl_schedule_constraints
*sc
;
3450 isl_schedule
*schedule
;
3452 domain
= "{ C[i0, i1] : 2 <= i0 <= 3999 and 0 <= i1 <= -1 + i0 }";
3453 dep
= "{ C[i0, i1] -> C[i0, 1 + i1] : i0 <= 3999 and i1 >= 0 and "
3455 "C[i0, -1 + i0] -> C[1 + i0, 0] : i0 <= 3998 and i0 >= 1 }";
3456 I
= isl_union_set_read_from_str(ctx
, domain
);
3457 D
= isl_union_map_read_from_str(ctx
, dep
);
3458 sc
= isl_schedule_constraints_on_domain(I
);
3459 sc
= isl_schedule_constraints_set_validity(sc
, isl_union_map_copy(D
));
3460 sc
= isl_schedule_constraints_set_coincidence(sc
, D
);
3461 isl_options_set_schedule_outer_coincidence(ctx
, 1);
3462 isl_options_set_schedule_max_coefficient(ctx
, 20);
3463 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3464 isl_options_set_schedule_max_coefficient(ctx
, -1);
3465 isl_options_set_schedule_outer_coincidence(ctx
, 0);
3466 isl_schedule_free(schedule
);
3474 int test_schedule(isl_ctx
*ctx
)
3476 const char *D
, *W
, *R
, *V
, *P
, *S
;
3478 /* Handle resulting schedule with zero bands. */
3479 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
3483 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
3484 W
= "{ S1[t,i] -> a[t,i] }";
3485 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
3486 "S1[t,i] -> a[t-1,i+1] }";
3487 S
= "{ S1[t,i] -> [t,i] }";
3488 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3491 /* Fig. 5 of CC2008 */
3492 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
3494 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
3495 "j >= 2 and j <= -1 + N }";
3496 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
3497 "j >= 2 and j <= -1 + N; "
3498 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
3499 "j >= 2 and j <= -1 + N }";
3500 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3501 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3504 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
3505 W
= "{ S1[i] -> a[i] }";
3506 R
= "{ S2[i] -> a[i+1] }";
3507 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3508 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3511 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
3512 W
= "{ S1[i] -> a[i] }";
3513 R
= "{ S2[i] -> a[9-i] }";
3514 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3515 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3518 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
3519 W
= "{ S1[i] -> a[i] }";
3520 R
= "[N] -> { S2[i] -> a[N-1-i] }";
3521 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3522 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3525 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
3526 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
3527 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
3528 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
3529 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3532 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3533 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
3534 R
= "{ S2[i,j] -> a[i-1,j] }";
3535 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3536 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3539 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3540 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
3541 R
= "{ S2[i,j] -> a[i,j-1] }";
3542 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3543 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3546 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
3547 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
3548 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
3549 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
3550 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
3551 "S_0[] -> [0, 0, 0] }";
3552 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
3554 ctx
->opt
->schedule_parametric
= 0;
3555 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3557 ctx
->opt
->schedule_parametric
= 1;
3559 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
3560 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
3561 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
3562 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
3563 "S4[i] -> a[i,N] }";
3564 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
3565 "S4[i] -> [4,i,0] }";
3566 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3569 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
3570 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3572 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3574 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
3576 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3577 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3580 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
3581 " S_2[t] : t >= 0 and t <= -1 + N; "
3582 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
3584 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
3585 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
3586 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
3587 "i >= 0 and i <= -1 + N }";
3588 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
3589 "i >= 0 and i <= -1 + N; "
3590 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
3591 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
3592 " S_0[t] -> [0, t, 0] }";
3594 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3596 ctx
->opt
->schedule_parametric
= 0;
3597 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3599 ctx
->opt
->schedule_parametric
= 1;
3601 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
3602 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
3603 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
3606 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3607 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3608 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3609 "j >= 0 and j <= -1 + N; "
3610 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3611 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3612 "j >= 0 and j <= -1 + N; "
3613 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3614 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3615 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3618 D
= "{ S_0[i] : i >= 0 }";
3619 W
= "{ S_0[i] -> a[i] : i >= 0 }";
3620 R
= "{ S_0[i] -> a[0] : i >= 0 }";
3621 S
= "{ S_0[i] -> [0, i, 0] }";
3622 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3625 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3626 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3627 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3628 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3629 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3632 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3633 "k <= -1 + n and k >= 0 }";
3634 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3635 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3636 "k <= -1 + n and k >= 0; "
3637 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3638 "k <= -1 + n and k >= 0; "
3639 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3640 "k <= -1 + n and k >= 0 }";
3641 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
3642 ctx
->opt
->schedule_outer_coincidence
= 1;
3643 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3645 ctx
->opt
->schedule_outer_coincidence
= 0;
3647 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
3648 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3649 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3650 "Stmt_for_body24[i0, i1, 1, 0]:"
3651 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3652 "Stmt_for_body7[i0, i1, i2]:"
3653 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3656 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
3657 "Stmt_for_body24[1, i1, i2, i3]:"
3658 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3660 "Stmt_for_body24[0, i1, i2, i3] -> "
3661 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3662 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3664 "Stmt_for_body24[0, i1, i2, i3] ->"
3665 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3666 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3667 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3668 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3669 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3670 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3671 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3672 "i1 <= 6 and i1 >= 0;"
3673 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3674 "Stmt_for_body7[i0, i1, i2] -> "
3675 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3676 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3677 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3678 "Stmt_for_body7[i0, i1, i2] -> "
3679 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3680 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3681 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3683 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3684 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3685 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3687 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3690 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3691 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3692 "j >= 1 and j <= 7;"
3693 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3694 "j >= 1 and j <= 8 }";
3696 S
= "{ S_0[i, j] -> [i + j, j] }";
3697 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3698 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3700 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3702 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3703 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3704 "j >= 0 and j <= -1 + i }";
3705 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3706 "i <= -1 + N and j >= 0;"
3707 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3710 S
= "{ S_0[i, j] -> [i, j] }";
3711 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3712 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3714 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3716 /* Test both algorithms on a case with only proximity dependences. */
3717 D
= "{ S[i,j] : 0 <= i <= 10 }";
3719 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3720 S
= "{ S[i, j] -> [j, i] }";
3721 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3722 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3724 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3725 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3728 D
= "{ A[a]; B[] }";
3730 P
= "{ A[a] -> B[] }";
3731 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3734 if (test_padded_schedule(ctx
) < 0)
3737 /* Check that check for progress is not confused by rational
3740 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3741 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3743 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3744 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3746 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3747 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3749 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3751 /* Check that we allow schedule rows that are only non-trivial
3752 * on some full-dimensional domains.
3754 D
= "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
3755 V
= "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
3756 "S1[j] -> S2[1] : 0 <= j <= 1 }";
3758 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3759 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3761 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3763 if (test_conditional_schedule_constraints(ctx
) < 0)
3766 if (test_strongly_satisfying_schedule(ctx
) < 0)
3769 if (test_conflicting_context_schedule(ctx
) < 0)
3772 if (test_bounded_coefficients_schedule(ctx
) < 0)
3778 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
3780 isl_union_map
*umap
;
3783 umap
= isl_union_map_read_from_str(ctx
, str
);
3784 test
= isl_union_map_plain_is_injective(umap
);
3785 isl_union_map_free(umap
);
3788 if (test
== injective
)
3791 isl_die(ctx
, isl_error_unknown
,
3792 "map not detected as injective", return -1);
3794 isl_die(ctx
, isl_error_unknown
,
3795 "map detected as injective", return -1);
3798 int test_injective(isl_ctx
*ctx
)
3802 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3804 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
3806 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
3808 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
3810 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3812 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3814 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3816 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3819 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3820 if (test_plain_injective(ctx
, str
, 1))
3822 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3823 if (test_plain_injective(ctx
, str
, 0))
3829 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
3837 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
3838 equal
= isl_aff_plain_is_equal(aff
, aff2
);
3844 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
3848 equal
= aff_plain_is_equal(aff
, str
);
3852 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
3853 "result not as expected", return -1);
3858 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3859 __isl_take isl_aff
*aff2
);
3861 ['+'] = { &isl_aff_add
},
3862 ['-'] = { &isl_aff_sub
},
3863 ['*'] = { &isl_aff_mul
},
3864 ['/'] = { &isl_aff_div
},
3872 } aff_bin_tests
[] = {
3873 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3874 "{ [i] -> [2i] }" },
3875 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3877 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3878 "{ [i] -> [2i] }" },
3879 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3880 "{ [i] -> [2i] }" },
3881 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
3882 "{ [i] -> [i/2] }" },
3883 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
3885 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3886 "{ [i] -> [NaN] }" },
3887 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3888 "{ [i] -> [NaN] }" },
3889 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3890 "{ [i] -> [NaN] }" },
3891 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3892 "{ [i] -> [NaN] }" },
3893 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
3894 "{ [i] -> [NaN] }" },
3895 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
3896 "{ [i] -> [NaN] }" },
3897 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3898 "{ [i] -> [NaN] }" },
3899 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3900 "{ [i] -> [NaN] }" },
3901 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3902 "{ [i] -> [NaN] }" },
3903 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3904 "{ [i] -> [NaN] }" },
3905 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
3906 "{ [i] -> [NaN] }" },
3907 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
3908 "{ [i] -> [NaN] }" },
3911 /* Perform some basic tests of binary operations on isl_aff objects.
3913 static int test_bin_aff(isl_ctx
*ctx
)
3916 isl_aff
*aff1
, *aff2
, *res
;
3917 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3918 __isl_take isl_aff
*aff2
);
3921 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
3922 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
3923 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
3924 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
3925 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
3926 aff1
= fn(aff1
, aff2
);
3927 if (isl_aff_is_nan(res
))
3928 ok
= isl_aff_is_nan(aff1
);
3930 ok
= isl_aff_plain_is_equal(aff1
, res
);
3936 isl_die(ctx
, isl_error_unknown
,
3937 "unexpected result", return -1);
3944 __isl_give isl_union_pw_multi_aff
*(*fn
)(
3945 __isl_take isl_union_pw_multi_aff
*upma1
,
3946 __isl_take isl_union_pw_multi_aff
*upma2
);
3950 } upma_bin_tests
[] = {
3951 { &isl_union_pw_multi_aff_add
, "{ A[] -> [0]; B[0] -> [1] }",
3952 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
3953 { &isl_union_pw_multi_aff_union_add
, "{ A[] -> [0]; B[0] -> [1] }",
3954 "{ B[x] -> [2] : x >= 0 }",
3955 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
3956 { &isl_union_pw_multi_aff_pullback_union_pw_multi_aff
,
3957 "{ A[] -> B[0]; C[x] -> B[1] : x < 10; C[y] -> B[2] : y >= 10 }",
3958 "{ D[i] -> A[] : i < 0; D[i] -> C[i + 5] : i >= 0 }",
3959 "{ D[i] -> B[0] : i < 0; D[i] -> B[1] : 0 <= i < 5; "
3960 "D[i] -> B[2] : i >= 5 }" },
3961 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
3962 "{ B[x] -> C[2] : x > 0 }",
3963 "{ B[x] -> A[1] : x <= 0; B[x] -> C[2] : x > 0 }" },
3964 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
3965 "{ B[x] -> A[2] : x >= 0 }",
3966 "{ B[x] -> A[1] : x < 0; B[x] -> A[2] : x > 0; B[0] -> A[3] }" },
3969 /* Perform some basic tests of binary operations on
3970 * isl_union_pw_multi_aff objects.
3972 static int test_bin_upma(isl_ctx
*ctx
)
3975 isl_union_pw_multi_aff
*upma1
, *upma2
, *res
;
3978 for (i
= 0; i
< ARRAY_SIZE(upma_bin_tests
); ++i
) {
3979 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
3980 upma_bin_tests
[i
].arg1
);
3981 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
3982 upma_bin_tests
[i
].arg2
);
3983 res
= isl_union_pw_multi_aff_read_from_str(ctx
,
3984 upma_bin_tests
[i
].res
);
3985 upma1
= upma_bin_tests
[i
].fn(upma1
, upma2
);
3986 ok
= isl_union_pw_multi_aff_plain_is_equal(upma1
, res
);
3987 isl_union_pw_multi_aff_free(upma1
);
3988 isl_union_pw_multi_aff_free(res
);
3992 isl_die(ctx
, isl_error_unknown
,
3993 "unexpected result", return -1);
4000 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4001 __isl_take isl_union_pw_multi_aff
*upma1
,
4002 __isl_take isl_union_pw_multi_aff
*upma2
);
4005 } upma_bin_fail_tests
[] = {
4006 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4007 "{ B[x] -> C[2] : x >= 0 }" },
4010 /* Perform some basic tests of binary operations on
4011 * isl_union_pw_multi_aff objects that are expected to fail.
4013 static int test_bin_upma_fail(isl_ctx
*ctx
)
4016 isl_union_pw_multi_aff
*upma1
, *upma2
;
4019 on_error
= isl_options_get_on_error(ctx
);
4020 isl_options_set_on_error(ctx
, ISL_ON_ERROR_CONTINUE
);
4021 n
= ARRAY_SIZE(upma_bin_fail_tests
);
4022 for (i
= 0; i
< n
; ++i
) {
4023 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4024 upma_bin_fail_tests
[i
].arg1
);
4025 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4026 upma_bin_fail_tests
[i
].arg2
);
4027 upma1
= upma_bin_fail_tests
[i
].fn(upma1
, upma2
);
4028 isl_union_pw_multi_aff_free(upma1
);
4032 isl_options_set_on_error(ctx
, on_error
);
4034 isl_die(ctx
, isl_error_unknown
,
4035 "operation not expected to succeed", return -1);
4040 int test_aff(isl_ctx
*ctx
)
4045 isl_local_space
*ls
;
4049 if (test_bin_aff(ctx
) < 0)
4051 if (test_bin_upma(ctx
) < 0)
4053 if (test_bin_upma_fail(ctx
) < 0)
4056 space
= isl_space_set_alloc(ctx
, 0, 1);
4057 ls
= isl_local_space_from_space(space
);
4058 aff
= isl_aff_zero_on_domain(ls
);
4060 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4061 aff
= isl_aff_scale_down_ui(aff
, 3);
4062 aff
= isl_aff_floor(aff
);
4063 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4064 aff
= isl_aff_scale_down_ui(aff
, 2);
4065 aff
= isl_aff_floor(aff
);
4066 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4069 set
= isl_set_read_from_str(ctx
, str
);
4070 aff
= isl_aff_gist(aff
, set
);
4072 aff
= isl_aff_add_constant_si(aff
, -16);
4073 zero
= isl_aff_plain_is_zero(aff
);
4079 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4081 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
4082 aff
= isl_aff_scale_down_ui(aff
, 64);
4083 aff
= isl_aff_floor(aff
);
4084 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
4092 int test_dim_max(isl_ctx
*ctx
)
4096 isl_set
*set1
, *set2
;
4101 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
4102 set
= isl_set_read_from_str(ctx
, str
);
4103 pwaff
= isl_set_dim_max(set
, 0);
4104 set1
= isl_set_from_pw_aff(pwaff
);
4105 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
4106 set2
= isl_set_read_from_str(ctx
, str
);
4107 equal
= isl_set_is_equal(set1
, set2
);
4113 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4115 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
4116 set
= isl_set_read_from_str(ctx
, str
);
4117 pwaff
= isl_set_dim_max(set
, 0);
4118 set1
= isl_set_from_pw_aff(pwaff
);
4119 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4120 set2
= isl_set_read_from_str(ctx
, str
);
4121 equal
= isl_set_is_equal(set1
, set2
);
4127 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4129 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
4130 set
= isl_set_read_from_str(ctx
, str
);
4131 pwaff
= isl_set_dim_max(set
, 0);
4132 set1
= isl_set_from_pw_aff(pwaff
);
4133 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4134 set2
= isl_set_read_from_str(ctx
, str
);
4135 equal
= isl_set_is_equal(set1
, set2
);
4141 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4143 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
4144 "0 <= i < N and 0 <= j < M }";
4145 map
= isl_map_read_from_str(ctx
, str
);
4146 set
= isl_map_range(map
);
4148 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
4149 set1
= isl_set_from_pw_aff(pwaff
);
4150 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
4151 set2
= isl_set_read_from_str(ctx
, str
);
4152 equal
= isl_set_is_equal(set1
, set2
);
4156 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
4157 set1
= isl_set_from_pw_aff(pwaff
);
4158 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
4159 set2
= isl_set_read_from_str(ctx
, str
);
4160 if (equal
>= 0 && equal
)
4161 equal
= isl_set_is_equal(set1
, set2
);
4170 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4172 /* Check that solutions are properly merged. */
4173 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
4174 "c <= -1 + n - 4a - 2b and c >= -2b and "
4175 "4a >= -4 + n and c >= 0 }";
4176 set
= isl_set_read_from_str(ctx
, str
);
4177 pwaff
= isl_set_dim_min(set
, 2);
4178 set1
= isl_set_from_pw_aff(pwaff
);
4179 str
= "[n] -> { [(0)] : n >= 1 }";
4180 set2
= isl_set_read_from_str(ctx
, str
);
4181 equal
= isl_set_is_equal(set1
, set2
);
4188 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4190 /* Check that empty solution lie in the right space. */
4191 str
= "[n] -> { [t,a] : 1 = 0 }";
4192 set
= isl_set_read_from_str(ctx
, str
);
4193 pwaff
= isl_set_dim_max(set
, 0);
4194 set1
= isl_set_from_pw_aff(pwaff
);
4195 str
= "[n] -> { [t] : 1 = 0 }";
4196 set2
= isl_set_read_from_str(ctx
, str
);
4197 equal
= isl_set_is_equal(set1
, set2
);
4204 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4209 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
4211 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
4215 isl_pw_multi_aff
*pma2
;
4221 ctx
= isl_pw_multi_aff_get_ctx(pma
);
4222 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4223 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
4224 isl_pw_multi_aff_free(pma2
);
4229 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
4230 * represented by "str".
4232 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
4237 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
4241 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
4242 "result not as expected", return -1);
4246 /* Basic test for isl_pw_multi_aff_product.
4248 * Check that multiple pieces are properly handled.
4250 static int test_product_pma(isl_ctx
*ctx
)
4254 isl_pw_multi_aff
*pma1
, *pma2
;
4256 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
4257 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4258 str
= "{ C[] -> D[] }";
4259 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4260 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
4261 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
4262 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
4263 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
4264 isl_pw_multi_aff_free(pma1
);
4271 int test_product(isl_ctx
*ctx
)
4275 isl_union_set
*uset1
, *uset2
;
4279 set
= isl_set_read_from_str(ctx
, str
);
4280 set
= isl_set_product(set
, isl_set_copy(set
));
4281 ok
= isl_set_is_wrapping(set
);
4286 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4289 uset1
= isl_union_set_read_from_str(ctx
, str
);
4290 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
4291 str
= "{ [[] -> []] }";
4292 uset2
= isl_union_set_read_from_str(ctx
, str
);
4293 ok
= isl_union_set_is_equal(uset1
, uset2
);
4294 isl_union_set_free(uset1
);
4295 isl_union_set_free(uset2
);
4299 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4301 if (test_product_pma(ctx
) < 0)
4307 /* Check that two sets are not considered disjoint just because
4308 * they have a different set of (named) parameters.
4310 static int test_disjoint(isl_ctx
*ctx
)
4313 isl_set
*set
, *set2
;
4316 str
= "[n] -> { [[]->[]] }";
4317 set
= isl_set_read_from_str(ctx
, str
);
4318 str
= "{ [[]->[]] }";
4319 set2
= isl_set_read_from_str(ctx
, str
);
4320 disjoint
= isl_set_is_disjoint(set
, set2
);
4326 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4331 int test_equal(isl_ctx
*ctx
)
4334 isl_set
*set
, *set2
;
4338 set
= isl_set_read_from_str(ctx
, str
);
4340 set2
= isl_set_read_from_str(ctx
, str
);
4341 equal
= isl_set_is_equal(set
, set2
);
4347 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4352 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
4353 enum isl_dim_type type
, unsigned pos
, int fixed
)
4357 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
4364 isl_die(ctx
, isl_error_unknown
,
4365 "map not detected as fixed", return -1);
4367 isl_die(ctx
, isl_error_unknown
,
4368 "map detected as fixed", return -1);
4371 int test_fixed(isl_ctx
*ctx
)
4376 str
= "{ [i] -> [i] }";
4377 map
= isl_map_read_from_str(ctx
, str
);
4378 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
4380 str
= "{ [i] -> [1] }";
4381 map
= isl_map_read_from_str(ctx
, str
);
4382 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4384 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
4385 map
= isl_map_read_from_str(ctx
, str
);
4386 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4388 map
= isl_map_read_from_str(ctx
, str
);
4389 map
= isl_map_neg(map
);
4390 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4396 struct isl_vertices_test_data
{
4399 const char *vertex
[2];
4400 } vertices_tests
[] = {
4401 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
4402 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
4403 { "{ A[t, i] : t = 14 and i = 1 }",
4404 1, { "{ A[14, 1] }" } },
4407 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
4409 static isl_stat
find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
4411 struct isl_vertices_test_data
*data
= user
;
4414 isl_basic_set
*bset
;
4415 isl_pw_multi_aff
*pma
;
4419 ctx
= isl_vertex_get_ctx(vertex
);
4420 bset
= isl_vertex_get_domain(vertex
);
4421 ma
= isl_vertex_get_expr(vertex
);
4422 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
4424 for (i
= 0; i
< data
->n
; ++i
) {
4425 isl_pw_multi_aff
*pma_i
;
4427 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
4428 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
4429 isl_pw_multi_aff_free(pma_i
);
4431 if (equal
< 0 || equal
)
4435 isl_pw_multi_aff_free(pma
);
4436 isl_vertex_free(vertex
);
4439 return isl_stat_error
;
4441 return equal
? isl_stat_ok
: isl_stat_error
;
4444 int test_vertices(isl_ctx
*ctx
)
4448 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
4449 isl_basic_set
*bset
;
4450 isl_vertices
*vertices
;
4454 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
4455 vertices
= isl_basic_set_compute_vertices(bset
);
4456 n
= isl_vertices_get_n_vertices(vertices
);
4457 if (vertices_tests
[i
].n
!= n
)
4459 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
4460 &vertices_tests
[i
]) < 0)
4462 isl_vertices_free(vertices
);
4463 isl_basic_set_free(bset
);
4468 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
4475 int test_union_pw(isl_ctx
*ctx
)
4479 isl_union_set
*uset
;
4480 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
4482 str
= "{ [x] -> x^2 }";
4483 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
4484 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
4485 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
4486 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
4487 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
4488 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
4489 isl_union_pw_qpolynomial_free(upwqp1
);
4490 isl_union_pw_qpolynomial_free(upwqp2
);
4494 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4499 /* Test that isl_union_pw_qpolynomial_eval picks up the function
4500 * defined over the correct domain space.
4502 static int test_eval(isl_ctx
*ctx
)
4507 isl_union_pw_qpolynomial
*upwqp
;
4511 str
= "{ A[x] -> x^2; B[x] -> -x^2 }";
4512 upwqp
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
4514 set
= isl_set_read_from_str(ctx
, str
);
4515 pnt
= isl_set_sample_point(set
);
4516 v
= isl_union_pw_qpolynomial_eval(upwqp
, pnt
);
4517 cmp
= isl_val_cmp_si(v
, 36);
4523 isl_die(ctx
, isl_error_unknown
, "unexpected value", return -1);
4528 int test_output(isl_ctx
*ctx
)
4536 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
4537 pa
= isl_pw_aff_read_from_str(ctx
, str
);
4539 p
= isl_printer_to_str(ctx
);
4540 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
4541 p
= isl_printer_print_pw_aff(p
, pa
);
4542 s
= isl_printer_get_str(p
);
4543 isl_printer_free(p
);
4544 isl_pw_aff_free(pa
);
4548 equal
= !strcmp(s
, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
4553 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4558 int test_sample(isl_ctx
*ctx
)
4561 isl_basic_set
*bset1
, *bset2
;
4564 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
4565 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
4566 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
4567 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
4568 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
4569 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
4570 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
4571 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
4572 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
4573 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
4574 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
4575 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
4576 "d - 1073741821e and "
4577 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
4578 "3j >= 1 - a + b + 2e and "
4579 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
4580 "3i <= 4 - a + 4b - e and "
4581 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
4582 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
4583 "c <= -1 + a and 3i >= -2 - a + 3e and "
4584 "1073741822e <= 1073741823 - a + 1073741822b + c and "
4585 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
4586 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
4587 "1073741823e >= 1 + 1073741823b - d and "
4588 "3i >= 1073741823b + c - 1073741823e - f and "
4589 "3i >= 1 + 2b + e + 3g }";
4590 bset1
= isl_basic_set_read_from_str(ctx
, str
);
4591 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
4592 empty
= isl_basic_set_is_empty(bset2
);
4593 subset
= isl_basic_set_is_subset(bset2
, bset1
);
4594 isl_basic_set_free(bset1
);
4595 isl_basic_set_free(bset2
);
4596 if (empty
< 0 || subset
< 0)
4599 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
4601 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
4606 int test_fixed_power(isl_ctx
*ctx
)
4614 str
= "{ [i] -> [i + 1] }";
4615 map
= isl_map_read_from_str(ctx
, str
);
4616 isl_int_set_si(exp
, 23);
4617 map
= isl_map_fixed_power(map
, exp
);
4618 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
4627 int test_slice(isl_ctx
*ctx
)
4633 str
= "{ [i] -> [j] }";
4634 map
= isl_map_read_from_str(ctx
, str
);
4635 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4636 equal
= map_check_equal(map
, "{ [i] -> [i] }");
4641 str
= "{ [i] -> [j] }";
4642 map
= isl_map_read_from_str(ctx
, str
);
4643 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4644 equal
= map_check_equal(map
, "{ [i] -> [j] }");
4649 str
= "{ [i] -> [j] }";
4650 map
= isl_map_read_from_str(ctx
, str
);
4651 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4652 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
4657 str
= "{ [i] -> [j] }";
4658 map
= isl_map_read_from_str(ctx
, str
);
4659 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4660 equal
= map_check_equal(map
, "{ [0] -> [j] }");
4665 str
= "{ [i] -> [j] }";
4666 map
= isl_map_read_from_str(ctx
, str
);
4667 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4668 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
4673 str
= "{ [i] -> [j] }";
4674 map
= isl_map_read_from_str(ctx
, str
);
4675 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4676 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
4684 int test_eliminate(isl_ctx
*ctx
)
4690 str
= "{ [i] -> [j] : i = 2j }";
4691 map
= isl_map_read_from_str(ctx
, str
);
4692 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
4693 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
4701 /* Check that isl_set_dim_residue_class detects that the values of j
4702 * in the set below are all odd and that it does not detect any spurious
4705 static int test_residue_class(isl_ctx
*ctx
)
4712 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
4713 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
4714 set
= isl_set_read_from_str(ctx
, str
);
4717 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
4719 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
4720 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
4729 int test_align_parameters(isl_ctx
*ctx
)
4733 isl_multi_aff
*ma1
, *ma2
;
4736 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
4737 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
4739 space
= isl_space_params_alloc(ctx
, 1);
4740 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
4741 ma1
= isl_multi_aff_align_params(ma1
, space
);
4743 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
4744 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
4746 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
4748 isl_multi_aff_free(ma1
);
4749 isl_multi_aff_free(ma2
);
4754 isl_die(ctx
, isl_error_unknown
,
4755 "result not as expected", return -1);
4760 static int test_list(isl_ctx
*ctx
)
4762 isl_id
*a
, *b
, *c
, *d
, *id
;
4766 a
= isl_id_alloc(ctx
, "a", NULL
);
4767 b
= isl_id_alloc(ctx
, "b", NULL
);
4768 c
= isl_id_alloc(ctx
, "c", NULL
);
4769 d
= isl_id_alloc(ctx
, "d", NULL
);
4771 list
= isl_id_list_alloc(ctx
, 4);
4772 list
= isl_id_list_add(list
, a
);
4773 list
= isl_id_list_add(list
, b
);
4774 list
= isl_id_list_add(list
, c
);
4775 list
= isl_id_list_add(list
, d
);
4776 list
= isl_id_list_drop(list
, 1, 1);
4778 if (isl_id_list_n_id(list
) != 3) {
4779 isl_id_list_free(list
);
4780 isl_die(ctx
, isl_error_unknown
,
4781 "unexpected number of elements in list", return -1);
4784 id
= isl_id_list_get_id(list
, 0);
4787 id
= isl_id_list_get_id(list
, 1);
4790 id
= isl_id_list_get_id(list
, 2);
4794 isl_id_list_free(list
);
4797 isl_die(ctx
, isl_error_unknown
,
4798 "unexpected elements in list", return -1);
4803 const char *set_conversion_tests
[] = {
4804 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4805 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4806 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4807 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4808 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
4811 /* Check that converting from isl_set to isl_pw_multi_aff and back
4812 * to isl_set produces the original isl_set.
4814 static int test_set_conversion(isl_ctx
*ctx
)
4818 isl_set
*set1
, *set2
;
4819 isl_pw_multi_aff
*pma
;
4822 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
4823 str
= set_conversion_tests
[i
];
4824 set1
= isl_set_read_from_str(ctx
, str
);
4825 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
4826 set2
= isl_set_from_pw_multi_aff(pma
);
4827 equal
= isl_set_is_equal(set1
, set2
);
4834 isl_die(ctx
, isl_error_unknown
, "bad conversion",
4841 /* Check that converting from isl_map to isl_pw_multi_aff and back
4842 * to isl_map produces the original isl_map.
4844 static int test_map_conversion(isl_ctx
*ctx
)
4847 isl_map
*map1
, *map2
;
4848 isl_pw_multi_aff
*pma
;
4851 str
= "{ [a, b, c, d] -> s0[a, b, e, f] : "
4852 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4853 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4854 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4856 map1
= isl_map_read_from_str(ctx
, str
);
4857 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
4858 map2
= isl_map_from_pw_multi_aff(pma
);
4859 equal
= isl_map_is_equal(map1
, map2
);
4866 isl_die(ctx
, isl_error_unknown
, "bad conversion", return -1);
4871 static int test_conversion(isl_ctx
*ctx
)
4873 if (test_set_conversion(ctx
) < 0)
4875 if (test_map_conversion(ctx
) < 0)
4880 /* Check that isl_basic_map_curry does not modify input.
4882 static int test_curry(isl_ctx
*ctx
)
4885 isl_basic_map
*bmap1
, *bmap2
;
4888 str
= "{ [A[] -> B[]] -> C[] }";
4889 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
4890 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
4891 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
4892 isl_basic_map_free(bmap1
);
4893 isl_basic_map_free(bmap2
);
4898 isl_die(ctx
, isl_error_unknown
,
4899 "curried map should not be equal to original",
4909 } preimage_tests
[] = {
4910 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4911 "{ A[j,i] -> B[i,j] }",
4912 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4913 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4914 "{ A[a,b] -> B[a/2,b/6] }",
4915 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4916 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4917 "{ A[a,b] -> B[a/2,b/6] }",
4918 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4919 "exists i,j : a = 2 i and b = 6 j }" },
4920 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4921 "[n] -> { : 0 <= n <= 100 }" },
4922 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4923 "{ A[a] -> B[2a] }",
4924 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4925 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4926 "{ A[a] -> B[([a/2])] }",
4927 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4928 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4929 "{ A[a] -> B[a,a,a/3] }",
4930 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4931 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4932 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4935 static int test_preimage_basic_set(isl_ctx
*ctx
)
4938 isl_basic_set
*bset1
, *bset2
;
4942 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
4943 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
4944 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
4945 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
4946 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
4947 equal
= isl_basic_set_is_equal(bset1
, bset2
);
4948 isl_basic_set_free(bset1
);
4949 isl_basic_set_free(bset2
);
4953 isl_die(ctx
, isl_error_unknown
, "bad preimage",
4964 } preimage_domain_tests
[] = {
4965 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4966 "{ A[j,i] -> B[i,j] }",
4967 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4968 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4969 "{ A[i] -> B[i + 1] }",
4970 "{ A[i] -> C[i + 1] }" },
4971 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4972 "{ A[i] -> B[i + 1] }",
4973 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4974 { "{ B[i] -> C[([i/2])] }",
4975 "{ A[i] -> B[2i] }",
4976 "{ A[i] -> C[i] }" },
4977 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4978 "{ A[i] -> B[([i/5]), ([i/7])] }",
4979 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4980 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4981 "[N] -> { A[] -> B[([N/5])] }",
4982 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4983 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4984 "{ A[i] -> B[2i] }",
4985 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4986 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4987 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4988 "{ A[i] -> B[2i] }",
4989 "{ A[i] -> C[2i] }" },
4992 static int test_preimage_union_map(isl_ctx
*ctx
)
4995 isl_union_map
*umap1
, *umap2
;
4999 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
5000 umap1
= isl_union_map_read_from_str(ctx
,
5001 preimage_domain_tests
[i
].map
);
5002 ma
= isl_multi_aff_read_from_str(ctx
,
5003 preimage_domain_tests
[i
].ma
);
5004 umap2
= isl_union_map_read_from_str(ctx
,
5005 preimage_domain_tests
[i
].res
);
5006 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
5007 equal
= isl_union_map_is_equal(umap1
, umap2
);
5008 isl_union_map_free(umap1
);
5009 isl_union_map_free(umap2
);
5013 isl_die(ctx
, isl_error_unknown
, "bad preimage",
5020 static int test_preimage(isl_ctx
*ctx
)
5022 if (test_preimage_basic_set(ctx
) < 0)
5024 if (test_preimage_union_map(ctx
) < 0)
5034 } pullback_tests
[] = {
5035 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
5036 "{ A[a,b] -> C[b + 2a] }" },
5037 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
5038 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
5039 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
5040 "{ A[a] -> C[(a)/6] }" },
5041 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
5042 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
5043 "{ A[a] -> C[(2a)/3] }" },
5044 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
5045 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
5046 "{ A[i,j] -> C[i + j, i + j] }"},
5047 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
5048 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
5049 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
5050 { "{ [i, j] -> [floor((i)/4) + floor((2*i+j)/5)] }",
5051 "{ [i, j] -> [floor((i)/3), j] }",
5052 "{ [i, j] -> [(floor((i)/12) + floor((j + 2*floor((i)/3))/5))] }" },
5055 static int test_pullback(isl_ctx
*ctx
)
5058 isl_multi_aff
*ma1
, *ma2
;
5062 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
5063 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
5064 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
5065 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
5066 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
5067 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
5068 isl_multi_aff_free(ma1
);
5069 isl_multi_aff_free(ma2
);
5073 isl_die(ctx
, isl_error_unknown
, "bad pullback",
5080 /* Check that negation is printed correctly and that equal expressions
5081 * are correctly identified.
5083 static int test_ast(isl_ctx
*ctx
)
5085 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
5089 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
5090 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
5091 expr
= isl_ast_expr_add(expr1
, expr2
);
5092 expr2
= isl_ast_expr_copy(expr
);
5093 expr
= isl_ast_expr_neg(expr
);
5094 expr2
= isl_ast_expr_neg(expr2
);
5095 equal
= isl_ast_expr_is_equal(expr
, expr2
);
5096 str
= isl_ast_expr_to_str(expr
);
5097 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
5099 isl_ast_expr_free(expr
);
5100 isl_ast_expr_free(expr2
);
5102 if (ok
< 0 || equal
< 0)
5105 isl_die(ctx
, isl_error_unknown
,
5106 "equal expressions not considered equal", return -1);
5108 isl_die(ctx
, isl_error_unknown
,
5109 "isl_ast_expr printed incorrectly", return -1);
5111 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
5112 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
5113 expr
= isl_ast_expr_add(expr1
, expr2
);
5114 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
5115 expr
= isl_ast_expr_sub(expr3
, expr
);
5116 str
= isl_ast_expr_to_str(expr
);
5117 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
5119 isl_ast_expr_free(expr
);
5124 isl_die(ctx
, isl_error_unknown
,
5125 "isl_ast_expr printed incorrectly", return -1);
5130 /* Check that isl_ast_build_expr_from_set returns a valid expression
5131 * for an empty set. Note that isl_ast_build_expr_from_set getting
5132 * called on an empty set probably indicates a bug in the caller.
5134 static int test_ast_build(isl_ctx
*ctx
)
5137 isl_ast_build
*build
;
5140 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5141 build
= isl_ast_build_from_context(set
);
5143 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
5144 expr
= isl_ast_build_expr_from_set(build
, set
);
5146 isl_ast_expr_free(expr
);
5147 isl_ast_build_free(build
);
5155 /* Internal data structure for before_for and after_for callbacks.
5157 * depth is the current depth
5158 * before is the number of times before_for has been called
5159 * after is the number of times after_for has been called
5161 struct isl_test_codegen_data
{
5167 /* This function is called before each for loop in the AST generated
5168 * from test_ast_gen1.
5170 * Increment the number of calls and the depth.
5171 * Check that the space returned by isl_ast_build_get_schedule_space
5172 * matches the target space of the schedule returned by
5173 * isl_ast_build_get_schedule.
5174 * Return an isl_id that is checked by the corresponding call
5177 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
5180 struct isl_test_codegen_data
*data
= user
;
5183 isl_union_map
*schedule
;
5184 isl_union_set
*uset
;
5189 ctx
= isl_ast_build_get_ctx(build
);
5191 if (data
->before
>= 3)
5192 isl_die(ctx
, isl_error_unknown
,
5193 "unexpected number of for nodes", return NULL
);
5194 if (data
->depth
>= 2)
5195 isl_die(ctx
, isl_error_unknown
,
5196 "unexpected depth", return NULL
);
5198 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
5202 schedule
= isl_ast_build_get_schedule(build
);
5203 uset
= isl_union_map_range(schedule
);
5206 if (isl_union_set_n_set(uset
) != 1) {
5207 isl_union_set_free(uset
);
5208 isl_die(ctx
, isl_error_unknown
,
5209 "expecting single range space", return NULL
);
5212 space
= isl_ast_build_get_schedule_space(build
);
5213 set
= isl_union_set_extract_set(uset
, space
);
5214 isl_union_set_free(uset
);
5215 empty
= isl_set_is_empty(set
);
5221 isl_die(ctx
, isl_error_unknown
,
5222 "spaces don't match", return NULL
);
5224 return isl_id_alloc(ctx
, name
, NULL
);
5227 /* This function is called after each for loop in the AST generated
5228 * from test_ast_gen1.
5230 * Increment the number of calls and decrement the depth.
5231 * Check that the annotation attached to the node matches
5232 * the isl_id returned by the corresponding call to before_for.
5234 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
5235 __isl_keep isl_ast_build
*build
, void *user
)
5237 struct isl_test_codegen_data
*data
= user
;
5245 if (data
->after
> data
->before
)
5246 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5247 "mismatch in number of for nodes",
5248 return isl_ast_node_free(node
));
5250 id
= isl_ast_node_get_annotation(node
);
5252 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5253 "missing annotation", return isl_ast_node_free(node
));
5255 name
= isl_id_get_name(id
);
5256 valid
= name
&& atoi(name
+ 1) == data
->depth
;
5260 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5261 "wrong annotation", return isl_ast_node_free(node
));
5266 /* Check that the before_each_for and after_each_for callbacks
5267 * are called for each for loop in the generated code,
5268 * that they are called in the right order and that the isl_id
5269 * returned from the before_each_for callback is attached to
5270 * the isl_ast_node passed to the corresponding after_each_for call.
5272 static int test_ast_gen1(isl_ctx
*ctx
)
5276 isl_union_map
*schedule
;
5277 isl_ast_build
*build
;
5279 struct isl_test_codegen_data data
;
5281 str
= "[N] -> { : N >= 10 }";
5282 set
= isl_set_read_from_str(ctx
, str
);
5283 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
5284 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
5285 schedule
= isl_union_map_read_from_str(ctx
, str
);
5290 build
= isl_ast_build_from_context(set
);
5291 build
= isl_ast_build_set_before_each_for(build
,
5292 &before_for
, &data
);
5293 build
= isl_ast_build_set_after_each_for(build
,
5295 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5296 isl_ast_build_free(build
);
5300 isl_ast_node_free(tree
);
5302 if (data
.before
!= 3 || data
.after
!= 3)
5303 isl_die(ctx
, isl_error_unknown
,
5304 "unexpected number of for nodes", return -1);
5309 /* Check that the AST generator handles domains that are integrally disjoint
5310 * but not rationally disjoint.
5312 static int test_ast_gen2(isl_ctx
*ctx
)
5316 isl_union_map
*schedule
;
5317 isl_union_map
*options
;
5318 isl_ast_build
*build
;
5321 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
5322 schedule
= isl_union_map_read_from_str(ctx
, str
);
5323 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5324 build
= isl_ast_build_from_context(set
);
5326 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
5327 options
= isl_union_map_read_from_str(ctx
, str
);
5328 build
= isl_ast_build_set_options(build
, options
);
5329 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5330 isl_ast_build_free(build
);
5333 isl_ast_node_free(tree
);
5338 /* Increment *user on each call.
5340 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
5341 __isl_keep isl_ast_build
*build
, void *user
)
5350 /* Test that unrolling tries to minimize the number of instances.
5351 * In particular, for the schedule given below, make sure it generates
5352 * 3 nodes (rather than 101).
5354 static int test_ast_gen3(isl_ctx
*ctx
)
5358 isl_union_map
*schedule
;
5359 isl_union_map
*options
;
5360 isl_ast_build
*build
;
5364 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
5365 schedule
= isl_union_map_read_from_str(ctx
, str
);
5366 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5368 str
= "{ [i] -> unroll[0] }";
5369 options
= isl_union_map_read_from_str(ctx
, str
);
5371 build
= isl_ast_build_from_context(set
);
5372 build
= isl_ast_build_set_options(build
, options
);
5373 build
= isl_ast_build_set_at_each_domain(build
,
5374 &count_domains
, &n_domain
);
5375 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5376 isl_ast_build_free(build
);
5380 isl_ast_node_free(tree
);
5383 isl_die(ctx
, isl_error_unknown
,
5384 "unexpected number of for nodes", return -1);
5389 /* Check that if the ast_build_exploit_nested_bounds options is set,
5390 * we do not get an outer if node in the generated AST,
5391 * while we do get such an outer if node if the options is not set.
5393 static int test_ast_gen4(isl_ctx
*ctx
)
5397 isl_union_map
*schedule
;
5398 isl_ast_build
*build
;
5400 enum isl_ast_node_type type
;
5403 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
5404 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
5406 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
5408 schedule
= isl_union_map_read_from_str(ctx
, str
);
5409 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5410 build
= isl_ast_build_from_context(set
);
5411 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5412 isl_ast_build_free(build
);
5416 type
= isl_ast_node_get_type(tree
);
5417 isl_ast_node_free(tree
);
5419 if (type
== isl_ast_node_if
)
5420 isl_die(ctx
, isl_error_unknown
,
5421 "not expecting if node", return -1);
5423 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
5425 schedule
= isl_union_map_read_from_str(ctx
, str
);
5426 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5427 build
= isl_ast_build_from_context(set
);
5428 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5429 isl_ast_build_free(build
);
5433 type
= isl_ast_node_get_type(tree
);
5434 isl_ast_node_free(tree
);
5436 if (type
!= isl_ast_node_if
)
5437 isl_die(ctx
, isl_error_unknown
,
5438 "expecting if node", return -1);
5440 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
5445 /* This function is called for each leaf in the AST generated
5446 * from test_ast_gen5.
5448 * We finalize the AST generation by extending the outer schedule
5449 * with a zero-dimensional schedule. If this results in any for loops,
5450 * then this means that we did not pass along enough information
5451 * about the outer schedule to the inner AST generation.
5453 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
5456 isl_union_map
*schedule
, *extra
;
5459 schedule
= isl_ast_build_get_schedule(build
);
5460 extra
= isl_union_map_copy(schedule
);
5461 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
5462 schedule
= isl_union_map_range_product(schedule
, extra
);
5463 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5464 isl_ast_build_free(build
);
5469 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
5470 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
5471 "code should not contain any for loop",
5472 return isl_ast_node_free(tree
));
5477 /* Check that we do not lose any information when going back and
5478 * forth between internal and external schedule.
5480 * In particular, we create an AST where we unroll the only
5481 * non-constant dimension in the schedule. We therefore do
5482 * not expect any for loops in the AST. However, older versions
5483 * of isl would not pass along enough information about the outer
5484 * schedule when performing an inner code generation from a create_leaf
5485 * callback, resulting in the inner code generation producing a for loop.
5487 static int test_ast_gen5(isl_ctx
*ctx
)
5491 isl_union_map
*schedule
, *options
;
5492 isl_ast_build
*build
;
5495 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
5496 schedule
= isl_union_map_read_from_str(ctx
, str
);
5498 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
5499 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
5500 options
= isl_union_map_read_from_str(ctx
, str
);
5502 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5503 build
= isl_ast_build_from_context(set
);
5504 build
= isl_ast_build_set_options(build
, options
);
5505 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
5506 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5507 isl_ast_build_free(build
);
5508 isl_ast_node_free(tree
);
5515 static int test_ast_gen(isl_ctx
*ctx
)
5517 if (test_ast_gen1(ctx
) < 0)
5519 if (test_ast_gen2(ctx
) < 0)
5521 if (test_ast_gen3(ctx
) < 0)
5523 if (test_ast_gen4(ctx
) < 0)
5525 if (test_ast_gen5(ctx
) < 0)
5530 /* Check if dropping output dimensions from an isl_pw_multi_aff
5533 static int test_pw_multi_aff(isl_ctx
*ctx
)
5536 isl_pw_multi_aff
*pma1
, *pma2
;
5539 str
= "{ [i,j] -> [i+j, 4i-j] }";
5540 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5541 str
= "{ [i,j] -> [4i-j] }";
5542 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5544 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
5546 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
5548 isl_pw_multi_aff_free(pma1
);
5549 isl_pw_multi_aff_free(pma2
);
5553 isl_die(ctx
, isl_error_unknown
,
5554 "expressions not equal", return -1);
5559 /* Check that we can properly parse multi piecewise affine expressions
5560 * where the piecewise affine expressions have different domains.
5562 static int test_multi_pw_aff(isl_ctx
*ctx
)
5565 isl_set
*dom
, *dom2
;
5566 isl_multi_pw_aff
*mpa1
, *mpa2
;
5571 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
5572 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
5573 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
5574 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
5575 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
5576 str
= "{ [i] -> [(i : i > 0), 2i] }";
5577 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
5579 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
5581 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
5582 dom
= isl_pw_aff_domain(pa
);
5583 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
5584 dom2
= isl_pw_aff_domain(pa
);
5585 equal_domain
= isl_set_is_equal(dom
, dom2
);
5589 isl_multi_pw_aff_free(mpa1
);
5590 isl_multi_pw_aff_free(mpa2
);
5595 isl_die(ctx
, isl_error_unknown
,
5596 "expressions not equal", return -1);
5598 if (equal_domain
< 0)
5601 isl_die(ctx
, isl_error_unknown
,
5602 "domains unexpectedly equal", return -1);
5607 /* This is a regression test for a bug where isl_basic_map_simplify
5608 * would end up in an infinite loop. In particular, we construct
5609 * an empty basic set that is not obviously empty.
5610 * isl_basic_set_is_empty marks the basic set as empty.
5611 * After projecting out i3, the variable can be dropped completely,
5612 * but isl_basic_map_simplify refrains from doing so if the basic set
5613 * is empty and would end up in an infinite loop if it didn't test
5614 * explicitly for empty basic maps in the outer loop.
5616 static int test_simplify(isl_ctx
*ctx
)
5619 isl_basic_set
*bset
;
5622 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
5623 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
5624 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
5626 bset
= isl_basic_set_read_from_str(ctx
, str
);
5627 empty
= isl_basic_set_is_empty(bset
);
5628 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
5629 isl_basic_set_free(bset
);
5633 isl_die(ctx
, isl_error_unknown
,
5634 "basic set should be empty", return -1);
5639 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
5640 * with gbr context would fail to disable the use of the shifted tableau
5641 * when transferring equalities for the input to the context, resulting
5642 * in invalid sample values.
5644 static int test_partial_lexmin(isl_ctx
*ctx
)
5647 isl_basic_set
*bset
;
5648 isl_basic_map
*bmap
;
5651 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
5652 bmap
= isl_basic_map_read_from_str(ctx
, str
);
5653 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
5654 bset
= isl_basic_set_read_from_str(ctx
, str
);
5655 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
5664 /* Check that the variable compression performed on the existentially
5665 * quantified variables inside isl_basic_set_compute_divs is not confused
5666 * by the implicit equalities among the parameters.
5668 static int test_compute_divs(isl_ctx
*ctx
)
5671 isl_basic_set
*bset
;
5674 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
5675 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
5676 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
5677 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
5678 bset
= isl_basic_set_read_from_str(ctx
, str
);
5679 set
= isl_basic_set_compute_divs(bset
);
5687 /* Check that the reaching domain elements and the prefix schedule
5688 * at a leaf node are the same before and after grouping.
5690 static int test_schedule_tree_group_1(isl_ctx
*ctx
)
5695 isl_union_set
*uset
;
5696 isl_multi_union_pw_aff
*mupa
;
5697 isl_union_pw_multi_aff
*upma1
, *upma2
;
5698 isl_union_set
*domain1
, *domain2
;
5699 isl_union_map
*umap1
, *umap2
;
5700 isl_schedule_node
*node
;
5702 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10 }";
5703 uset
= isl_union_set_read_from_str(ctx
, str
);
5704 node
= isl_schedule_node_from_domain(uset
);
5705 node
= isl_schedule_node_child(node
, 0);
5706 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [9 - i] }]";
5707 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5708 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5709 node
= isl_schedule_node_child(node
, 0);
5710 str
= "[{ S1[i,j] -> [j]; S2[i,j] -> [j] }]";
5711 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5712 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5713 node
= isl_schedule_node_child(node
, 0);
5714 umap1
= isl_schedule_node_get_prefix_schedule_union_map(node
);
5715 upma1
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
5716 domain1
= isl_schedule_node_get_domain(node
);
5717 id
= isl_id_alloc(ctx
, "group", NULL
);
5718 node
= isl_schedule_node_parent(node
);
5719 node
= isl_schedule_node_group(node
, id
);
5720 node
= isl_schedule_node_child(node
, 0);
5721 umap2
= isl_schedule_node_get_prefix_schedule_union_map(node
);
5722 upma2
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
5723 domain2
= isl_schedule_node_get_domain(node
);
5724 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
5725 if (equal
>= 0 && equal
)
5726 equal
= isl_union_set_is_equal(domain1
, domain2
);
5727 if (equal
>= 0 && equal
)
5728 equal
= isl_union_map_is_equal(umap1
, umap2
);
5729 isl_union_map_free(umap1
);
5730 isl_union_map_free(umap2
);
5731 isl_union_set_free(domain1
);
5732 isl_union_set_free(domain2
);
5733 isl_union_pw_multi_aff_free(upma1
);
5734 isl_union_pw_multi_aff_free(upma2
);
5735 isl_schedule_node_free(node
);
5740 isl_die(ctx
, isl_error_unknown
,
5741 "expressions not equal", return -1);
5746 /* Check that we can have nested groupings and that the union map
5747 * schedule representation is the same before and after the grouping.
5748 * Note that after the grouping, the union map representation contains
5749 * the domain constraints from the ranges of the expansion nodes,
5750 * while they are missing from the union map representation of
5751 * the tree without expansion nodes.
5753 * Also check that the global expansion is as expected.
5755 static int test_schedule_tree_group_2(isl_ctx
*ctx
)
5757 int equal
, equal_expansion
;
5760 isl_union_set
*uset
;
5761 isl_union_map
*umap1
, *umap2
;
5762 isl_union_map
*expansion1
, *expansion2
;
5763 isl_union_set_list
*filters
;
5764 isl_multi_union_pw_aff
*mupa
;
5765 isl_schedule
*schedule
;
5766 isl_schedule_node
*node
;
5768 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10; "
5769 "S3[i,j] : 0 <= i,j < 10 }";
5770 uset
= isl_union_set_read_from_str(ctx
, str
);
5771 node
= isl_schedule_node_from_domain(uset
);
5772 node
= isl_schedule_node_child(node
, 0);
5773 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [i]; S3[i,j] -> [i] }]";
5774 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5775 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5776 node
= isl_schedule_node_child(node
, 0);
5777 str
= "{ S1[i,j] }";
5778 uset
= isl_union_set_read_from_str(ctx
, str
);
5779 filters
= isl_union_set_list_from_union_set(uset
);
5780 str
= "{ S2[i,j]; S3[i,j] }";
5781 uset
= isl_union_set_read_from_str(ctx
, str
);
5782 filters
= isl_union_set_list_add(filters
, uset
);
5783 node
= isl_schedule_node_insert_sequence(node
, filters
);
5784 node
= isl_schedule_node_child(node
, 1);
5785 node
= isl_schedule_node_child(node
, 0);
5786 str
= "{ S2[i,j] }";
5787 uset
= isl_union_set_read_from_str(ctx
, str
);
5788 filters
= isl_union_set_list_from_union_set(uset
);
5789 str
= "{ S3[i,j] }";
5790 uset
= isl_union_set_read_from_str(ctx
, str
);
5791 filters
= isl_union_set_list_add(filters
, uset
);
5792 node
= isl_schedule_node_insert_sequence(node
, filters
);
5794 schedule
= isl_schedule_node_get_schedule(node
);
5795 umap1
= isl_schedule_get_map(schedule
);
5796 uset
= isl_schedule_get_domain(schedule
);
5797 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
5798 isl_schedule_free(schedule
);
5800 node
= isl_schedule_node_parent(node
);
5801 node
= isl_schedule_node_parent(node
);
5802 id
= isl_id_alloc(ctx
, "group1", NULL
);
5803 node
= isl_schedule_node_group(node
, id
);
5804 node
= isl_schedule_node_child(node
, 1);
5805 node
= isl_schedule_node_child(node
, 0);
5806 id
= isl_id_alloc(ctx
, "group2", NULL
);
5807 node
= isl_schedule_node_group(node
, id
);
5809 schedule
= isl_schedule_node_get_schedule(node
);
5810 umap2
= isl_schedule_get_map(schedule
);
5811 isl_schedule_free(schedule
);
5813 node
= isl_schedule_node_root(node
);
5814 node
= isl_schedule_node_child(node
, 0);
5815 expansion1
= isl_schedule_node_get_subtree_expansion(node
);
5816 isl_schedule_node_free(node
);
5818 str
= "{ group1[i] -> S1[i,j] : 0 <= i,j < 10; "
5819 "group1[i] -> S2[i,j] : 0 <= i,j < 10; "
5820 "group1[i] -> S3[i,j] : 0 <= i,j < 10 }";
5822 expansion2
= isl_union_map_read_from_str(ctx
, str
);
5824 equal
= isl_union_map_is_equal(umap1
, umap2
);
5825 equal_expansion
= isl_union_map_is_equal(expansion1
, expansion2
);
5827 isl_union_map_free(umap1
);
5828 isl_union_map_free(umap2
);
5829 isl_union_map_free(expansion1
);
5830 isl_union_map_free(expansion2
);
5832 if (equal
< 0 || equal_expansion
< 0)
5835 isl_die(ctx
, isl_error_unknown
,
5836 "expressions not equal", return -1);
5837 if (!equal_expansion
)
5838 isl_die(ctx
, isl_error_unknown
,
5839 "unexpected expansion", return -1);
5844 /* Some tests for the isl_schedule_node_group function.
5846 static int test_schedule_tree_group(isl_ctx
*ctx
)
5848 if (test_schedule_tree_group_1(ctx
) < 0)
5850 if (test_schedule_tree_group_2(ctx
) < 0)
5859 { "{ rat: [i] : 0 <= i <= 10 }",
5860 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
5861 { "{ rat: [i] : FALSE }",
5862 "{ rat: coefficients[[cst] -> [a]] }" },
5864 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
5871 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
5872 "{ rat: [i] : 0 <= i <= 10 }" },
5873 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
5875 { "{ rat: coefficients[[cst] -> [a]] }",
5876 "{ rat: [i] : FALSE }" },
5879 /* Test the basic functionality of isl_basic_set_coefficients and
5880 * isl_basic_set_solutions.
5882 static int test_dual(isl_ctx
*ctx
)
5886 for (i
= 0; i
< ARRAY_SIZE(coef_tests
); ++i
) {
5888 isl_basic_set
*bset1
, *bset2
;
5890 bset1
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].set
);
5891 bset2
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].dual
);
5892 bset1
= isl_basic_set_coefficients(bset1
);
5893 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5894 isl_basic_set_free(bset1
);
5895 isl_basic_set_free(bset2
);
5899 isl_die(ctx
, isl_error_unknown
,
5900 "incorrect dual", return -1);
5903 for (i
= 0; i
< ARRAY_SIZE(sol_tests
); ++i
) {
5905 isl_basic_set
*bset1
, *bset2
;
5907 bset1
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].set
);
5908 bset2
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].dual
);
5909 bset1
= isl_basic_set_solutions(bset1
);
5910 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5911 isl_basic_set_free(bset1
);
5912 isl_basic_set_free(bset2
);
5916 isl_die(ctx
, isl_error_unknown
,
5917 "incorrect dual", return -1);
5927 const char *schedule
;
5932 { 0, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
5933 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5935 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
5936 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5938 { 1, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
5939 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5941 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
5942 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5944 { 0, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
5945 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5947 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
5948 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
5950 { 1, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
5951 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
5953 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
5954 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
5958 /* Basic tiling tests. Create a schedule tree with a domain and a band node,
5959 * tile the band and then check if the tile and point bands have the
5960 * expected partial schedule.
5962 static int test_tile(isl_ctx
*ctx
)
5968 scale
= isl_options_get_tile_scale_tile_loops(ctx
);
5969 shift
= isl_options_get_tile_shift_point_loops(ctx
);
5971 for (i
= 0; i
< ARRAY_SIZE(tile_tests
); ++i
) {
5975 isl_union_set
*domain
;
5976 isl_multi_union_pw_aff
*mupa
, *mupa2
;
5977 isl_schedule_node
*node
;
5978 isl_multi_val
*sizes
;
5980 opt
= tile_tests
[i
].scale_tile
;
5981 isl_options_set_tile_scale_tile_loops(ctx
, opt
);
5982 opt
= tile_tests
[i
].shift_point
;
5983 isl_options_set_tile_shift_point_loops(ctx
, opt
);
5985 str
= tile_tests
[i
].domain
;
5986 domain
= isl_union_set_read_from_str(ctx
, str
);
5987 node
= isl_schedule_node_from_domain(domain
);
5988 node
= isl_schedule_node_child(node
, 0);
5989 str
= tile_tests
[i
].schedule
;
5990 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5991 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
5992 str
= tile_tests
[i
].sizes
;
5993 sizes
= isl_multi_val_read_from_str(ctx
, str
);
5994 node
= isl_schedule_node_band_tile(node
, sizes
);
5996 str
= tile_tests
[i
].tile
;
5997 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
5998 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
5999 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
, mupa2
);
6000 isl_multi_union_pw_aff_free(mupa
);
6001 isl_multi_union_pw_aff_free(mupa2
);
6003 node
= isl_schedule_node_child(node
, 0);
6005 str
= tile_tests
[i
].point
;
6006 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6007 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
6008 if (equal
>= 0 && equal
)
6009 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
,
6011 isl_multi_union_pw_aff_free(mupa
);
6012 isl_multi_union_pw_aff_free(mupa2
);
6014 isl_schedule_node_free(node
);
6019 isl_die(ctx
, isl_error_unknown
,
6020 "unexpected result", return -1);
6023 isl_options_set_tile_scale_tile_loops(ctx
, scale
);
6024 isl_options_set_tile_shift_point_loops(ctx
, shift
);
6029 /* Check that the domain hash of a space is equal to the hash
6030 * of the domain of the space.
6032 static int test_domain_hash(isl_ctx
*ctx
)
6036 uint32_t hash1
, hash2
;
6038 map
= isl_map_read_from_str(ctx
, "[n] -> { A[B[x] -> C[]] -> D[] }");
6039 space
= isl_map_get_space(map
);
6041 hash1
= isl_space_get_domain_hash(space
);
6042 space
= isl_space_domain(space
);
6043 hash2
= isl_space_get_hash(space
);
6044 isl_space_free(space
);
6049 isl_die(ctx
, isl_error_unknown
,
6050 "domain hash not equal to hash of domain", return -1);
6057 int (*fn
)(isl_ctx
*ctx
);
6059 { "domain hash", &test_domain_hash
},
6060 { "dual", &test_dual
},
6061 { "dependence analysis", &test_flow
},
6062 { "val", &test_val
},
6063 { "compute divs", &test_compute_divs
},
6064 { "partial lexmin", &test_partial_lexmin
},
6065 { "simplify", &test_simplify
},
6066 { "curry", &test_curry
},
6067 { "piecewise multi affine expressions", &test_pw_multi_aff
},
6068 { "multi piecewise affine expressions", &test_multi_pw_aff
},
6069 { "conversion", &test_conversion
},
6070 { "list", &test_list
},
6071 { "align parameters", &test_align_parameters
},
6072 { "preimage", &test_preimage
},
6073 { "pullback", &test_pullback
},
6074 { "AST", &test_ast
},
6075 { "AST build", &test_ast_build
},
6076 { "AST generation", &test_ast_gen
},
6077 { "eliminate", &test_eliminate
},
6078 { "residue class", &test_residue_class
},
6079 { "div", &test_div
},
6080 { "slice", &test_slice
},
6081 { "fixed power", &test_fixed_power
},
6082 { "sample", &test_sample
},
6083 { "output", &test_output
},
6084 { "vertices", &test_vertices
},
6085 { "fixed", &test_fixed
},
6086 { "equal", &test_equal
},
6087 { "disjoint", &test_disjoint
},
6088 { "product", &test_product
},
6089 { "dim_max", &test_dim_max
},
6090 { "affine", &test_aff
},
6091 { "injective", &test_injective
},
6092 { "schedule", &test_schedule
},
6093 { "schedule tree grouping", &test_schedule_tree_group
},
6094 { "tile", &test_tile
},
6095 { "union_pw", &test_union_pw
},
6096 { "eval", &test_eval
},
6097 { "parse", &test_parse
},
6098 { "single-valued", &test_sv
},
6099 { "affine hull", &test_affine_hull
},
6100 { "simple_hull", &test_simple_hull
},
6101 { "coalesce", &test_coalesce
},
6102 { "factorize", &test_factorize
},
6103 { "subset", &test_subset
},
6104 { "subtract", &test_subtract
},
6105 { "lexmin", &test_lexmin
},
6106 { "min", &test_min
},
6107 { "gist", &test_gist
},
6108 { "piecewise quasi-polynomials", &test_pwqp
},
6109 { "lift", &test_lift
},
6110 { "bound", &test_bound
},
6111 { "union", &test_union
},
6112 { "split periods", &test_split_periods
},
6113 { "lexicographic order", &test_lex
},
6114 { "bijectivity", &test_bijective
},
6115 { "dataflow analysis", &test_dep
},
6116 { "reading", &test_read
},
6117 { "bounded", &test_bounded
},
6118 { "construction", &test_construction
},
6119 { "dimension manipulation", &test_dim
},
6120 { "map application", &test_application
},
6121 { "convex hull", &test_convex_hull
},
6122 { "transitive closure", &test_closure
},
6125 int main(int argc
, char **argv
)
6128 struct isl_ctx
*ctx
;
6129 struct isl_options
*options
;
6131 srcdir
= getenv("srcdir");
6134 options
= isl_options_new_with_defaults();
6136 argc
= isl_options_parse(options
, argc
, argv
, ISL_ARG_ALL
);
6138 ctx
= isl_ctx_alloc_with_options(&isl_options_args
, options
);
6139 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
6140 printf("%s\n", tests
[i
].name
);
6141 if (tests
[i
].fn(ctx
) < 0)