2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
12 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
15 * B.P. 105 - 78153 Le Chesnay, France
21 #include <isl_ctx_private.h>
22 #include <isl_map_private.h>
23 #include <isl_aff_private.h>
26 #include <isl_constraint_private.h>
27 #include <isl/polynomial.h>
28 #include <isl/union_map.h>
29 #include <isl_factorization.h>
30 #include <isl/schedule.h>
31 #include <isl_options_private.h>
32 #include <isl/vertices.h>
33 #include <isl/ast_build.h>
36 #include <isl_ast_build_expr.h>
37 #include <isl/options.h>
39 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
43 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
46 char *pattern
= "%s/test_inputs/%s.%s";
48 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
50 filename
= isl_alloc_array(ctx
, char, length
);
55 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
60 void test_parse_map(isl_ctx
*ctx
, const char *str
)
64 map
= isl_map_read_from_str(ctx
, str
);
69 int test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
74 map
= isl_map_read_from_str(ctx
, str
);
75 map2
= isl_map_read_from_str(ctx
, str2
);
76 equal
= isl_map_is_equal(map
, map2
);
83 isl_die(ctx
, isl_error_unknown
, "maps not equal",
89 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
91 isl_pw_qpolynomial
*pwqp
;
93 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
95 isl_pw_qpolynomial_free(pwqp
);
98 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
102 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
104 isl_pw_aff_free(pwaff
);
107 int test_parse(struct isl_ctx
*ctx
)
110 const char *str
, *str2
;
112 str
= "{ [i] -> [-i] }";
113 map
= isl_map_read_from_str(ctx
, str
);
117 str
= "{ A[i] -> L[([i/3])] }";
118 map
= isl_map_read_from_str(ctx
, str
);
122 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
123 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
124 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
126 str
= "{ [x,y] : [([x/2]+y)/3] >= 1 }";
127 str2
= "{ [x, y] : 2y >= 6 - x }";
128 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
131 if (test_parse_map_equal(ctx
, "{ [x,y] : x <= min(y, 2*y+3) }",
132 "{ [x,y] : x <= y, 2*y + 3 }") < 0)
134 str
= "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }";
135 if (test_parse_map_equal(ctx
, "{ [x,y] : x >= min(y, 2*y+3) }",
139 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
140 map
= isl_map_read_from_str(ctx
, str
);
141 str
= "{ [new, old] -> [o0, o1] : "
142 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
143 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
144 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
145 map2
= isl_map_read_from_str(ctx
, str
);
146 assert(isl_map_is_equal(map
, map2
));
150 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
151 map
= isl_map_read_from_str(ctx
, str
);
152 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
153 map2
= isl_map_read_from_str(ctx
, str
);
154 assert(isl_map_is_equal(map
, map2
));
158 str
= "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }";
159 str2
= "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }";
160 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
163 str
= "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }";
164 str2
= "{ [i,j] -> [min(i,j)] }";
165 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
168 str
= "{ [i,j] : i != j }";
169 str2
= "{ [i,j] : i < j or i > j }";
170 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
173 str
= "{ [i,j] : (i+1)*2 >= j }";
174 str2
= "{ [i, j] : j <= 2 + 2i }";
175 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
178 str
= "{ [i] -> [i > 0 ? 4 : 5] }";
179 str2
= "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }";
180 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
183 str
= "[N=2,M] -> { [i=[(M+N)/4]] }";
184 str2
= "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }";
185 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
188 str
= "{ [x] : x >= 0 }";
189 str2
= "{ [x] : x-0 >= 0 }";
190 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
193 str
= "{ [i] : ((i > 10)) }";
194 str2
= "{ [i] : i >= 11 }";
195 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
198 str
= "{ [i] -> [0] }";
199 str2
= "{ [i] -> [0 * i] }";
200 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
203 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
204 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
205 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
206 test_parse_pwqp(ctx
, "{ [x] -> ([(x)/2] * [(x)/3]) }");
208 if (test_parse_map_equal(ctx
, "{ [a] -> [b] : (not false) }",
209 "{ [a] -> [b] : true }") < 0)
212 if (test_parse_map_equal(ctx
, "{ [i] : i/2 <= 5 }",
213 "{ [i] : i <= 10 }") < 0)
216 if (test_parse_map_equal(ctx
, "{Sym=[n] [i] : i <= n }",
217 "[n] -> { [i] : i <= n }") < 0)
220 if (test_parse_map_equal(ctx
, "{ [*] }", "{ [a] }") < 0)
223 if (test_parse_map_equal(ctx
, "{ [i] : 2*floor(i/2) = i }",
224 "{ [i] : exists a : i = 2 a }") < 0)
227 if (test_parse_map_equal(ctx
, "{ [a] -> [b] : a = 5 implies b = 5 }",
228 "{ [a] -> [b] : a != 5 or b = 5 }") < 0)
231 if (test_parse_map_equal(ctx
, "{ [a] -> [a - 1 : a > 0] }",
232 "{ [a] -> [a - 1] : a > 0 }") < 0)
234 if (test_parse_map_equal(ctx
,
235 "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
236 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }") < 0)
238 if (test_parse_map_equal(ctx
,
239 "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
240 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
242 if (test_parse_map_equal(ctx
,
243 "{ [a] -> [(a * 2) : a >= 0; 0 : a < 0] }",
244 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
246 if (test_parse_map_equal(ctx
,
247 "{ [a] -> [(a * 2 : a >= 0); 0 : a < 0] }",
248 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
250 if (test_parse_map_equal(ctx
,
251 "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
252 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }") < 0)
258 void test_read(struct isl_ctx
*ctx
)
262 struct isl_basic_set
*bset1
, *bset2
;
263 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
265 filename
= get_filename(ctx
, "set", "omega");
267 input
= fopen(filename
, "r");
270 bset1
= isl_basic_set_read_from_file(ctx
, input
);
271 bset2
= isl_basic_set_read_from_str(ctx
, str
);
273 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
275 isl_basic_set_free(bset1
);
276 isl_basic_set_free(bset2
);
282 void test_bounded(struct isl_ctx
*ctx
)
287 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
288 bounded
= isl_set_is_bounded(set
);
292 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
293 bounded
= isl_set_is_bounded(set
);
297 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
298 bounded
= isl_set_is_bounded(set
);
303 /* Construct the basic set { [i] : 5 <= i <= N } */
304 void test_construction(struct isl_ctx
*ctx
)
309 struct isl_basic_set
*bset
;
310 struct isl_constraint
*c
;
314 dim
= isl_space_set_alloc(ctx
, 1, 1);
315 bset
= isl_basic_set_universe(isl_space_copy(dim
));
316 ls
= isl_local_space_from_space(dim
);
318 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
319 isl_int_set_si(v
, -1);
320 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
321 isl_int_set_si(v
, 1);
322 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
323 bset
= isl_basic_set_add_constraint(bset
, c
);
325 c
= isl_inequality_alloc(isl_local_space_copy(ls
));
326 isl_int_set_si(v
, 1);
327 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
328 isl_int_set_si(v
, -5);
329 isl_constraint_set_constant(c
, v
);
330 bset
= isl_basic_set_add_constraint(bset
, c
);
332 isl_local_space_free(ls
);
333 isl_basic_set_free(bset
);
338 void test_dim(struct isl_ctx
*ctx
)
341 isl_map
*map1
, *map2
;
343 map1
= isl_map_read_from_str(ctx
,
344 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
345 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
346 map2
= isl_map_read_from_str(ctx
,
347 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
348 assert(isl_map_is_equal(map1
, map2
));
351 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
352 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
353 assert(isl_map_is_equal(map1
, map2
));
358 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
359 map1
= isl_map_read_from_str(ctx
, str
);
360 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
361 map2
= isl_map_read_from_str(ctx
, str
);
362 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
363 assert(isl_map_is_equal(map1
, map2
));
370 __isl_give isl_val
*(*op
)(__isl_take isl_val
*v
);
374 { &isl_val_neg
, "0", "0" },
375 { &isl_val_abs
, "0", "0" },
376 { &isl_val_2exp
, "0", "1" },
377 { &isl_val_floor
, "0", "0" },
378 { &isl_val_ceil
, "0", "0" },
379 { &isl_val_neg
, "1", "-1" },
380 { &isl_val_neg
, "-1", "1" },
381 { &isl_val_neg
, "1/2", "-1/2" },
382 { &isl_val_neg
, "-1/2", "1/2" },
383 { &isl_val_neg
, "infty", "-infty" },
384 { &isl_val_neg
, "-infty", "infty" },
385 { &isl_val_neg
, "NaN", "NaN" },
386 { &isl_val_abs
, "1", "1" },
387 { &isl_val_abs
, "-1", "1" },
388 { &isl_val_abs
, "1/2", "1/2" },
389 { &isl_val_abs
, "-1/2", "1/2" },
390 { &isl_val_abs
, "infty", "infty" },
391 { &isl_val_abs
, "-infty", "infty" },
392 { &isl_val_abs
, "NaN", "NaN" },
393 { &isl_val_floor
, "1", "1" },
394 { &isl_val_floor
, "-1", "-1" },
395 { &isl_val_floor
, "1/2", "0" },
396 { &isl_val_floor
, "-1/2", "-1" },
397 { &isl_val_floor
, "infty", "infty" },
398 { &isl_val_floor
, "-infty", "-infty" },
399 { &isl_val_floor
, "NaN", "NaN" },
400 { &isl_val_ceil
, "1", "1" },
401 { &isl_val_ceil
, "-1", "-1" },
402 { &isl_val_ceil
, "1/2", "1" },
403 { &isl_val_ceil
, "-1/2", "0" },
404 { &isl_val_ceil
, "infty", "infty" },
405 { &isl_val_ceil
, "-infty", "-infty" },
406 { &isl_val_ceil
, "NaN", "NaN" },
407 { &isl_val_2exp
, "-3", "1/8" },
408 { &isl_val_2exp
, "-1", "1/2" },
409 { &isl_val_2exp
, "1", "2" },
410 { &isl_val_2exp
, "2", "4" },
411 { &isl_val_2exp
, "3", "8" },
412 { &isl_val_inv
, "1", "1" },
413 { &isl_val_inv
, "2", "1/2" },
414 { &isl_val_inv
, "1/2", "2" },
415 { &isl_val_inv
, "-2", "-1/2" },
416 { &isl_val_inv
, "-1/2", "-2" },
417 { &isl_val_inv
, "0", "NaN" },
418 { &isl_val_inv
, "NaN", "NaN" },
419 { &isl_val_inv
, "infty", "0" },
420 { &isl_val_inv
, "-infty", "0" },
423 /* Perform some basic tests of unary operations on isl_val objects.
425 static int test_un_val(isl_ctx
*ctx
)
429 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v
);
432 for (i
= 0; i
< ARRAY_SIZE(val_un_tests
); ++i
) {
433 v
= isl_val_read_from_str(ctx
, val_un_tests
[i
].arg
);
434 res
= isl_val_read_from_str(ctx
, val_un_tests
[i
].res
);
435 fn
= val_un_tests
[i
].op
;
437 if (isl_val_is_nan(res
))
438 ok
= isl_val_is_nan(v
);
440 ok
= isl_val_eq(v
, res
);
446 isl_die(ctx
, isl_error_unknown
,
447 "unexpected result", return -1);
454 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
455 __isl_take isl_val
*v2
);
457 ['+'] = { &isl_val_add
},
458 ['-'] = { &isl_val_sub
},
459 ['*'] = { &isl_val_mul
},
460 ['/'] = { &isl_val_div
},
461 ['g'] = { &isl_val_gcd
},
462 ['m'] = { &isl_val_min
},
463 ['M'] = { &isl_val_max
},
471 } val_bin_tests
[] = {
472 { "0", '+', "0", "0" },
473 { "1", '+', "0", "1" },
474 { "1", '+', "1", "2" },
475 { "1", '-', "1", "0" },
476 { "1", '*', "1", "1" },
477 { "1", '/', "1", "1" },
478 { "2", '*', "3", "6" },
479 { "2", '*', "1/2", "1" },
480 { "2", '*', "1/3", "2/3" },
481 { "2/3", '*', "3/5", "2/5" },
482 { "2/3", '*', "7/5", "14/15" },
483 { "2", '/', "1/2", "4" },
484 { "-2", '/', "-1/2", "4" },
485 { "-2", '/', "1/2", "-4" },
486 { "2", '/', "-1/2", "-4" },
487 { "2", '/', "2", "1" },
488 { "2", '/', "3", "2/3" },
489 { "2/3", '/', "5/3", "2/5" },
490 { "2/3", '/', "5/7", "14/15" },
491 { "0", '/', "0", "NaN" },
492 { "42", '/', "0", "NaN" },
493 { "-42", '/', "0", "NaN" },
494 { "infty", '/', "0", "NaN" },
495 { "-infty", '/', "0", "NaN" },
496 { "NaN", '/', "0", "NaN" },
497 { "0", '/', "NaN", "NaN" },
498 { "42", '/', "NaN", "NaN" },
499 { "-42", '/', "NaN", "NaN" },
500 { "infty", '/', "NaN", "NaN" },
501 { "-infty", '/', "NaN", "NaN" },
502 { "NaN", '/', "NaN", "NaN" },
503 { "0", '/', "infty", "0" },
504 { "42", '/', "infty", "0" },
505 { "-42", '/', "infty", "0" },
506 { "infty", '/', "infty", "NaN" },
507 { "-infty", '/', "infty", "NaN" },
508 { "NaN", '/', "infty", "NaN" },
509 { "0", '/', "-infty", "0" },
510 { "42", '/', "-infty", "0" },
511 { "-42", '/', "-infty", "0" },
512 { "infty", '/', "-infty", "NaN" },
513 { "-infty", '/', "-infty", "NaN" },
514 { "NaN", '/', "-infty", "NaN" },
515 { "1", '-', "1/3", "2/3" },
516 { "1/3", '+', "1/2", "5/6" },
517 { "1/2", '+', "1/2", "1" },
518 { "3/4", '-', "1/4", "1/2" },
519 { "1/2", '-', "1/3", "1/6" },
520 { "infty", '+', "42", "infty" },
521 { "infty", '+', "infty", "infty" },
522 { "42", '+', "infty", "infty" },
523 { "infty", '-', "infty", "NaN" },
524 { "infty", '*', "infty", "infty" },
525 { "infty", '*', "-infty", "-infty" },
526 { "-infty", '*', "infty", "-infty" },
527 { "-infty", '*', "-infty", "infty" },
528 { "0", '*', "infty", "NaN" },
529 { "1", '*', "infty", "infty" },
530 { "infty", '*', "0", "NaN" },
531 { "infty", '*', "42", "infty" },
532 { "42", '-', "infty", "-infty" },
533 { "infty", '+', "-infty", "NaN" },
534 { "4", 'g', "6", "2" },
535 { "5", 'g', "6", "1" },
536 { "42", 'm', "3", "3" },
537 { "42", 'M', "3", "42" },
538 { "3", 'm', "42", "3" },
539 { "3", 'M', "42", "42" },
540 { "42", 'm', "infty", "42" },
541 { "42", 'M', "infty", "infty" },
542 { "42", 'm', "-infty", "-infty" },
543 { "42", 'M', "-infty", "42" },
544 { "42", 'm', "NaN", "NaN" },
545 { "42", 'M', "NaN", "NaN" },
546 { "infty", 'm', "-infty", "-infty" },
547 { "infty", 'M', "-infty", "infty" },
550 /* Perform some basic tests of binary operations on isl_val objects.
552 static int test_bin_val(isl_ctx
*ctx
)
555 isl_val
*v1
, *v2
, *res
;
556 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
557 __isl_take isl_val
*v2
);
560 for (i
= 0; i
< ARRAY_SIZE(val_bin_tests
); ++i
) {
561 v1
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg1
);
562 v2
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg2
);
563 res
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].res
);
564 fn
= val_bin_op
[val_bin_tests
[i
].op
].fn
;
566 if (isl_val_is_nan(res
))
567 ok
= isl_val_is_nan(v1
);
569 ok
= isl_val_eq(v1
, res
);
575 isl_die(ctx
, isl_error_unknown
,
576 "unexpected result", return -1);
582 /* Perform some basic tests on isl_val objects.
584 static int test_val(isl_ctx
*ctx
)
586 if (test_un_val(ctx
) < 0)
588 if (test_bin_val(ctx
) < 0)
593 static int test_div(isl_ctx
*ctx
)
602 struct isl_basic_set
*bset
;
603 struct isl_constraint
*c
;
608 dim
= isl_space_set_alloc(ctx
, 0, 3);
609 bset
= isl_basic_set_universe(isl_space_copy(dim
));
610 ls
= isl_local_space_from_space(dim
);
612 c
= isl_equality_alloc(isl_local_space_copy(ls
));
613 isl_int_set_si(v
, -1);
614 isl_constraint_set_constant(c
, v
);
615 isl_int_set_si(v
, 1);
616 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
617 isl_int_set_si(v
, 3);
618 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
619 bset
= isl_basic_set_add_constraint(bset
, c
);
621 c
= isl_equality_alloc(isl_local_space_copy(ls
));
622 isl_int_set_si(v
, 1);
623 isl_constraint_set_constant(c
, v
);
624 isl_int_set_si(v
, -1);
625 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
626 isl_int_set_si(v
, 3);
627 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
628 bset
= isl_basic_set_add_constraint(bset
, c
);
630 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
632 assert(bset
&& bset
->n_div
== 1);
633 isl_local_space_free(ls
);
634 isl_basic_set_free(bset
);
637 dim
= isl_space_set_alloc(ctx
, 0, 3);
638 bset
= isl_basic_set_universe(isl_space_copy(dim
));
639 ls
= isl_local_space_from_space(dim
);
641 c
= isl_equality_alloc(isl_local_space_copy(ls
));
642 isl_int_set_si(v
, 1);
643 isl_constraint_set_constant(c
, v
);
644 isl_int_set_si(v
, -1);
645 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
646 isl_int_set_si(v
, 3);
647 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
648 bset
= isl_basic_set_add_constraint(bset
, c
);
650 c
= isl_equality_alloc(isl_local_space_copy(ls
));
651 isl_int_set_si(v
, -1);
652 isl_constraint_set_constant(c
, v
);
653 isl_int_set_si(v
, 1);
654 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
655 isl_int_set_si(v
, 3);
656 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
657 bset
= isl_basic_set_add_constraint(bset
, c
);
659 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
661 assert(bset
&& bset
->n_div
== 1);
662 isl_local_space_free(ls
);
663 isl_basic_set_free(bset
);
666 dim
= isl_space_set_alloc(ctx
, 0, 3);
667 bset
= isl_basic_set_universe(isl_space_copy(dim
));
668 ls
= isl_local_space_from_space(dim
);
670 c
= isl_equality_alloc(isl_local_space_copy(ls
));
671 isl_int_set_si(v
, 1);
672 isl_constraint_set_constant(c
, v
);
673 isl_int_set_si(v
, -1);
674 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
675 isl_int_set_si(v
, 3);
676 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
677 bset
= isl_basic_set_add_constraint(bset
, c
);
679 c
= isl_equality_alloc(isl_local_space_copy(ls
));
680 isl_int_set_si(v
, -3);
681 isl_constraint_set_constant(c
, v
);
682 isl_int_set_si(v
, 1);
683 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
684 isl_int_set_si(v
, 4);
685 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
686 bset
= isl_basic_set_add_constraint(bset
, c
);
688 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
690 assert(bset
&& bset
->n_div
== 1);
691 isl_local_space_free(ls
);
692 isl_basic_set_free(bset
);
695 dim
= isl_space_set_alloc(ctx
, 0, 3);
696 bset
= isl_basic_set_universe(isl_space_copy(dim
));
697 ls
= isl_local_space_from_space(dim
);
699 c
= isl_equality_alloc(isl_local_space_copy(ls
));
700 isl_int_set_si(v
, 2);
701 isl_constraint_set_constant(c
, v
);
702 isl_int_set_si(v
, -1);
703 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
704 isl_int_set_si(v
, 3);
705 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
706 bset
= isl_basic_set_add_constraint(bset
, c
);
708 c
= isl_equality_alloc(isl_local_space_copy(ls
));
709 isl_int_set_si(v
, -1);
710 isl_constraint_set_constant(c
, v
);
711 isl_int_set_si(v
, 1);
712 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
713 isl_int_set_si(v
, 6);
714 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
715 bset
= isl_basic_set_add_constraint(bset
, c
);
717 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
719 assert(isl_basic_set_is_empty(bset
));
720 isl_local_space_free(ls
);
721 isl_basic_set_free(bset
);
724 dim
= isl_space_set_alloc(ctx
, 0, 3);
725 bset
= isl_basic_set_universe(isl_space_copy(dim
));
726 ls
= isl_local_space_from_space(dim
);
728 c
= isl_equality_alloc(isl_local_space_copy(ls
));
729 isl_int_set_si(v
, -1);
730 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
731 isl_int_set_si(v
, 3);
732 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
733 bset
= isl_basic_set_add_constraint(bset
, c
);
735 c
= isl_equality_alloc(isl_local_space_copy(ls
));
736 isl_int_set_si(v
, 1);
737 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
738 isl_int_set_si(v
, -3);
739 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
740 bset
= isl_basic_set_add_constraint(bset
, c
);
742 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
744 assert(bset
&& bset
->n_div
== 0);
745 isl_basic_set_free(bset
);
746 isl_local_space_free(ls
);
749 dim
= isl_space_set_alloc(ctx
, 0, 3);
750 bset
= isl_basic_set_universe(isl_space_copy(dim
));
751 ls
= isl_local_space_from_space(dim
);
753 c
= isl_equality_alloc(isl_local_space_copy(ls
));
754 isl_int_set_si(v
, -1);
755 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
756 isl_int_set_si(v
, 6);
757 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
758 bset
= isl_basic_set_add_constraint(bset
, c
);
760 c
= isl_equality_alloc(isl_local_space_copy(ls
));
761 isl_int_set_si(v
, 1);
762 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
763 isl_int_set_si(v
, -3);
764 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
765 bset
= isl_basic_set_add_constraint(bset
, c
);
767 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
769 assert(bset
&& bset
->n_div
== 1);
770 isl_basic_set_free(bset
);
771 isl_local_space_free(ls
);
774 /* This test is a bit tricky. We set up an equality
776 * Normalization of divs creates _two_ divs
779 * Afterwards e0 is removed again because it has coefficient -1
780 * and we end up with the original equality and div again.
781 * Perhaps we can avoid the introduction of this temporary div.
783 dim
= isl_space_set_alloc(ctx
, 0, 4);
784 bset
= isl_basic_set_universe(isl_space_copy(dim
));
785 ls
= isl_local_space_from_space(dim
);
787 c
= isl_equality_alloc(isl_local_space_copy(ls
));
788 isl_int_set_si(v
, -1);
789 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
790 isl_int_set_si(v
, -3);
791 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
792 isl_int_set_si(v
, -3);
793 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
794 isl_int_set_si(v
, 6);
795 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
796 bset
= isl_basic_set_add_constraint(bset
, c
);
798 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
800 /* Test disabled for now */
802 assert(bset && bset->n_div == 1);
804 isl_local_space_free(ls
);
805 isl_basic_set_free(bset
);
808 dim
= isl_space_set_alloc(ctx
, 0, 5);
809 bset
= isl_basic_set_universe(isl_space_copy(dim
));
810 ls
= isl_local_space_from_space(dim
);
812 c
= isl_equality_alloc(isl_local_space_copy(ls
));
813 isl_int_set_si(v
, -1);
814 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
815 isl_int_set_si(v
, -3);
816 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
817 isl_int_set_si(v
, -3);
818 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
819 isl_int_set_si(v
, 6);
820 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
821 bset
= isl_basic_set_add_constraint(bset
, c
);
823 c
= isl_equality_alloc(isl_local_space_copy(ls
));
824 isl_int_set_si(v
, -1);
825 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
826 isl_int_set_si(v
, 1);
827 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
828 isl_int_set_si(v
, 1);
829 isl_constraint_set_constant(c
, v
);
830 bset
= isl_basic_set_add_constraint(bset
, c
);
832 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
834 /* Test disabled for now */
836 assert(bset && bset->n_div == 1);
838 isl_local_space_free(ls
);
839 isl_basic_set_free(bset
);
842 dim
= isl_space_set_alloc(ctx
, 0, 4);
843 bset
= isl_basic_set_universe(isl_space_copy(dim
));
844 ls
= isl_local_space_from_space(dim
);
846 c
= isl_equality_alloc(isl_local_space_copy(ls
));
847 isl_int_set_si(v
, 1);
848 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
849 isl_int_set_si(v
, -1);
850 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
851 isl_int_set_si(v
, -2);
852 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
853 bset
= isl_basic_set_add_constraint(bset
, c
);
855 c
= isl_equality_alloc(isl_local_space_copy(ls
));
856 isl_int_set_si(v
, -1);
857 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
858 isl_int_set_si(v
, 3);
859 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
860 isl_int_set_si(v
, 2);
861 isl_constraint_set_constant(c
, v
);
862 bset
= isl_basic_set_add_constraint(bset
, c
);
864 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
866 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
868 assert(!isl_basic_set_is_empty(bset
));
870 isl_local_space_free(ls
);
871 isl_basic_set_free(bset
);
874 dim
= isl_space_set_alloc(ctx
, 0, 3);
875 bset
= isl_basic_set_universe(isl_space_copy(dim
));
876 ls
= isl_local_space_from_space(dim
);
878 c
= isl_equality_alloc(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
, -2);
882 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
883 bset
= isl_basic_set_add_constraint(bset
, c
);
885 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
887 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
889 isl_local_space_free(ls
);
890 isl_basic_set_free(bset
);
894 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
895 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
896 set
= isl_set_read_from_str(ctx
, str
);
897 set
= isl_set_compute_divs(set
);
902 str
= "{ [i,j] : 2*[i/2] + 3 * [j/4] <= 10 and 2 i = j }";
903 bset
= isl_basic_set_read_from_str(ctx
, str
);
904 n
= isl_basic_set_dim(bset
, isl_dim_div
);
905 isl_basic_set_free(bset
);
909 isl_die(ctx
, isl_error_unknown
,
910 "expecting no existentials", return -1);
912 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
913 set
= isl_set_read_from_str(ctx
, str
);
914 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
915 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
916 empty
= isl_set_is_empty(set
);
921 isl_die(ctx
, isl_error_unknown
,
922 "result not as accurate as expected", return -1);
927 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
931 struct isl_basic_set
*bset1
, *bset2
;
932 struct isl_basic_map
*bmap
;
934 filename
= get_filename(ctx
, name
, "omega");
936 input
= fopen(filename
, "r");
939 bset1
= isl_basic_set_read_from_file(ctx
, input
);
940 bmap
= isl_basic_map_read_from_file(ctx
, input
);
942 bset1
= isl_basic_set_apply(bset1
, bmap
);
944 bset2
= isl_basic_set_read_from_file(ctx
, input
);
946 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
948 isl_basic_set_free(bset1
);
949 isl_basic_set_free(bset2
);
955 void test_application(struct isl_ctx
*ctx
)
957 test_application_case(ctx
, "application");
958 test_application_case(ctx
, "application2");
961 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
965 struct isl_basic_set
*bset1
, *bset2
;
967 filename
= get_filename(ctx
, name
, "polylib");
969 input
= fopen(filename
, "r");
972 bset1
= isl_basic_set_read_from_file(ctx
, input
);
973 bset2
= isl_basic_set_read_from_file(ctx
, input
);
975 bset1
= isl_basic_set_affine_hull(bset1
);
977 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
979 isl_basic_set_free(bset1
);
980 isl_basic_set_free(bset2
);
986 int test_affine_hull(struct isl_ctx
*ctx
)
990 isl_basic_set
*bset
, *bset2
;
994 test_affine_hull_case(ctx
, "affine2");
995 test_affine_hull_case(ctx
, "affine");
996 test_affine_hull_case(ctx
, "affine3");
998 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
999 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
1000 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
1001 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
1002 set
= isl_set_read_from_str(ctx
, str
);
1003 bset
= isl_set_affine_hull(set
);
1004 n
= isl_basic_set_dim(bset
, isl_dim_div
);
1005 isl_basic_set_free(bset
);
1007 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
1010 /* Check that isl_map_affine_hull is not confused by
1011 * the reordering of divs in isl_map_align_divs.
1013 str
= "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1014 "32e0 = b and 32e1 = c); "
1015 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1016 set
= isl_set_read_from_str(ctx
, str
);
1017 bset
= isl_set_affine_hull(set
);
1018 isl_basic_set_free(bset
);
1022 str
= "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1023 "32e2 = 31 + 31e0 }";
1024 set
= isl_set_read_from_str(ctx
, str
);
1025 bset
= isl_set_affine_hull(set
);
1026 str
= "{ [a] : exists e : a = 32 e }";
1027 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1028 subset
= isl_basic_set_is_subset(bset
, bset2
);
1029 isl_basic_set_free(bset
);
1030 isl_basic_set_free(bset2
);
1034 isl_die(ctx
, isl_error_unknown
, "not as accurate as expected",
1040 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
1044 struct isl_basic_set
*bset1
, *bset2
;
1045 struct isl_set
*set
;
1047 filename
= get_filename(ctx
, name
, "polylib");
1049 input
= fopen(filename
, "r");
1052 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1053 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1055 set
= isl_basic_set_union(bset1
, bset2
);
1056 bset1
= isl_set_convex_hull(set
);
1058 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1060 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1062 isl_basic_set_free(bset1
);
1063 isl_basic_set_free(bset2
);
1072 } convex_hull_tests
[] = {
1073 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1074 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1075 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1076 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1077 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1078 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1079 "i2 <= 5 and i2 >= 4; "
1080 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1081 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1082 "i2 <= 5 + i0 and i2 >= i0 }" },
1083 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1084 "{ [x, y] : 1 = 0 }" },
1087 void test_convex_hull_algo(struct isl_ctx
*ctx
, int convex
)
1090 int orig_convex
= ctx
->opt
->convex
;
1091 ctx
->opt
->convex
= convex
;
1093 test_convex_hull_case(ctx
, "convex0");
1094 test_convex_hull_case(ctx
, "convex1");
1095 test_convex_hull_case(ctx
, "convex2");
1096 test_convex_hull_case(ctx
, "convex3");
1097 test_convex_hull_case(ctx
, "convex4");
1098 test_convex_hull_case(ctx
, "convex5");
1099 test_convex_hull_case(ctx
, "convex6");
1100 test_convex_hull_case(ctx
, "convex7");
1101 test_convex_hull_case(ctx
, "convex8");
1102 test_convex_hull_case(ctx
, "convex9");
1103 test_convex_hull_case(ctx
, "convex10");
1104 test_convex_hull_case(ctx
, "convex11");
1105 test_convex_hull_case(ctx
, "convex12");
1106 test_convex_hull_case(ctx
, "convex13");
1107 test_convex_hull_case(ctx
, "convex14");
1108 test_convex_hull_case(ctx
, "convex15");
1110 for (i
= 0; i
< ARRAY_SIZE(convex_hull_tests
); ++i
) {
1111 isl_set
*set1
, *set2
;
1113 set1
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].set
);
1114 set2
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].hull
);
1115 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
1116 assert(isl_set_is_equal(set1
, set2
));
1121 ctx
->opt
->convex
= orig_convex
;
1124 void test_convex_hull(struct isl_ctx
*ctx
)
1126 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
);
1127 test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
);
1130 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
1134 struct isl_basic_set
*bset1
, *bset2
;
1136 filename
= get_filename(ctx
, name
, "polylib");
1138 input
= fopen(filename
, "r");
1141 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1142 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1144 bset1
= isl_basic_set_gist(bset1
, bset2
);
1146 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1148 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1150 isl_basic_set_free(bset1
);
1151 isl_basic_set_free(bset2
);
1159 const char *context
;
1162 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1163 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1164 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1165 "{ [a, b, c] : a <= 15 }" },
1166 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1167 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1168 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1169 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1170 { "{ [m, n, a, b] : a <= 2147 + n }",
1171 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1172 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1173 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1175 "{ [m, n, ku, kl] }" },
1178 static int test_gist(struct isl_ctx
*ctx
)
1182 isl_basic_set
*bset1
, *bset2
;
1183 isl_map
*map1
, *map2
;
1186 for (i
= 0; i
< ARRAY_SIZE(gist_tests
); ++i
) {
1188 isl_set
*set1
, *set2
, *copy
;
1190 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1191 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].context
);
1192 copy
= isl_set_copy(set1
);
1193 set1
= isl_set_gist(set1
, set2
);
1194 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].gist
);
1195 equal
= isl_set_is_equal(set1
, set2
);
1198 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1199 equal_input
= isl_set_is_equal(set1
, copy
);
1202 if (equal
< 0 || equal_input
< 0)
1205 isl_die(ctx
, isl_error_unknown
,
1206 "incorrect gist result", return -1);
1208 isl_die(ctx
, isl_error_unknown
,
1209 "gist modified input", return -1);
1212 test_gist_case(ctx
, "gist1");
1214 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1215 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1216 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1217 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1218 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1219 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1220 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1221 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1222 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1223 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1224 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1225 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1226 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1227 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1228 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1229 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1230 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1231 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1232 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1233 bset1
= isl_basic_set_gist(bset1
, bset2
);
1234 assert(bset1
&& bset1
->n_div
== 0);
1235 isl_basic_set_free(bset1
);
1237 /* Check that the integer divisions of the second disjunct
1238 * do not spread to the first disjunct.
1240 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1241 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1242 "(exists (e0 = [(-1 + t1)/16], "
1243 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1244 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1245 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1246 "o0 <= 4294967295 and t1 <= -1)) }";
1247 map1
= isl_map_read_from_str(ctx
, str
);
1248 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1249 map2
= isl_map_read_from_str(ctx
, str
);
1250 map1
= isl_map_gist(map1
, map2
);
1254 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1255 isl_map_free(map1
); return -1);
1256 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1257 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1258 isl_map_free(map1
); return -1);
1264 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1266 isl_set
*set
, *set2
;
1270 set
= isl_set_read_from_str(ctx
, str
);
1271 set
= isl_set_coalesce(set
);
1272 set2
= isl_set_read_from_str(ctx
, str
);
1273 equal
= isl_set_is_equal(set
, set2
);
1274 one
= set
&& set
->n
== 1;
1281 isl_die(ctx
, isl_error_unknown
,
1282 "coalesced set not equal to input", return -1);
1283 if (check_one
&& !one
)
1284 isl_die(ctx
, isl_error_unknown
,
1285 "coalesced set should not be a union", return -1);
1290 /* Inputs for coalescing tests with unbounded wrapping.
1291 * "str" is a string representation of the input set.
1292 * "single_disjunct" is set if we expect the result to consist of
1293 * a single disjunct.
1296 int single_disjunct
;
1298 } coalesce_unbounded_tests
[] = {
1299 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1300 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1301 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1302 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1304 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1305 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1306 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1307 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1310 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1311 * option turned off.
1313 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1319 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1320 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1322 for (i
= 0; i
< ARRAY_SIZE(coalesce_unbounded_tests
); ++i
) {
1323 const char *str
= coalesce_unbounded_tests
[i
].str
;
1324 int check_one
= coalesce_unbounded_tests
[i
].single_disjunct
;
1325 if (test_coalesce_set(ctx
, str
, check_one
) >= 0)
1331 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1336 /* Inputs for coalescing tests.
1337 * "str" is a string representation of the input set.
1338 * "single_disjunct" is set if we expect the result to consist of
1339 * a single disjunct.
1342 int single_disjunct
;
1344 } coalesce_tests
[] = {
1345 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1346 "y >= x & x >= 2 & 5 >= y }" },
1347 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1348 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1349 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1350 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1351 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1352 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1353 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1354 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1355 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1356 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1357 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1358 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1359 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1360 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1361 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1362 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1363 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1364 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1365 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1366 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1367 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1368 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1369 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1370 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1371 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1372 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1373 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1374 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1375 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1376 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1377 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1378 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1379 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1380 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1381 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1382 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1383 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1384 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1385 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1386 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1387 "[o0, o1, o2, o3, o4, o5, o6]] : "
1388 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1389 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1390 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1391 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1392 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1393 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1394 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1395 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1396 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1397 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1398 "o6 >= i3 + i6 - o3 and M >= 0 and "
1399 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1400 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1401 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1402 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1403 "(o0 = 0 and M >= 2 and N >= 3) or "
1404 "(M = 0 and o0 = 0 and N >= 3) }" },
1405 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1406 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1407 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1408 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1409 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1410 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1411 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1412 "(y = 3 and x = 1) }" },
1413 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1414 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1415 "i1 <= M and i3 <= M and i4 <= M) or "
1416 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1417 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1418 "i4 <= -1 + M) }" },
1419 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1420 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1421 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1422 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1423 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1424 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1425 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1426 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1427 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1428 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1429 { 0, "{ [a, b] : exists e : 2e = a and "
1430 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1431 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1432 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1433 "j >= 1 and j' <= i + j - i' and i >= 1; "
1435 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1436 "[i,j] : exists a : j = 3a }" },
1437 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1438 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1440 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1441 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1442 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1443 "c <= 6 + 8a and a >= 3; "
1444 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1445 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1446 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1447 "[x,0] : 3 <= x <= 4 }" },
1448 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1449 "[x,0] : 4 <= x <= 5 }" },
1450 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1451 "[x,0] : 3 <= x <= 5 }" },
1452 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1453 "[x,0] : 3 <= x <= 4 }" },
1454 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1456 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1457 { 1, "{ [0,0]; [1,1] }" },
1458 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1461 /* Test the functionality of isl_set_coalesce.
1462 * That is, check that the output is always equal to the input
1463 * and in some cases that the result consists of a single disjunct.
1465 static int test_coalesce(struct isl_ctx
*ctx
)
1469 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
1470 const char *str
= coalesce_tests
[i
].str
;
1471 int check_one
= coalesce_tests
[i
].single_disjunct
;
1472 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
1476 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1482 void test_closure(struct isl_ctx
*ctx
)
1486 isl_map
*up
, *right
;
1487 isl_map
*map
, *map2
;
1490 /* COCOA example 1 */
1491 map
= isl_map_read_from_str(ctx
,
1492 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1493 "1 <= i and i < n and 1 <= j and j < n or "
1494 "i2 = i + 1 and j2 = j - 1 and "
1495 "1 <= i and i < n and 2 <= j and j <= n }");
1496 map
= isl_map_power(map
, &exact
);
1500 /* COCOA example 1 */
1501 map
= isl_map_read_from_str(ctx
,
1502 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1503 "1 <= i and i < n and 1 <= j and j < n or "
1504 "i2 = i + 1 and j2 = j - 1 and "
1505 "1 <= i and i < n and 2 <= j and j <= n }");
1506 map
= isl_map_transitive_closure(map
, &exact
);
1508 map2
= isl_map_read_from_str(ctx
,
1509 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1510 "1 <= i and i < n and 1 <= j and j <= n and "
1511 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1512 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1513 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1514 assert(isl_map_is_equal(map
, map2
));
1518 map
= isl_map_read_from_str(ctx
,
1519 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1520 " 0 <= y and y <= n }");
1521 map
= isl_map_transitive_closure(map
, &exact
);
1522 map2
= isl_map_read_from_str(ctx
,
1523 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1524 " 0 <= y and y <= n }");
1525 assert(isl_map_is_equal(map
, map2
));
1529 /* COCOA example 2 */
1530 map
= isl_map_read_from_str(ctx
,
1531 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1532 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1533 "i2 = i + 2 and j2 = j - 2 and "
1534 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
1535 map
= isl_map_transitive_closure(map
, &exact
);
1537 map2
= isl_map_read_from_str(ctx
,
1538 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1539 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
1540 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1541 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
1542 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
1543 assert(isl_map_is_equal(map
, map2
));
1547 /* COCOA Fig.2 left */
1548 map
= isl_map_read_from_str(ctx
,
1549 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
1550 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
1552 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
1553 "j <= 2 i - 3 and j <= n - 2 or "
1554 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1555 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1556 map
= isl_map_transitive_closure(map
, &exact
);
1560 /* COCOA Fig.2 right */
1561 map
= isl_map_read_from_str(ctx
,
1562 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1563 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1565 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1566 "j <= 2 i - 4 and j <= n - 3 or "
1567 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1568 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1569 map
= isl_map_power(map
, &exact
);
1573 /* COCOA Fig.2 right */
1574 map
= isl_map_read_from_str(ctx
,
1575 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
1576 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
1578 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
1579 "j <= 2 i - 4 and j <= n - 3 or "
1580 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
1581 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
1582 map
= isl_map_transitive_closure(map
, &exact
);
1584 map2
= isl_map_read_from_str(ctx
,
1585 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
1586 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
1587 "j <= n and 3 + i + 2 j <= 3 n and "
1588 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
1589 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
1590 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
1591 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
1592 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
1593 assert(isl_map_is_equal(map
, map2
));
1597 /* COCOA Fig.1 right */
1598 dom
= isl_set_read_from_str(ctx
,
1599 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1600 "2 x - 3 y + 3 >= 0 }");
1601 right
= isl_map_read_from_str(ctx
,
1602 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1603 up
= isl_map_read_from_str(ctx
,
1604 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1605 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1606 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1607 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1608 up
= isl_map_intersect_range(up
, dom
);
1609 map
= isl_map_union(up
, right
);
1610 map
= isl_map_transitive_closure(map
, &exact
);
1612 map2
= isl_map_read_from_str(ctx
,
1613 "{ [0,0] -> [0,1]; [0,0] -> [1,1]; [0,1] -> [1,1]; "
1614 " [2,2] -> [3,2]; [2,2] -> [3,3]; [3,2] -> [3,3] }");
1615 assert(isl_map_is_equal(map
, map2
));
1619 /* COCOA Theorem 1 counter example */
1620 map
= isl_map_read_from_str(ctx
,
1621 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
1622 "i2 = 1 and j2 = j or "
1623 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
1624 map
= isl_map_transitive_closure(map
, &exact
);
1628 map
= isl_map_read_from_str(ctx
,
1629 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
1630 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
1631 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
1632 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
1633 map
= isl_map_transitive_closure(map
, &exact
);
1637 /* Kelly et al 1996, fig 12 */
1638 map
= isl_map_read_from_str(ctx
,
1639 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
1640 "1 <= i,j,j+1 <= n or "
1641 "j = n and j2 = 1 and i2 = i + 1 and "
1642 "1 <= i,i+1 <= n }");
1643 map
= isl_map_transitive_closure(map
, &exact
);
1645 map2
= isl_map_read_from_str(ctx
,
1646 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
1647 "1 <= i <= n and i = i2 or "
1648 "1 <= i < i2 <= n and 1 <= j <= n and "
1650 assert(isl_map_is_equal(map
, map2
));
1654 /* Omega's closure4 */
1655 map
= isl_map_read_from_str(ctx
,
1656 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
1657 "1 <= x,y <= 10 or "
1658 "x2 = x + 1 and y2 = y and "
1659 "1 <= x <= 20 && 5 <= y <= 15 }");
1660 map
= isl_map_transitive_closure(map
, &exact
);
1664 map
= isl_map_read_from_str(ctx
,
1665 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
1666 map
= isl_map_transitive_closure(map
, &exact
);
1668 map2
= isl_map_read_from_str(ctx
,
1669 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
1670 assert(isl_map_is_equal(map
, map2
));
1674 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
1675 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
1676 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
1677 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
1678 map
= isl_map_read_from_str(ctx
, str
);
1679 map
= isl_map_transitive_closure(map
, &exact
);
1681 map2
= isl_map_read_from_str(ctx
, str
);
1682 assert(isl_map_is_equal(map
, map2
));
1686 str
= "{[0] -> [1]; [2] -> [3]}";
1687 map
= isl_map_read_from_str(ctx
, str
);
1688 map
= isl_map_transitive_closure(map
, &exact
);
1690 map2
= isl_map_read_from_str(ctx
, str
);
1691 assert(isl_map_is_equal(map
, map2
));
1695 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
1696 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
1697 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
1698 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1699 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1700 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
1701 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
1702 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
1703 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1704 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1705 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
1706 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
1707 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
1708 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1709 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
1710 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
1711 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
1712 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
1713 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
1714 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
1715 map
= isl_map_read_from_str(ctx
, str
);
1716 map
= isl_map_transitive_closure(map
, NULL
);
1721 void test_lex(struct isl_ctx
*ctx
)
1726 dim
= isl_space_set_alloc(ctx
, 0, 0);
1727 map
= isl_map_lex_le(dim
);
1728 assert(!isl_map_is_empty(map
));
1732 static int test_lexmin(struct isl_ctx
*ctx
)
1736 isl_basic_map
*bmap
;
1737 isl_map
*map
, *map2
;
1740 isl_pw_multi_aff
*pma
;
1742 str
= "[p0, p1] -> { [] -> [] : "
1743 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
1744 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
1745 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
1746 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
1747 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
1748 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
1749 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
1750 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
1751 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
1752 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
1753 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
1754 map
= isl_map_read_from_str(ctx
, str
);
1755 map
= isl_map_lexmin(map
);
1758 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
1759 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
1760 set
= isl_set_read_from_str(ctx
, str
);
1761 set
= isl_set_lexmax(set
);
1762 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
1763 set2
= isl_set_read_from_str(ctx
, str
);
1764 set
= isl_set_intersect(set
, set2
);
1765 assert(!isl_set_is_empty(set
));
1768 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
1769 map
= isl_map_read_from_str(ctx
, str
);
1770 map
= isl_map_lexmin(map
);
1771 str
= "{ [x] -> [5] : 6 <= x <= 8; "
1772 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
1773 map2
= isl_map_read_from_str(ctx
, str
);
1774 assert(isl_map_is_equal(map
, map2
));
1778 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
1779 map
= isl_map_read_from_str(ctx
, str
);
1780 map2
= isl_map_copy(map
);
1781 map
= isl_map_lexmin(map
);
1782 assert(isl_map_is_equal(map
, map2
));
1786 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
1787 map
= isl_map_read_from_str(ctx
, str
);
1788 map
= isl_map_lexmin(map
);
1789 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
1790 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
1791 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
1792 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
1793 map2
= isl_map_read_from_str(ctx
, str
);
1794 assert(isl_map_is_equal(map
, map2
));
1798 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1799 " 8i' <= i and 8i' >= -7 + i }";
1800 bmap
= isl_basic_map_read_from_str(ctx
, str
);
1801 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
1802 map2
= isl_map_from_pw_multi_aff(pma
);
1803 map
= isl_map_from_basic_map(bmap
);
1804 assert(isl_map_is_equal(map
, map2
));
1808 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
1809 map
= isl_map_read_from_str(ctx
, str
);
1810 map
= isl_map_lexmin(map
);
1811 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
1812 map2
= isl_map_read_from_str(ctx
, str
);
1813 assert(isl_map_is_equal(map
, map2
));
1817 /* Check that empty pieces are properly combined. */
1818 str
= "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
1819 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
1820 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
1821 map
= isl_map_read_from_str(ctx
, str
);
1822 map
= isl_map_lexmin(map
);
1823 str
= "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
1824 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
1826 map2
= isl_map_read_from_str(ctx
, str
);
1827 assert(isl_map_is_equal(map
, map2
));
1831 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
1832 " 8i' <= i and 8i' >= -7 + i }";
1833 set
= isl_set_read_from_str(ctx
, str
);
1834 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
1835 set2
= isl_set_from_pw_multi_aff(pma
);
1836 equal
= isl_set_is_equal(set
, set2
);
1842 isl_die(ctx
, isl_error_unknown
,
1843 "unexpected difference between set and "
1844 "piecewise affine expression", return -1);
1849 /* Check that isl_set_min_val and isl_set_max_val compute the correct
1850 * result on non-convex inputs.
1852 static int test_min(struct isl_ctx
*ctx
)
1859 set
= isl_set_read_from_str(ctx
, "{ [-1]; [1] }");
1860 aff
= isl_aff_read_from_str(ctx
, "{ [x] -> [x] }");
1861 val
= isl_set_min_val(set
, aff
);
1862 min_ok
= isl_val_is_negone(val
);
1864 val
= isl_set_max_val(set
, aff
);
1865 max_ok
= isl_val_is_one(val
);
1870 if (min_ok
< 0 || max_ok
< 0)
1873 isl_die(ctx
, isl_error_unknown
,
1874 "unexpected minimum", return -1);
1876 isl_die(ctx
, isl_error_unknown
,
1877 "unexpected maximum", return -1);
1887 static int collect_must_may(__isl_take isl_map
*dep
, int must
,
1888 void *dep_user
, void *user
)
1890 struct must_may
*mm
= (struct must_may
*)user
;
1893 mm
->must
= isl_map_union(mm
->must
, dep
);
1895 mm
->may
= isl_map_union(mm
->may
, dep
);
1900 static int common_space(void *first
, void *second
)
1902 int depth
= *(int *)first
;
1906 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
1914 map2
= isl_map_read_from_str(map
->ctx
, str
);
1915 equal
= isl_map_is_equal(map
, map2
);
1921 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
1925 equal
= map_is_equal(map
, str
);
1929 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
1930 "result not as expected", return -1);
1934 void test_dep(struct isl_ctx
*ctx
)
1939 isl_access_info
*ai
;
1946 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1947 map
= isl_map_read_from_str(ctx
, str
);
1948 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1950 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1951 map
= isl_map_read_from_str(ctx
, str
);
1952 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1954 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1955 map
= isl_map_read_from_str(ctx
, str
);
1956 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1958 flow
= isl_access_info_compute_flow(ai
);
1959 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1960 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1961 mm
.may
= isl_map_empty(dim
);
1963 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1965 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
1966 " [1,10,0] -> [2,5,0] }";
1967 assert(map_is_equal(mm
.must
, str
));
1968 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
1969 assert(map_is_equal(mm
.may
, str
));
1971 isl_map_free(mm
.must
);
1972 isl_map_free(mm
.may
);
1973 isl_flow_free(flow
);
1976 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
1977 map
= isl_map_read_from_str(ctx
, str
);
1978 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
1980 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
1981 map
= isl_map_read_from_str(ctx
, str
);
1982 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
1984 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
1985 map
= isl_map_read_from_str(ctx
, str
);
1986 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
1988 flow
= isl_access_info_compute_flow(ai
);
1989 dim
= isl_space_alloc(ctx
, 0, 3, 3);
1990 mm
.must
= isl_map_empty(isl_space_copy(dim
));
1991 mm
.may
= isl_map_empty(dim
);
1993 isl_flow_foreach(flow
, collect_must_may
, &mm
);
1995 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
1996 assert(map_is_equal(mm
.must
, str
));
1997 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
1998 assert(map_is_equal(mm
.may
, str
));
2000 isl_map_free(mm
.must
);
2001 isl_map_free(mm
.may
);
2002 isl_flow_free(flow
);
2005 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2006 map
= isl_map_read_from_str(ctx
, str
);
2007 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2009 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2010 map
= isl_map_read_from_str(ctx
, str
);
2011 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2013 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2014 map
= isl_map_read_from_str(ctx
, str
);
2015 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2017 flow
= isl_access_info_compute_flow(ai
);
2018 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2019 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2020 mm
.may
= isl_map_empty(dim
);
2022 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2024 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2025 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2026 assert(map_is_equal(mm
.may
, str
));
2027 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2028 assert(map_is_equal(mm
.must
, str
));
2030 isl_map_free(mm
.must
);
2031 isl_map_free(mm
.may
);
2032 isl_flow_free(flow
);
2035 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2036 map
= isl_map_read_from_str(ctx
, str
);
2037 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2039 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2040 map
= isl_map_read_from_str(ctx
, str
);
2041 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2043 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2044 map
= isl_map_read_from_str(ctx
, str
);
2045 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2047 flow
= isl_access_info_compute_flow(ai
);
2048 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2049 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2050 mm
.may
= isl_map_empty(dim
);
2052 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2054 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2055 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2056 assert(map_is_equal(mm
.may
, str
));
2057 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2058 assert(map_is_equal(mm
.must
, str
));
2060 isl_map_free(mm
.must
);
2061 isl_map_free(mm
.may
);
2062 isl_flow_free(flow
);
2065 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2066 map
= isl_map_read_from_str(ctx
, str
);
2067 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2069 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2070 map
= isl_map_read_from_str(ctx
, str
);
2071 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2073 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2074 map
= isl_map_read_from_str(ctx
, str
);
2075 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2077 flow
= isl_access_info_compute_flow(ai
);
2078 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2079 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2080 mm
.may
= isl_map_empty(dim
);
2082 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2084 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2085 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2086 assert(map_is_equal(mm
.may
, str
));
2087 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2088 assert(map_is_equal(mm
.must
, str
));
2090 isl_map_free(mm
.must
);
2091 isl_map_free(mm
.may
);
2092 isl_flow_free(flow
);
2097 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2098 map
= isl_map_read_from_str(ctx
, str
);
2099 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2101 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2102 map
= isl_map_read_from_str(ctx
, str
);
2103 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2105 flow
= isl_access_info_compute_flow(ai
);
2106 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2107 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2108 mm
.may
= isl_map_empty(dim
);
2110 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2112 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2113 assert(map_is_equal(mm
.must
, str
));
2114 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2115 assert(map_is_equal(mm
.may
, str
));
2117 isl_map_free(mm
.must
);
2118 isl_map_free(mm
.may
);
2119 isl_flow_free(flow
);
2122 /* Check that the dependence analysis proceeds without errors.
2123 * Earlier versions of isl would break down during the analysis
2124 * due to the use of the wrong spaces.
2126 static int test_flow(isl_ctx
*ctx
)
2129 isl_union_map
*access
, *schedule
;
2130 isl_union_map
*must_dep
, *may_dep
;
2133 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2134 access
= isl_union_map_read_from_str(ctx
, str
);
2135 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2136 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2137 "S2[] -> [1,0,0,0]; "
2138 "S3[] -> [-1,0,0,0] }";
2139 schedule
= isl_union_map_read_from_str(ctx
, str
);
2140 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2141 isl_union_map_copy(access
), schedule
,
2142 &must_dep
, &may_dep
, NULL
, NULL
);
2143 isl_union_map_free(may_dep
);
2144 isl_union_map_free(must_dep
);
2153 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2154 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2155 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2156 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2157 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2158 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2159 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2160 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2161 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2164 int test_sv(isl_ctx
*ctx
)
2166 isl_union_map
*umap
;
2170 for (i
= 0; i
< ARRAY_SIZE(sv_tests
); ++i
) {
2171 umap
= isl_union_map_read_from_str(ctx
, sv_tests
[i
].map
);
2172 sv
= isl_union_map_is_single_valued(umap
);
2173 isl_union_map_free(umap
);
2176 if (sv_tests
[i
].sv
&& !sv
)
2177 isl_die(ctx
, isl_error_internal
,
2178 "map not detected as single valued", return -1);
2179 if (!sv_tests
[i
].sv
&& sv
)
2180 isl_die(ctx
, isl_error_internal
,
2181 "map detected as single valued", return -1);
2187 void test_bijective_case(struct isl_ctx
*ctx
, const char *str
, int bijective
)
2191 map
= isl_map_read_from_str(ctx
, str
);
2193 assert(isl_map_is_bijective(map
));
2195 assert(!isl_map_is_bijective(map
));
2199 void test_bijective(struct isl_ctx
*ctx
)
2201 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i]}", 0);
2202 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=i}", 1);
2203 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=0}", 1);
2204 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i] : j=N}", 1);
2205 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [j,i]}", 1);
2206 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i+j]}", 0);
2207 test_bijective_case(ctx
, "[N,M]->{[i,j] -> []}", 0);
2208 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,j,N]}", 1);
2209 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i]}", 0);
2210 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [i,i]}", 0);
2211 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,i]}", 0);
2212 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [2i,j]}", 1);
2213 test_bijective_case(ctx
, "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1);
2216 /* Inputs for isl_pw_qpolynomial_gist tests.
2217 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2223 } pwqp_gist_tests
[] = {
2224 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2225 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2226 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2227 "{ [i] -> -1/2 + 1/2 * i }" },
2228 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2231 static int test_pwqp(struct isl_ctx
*ctx
)
2236 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
2239 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2240 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2242 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
2245 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2246 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2248 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2250 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2252 isl_pw_qpolynomial_free(pwqp1
);
2254 for (i
= 0; i
< ARRAY_SIZE(pwqp_gist_tests
); ++i
) {
2255 str
= pwqp_gist_tests
[i
].pwqp
;
2256 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2257 str
= pwqp_gist_tests
[i
].set
;
2258 set
= isl_set_read_from_str(ctx
, str
);
2259 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2260 str
= pwqp_gist_tests
[i
].gist
;
2261 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2262 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2263 equal
= isl_pw_qpolynomial_is_zero(pwqp1
);
2264 isl_pw_qpolynomial_free(pwqp1
);
2269 isl_die(ctx
, isl_error_unknown
,
2270 "unexpected result", return -1);
2273 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
2274 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2275 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
2276 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2278 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2280 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2282 isl_pw_qpolynomial_free(pwqp1
);
2284 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
2285 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2286 str
= "{ [x] -> x }";
2287 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2289 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2291 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2293 isl_pw_qpolynomial_free(pwqp1
);
2295 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2296 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2297 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2298 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
2299 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2300 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2301 isl_pw_qpolynomial_free(pwqp1
);
2303 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2304 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2305 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2306 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2307 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
2308 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
2309 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2310 isl_pw_qpolynomial_free(pwqp1
);
2311 isl_pw_qpolynomial_free(pwqp2
);
2315 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2317 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2318 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2319 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2320 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2321 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
2323 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2324 isl_pw_qpolynomial_free(pwqp1
);
2325 isl_pw_qpolynomial_free(pwqp2
);
2329 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2334 void test_split_periods(isl_ctx
*ctx
)
2337 isl_pw_qpolynomial
*pwqp
;
2339 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2340 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2341 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2342 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2344 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
2347 isl_pw_qpolynomial_free(pwqp
);
2350 void test_union(isl_ctx
*ctx
)
2353 isl_union_set
*uset1
, *uset2
;
2354 isl_union_map
*umap1
, *umap2
;
2356 str
= "{ [i] : 0 <= i <= 1 }";
2357 uset1
= isl_union_set_read_from_str(ctx
, str
);
2358 str
= "{ [1] -> [0] }";
2359 umap1
= isl_union_map_read_from_str(ctx
, str
);
2361 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
2362 assert(isl_union_map_is_equal(umap1
, umap2
));
2364 isl_union_map_free(umap1
);
2365 isl_union_map_free(umap2
);
2367 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2368 umap1
= isl_union_map_read_from_str(ctx
, str
);
2369 str
= "{ A[i]; B[i] }";
2370 uset1
= isl_union_set_read_from_str(ctx
, str
);
2372 uset2
= isl_union_map_domain(umap1
);
2374 assert(isl_union_set_is_equal(uset1
, uset2
));
2376 isl_union_set_free(uset1
);
2377 isl_union_set_free(uset2
);
2380 void test_bound(isl_ctx
*ctx
)
2383 isl_pw_qpolynomial
*pwqp
;
2384 isl_pw_qpolynomial_fold
*pwf
;
2386 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
2387 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2388 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2389 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 4);
2390 isl_pw_qpolynomial_fold_free(pwf
);
2392 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2393 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2394 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2395 assert(isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
) == 1);
2396 isl_pw_qpolynomial_fold_free(pwf
);
2399 void test_lift(isl_ctx
*ctx
)
2402 isl_basic_map
*bmap
;
2403 isl_basic_set
*bset
;
2405 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
2406 bset
= isl_basic_set_read_from_str(ctx
, str
);
2407 bset
= isl_basic_set_lift(bset
);
2408 bmap
= isl_basic_map_from_range(bset
);
2409 bset
= isl_basic_map_domain(bmap
);
2410 isl_basic_set_free(bset
);
2417 } subset_tests
[] = {
2419 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2420 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2421 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2423 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2424 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2425 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2426 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2427 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2428 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2429 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2430 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2431 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
2432 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
2433 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
2434 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
2435 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
2436 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
2437 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
2438 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
2439 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
2440 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
2441 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
2442 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
2443 "4e0 <= -57 + i0 + i1)) or "
2444 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
2445 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
2446 "4e0 >= -61 + i0 + i1)) or "
2447 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
2450 static int test_subset(isl_ctx
*ctx
)
2453 isl_set
*set1
, *set2
;
2456 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
2457 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
2458 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
2459 subset
= isl_set_is_subset(set1
, set2
);
2464 if (subset
!= subset_tests
[i
].subset
)
2465 isl_die(ctx
, isl_error_unknown
,
2466 "incorrect subset result", return -1);
2473 const char *minuend
;
2474 const char *subtrahend
;
2475 const char *difference
;
2476 } subtract_domain_tests
[] = {
2477 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
2478 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
2479 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
2482 static int test_subtract(isl_ctx
*ctx
)
2485 isl_union_map
*umap1
, *umap2
;
2486 isl_union_pw_multi_aff
*upma1
, *upma2
;
2487 isl_union_set
*uset
;
2490 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2491 umap1
= isl_union_map_read_from_str(ctx
,
2492 subtract_domain_tests
[i
].minuend
);
2493 uset
= isl_union_set_read_from_str(ctx
,
2494 subtract_domain_tests
[i
].subtrahend
);
2495 umap2
= isl_union_map_read_from_str(ctx
,
2496 subtract_domain_tests
[i
].difference
);
2497 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
2498 equal
= isl_union_map_is_equal(umap1
, umap2
);
2499 isl_union_map_free(umap1
);
2500 isl_union_map_free(umap2
);
2504 isl_die(ctx
, isl_error_unknown
,
2505 "incorrect subtract domain result", return -1);
2508 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
2509 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
2510 subtract_domain_tests
[i
].minuend
);
2511 uset
= isl_union_set_read_from_str(ctx
,
2512 subtract_domain_tests
[i
].subtrahend
);
2513 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
2514 subtract_domain_tests
[i
].difference
);
2515 upma1
= isl_union_pw_multi_aff_subtract_domain(upma1
, uset
);
2516 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
2517 isl_union_pw_multi_aff_free(upma1
);
2518 isl_union_pw_multi_aff_free(upma2
);
2522 isl_die(ctx
, isl_error_unknown
,
2523 "incorrect subtract domain result", return -1);
2529 int test_factorize(isl_ctx
*ctx
)
2532 isl_basic_set
*bset
;
2535 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
2536 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
2537 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
2538 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
2539 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
2540 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
2541 "3i5 >= -2i0 - i2 + 3i4 }";
2542 bset
= isl_basic_set_read_from_str(ctx
, str
);
2543 f
= isl_basic_set_factorizer(bset
);
2544 isl_basic_set_free(bset
);
2545 isl_factorizer_free(f
);
2547 isl_die(ctx
, isl_error_unknown
,
2548 "failed to construct factorizer", return -1);
2550 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
2551 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
2552 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
2553 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
2554 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
2555 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
2556 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
2557 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
2558 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
2559 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
2560 bset
= isl_basic_set_read_from_str(ctx
, str
);
2561 f
= isl_basic_set_factorizer(bset
);
2562 isl_basic_set_free(bset
);
2563 isl_factorizer_free(f
);
2565 isl_die(ctx
, isl_error_unknown
,
2566 "failed to construct factorizer", return -1);
2571 static int check_injective(__isl_take isl_map
*map
, void *user
)
2573 int *injective
= user
;
2575 *injective
= isl_map_is_injective(map
);
2578 if (*injective
< 0 || !*injective
)
2584 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
2585 const char *r
, const char *s
, int tilable
, int parallel
)
2589 isl_union_map
*W
, *R
, *S
;
2590 isl_union_map
*empty
;
2591 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
2592 isl_union_map
*validity
, *proximity
, *coincidence
;
2593 isl_union_map
*schedule
;
2594 isl_union_map
*test
;
2595 isl_union_set
*delta
;
2596 isl_union_set
*domain
;
2600 isl_schedule_constraints
*sc
;
2601 isl_schedule
*sched
;
2602 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
2604 D
= isl_union_set_read_from_str(ctx
, d
);
2605 W
= isl_union_map_read_from_str(ctx
, w
);
2606 R
= isl_union_map_read_from_str(ctx
, r
);
2607 S
= isl_union_map_read_from_str(ctx
, s
);
2609 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
2610 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
2612 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
2613 isl_union_map_compute_flow(isl_union_map_copy(R
),
2614 isl_union_map_copy(W
), empty
,
2615 isl_union_map_copy(S
),
2616 &dep_raw
, NULL
, NULL
, NULL
);
2617 isl_union_map_compute_flow(isl_union_map_copy(W
),
2618 isl_union_map_copy(W
),
2619 isl_union_map_copy(R
),
2620 isl_union_map_copy(S
),
2621 &dep_waw
, &dep_war
, NULL
, NULL
);
2623 dep
= isl_union_map_union(dep_waw
, dep_war
);
2624 dep
= isl_union_map_union(dep
, dep_raw
);
2625 validity
= isl_union_map_copy(dep
);
2626 coincidence
= isl_union_map_copy(dep
);
2627 proximity
= isl_union_map_copy(dep
);
2629 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
2630 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
2631 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
2632 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
2633 sched
= isl_schedule_constraints_compute_schedule(sc
);
2634 schedule
= isl_schedule_get_map(sched
);
2635 isl_schedule_free(sched
);
2636 isl_union_map_free(W
);
2637 isl_union_map_free(R
);
2638 isl_union_map_free(S
);
2641 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
2643 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
2644 is_complete
= isl_union_set_is_subset(D
, domain
);
2645 isl_union_set_free(D
);
2646 isl_union_set_free(domain
);
2648 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
2649 test
= isl_union_map_apply_range(test
, dep
);
2650 test
= isl_union_map_apply_range(test
, schedule
);
2652 delta
= isl_union_map_deltas(test
);
2653 if (isl_union_set_n_set(delta
) == 0) {
2657 isl_union_set_free(delta
);
2659 delta_set
= isl_set_from_union_set(delta
);
2661 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2662 for (i
= 0; i
< tilable
; ++i
)
2663 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
2664 is_tilable
= isl_set_is_subset(delta_set
, slice
);
2665 isl_set_free(slice
);
2667 slice
= isl_set_universe(isl_set_get_space(delta_set
));
2668 for (i
= 0; i
< parallel
; ++i
)
2669 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
2670 is_parallel
= isl_set_is_subset(delta_set
, slice
);
2671 isl_set_free(slice
);
2673 origin
= isl_set_universe(isl_set_get_space(delta_set
));
2674 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
2675 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
2677 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
2678 delta_set
= isl_set_lexmin(delta_set
);
2680 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
2682 isl_set_free(origin
);
2683 isl_set_free(delta_set
);
2686 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
2687 is_injection
< 0 || is_complete
< 0)
2690 isl_die(ctx
, isl_error_unknown
,
2691 "generated schedule incomplete", return -1);
2693 isl_die(ctx
, isl_error_unknown
,
2694 "generated schedule not injective on each statement",
2697 isl_die(ctx
, isl_error_unknown
,
2698 "negative dependences in generated schedule",
2701 isl_die(ctx
, isl_error_unknown
,
2702 "generated schedule not as tilable as expected",
2705 isl_die(ctx
, isl_error_unknown
,
2706 "generated schedule not as parallel as expected",
2712 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
2713 const char *domain
, const char *validity
, const char *proximity
)
2717 isl_union_map
*prox
;
2718 isl_schedule_constraints
*sc
;
2719 isl_schedule
*schedule
;
2720 isl_union_map
*sched
;
2722 dom
= isl_union_set_read_from_str(ctx
, domain
);
2723 dep
= isl_union_map_read_from_str(ctx
, validity
);
2724 prox
= isl_union_map_read_from_str(ctx
, proximity
);
2725 sc
= isl_schedule_constraints_on_domain(dom
);
2726 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
2727 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
2728 schedule
= isl_schedule_constraints_compute_schedule(sc
);
2729 sched
= isl_schedule_get_map(schedule
);
2730 isl_schedule_free(schedule
);
2735 /* Check that a schedule can be constructed on the given domain
2736 * with the given validity and proximity constraints.
2738 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
2739 const char *validity
, const char *proximity
)
2741 isl_union_map
*sched
;
2743 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
2747 isl_union_map_free(sched
);
2751 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
2752 const char *validity
, const char *proximity
, const char *expected_sched
)
2754 isl_union_map
*sched1
, *sched2
;
2757 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
2758 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
2760 equal
= isl_union_map_is_equal(sched1
, sched2
);
2761 isl_union_map_free(sched1
);
2762 isl_union_map_free(sched2
);
2767 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
2773 /* Check that the schedule map is properly padded, even after being
2774 * reconstructed from the band forest.
2776 static int test_padded_schedule(isl_ctx
*ctx
)
2780 isl_union_map
*validity
, *proximity
;
2781 isl_schedule_constraints
*sc
;
2782 isl_schedule
*sched
;
2783 isl_union_map
*map1
, *map2
;
2784 isl_band_list
*list
;
2787 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
2788 D
= isl_union_set_read_from_str(ctx
, str
);
2789 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
2790 proximity
= isl_union_map_copy(validity
);
2791 sc
= isl_schedule_constraints_on_domain(D
);
2792 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
2793 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
2794 sched
= isl_schedule_constraints_compute_schedule(sc
);
2795 map1
= isl_schedule_get_map(sched
);
2796 list
= isl_schedule_get_band_forest(sched
);
2797 isl_band_list_free(list
);
2798 map2
= isl_schedule_get_map(sched
);
2799 isl_schedule_free(sched
);
2800 equal
= isl_union_map_is_equal(map1
, map2
);
2801 isl_union_map_free(map1
);
2802 isl_union_map_free(map2
);
2807 isl_die(ctx
, isl_error_unknown
,
2808 "reconstructed schedule map not the same as original",
2814 /* Input for testing of schedule construction based on
2815 * conditional constraints.
2817 * domain is the iteration domain
2818 * flow are the flow dependences, which determine the validity and
2819 * proximity constraints
2820 * condition are the conditions on the conditional validity constraints
2821 * conditional_validity are the conditional validity constraints
2822 * outer_band_n is the expected number of members in the outer band
2827 const char *condition
;
2828 const char *conditional_validity
;
2830 } live_range_tests
[] = {
2831 /* Contrived example that illustrates that we need to keep
2832 * track of tagged condition dependences and
2833 * tagged conditional validity dependences
2834 * in isl_sched_edge separately.
2835 * In particular, the conditional validity constraints on A
2836 * cannot be satisfied,
2837 * but they can be ignored because there are no corresponding
2838 * condition constraints. However, we do have an additional
2839 * conditional validity constraint that maps to the same
2840 * dependence relation
2841 * as the condition constraint on B. If we did not make a distinction
2842 * between tagged condition and tagged conditional validity
2843 * dependences, then we
2844 * could end up treating this shared dependence as an condition
2845 * constraint on A, forcing a localization of the conditions,
2846 * which is impossible.
2848 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
2849 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
2850 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
2851 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2852 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
2853 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
2856 /* TACO 2013 Fig. 7 */
2857 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2858 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2859 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2860 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
2861 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
2862 "0 <= i < n and 0 <= j < n - 1 }",
2863 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
2864 "0 <= i < n and 0 <= j < j' < n;"
2865 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
2866 "0 <= i < i' < n and 0 <= j,j' < n;"
2867 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
2868 "0 <= i,j,j' < n and j < j' }",
2871 /* TACO 2013 Fig. 7, without tags */
2872 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
2873 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2874 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2875 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
2876 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
2877 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
2878 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
2879 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
2882 /* TACO 2013 Fig. 12 */
2883 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
2884 "S3[i,3] : 0 <= i <= 1 }",
2885 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
2886 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
2887 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
2888 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
2889 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2890 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
2891 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
2892 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
2893 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
2894 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
2895 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
2900 /* Test schedule construction based on conditional constraints.
2901 * In particular, check the number of members in the outer band
2902 * as an indication of whether tiling is possible or not.
2904 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
2907 isl_union_set
*domain
;
2908 isl_union_map
*condition
;
2909 isl_union_map
*flow
;
2910 isl_union_map
*validity
;
2911 isl_schedule_constraints
*sc
;
2912 isl_schedule
*schedule
;
2913 isl_band_list
*list
;
2917 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
2918 domain
= isl_union_set_read_from_str(ctx
,
2919 live_range_tests
[i
].domain
);
2920 flow
= isl_union_map_read_from_str(ctx
,
2921 live_range_tests
[i
].flow
);
2922 condition
= isl_union_map_read_from_str(ctx
,
2923 live_range_tests
[i
].condition
);
2924 validity
= isl_union_map_read_from_str(ctx
,
2925 live_range_tests
[i
].conditional_validity
);
2926 sc
= isl_schedule_constraints_on_domain(domain
);
2927 sc
= isl_schedule_constraints_set_validity(sc
,
2928 isl_union_map_copy(flow
));
2929 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
2930 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
2931 condition
, validity
);
2932 schedule
= isl_schedule_constraints_compute_schedule(sc
);
2933 list
= isl_schedule_get_band_forest(schedule
);
2934 band
= isl_band_list_get_band(list
, 0);
2935 n_member
= isl_band_n_member(band
);
2936 isl_band_free(band
);
2937 isl_band_list_free(list
);
2938 isl_schedule_free(schedule
);
2942 if (n_member
!= live_range_tests
[i
].outer_band_n
)
2943 isl_die(ctx
, isl_error_unknown
,
2944 "unexpected number of members in outer band",
2950 int test_schedule(isl_ctx
*ctx
)
2952 const char *D
, *W
, *R
, *V
, *P
, *S
;
2954 /* Handle resulting schedule with zero bands. */
2955 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
2959 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
2960 W
= "{ S1[t,i] -> a[t,i] }";
2961 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
2962 "S1[t,i] -> a[t-1,i+1] }";
2963 S
= "{ S1[t,i] -> [t,i] }";
2964 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2967 /* Fig. 5 of CC2008 */
2968 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
2970 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
2971 "j >= 2 and j <= -1 + N }";
2972 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
2973 "j >= 2 and j <= -1 + N; "
2974 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
2975 "j >= 2 and j <= -1 + N }";
2976 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
2977 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
2980 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
2981 W
= "{ S1[i] -> a[i] }";
2982 R
= "{ S2[i] -> a[i+1] }";
2983 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2984 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2987 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
2988 W
= "{ S1[i] -> a[i] }";
2989 R
= "{ S2[i] -> a[9-i] }";
2990 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2991 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
2994 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
2995 W
= "{ S1[i] -> a[i] }";
2996 R
= "[N] -> { S2[i] -> a[N-1-i] }";
2997 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
2998 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3001 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
3002 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
3003 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
3004 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
3005 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3008 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3009 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
3010 R
= "{ S2[i,j] -> a[i-1,j] }";
3011 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3012 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3015 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3016 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
3017 R
= "{ S2[i,j] -> a[i,j-1] }";
3018 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3019 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3022 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
3023 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
3024 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
3025 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
3026 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
3027 "S_0[] -> [0, 0, 0] }";
3028 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
3030 ctx
->opt
->schedule_parametric
= 0;
3031 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3033 ctx
->opt
->schedule_parametric
= 1;
3035 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
3036 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
3037 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
3038 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
3039 "S4[i] -> a[i,N] }";
3040 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
3041 "S4[i] -> [4,i,0] }";
3042 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3045 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
3046 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3048 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3050 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
3052 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3053 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3056 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
3057 " S_2[t] : t >= 0 and t <= -1 + N; "
3058 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
3060 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
3061 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
3062 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
3063 "i >= 0 and i <= -1 + N }";
3064 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
3065 "i >= 0 and i <= -1 + N; "
3066 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
3067 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
3068 " S_0[t] -> [0, t, 0] }";
3070 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3072 ctx
->opt
->schedule_parametric
= 0;
3073 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3075 ctx
->opt
->schedule_parametric
= 1;
3077 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
3078 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
3079 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
3082 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3083 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3084 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3085 "j >= 0 and j <= -1 + N; "
3086 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3087 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3088 "j >= 0 and j <= -1 + N; "
3089 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3090 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3091 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3094 D
= "{ S_0[i] : i >= 0 }";
3095 W
= "{ S_0[i] -> a[i] : i >= 0 }";
3096 R
= "{ S_0[i] -> a[0] : i >= 0 }";
3097 S
= "{ S_0[i] -> [0, i, 0] }";
3098 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3101 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3102 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3103 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3104 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3105 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3108 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3109 "k <= -1 + n and k >= 0 }";
3110 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3111 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3112 "k <= -1 + n and k >= 0; "
3113 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3114 "k <= -1 + n and k >= 0; "
3115 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3116 "k <= -1 + n and k >= 0 }";
3117 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
3118 ctx
->opt
->schedule_outer_coincidence
= 1;
3119 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3121 ctx
->opt
->schedule_outer_coincidence
= 0;
3123 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
3124 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3125 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3126 "Stmt_for_body24[i0, i1, 1, 0]:"
3127 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3128 "Stmt_for_body7[i0, i1, i2]:"
3129 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3132 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
3133 "Stmt_for_body24[1, i1, i2, i3]:"
3134 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3136 "Stmt_for_body24[0, i1, i2, i3] -> "
3137 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3138 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3140 "Stmt_for_body24[0, i1, i2, i3] ->"
3141 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3142 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3143 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3144 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3145 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3146 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3147 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3148 "i1 <= 6 and i1 >= 0;"
3149 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3150 "Stmt_for_body7[i0, i1, i2] -> "
3151 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3152 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3153 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3154 "Stmt_for_body7[i0, i1, i2] -> "
3155 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3156 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3157 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3159 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3160 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
3161 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
3163 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3166 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
3167 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
3168 "j >= 1 and j <= 7;"
3169 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
3170 "j >= 1 and j <= 8 }";
3172 S
= "{ S_0[i, j] -> [i + j, j] }";
3173 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3174 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3176 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3178 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
3179 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
3180 "j >= 0 and j <= -1 + i }";
3181 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
3182 "i <= -1 + N and j >= 0;"
3183 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
3186 S
= "{ S_0[i, j] -> [i, j] }";
3187 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3188 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3190 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3192 /* Test both algorithms on a case with only proximity dependences. */
3193 D
= "{ S[i,j] : 0 <= i <= 10 }";
3195 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
3196 S
= "{ S[i, j] -> [j, i] }";
3197 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3198 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3200 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3201 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
3204 D
= "{ A[a]; B[] }";
3206 P
= "{ A[a] -> B[] }";
3207 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3210 if (test_padded_schedule(ctx
) < 0)
3213 /* Check that check for progress is not confused by rational
3216 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
3217 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
3219 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
3220 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
3222 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3223 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3225 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3227 /* Check that we allow schedule rows that are only non-trivial
3228 * on some full-dimensional domains.
3230 D
= "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
3231 V
= "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
3232 "S1[j] -> S2[1] : 0 <= j <= 1 }";
3234 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
3235 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
3237 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
3239 if (test_conditional_schedule_constraints(ctx
) < 0)
3245 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
3247 isl_union_map
*umap
;
3250 umap
= isl_union_map_read_from_str(ctx
, str
);
3251 test
= isl_union_map_plain_is_injective(umap
);
3252 isl_union_map_free(umap
);
3255 if (test
== injective
)
3258 isl_die(ctx
, isl_error_unknown
,
3259 "map not detected as injective", return -1);
3261 isl_die(ctx
, isl_error_unknown
,
3262 "map detected as injective", return -1);
3265 int test_injective(isl_ctx
*ctx
)
3269 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
3271 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
3273 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
3275 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
3277 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
3279 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
3281 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
3283 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
3286 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
3287 if (test_plain_injective(ctx
, str
, 1))
3289 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
3290 if (test_plain_injective(ctx
, str
, 0))
3296 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
3304 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
3305 equal
= isl_aff_plain_is_equal(aff
, aff2
);
3311 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
3315 equal
= aff_plain_is_equal(aff
, str
);
3319 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
3320 "result not as expected", return -1);
3325 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3326 __isl_take isl_aff
*aff2
);
3328 ['+'] = { &isl_aff_add
},
3329 ['-'] = { &isl_aff_sub
},
3330 ['*'] = { &isl_aff_mul
},
3331 ['/'] = { &isl_aff_div
},
3339 } aff_bin_tests
[] = {
3340 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
3341 "{ [i] -> [2i] }" },
3342 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
3344 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
3345 "{ [i] -> [2i] }" },
3346 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
3347 "{ [i] -> [2i] }" },
3348 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
3349 "{ [i] -> [i/2] }" },
3350 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
3352 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
3353 "{ [i] -> [NaN] }" },
3354 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
3355 "{ [i] -> [NaN] }" },
3356 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
3357 "{ [i] -> [NaN] }" },
3358 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
3359 "{ [i] -> [NaN] }" },
3360 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
3361 "{ [i] -> [NaN] }" },
3362 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
3363 "{ [i] -> [NaN] }" },
3364 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
3365 "{ [i] -> [NaN] }" },
3366 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
3367 "{ [i] -> [NaN] }" },
3368 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
3369 "{ [i] -> [NaN] }" },
3370 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
3371 "{ [i] -> [NaN] }" },
3372 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
3373 "{ [i] -> [NaN] }" },
3374 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
3375 "{ [i] -> [NaN] }" },
3378 /* Perform some basic tests of binary operations on isl_aff objects.
3380 static int test_bin_aff(isl_ctx
*ctx
)
3383 isl_aff
*aff1
, *aff2
, *res
;
3384 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
3385 __isl_take isl_aff
*aff2
);
3388 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
3389 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
3390 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
3391 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
3392 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
3393 aff1
= fn(aff1
, aff2
);
3394 if (isl_aff_is_nan(res
))
3395 ok
= isl_aff_is_nan(aff1
);
3397 ok
= isl_aff_plain_is_equal(aff1
, res
);
3403 isl_die(ctx
, isl_error_unknown
,
3404 "unexpected result", return -1);
3411 __isl_give isl_union_pw_multi_aff
*(*fn
)(
3412 __isl_take isl_union_pw_multi_aff
*upma1
,
3413 __isl_take isl_union_pw_multi_aff
*upma2
);
3417 } upma_bin_tests
[] = {
3418 { &isl_union_pw_multi_aff_add
, "{ A[] -> [0]; B[0] -> [1] }",
3419 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
3420 { &isl_union_pw_multi_aff_union_add
, "{ A[] -> [0]; B[0] -> [1] }",
3421 "{ B[x] -> [2] : x >= 0 }",
3422 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
3425 /* Perform some basic tests of binary operations on
3426 * isl_union_pw_multi_aff objects.
3428 static int test_bin_upma(isl_ctx
*ctx
)
3431 isl_union_pw_multi_aff
*upma1
, *upma2
, *res
;
3434 for (i
= 0; i
< ARRAY_SIZE(upma_bin_tests
); ++i
) {
3435 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
3436 upma_bin_tests
[i
].arg1
);
3437 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
3438 upma_bin_tests
[i
].arg2
);
3439 res
= isl_union_pw_multi_aff_read_from_str(ctx
,
3440 upma_bin_tests
[i
].res
);
3441 upma1
= upma_bin_tests
[i
].fn(upma1
, upma2
);
3442 ok
= isl_union_pw_multi_aff_plain_is_equal(upma1
, res
);
3443 isl_union_pw_multi_aff_free(upma1
);
3444 isl_union_pw_multi_aff_free(res
);
3448 isl_die(ctx
, isl_error_unknown
,
3449 "unexpected result", return -1);
3455 int test_aff(isl_ctx
*ctx
)
3460 isl_local_space
*ls
;
3464 if (test_bin_aff(ctx
) < 0)
3466 if (test_bin_upma(ctx
) < 0)
3469 space
= isl_space_set_alloc(ctx
, 0, 1);
3470 ls
= isl_local_space_from_space(space
);
3471 aff
= isl_aff_zero_on_domain(ls
);
3473 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3474 aff
= isl_aff_scale_down_ui(aff
, 3);
3475 aff
= isl_aff_floor(aff
);
3476 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3477 aff
= isl_aff_scale_down_ui(aff
, 2);
3478 aff
= isl_aff_floor(aff
);
3479 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
3482 set
= isl_set_read_from_str(ctx
, str
);
3483 aff
= isl_aff_gist(aff
, set
);
3485 aff
= isl_aff_add_constant_si(aff
, -16);
3486 zero
= isl_aff_plain_is_zero(aff
);
3492 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3494 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
3495 aff
= isl_aff_scale_down_ui(aff
, 64);
3496 aff
= isl_aff_floor(aff
);
3497 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
3505 int test_dim_max(isl_ctx
*ctx
)
3509 isl_set
*set1
, *set2
;
3514 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
3515 set
= isl_set_read_from_str(ctx
, str
);
3516 pwaff
= isl_set_dim_max(set
, 0);
3517 set1
= isl_set_from_pw_aff(pwaff
);
3518 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
3519 set2
= isl_set_read_from_str(ctx
, str
);
3520 equal
= isl_set_is_equal(set1
, set2
);
3526 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3528 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
3529 set
= isl_set_read_from_str(ctx
, str
);
3530 pwaff
= isl_set_dim_max(set
, 0);
3531 set1
= isl_set_from_pw_aff(pwaff
);
3532 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3533 set2
= isl_set_read_from_str(ctx
, str
);
3534 equal
= isl_set_is_equal(set1
, set2
);
3540 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3542 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
3543 set
= isl_set_read_from_str(ctx
, str
);
3544 pwaff
= isl_set_dim_max(set
, 0);
3545 set1
= isl_set_from_pw_aff(pwaff
);
3546 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
3547 set2
= isl_set_read_from_str(ctx
, str
);
3548 equal
= isl_set_is_equal(set1
, set2
);
3554 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3556 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
3557 "0 <= i < N and 0 <= j < M }";
3558 map
= isl_map_read_from_str(ctx
, str
);
3559 set
= isl_map_range(map
);
3561 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
3562 set1
= isl_set_from_pw_aff(pwaff
);
3563 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
3564 set2
= isl_set_read_from_str(ctx
, str
);
3565 equal
= isl_set_is_equal(set1
, set2
);
3569 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
3570 set1
= isl_set_from_pw_aff(pwaff
);
3571 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
3572 set2
= isl_set_read_from_str(ctx
, str
);
3573 if (equal
>= 0 && equal
)
3574 equal
= isl_set_is_equal(set1
, set2
);
3583 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3585 /* Check that solutions are properly merged. */
3586 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
3587 "c <= -1 + n - 4a - 2b and c >= -2b and "
3588 "4a >= -4 + n and c >= 0 }";
3589 set
= isl_set_read_from_str(ctx
, str
);
3590 pwaff
= isl_set_dim_min(set
, 2);
3591 set1
= isl_set_from_pw_aff(pwaff
);
3592 str
= "[n] -> { [(0)] : n >= 1 }";
3593 set2
= isl_set_read_from_str(ctx
, str
);
3594 equal
= isl_set_is_equal(set1
, set2
);
3601 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3603 /* Check that empty solution lie in the right space. */
3604 str
= "[n] -> { [t,a] : 1 = 0 }";
3605 set
= isl_set_read_from_str(ctx
, str
);
3606 pwaff
= isl_set_dim_max(set
, 0);
3607 set1
= isl_set_from_pw_aff(pwaff
);
3608 str
= "[n] -> { [t] : 1 = 0 }";
3609 set2
= isl_set_read_from_str(ctx
, str
);
3610 equal
= isl_set_is_equal(set1
, set2
);
3617 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3622 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
3624 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
3628 isl_pw_multi_aff
*pma2
;
3634 ctx
= isl_pw_multi_aff_get_ctx(pma
);
3635 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3636 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
3637 isl_pw_multi_aff_free(pma2
);
3642 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
3643 * represented by "str".
3645 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
3650 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
3654 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
3655 "result not as expected", return -1);
3659 /* Basic test for isl_pw_multi_aff_product.
3661 * Check that multiple pieces are properly handled.
3663 static int test_product_pma(isl_ctx
*ctx
)
3667 isl_pw_multi_aff
*pma1
, *pma2
;
3669 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
3670 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3671 str
= "{ C[] -> D[] }";
3672 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
3673 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
3674 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
3675 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
3676 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
3677 isl_pw_multi_aff_free(pma1
);
3684 int test_product(isl_ctx
*ctx
)
3688 isl_union_set
*uset1
, *uset2
;
3692 set
= isl_set_read_from_str(ctx
, str
);
3693 set
= isl_set_product(set
, isl_set_copy(set
));
3694 ok
= isl_set_is_wrapping(set
);
3699 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3702 uset1
= isl_union_set_read_from_str(ctx
, str
);
3703 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
3704 str
= "{ [[] -> []] }";
3705 uset2
= isl_union_set_read_from_str(ctx
, str
);
3706 ok
= isl_union_set_is_equal(uset1
, uset2
);
3707 isl_union_set_free(uset1
);
3708 isl_union_set_free(uset2
);
3712 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3714 if (test_product_pma(ctx
) < 0)
3720 /* Check that two sets are not considered disjoint just because
3721 * they have a different set of (named) parameters.
3723 static int test_disjoint(isl_ctx
*ctx
)
3726 isl_set
*set
, *set2
;
3729 str
= "[n] -> { [[]->[]] }";
3730 set
= isl_set_read_from_str(ctx
, str
);
3731 str
= "{ [[]->[]] }";
3732 set2
= isl_set_read_from_str(ctx
, str
);
3733 disjoint
= isl_set_is_disjoint(set
, set2
);
3739 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3744 int test_equal(isl_ctx
*ctx
)
3747 isl_set
*set
, *set2
;
3751 set
= isl_set_read_from_str(ctx
, str
);
3753 set2
= isl_set_read_from_str(ctx
, str
);
3754 equal
= isl_set_is_equal(set
, set2
);
3760 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3765 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
3766 enum isl_dim_type type
, unsigned pos
, int fixed
)
3770 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
3777 isl_die(ctx
, isl_error_unknown
,
3778 "map not detected as fixed", return -1);
3780 isl_die(ctx
, isl_error_unknown
,
3781 "map detected as fixed", return -1);
3784 int test_fixed(isl_ctx
*ctx
)
3789 str
= "{ [i] -> [i] }";
3790 map
= isl_map_read_from_str(ctx
, str
);
3791 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
3793 str
= "{ [i] -> [1] }";
3794 map
= isl_map_read_from_str(ctx
, str
);
3795 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
3797 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
3798 map
= isl_map_read_from_str(ctx
, str
);
3799 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
3801 map
= isl_map_read_from_str(ctx
, str
);
3802 map
= isl_map_neg(map
);
3803 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
3809 struct isl_vertices_test_data
{
3812 const char *vertex
[2];
3813 } vertices_tests
[] = {
3814 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
3815 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
3816 { "{ A[t, i] : t = 14 and i = 1 }",
3817 1, { "{ A[14, 1] }" } },
3820 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
3822 static int find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
3824 struct isl_vertices_test_data
*data
= user
;
3827 isl_basic_set
*bset
;
3828 isl_pw_multi_aff
*pma
;
3832 ctx
= isl_vertex_get_ctx(vertex
);
3833 bset
= isl_vertex_get_domain(vertex
);
3834 ma
= isl_vertex_get_expr(vertex
);
3835 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
3837 for (i
= 0; i
< data
->n
; ++i
) {
3838 isl_pw_multi_aff
*pma_i
;
3840 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
3841 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
3842 isl_pw_multi_aff_free(pma_i
);
3844 if (equal
< 0 || equal
)
3848 isl_pw_multi_aff_free(pma
);
3849 isl_vertex_free(vertex
);
3854 return equal
? 0 : - 1;
3857 int test_vertices(isl_ctx
*ctx
)
3861 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
3862 isl_basic_set
*bset
;
3863 isl_vertices
*vertices
;
3867 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
3868 vertices
= isl_basic_set_compute_vertices(bset
);
3869 n
= isl_vertices_get_n_vertices(vertices
);
3870 if (vertices_tests
[i
].n
!= n
)
3872 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
3873 &vertices_tests
[i
]) < 0)
3875 isl_vertices_free(vertices
);
3876 isl_basic_set_free(bset
);
3881 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
3888 int test_union_pw(isl_ctx
*ctx
)
3892 isl_union_set
*uset
;
3893 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
3895 str
= "{ [x] -> x^2 }";
3896 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
3897 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
3898 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
3899 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
3900 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
3901 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
3902 isl_union_pw_qpolynomial_free(upwqp1
);
3903 isl_union_pw_qpolynomial_free(upwqp2
);
3907 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3912 int test_output(isl_ctx
*ctx
)
3920 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
3921 pa
= isl_pw_aff_read_from_str(ctx
, str
);
3923 p
= isl_printer_to_str(ctx
);
3924 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
3925 p
= isl_printer_print_pw_aff(p
, pa
);
3926 s
= isl_printer_get_str(p
);
3927 isl_printer_free(p
);
3928 isl_pw_aff_free(pa
);
3932 equal
= !strcmp(s
, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
3937 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3942 int test_sample(isl_ctx
*ctx
)
3945 isl_basic_set
*bset1
, *bset2
;
3948 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
3949 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
3950 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
3951 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
3952 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
3953 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
3954 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
3955 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
3956 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
3957 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
3958 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
3959 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
3960 "d - 1073741821e and "
3961 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
3962 "3j >= 1 - a + b + 2e and "
3963 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
3964 "3i <= 4 - a + 4b - e and "
3965 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
3966 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
3967 "c <= -1 + a and 3i >= -2 - a + 3e and "
3968 "1073741822e <= 1073741823 - a + 1073741822b + c and "
3969 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
3970 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
3971 "1073741823e >= 1 + 1073741823b - d and "
3972 "3i >= 1073741823b + c - 1073741823e - f and "
3973 "3i >= 1 + 2b + e + 3g }";
3974 bset1
= isl_basic_set_read_from_str(ctx
, str
);
3975 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
3976 empty
= isl_basic_set_is_empty(bset2
);
3977 subset
= isl_basic_set_is_subset(bset2
, bset1
);
3978 isl_basic_set_free(bset1
);
3979 isl_basic_set_free(bset2
);
3980 if (empty
< 0 || subset
< 0)
3983 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
3985 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
3990 int test_fixed_power(isl_ctx
*ctx
)
3998 str
= "{ [i] -> [i + 1] }";
3999 map
= isl_map_read_from_str(ctx
, str
);
4000 isl_int_set_si(exp
, 23);
4001 map
= isl_map_fixed_power(map
, exp
);
4002 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
4011 int test_slice(isl_ctx
*ctx
)
4017 str
= "{ [i] -> [j] }";
4018 map
= isl_map_read_from_str(ctx
, str
);
4019 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4020 equal
= map_check_equal(map
, "{ [i] -> [i] }");
4025 str
= "{ [i] -> [j] }";
4026 map
= isl_map_read_from_str(ctx
, str
);
4027 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4028 equal
= map_check_equal(map
, "{ [i] -> [j] }");
4033 str
= "{ [i] -> [j] }";
4034 map
= isl_map_read_from_str(ctx
, str
);
4035 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4036 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
4041 str
= "{ [i] -> [j] }";
4042 map
= isl_map_read_from_str(ctx
, str
);
4043 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4044 equal
= map_check_equal(map
, "{ [0] -> [j] }");
4049 str
= "{ [i] -> [j] }";
4050 map
= isl_map_read_from_str(ctx
, str
);
4051 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
4052 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
4057 str
= "{ [i] -> [j] }";
4058 map
= isl_map_read_from_str(ctx
, str
);
4059 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
4060 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
4068 int test_eliminate(isl_ctx
*ctx
)
4074 str
= "{ [i] -> [j] : i = 2j }";
4075 map
= isl_map_read_from_str(ctx
, str
);
4076 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
4077 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
4085 /* Check that isl_set_dim_residue_class detects that the values of j
4086 * in the set below are all odd and that it does not detect any spurious
4089 static int test_residue_class(isl_ctx
*ctx
)
4096 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
4097 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
4098 set
= isl_set_read_from_str(ctx
, str
);
4101 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
4103 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
4104 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
4113 int test_align_parameters(isl_ctx
*ctx
)
4117 isl_multi_aff
*ma1
, *ma2
;
4120 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
4121 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
4123 space
= isl_space_params_alloc(ctx
, 1);
4124 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
4125 ma1
= isl_multi_aff_align_params(ma1
, space
);
4127 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
4128 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
4130 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
4132 isl_multi_aff_free(ma1
);
4133 isl_multi_aff_free(ma2
);
4138 isl_die(ctx
, isl_error_unknown
,
4139 "result not as expected", return -1);
4144 static int test_list(isl_ctx
*ctx
)
4146 isl_id
*a
, *b
, *c
, *d
, *id
;
4150 a
= isl_id_alloc(ctx
, "a", NULL
);
4151 b
= isl_id_alloc(ctx
, "b", NULL
);
4152 c
= isl_id_alloc(ctx
, "c", NULL
);
4153 d
= isl_id_alloc(ctx
, "d", NULL
);
4155 list
= isl_id_list_alloc(ctx
, 4);
4156 list
= isl_id_list_add(list
, a
);
4157 list
= isl_id_list_add(list
, b
);
4158 list
= isl_id_list_add(list
, c
);
4159 list
= isl_id_list_add(list
, d
);
4160 list
= isl_id_list_drop(list
, 1, 1);
4162 if (isl_id_list_n_id(list
) != 3) {
4163 isl_id_list_free(list
);
4164 isl_die(ctx
, isl_error_unknown
,
4165 "unexpected number of elements in list", return -1);
4168 id
= isl_id_list_get_id(list
, 0);
4171 id
= isl_id_list_get_id(list
, 1);
4174 id
= isl_id_list_get_id(list
, 2);
4178 isl_id_list_free(list
);
4181 isl_die(ctx
, isl_error_unknown
,
4182 "unexpected elements in list", return -1);
4187 const char *set_conversion_tests
[] = {
4188 "[N] -> { [i] : N - 1 <= 2 i <= N }",
4189 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
4190 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4191 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
4192 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
4195 /* Check that converting from isl_set to isl_pw_multi_aff and back
4196 * to isl_set produces the original isl_set.
4198 static int test_set_conversion(isl_ctx
*ctx
)
4202 isl_set
*set1
, *set2
;
4203 isl_pw_multi_aff
*pma
;
4206 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
4207 str
= set_conversion_tests
[i
];
4208 set1
= isl_set_read_from_str(ctx
, str
);
4209 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
4210 set2
= isl_set_from_pw_multi_aff(pma
);
4211 equal
= isl_set_is_equal(set1
, set2
);
4218 isl_die(ctx
, isl_error_unknown
, "bad conversion",
4225 /* Check that converting from isl_map to isl_pw_multi_aff and back
4226 * to isl_map produces the original isl_map.
4228 static int test_map_conversion(isl_ctx
*ctx
)
4231 isl_map
*map1
, *map2
;
4232 isl_pw_multi_aff
*pma
;
4235 str
= "{ [a, b, c, d] -> s0[a, b, e, f] : "
4236 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
4237 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
4238 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
4240 map1
= isl_map_read_from_str(ctx
, str
);
4241 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
4242 map2
= isl_map_from_pw_multi_aff(pma
);
4243 equal
= isl_map_is_equal(map1
, map2
);
4250 isl_die(ctx
, isl_error_unknown
, "bad conversion", return -1);
4255 static int test_conversion(isl_ctx
*ctx
)
4257 if (test_set_conversion(ctx
) < 0)
4259 if (test_map_conversion(ctx
) < 0)
4264 /* Check that isl_basic_map_curry does not modify input.
4266 static int test_curry(isl_ctx
*ctx
)
4269 isl_basic_map
*bmap1
, *bmap2
;
4272 str
= "{ [A[] -> B[]] -> C[] }";
4273 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
4274 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
4275 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
4276 isl_basic_map_free(bmap1
);
4277 isl_basic_map_free(bmap2
);
4282 isl_die(ctx
, isl_error_unknown
,
4283 "curried map should not be equal to original",
4293 } preimage_tests
[] = {
4294 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
4295 "{ A[j,i] -> B[i,j] }",
4296 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
4297 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4298 "{ A[a,b] -> B[a/2,b/6] }",
4299 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
4300 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
4301 "{ A[a,b] -> B[a/2,b/6] }",
4302 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
4303 "exists i,j : a = 2 i and b = 6 j }" },
4304 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
4305 "[n] -> { : 0 <= n <= 100 }" },
4306 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4307 "{ A[a] -> B[2a] }",
4308 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
4309 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
4310 "{ A[a] -> B[([a/2])] }",
4311 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
4312 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
4313 "{ A[a] -> B[a,a,a/3] }",
4314 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
4315 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
4316 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
4319 static int test_preimage_basic_set(isl_ctx
*ctx
)
4322 isl_basic_set
*bset1
, *bset2
;
4326 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
4327 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
4328 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
4329 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
4330 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
4331 equal
= isl_basic_set_is_equal(bset1
, bset2
);
4332 isl_basic_set_free(bset1
);
4333 isl_basic_set_free(bset2
);
4337 isl_die(ctx
, isl_error_unknown
, "bad preimage",
4348 } preimage_domain_tests
[] = {
4349 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
4350 "{ A[j,i] -> B[i,j] }",
4351 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
4352 { "{ B[i] -> C[i]; D[i] -> E[i] }",
4353 "{ A[i] -> B[i + 1] }",
4354 "{ A[i] -> C[i + 1] }" },
4355 { "{ B[i] -> C[i]; B[i] -> E[i] }",
4356 "{ A[i] -> B[i + 1] }",
4357 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
4358 { "{ B[i] -> C[([i/2])] }",
4359 "{ A[i] -> B[2i] }",
4360 "{ A[i] -> C[i] }" },
4361 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
4362 "{ A[i] -> B[([i/5]), ([i/7])] }",
4363 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
4364 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
4365 "[N] -> { A[] -> B[([N/5])] }",
4366 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
4367 { "{ B[i] -> C[i] : exists a : i = 5 a }",
4368 "{ A[i] -> B[2i] }",
4369 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
4370 { "{ B[i] -> C[i] : exists a : i = 2 a; "
4371 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
4372 "{ A[i] -> B[2i] }",
4373 "{ A[i] -> C[2i] }" },
4376 static int test_preimage_union_map(isl_ctx
*ctx
)
4379 isl_union_map
*umap1
, *umap2
;
4383 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
4384 umap1
= isl_union_map_read_from_str(ctx
,
4385 preimage_domain_tests
[i
].map
);
4386 ma
= isl_multi_aff_read_from_str(ctx
,
4387 preimage_domain_tests
[i
].ma
);
4388 umap2
= isl_union_map_read_from_str(ctx
,
4389 preimage_domain_tests
[i
].res
);
4390 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
4391 equal
= isl_union_map_is_equal(umap1
, umap2
);
4392 isl_union_map_free(umap1
);
4393 isl_union_map_free(umap2
);
4397 isl_die(ctx
, isl_error_unknown
, "bad preimage",
4404 static int test_preimage(isl_ctx
*ctx
)
4406 if (test_preimage_basic_set(ctx
) < 0)
4408 if (test_preimage_union_map(ctx
) < 0)
4418 } pullback_tests
[] = {
4419 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
4420 "{ A[a,b] -> C[b + 2a] }" },
4421 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
4422 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
4423 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
4424 "{ A[a] -> C[(a)/6] }" },
4425 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
4426 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
4427 "{ A[a] -> C[(2a)/3] }" },
4428 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
4429 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
4430 "{ A[i,j] -> C[i + j, i + j] }"},
4431 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
4432 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
4433 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
4436 static int test_pullback(isl_ctx
*ctx
)
4439 isl_multi_aff
*ma1
, *ma2
;
4443 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
4444 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
4445 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
4446 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
4447 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
4448 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
4449 isl_multi_aff_free(ma1
);
4450 isl_multi_aff_free(ma2
);
4454 isl_die(ctx
, isl_error_unknown
, "bad pullback",
4461 /* Check that negation is printed correctly.
4463 static int test_ast(isl_ctx
*ctx
)
4465 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
4469 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
4470 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
4471 expr
= isl_ast_expr_add(expr1
, expr2
);
4472 expr
= isl_ast_expr_neg(expr
);
4473 str
= isl_ast_expr_to_str(expr
);
4474 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
4476 isl_ast_expr_free(expr
);
4481 isl_die(ctx
, isl_error_unknown
,
4482 "isl_ast_expr printed incorrectly", return -1);
4484 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
4485 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
4486 expr
= isl_ast_expr_add(expr1
, expr2
);
4487 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
4488 expr
= isl_ast_expr_sub(expr3
, expr
);
4489 str
= isl_ast_expr_to_str(expr
);
4490 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
4492 isl_ast_expr_free(expr
);
4497 isl_die(ctx
, isl_error_unknown
,
4498 "isl_ast_expr printed incorrectly", return -1);
4503 /* Check that isl_ast_build_expr_from_set returns a valid expression
4504 * for an empty set. Note that isl_ast_build_expr_from_set getting
4505 * called on an empty set probably indicates a bug in the caller.
4507 static int test_ast_build(isl_ctx
*ctx
)
4510 isl_ast_build
*build
;
4513 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4514 build
= isl_ast_build_from_context(set
);
4516 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
4517 expr
= isl_ast_build_expr_from_set(build
, set
);
4519 isl_ast_expr_free(expr
);
4520 isl_ast_build_free(build
);
4528 /* Internal data structure for before_for and after_for callbacks.
4530 * depth is the current depth
4531 * before is the number of times before_for has been called
4532 * after is the number of times after_for has been called
4534 struct isl_test_codegen_data
{
4540 /* This function is called before each for loop in the AST generated
4541 * from test_ast_gen1.
4543 * Increment the number of calls and the depth.
4544 * Check that the space returned by isl_ast_build_get_schedule_space
4545 * matches the target space of the schedule returned by
4546 * isl_ast_build_get_schedule.
4547 * Return an isl_id that is checked by the corresponding call
4550 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
4553 struct isl_test_codegen_data
*data
= user
;
4556 isl_union_map
*schedule
;
4557 isl_union_set
*uset
;
4562 ctx
= isl_ast_build_get_ctx(build
);
4564 if (data
->before
>= 3)
4565 isl_die(ctx
, isl_error_unknown
,
4566 "unexpected number of for nodes", return NULL
);
4567 if (data
->depth
>= 2)
4568 isl_die(ctx
, isl_error_unknown
,
4569 "unexpected depth", return NULL
);
4571 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
4575 schedule
= isl_ast_build_get_schedule(build
);
4576 uset
= isl_union_map_range(schedule
);
4579 if (isl_union_set_n_set(uset
) != 1) {
4580 isl_union_set_free(uset
);
4581 isl_die(ctx
, isl_error_unknown
,
4582 "expecting single range space", return NULL
);
4585 space
= isl_ast_build_get_schedule_space(build
);
4586 set
= isl_union_set_extract_set(uset
, space
);
4587 isl_union_set_free(uset
);
4588 empty
= isl_set_is_empty(set
);
4594 isl_die(ctx
, isl_error_unknown
,
4595 "spaces don't match", return NULL
);
4597 return isl_id_alloc(ctx
, name
, NULL
);
4600 /* This function is called after each for loop in the AST generated
4601 * from test_ast_gen1.
4603 * Increment the number of calls and decrement the depth.
4604 * Check that the annotation attached to the node matches
4605 * the isl_id returned by the corresponding call to before_for.
4607 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
4608 __isl_keep isl_ast_build
*build
, void *user
)
4610 struct isl_test_codegen_data
*data
= user
;
4618 if (data
->after
> data
->before
)
4619 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
4620 "mismatch in number of for nodes",
4621 return isl_ast_node_free(node
));
4623 id
= isl_ast_node_get_annotation(node
);
4625 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
4626 "missing annotation", return isl_ast_node_free(node
));
4628 name
= isl_id_get_name(id
);
4629 valid
= name
&& atoi(name
+ 1) == data
->depth
;
4633 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
4634 "wrong annotation", return isl_ast_node_free(node
));
4639 /* Check that the before_each_for and after_each_for callbacks
4640 * are called for each for loop in the generated code,
4641 * that they are called in the right order and that the isl_id
4642 * returned from the before_each_for callback is attached to
4643 * the isl_ast_node passed to the corresponding after_each_for call.
4645 static int test_ast_gen1(isl_ctx
*ctx
)
4649 isl_union_map
*schedule
;
4650 isl_ast_build
*build
;
4652 struct isl_test_codegen_data data
;
4654 str
= "[N] -> { : N >= 10 }";
4655 set
= isl_set_read_from_str(ctx
, str
);
4656 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
4657 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
4658 schedule
= isl_union_map_read_from_str(ctx
, str
);
4663 build
= isl_ast_build_from_context(set
);
4664 build
= isl_ast_build_set_before_each_for(build
,
4665 &before_for
, &data
);
4666 build
= isl_ast_build_set_after_each_for(build
,
4668 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4669 isl_ast_build_free(build
);
4673 isl_ast_node_free(tree
);
4675 if (data
.before
!= 3 || data
.after
!= 3)
4676 isl_die(ctx
, isl_error_unknown
,
4677 "unexpected number of for nodes", return -1);
4682 /* Check that the AST generator handles domains that are integrally disjoint
4683 * but not ratinoally disjoint.
4685 static int test_ast_gen2(isl_ctx
*ctx
)
4689 isl_union_map
*schedule
;
4690 isl_union_map
*options
;
4691 isl_ast_build
*build
;
4694 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
4695 schedule
= isl_union_map_read_from_str(ctx
, str
);
4696 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4697 build
= isl_ast_build_from_context(set
);
4699 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
4700 options
= isl_union_map_read_from_str(ctx
, str
);
4701 build
= isl_ast_build_set_options(build
, options
);
4702 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4703 isl_ast_build_free(build
);
4706 isl_ast_node_free(tree
);
4711 /* Increment *user on each call.
4713 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
4714 __isl_keep isl_ast_build
*build
, void *user
)
4723 /* Test that unrolling tries to minimize the number of instances.
4724 * In particular, for the schedule given below, make sure it generates
4725 * 3 nodes (rather than 101).
4727 static int test_ast_gen3(isl_ctx
*ctx
)
4731 isl_union_map
*schedule
;
4732 isl_union_map
*options
;
4733 isl_ast_build
*build
;
4737 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
4738 schedule
= isl_union_map_read_from_str(ctx
, str
);
4739 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4741 str
= "{ [i] -> unroll[0] }";
4742 options
= isl_union_map_read_from_str(ctx
, str
);
4744 build
= isl_ast_build_from_context(set
);
4745 build
= isl_ast_build_set_options(build
, options
);
4746 build
= isl_ast_build_set_at_each_domain(build
,
4747 &count_domains
, &n_domain
);
4748 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4749 isl_ast_build_free(build
);
4753 isl_ast_node_free(tree
);
4756 isl_die(ctx
, isl_error_unknown
,
4757 "unexpected number of for nodes", return -1);
4762 /* Check that if the ast_build_exploit_nested_bounds options is set,
4763 * we do not get an outer if node in the generated AST,
4764 * while we do get such an outer if node if the options is not set.
4766 static int test_ast_gen4(isl_ctx
*ctx
)
4770 isl_union_map
*schedule
;
4771 isl_ast_build
*build
;
4773 enum isl_ast_node_type type
;
4776 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
4777 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
4779 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
4781 schedule
= isl_union_map_read_from_str(ctx
, str
);
4782 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4783 build
= isl_ast_build_from_context(set
);
4784 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4785 isl_ast_build_free(build
);
4789 type
= isl_ast_node_get_type(tree
);
4790 isl_ast_node_free(tree
);
4792 if (type
== isl_ast_node_if
)
4793 isl_die(ctx
, isl_error_unknown
,
4794 "not expecting if node", return -1);
4796 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
4798 schedule
= isl_union_map_read_from_str(ctx
, str
);
4799 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4800 build
= isl_ast_build_from_context(set
);
4801 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4802 isl_ast_build_free(build
);
4806 type
= isl_ast_node_get_type(tree
);
4807 isl_ast_node_free(tree
);
4809 if (type
!= isl_ast_node_if
)
4810 isl_die(ctx
, isl_error_unknown
,
4811 "expecting if node", return -1);
4813 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
4818 /* This function is called for each leaf in the AST generated
4819 * from test_ast_gen5.
4821 * We finalize the AST generation by extending the outer schedule
4822 * with a zero-dimensional schedule. If this results in any for loops,
4823 * then this means that we did not pass along enough information
4824 * about the outer schedule to the inner AST generation.
4826 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
4829 isl_union_map
*schedule
, *extra
;
4832 schedule
= isl_ast_build_get_schedule(build
);
4833 extra
= isl_union_map_copy(schedule
);
4834 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
4835 schedule
= isl_union_map_range_product(schedule
, extra
);
4836 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4837 isl_ast_build_free(build
);
4842 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
4843 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
4844 "code should not contain any for loop",
4845 return isl_ast_node_free(tree
));
4850 /* Check that we do not lose any information when going back and
4851 * forth between internal and external schedule.
4853 * In particular, we create an AST where we unroll the only
4854 * non-constant dimension in the schedule. We therefore do
4855 * not expect any for loops in the AST. However, older versions
4856 * of isl would not pass along enough information about the outer
4857 * schedule when performing an inner code generation from a create_leaf
4858 * callback, resulting in the inner code generation producing a for loop.
4860 static int test_ast_gen5(isl_ctx
*ctx
)
4864 isl_union_map
*schedule
, *options
;
4865 isl_ast_build
*build
;
4868 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
4869 schedule
= isl_union_map_read_from_str(ctx
, str
);
4871 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
4872 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
4873 options
= isl_union_map_read_from_str(ctx
, str
);
4875 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
4876 build
= isl_ast_build_from_context(set
);
4877 build
= isl_ast_build_set_options(build
, options
);
4878 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
4879 tree
= isl_ast_build_ast_from_schedule(build
, schedule
);
4880 isl_ast_build_free(build
);
4881 isl_ast_node_free(tree
);
4888 static int test_ast_gen(isl_ctx
*ctx
)
4890 if (test_ast_gen1(ctx
) < 0)
4892 if (test_ast_gen2(ctx
) < 0)
4894 if (test_ast_gen3(ctx
) < 0)
4896 if (test_ast_gen4(ctx
) < 0)
4898 if (test_ast_gen5(ctx
) < 0)
4903 /* Check if dropping output dimensions from an isl_pw_multi_aff
4906 static int test_pw_multi_aff(isl_ctx
*ctx
)
4909 isl_pw_multi_aff
*pma1
, *pma2
;
4912 str
= "{ [i,j] -> [i+j, 4i-j] }";
4913 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4914 str
= "{ [i,j] -> [4i-j] }";
4915 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4917 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
4919 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
4921 isl_pw_multi_aff_free(pma1
);
4922 isl_pw_multi_aff_free(pma2
);
4926 isl_die(ctx
, isl_error_unknown
,
4927 "expressions not equal", return -1);
4932 /* Check that we can properly parse multi piecewise affine expressions
4933 * where the piecewise affine expressions have different domains.
4935 static int test_multi_pw_aff(isl_ctx
*ctx
)
4938 isl_set
*dom
, *dom2
;
4939 isl_multi_pw_aff
*mpa1
, *mpa2
;
4944 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
4945 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
4946 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
4947 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
4948 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
4949 str
= "{ [i] -> [(i : i > 0), 2i] }";
4950 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
4952 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
4954 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
4955 dom
= isl_pw_aff_domain(pa
);
4956 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
4957 dom2
= isl_pw_aff_domain(pa
);
4958 equal_domain
= isl_set_is_equal(dom
, dom2
);
4962 isl_multi_pw_aff_free(mpa1
);
4963 isl_multi_pw_aff_free(mpa2
);
4968 isl_die(ctx
, isl_error_unknown
,
4969 "expressions not equal", return -1);
4971 if (equal_domain
< 0)
4974 isl_die(ctx
, isl_error_unknown
,
4975 "domains unexpectedly equal", return -1);
4980 /* This is a regression test for a bug where isl_basic_map_simplify
4981 * would end up in an infinite loop. In particular, we construct
4982 * an empty basic set that is not obviously empty.
4983 * isl_basic_set_is_empty marks the basic set as empty.
4984 * After projecting out i3, the variable can be dropped completely,
4985 * but isl_basic_map_simplify refrains from doing so if the basic set
4986 * is empty and would end up in an infinite loop if it didn't test
4987 * explicitly for empty basic maps in the outer loop.
4989 static int test_simplify(isl_ctx
*ctx
)
4992 isl_basic_set
*bset
;
4995 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
4996 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
4997 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
4999 bset
= isl_basic_set_read_from_str(ctx
, str
);
5000 empty
= isl_basic_set_is_empty(bset
);
5001 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
5002 isl_basic_set_free(bset
);
5006 isl_die(ctx
, isl_error_unknown
,
5007 "basic set should be empty", return -1);
5012 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
5013 * with gbr context would fail to disable the use of the shifted tableau
5014 * when transferring equalities for the input to the context, resulting
5015 * in invalid sample values.
5017 static int test_partial_lexmin(isl_ctx
*ctx
)
5020 isl_basic_set
*bset
;
5021 isl_basic_map
*bmap
;
5024 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
5025 bmap
= isl_basic_map_read_from_str(ctx
, str
);
5026 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
5027 bset
= isl_basic_set_read_from_str(ctx
, str
);
5028 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
5037 /* Check that the variable compression performed on the existentially
5038 * quantified variables inside isl_basic_set_compute_divs is not confused
5039 * by the implicit equalities among the parameters.
5041 static int test_compute_divs(isl_ctx
*ctx
)
5044 isl_basic_set
*bset
;
5047 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
5048 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
5049 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
5050 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
5051 bset
= isl_basic_set_read_from_str(ctx
, str
);
5052 set
= isl_basic_set_compute_divs(bset
);
5064 { "{ rat: [i] : 0 <= i <= 10 }",
5065 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
5066 { "{ rat: [i] : FALSE }",
5067 "{ rat: coefficients[[cst] -> [a]] }" },
5069 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
5076 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
5077 "{ rat: [i] : 0 <= i <= 10 }" },
5078 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
5080 { "{ rat: coefficients[[cst] -> [a]] }",
5081 "{ rat: [i] : FALSE }" },
5084 /* Test the basic functionality of isl_basic_set_coefficients and
5085 * isl_basic_set_solutions.
5087 static int test_dual(isl_ctx
*ctx
)
5091 for (i
= 0; i
< ARRAY_SIZE(coef_tests
); ++i
) {
5093 isl_basic_set
*bset1
, *bset2
;
5095 bset1
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].set
);
5096 bset2
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].dual
);
5097 bset1
= isl_basic_set_coefficients(bset1
);
5098 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5099 isl_basic_set_free(bset1
);
5100 isl_basic_set_free(bset2
);
5104 isl_die(ctx
, isl_error_unknown
,
5105 "incorrect dual", return -1);
5108 for (i
= 0; i
< ARRAY_SIZE(sol_tests
); ++i
) {
5110 isl_basic_set
*bset1
, *bset2
;
5112 bset1
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].set
);
5113 bset2
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].dual
);
5114 bset1
= isl_basic_set_solutions(bset1
);
5115 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5116 isl_basic_set_free(bset1
);
5117 isl_basic_set_free(bset2
);
5121 isl_die(ctx
, isl_error_unknown
,
5122 "incorrect dual", return -1);
5130 int (*fn
)(isl_ctx
*ctx
);
5132 { "dual", &test_dual
},
5133 { "dependence analysis", &test_flow
},
5134 { "val", &test_val
},
5135 { "compute divs", &test_compute_divs
},
5136 { "partial lexmin", &test_partial_lexmin
},
5137 { "simplify", &test_simplify
},
5138 { "curry", &test_curry
},
5139 { "piecewise multi affine expressions", &test_pw_multi_aff
},
5140 { "multi piecewise affine expressions", &test_multi_pw_aff
},
5141 { "conversion", &test_conversion
},
5142 { "list", &test_list
},
5143 { "align parameters", &test_align_parameters
},
5144 { "preimage", &test_preimage
},
5145 { "pullback", &test_pullback
},
5146 { "AST", &test_ast
},
5147 { "AST build", &test_ast_build
},
5148 { "AST generation", &test_ast_gen
},
5149 { "eliminate", &test_eliminate
},
5150 { "residue class", &test_residue_class
},
5151 { "div", &test_div
},
5152 { "slice", &test_slice
},
5153 { "fixed power", &test_fixed_power
},
5154 { "sample", &test_sample
},
5155 { "output", &test_output
},
5156 { "vertices", &test_vertices
},
5157 { "fixed", &test_fixed
},
5158 { "equal", &test_equal
},
5159 { "disjoint", &test_disjoint
},
5160 { "product", &test_product
},
5161 { "dim_max", &test_dim_max
},
5162 { "affine", &test_aff
},
5163 { "injective", &test_injective
},
5164 { "schedule", &test_schedule
},
5165 { "union_pw", &test_union_pw
},
5166 { "parse", &test_parse
},
5167 { "single-valued", &test_sv
},
5168 { "affine hull", &test_affine_hull
},
5169 { "coalesce", &test_coalesce
},
5170 { "factorize", &test_factorize
},
5171 { "subset", &test_subset
},
5172 { "subtract", &test_subtract
},
5173 { "lexmin", &test_lexmin
},
5174 { "min", &test_min
},
5175 { "gist", &test_gist
},
5176 { "piecewise quasi-polynomials", &test_pwqp
},
5179 int main(int argc
, char **argv
)
5182 struct isl_ctx
*ctx
;
5183 struct isl_options
*options
;
5185 srcdir
= getenv("srcdir");
5188 options
= isl_options_new_with_defaults();
5190 argc
= isl_options_parse(options
, argc
, argv
, ISL_ARG_ALL
);
5192 ctx
= isl_ctx_alloc_with_options(&isl_options_args
, options
);
5193 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
5194 printf("%s\n", tests
[i
].name
);
5195 if (tests
[i
].fn(ctx
) < 0)
5201 test_split_periods(ctx
);
5203 test_bijective(ctx
);
5207 test_construction(ctx
);
5209 test_application(ctx
);
5210 test_convex_hull(ctx
);