2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
12 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
15 * B.P. 105 - 78153 Le Chesnay, France
21 #include <isl_ctx_private.h>
22 #include <isl_map_private.h>
23 #include <isl_aff_private.h>
24 #include <isl_space_private.h>
27 #include <isl_constraint_private.h>
28 #include <isl/polynomial.h>
29 #include <isl/union_set.h>
30 #include <isl/union_map.h>
31 #include <isl_factorization.h>
32 #include <isl/schedule.h>
33 #include <isl/schedule_node.h>
34 #include <isl_options_private.h>
35 #include <isl/vertices.h>
36 #include <isl/ast_build.h>
39 #include <isl_ast_build_expr.h>
40 #include <isl/options.h>
42 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
46 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
49 char *pattern
= "%s/test_inputs/%s.%s";
51 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
53 filename
= isl_alloc_array(ctx
, char, length
);
58 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
63 void test_parse_map(isl_ctx
*ctx
, const char *str
)
67 map
= isl_map_read_from_str(ctx
, str
);
72 int test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
77 map
= isl_map_read_from_str(ctx
, str
);
78 map2
= isl_map_read_from_str(ctx
, str2
);
79 equal
= isl_map_is_equal(map
, map2
);
86 isl_die(ctx
, isl_error_unknown
, "maps not equal",
92 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
94 isl_pw_qpolynomial
*pwqp
;
96 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
98 isl_pw_qpolynomial_free(pwqp
);
101 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
105 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
107 isl_pw_aff_free(pwaff
);
110 /* Check that we can read an isl_multi_val from "str" without errors.
112 static int test_parse_multi_val(isl_ctx
*ctx
, const char *str
)
116 mv
= isl_multi_val_read_from_str(ctx
, str
);
117 isl_multi_val_free(mv
);
122 /* Pairs of binary relation representations that should represent
123 * the same binary relations.
128 } parse_map_equal_tests
[] = {
129 { "{ [x,y] : [([x/2]+y)/3] >= 1 }",
130 "{ [x, y] : 2y >= 6 - x }" },
131 { "{ [x,y] : x <= min(y, 2*y+3) }",
132 "{ [x,y] : x <= y, 2*y + 3 }" },
133 { "{ [x,y] : x >= min(y, 2*y+3) }",
134 "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }" },
135 { "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }",
136 "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }" },
137 { "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }",
138 "{ [i,j] -> [min(i,j)] }" },
139 { "{ [i,j] : i != j }",
140 "{ [i,j] : i < j or i > j }" },
141 { "{ [i,j] : (i+1)*2 >= j }",
142 "{ [i, j] : j <= 2 + 2i }" },
143 { "{ [i] -> [i > 0 ? 4 : 5] }",
144 "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }" },
145 { "[N=2,M] -> { [i=[(M+N)/4]] }",
146 "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }" },
147 { "{ [x] : x >= 0 }",
148 "{ [x] : x-0 >= 0 }" },
149 { "{ [i] : ((i > 10)) }",
150 "{ [i] : i >= 11 }" },
152 "{ [i] -> [0 * i] }" },
153 { "{ [a] -> [b] : (not false) }",
154 "{ [a] -> [b] : true }" },
155 { "{ [i] : i/2 <= 5 }",
156 "{ [i] : i <= 10 }" },
157 { "{Sym=[n] [i] : i <= n }",
158 "[n] -> { [i] : i <= n }" },
161 { "{ [i] : 2*floor(i/2) = i }",
162 "{ [i] : exists a : i = 2 a }" },
163 { "{ [a] -> [b] : a = 5 implies b = 5 }",
164 "{ [a] -> [b] : a != 5 or b = 5 }" },
165 { "{ [a] -> [a - 1 : a > 0] }",
166 "{ [a] -> [a - 1] : a > 0 }" },
167 { "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
168 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }" },
169 { "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
170 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
171 { "{ [a] -> [(a * 2) : a >= 0; 0 : a < 0] }",
172 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
173 { "{ [a] -> [(a * 2 : a >= 0); 0 : a < 0] }",
174 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
175 { "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
176 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
177 { "{ [a,b] -> [i,j] : a,b << i,j }",
178 "{ [a,b] -> [i,j] : a < i or (a = i and b < j) }" },
179 { "{ [a,b] -> [i,j] : a,b <<= i,j }",
180 "{ [a,b] -> [i,j] : a < i or (a = i and b <= j) }" },
181 { "{ [a,b] -> [i,j] : a,b >> i,j }",
182 "{ [a,b] -> [i,j] : a > i or (a = i and b > j) }" },
183 { "{ [a,b] -> [i,j] : a,b >>= i,j }",
184 "{ [a,b] -> [i,j] : a > i or (a = i and b >= j) }" },
185 { "{ [n] -> [i] : exists (a, b, c: 8b <= i - 32a and "
186 "8b >= -7 + i - 32 a and b >= 0 and b <= 3 and "
187 "8c < n - 32a and i < n and c >= 0 and "
188 "c <= 3 and c >= -4a) }",
189 "{ [n] -> [i] : 0 <= i < n }" },
190 { "{ [x] -> [] : exists (a, b: 0 <= a <= 1 and 0 <= b <= 3 and "
191 "2b <= x - 8a and 2b >= -1 + x - 8a) }",
192 "{ [x] -> [] : 0 <= x <= 15 }" },
195 int test_parse(struct isl_ctx
*ctx
)
199 const char *str
, *str2
;
201 if (test_parse_multi_val(ctx
, "{ A[B[2] -> C[5, 7]] }") < 0)
203 if (test_parse_multi_val(ctx
, "[n] -> { [2] }") < 0)
205 if (test_parse_multi_val(ctx
, "{ A[4, infty, NaN, -1/2, 2/3] }") < 0)
208 str
= "{ [i] -> [-i] }";
209 map
= isl_map_read_from_str(ctx
, str
);
213 str
= "{ A[i] -> L[([i/3])] }";
214 map
= isl_map_read_from_str(ctx
, str
);
218 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
219 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
220 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
222 for (i
= 0; i
< ARRAY_SIZE(parse_map_equal_tests
); ++i
) {
223 str
= parse_map_equal_tests
[i
].map1
;
224 str2
= parse_map_equal_tests
[i
].map2
;
225 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
229 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
230 map
= isl_map_read_from_str(ctx
, str
);
231 str
= "{ [new, old] -> [o0, o1] : "
232 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
233 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
234 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
235 map2
= isl_map_read_from_str(ctx
, str
);
236 assert(isl_map_is_equal(map
, map2
));
240 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
241 map
= isl_map_read_from_str(ctx
, str
);
242 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
243 map2
= isl_map_read_from_str(ctx
, str
);
244 assert(isl_map_is_equal(map
, map2
));
248 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
249 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
250 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
251 test_parse_pwqp(ctx
, "{ [x] -> ([(x)/2] * [(x)/3]) }");
252 test_parse_pwaff(ctx
, "{ [] -> [(100)] }");
257 static int test_read(isl_ctx
*ctx
)
261 isl_basic_set
*bset1
, *bset2
;
262 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 equal
= isl_basic_set_is_equal(bset1
, bset2
);
275 isl_basic_set_free(bset1
);
276 isl_basic_set_free(bset2
);
284 isl_die(ctx
, isl_error_unknown
,
285 "read sets not equal", return -1);
290 static int test_bounded(isl_ctx
*ctx
)
295 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
296 bounded
= isl_set_is_bounded(set
);
302 isl_die(ctx
, isl_error_unknown
,
303 "set not considered bounded", return -1);
305 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
306 bounded
= isl_set_is_bounded(set
);
313 isl_die(ctx
, isl_error_unknown
,
314 "set considered bounded", return -1);
316 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
317 bounded
= isl_set_is_bounded(set
);
323 isl_die(ctx
, isl_error_unknown
,
324 "set considered bounded", return -1);
329 /* Construct the basic set { [i] : 5 <= i <= N } */
330 static int test_construction(isl_ctx
*ctx
)
340 dim
= isl_space_set_alloc(ctx
, 1, 1);
341 bset
= isl_basic_set_universe(isl_space_copy(dim
));
342 ls
= isl_local_space_from_space(dim
);
344 c
= isl_constraint_alloc_inequality(isl_local_space_copy(ls
));
345 isl_int_set_si(v
, -1);
346 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
347 isl_int_set_si(v
, 1);
348 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
349 bset
= isl_basic_set_add_constraint(bset
, c
);
351 c
= isl_constraint_alloc_inequality(isl_local_space_copy(ls
));
352 isl_int_set_si(v
, 1);
353 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
354 isl_int_set_si(v
, -5);
355 isl_constraint_set_constant(c
, v
);
356 bset
= isl_basic_set_add_constraint(bset
, c
);
358 isl_local_space_free(ls
);
359 isl_basic_set_free(bset
);
366 static int test_dim(isl_ctx
*ctx
)
369 isl_map
*map1
, *map2
;
372 map1
= isl_map_read_from_str(ctx
,
373 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
374 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
375 map2
= isl_map_read_from_str(ctx
,
376 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
377 equal
= isl_map_is_equal(map1
, map2
);
380 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
381 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
382 if (equal
>= 0 && equal
)
383 equal
= isl_map_is_equal(map1
, map2
);
391 isl_die(ctx
, isl_error_unknown
,
392 "unexpected result", return -1);
394 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
395 map1
= isl_map_read_from_str(ctx
, str
);
396 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
397 map2
= isl_map_read_from_str(ctx
, str
);
398 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
399 equal
= isl_map_is_equal(map1
, map2
);
406 isl_die(ctx
, isl_error_unknown
,
407 "unexpected result", return -1);
413 __isl_give isl_val
*(*op
)(__isl_take isl_val
*v
);
417 { &isl_val_neg
, "0", "0" },
418 { &isl_val_abs
, "0", "0" },
419 { &isl_val_2exp
, "0", "1" },
420 { &isl_val_floor
, "0", "0" },
421 { &isl_val_ceil
, "0", "0" },
422 { &isl_val_neg
, "1", "-1" },
423 { &isl_val_neg
, "-1", "1" },
424 { &isl_val_neg
, "1/2", "-1/2" },
425 { &isl_val_neg
, "-1/2", "1/2" },
426 { &isl_val_neg
, "infty", "-infty" },
427 { &isl_val_neg
, "-infty", "infty" },
428 { &isl_val_neg
, "NaN", "NaN" },
429 { &isl_val_abs
, "1", "1" },
430 { &isl_val_abs
, "-1", "1" },
431 { &isl_val_abs
, "1/2", "1/2" },
432 { &isl_val_abs
, "-1/2", "1/2" },
433 { &isl_val_abs
, "infty", "infty" },
434 { &isl_val_abs
, "-infty", "infty" },
435 { &isl_val_abs
, "NaN", "NaN" },
436 { &isl_val_floor
, "1", "1" },
437 { &isl_val_floor
, "-1", "-1" },
438 { &isl_val_floor
, "1/2", "0" },
439 { &isl_val_floor
, "-1/2", "-1" },
440 { &isl_val_floor
, "infty", "infty" },
441 { &isl_val_floor
, "-infty", "-infty" },
442 { &isl_val_floor
, "NaN", "NaN" },
443 { &isl_val_ceil
, "1", "1" },
444 { &isl_val_ceil
, "-1", "-1" },
445 { &isl_val_ceil
, "1/2", "1" },
446 { &isl_val_ceil
, "-1/2", "0" },
447 { &isl_val_ceil
, "infty", "infty" },
448 { &isl_val_ceil
, "-infty", "-infty" },
449 { &isl_val_ceil
, "NaN", "NaN" },
450 { &isl_val_2exp
, "-3", "1/8" },
451 { &isl_val_2exp
, "-1", "1/2" },
452 { &isl_val_2exp
, "1", "2" },
453 { &isl_val_2exp
, "2", "4" },
454 { &isl_val_2exp
, "3", "8" },
455 { &isl_val_inv
, "1", "1" },
456 { &isl_val_inv
, "2", "1/2" },
457 { &isl_val_inv
, "1/2", "2" },
458 { &isl_val_inv
, "-2", "-1/2" },
459 { &isl_val_inv
, "-1/2", "-2" },
460 { &isl_val_inv
, "0", "NaN" },
461 { &isl_val_inv
, "NaN", "NaN" },
462 { &isl_val_inv
, "infty", "0" },
463 { &isl_val_inv
, "-infty", "0" },
466 /* Perform some basic tests of unary operations on isl_val objects.
468 static int test_un_val(isl_ctx
*ctx
)
472 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v
);
475 for (i
= 0; i
< ARRAY_SIZE(val_un_tests
); ++i
) {
476 v
= isl_val_read_from_str(ctx
, val_un_tests
[i
].arg
);
477 res
= isl_val_read_from_str(ctx
, val_un_tests
[i
].res
);
478 fn
= val_un_tests
[i
].op
;
480 if (isl_val_is_nan(res
))
481 ok
= isl_val_is_nan(v
);
483 ok
= isl_val_eq(v
, res
);
489 isl_die(ctx
, isl_error_unknown
,
490 "unexpected result", return -1);
497 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
498 __isl_take isl_val
*v2
);
500 ['+'] = { &isl_val_add
},
501 ['-'] = { &isl_val_sub
},
502 ['*'] = { &isl_val_mul
},
503 ['/'] = { &isl_val_div
},
504 ['g'] = { &isl_val_gcd
},
505 ['m'] = { &isl_val_min
},
506 ['M'] = { &isl_val_max
},
514 } val_bin_tests
[] = {
515 { "0", '+', "0", "0" },
516 { "1", '+', "0", "1" },
517 { "1", '+', "1", "2" },
518 { "1", '-', "1", "0" },
519 { "1", '*', "1", "1" },
520 { "1", '/', "1", "1" },
521 { "2", '*', "3", "6" },
522 { "2", '*', "1/2", "1" },
523 { "2", '*', "1/3", "2/3" },
524 { "2/3", '*', "3/5", "2/5" },
525 { "2/3", '*', "7/5", "14/15" },
526 { "2", '/', "1/2", "4" },
527 { "-2", '/', "-1/2", "4" },
528 { "-2", '/', "1/2", "-4" },
529 { "2", '/', "-1/2", "-4" },
530 { "2", '/', "2", "1" },
531 { "2", '/', "3", "2/3" },
532 { "2/3", '/', "5/3", "2/5" },
533 { "2/3", '/', "5/7", "14/15" },
534 { "0", '/', "0", "NaN" },
535 { "42", '/', "0", "NaN" },
536 { "-42", '/', "0", "NaN" },
537 { "infty", '/', "0", "NaN" },
538 { "-infty", '/', "0", "NaN" },
539 { "NaN", '/', "0", "NaN" },
540 { "0", '/', "NaN", "NaN" },
541 { "42", '/', "NaN", "NaN" },
542 { "-42", '/', "NaN", "NaN" },
543 { "infty", '/', "NaN", "NaN" },
544 { "-infty", '/', "NaN", "NaN" },
545 { "NaN", '/', "NaN", "NaN" },
546 { "0", '/', "infty", "0" },
547 { "42", '/', "infty", "0" },
548 { "-42", '/', "infty", "0" },
549 { "infty", '/', "infty", "NaN" },
550 { "-infty", '/', "infty", "NaN" },
551 { "NaN", '/', "infty", "NaN" },
552 { "0", '/', "-infty", "0" },
553 { "42", '/', "-infty", "0" },
554 { "-42", '/', "-infty", "0" },
555 { "infty", '/', "-infty", "NaN" },
556 { "-infty", '/', "-infty", "NaN" },
557 { "NaN", '/', "-infty", "NaN" },
558 { "1", '-', "1/3", "2/3" },
559 { "1/3", '+', "1/2", "5/6" },
560 { "1/2", '+', "1/2", "1" },
561 { "3/4", '-', "1/4", "1/2" },
562 { "1/2", '-', "1/3", "1/6" },
563 { "infty", '+', "42", "infty" },
564 { "infty", '+', "infty", "infty" },
565 { "42", '+', "infty", "infty" },
566 { "infty", '-', "infty", "NaN" },
567 { "infty", '*', "infty", "infty" },
568 { "infty", '*', "-infty", "-infty" },
569 { "-infty", '*', "infty", "-infty" },
570 { "-infty", '*', "-infty", "infty" },
571 { "0", '*', "infty", "NaN" },
572 { "1", '*', "infty", "infty" },
573 { "infty", '*', "0", "NaN" },
574 { "infty", '*', "42", "infty" },
575 { "42", '-', "infty", "-infty" },
576 { "infty", '+', "-infty", "NaN" },
577 { "4", 'g', "6", "2" },
578 { "5", 'g', "6", "1" },
579 { "42", 'm', "3", "3" },
580 { "42", 'M', "3", "42" },
581 { "3", 'm', "42", "3" },
582 { "3", 'M', "42", "42" },
583 { "42", 'm', "infty", "42" },
584 { "42", 'M', "infty", "infty" },
585 { "42", 'm', "-infty", "-infty" },
586 { "42", 'M', "-infty", "42" },
587 { "42", 'm', "NaN", "NaN" },
588 { "42", 'M', "NaN", "NaN" },
589 { "infty", 'm', "-infty", "-infty" },
590 { "infty", 'M', "-infty", "infty" },
593 /* Perform some basic tests of binary operations on isl_val objects.
595 static int test_bin_val(isl_ctx
*ctx
)
598 isl_val
*v1
, *v2
, *res
;
599 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
600 __isl_take isl_val
*v2
);
603 for (i
= 0; i
< ARRAY_SIZE(val_bin_tests
); ++i
) {
604 v1
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg1
);
605 v2
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg2
);
606 res
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].res
);
607 fn
= val_bin_op
[val_bin_tests
[i
].op
].fn
;
609 if (isl_val_is_nan(res
))
610 ok
= isl_val_is_nan(v1
);
612 ok
= isl_val_eq(v1
, res
);
618 isl_die(ctx
, isl_error_unknown
,
619 "unexpected result", return -1);
625 /* Perform some basic tests on isl_val objects.
627 static int test_val(isl_ctx
*ctx
)
629 if (test_un_val(ctx
) < 0)
631 if (test_bin_val(ctx
) < 0)
636 /* Sets described using existentially quantified variables that
637 * can also be described without.
639 static const char *elimination_tests
[] = {
640 "{ [i,j] : 2 * [i/2] + 3 * [j/4] <= 10 and 2 i = j }",
641 "{ [m, w] : exists a : w - 2m - 5 <= 3a <= m - 2w }",
642 "{ [m, w] : exists a : w >= 0 and a < m and -1 + w <= a <= 2m - w }",
645 /* Check that redundant existentially quantified variables are
648 static int test_elimination(isl_ctx
*ctx
)
654 for (i
= 0; i
< ARRAY_SIZE(elimination_tests
); ++i
) {
655 bset
= isl_basic_set_read_from_str(ctx
, elimination_tests
[i
]);
656 n
= isl_basic_set_dim(bset
, isl_dim_div
);
657 isl_basic_set_free(bset
);
661 isl_die(ctx
, isl_error_unknown
,
662 "expecting no existentials", return -1);
668 static int test_div(isl_ctx
*ctx
)
676 struct isl_basic_set
*bset
;
677 struct isl_constraint
*c
;
682 dim
= isl_space_set_alloc(ctx
, 0, 3);
683 bset
= isl_basic_set_universe(isl_space_copy(dim
));
684 ls
= isl_local_space_from_space(dim
);
686 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
687 isl_int_set_si(v
, -1);
688 isl_constraint_set_constant(c
, v
);
689 isl_int_set_si(v
, 1);
690 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
691 isl_int_set_si(v
, 3);
692 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
693 bset
= isl_basic_set_add_constraint(bset
, c
);
695 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
696 isl_int_set_si(v
, 1);
697 isl_constraint_set_constant(c
, v
);
698 isl_int_set_si(v
, -1);
699 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
700 isl_int_set_si(v
, 3);
701 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
702 bset
= isl_basic_set_add_constraint(bset
, c
);
704 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
706 assert(bset
&& bset
->n_div
== 1);
707 isl_local_space_free(ls
);
708 isl_basic_set_free(bset
);
711 dim
= isl_space_set_alloc(ctx
, 0, 3);
712 bset
= isl_basic_set_universe(isl_space_copy(dim
));
713 ls
= isl_local_space_from_space(dim
);
715 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
716 isl_int_set_si(v
, 1);
717 isl_constraint_set_constant(c
, v
);
718 isl_int_set_si(v
, -1);
719 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
720 isl_int_set_si(v
, 3);
721 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
722 bset
= isl_basic_set_add_constraint(bset
, c
);
724 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
725 isl_int_set_si(v
, -1);
726 isl_constraint_set_constant(c
, v
);
727 isl_int_set_si(v
, 1);
728 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
729 isl_int_set_si(v
, 3);
730 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
731 bset
= isl_basic_set_add_constraint(bset
, c
);
733 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
735 assert(bset
&& bset
->n_div
== 1);
736 isl_local_space_free(ls
);
737 isl_basic_set_free(bset
);
740 dim
= isl_space_set_alloc(ctx
, 0, 3);
741 bset
= isl_basic_set_universe(isl_space_copy(dim
));
742 ls
= isl_local_space_from_space(dim
);
744 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
745 isl_int_set_si(v
, 1);
746 isl_constraint_set_constant(c
, v
);
747 isl_int_set_si(v
, -1);
748 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
749 isl_int_set_si(v
, 3);
750 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
751 bset
= isl_basic_set_add_constraint(bset
, c
);
753 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
754 isl_int_set_si(v
, -3);
755 isl_constraint_set_constant(c
, v
);
756 isl_int_set_si(v
, 1);
757 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
758 isl_int_set_si(v
, 4);
759 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
760 bset
= isl_basic_set_add_constraint(bset
, c
);
762 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
764 assert(bset
&& bset
->n_div
== 1);
765 isl_local_space_free(ls
);
766 isl_basic_set_free(bset
);
769 dim
= isl_space_set_alloc(ctx
, 0, 3);
770 bset
= isl_basic_set_universe(isl_space_copy(dim
));
771 ls
= isl_local_space_from_space(dim
);
773 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
774 isl_int_set_si(v
, 2);
775 isl_constraint_set_constant(c
, v
);
776 isl_int_set_si(v
, -1);
777 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
778 isl_int_set_si(v
, 3);
779 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
780 bset
= isl_basic_set_add_constraint(bset
, c
);
782 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
783 isl_int_set_si(v
, -1);
784 isl_constraint_set_constant(c
, v
);
785 isl_int_set_si(v
, 1);
786 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
787 isl_int_set_si(v
, 6);
788 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
789 bset
= isl_basic_set_add_constraint(bset
, c
);
791 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
793 assert(isl_basic_set_is_empty(bset
));
794 isl_local_space_free(ls
);
795 isl_basic_set_free(bset
);
798 dim
= isl_space_set_alloc(ctx
, 0, 3);
799 bset
= isl_basic_set_universe(isl_space_copy(dim
));
800 ls
= isl_local_space_from_space(dim
);
802 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
803 isl_int_set_si(v
, -1);
804 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
805 isl_int_set_si(v
, 3);
806 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
807 bset
= isl_basic_set_add_constraint(bset
, c
);
809 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
810 isl_int_set_si(v
, 1);
811 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
812 isl_int_set_si(v
, -3);
813 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
814 bset
= isl_basic_set_add_constraint(bset
, c
);
816 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
818 assert(bset
&& bset
->n_div
== 0);
819 isl_basic_set_free(bset
);
820 isl_local_space_free(ls
);
823 dim
= isl_space_set_alloc(ctx
, 0, 3);
824 bset
= isl_basic_set_universe(isl_space_copy(dim
));
825 ls
= isl_local_space_from_space(dim
);
827 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
828 isl_int_set_si(v
, -1);
829 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
830 isl_int_set_si(v
, 6);
831 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
832 bset
= isl_basic_set_add_constraint(bset
, c
);
834 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
835 isl_int_set_si(v
, 1);
836 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
837 isl_int_set_si(v
, -3);
838 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
839 bset
= isl_basic_set_add_constraint(bset
, c
);
841 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
843 assert(bset
&& bset
->n_div
== 1);
844 isl_basic_set_free(bset
);
845 isl_local_space_free(ls
);
848 /* This test is a bit tricky. We set up an equality
850 * Normalization of divs creates _two_ divs
853 * Afterwards e0 is removed again because it has coefficient -1
854 * and we end up with the original equality and div again.
855 * Perhaps we can avoid the introduction of this temporary div.
857 dim
= isl_space_set_alloc(ctx
, 0, 4);
858 bset
= isl_basic_set_universe(isl_space_copy(dim
));
859 ls
= isl_local_space_from_space(dim
);
861 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
862 isl_int_set_si(v
, -1);
863 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
864 isl_int_set_si(v
, -3);
865 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
866 isl_int_set_si(v
, -3);
867 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
868 isl_int_set_si(v
, 6);
869 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
870 bset
= isl_basic_set_add_constraint(bset
, c
);
872 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
874 /* Test disabled for now */
876 assert(bset && bset->n_div == 1);
878 isl_local_space_free(ls
);
879 isl_basic_set_free(bset
);
882 dim
= isl_space_set_alloc(ctx
, 0, 5);
883 bset
= isl_basic_set_universe(isl_space_copy(dim
));
884 ls
= isl_local_space_from_space(dim
);
886 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
887 isl_int_set_si(v
, -1);
888 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
889 isl_int_set_si(v
, -3);
890 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
891 isl_int_set_si(v
, -3);
892 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
893 isl_int_set_si(v
, 6);
894 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
895 bset
= isl_basic_set_add_constraint(bset
, c
);
897 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
898 isl_int_set_si(v
, -1);
899 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
900 isl_int_set_si(v
, 1);
901 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
902 isl_int_set_si(v
, 1);
903 isl_constraint_set_constant(c
, v
);
904 bset
= isl_basic_set_add_constraint(bset
, c
);
906 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
908 /* Test disabled for now */
910 assert(bset && bset->n_div == 1);
912 isl_local_space_free(ls
);
913 isl_basic_set_free(bset
);
916 dim
= isl_space_set_alloc(ctx
, 0, 4);
917 bset
= isl_basic_set_universe(isl_space_copy(dim
));
918 ls
= isl_local_space_from_space(dim
);
920 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
921 isl_int_set_si(v
, 1);
922 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
923 isl_int_set_si(v
, -1);
924 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
925 isl_int_set_si(v
, -2);
926 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
927 bset
= isl_basic_set_add_constraint(bset
, c
);
929 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
930 isl_int_set_si(v
, -1);
931 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
932 isl_int_set_si(v
, 3);
933 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
934 isl_int_set_si(v
, 2);
935 isl_constraint_set_constant(c
, v
);
936 bset
= isl_basic_set_add_constraint(bset
, c
);
938 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
940 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
942 assert(!isl_basic_set_is_empty(bset
));
944 isl_local_space_free(ls
);
945 isl_basic_set_free(bset
);
948 dim
= isl_space_set_alloc(ctx
, 0, 3);
949 bset
= isl_basic_set_universe(isl_space_copy(dim
));
950 ls
= isl_local_space_from_space(dim
);
952 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
953 isl_int_set_si(v
, 1);
954 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
955 isl_int_set_si(v
, -2);
956 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
957 bset
= isl_basic_set_add_constraint(bset
, c
);
959 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
961 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
963 isl_local_space_free(ls
);
964 isl_basic_set_free(bset
);
968 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
969 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
970 set
= isl_set_read_from_str(ctx
, str
);
971 set
= isl_set_compute_divs(set
);
976 if (test_elimination(ctx
) < 0)
979 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
980 set
= isl_set_read_from_str(ctx
, str
);
981 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
982 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
983 empty
= isl_set_is_empty(set
);
988 isl_die(ctx
, isl_error_unknown
,
989 "result not as accurate as expected", return -1);
994 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
998 struct isl_basic_set
*bset1
, *bset2
;
999 struct isl_basic_map
*bmap
;
1001 filename
= get_filename(ctx
, name
, "omega");
1003 input
= fopen(filename
, "r");
1006 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1007 bmap
= isl_basic_map_read_from_file(ctx
, input
);
1009 bset1
= isl_basic_set_apply(bset1
, bmap
);
1011 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1013 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1015 isl_basic_set_free(bset1
);
1016 isl_basic_set_free(bset2
);
1022 static int test_application(isl_ctx
*ctx
)
1024 test_application_case(ctx
, "application");
1025 test_application_case(ctx
, "application2");
1030 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
1034 struct isl_basic_set
*bset1
, *bset2
;
1036 filename
= get_filename(ctx
, name
, "polylib");
1038 input
= fopen(filename
, "r");
1041 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1042 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1044 bset1
= isl_basic_set_affine_hull(bset1
);
1046 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1048 isl_basic_set_free(bset1
);
1049 isl_basic_set_free(bset2
);
1055 int test_affine_hull(struct isl_ctx
*ctx
)
1059 isl_basic_set
*bset
, *bset2
;
1063 test_affine_hull_case(ctx
, "affine2");
1064 test_affine_hull_case(ctx
, "affine");
1065 test_affine_hull_case(ctx
, "affine3");
1067 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
1068 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
1069 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
1070 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
1071 set
= isl_set_read_from_str(ctx
, str
);
1072 bset
= isl_set_affine_hull(set
);
1073 n
= isl_basic_set_dim(bset
, isl_dim_div
);
1074 isl_basic_set_free(bset
);
1076 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
1079 /* Check that isl_map_affine_hull is not confused by
1080 * the reordering of divs in isl_map_align_divs.
1082 str
= "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1083 "32e0 = b and 32e1 = c); "
1084 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1085 set
= isl_set_read_from_str(ctx
, str
);
1086 bset
= isl_set_affine_hull(set
);
1087 isl_basic_set_free(bset
);
1091 str
= "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1092 "32e2 = 31 + 31e0 }";
1093 set
= isl_set_read_from_str(ctx
, str
);
1094 bset
= isl_set_affine_hull(set
);
1095 str
= "{ [a] : exists e : a = 32 e }";
1096 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1097 subset
= isl_basic_set_is_subset(bset
, bset2
);
1098 isl_basic_set_free(bset
);
1099 isl_basic_set_free(bset2
);
1103 isl_die(ctx
, isl_error_unknown
, "not as accurate as expected",
1109 /* Pairs of maps and the corresponding expected results of
1110 * isl_map_plain_unshifted_simple_hull.
1115 } plain_unshifted_simple_hull_tests
[] = {
1116 { "{ [i] -> [j] : i >= 1 and j >= 1 or i >= 2 and j <= 10 }",
1117 "{ [i] -> [j] : i >= 1 }" },
1118 { "{ [n] -> [i,j,k] : (i mod 3 = 2 and j mod 4 = 2) or "
1119 "(j mod 4 = 2 and k mod 6 = n) }",
1120 "{ [n] -> [i,j,k] : j mod 4 = 2 }" },
1123 /* Basic tests for isl_map_plain_unshifted_simple_hull.
1125 static int test_plain_unshifted_simple_hull(isl_ctx
*ctx
)
1129 isl_basic_map
*hull
, *expected
;
1132 for (i
= 0; i
< ARRAY_SIZE(plain_unshifted_simple_hull_tests
); ++i
) {
1134 str
= plain_unshifted_simple_hull_tests
[i
].map
;
1135 map
= isl_map_read_from_str(ctx
, str
);
1136 str
= plain_unshifted_simple_hull_tests
[i
].hull
;
1137 expected
= isl_basic_map_read_from_str(ctx
, str
);
1138 hull
= isl_map_plain_unshifted_simple_hull(map
);
1139 equal
= isl_basic_map_is_equal(hull
, expected
);
1140 isl_basic_map_free(hull
);
1141 isl_basic_map_free(expected
);
1145 isl_die(ctx
, isl_error_unknown
, "unexpected hull",
1152 /* Pairs of sets and the corresponding expected results of
1153 * isl_set_unshifted_simple_hull.
1158 } unshifted_simple_hull_tests
[] = {
1159 { "{ [0,x,y] : x <= -1; [1,x,y] : x <= y <= -x; [2,x,y] : x <= 1 }",
1160 "{ [t,x,y] : 0 <= t <= 2 and x <= 1 }" },
1163 /* Basic tests for isl_set_unshifted_simple_hull.
1165 static int test_unshifted_simple_hull(isl_ctx
*ctx
)
1169 isl_basic_set
*hull
, *expected
;
1172 for (i
= 0; i
< ARRAY_SIZE(unshifted_simple_hull_tests
); ++i
) {
1174 str
= unshifted_simple_hull_tests
[i
].set
;
1175 set
= isl_set_read_from_str(ctx
, str
);
1176 str
= unshifted_simple_hull_tests
[i
].hull
;
1177 expected
= isl_basic_set_read_from_str(ctx
, str
);
1178 hull
= isl_set_unshifted_simple_hull(set
);
1179 equal
= isl_basic_set_is_equal(hull
, expected
);
1180 isl_basic_set_free(hull
);
1181 isl_basic_set_free(expected
);
1185 isl_die(ctx
, isl_error_unknown
, "unexpected hull",
1192 static int test_simple_hull(struct isl_ctx
*ctx
)
1196 isl_basic_set
*bset
;
1199 str
= "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x;"
1200 "[y, x] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }";
1201 set
= isl_set_read_from_str(ctx
, str
);
1202 bset
= isl_set_simple_hull(set
);
1203 is_empty
= isl_basic_set_is_empty(bset
);
1204 isl_basic_set_free(bset
);
1206 if (is_empty
== isl_bool_error
)
1209 if (is_empty
== isl_bool_false
)
1210 isl_die(ctx
, isl_error_unknown
, "Empty set should be detected",
1213 if (test_plain_unshifted_simple_hull(ctx
) < 0)
1215 if (test_unshifted_simple_hull(ctx
) < 0)
1221 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
1225 struct isl_basic_set
*bset1
, *bset2
;
1226 struct isl_set
*set
;
1228 filename
= get_filename(ctx
, name
, "polylib");
1230 input
= fopen(filename
, "r");
1233 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1234 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1236 set
= isl_basic_set_union(bset1
, bset2
);
1237 bset1
= isl_set_convex_hull(set
);
1239 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1241 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1243 isl_basic_set_free(bset1
);
1244 isl_basic_set_free(bset2
);
1253 } convex_hull_tests
[] = {
1254 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1255 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1256 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1257 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1258 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1259 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1260 "i2 <= 5 and i2 >= 4; "
1261 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1262 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1263 "i2 <= 5 + i0 and i2 >= i0 }" },
1264 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1265 "{ [x, y] : 1 = 0 }" },
1268 static int test_convex_hull_algo(isl_ctx
*ctx
, int convex
)
1271 int orig_convex
= ctx
->opt
->convex
;
1272 ctx
->opt
->convex
= convex
;
1274 test_convex_hull_case(ctx
, "convex0");
1275 test_convex_hull_case(ctx
, "convex1");
1276 test_convex_hull_case(ctx
, "convex2");
1277 test_convex_hull_case(ctx
, "convex3");
1278 test_convex_hull_case(ctx
, "convex4");
1279 test_convex_hull_case(ctx
, "convex5");
1280 test_convex_hull_case(ctx
, "convex6");
1281 test_convex_hull_case(ctx
, "convex7");
1282 test_convex_hull_case(ctx
, "convex8");
1283 test_convex_hull_case(ctx
, "convex9");
1284 test_convex_hull_case(ctx
, "convex10");
1285 test_convex_hull_case(ctx
, "convex11");
1286 test_convex_hull_case(ctx
, "convex12");
1287 test_convex_hull_case(ctx
, "convex13");
1288 test_convex_hull_case(ctx
, "convex14");
1289 test_convex_hull_case(ctx
, "convex15");
1291 for (i
= 0; i
< ARRAY_SIZE(convex_hull_tests
); ++i
) {
1292 isl_set
*set1
, *set2
;
1295 set1
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].set
);
1296 set2
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].hull
);
1297 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
1298 equal
= isl_set_is_equal(set1
, set2
);
1305 isl_die(ctx
, isl_error_unknown
,
1306 "unexpected convex hull", return -1);
1309 ctx
->opt
->convex
= orig_convex
;
1314 static int test_convex_hull(isl_ctx
*ctx
)
1316 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
) < 0)
1318 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
) < 0)
1323 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
1327 struct isl_basic_set
*bset1
, *bset2
;
1329 filename
= get_filename(ctx
, name
, "polylib");
1331 input
= fopen(filename
, "r");
1334 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1335 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1337 bset1
= isl_basic_set_gist(bset1
, bset2
);
1339 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1341 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1343 isl_basic_set_free(bset1
);
1344 isl_basic_set_free(bset2
);
1350 /* Inputs to isl_map_plain_gist_basic_map, along with the expected output.
1354 const char *context
;
1356 } plain_gist_tests
[] = {
1357 { "{ [i] -> [j] : i >= 1 and j >= 1 or i >= 2 and j <= 10 }",
1358 "{ [i] -> [j] : i >= 1 }",
1359 "{ [i] -> [j] : j >= 1 or i >= 2 and j <= 10 }" },
1360 { "{ [n] -> [i,j,k] : (i mod 3 = 2 and j mod 4 = 2) or "
1361 "(j mod 4 = 2 and k mod 6 = n) }",
1362 "{ [n] -> [i,j,k] : j mod 4 = 2 }",
1363 "{ [n] -> [i,j,k] : (i mod 3 = 2) or (k mod 6 = n) }" },
1364 { "{ [i] -> [j] : i > j and (exists a,b : i <= 2a + 5b <= 2) }",
1365 "{ [i] -> [j] : i > j }",
1366 "{ [i] -> [j] : exists a,b : i <= 2a + 5b <= 2 }" },
1369 /* Basic tests for isl_map_plain_gist_basic_map.
1371 static int test_plain_gist(isl_ctx
*ctx
)
1375 for (i
= 0; i
< ARRAY_SIZE(plain_gist_tests
); ++i
) {
1378 isl_map
*map
, *gist
;
1379 isl_basic_map
*context
;
1381 map
= isl_map_read_from_str(ctx
, plain_gist_tests
[i
].map
);
1382 str
= plain_gist_tests
[i
].context
;
1383 context
= isl_basic_map_read_from_str(ctx
, str
);
1384 map
= isl_map_plain_gist_basic_map(map
, context
);
1385 gist
= isl_map_read_from_str(ctx
, plain_gist_tests
[i
].gist
);
1386 equal
= isl_map_is_equal(map
, gist
);
1392 isl_die(ctx
, isl_error_unknown
,
1393 "incorrect gist result", return -1);
1401 const char *context
;
1404 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1405 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1406 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1407 "{ [a, b, c] : a <= 15 }" },
1408 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1409 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1410 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1411 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1412 { "{ [m, n, a, b] : a <= 2147 + n }",
1413 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1414 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1415 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1417 "{ [m, n, ku, kl] }" },
1418 { "{ [a, a, b] : a >= 10 }",
1419 "{ [a, b, c] : c >= a and c <= b and c >= 2 }",
1420 "{ [a, a, b] : a >= 10 }" },
1421 { "{ [i, j] : i >= 0 and i + j >= 0 }", "{ [i, j] : i <= 0 }",
1422 "{ [0, j] : j >= 0 }" },
1423 /* Check that no constraints on i6 are introduced in the gist */
1424 { "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1425 "20e0 <= 1530 - 4t1 - 5i4 and 20e0 >= 1511 - 4t1 - 5i4 and "
1426 "5e0 <= 381 - t1 and i4 <= 1) }",
1427 "[t1] -> { [i4, i6] : exists (e0 = floor((-t1 + i6)/5): "
1428 "5e0 = -t1 + i6 and i6 <= 6 and i6 >= 3) }",
1429 "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1430 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 <= 1530 - 4t1 - 5i4 and "
1431 "20e0 >= 1511 - 4t1 - 5i4) }" },
1432 /* Check that no constraints on i6 are introduced in the gist */
1433 { "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((1 + i4)/2), "
1434 "e1 = floor((1530 - 4t1 - 5i4)/20), "
1435 "e2 = floor((-4t1 - 5i4 + 10*floor((1 + i4)/2))/20), "
1436 "e3 = floor((-1 + i4)/2): t2 = 0 and 2e3 = -1 + i4 and "
1437 "20e2 >= -19 - 4t1 - 5i4 + 10e0 and 5e2 <= 1 - t1 and "
1438 "2e0 <= 1 + i4 and 2e0 >= i4 and "
1439 "20e1 <= 1530 - 4t1 - 5i4 and "
1440 "20e1 >= 1511 - 4t1 - 5i4 and i4 <= 1 and "
1441 "5e1 <= 381 - t1 and 20e2 <= -4t1 - 5i4 + 10e0) }",
1442 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((-17 + i4)/2), "
1443 "e1 = floor((-t1 + i6)/5): 5e1 = -t1 + i6 and "
1444 "2e0 <= -17 + i4 and 2e0 >= -18 + i4 and "
1445 "10e0 <= -91 + 5i4 + 4i6 and "
1446 "10e0 >= -105 + 5i4 + 4i6) }",
1447 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((381 - t1)/5), "
1448 "e1 = floor((-1 + i4)/2): t2 = 0 and 2e1 = -1 + i4 and "
1449 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 >= 1511 - 4t1 - 5i4) }" },
1450 { "{ [0, 0, q, p] : -5 <= q <= 5 and p >= 0 }",
1451 "{ [a, b, q, p] : b >= 1 + a }",
1452 "{ [a, b, q, p] : false }" },
1453 { "[n] -> { [x] : x = n && x mod 32 = 0 }",
1454 "[n] -> { [x] : x mod 32 = 0 }",
1455 "[n] -> { [x = n] }" },
1456 { "{ [x] : x mod 6 = 0 }", "{ [x] : x mod 3 = 0 }",
1457 "{ [x] : x mod 2 = 0 }" },
1458 { "{ [x] : x mod 3200 = 0 }", "{ [x] : x mod 10000 = 0 }",
1459 "{ [x] : x mod 128 = 0 }" },
1460 { "{ [x] : x mod 3200 = 0 }", "{ [x] : x mod 10 = 0 }",
1461 "{ [x] : x mod 3200 = 0 }" },
1462 { "{ [a, b, c] : a mod 2 = 0 and a = c }",
1463 "{ [a, b, c] : b mod 2 = 0 and b = c }",
1464 "{ [a, b, c = a] }" },
1465 { "{ [a, b, c] : a mod 6 = 0 and a = c }",
1466 "{ [a, b, c] : b mod 2 = 0 and b = c }",
1467 "{ [a, b, c = a] : a mod 3 = 0 }" },
1468 { "{ [x] : 0 <= x <= 4 or 6 <= x <= 9 }",
1469 "{ [x] : 1 <= x <= 3 or 7 <= x <= 8 }",
1471 { "{ [x,y] : x < 0 and 0 <= y <= 4 or x >= -2 and -x <= y <= 10 + x }",
1472 "{ [x,y] : 1 <= y <= 3 }",
1476 /* Check that isl_set_gist behaves as expected.
1478 * For the test cases in gist_tests, besides checking that the result
1479 * is as expected, also check that applying the gist operation does
1480 * not modify the input set (an earlier version of isl would do that) and
1481 * that the test case is consistent, i.e., that the gist has the same
1482 * intersection with the context as the input set.
1484 static int test_gist(struct isl_ctx
*ctx
)
1488 isl_basic_set
*bset1
, *bset2
;
1489 isl_map
*map1
, *map2
;
1492 for (i
= 0; i
< ARRAY_SIZE(gist_tests
); ++i
) {
1493 int equal_input
, equal_intersection
;
1494 isl_set
*set1
, *set2
, *copy
, *context
;
1496 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1497 context
= isl_set_read_from_str(ctx
, gist_tests
[i
].context
);
1498 copy
= isl_set_copy(set1
);
1499 set1
= isl_set_gist(set1
, isl_set_copy(context
));
1500 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].gist
);
1501 equal
= isl_set_is_equal(set1
, set2
);
1503 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1504 equal_input
= isl_set_is_equal(set1
, copy
);
1506 set1
= isl_set_intersect(set1
, isl_set_copy(context
));
1507 set2
= isl_set_intersect(set2
, context
);
1508 equal_intersection
= isl_set_is_equal(set1
, set2
);
1511 if (equal
< 0 || equal_input
< 0 || equal_intersection
< 0)
1514 isl_die(ctx
, isl_error_unknown
,
1515 "incorrect gist result", return -1);
1517 isl_die(ctx
, isl_error_unknown
,
1518 "gist modified input", return -1);
1520 isl_die(ctx
, isl_error_unknown
,
1521 "inconsistent gist test case", return -1);
1524 test_gist_case(ctx
, "gist1");
1526 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1527 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1528 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1529 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1530 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1531 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1532 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1533 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1534 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1535 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1536 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1537 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1538 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1539 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1540 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1541 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1542 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1543 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1544 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1545 bset1
= isl_basic_set_gist(bset1
, bset2
);
1546 assert(bset1
&& bset1
->n_div
== 0);
1547 isl_basic_set_free(bset1
);
1549 /* Check that the integer divisions of the second disjunct
1550 * do not spread to the first disjunct.
1552 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1553 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1554 "(exists (e0 = [(-1 + t1)/16], "
1555 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1556 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1557 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1558 "o0 <= 4294967295 and t1 <= -1)) }";
1559 map1
= isl_map_read_from_str(ctx
, str
);
1560 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1561 map2
= isl_map_read_from_str(ctx
, str
);
1562 map1
= isl_map_gist(map1
, map2
);
1566 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1567 isl_map_free(map1
); return -1);
1568 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1569 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1570 isl_map_free(map1
); return -1);
1573 if (test_plain_gist(ctx
) < 0)
1579 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1581 isl_set
*set
, *set2
;
1585 set
= isl_set_read_from_str(ctx
, str
);
1586 set
= isl_set_coalesce(set
);
1587 set2
= isl_set_read_from_str(ctx
, str
);
1588 equal
= isl_set_is_equal(set
, set2
);
1589 one
= set
&& set
->n
== 1;
1596 isl_die(ctx
, isl_error_unknown
,
1597 "coalesced set not equal to input", return -1);
1598 if (check_one
&& !one
)
1599 isl_die(ctx
, isl_error_unknown
,
1600 "coalesced set should not be a union", return -1);
1605 /* Inputs for coalescing tests with unbounded wrapping.
1606 * "str" is a string representation of the input set.
1607 * "single_disjunct" is set if we expect the result to consist of
1608 * a single disjunct.
1611 int single_disjunct
;
1613 } coalesce_unbounded_tests
[] = {
1614 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1615 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1616 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1617 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1619 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1620 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1621 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1622 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1625 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1626 * option turned off.
1628 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1634 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1635 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1637 for (i
= 0; i
< ARRAY_SIZE(coalesce_unbounded_tests
); ++i
) {
1638 const char *str
= coalesce_unbounded_tests
[i
].str
;
1639 int check_one
= coalesce_unbounded_tests
[i
].single_disjunct
;
1640 if (test_coalesce_set(ctx
, str
, check_one
) >= 0)
1646 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1651 /* Inputs for coalescing tests.
1652 * "str" is a string representation of the input set.
1653 * "single_disjunct" is set if we expect the result to consist of
1654 * a single disjunct.
1657 int single_disjunct
;
1659 } coalesce_tests
[] = {
1660 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1661 "y >= x & x >= 2 & 5 >= y }" },
1662 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1663 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1664 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1665 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1666 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1667 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1668 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1669 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1670 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1671 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1672 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1673 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1674 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1675 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1676 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1677 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1678 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1679 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1680 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1681 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1682 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1683 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1684 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1685 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1686 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1687 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1688 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1689 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1690 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1691 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1692 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1693 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1694 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1695 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1696 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1697 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1698 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1699 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1700 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1701 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1702 "[o0, o1, o2, o3, o4, o5, o6]] : "
1703 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1704 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1705 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1706 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1707 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1708 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1709 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1710 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1711 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1712 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1713 "o6 >= i3 + i6 - o3 and M >= 0 and "
1714 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1715 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1716 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1717 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1718 "(o0 = 0 and M >= 2 and N >= 3) or "
1719 "(M = 0 and o0 = 0 and N >= 3) }" },
1720 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1721 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1722 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1723 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1724 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1725 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1726 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1727 "(y = 3 and x = 1) }" },
1728 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1729 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1730 "i1 <= M and i3 <= M and i4 <= M) or "
1731 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1732 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1733 "i4 <= -1 + M) }" },
1734 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1735 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1736 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1737 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1738 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1739 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1740 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1741 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1742 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1743 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1744 { 0, "{ [a, b] : exists e : 2e = a and "
1745 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1746 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1747 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1748 "j >= 1 and j' <= i + j - i' and i >= 1; "
1750 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1751 "[i,j] : exists a : j = 3a }" },
1752 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1753 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1755 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1756 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1757 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1758 "c <= 6 + 8a and a >= 3; "
1759 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1760 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1761 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1762 "[x,0] : 3 <= x <= 4 }" },
1763 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1764 "[x,0] : 4 <= x <= 5 }" },
1765 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1766 "[x,0] : 3 <= x <= 5 }" },
1767 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1768 "[x,0] : 3 <= x <= 4 }" },
1769 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1771 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1772 { 1, "{ [0,0]; [1,1] }" },
1773 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1774 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1776 "[k, 0, k] : k <= 6 and k >= 1 }" },
1777 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1778 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1779 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1780 { 1, "[n] -> { [1] : n >= 0;"
1781 "[x] : exists (e0 = floor((x)/2): x >= 2 and "
1782 "2e0 >= -1 + x and 2e0 <= x and 2e0 <= n) }" },
1783 { 1, "[n] -> { [x, y] : exists (e0 = floor((x)/2), e1 = floor((y)/3): "
1784 "3e1 = y and x >= 2 and 2e0 >= -1 + x and "
1785 "2e0 <= x and 2e0 <= n);"
1786 "[1, y] : exists (e0 = floor((y)/3): 3e0 = y and "
1788 { 1, "[t1] -> { [i0] : (exists (e0 = floor((63t1)/64): "
1789 "128e0 >= -134 + 127t1 and t1 >= 2 and "
1790 "64e0 <= 63t1 and 64e0 >= -63 + 63t1)) or "
1792 { 1, "{ [i, i] : exists (e0 = floor((1 + 2i)/3): 3e0 <= 2i and "
1793 "3e0 >= -1 + 2i and i <= 9 and i >= 1);"
1795 { 1, "{ [t1] : exists (e0 = floor((-11 + t1)/2): 2e0 = -11 + t1 and "
1796 "t1 >= 13 and t1 <= 16);"
1797 "[t1] : t1 <= 15 and t1 >= 12 }" },
1798 { 1, "{ [x,y] : x = 3y and 0 <= y <= 2; [-3,-1] }" },
1799 { 1, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-2] }" },
1800 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-2,-2] }" },
1801 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-1] }" },
1802 { 1, "{ [i] : exists j : i = 4 j and 0 <= i <= 100;"
1803 "[i] : exists j : 1 <= i <= 100 and i >= 4j + 1 and "
1805 { 1, "{ [c0] : (exists (e0 : c0 - 1 <= 3e0 <= c0)) or "
1806 "(exists (e0 : 3e0 = -2 + c0)) }" },
1807 { 0, "[n, b0, t0] -> "
1808 "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1809 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1810 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1811 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1812 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 >= 8 + n and "
1813 "3i4 <= -96 + 3t0 + i0 and 3i4 >= -95 - n + 3t0 + i0 and "
1814 "i8 >= -157 + i0 - 4i4 and i8 >= 0 and "
1815 "i8 <= -33 + i0 - 4i4 and 3i8 <= -91 + 4n - i0)) or "
1816 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1817 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1818 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1819 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 <= 7 + n and "
1820 "4i4 <= -3 + i0 and 3i4 <= -96 + 3t0 + i0 and "
1821 "3i4 >= -95 - n + 3t0 + i0 and i8 >= -157 + i0 - 4i4 and "
1822 "i8 >= 0 and i8 <= -4 + i0 - 3i4 and i8 <= -41 + i0));"
1823 "[i0, i1, i2, i3, 0, i5, i6, i7, i8, i9, i10, i11, i12] : "
1824 "(exists (e0 = floor((i8)/32): b0 = 0 and 32e0 = i8 and "
1825 "n <= 2147483647 and t0 <= 31 and t0 >= 0 and i0 >= 11 and "
1826 "i0 >= 96 - 3t0 and i0 <= 95 + n - 3t0 and i0 <= 7 + n and "
1827 "i8 >= -40 + i0 and i8 <= -10 + i0)) }" },
1828 { 0, "{ [i0, i1, i2] : "
1829 "(exists (e0, e1 = floor((i0)/32), e2 = floor((i1)/32): "
1830 "32e1 = i0 and 32e2 = i1 and i1 >= -31 + i0 and "
1831 "i1 <= 31 + i0 and i2 >= -30 + i0 and i2 >= -30 + i1 and "
1832 "32e0 >= -30 + i0 and 32e0 >= -30 + i1 and "
1833 "32e0 >= -31 + i2 and 32e0 <= 30 + i2 and 32e0 <= 31 + i1 and "
1834 "32e0 <= 31 + i0)) or "
1836 { 1, "{ [a, b, c] : 2b = 1 + a and 2c = 2 + a; [0, 0, 0] }" },
1837 { 1, "{ [a, a, b, c] : 32*floor((a)/32) = a and 2*floor((b)/2) = b and "
1838 "2*floor((c)/2) = c and 0 <= a <= 192;"
1839 "[224, 224, b, c] : 2*floor((b)/2) = b and 2*floor((c)/2) = c }"
1841 { 1, "[n] -> { [a,b] : (exists e : 1 <= a <= 7e and 9e <= b <= n) or "
1842 "(0 <= a <= b <= n) }" },
1843 { 1, "{ [a, b] : 0 <= a <= 2 and b >= 0 and "
1844 "((0 < b <= 13) or (2*floor((a + b)/2) >= -5 + a + 2b)) }" },
1845 { 1, "{ [a] : (2 <= a <= 5) or (a mod 2 = 1 and 1 <= a <= 5) }" },
1846 { 1, "{ [a, b, c] : (b = -1 + a and 0 < a <= 3 and "
1847 "9*floor((-4a + 2c)/9) <= -3 - 4a + 2c) or "
1848 "(exists (e0 = floor((-16 + 2c)/9): a = 4 and "
1849 "b = 3 and 9e0 <= -19 + 2c)) }" },
1850 { 0, "{ [a, b, c] : (b <= 2 and b <= -2 + a) or "
1851 "(b = -1 + a and 0 < a <= 3 and "
1852 "9*floor((-4a + 2c)/9) <= -3 - 4a + 2c) or "
1853 "(exists (e0 = floor((-16 + 2c)/9): a = 4 and "
1854 "b = 3 and 9e0 <= -19 + 2c)) }" },
1855 { 1, "{ [y, x] : (x - y) mod 3 = 2 and 2 <= y <= 200 and 0 <= x <= 2;"
1857 { 1, "{ [x, y] : (x - y) mod 3 = 2 and 2 <= y <= 200 and 0 <= x <= 2;"
1859 { 1, "{ [1, y] : -1 <= y <= 1; [x, -x] : 0 <= x <= 1 }" },
1860 { 1, "{ [1, y] : 0 <= y <= 1; [x, -x] : 0 <= x <= 1 }" },
1861 { 1, "{ [x, y] : 0 <= x <= 10 and x - 4*floor(x/4) <= 1 and y <= 0; "
1862 "[x, y] : 0 <= x <= 10 and x - 4*floor(x/4) > 1 and y <= 0; "
1863 "[x, y] : 0 <= x <= 10 and x - 5*floor(x/5) <= 1 and 0 < y; "
1864 "[x, y] : 0 <= x <= 10 and x - 5*floor(x/5) > 1 and 0 < y }" },
1865 { 1, "{ [x, 0] : 0 <= x <= 10 and x mod 2 = 0; "
1866 "[x, 0] : 0 <= x <= 10 and x mod 2 = 1; "
1867 "[x, y] : 0 <= x <= 10 and 1 <= y <= 10 }" },
1870 /* A specialized coalescing test case that would result
1871 * in a segmentation fault or a failed assertion in earlier versions of isl.
1873 static int test_coalesce_special(struct isl_ctx
*ctx
)
1876 isl_map
*map1
, *map2
;
1878 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1879 "[[S_L309_IN[] -> T11[]] -> ce_imag2[1, o1]] : "
1880 "(y = 201 and o1 <= 239 and o1 >= 212) or "
1881 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 198 and y >= 3 and "
1882 "o1 <= 239 and o1 >= 212)) or "
1883 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 201 and y >= 3 and "
1884 "o1 <= 241 and o1 >= 240));"
1885 "[S_L220_OUT[] -> T7[]] -> "
1886 "[[S_L309_IN[] -> T11[]] -> ce_imag2[0, o1]] : "
1887 "(y = 2 and o1 <= 241 and o1 >= 212) or "
1888 "(exists (e0 = [(-2 + y)/3]: 3e0 = -2 + y and y <= 200 and "
1889 "y >= 5 and o1 <= 241 and o1 >= 212)) }";
1890 map1
= isl_map_read_from_str(ctx
, str
);
1891 map1
= isl_map_align_divs(map1
);
1892 map1
= isl_map_coalesce(map1
);
1893 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1894 "[[S_L309_IN[] -> T11[]] -> ce_imag2[o0, o1]] : "
1895 "exists (e0 = [(-1 - y + o0)/3]: 3e0 = -1 - y + o0 and "
1896 "y <= 201 and o0 <= 2 and o1 >= 212 and o1 <= 241 and "
1897 "o0 >= 3 - y and o0 <= -2 + y and o0 >= 0) }";
1898 map2
= isl_map_read_from_str(ctx
, str
);
1899 map2
= isl_map_union(map2
, map1
);
1900 map2
= isl_map_align_divs(map2
);
1901 map2
= isl_map_coalesce(map2
);
1909 /* A specialized coalescing test case that would result in an assertion
1910 * in an earlier version of isl.
1911 * The explicit call to isl_basic_set_union prevents the implicit
1912 * equality constraints in the first basic map from being detected prior
1913 * to the call to isl_set_coalesce, at least at the point
1914 * where this test case was introduced.
1916 static int test_coalesce_special2(struct isl_ctx
*ctx
)
1919 isl_basic_set
*bset1
, *bset2
;
1922 str
= "{ [x, y] : x, y >= 0 and x + 2y <= 1 and 2x + y <= 1 }";
1923 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1924 str
= "{ [x,0] : -1 <= x <= 1 and x mod 2 = 1 }" ;
1925 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1926 set
= isl_basic_set_union(bset1
, bset2
);
1927 set
= isl_set_coalesce(set
);
1935 /* Test the functionality of isl_set_coalesce.
1936 * That is, check that the output is always equal to the input
1937 * and in some cases that the result consists of a single disjunct.
1939 static int test_coalesce(struct isl_ctx
*ctx
)
1943 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
1944 const char *str
= coalesce_tests
[i
].str
;
1945 int check_one
= coalesce_tests
[i
].single_disjunct
;
1946 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
1950 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1952 if (test_coalesce_special(ctx
) < 0)
1954 if (test_coalesce_special2(ctx
) < 0)
1960 /* Construct a representation of the graph on the right of Figure 1
1961 * in "Computing the Transitive Closure of a Union of
1962 * Affine Integer Tuple Relations".
1964 static __isl_give isl_map
*cocoa_fig_1_right_graph(isl_ctx
*ctx
)
1967 isl_map
*up
, *right
;
1969 dom
= isl_set_read_from_str(ctx
,
1970 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1971 "2 x - 3 y + 3 >= 0 }");
1972 right
= isl_map_read_from_str(ctx
,
1973 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1974 up
= isl_map_read_from_str(ctx
,
1975 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1976 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1977 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1978 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1979 up
= isl_map_intersect_range(up
, dom
);
1980 return isl_map_union(up
, right
);
1983 /* Construct a representation of the power of the graph
1984 * on the right of Figure 1 in "Computing the Transitive Closure of
1985 * a Union of Affine Integer Tuple Relations".
1987 static __isl_give isl_map
*cocoa_fig_1_right_power(isl_ctx
*ctx
)
1989 return isl_map_read_from_str(ctx
,
1990 "{ [1] -> [[0,0] -> [0,1]]; [2] -> [[0,0] -> [1,1]]; "
1991 " [1] -> [[0,1] -> [1,1]]; [1] -> [[2,2] -> [3,2]]; "
1992 " [2] -> [[2,2] -> [3,3]]; [1] -> [[3,2] -> [3,3]] }");
1995 /* Construct a representation of the transitive closure of the graph
1996 * on the right of Figure 1 in "Computing the Transitive Closure of
1997 * a Union of Affine Integer Tuple Relations".
1999 static __isl_give isl_map
*cocoa_fig_1_right_tc(isl_ctx
*ctx
)
2001 return isl_set_unwrap(isl_map_range(cocoa_fig_1_right_power(ctx
)));
2004 static int test_closure(isl_ctx
*ctx
)
2007 isl_map
*map
, *map2
;
2010 /* COCOA example 1 */
2011 map
= isl_map_read_from_str(ctx
,
2012 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
2013 "1 <= i and i < n and 1 <= j and j < n or "
2014 "i2 = i + 1 and j2 = j - 1 and "
2015 "1 <= i and i < n and 2 <= j and j <= n }");
2016 map
= isl_map_power(map
, &exact
);
2020 /* COCOA example 1 */
2021 map
= isl_map_read_from_str(ctx
,
2022 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
2023 "1 <= i and i < n and 1 <= j and j < n or "
2024 "i2 = i + 1 and j2 = j - 1 and "
2025 "1 <= i and i < n and 2 <= j and j <= n }");
2026 map
= isl_map_transitive_closure(map
, &exact
);
2028 map2
= isl_map_read_from_str(ctx
,
2029 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
2030 "1 <= i and i < n and 1 <= j and j <= n and "
2031 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
2032 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
2033 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
2034 assert(isl_map_is_equal(map
, map2
));
2038 map
= isl_map_read_from_str(ctx
,
2039 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
2040 " 0 <= y and y <= n }");
2041 map
= isl_map_transitive_closure(map
, &exact
);
2042 map2
= isl_map_read_from_str(ctx
,
2043 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
2044 " 0 <= y and y <= n }");
2045 assert(isl_map_is_equal(map
, map2
));
2049 /* COCOA example 2 */
2050 map
= isl_map_read_from_str(ctx
,
2051 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
2052 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
2053 "i2 = i + 2 and j2 = j - 2 and "
2054 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
2055 map
= isl_map_transitive_closure(map
, &exact
);
2057 map2
= isl_map_read_from_str(ctx
,
2058 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
2059 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
2060 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
2061 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
2062 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
2063 assert(isl_map_is_equal(map
, map2
));
2067 /* COCOA Fig.2 left */
2068 map
= isl_map_read_from_str(ctx
,
2069 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
2070 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
2072 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
2073 "j <= 2 i - 3 and j <= n - 2 or "
2074 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2075 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2076 map
= isl_map_transitive_closure(map
, &exact
);
2080 /* COCOA Fig.2 right */
2081 map
= isl_map_read_from_str(ctx
,
2082 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
2083 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
2085 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
2086 "j <= 2 i - 4 and j <= n - 3 or "
2087 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2088 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2089 map
= isl_map_power(map
, &exact
);
2093 /* COCOA Fig.2 right */
2094 map
= isl_map_read_from_str(ctx
,
2095 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
2096 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
2098 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
2099 "j <= 2 i - 4 and j <= n - 3 or "
2100 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2101 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2102 map
= isl_map_transitive_closure(map
, &exact
);
2104 map2
= isl_map_read_from_str(ctx
,
2105 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
2106 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
2107 "j <= n and 3 + i + 2 j <= 3 n and "
2108 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
2109 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
2110 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
2111 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
2112 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
2113 assert(isl_map_is_equal(map
, map2
));
2117 map
= cocoa_fig_1_right_graph(ctx
);
2118 map
= isl_map_transitive_closure(map
, &exact
);
2120 map2
= cocoa_fig_1_right_tc(ctx
);
2121 assert(isl_map_is_equal(map
, map2
));
2125 map
= cocoa_fig_1_right_graph(ctx
);
2126 map
= isl_map_power(map
, &exact
);
2127 map2
= cocoa_fig_1_right_power(ctx
);
2128 equal
= isl_map_is_equal(map
, map2
);
2134 isl_die(ctx
, isl_error_unknown
, "power not exact", return -1);
2136 isl_die(ctx
, isl_error_unknown
, "unexpected power", return -1);
2138 /* COCOA Theorem 1 counter example */
2139 map
= isl_map_read_from_str(ctx
,
2140 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
2141 "i2 = 1 and j2 = j or "
2142 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
2143 map
= isl_map_transitive_closure(map
, &exact
);
2147 map
= isl_map_read_from_str(ctx
,
2148 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
2149 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
2150 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
2151 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
2152 map
= isl_map_transitive_closure(map
, &exact
);
2156 /* Kelly et al 1996, fig 12 */
2157 map
= isl_map_read_from_str(ctx
,
2158 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
2159 "1 <= i,j,j+1 <= n or "
2160 "j = n and j2 = 1 and i2 = i + 1 and "
2161 "1 <= i,i+1 <= n }");
2162 map
= isl_map_transitive_closure(map
, &exact
);
2164 map2
= isl_map_read_from_str(ctx
,
2165 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
2166 "1 <= i <= n and i = i2 or "
2167 "1 <= i < i2 <= n and 1 <= j <= n and "
2169 assert(isl_map_is_equal(map
, map2
));
2173 /* Omega's closure4 */
2174 map
= isl_map_read_from_str(ctx
,
2175 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
2176 "1 <= x,y <= 10 or "
2177 "x2 = x + 1 and y2 = y and "
2178 "1 <= x <= 20 && 5 <= y <= 15 }");
2179 map
= isl_map_transitive_closure(map
, &exact
);
2183 map
= isl_map_read_from_str(ctx
,
2184 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
2185 map
= isl_map_transitive_closure(map
, &exact
);
2187 map2
= isl_map_read_from_str(ctx
,
2188 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
2189 assert(isl_map_is_equal(map
, map2
));
2193 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
2194 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
2195 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
2196 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
2197 map
= isl_map_read_from_str(ctx
, str
);
2198 map
= isl_map_transitive_closure(map
, &exact
);
2200 map2
= isl_map_read_from_str(ctx
, str
);
2201 assert(isl_map_is_equal(map
, map2
));
2205 str
= "{[0] -> [1]; [2] -> [3]}";
2206 map
= isl_map_read_from_str(ctx
, str
);
2207 map
= isl_map_transitive_closure(map
, &exact
);
2209 map2
= isl_map_read_from_str(ctx
, str
);
2210 assert(isl_map_is_equal(map
, map2
));
2214 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
2215 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
2216 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
2217 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2218 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2219 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
2220 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
2221 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
2222 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2223 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2224 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
2225 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
2226 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
2227 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2228 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2229 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
2230 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
2231 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
2232 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2233 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
2234 map
= isl_map_read_from_str(ctx
, str
);
2235 map
= isl_map_transitive_closure(map
, NULL
);
2242 static int test_lex(struct isl_ctx
*ctx
)
2248 dim
= isl_space_set_alloc(ctx
, 0, 0);
2249 map
= isl_map_lex_le(dim
);
2250 empty
= isl_map_is_empty(map
);
2256 isl_die(ctx
, isl_error_unknown
,
2257 "expecting non-empty result", return -1);
2262 /* Inputs for isl_map_lexmin tests.
2263 * "map" is the input and "lexmin" is the expected result.
2268 } lexmin_tests
[] = {
2269 { "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }",
2270 "{ [x] -> [5] : 6 <= x <= 8; "
2271 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }" },
2272 { "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }",
2273 "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }" },
2274 { "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }",
2275 "{ [x] -> [y] : (4y = x and x >= 0) or "
2276 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
2277 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
2278 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }" },
2279 { "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }",
2280 "{ T[a] -> S[b, c] : 2b = a and 2c = a }" },
2281 /* Check that empty pieces are properly combined. */
2282 { "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
2283 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
2284 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }",
2285 "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
2286 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
2288 { "{ [i, k, j] -> [a, b, c, d] : 8*floor((b)/8) = b and k <= 255 and "
2289 "a <= 255 and c <= 255 and d <= 255 - j and "
2290 "255 - j <= 7d <= 7 - i and 240d <= 239 + a and "
2291 "247d <= 247 + k - j and 247d <= 247 + k - b and "
2292 "247d <= 247 + i and 248 - b <= 248d <= c and "
2293 "254d >= i - a + b and 254d >= -a + b and "
2294 "255d >= -i + a - b and 1792d >= -63736 + 257b }",
2296 "[-127762 + i + 502j, -62992 + 248j, 63240 - 248j, 255 - j] : "
2297 "k <= 255 and 7j >= 1778 + i and 246j >= 62738 - k and "
2298 "247j >= 62738 - i and 509j <= 129795 + i and "
2299 "742j >= 188724 - i; "
2300 "[0, k, j] -> [1, 0, 248, 1] : k <= 255 and 248 <= j <= 254, k }" },
2301 { "{ [a] -> [b] : 0 <= b <= 255 and -509 + a <= 512b < a and "
2302 "16*floor((8 + b)/16) <= 7 + b; "
2304 "{ [a] -> [b = 1] : a >= 510 or a <= 0; "
2305 "[a] -> [b = 0] : 0 < a <= 509 }" },
2308 static int test_lexmin(struct isl_ctx
*ctx
)
2313 isl_basic_map
*bmap
;
2314 isl_map
*map
, *map2
;
2317 isl_pw_multi_aff
*pma
;
2319 str
= "[p0, p1] -> { [] -> [] : "
2320 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
2321 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
2322 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
2323 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
2324 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
2325 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
2326 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
2327 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
2328 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
2329 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
2330 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
2331 map
= isl_map_read_from_str(ctx
, str
);
2332 map
= isl_map_lexmin(map
);
2335 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
2336 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
2337 set
= isl_set_read_from_str(ctx
, str
);
2338 set
= isl_set_lexmax(set
);
2339 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
2340 set2
= isl_set_read_from_str(ctx
, str
);
2341 set
= isl_set_intersect(set
, set2
);
2342 assert(!isl_set_is_empty(set
));
2345 for (i
= 0; i
< ARRAY_SIZE(lexmin_tests
); ++i
) {
2346 map
= isl_map_read_from_str(ctx
, lexmin_tests
[i
].map
);
2347 map
= isl_map_lexmin(map
);
2348 map2
= isl_map_read_from_str(ctx
, lexmin_tests
[i
].lexmin
);
2349 equal
= isl_map_is_equal(map
, map2
);
2356 isl_die(ctx
, isl_error_unknown
,
2357 "unexpected result", return -1);
2360 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2361 " 8i' <= i and 8i' >= -7 + i }";
2362 bmap
= isl_basic_map_read_from_str(ctx
, str
);
2363 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
2364 map2
= isl_map_from_pw_multi_aff(pma
);
2365 map
= isl_map_from_basic_map(bmap
);
2366 assert(isl_map_is_equal(map
, map2
));
2370 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2371 " 8i' <= i and 8i' >= -7 + i }";
2372 set
= isl_set_read_from_str(ctx
, str
);
2373 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
2374 set2
= isl_set_from_pw_multi_aff(pma
);
2375 equal
= isl_set_is_equal(set
, set2
);
2381 isl_die(ctx
, isl_error_unknown
,
2382 "unexpected difference between set and "
2383 "piecewise affine expression", return -1);
2388 /* A specialized isl_set_min_val test case that would return the wrong result
2389 * in earlier versions of isl.
2390 * The explicit call to isl_basic_set_union prevents the second basic set
2391 * from being determined to be empty prior to the call to isl_set_min_val,
2392 * at least at the point where this test case was introduced.
2394 static int test_min_special(isl_ctx
*ctx
)
2397 isl_basic_set
*bset1
, *bset2
;
2403 str
= "{ [a, b] : a >= 2 and b >= 0 and 14 - a <= b <= 9 }";
2404 bset1
= isl_basic_set_read_from_str(ctx
, str
);
2405 str
= "{ [a, b] : 1 <= a, b and a + b <= 1 }";
2406 bset2
= isl_basic_set_read_from_str(ctx
, str
);
2407 set
= isl_basic_set_union(bset1
, bset2
);
2408 obj
= isl_aff_read_from_str(ctx
, "{ [a, b] -> [a] }");
2410 res
= isl_set_min_val(set
, obj
);
2411 ok
= isl_val_cmp_si(res
, 5) == 0;
2420 isl_die(ctx
, isl_error_unknown
, "unexpected minimum",
2429 __isl_give isl_val
*(*fn
)(__isl_keep isl_set
*set
,
2430 __isl_keep isl_aff
*obj
);
2433 { "{ [-1]; [1] }", "{ [x] -> [x] }", &isl_set_min_val
, "-1" },
2434 { "{ [-1]; [1] }", "{ [x] -> [x] }", &isl_set_max_val
, "1" },
2435 { "{ [a, b] : 0 <= a, b <= 100 and b mod 2 = 0}",
2436 "{ [a, b] -> [floor((b - 2*floor((-a)/4))/5)] }",
2437 &isl_set_max_val
, "30" },
2441 /* Perform basic isl_set_min_val and isl_set_max_val tests.
2442 * In particular, check the results on non-convex inputs.
2444 static int test_min(struct isl_ctx
*ctx
)
2452 for (i
= 0; i
< ARRAY_SIZE(opt_tests
); ++i
) {
2453 set
= isl_set_read_from_str(ctx
, opt_tests
[i
].set
);
2454 obj
= isl_aff_read_from_str(ctx
, opt_tests
[i
].obj
);
2455 res
= isl_val_read_from_str(ctx
, opt_tests
[i
].res
);
2456 val
= opt_tests
[i
].fn(set
, obj
);
2457 ok
= isl_val_eq(res
, val
);
2466 isl_die(ctx
, isl_error_unknown
,
2467 "unexpected optimum", return -1);
2470 if (test_min_special(ctx
) < 0)
2481 static isl_stat
collect_must_may(__isl_take isl_map
*dep
, int must
,
2482 void *dep_user
, void *user
)
2484 struct must_may
*mm
= (struct must_may
*)user
;
2487 mm
->must
= isl_map_union(mm
->must
, dep
);
2489 mm
->may
= isl_map_union(mm
->may
, dep
);
2494 static int common_space(void *first
, void *second
)
2496 int depth
= *(int *)first
;
2500 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
2508 map2
= isl_map_read_from_str(map
->ctx
, str
);
2509 equal
= isl_map_is_equal(map
, map2
);
2515 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
2519 equal
= map_is_equal(map
, str
);
2523 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
2524 "result not as expected", return -1);
2528 static int test_dep(struct isl_ctx
*ctx
)
2533 isl_access_info
*ai
;
2540 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2541 map
= isl_map_read_from_str(ctx
, str
);
2542 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2544 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2545 map
= isl_map_read_from_str(ctx
, str
);
2546 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2548 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2549 map
= isl_map_read_from_str(ctx
, str
);
2550 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2552 flow
= isl_access_info_compute_flow(ai
);
2553 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2554 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2555 mm
.may
= isl_map_empty(dim
);
2557 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2559 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
2560 " [1,10,0] -> [2,5,0] }";
2561 assert(map_is_equal(mm
.must
, str
));
2562 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2563 assert(map_is_equal(mm
.may
, str
));
2565 isl_map_free(mm
.must
);
2566 isl_map_free(mm
.may
);
2567 isl_flow_free(flow
);
2570 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2571 map
= isl_map_read_from_str(ctx
, str
);
2572 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2574 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2575 map
= isl_map_read_from_str(ctx
, str
);
2576 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2578 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2579 map
= isl_map_read_from_str(ctx
, str
);
2580 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2582 flow
= isl_access_info_compute_flow(ai
);
2583 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2584 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2585 mm
.may
= isl_map_empty(dim
);
2587 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2589 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2590 assert(map_is_equal(mm
.must
, str
));
2591 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2592 assert(map_is_equal(mm
.may
, str
));
2594 isl_map_free(mm
.must
);
2595 isl_map_free(mm
.may
);
2596 isl_flow_free(flow
);
2599 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2600 map
= isl_map_read_from_str(ctx
, str
);
2601 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2603 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2604 map
= isl_map_read_from_str(ctx
, str
);
2605 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2607 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2608 map
= isl_map_read_from_str(ctx
, str
);
2609 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2611 flow
= isl_access_info_compute_flow(ai
);
2612 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2613 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2614 mm
.may
= isl_map_empty(dim
);
2616 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2618 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2619 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2620 assert(map_is_equal(mm
.may
, str
));
2621 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2622 assert(map_is_equal(mm
.must
, str
));
2624 isl_map_free(mm
.must
);
2625 isl_map_free(mm
.may
);
2626 isl_flow_free(flow
);
2629 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2630 map
= isl_map_read_from_str(ctx
, str
);
2631 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2633 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2634 map
= isl_map_read_from_str(ctx
, str
);
2635 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2637 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2638 map
= isl_map_read_from_str(ctx
, str
);
2639 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2641 flow
= isl_access_info_compute_flow(ai
);
2642 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2643 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2644 mm
.may
= isl_map_empty(dim
);
2646 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2648 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2649 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2650 assert(map_is_equal(mm
.may
, str
));
2651 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2652 assert(map_is_equal(mm
.must
, str
));
2654 isl_map_free(mm
.must
);
2655 isl_map_free(mm
.may
);
2656 isl_flow_free(flow
);
2659 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2660 map
= isl_map_read_from_str(ctx
, str
);
2661 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2663 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2664 map
= isl_map_read_from_str(ctx
, str
);
2665 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2667 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2668 map
= isl_map_read_from_str(ctx
, str
);
2669 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2671 flow
= isl_access_info_compute_flow(ai
);
2672 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2673 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2674 mm
.may
= isl_map_empty(dim
);
2676 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2678 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2679 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2680 assert(map_is_equal(mm
.may
, str
));
2681 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2682 assert(map_is_equal(mm
.must
, str
));
2684 isl_map_free(mm
.must
);
2685 isl_map_free(mm
.may
);
2686 isl_flow_free(flow
);
2691 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2692 map
= isl_map_read_from_str(ctx
, str
);
2693 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2695 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2696 map
= isl_map_read_from_str(ctx
, str
);
2697 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2699 flow
= isl_access_info_compute_flow(ai
);
2700 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2701 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2702 mm
.may
= isl_map_empty(dim
);
2704 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2706 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2707 assert(map_is_equal(mm
.must
, str
));
2708 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2709 assert(map_is_equal(mm
.may
, str
));
2711 isl_map_free(mm
.must
);
2712 isl_map_free(mm
.may
);
2713 isl_flow_free(flow
);
2718 /* Check that the dependence analysis proceeds without errors.
2719 * Earlier versions of isl would break down during the analysis
2720 * due to the use of the wrong spaces.
2722 static int test_flow(isl_ctx
*ctx
)
2725 isl_union_map
*access
, *schedule
;
2726 isl_union_map
*must_dep
, *may_dep
;
2729 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2730 access
= isl_union_map_read_from_str(ctx
, str
);
2731 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2732 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2733 "S2[] -> [1,0,0,0]; "
2734 "S3[] -> [-1,0,0,0] }";
2735 schedule
= isl_union_map_read_from_str(ctx
, str
);
2736 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2737 isl_union_map_copy(access
), schedule
,
2738 &must_dep
, &may_dep
, NULL
, NULL
);
2739 isl_union_map_free(may_dep
);
2740 isl_union_map_free(must_dep
);
2749 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2750 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2751 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2752 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2753 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2754 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2755 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2756 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2757 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2760 int test_sv(isl_ctx
*ctx
)
2762 isl_union_map
*umap
;
2766 for (i
= 0; i
< ARRAY_SIZE(sv_tests
); ++i
) {
2767 umap
= isl_union_map_read_from_str(ctx
, sv_tests
[i
].map
);
2768 sv
= isl_union_map_is_single_valued(umap
);
2769 isl_union_map_free(umap
);
2772 if (sv_tests
[i
].sv
&& !sv
)
2773 isl_die(ctx
, isl_error_internal
,
2774 "map not detected as single valued", return -1);
2775 if (!sv_tests
[i
].sv
&& sv
)
2776 isl_die(ctx
, isl_error_internal
,
2777 "map detected as single valued", return -1);
2786 } bijective_tests
[] = {
2787 { "[N,M]->{[i,j] -> [i]}", 0 },
2788 { "[N,M]->{[i,j] -> [i] : j=i}", 1 },
2789 { "[N,M]->{[i,j] -> [i] : j=0}", 1 },
2790 { "[N,M]->{[i,j] -> [i] : j=N}", 1 },
2791 { "[N,M]->{[i,j] -> [j,i]}", 1 },
2792 { "[N,M]->{[i,j] -> [i+j]}", 0 },
2793 { "[N,M]->{[i,j] -> []}", 0 },
2794 { "[N,M]->{[i,j] -> [i,j,N]}", 1 },
2795 { "[N,M]->{[i,j] -> [2i]}", 0 },
2796 { "[N,M]->{[i,j] -> [i,i]}", 0 },
2797 { "[N,M]->{[i,j] -> [2i,i]}", 0 },
2798 { "[N,M]->{[i,j] -> [2i,j]}", 1 },
2799 { "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1 },
2802 static int test_bijective(struct isl_ctx
*ctx
)
2808 for (i
= 0; i
< ARRAY_SIZE(bijective_tests
); ++i
) {
2809 map
= isl_map_read_from_str(ctx
, bijective_tests
[i
].str
);
2810 bijective
= isl_map_is_bijective(map
);
2814 if (bijective_tests
[i
].bijective
&& !bijective
)
2815 isl_die(ctx
, isl_error_internal
,
2816 "map not detected as bijective", return -1);
2817 if (!bijective_tests
[i
].bijective
&& bijective
)
2818 isl_die(ctx
, isl_error_internal
,
2819 "map detected as bijective", return -1);
2825 /* Inputs for isl_pw_qpolynomial_gist tests.
2826 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2832 } pwqp_gist_tests
[] = {
2833 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2834 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2835 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2836 "{ [i] -> -1/2 + 1/2 * i }" },
2837 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2840 static int test_pwqp(struct isl_ctx
*ctx
)
2845 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
2848 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2849 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2851 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
2854 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2855 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2857 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2859 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2861 isl_pw_qpolynomial_free(pwqp1
);
2863 for (i
= 0; i
< ARRAY_SIZE(pwqp_gist_tests
); ++i
) {
2864 str
= pwqp_gist_tests
[i
].pwqp
;
2865 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2866 str
= pwqp_gist_tests
[i
].set
;
2867 set
= isl_set_read_from_str(ctx
, str
);
2868 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2869 str
= pwqp_gist_tests
[i
].gist
;
2870 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2871 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2872 equal
= isl_pw_qpolynomial_is_zero(pwqp1
);
2873 isl_pw_qpolynomial_free(pwqp1
);
2878 isl_die(ctx
, isl_error_unknown
,
2879 "unexpected result", return -1);
2882 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
2883 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2884 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
2885 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2887 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2889 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2891 isl_pw_qpolynomial_free(pwqp1
);
2893 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
2894 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2895 str
= "{ [x] -> x }";
2896 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2898 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2900 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2902 isl_pw_qpolynomial_free(pwqp1
);
2904 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2905 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2906 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2907 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
2908 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2909 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2910 isl_pw_qpolynomial_free(pwqp1
);
2912 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2913 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2914 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2915 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2916 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
2917 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
2918 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2919 isl_pw_qpolynomial_free(pwqp1
);
2920 isl_pw_qpolynomial_free(pwqp2
);
2924 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2926 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2927 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2928 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2929 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2930 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
2932 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2933 isl_pw_qpolynomial_free(pwqp1
);
2934 isl_pw_qpolynomial_free(pwqp2
);
2938 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2943 static int test_split_periods(isl_ctx
*ctx
)
2946 isl_pw_qpolynomial
*pwqp
;
2948 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2949 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2950 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2951 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2953 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
2955 isl_pw_qpolynomial_free(pwqp
);
2963 static int test_union(isl_ctx
*ctx
)
2966 isl_union_set
*uset1
, *uset2
;
2967 isl_union_map
*umap1
, *umap2
;
2970 str
= "{ [i] : 0 <= i <= 1 }";
2971 uset1
= isl_union_set_read_from_str(ctx
, str
);
2972 str
= "{ [1] -> [0] }";
2973 umap1
= isl_union_map_read_from_str(ctx
, str
);
2975 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
2976 equal
= isl_union_map_is_equal(umap1
, umap2
);
2978 isl_union_map_free(umap1
);
2979 isl_union_map_free(umap2
);
2984 isl_die(ctx
, isl_error_unknown
, "union maps not equal",
2987 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2988 umap1
= isl_union_map_read_from_str(ctx
, str
);
2989 str
= "{ A[i]; B[i] }";
2990 uset1
= isl_union_set_read_from_str(ctx
, str
);
2992 uset2
= isl_union_map_domain(umap1
);
2994 equal
= isl_union_set_is_equal(uset1
, uset2
);
2996 isl_union_set_free(uset1
);
2997 isl_union_set_free(uset2
);
3002 isl_die(ctx
, isl_error_unknown
, "union sets not equal",
3008 /* Check that computing a bound of a non-zero polynomial over an unbounded
3009 * domain does not produce a rational value.
3010 * In particular, check that the upper bound is infinity.
3012 static int test_bound_unbounded_domain(isl_ctx
*ctx
)
3015 isl_pw_qpolynomial
*pwqp
;
3016 isl_pw_qpolynomial_fold
*pwf
, *pwf2
;
3019 str
= "{ [m,n] -> -m * n }";
3020 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3021 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3023 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3024 pwf2
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3025 equal
= isl_pw_qpolynomial_fold_plain_is_equal(pwf
, pwf2
);
3026 isl_pw_qpolynomial_fold_free(pwf
);
3027 isl_pw_qpolynomial_fold_free(pwf2
);
3032 isl_die(ctx
, isl_error_unknown
,
3033 "expecting infinite polynomial bound", return -1);
3038 static int test_bound(isl_ctx
*ctx
)
3042 isl_pw_qpolynomial
*pwqp
;
3043 isl_pw_qpolynomial_fold
*pwf
;
3045 if (test_bound_unbounded_domain(ctx
) < 0)
3048 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
3049 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3050 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3051 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
3052 isl_pw_qpolynomial_fold_free(pwf
);
3054 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
3057 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
3058 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3059 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3060 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
3061 isl_pw_qpolynomial_fold_free(pwf
);
3063 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
3069 static int test_lift(isl_ctx
*ctx
)
3072 isl_basic_map
*bmap
;
3073 isl_basic_set
*bset
;
3075 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
3076 bset
= isl_basic_set_read_from_str(ctx
, str
);
3077 bset
= isl_basic_set_lift(bset
);
3078 bmap
= isl_basic_map_from_range(bset
);
3079 bset
= isl_basic_map_domain(bmap
);
3080 isl_basic_set_free(bset
);
3089 } subset_tests
[] = {
3091 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
3092 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
3093 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
3095 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
3096 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
3097 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
3098 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
3099 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
3100 "256e0 <= 255i and 256e0 >= -255 + 255i and "
3101 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
3102 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
3103 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
3104 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
3105 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
3106 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
3107 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
3108 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
3109 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
3110 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
3111 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
3112 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
3113 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
3114 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
3115 "4e0 <= -57 + i0 + i1)) or "
3116 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
3117 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
3118 "4e0 >= -61 + i0 + i1)) or "
3119 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
3120 { "[a, b] -> { : a = 0 and b = -1 }", "[b, a] -> { : b >= -10 }", 1 },
3123 static int test_subset(isl_ctx
*ctx
)
3126 isl_set
*set1
, *set2
;
3129 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
3130 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
3131 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
3132 subset
= isl_set_is_subset(set1
, set2
);
3137 if (subset
!= subset_tests
[i
].subset
)
3138 isl_die(ctx
, isl_error_unknown
,
3139 "incorrect subset result", return -1);
3146 const char *minuend
;
3147 const char *subtrahend
;
3148 const char *difference
;
3149 } subtract_domain_tests
[] = {
3150 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
3151 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
3152 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
3155 static int test_subtract(isl_ctx
*ctx
)
3158 isl_union_map
*umap1
, *umap2
;
3159 isl_union_pw_multi_aff
*upma1
, *upma2
;
3160 isl_union_set
*uset
;
3163 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
3164 umap1
= isl_union_map_read_from_str(ctx
,
3165 subtract_domain_tests
[i
].minuend
);
3166 uset
= isl_union_set_read_from_str(ctx
,
3167 subtract_domain_tests
[i
].subtrahend
);
3168 umap2
= isl_union_map_read_from_str(ctx
,
3169 subtract_domain_tests
[i
].difference
);
3170 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
3171 equal
= isl_union_map_is_equal(umap1
, umap2
);
3172 isl_union_map_free(umap1
);
3173 isl_union_map_free(umap2
);
3177 isl_die(ctx
, isl_error_unknown
,
3178 "incorrect subtract domain result", return -1);
3181 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
3182 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
3183 subtract_domain_tests
[i
].minuend
);
3184 uset
= isl_union_set_read_from_str(ctx
,
3185 subtract_domain_tests
[i
].subtrahend
);
3186 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
3187 subtract_domain_tests
[i
].difference
);
3188 upma1
= isl_union_pw_multi_aff_subtract_domain(upma1
, uset
);
3189 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
3190 isl_union_pw_multi_aff_free(upma1
);
3191 isl_union_pw_multi_aff_free(upma2
);
3195 isl_die(ctx
, isl_error_unknown
,
3196 "incorrect subtract domain result", return -1);
3202 /* Check that intersecting the empty basic set with another basic set
3203 * does not increase the number of constraints. In particular,
3204 * the empty basic set should maintain its canonical representation.
3206 static int test_intersect(isl_ctx
*ctx
)
3209 isl_basic_set
*bset1
, *bset2
;
3211 bset1
= isl_basic_set_read_from_str(ctx
, "{ [a,b,c] : 1 = 0 }");
3212 bset2
= isl_basic_set_read_from_str(ctx
, "{ [1,2,3] }");
3213 n1
= isl_basic_set_n_constraint(bset1
);
3214 bset1
= isl_basic_set_intersect(bset1
, bset2
);
3215 n2
= isl_basic_set_n_constraint(bset1
);
3216 isl_basic_set_free(bset1
);
3220 isl_die(ctx
, isl_error_unknown
,
3221 "number of constraints of empty set changed",
3227 int test_factorize(isl_ctx
*ctx
)
3230 isl_basic_set
*bset
;
3233 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
3234 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
3235 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
3236 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
3237 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
3238 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
3239 "3i5 >= -2i0 - i2 + 3i4 }";
3240 bset
= isl_basic_set_read_from_str(ctx
, str
);
3241 f
= isl_basic_set_factorizer(bset
);
3242 isl_basic_set_free(bset
);
3243 isl_factorizer_free(f
);
3245 isl_die(ctx
, isl_error_unknown
,
3246 "failed to construct factorizer", return -1);
3248 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
3249 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
3250 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
3251 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
3252 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
3253 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
3254 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
3255 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
3256 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
3257 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
3258 bset
= isl_basic_set_read_from_str(ctx
, str
);
3259 f
= isl_basic_set_factorizer(bset
);
3260 isl_basic_set_free(bset
);
3261 isl_factorizer_free(f
);
3263 isl_die(ctx
, isl_error_unknown
,
3264 "failed to construct factorizer", return -1);
3269 static isl_stat
check_injective(__isl_take isl_map
*map
, void *user
)
3271 int *injective
= user
;
3273 *injective
= isl_map_is_injective(map
);
3276 if (*injective
< 0 || !*injective
)
3277 return isl_stat_error
;
3282 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
3283 const char *r
, const char *s
, int tilable
, int parallel
)
3287 isl_union_map
*W
, *R
, *S
;
3288 isl_union_map
*empty
;
3289 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
3290 isl_union_map
*validity
, *proximity
, *coincidence
;
3291 isl_union_map
*schedule
;
3292 isl_union_map
*test
;
3293 isl_union_set
*delta
;
3294 isl_union_set
*domain
;
3298 isl_schedule_constraints
*sc
;
3299 isl_schedule
*sched
;
3300 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
3302 D
= isl_union_set_read_from_str(ctx
, d
);
3303 W
= isl_union_map_read_from_str(ctx
, w
);
3304 R
= isl_union_map_read_from_str(ctx
, r
);
3305 S
= isl_union_map_read_from_str(ctx
, s
);
3307 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
3308 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
3310 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
3311 isl_union_map_compute_flow(isl_union_map_copy(R
),
3312 isl_union_map_copy(W
), empty
,
3313 isl_union_map_copy(S
),
3314 &dep_raw
, NULL
, NULL
, NULL
);
3315 isl_union_map_compute_flow(isl_union_map_copy(W
),
3316 isl_union_map_copy(W
),
3317 isl_union_map_copy(R
),
3318 isl_union_map_copy(S
),
3319 &dep_waw
, &dep_war
, NULL
, NULL
);
3321 dep
= isl_union_map_union(dep_waw
, dep_war
);
3322 dep
= isl_union_map_union(dep
, dep_raw
);
3323 validity
= isl_union_map_copy(dep
);
3324 coincidence
= isl_union_map_copy(dep
);
3325 proximity
= isl_union_map_copy(dep
);
3327 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
3328 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3329 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
3330 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3331 sched
= isl_schedule_constraints_compute_schedule(sc
);
3332 schedule
= isl_schedule_get_map(sched
);
3333 isl_schedule_free(sched
);
3334 isl_union_map_free(W
);
3335 isl_union_map_free(R
);
3336 isl_union_map_free(S
);
3339 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
3341 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
3342 is_complete
= isl_union_set_is_subset(D
, domain
);
3343 isl_union_set_free(D
);
3344 isl_union_set_free(domain
);
3346 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
3347 test
= isl_union_map_apply_range(test
, dep
);
3348 test
= isl_union_map_apply_range(test
, schedule
);
3350 delta
= isl_union_map_deltas(test
);
3351 if (isl_union_set_n_set(delta
) == 0) {
3355 isl_union_set_free(delta
);
3357 delta_set
= isl_set_from_union_set(delta
);
3359 slice
= isl_set_universe(isl_set_get_space(delta_set
));
3360 for (i
= 0; i
< tilable
; ++i
)
3361 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
3362 is_tilable
= isl_set_is_subset(delta_set
, slice
);
3363 isl_set_free(slice
);
3365 slice
= isl_set_universe(isl_set_get_space(delta_set
));
3366 for (i
= 0; i
< parallel
; ++i
)
3367 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
3368 is_parallel
= isl_set_is_subset(delta_set
, slice
);
3369 isl_set_free(slice
);
3371 origin
= isl_set_universe(isl_set_get_space(delta_set
));
3372 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
3373 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
3375 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
3376 delta_set
= isl_set_lexmin(delta_set
);
3378 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
3380 isl_set_free(origin
);
3381 isl_set_free(delta_set
);
3384 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
3385 is_injection
< 0 || is_complete
< 0)
3388 isl_die(ctx
, isl_error_unknown
,
3389 "generated schedule incomplete", return -1);
3391 isl_die(ctx
, isl_error_unknown
,
3392 "generated schedule not injective on each statement",
3395 isl_die(ctx
, isl_error_unknown
,
3396 "negative dependences in generated schedule",
3399 isl_die(ctx
, isl_error_unknown
,
3400 "generated schedule not as tilable as expected",
3403 isl_die(ctx
, isl_error_unknown
,
3404 "generated schedule not as parallel as expected",
3410 /* Compute a schedule for the given instance set, validity constraints,
3411 * proximity constraints and context and return a corresponding union map
3414 static __isl_give isl_union_map
*compute_schedule_with_context(isl_ctx
*ctx
,
3415 const char *domain
, const char *validity
, const char *proximity
,
3416 const char *context
)
3421 isl_union_map
*prox
;
3422 isl_schedule_constraints
*sc
;
3423 isl_schedule
*schedule
;
3424 isl_union_map
*sched
;
3426 con
= isl_set_read_from_str(ctx
, context
);
3427 dom
= isl_union_set_read_from_str(ctx
, domain
);
3428 dep
= isl_union_map_read_from_str(ctx
, validity
);
3429 prox
= isl_union_map_read_from_str(ctx
, proximity
);
3430 sc
= isl_schedule_constraints_on_domain(dom
);
3431 sc
= isl_schedule_constraints_set_context(sc
, con
);
3432 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
3433 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
3434 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3435 sched
= isl_schedule_get_map(schedule
);
3436 isl_schedule_free(schedule
);
3441 /* Compute a schedule for the given instance set, validity constraints and
3442 * proximity constraints and return a corresponding union map representation.
3444 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
3445 const char *domain
, const char *validity
, const char *proximity
)
3447 return compute_schedule_with_context(ctx
, domain
, validity
, proximity
,
3451 /* Check that a schedule can be constructed on the given domain
3452 * with the given validity and proximity constraints.
3454 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
3455 const char *validity
, const char *proximity
)
3457 isl_union_map
*sched
;
3459 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
3463 isl_union_map_free(sched
);
3467 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
3468 const char *validity
, const char *proximity
, const char *expected_sched
)
3470 isl_union_map
*sched1
, *sched2
;
3473 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
3474 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
3476 equal
= isl_union_map_is_equal(sched1
, sched2
);
3477 isl_union_map_free(sched1
);
3478 isl_union_map_free(sched2
);
3483 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
3489 /* Check that the schedule map is properly padded, even after being
3490 * reconstructed from the band forest.
3492 static int test_padded_schedule(isl_ctx
*ctx
)
3496 isl_union_map
*validity
, *proximity
;
3497 isl_schedule_constraints
*sc
;
3498 isl_schedule
*sched
;
3499 isl_union_map
*map1
, *map2
;
3500 isl_band_list
*list
;
3503 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
3504 D
= isl_union_set_read_from_str(ctx
, str
);
3505 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
3506 proximity
= isl_union_map_copy(validity
);
3507 sc
= isl_schedule_constraints_on_domain(D
);
3508 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3509 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3510 sched
= isl_schedule_constraints_compute_schedule(sc
);
3511 map1
= isl_schedule_get_map(sched
);
3512 list
= isl_schedule_get_band_forest(sched
);
3513 isl_band_list_free(list
);
3514 map2
= isl_schedule_get_map(sched
);
3515 isl_schedule_free(sched
);
3516 equal
= isl_union_map_is_equal(map1
, map2
);
3517 isl_union_map_free(map1
);
3518 isl_union_map_free(map2
);
3523 isl_die(ctx
, isl_error_unknown
,
3524 "reconstructed schedule map not the same as original",
3530 /* Check that conditional validity constraints are also taken into
3531 * account across bands.
3532 * In particular, try to make sure that live ranges D[1,0]->C[2,1] and
3533 * D[2,0]->C[3,0] are not local in the outer band of the generated schedule
3534 * and then check that the adjacent order constraint C[2,1]->D[2,0]
3535 * is enforced by the rest of the schedule.
3537 static int test_special_conditional_schedule_constraints(isl_ctx
*ctx
)
3540 isl_union_set
*domain
;
3541 isl_union_map
*validity
, *proximity
, *condition
;
3542 isl_union_map
*sink
, *source
, *dep
;
3543 isl_schedule_constraints
*sc
;
3544 isl_schedule
*schedule
;
3545 isl_union_access_info
*access
;
3546 isl_union_flow
*flow
;
3549 str
= "[n] -> { C[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3550 "A[k] : k >= 1 and k <= -1 + n; "
3551 "B[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3552 "D[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k }";
3553 domain
= isl_union_set_read_from_str(ctx
, str
);
3554 sc
= isl_schedule_constraints_on_domain(domain
);
3555 str
= "[n] -> { D[k, i] -> C[1 + k, k - i] : "
3556 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3557 "D[k, i] -> C[1 + k, i] : "
3558 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3559 "D[k, 0] -> C[1 + k, k] : k >= 1 and k <= -2 + n; "
3560 "D[k, 0] -> C[1 + k, 0] : k >= 1 and k <= -2 + n }";
3561 validity
= isl_union_map_read_from_str(ctx
, str
);
3562 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3563 str
= "[n] -> { C[k, i] -> D[k, i] : "
3564 "0 <= i <= -1 + k and k <= -1 + n }";
3565 proximity
= isl_union_map_read_from_str(ctx
, str
);
3566 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3567 str
= "[n] -> { [D[k, i] -> a[]] -> [C[1 + k, k - i] -> b[]] : "
3568 "i <= -1 + k and i >= 1 and k <= -2 + n; "
3569 "[B[k, i] -> c[]] -> [B[k, 1 + i] -> c[]] : "
3570 "k <= -1 + n and i >= 0 and i <= -2 + k }";
3571 condition
= isl_union_map_read_from_str(ctx
, str
);
3572 str
= "[n] -> { [B[k, i] -> e[]] -> [D[k, i] -> a[]] : "
3573 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3574 "[C[k, i] -> b[]] -> [D[k', -1 + k - i] -> a[]] : "
3575 "i >= 0 and i <= -1 + k and k <= -1 + n and "
3576 "k' <= -1 + n and k' >= k - i and k' >= 1 + k; "
3577 "[C[k, i] -> b[]] -> [D[k, -1 + k - i] -> a[]] : "
3578 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3579 "[B[k, i] -> c[]] -> [A[k'] -> d[]] : "
3580 "k <= -1 + n and i >= 0 and i <= -1 + k and "
3581 "k' >= 1 and k' <= -1 + n and k' >= 1 + k }";
3582 validity
= isl_union_map_read_from_str(ctx
, str
);
3583 sc
= isl_schedule_constraints_set_conditional_validity(sc
, condition
,
3585 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3586 str
= "{ D[2,0] -> [] }";
3587 sink
= isl_union_map_read_from_str(ctx
, str
);
3588 access
= isl_union_access_info_from_sink(sink
);
3589 str
= "{ C[2,1] -> [] }";
3590 source
= isl_union_map_read_from_str(ctx
, str
);
3591 access
= isl_union_access_info_set_must_source(access
, source
);
3592 access
= isl_union_access_info_set_schedule(access
, schedule
);
3593 flow
= isl_union_access_info_compute_flow(access
);
3594 dep
= isl_union_flow_get_must_dependence(flow
);
3595 isl_union_flow_free(flow
);
3596 empty
= isl_union_map_is_empty(dep
);
3597 isl_union_map_free(dep
);
3602 isl_die(ctx
, isl_error_unknown
,
3603 "conditional validity not respected", return -1);
3608 /* Input for testing of schedule construction based on
3609 * conditional constraints.
3611 * domain is the iteration domain
3612 * flow are the flow dependences, which determine the validity and
3613 * proximity constraints
3614 * condition are the conditions on the conditional validity constraints
3615 * conditional_validity are the conditional validity constraints
3616 * outer_band_n is the expected number of members in the outer band
3621 const char *condition
;
3622 const char *conditional_validity
;
3624 } live_range_tests
[] = {
3625 /* Contrived example that illustrates that we need to keep
3626 * track of tagged condition dependences and
3627 * tagged conditional validity dependences
3628 * in isl_sched_edge separately.
3629 * In particular, the conditional validity constraints on A
3630 * cannot be satisfied,
3631 * but they can be ignored because there are no corresponding
3632 * condition constraints. However, we do have an additional
3633 * conditional validity constraint that maps to the same
3634 * dependence relation
3635 * as the condition constraint on B. If we did not make a distinction
3636 * between tagged condition and tagged conditional validity
3637 * dependences, then we
3638 * could end up treating this shared dependence as an condition
3639 * constraint on A, forcing a localization of the conditions,
3640 * which is impossible.
3642 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
3643 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
3644 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
3645 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3646 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3647 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
3650 /* TACO 2013 Fig. 7 */
3651 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3652 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3653 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3654 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
3655 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
3656 "0 <= i < n and 0 <= j < n - 1 }",
3657 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
3658 "0 <= i < n and 0 <= j < j' < n;"
3659 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
3660 "0 <= i < i' < n and 0 <= j,j' < n;"
3661 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
3662 "0 <= i,j,j' < n and j < j' }",
3665 /* TACO 2013 Fig. 7, without tags */
3666 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3667 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3668 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3669 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3670 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3671 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
3672 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
3673 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
3676 /* TACO 2013 Fig. 12 */
3677 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
3678 "S3[i,3] : 0 <= i <= 1 }",
3679 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
3680 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
3681 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
3682 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
3683 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3684 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
3685 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3686 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
3687 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
3688 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
3689 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
3694 /* Test schedule construction based on conditional constraints.
3695 * In particular, check the number of members in the outer band node
3696 * as an indication of whether tiling is possible or not.
3698 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
3701 isl_union_set
*domain
;
3702 isl_union_map
*condition
;
3703 isl_union_map
*flow
;
3704 isl_union_map
*validity
;
3705 isl_schedule_constraints
*sc
;
3706 isl_schedule
*schedule
;
3707 isl_schedule_node
*node
;
3710 if (test_special_conditional_schedule_constraints(ctx
) < 0)
3713 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
3714 domain
= isl_union_set_read_from_str(ctx
,
3715 live_range_tests
[i
].domain
);
3716 flow
= isl_union_map_read_from_str(ctx
,
3717 live_range_tests
[i
].flow
);
3718 condition
= isl_union_map_read_from_str(ctx
,
3719 live_range_tests
[i
].condition
);
3720 validity
= isl_union_map_read_from_str(ctx
,
3721 live_range_tests
[i
].conditional_validity
);
3722 sc
= isl_schedule_constraints_on_domain(domain
);
3723 sc
= isl_schedule_constraints_set_validity(sc
,
3724 isl_union_map_copy(flow
));
3725 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
3726 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
3727 condition
, validity
);
3728 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3729 node
= isl_schedule_get_root(schedule
);
3731 isl_schedule_node_get_type(node
) != isl_schedule_node_band
)
3732 node
= isl_schedule_node_first_child(node
);
3733 n_member
= isl_schedule_node_band_n_member(node
);
3734 isl_schedule_node_free(node
);
3735 isl_schedule_free(schedule
);
3739 if (n_member
!= live_range_tests
[i
].outer_band_n
)
3740 isl_die(ctx
, isl_error_unknown
,
3741 "unexpected number of members in outer band",
3747 /* Check that the schedule computed for the given instance set and
3748 * dependence relation strongly satisfies the dependences.
3749 * In particular, check that no instance is scheduled before
3750 * or together with an instance on which it depends.
3751 * Earlier versions of isl would produce a schedule that
3752 * only weakly satisfies the dependences.
3754 static int test_strongly_satisfying_schedule(isl_ctx
*ctx
)
3756 const char *domain
, *dep
;
3757 isl_union_map
*D
, *schedule
;
3761 domain
= "{ B[i0, i1] : 0 <= i0 <= 1 and 0 <= i1 <= 11; "
3762 "A[i0] : 0 <= i0 <= 1 }";
3763 dep
= "{ B[i0, i1] -> B[i0, 1 + i1] : 0 <= i0 <= 1 and 0 <= i1 <= 10; "
3764 "B[0, 11] -> A[1]; A[i0] -> B[i0, 0] : 0 <= i0 <= 1 }";
3765 schedule
= compute_schedule(ctx
, domain
, dep
, dep
);
3766 D
= isl_union_map_read_from_str(ctx
, dep
);
3767 D
= isl_union_map_apply_domain(D
, isl_union_map_copy(schedule
));
3768 D
= isl_union_map_apply_range(D
, schedule
);
3769 map
= isl_map_from_union_map(D
);
3770 ge
= isl_map_lex_ge(isl_space_domain(isl_map_get_space(map
)));
3771 map
= isl_map_intersect(map
, ge
);
3772 empty
= isl_map_is_empty(map
);
3778 isl_die(ctx
, isl_error_unknown
,
3779 "dependences not strongly satisfied", return -1);
3784 /* Compute a schedule for input where the instance set constraints
3785 * conflict with the context constraints.
3786 * Earlier versions of isl did not properly handle this situation.
3788 static int test_conflicting_context_schedule(isl_ctx
*ctx
)
3790 isl_union_map
*schedule
;
3791 const char *domain
, *context
;
3793 domain
= "[n] -> { A[] : n >= 0 }";
3794 context
= "[n] -> { : n < 0 }";
3795 schedule
= compute_schedule_with_context(ctx
,
3796 domain
, "{}", "{}", context
);
3797 isl_union_map_free(schedule
);
3805 /* Check that the dependence carrying step is not confused by
3806 * a bound on the coefficient size.
3807 * In particular, force the scheduler to move to a dependence carrying
3808 * step by demanding outer coincidence and bound the size of
3809 * the coefficients. Earlier versions of isl would take this
3810 * bound into account while carrying dependences, breaking
3811 * fundamental assumptions.
3812 * On the other hand, the dependence carrying step now tries
3813 * to prevent loop coalescing by default, so check that indeed
3814 * no loop coalescing occurs by comparing the computed schedule
3815 * to the expected non-coalescing schedule.
3817 static int test_bounded_coefficients_schedule(isl_ctx
*ctx
)
3819 const char *domain
, *dep
;
3822 isl_schedule_constraints
*sc
;
3823 isl_schedule
*schedule
;
3824 isl_union_map
*sched1
, *sched2
;
3827 domain
= "{ C[i0, i1] : 2 <= i0 <= 3999 and 0 <= i1 <= -1 + i0 }";
3828 dep
= "{ C[i0, i1] -> C[i0, 1 + i1] : i0 <= 3999 and i1 >= 0 and "
3830 "C[i0, -1 + i0] -> C[1 + i0, 0] : i0 <= 3998 and i0 >= 1 }";
3831 I
= isl_union_set_read_from_str(ctx
, domain
);
3832 D
= isl_union_map_read_from_str(ctx
, dep
);
3833 sc
= isl_schedule_constraints_on_domain(I
);
3834 sc
= isl_schedule_constraints_set_validity(sc
, isl_union_map_copy(D
));
3835 sc
= isl_schedule_constraints_set_coincidence(sc
, D
);
3836 isl_options_set_schedule_outer_coincidence(ctx
, 1);
3837 isl_options_set_schedule_max_coefficient(ctx
, 20);
3838 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3839 isl_options_set_schedule_max_coefficient(ctx
, -1);
3840 isl_options_set_schedule_outer_coincidence(ctx
, 0);
3841 sched1
= isl_schedule_get_map(schedule
);
3842 isl_schedule_free(schedule
);
3844 sched2
= isl_union_map_read_from_str(ctx
, "{ C[x,y] -> [x,y] }");
3845 equal
= isl_union_map_is_equal(sched1
, sched2
);
3846 isl_union_map_free(sched1
);
3847 isl_union_map_free(sched2
);
3852 isl_die(ctx
, isl_error_unknown
,
3853 "unexpected schedule", return -1);
3858 /* Check that a set of schedule constraints that only allow for
3859 * a coalescing schedule still produces a schedule even if the user
3860 * request a non-coalescing schedule. Earlier versions of isl
3861 * would not handle this case correctly.
3863 static int test_coalescing_schedule(isl_ctx
*ctx
)
3865 const char *domain
, *dep
;
3868 isl_schedule_constraints
*sc
;
3869 isl_schedule
*schedule
;
3870 int treat_coalescing
;
3872 domain
= "{ S[a, b] : 0 <= a <= 1 and 0 <= b <= 1 }";
3873 dep
= "{ S[a, b] -> S[a + b, 1 - b] }";
3874 I
= isl_union_set_read_from_str(ctx
, domain
);
3875 D
= isl_union_map_read_from_str(ctx
, dep
);
3876 sc
= isl_schedule_constraints_on_domain(I
);
3877 sc
= isl_schedule_constraints_set_validity(sc
, D
);
3878 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
3879 isl_options_set_schedule_treat_coalescing(ctx
, 1);
3880 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3881 isl_options_set_schedule_treat_coalescing(ctx
, treat_coalescing
);
3882 isl_schedule_free(schedule
);
3888 int test_schedule(isl_ctx
*ctx
)
3890 const char *D
, *W
, *R
, *V
, *P
, *S
;
3891 int max_coincidence
;
3892 int treat_coalescing
;
3894 /* Handle resulting schedule with zero bands. */
3895 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
3899 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
3900 W
= "{ S1[t,i] -> a[t,i] }";
3901 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
3902 "S1[t,i] -> a[t-1,i+1] }";
3903 S
= "{ S1[t,i] -> [t,i] }";
3904 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3907 /* Fig. 5 of CC2008 */
3908 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
3910 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
3911 "j >= 2 and j <= -1 + N }";
3912 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
3913 "j >= 2 and j <= -1 + N; "
3914 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
3915 "j >= 2 and j <= -1 + N }";
3916 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3917 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3920 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
3921 W
= "{ S1[i] -> a[i] }";
3922 R
= "{ S2[i] -> a[i+1] }";
3923 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3924 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3927 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
3928 W
= "{ S1[i] -> a[i] }";
3929 R
= "{ S2[i] -> a[9-i] }";
3930 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3931 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3934 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
3935 W
= "{ S1[i] -> a[i] }";
3936 R
= "[N] -> { S2[i] -> a[N-1-i] }";
3937 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3938 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3941 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
3942 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
3943 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
3944 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
3945 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3948 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3949 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
3950 R
= "{ S2[i,j] -> a[i-1,j] }";
3951 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3952 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3955 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3956 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
3957 R
= "{ S2[i,j] -> a[i,j-1] }";
3958 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3959 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3962 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
3963 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
3964 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
3965 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
3966 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
3967 "S_0[] -> [0, 0, 0] }";
3968 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
3970 ctx
->opt
->schedule_parametric
= 0;
3971 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3973 ctx
->opt
->schedule_parametric
= 1;
3975 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
3976 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
3977 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
3978 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
3979 "S4[i] -> a[i,N] }";
3980 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
3981 "S4[i] -> [4,i,0] }";
3982 max_coincidence
= isl_options_get_schedule_maximize_coincidence(ctx
);
3983 isl_options_set_schedule_maximize_coincidence(ctx
, 0);
3984 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3986 isl_options_set_schedule_maximize_coincidence(ctx
, max_coincidence
);
3988 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
3989 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3991 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3993 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
3995 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3996 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3999 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
4000 " S_2[t] : t >= 0 and t <= -1 + N; "
4001 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
4003 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
4004 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
4005 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
4006 "i >= 0 and i <= -1 + N }";
4007 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
4008 "i >= 0 and i <= -1 + N; "
4009 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
4010 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
4011 " S_0[t] -> [0, t, 0] }";
4013 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
4015 ctx
->opt
->schedule_parametric
= 0;
4016 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4018 ctx
->opt
->schedule_parametric
= 1;
4020 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
4021 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
4022 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
4025 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
4026 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
4027 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
4028 "j >= 0 and j <= -1 + N; "
4029 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
4030 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
4031 "j >= 0 and j <= -1 + N; "
4032 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
4033 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
4034 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4037 D
= "{ S_0[i] : i >= 0 }";
4038 W
= "{ S_0[i] -> a[i] : i >= 0 }";
4039 R
= "{ S_0[i] -> a[0] : i >= 0 }";
4040 S
= "{ S_0[i] -> [0, i, 0] }";
4041 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4044 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
4045 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
4046 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
4047 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
4048 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4051 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
4052 "k <= -1 + n and k >= 0 }";
4053 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
4054 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
4055 "k <= -1 + n and k >= 0; "
4056 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
4057 "k <= -1 + n and k >= 0; "
4058 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
4059 "k <= -1 + n and k >= 0 }";
4060 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
4061 ctx
->opt
->schedule_outer_coincidence
= 1;
4062 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4064 ctx
->opt
->schedule_outer_coincidence
= 0;
4066 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
4067 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
4068 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
4069 "Stmt_for_body24[i0, i1, 1, 0]:"
4070 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
4071 "Stmt_for_body7[i0, i1, i2]:"
4072 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
4075 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
4076 "Stmt_for_body24[1, i1, i2, i3]:"
4077 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
4079 "Stmt_for_body24[0, i1, i2, i3] -> "
4080 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
4081 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
4083 "Stmt_for_body24[0, i1, i2, i3] ->"
4084 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
4085 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
4086 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
4087 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
4088 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
4089 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
4090 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
4091 "i1 <= 6 and i1 >= 0;"
4092 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
4093 "Stmt_for_body7[i0, i1, i2] -> "
4094 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
4095 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
4096 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
4097 "Stmt_for_body7[i0, i1, i2] -> "
4098 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
4099 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
4100 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
4102 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
4103 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
4104 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
4106 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4107 isl_options_set_schedule_treat_coalescing(ctx
, 0);
4108 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4110 isl_options_set_schedule_treat_coalescing(ctx
, treat_coalescing
);
4112 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
4113 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
4114 "j >= 1 and j <= 7;"
4115 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
4116 "j >= 1 and j <= 8 }";
4118 S
= "{ S_0[i, j] -> [i + j, j] }";
4119 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4120 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4122 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4124 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
4125 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
4126 "j >= 0 and j <= -1 + i }";
4127 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
4128 "i <= -1 + N and j >= 0;"
4129 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
4132 S
= "{ S_0[i, j] -> [i, j] }";
4133 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4134 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4136 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4138 /* Test both algorithms on a case with only proximity dependences. */
4139 D
= "{ S[i,j] : 0 <= i <= 10 }";
4141 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
4142 S
= "{ S[i, j] -> [j, i] }";
4143 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4144 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4146 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4147 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4150 D
= "{ A[a]; B[] }";
4152 P
= "{ A[a] -> B[] }";
4153 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4156 if (test_padded_schedule(ctx
) < 0)
4159 /* Check that check for progress is not confused by rational
4162 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
4163 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
4165 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
4166 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
4168 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4169 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4171 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4173 /* Check that we allow schedule rows that are only non-trivial
4174 * on some full-dimensional domains.
4176 D
= "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
4177 V
= "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
4178 "S1[j] -> S2[1] : 0 <= j <= 1 }";
4180 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4181 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4183 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4185 if (test_conditional_schedule_constraints(ctx
) < 0)
4188 if (test_strongly_satisfying_schedule(ctx
) < 0)
4191 if (test_conflicting_context_schedule(ctx
) < 0)
4194 if (test_bounded_coefficients_schedule(ctx
) < 0)
4196 if (test_coalescing_schedule(ctx
) < 0)
4202 /* Perform scheduling tests using the whole component scheduler.
4204 static int test_schedule_whole(isl_ctx
*ctx
)
4209 whole
= isl_options_get_schedule_whole_component(ctx
);
4210 isl_options_set_schedule_whole_component(ctx
, 1);
4211 r
= test_schedule(ctx
);
4212 isl_options_set_schedule_whole_component(ctx
, whole
);
4217 /* Perform scheduling tests using the incremental scheduler.
4219 static int test_schedule_incremental(isl_ctx
*ctx
)
4224 whole
= isl_options_get_schedule_whole_component(ctx
);
4225 isl_options_set_schedule_whole_component(ctx
, 0);
4226 r
= test_schedule(ctx
);
4227 isl_options_set_schedule_whole_component(ctx
, whole
);
4232 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
4234 isl_union_map
*umap
;
4237 umap
= isl_union_map_read_from_str(ctx
, str
);
4238 test
= isl_union_map_plain_is_injective(umap
);
4239 isl_union_map_free(umap
);
4242 if (test
== injective
)
4245 isl_die(ctx
, isl_error_unknown
,
4246 "map not detected as injective", return -1);
4248 isl_die(ctx
, isl_error_unknown
,
4249 "map detected as injective", return -1);
4252 int test_injective(isl_ctx
*ctx
)
4256 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
4258 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
4260 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
4262 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
4264 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
4266 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
4268 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
4270 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
4273 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
4274 if (test_plain_injective(ctx
, str
, 1))
4276 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
4277 if (test_plain_injective(ctx
, str
, 0))
4283 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
4291 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
4292 equal
= isl_aff_plain_is_equal(aff
, aff2
);
4298 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
4302 equal
= aff_plain_is_equal(aff
, str
);
4306 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
4307 "result not as expected", return -1);
4312 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
4313 __isl_take isl_aff
*aff2
);
4315 ['+'] = { &isl_aff_add
},
4316 ['-'] = { &isl_aff_sub
},
4317 ['*'] = { &isl_aff_mul
},
4318 ['/'] = { &isl_aff_div
},
4326 } aff_bin_tests
[] = {
4327 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
4328 "{ [i] -> [2i] }" },
4329 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
4331 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
4332 "{ [i] -> [2i] }" },
4333 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
4334 "{ [i] -> [2i] }" },
4335 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
4336 "{ [i] -> [i/2] }" },
4337 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
4339 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
4340 "{ [i] -> [NaN] }" },
4341 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
4342 "{ [i] -> [NaN] }" },
4343 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
4344 "{ [i] -> [NaN] }" },
4345 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
4346 "{ [i] -> [NaN] }" },
4347 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
4348 "{ [i] -> [NaN] }" },
4349 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
4350 "{ [i] -> [NaN] }" },
4351 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
4352 "{ [i] -> [NaN] }" },
4353 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
4354 "{ [i] -> [NaN] }" },
4355 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
4356 "{ [i] -> [NaN] }" },
4357 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
4358 "{ [i] -> [NaN] }" },
4359 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
4360 "{ [i] -> [NaN] }" },
4361 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
4362 "{ [i] -> [NaN] }" },
4365 /* Perform some basic tests of binary operations on isl_aff objects.
4367 static int test_bin_aff(isl_ctx
*ctx
)
4370 isl_aff
*aff1
, *aff2
, *res
;
4371 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
4372 __isl_take isl_aff
*aff2
);
4375 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
4376 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
4377 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
4378 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
4379 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
4380 aff1
= fn(aff1
, aff2
);
4381 if (isl_aff_is_nan(res
))
4382 ok
= isl_aff_is_nan(aff1
);
4384 ok
= isl_aff_plain_is_equal(aff1
, res
);
4390 isl_die(ctx
, isl_error_unknown
,
4391 "unexpected result", return -1);
4398 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4399 __isl_take isl_union_pw_multi_aff
*upma1
,
4400 __isl_take isl_union_pw_multi_aff
*upma2
);
4404 } upma_bin_tests
[] = {
4405 { &isl_union_pw_multi_aff_add
, "{ A[] -> [0]; B[0] -> [1] }",
4406 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
4407 { &isl_union_pw_multi_aff_union_add
, "{ A[] -> [0]; B[0] -> [1] }",
4408 "{ B[x] -> [2] : x >= 0 }",
4409 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
4410 { &isl_union_pw_multi_aff_pullback_union_pw_multi_aff
,
4411 "{ A[] -> B[0]; C[x] -> B[1] : x < 10; C[y] -> B[2] : y >= 10 }",
4412 "{ D[i] -> A[] : i < 0; D[i] -> C[i + 5] : i >= 0 }",
4413 "{ D[i] -> B[0] : i < 0; D[i] -> B[1] : 0 <= i < 5; "
4414 "D[i] -> B[2] : i >= 5 }" },
4415 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4416 "{ B[x] -> C[2] : x > 0 }",
4417 "{ B[x] -> A[1] : x <= 0; B[x] -> C[2] : x > 0 }" },
4418 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4419 "{ B[x] -> A[2] : x >= 0 }",
4420 "{ B[x] -> A[1] : x < 0; B[x] -> A[2] : x > 0; B[0] -> A[3] }" },
4423 /* Perform some basic tests of binary operations on
4424 * isl_union_pw_multi_aff objects.
4426 static int test_bin_upma(isl_ctx
*ctx
)
4429 isl_union_pw_multi_aff
*upma1
, *upma2
, *res
;
4432 for (i
= 0; i
< ARRAY_SIZE(upma_bin_tests
); ++i
) {
4433 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4434 upma_bin_tests
[i
].arg1
);
4435 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4436 upma_bin_tests
[i
].arg2
);
4437 res
= isl_union_pw_multi_aff_read_from_str(ctx
,
4438 upma_bin_tests
[i
].res
);
4439 upma1
= upma_bin_tests
[i
].fn(upma1
, upma2
);
4440 ok
= isl_union_pw_multi_aff_plain_is_equal(upma1
, res
);
4441 isl_union_pw_multi_aff_free(upma1
);
4442 isl_union_pw_multi_aff_free(res
);
4446 isl_die(ctx
, isl_error_unknown
,
4447 "unexpected result", return -1);
4454 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4455 __isl_take isl_union_pw_multi_aff
*upma1
,
4456 __isl_take isl_union_pw_multi_aff
*upma2
);
4459 } upma_bin_fail_tests
[] = {
4460 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4461 "{ B[x] -> C[2] : x >= 0 }" },
4464 /* Perform some basic tests of binary operations on
4465 * isl_union_pw_multi_aff objects that are expected to fail.
4467 static int test_bin_upma_fail(isl_ctx
*ctx
)
4470 isl_union_pw_multi_aff
*upma1
, *upma2
;
4473 on_error
= isl_options_get_on_error(ctx
);
4474 isl_options_set_on_error(ctx
, ISL_ON_ERROR_CONTINUE
);
4475 n
= ARRAY_SIZE(upma_bin_fail_tests
);
4476 for (i
= 0; i
< n
; ++i
) {
4477 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4478 upma_bin_fail_tests
[i
].arg1
);
4479 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4480 upma_bin_fail_tests
[i
].arg2
);
4481 upma1
= upma_bin_fail_tests
[i
].fn(upma1
, upma2
);
4482 isl_union_pw_multi_aff_free(upma1
);
4486 isl_options_set_on_error(ctx
, on_error
);
4488 isl_die(ctx
, isl_error_unknown
,
4489 "operation not expected to succeed", return -1);
4494 int test_aff(isl_ctx
*ctx
)
4499 isl_local_space
*ls
;
4503 if (test_bin_aff(ctx
) < 0)
4505 if (test_bin_upma(ctx
) < 0)
4507 if (test_bin_upma_fail(ctx
) < 0)
4510 space
= isl_space_set_alloc(ctx
, 0, 1);
4511 ls
= isl_local_space_from_space(space
);
4512 aff
= isl_aff_zero_on_domain(ls
);
4514 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4515 aff
= isl_aff_scale_down_ui(aff
, 3);
4516 aff
= isl_aff_floor(aff
);
4517 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4518 aff
= isl_aff_scale_down_ui(aff
, 2);
4519 aff
= isl_aff_floor(aff
);
4520 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4523 set
= isl_set_read_from_str(ctx
, str
);
4524 aff
= isl_aff_gist(aff
, set
);
4526 aff
= isl_aff_add_constant_si(aff
, -16);
4527 zero
= isl_aff_plain_is_zero(aff
);
4533 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4535 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
4536 aff
= isl_aff_scale_down_ui(aff
, 64);
4537 aff
= isl_aff_floor(aff
);
4538 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
4546 int test_dim_max(isl_ctx
*ctx
)
4550 isl_set
*set1
, *set2
;
4555 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
4556 set
= isl_set_read_from_str(ctx
, str
);
4557 pwaff
= isl_set_dim_max(set
, 0);
4558 set1
= isl_set_from_pw_aff(pwaff
);
4559 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
4560 set2
= isl_set_read_from_str(ctx
, str
);
4561 equal
= isl_set_is_equal(set1
, set2
);
4567 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4569 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
4570 set
= isl_set_read_from_str(ctx
, str
);
4571 pwaff
= isl_set_dim_max(set
, 0);
4572 set1
= isl_set_from_pw_aff(pwaff
);
4573 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4574 set2
= isl_set_read_from_str(ctx
, str
);
4575 equal
= isl_set_is_equal(set1
, set2
);
4581 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4583 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
4584 set
= isl_set_read_from_str(ctx
, str
);
4585 pwaff
= isl_set_dim_max(set
, 0);
4586 set1
= isl_set_from_pw_aff(pwaff
);
4587 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4588 set2
= isl_set_read_from_str(ctx
, str
);
4589 equal
= isl_set_is_equal(set1
, set2
);
4595 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4597 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
4598 "0 <= i < N and 0 <= j < M }";
4599 map
= isl_map_read_from_str(ctx
, str
);
4600 set
= isl_map_range(map
);
4602 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
4603 set1
= isl_set_from_pw_aff(pwaff
);
4604 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
4605 set2
= isl_set_read_from_str(ctx
, str
);
4606 equal
= isl_set_is_equal(set1
, set2
);
4610 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
4611 set1
= isl_set_from_pw_aff(pwaff
);
4612 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
4613 set2
= isl_set_read_from_str(ctx
, str
);
4614 if (equal
>= 0 && equal
)
4615 equal
= isl_set_is_equal(set1
, set2
);
4624 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4626 /* Check that solutions are properly merged. */
4627 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
4628 "c <= -1 + n - 4a - 2b and c >= -2b and "
4629 "4a >= -4 + n and c >= 0 }";
4630 set
= isl_set_read_from_str(ctx
, str
);
4631 pwaff
= isl_set_dim_min(set
, 2);
4632 set1
= isl_set_from_pw_aff(pwaff
);
4633 str
= "[n] -> { [(0)] : n >= 1 }";
4634 set2
= isl_set_read_from_str(ctx
, str
);
4635 equal
= isl_set_is_equal(set1
, set2
);
4642 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4644 /* Check that empty solution lie in the right space. */
4645 str
= "[n] -> { [t,a] : 1 = 0 }";
4646 set
= isl_set_read_from_str(ctx
, str
);
4647 pwaff
= isl_set_dim_max(set
, 0);
4648 set1
= isl_set_from_pw_aff(pwaff
);
4649 str
= "[n] -> { [t] : 1 = 0 }";
4650 set2
= isl_set_read_from_str(ctx
, str
);
4651 equal
= isl_set_is_equal(set1
, set2
);
4658 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4663 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
4665 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
4669 isl_pw_multi_aff
*pma2
;
4675 ctx
= isl_pw_multi_aff_get_ctx(pma
);
4676 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4677 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
4678 isl_pw_multi_aff_free(pma2
);
4683 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
4684 * represented by "str".
4686 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
4691 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
4695 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
4696 "result not as expected", return -1);
4700 /* Basic test for isl_pw_multi_aff_product.
4702 * Check that multiple pieces are properly handled.
4704 static int test_product_pma(isl_ctx
*ctx
)
4708 isl_pw_multi_aff
*pma1
, *pma2
;
4710 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
4711 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4712 str
= "{ C[] -> D[] }";
4713 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4714 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
4715 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
4716 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
4717 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
4718 isl_pw_multi_aff_free(pma1
);
4725 int test_product(isl_ctx
*ctx
)
4729 isl_union_set
*uset1
, *uset2
;
4733 set
= isl_set_read_from_str(ctx
, str
);
4734 set
= isl_set_product(set
, isl_set_copy(set
));
4735 ok
= isl_set_is_wrapping(set
);
4740 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4743 uset1
= isl_union_set_read_from_str(ctx
, str
);
4744 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
4745 str
= "{ [[] -> []] }";
4746 uset2
= isl_union_set_read_from_str(ctx
, str
);
4747 ok
= isl_union_set_is_equal(uset1
, uset2
);
4748 isl_union_set_free(uset1
);
4749 isl_union_set_free(uset2
);
4753 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4755 if (test_product_pma(ctx
) < 0)
4761 /* Check that two sets are not considered disjoint just because
4762 * they have a different set of (named) parameters.
4764 static int test_disjoint(isl_ctx
*ctx
)
4767 isl_set
*set
, *set2
;
4770 str
= "[n] -> { [[]->[]] }";
4771 set
= isl_set_read_from_str(ctx
, str
);
4772 str
= "{ [[]->[]] }";
4773 set2
= isl_set_read_from_str(ctx
, str
);
4774 disjoint
= isl_set_is_disjoint(set
, set2
);
4780 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4785 int test_equal(isl_ctx
*ctx
)
4788 isl_set
*set
, *set2
;
4792 set
= isl_set_read_from_str(ctx
, str
);
4794 set2
= isl_set_read_from_str(ctx
, str
);
4795 equal
= isl_set_is_equal(set
, set2
);
4801 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4806 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
4807 enum isl_dim_type type
, unsigned pos
, int fixed
)
4811 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
4818 isl_die(ctx
, isl_error_unknown
,
4819 "map not detected as fixed", return -1);
4821 isl_die(ctx
, isl_error_unknown
,
4822 "map detected as fixed", return -1);
4825 int test_fixed(isl_ctx
*ctx
)
4830 str
= "{ [i] -> [i] }";
4831 map
= isl_map_read_from_str(ctx
, str
);
4832 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
4834 str
= "{ [i] -> [1] }";
4835 map
= isl_map_read_from_str(ctx
, str
);
4836 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4838 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
4839 map
= isl_map_read_from_str(ctx
, str
);
4840 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4842 map
= isl_map_read_from_str(ctx
, str
);
4843 map
= isl_map_neg(map
);
4844 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4850 struct isl_vertices_test_data
{
4853 const char *vertex
[2];
4854 } vertices_tests
[] = {
4855 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
4856 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
4857 { "{ A[t, i] : t = 14 and i = 1 }",
4858 1, { "{ A[14, 1] }" } },
4861 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
4863 static isl_stat
find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
4865 struct isl_vertices_test_data
*data
= user
;
4868 isl_basic_set
*bset
;
4869 isl_pw_multi_aff
*pma
;
4873 ctx
= isl_vertex_get_ctx(vertex
);
4874 bset
= isl_vertex_get_domain(vertex
);
4875 ma
= isl_vertex_get_expr(vertex
);
4876 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
4878 for (i
= 0; i
< data
->n
; ++i
) {
4879 isl_pw_multi_aff
*pma_i
;
4881 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
4882 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
4883 isl_pw_multi_aff_free(pma_i
);
4885 if (equal
< 0 || equal
)
4889 isl_pw_multi_aff_free(pma
);
4890 isl_vertex_free(vertex
);
4893 return isl_stat_error
;
4895 return equal
? isl_stat_ok
: isl_stat_error
;
4898 int test_vertices(isl_ctx
*ctx
)
4902 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
4903 isl_basic_set
*bset
;
4904 isl_vertices
*vertices
;
4908 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
4909 vertices
= isl_basic_set_compute_vertices(bset
);
4910 n
= isl_vertices_get_n_vertices(vertices
);
4911 if (vertices_tests
[i
].n
!= n
)
4913 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
4914 &vertices_tests
[i
]) < 0)
4916 isl_vertices_free(vertices
);
4917 isl_basic_set_free(bset
);
4922 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
4929 int test_union_pw(isl_ctx
*ctx
)
4933 isl_union_set
*uset
;
4934 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
4936 str
= "{ [x] -> x^2 }";
4937 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
4938 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
4939 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
4940 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
4941 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
4942 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
4943 isl_union_pw_qpolynomial_free(upwqp1
);
4944 isl_union_pw_qpolynomial_free(upwqp2
);
4948 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4953 /* Test that isl_union_pw_qpolynomial_eval picks up the function
4954 * defined over the correct domain space.
4956 static int test_eval(isl_ctx
*ctx
)
4961 isl_union_pw_qpolynomial
*upwqp
;
4965 str
= "{ A[x] -> x^2; B[x] -> -x^2 }";
4966 upwqp
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
4968 set
= isl_set_read_from_str(ctx
, str
);
4969 pnt
= isl_set_sample_point(set
);
4970 v
= isl_union_pw_qpolynomial_eval(upwqp
, pnt
);
4971 cmp
= isl_val_cmp_si(v
, 36);
4977 isl_die(ctx
, isl_error_unknown
, "unexpected value", return -1);
4982 /* Descriptions of sets that are tested for reparsing after printing.
4984 const char *output_tests
[] = {
4985 "{ [1, y] : 0 <= y <= 1; [x, -x] : 0 <= x <= 1 }",
4988 /* Check that printing a set and reparsing a set from the printed output
4989 * results in the same set.
4991 static int test_output_set(isl_ctx
*ctx
)
4995 isl_set
*set1
, *set2
;
4998 for (i
= 0; i
< ARRAY_SIZE(output_tests
); ++i
) {
4999 set1
= isl_set_read_from_str(ctx
, output_tests
[i
]);
5000 str
= isl_set_to_str(set1
);
5001 set2
= isl_set_read_from_str(ctx
, str
);
5003 equal
= isl_set_is_equal(set1
, set2
);
5009 isl_die(ctx
, isl_error_unknown
,
5010 "parsed output not the same", return -1);
5016 int test_output(isl_ctx
*ctx
)
5024 if (test_output_set(ctx
) < 0)
5027 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
5028 pa
= isl_pw_aff_read_from_str(ctx
, str
);
5030 p
= isl_printer_to_str(ctx
);
5031 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
5032 p
= isl_printer_print_pw_aff(p
, pa
);
5033 s
= isl_printer_get_str(p
);
5034 isl_printer_free(p
);
5035 isl_pw_aff_free(pa
);
5039 equal
= !strcmp(s
, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
5044 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5049 int test_sample(isl_ctx
*ctx
)
5052 isl_basic_set
*bset1
, *bset2
;
5055 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
5056 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
5057 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
5058 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
5059 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
5060 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
5061 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
5062 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
5063 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
5064 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
5065 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
5066 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
5067 "d - 1073741821e and "
5068 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
5069 "3j >= 1 - a + b + 2e and "
5070 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
5071 "3i <= 4 - a + 4b - e and "
5072 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
5073 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
5074 "c <= -1 + a and 3i >= -2 - a + 3e and "
5075 "1073741822e <= 1073741823 - a + 1073741822b + c and "
5076 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
5077 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
5078 "1073741823e >= 1 + 1073741823b - d and "
5079 "3i >= 1073741823b + c - 1073741823e - f and "
5080 "3i >= 1 + 2b + e + 3g }";
5081 bset1
= isl_basic_set_read_from_str(ctx
, str
);
5082 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
5083 empty
= isl_basic_set_is_empty(bset2
);
5084 subset
= isl_basic_set_is_subset(bset2
, bset1
);
5085 isl_basic_set_free(bset1
);
5086 isl_basic_set_free(bset2
);
5087 if (empty
< 0 || subset
< 0)
5090 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
5092 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
5097 int test_fixed_power(isl_ctx
*ctx
)
5105 str
= "{ [i] -> [i + 1] }";
5106 map
= isl_map_read_from_str(ctx
, str
);
5107 isl_int_set_si(exp
, 23);
5108 map
= isl_map_fixed_power(map
, exp
);
5109 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
5118 int test_slice(isl_ctx
*ctx
)
5124 str
= "{ [i] -> [j] }";
5125 map
= isl_map_read_from_str(ctx
, str
);
5126 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5127 equal
= map_check_equal(map
, "{ [i] -> [i] }");
5132 str
= "{ [i] -> [j] }";
5133 map
= isl_map_read_from_str(ctx
, str
);
5134 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5135 equal
= map_check_equal(map
, "{ [i] -> [j] }");
5140 str
= "{ [i] -> [j] }";
5141 map
= isl_map_read_from_str(ctx
, str
);
5142 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5143 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
5148 str
= "{ [i] -> [j] }";
5149 map
= isl_map_read_from_str(ctx
, str
);
5150 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5151 equal
= map_check_equal(map
, "{ [0] -> [j] }");
5156 str
= "{ [i] -> [j] }";
5157 map
= isl_map_read_from_str(ctx
, str
);
5158 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5159 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
5164 str
= "{ [i] -> [j] }";
5165 map
= isl_map_read_from_str(ctx
, str
);
5166 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5167 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
5175 int test_eliminate(isl_ctx
*ctx
)
5181 str
= "{ [i] -> [j] : i = 2j }";
5182 map
= isl_map_read_from_str(ctx
, str
);
5183 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
5184 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
5192 /* Check that isl_set_dim_residue_class detects that the values of j
5193 * in the set below are all odd and that it does not detect any spurious
5196 static int test_residue_class(isl_ctx
*ctx
)
5203 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
5204 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
5205 set
= isl_set_read_from_str(ctx
, str
);
5208 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
5210 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
5211 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
5220 int test_align_parameters(isl_ctx
*ctx
)
5224 isl_multi_aff
*ma1
, *ma2
;
5227 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
5228 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
5230 space
= isl_space_params_alloc(ctx
, 1);
5231 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
5232 ma1
= isl_multi_aff_align_params(ma1
, space
);
5234 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
5235 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
5237 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
5239 isl_multi_aff_free(ma1
);
5240 isl_multi_aff_free(ma2
);
5245 isl_die(ctx
, isl_error_unknown
,
5246 "result not as expected", return -1);
5251 static int test_list(isl_ctx
*ctx
)
5253 isl_id
*a
, *b
, *c
, *d
, *id
;
5257 a
= isl_id_alloc(ctx
, "a", NULL
);
5258 b
= isl_id_alloc(ctx
, "b", NULL
);
5259 c
= isl_id_alloc(ctx
, "c", NULL
);
5260 d
= isl_id_alloc(ctx
, "d", NULL
);
5262 list
= isl_id_list_alloc(ctx
, 4);
5263 list
= isl_id_list_add(list
, a
);
5264 list
= isl_id_list_add(list
, b
);
5265 list
= isl_id_list_add(list
, c
);
5266 list
= isl_id_list_add(list
, d
);
5267 list
= isl_id_list_drop(list
, 1, 1);
5269 if (isl_id_list_n_id(list
) != 3) {
5270 isl_id_list_free(list
);
5271 isl_die(ctx
, isl_error_unknown
,
5272 "unexpected number of elements in list", return -1);
5275 id
= isl_id_list_get_id(list
, 0);
5278 id
= isl_id_list_get_id(list
, 1);
5281 id
= isl_id_list_get_id(list
, 2);
5285 isl_id_list_free(list
);
5288 isl_die(ctx
, isl_error_unknown
,
5289 "unexpected elements in list", return -1);
5294 const char *set_conversion_tests
[] = {
5295 "[N] -> { [i] : N - 1 <= 2 i <= N }",
5296 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
5297 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
5298 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
5299 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
5300 "[a, b] -> { [c, d] : (4*floor((-a + c)/4) = -a + c and "
5301 "32*floor((-b + d)/32) = -b + d and 5 <= c <= 8 and "
5302 "-3 + c <= d <= 28 + c) }",
5305 /* Check that converting from isl_set to isl_pw_multi_aff and back
5306 * to isl_set produces the original isl_set.
5308 static int test_set_conversion(isl_ctx
*ctx
)
5312 isl_set
*set1
, *set2
;
5313 isl_pw_multi_aff
*pma
;
5316 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
5317 str
= set_conversion_tests
[i
];
5318 set1
= isl_set_read_from_str(ctx
, str
);
5319 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
5320 set2
= isl_set_from_pw_multi_aff(pma
);
5321 equal
= isl_set_is_equal(set1
, set2
);
5328 isl_die(ctx
, isl_error_unknown
, "bad conversion",
5335 const char *conversion_tests
[] = {
5336 "{ [a, b, c, d] -> s0[a, b, e, f] : "
5337 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
5338 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
5339 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
5341 "{ [a, b] -> [c] : exists (e0 = floor((-a - b + c)/5): "
5342 "5e0 = -a - b + c and c >= -a and c <= 4 - a) }",
5343 "{ [a, b] -> [c] : exists d : 18 * d = -3 - a + 2c and 1 <= c <= 3 }",
5346 /* Check that converting from isl_map to isl_pw_multi_aff and back
5347 * to isl_map produces the original isl_map.
5349 static int test_map_conversion(isl_ctx
*ctx
)
5352 isl_map
*map1
, *map2
;
5353 isl_pw_multi_aff
*pma
;
5356 for (i
= 0; i
< ARRAY_SIZE(conversion_tests
); ++i
) {
5357 map1
= isl_map_read_from_str(ctx
, conversion_tests
[i
]);
5358 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
5359 map2
= isl_map_from_pw_multi_aff(pma
);
5360 equal
= isl_map_is_equal(map1
, map2
);
5367 isl_die(ctx
, isl_error_unknown
, "bad conversion",
5374 static int test_conversion(isl_ctx
*ctx
)
5376 if (test_set_conversion(ctx
) < 0)
5378 if (test_map_conversion(ctx
) < 0)
5383 /* Check that isl_basic_map_curry does not modify input.
5385 static int test_curry(isl_ctx
*ctx
)
5388 isl_basic_map
*bmap1
, *bmap2
;
5391 str
= "{ [A[] -> B[]] -> C[] }";
5392 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
5393 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
5394 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
5395 isl_basic_map_free(bmap1
);
5396 isl_basic_map_free(bmap2
);
5401 isl_die(ctx
, isl_error_unknown
,
5402 "curried map should not be equal to original",
5412 } preimage_tests
[] = {
5413 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
5414 "{ A[j,i] -> B[i,j] }",
5415 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
5416 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
5417 "{ A[a,b] -> B[a/2,b/6] }",
5418 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
5419 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
5420 "{ A[a,b] -> B[a/2,b/6] }",
5421 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
5422 "exists i,j : a = 2 i and b = 6 j }" },
5423 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
5424 "[n] -> { : 0 <= n <= 100 }" },
5425 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
5426 "{ A[a] -> B[2a] }",
5427 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
5428 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
5429 "{ A[a] -> B[([a/2])] }",
5430 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
5431 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
5432 "{ A[a] -> B[a,a,a/3] }",
5433 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
5434 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
5435 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
5438 static int test_preimage_basic_set(isl_ctx
*ctx
)
5441 isl_basic_set
*bset1
, *bset2
;
5445 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
5446 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
5447 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
5448 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
5449 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
5450 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5451 isl_basic_set_free(bset1
);
5452 isl_basic_set_free(bset2
);
5456 isl_die(ctx
, isl_error_unknown
, "bad preimage",
5467 } preimage_domain_tests
[] = {
5468 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
5469 "{ A[j,i] -> B[i,j] }",
5470 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
5471 { "{ B[i] -> C[i]; D[i] -> E[i] }",
5472 "{ A[i] -> B[i + 1] }",
5473 "{ A[i] -> C[i + 1] }" },
5474 { "{ B[i] -> C[i]; B[i] -> E[i] }",
5475 "{ A[i] -> B[i + 1] }",
5476 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
5477 { "{ B[i] -> C[([i/2])] }",
5478 "{ A[i] -> B[2i] }",
5479 "{ A[i] -> C[i] }" },
5480 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
5481 "{ A[i] -> B[([i/5]), ([i/7])] }",
5482 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
5483 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
5484 "[N] -> { A[] -> B[([N/5])] }",
5485 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
5486 { "{ B[i] -> C[i] : exists a : i = 5 a }",
5487 "{ A[i] -> B[2i] }",
5488 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
5489 { "{ B[i] -> C[i] : exists a : i = 2 a; "
5490 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
5491 "{ A[i] -> B[2i] }",
5492 "{ A[i] -> C[2i] }" },
5493 { "{ A[i] -> B[i] }", "{ C[i] -> A[(i + floor(i/3))/2] }",
5494 "{ C[i] -> B[j] : 2j = i + floor(i/3) }" },
5497 static int test_preimage_union_map(isl_ctx
*ctx
)
5500 isl_union_map
*umap1
, *umap2
;
5504 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
5505 umap1
= isl_union_map_read_from_str(ctx
,
5506 preimage_domain_tests
[i
].map
);
5507 ma
= isl_multi_aff_read_from_str(ctx
,
5508 preimage_domain_tests
[i
].ma
);
5509 umap2
= isl_union_map_read_from_str(ctx
,
5510 preimage_domain_tests
[i
].res
);
5511 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
5512 equal
= isl_union_map_is_equal(umap1
, umap2
);
5513 isl_union_map_free(umap1
);
5514 isl_union_map_free(umap2
);
5518 isl_die(ctx
, isl_error_unknown
, "bad preimage",
5525 static int test_preimage(isl_ctx
*ctx
)
5527 if (test_preimage_basic_set(ctx
) < 0)
5529 if (test_preimage_union_map(ctx
) < 0)
5539 } pullback_tests
[] = {
5540 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
5541 "{ A[a,b] -> C[b + 2a] }" },
5542 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
5543 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
5544 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
5545 "{ A[a] -> C[(a)/6] }" },
5546 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
5547 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
5548 "{ A[a] -> C[(2a)/3] }" },
5549 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
5550 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
5551 "{ A[i,j] -> C[i + j, i + j] }"},
5552 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
5553 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
5554 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
5555 { "{ [i, j] -> [floor((i)/4) + floor((2*i+j)/5)] }",
5556 "{ [i, j] -> [floor((i)/3), j] }",
5557 "{ [i, j] -> [(floor((i)/12) + floor((j + 2*floor((i)/3))/5))] }" },
5560 static int test_pullback(isl_ctx
*ctx
)
5563 isl_multi_aff
*ma1
, *ma2
;
5567 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
5568 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
5569 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
5570 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
5571 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
5572 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
5573 isl_multi_aff_free(ma1
);
5574 isl_multi_aff_free(ma2
);
5578 isl_die(ctx
, isl_error_unknown
, "bad pullback",
5585 /* Check that negation is printed correctly and that equal expressions
5586 * are correctly identified.
5588 static int test_ast(isl_ctx
*ctx
)
5590 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
5594 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
5595 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
5596 expr
= isl_ast_expr_add(expr1
, expr2
);
5597 expr2
= isl_ast_expr_copy(expr
);
5598 expr
= isl_ast_expr_neg(expr
);
5599 expr2
= isl_ast_expr_neg(expr2
);
5600 equal
= isl_ast_expr_is_equal(expr
, expr2
);
5601 str
= isl_ast_expr_to_C_str(expr
);
5602 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
5604 isl_ast_expr_free(expr
);
5605 isl_ast_expr_free(expr2
);
5607 if (ok
< 0 || equal
< 0)
5610 isl_die(ctx
, isl_error_unknown
,
5611 "equal expressions not considered equal", return -1);
5613 isl_die(ctx
, isl_error_unknown
,
5614 "isl_ast_expr printed incorrectly", return -1);
5616 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
5617 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
5618 expr
= isl_ast_expr_add(expr1
, expr2
);
5619 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
5620 expr
= isl_ast_expr_sub(expr3
, expr
);
5621 str
= isl_ast_expr_to_C_str(expr
);
5622 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
5624 isl_ast_expr_free(expr
);
5629 isl_die(ctx
, isl_error_unknown
,
5630 "isl_ast_expr printed incorrectly", return -1);
5635 /* Check that isl_ast_build_expr_from_set returns a valid expression
5636 * for an empty set. Note that isl_ast_build_expr_from_set getting
5637 * called on an empty set probably indicates a bug in the caller.
5639 static int test_ast_build(isl_ctx
*ctx
)
5642 isl_ast_build
*build
;
5645 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5646 build
= isl_ast_build_from_context(set
);
5648 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
5649 expr
= isl_ast_build_expr_from_set(build
, set
);
5651 isl_ast_expr_free(expr
);
5652 isl_ast_build_free(build
);
5660 /* Internal data structure for before_for and after_for callbacks.
5662 * depth is the current depth
5663 * before is the number of times before_for has been called
5664 * after is the number of times after_for has been called
5666 struct isl_test_codegen_data
{
5672 /* This function is called before each for loop in the AST generated
5673 * from test_ast_gen1.
5675 * Increment the number of calls and the depth.
5676 * Check that the space returned by isl_ast_build_get_schedule_space
5677 * matches the target space of the schedule returned by
5678 * isl_ast_build_get_schedule.
5679 * Return an isl_id that is checked by the corresponding call
5682 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
5685 struct isl_test_codegen_data
*data
= user
;
5688 isl_union_map
*schedule
;
5689 isl_union_set
*uset
;
5694 ctx
= isl_ast_build_get_ctx(build
);
5696 if (data
->before
>= 3)
5697 isl_die(ctx
, isl_error_unknown
,
5698 "unexpected number of for nodes", return NULL
);
5699 if (data
->depth
>= 2)
5700 isl_die(ctx
, isl_error_unknown
,
5701 "unexpected depth", return NULL
);
5703 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
5707 schedule
= isl_ast_build_get_schedule(build
);
5708 uset
= isl_union_map_range(schedule
);
5711 if (isl_union_set_n_set(uset
) != 1) {
5712 isl_union_set_free(uset
);
5713 isl_die(ctx
, isl_error_unknown
,
5714 "expecting single range space", return NULL
);
5717 space
= isl_ast_build_get_schedule_space(build
);
5718 set
= isl_union_set_extract_set(uset
, space
);
5719 isl_union_set_free(uset
);
5720 empty
= isl_set_is_empty(set
);
5726 isl_die(ctx
, isl_error_unknown
,
5727 "spaces don't match", return NULL
);
5729 return isl_id_alloc(ctx
, name
, NULL
);
5732 /* This function is called after each for loop in the AST generated
5733 * from test_ast_gen1.
5735 * Increment the number of calls and decrement the depth.
5736 * Check that the annotation attached to the node matches
5737 * the isl_id returned by the corresponding call to before_for.
5739 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
5740 __isl_keep isl_ast_build
*build
, void *user
)
5742 struct isl_test_codegen_data
*data
= user
;
5750 if (data
->after
> data
->before
)
5751 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5752 "mismatch in number of for nodes",
5753 return isl_ast_node_free(node
));
5755 id
= isl_ast_node_get_annotation(node
);
5757 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5758 "missing annotation", return isl_ast_node_free(node
));
5760 name
= isl_id_get_name(id
);
5761 valid
= name
&& atoi(name
+ 1) == data
->depth
;
5765 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5766 "wrong annotation", return isl_ast_node_free(node
));
5771 /* Check that the before_each_for and after_each_for callbacks
5772 * are called for each for loop in the generated code,
5773 * that they are called in the right order and that the isl_id
5774 * returned from the before_each_for callback is attached to
5775 * the isl_ast_node passed to the corresponding after_each_for call.
5777 static int test_ast_gen1(isl_ctx
*ctx
)
5781 isl_union_map
*schedule
;
5782 isl_ast_build
*build
;
5784 struct isl_test_codegen_data data
;
5786 str
= "[N] -> { : N >= 10 }";
5787 set
= isl_set_read_from_str(ctx
, str
);
5788 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
5789 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
5790 schedule
= isl_union_map_read_from_str(ctx
, str
);
5795 build
= isl_ast_build_from_context(set
);
5796 build
= isl_ast_build_set_before_each_for(build
,
5797 &before_for
, &data
);
5798 build
= isl_ast_build_set_after_each_for(build
,
5800 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5801 isl_ast_build_free(build
);
5805 isl_ast_node_free(tree
);
5807 if (data
.before
!= 3 || data
.after
!= 3)
5808 isl_die(ctx
, isl_error_unknown
,
5809 "unexpected number of for nodes", return -1);
5814 /* Check that the AST generator handles domains that are integrally disjoint
5815 * but not rationally disjoint.
5817 static int test_ast_gen2(isl_ctx
*ctx
)
5821 isl_union_map
*schedule
;
5822 isl_union_map
*options
;
5823 isl_ast_build
*build
;
5826 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
5827 schedule
= isl_union_map_read_from_str(ctx
, str
);
5828 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5829 build
= isl_ast_build_from_context(set
);
5831 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
5832 options
= isl_union_map_read_from_str(ctx
, str
);
5833 build
= isl_ast_build_set_options(build
, options
);
5834 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5835 isl_ast_build_free(build
);
5838 isl_ast_node_free(tree
);
5843 /* Increment *user on each call.
5845 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
5846 __isl_keep isl_ast_build
*build
, void *user
)
5855 /* Test that unrolling tries to minimize the number of instances.
5856 * In particular, for the schedule given below, make sure it generates
5857 * 3 nodes (rather than 101).
5859 static int test_ast_gen3(isl_ctx
*ctx
)
5863 isl_union_map
*schedule
;
5864 isl_union_map
*options
;
5865 isl_ast_build
*build
;
5869 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
5870 schedule
= isl_union_map_read_from_str(ctx
, str
);
5871 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5873 str
= "{ [i] -> unroll[0] }";
5874 options
= isl_union_map_read_from_str(ctx
, str
);
5876 build
= isl_ast_build_from_context(set
);
5877 build
= isl_ast_build_set_options(build
, options
);
5878 build
= isl_ast_build_set_at_each_domain(build
,
5879 &count_domains
, &n_domain
);
5880 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5881 isl_ast_build_free(build
);
5885 isl_ast_node_free(tree
);
5888 isl_die(ctx
, isl_error_unknown
,
5889 "unexpected number of for nodes", return -1);
5894 /* Check that if the ast_build_exploit_nested_bounds options is set,
5895 * we do not get an outer if node in the generated AST,
5896 * while we do get such an outer if node if the options is not set.
5898 static int test_ast_gen4(isl_ctx
*ctx
)
5902 isl_union_map
*schedule
;
5903 isl_ast_build
*build
;
5905 enum isl_ast_node_type type
;
5908 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
5909 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
5911 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
5913 schedule
= isl_union_map_read_from_str(ctx
, str
);
5914 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5915 build
= isl_ast_build_from_context(set
);
5916 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5917 isl_ast_build_free(build
);
5921 type
= isl_ast_node_get_type(tree
);
5922 isl_ast_node_free(tree
);
5924 if (type
== isl_ast_node_if
)
5925 isl_die(ctx
, isl_error_unknown
,
5926 "not expecting if node", return -1);
5928 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
5930 schedule
= isl_union_map_read_from_str(ctx
, str
);
5931 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5932 build
= isl_ast_build_from_context(set
);
5933 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5934 isl_ast_build_free(build
);
5938 type
= isl_ast_node_get_type(tree
);
5939 isl_ast_node_free(tree
);
5941 if (type
!= isl_ast_node_if
)
5942 isl_die(ctx
, isl_error_unknown
,
5943 "expecting if node", return -1);
5945 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
5950 /* This function is called for each leaf in the AST generated
5951 * from test_ast_gen5.
5953 * We finalize the AST generation by extending the outer schedule
5954 * with a zero-dimensional schedule. If this results in any for loops,
5955 * then this means that we did not pass along enough information
5956 * about the outer schedule to the inner AST generation.
5958 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
5961 isl_union_map
*schedule
, *extra
;
5964 schedule
= isl_ast_build_get_schedule(build
);
5965 extra
= isl_union_map_copy(schedule
);
5966 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
5967 schedule
= isl_union_map_range_product(schedule
, extra
);
5968 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5969 isl_ast_build_free(build
);
5974 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
5975 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
5976 "code should not contain any for loop",
5977 return isl_ast_node_free(tree
));
5982 /* Check that we do not lose any information when going back and
5983 * forth between internal and external schedule.
5985 * In particular, we create an AST where we unroll the only
5986 * non-constant dimension in the schedule. We therefore do
5987 * not expect any for loops in the AST. However, older versions
5988 * of isl would not pass along enough information about the outer
5989 * schedule when performing an inner code generation from a create_leaf
5990 * callback, resulting in the inner code generation producing a for loop.
5992 static int test_ast_gen5(isl_ctx
*ctx
)
5996 isl_union_map
*schedule
, *options
;
5997 isl_ast_build
*build
;
6000 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
6001 schedule
= isl_union_map_read_from_str(ctx
, str
);
6003 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
6004 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
6005 options
= isl_union_map_read_from_str(ctx
, str
);
6007 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6008 build
= isl_ast_build_from_context(set
);
6009 build
= isl_ast_build_set_options(build
, options
);
6010 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
6011 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6012 isl_ast_build_free(build
);
6013 isl_ast_node_free(tree
);
6020 static int test_ast_gen(isl_ctx
*ctx
)
6022 if (test_ast_gen1(ctx
) < 0)
6024 if (test_ast_gen2(ctx
) < 0)
6026 if (test_ast_gen3(ctx
) < 0)
6028 if (test_ast_gen4(ctx
) < 0)
6030 if (test_ast_gen5(ctx
) < 0)
6035 /* Check if dropping output dimensions from an isl_pw_multi_aff
6038 static int test_pw_multi_aff(isl_ctx
*ctx
)
6041 isl_pw_multi_aff
*pma1
, *pma2
;
6044 str
= "{ [i,j] -> [i+j, 4i-j] }";
6045 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
6046 str
= "{ [i,j] -> [4i-j] }";
6047 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
6049 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
6051 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
6053 isl_pw_multi_aff_free(pma1
);
6054 isl_pw_multi_aff_free(pma2
);
6058 isl_die(ctx
, isl_error_unknown
,
6059 "expressions not equal", return -1);
6064 /* Check that we can properly parse multi piecewise affine expressions
6065 * where the piecewise affine expressions have different domains.
6067 static int test_multi_pw_aff(isl_ctx
*ctx
)
6070 isl_set
*dom
, *dom2
;
6071 isl_multi_pw_aff
*mpa1
, *mpa2
;
6076 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
6077 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
6078 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
6079 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
6080 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
6081 str
= "{ [i] -> [(i : i > 0), 2i] }";
6082 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
6084 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
6086 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
6087 dom
= isl_pw_aff_domain(pa
);
6088 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
6089 dom2
= isl_pw_aff_domain(pa
);
6090 equal_domain
= isl_set_is_equal(dom
, dom2
);
6094 isl_multi_pw_aff_free(mpa1
);
6095 isl_multi_pw_aff_free(mpa2
);
6100 isl_die(ctx
, isl_error_unknown
,
6101 "expressions not equal", return -1);
6103 if (equal_domain
< 0)
6106 isl_die(ctx
, isl_error_unknown
,
6107 "domains unexpectedly equal", return -1);
6112 /* This is a regression test for a bug where isl_basic_map_simplify
6113 * would end up in an infinite loop. In particular, we construct
6114 * an empty basic set that is not obviously empty.
6115 * isl_basic_set_is_empty marks the basic set as empty.
6116 * After projecting out i3, the variable can be dropped completely,
6117 * but isl_basic_map_simplify refrains from doing so if the basic set
6118 * is empty and would end up in an infinite loop if it didn't test
6119 * explicitly for empty basic maps in the outer loop.
6121 static int test_simplify_1(isl_ctx
*ctx
)
6124 isl_basic_set
*bset
;
6127 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
6128 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
6129 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
6131 bset
= isl_basic_set_read_from_str(ctx
, str
);
6132 empty
= isl_basic_set_is_empty(bset
);
6133 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
6134 isl_basic_set_free(bset
);
6138 isl_die(ctx
, isl_error_unknown
,
6139 "basic set should be empty", return -1);
6144 /* Check that the equality in the set description below
6145 * is simplified away.
6147 static int test_simplify_2(isl_ctx
*ctx
)
6150 isl_basic_set
*bset
;
6153 str
= "{ [a] : exists e0, e1: 32e1 = 31 + 31a + 31e0 }";
6154 bset
= isl_basic_set_read_from_str(ctx
, str
);
6155 universe
= isl_basic_set_plain_is_universe(bset
);
6156 isl_basic_set_free(bset
);
6161 isl_die(ctx
, isl_error_unknown
,
6162 "equality not simplified away", return -1);
6166 /* Some simplification tests.
6168 static int test_simplify(isl_ctx
*ctx
)
6170 if (test_simplify_1(ctx
) < 0)
6172 if (test_simplify_2(ctx
) < 0)
6177 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
6178 * with gbr context would fail to disable the use of the shifted tableau
6179 * when transferring equalities for the input to the context, resulting
6180 * in invalid sample values.
6182 static int test_partial_lexmin(isl_ctx
*ctx
)
6185 isl_basic_set
*bset
;
6186 isl_basic_map
*bmap
;
6189 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
6190 bmap
= isl_basic_map_read_from_str(ctx
, str
);
6191 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
6192 bset
= isl_basic_set_read_from_str(ctx
, str
);
6193 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
6202 /* Check that the variable compression performed on the existentially
6203 * quantified variables inside isl_basic_set_compute_divs is not confused
6204 * by the implicit equalities among the parameters.
6206 static int test_compute_divs(isl_ctx
*ctx
)
6209 isl_basic_set
*bset
;
6212 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
6213 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
6214 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
6215 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
6216 bset
= isl_basic_set_read_from_str(ctx
, str
);
6217 set
= isl_basic_set_compute_divs(bset
);
6225 /* Check that the reaching domain elements and the prefix schedule
6226 * at a leaf node are the same before and after grouping.
6228 static int test_schedule_tree_group_1(isl_ctx
*ctx
)
6233 isl_union_set
*uset
;
6234 isl_multi_union_pw_aff
*mupa
;
6235 isl_union_pw_multi_aff
*upma1
, *upma2
;
6236 isl_union_set
*domain1
, *domain2
;
6237 isl_union_map
*umap1
, *umap2
;
6238 isl_schedule_node
*node
;
6240 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10 }";
6241 uset
= isl_union_set_read_from_str(ctx
, str
);
6242 node
= isl_schedule_node_from_domain(uset
);
6243 node
= isl_schedule_node_child(node
, 0);
6244 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [9 - i] }]";
6245 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6246 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6247 node
= isl_schedule_node_child(node
, 0);
6248 str
= "[{ S1[i,j] -> [j]; S2[i,j] -> [j] }]";
6249 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6250 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6251 node
= isl_schedule_node_child(node
, 0);
6252 umap1
= isl_schedule_node_get_prefix_schedule_union_map(node
);
6253 upma1
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
6254 domain1
= isl_schedule_node_get_domain(node
);
6255 id
= isl_id_alloc(ctx
, "group", NULL
);
6256 node
= isl_schedule_node_parent(node
);
6257 node
= isl_schedule_node_group(node
, id
);
6258 node
= isl_schedule_node_child(node
, 0);
6259 umap2
= isl_schedule_node_get_prefix_schedule_union_map(node
);
6260 upma2
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
6261 domain2
= isl_schedule_node_get_domain(node
);
6262 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
6263 if (equal
>= 0 && equal
)
6264 equal
= isl_union_set_is_equal(domain1
, domain2
);
6265 if (equal
>= 0 && equal
)
6266 equal
= isl_union_map_is_equal(umap1
, umap2
);
6267 isl_union_map_free(umap1
);
6268 isl_union_map_free(umap2
);
6269 isl_union_set_free(domain1
);
6270 isl_union_set_free(domain2
);
6271 isl_union_pw_multi_aff_free(upma1
);
6272 isl_union_pw_multi_aff_free(upma2
);
6273 isl_schedule_node_free(node
);
6278 isl_die(ctx
, isl_error_unknown
,
6279 "expressions not equal", return -1);
6284 /* Check that we can have nested groupings and that the union map
6285 * schedule representation is the same before and after the grouping.
6286 * Note that after the grouping, the union map representation contains
6287 * the domain constraints from the ranges of the expansion nodes,
6288 * while they are missing from the union map representation of
6289 * the tree without expansion nodes.
6291 * Also check that the global expansion is as expected.
6293 static int test_schedule_tree_group_2(isl_ctx
*ctx
)
6295 int equal
, equal_expansion
;
6298 isl_union_set
*uset
;
6299 isl_union_map
*umap1
, *umap2
;
6300 isl_union_map
*expansion1
, *expansion2
;
6301 isl_union_set_list
*filters
;
6302 isl_multi_union_pw_aff
*mupa
;
6303 isl_schedule
*schedule
;
6304 isl_schedule_node
*node
;
6306 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10; "
6307 "S3[i,j] : 0 <= i,j < 10 }";
6308 uset
= isl_union_set_read_from_str(ctx
, str
);
6309 node
= isl_schedule_node_from_domain(uset
);
6310 node
= isl_schedule_node_child(node
, 0);
6311 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [i]; S3[i,j] -> [i] }]";
6312 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6313 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6314 node
= isl_schedule_node_child(node
, 0);
6315 str
= "{ S1[i,j] }";
6316 uset
= isl_union_set_read_from_str(ctx
, str
);
6317 filters
= isl_union_set_list_from_union_set(uset
);
6318 str
= "{ S2[i,j]; S3[i,j] }";
6319 uset
= isl_union_set_read_from_str(ctx
, str
);
6320 filters
= isl_union_set_list_add(filters
, uset
);
6321 node
= isl_schedule_node_insert_sequence(node
, filters
);
6322 node
= isl_schedule_node_child(node
, 1);
6323 node
= isl_schedule_node_child(node
, 0);
6324 str
= "{ S2[i,j] }";
6325 uset
= isl_union_set_read_from_str(ctx
, str
);
6326 filters
= isl_union_set_list_from_union_set(uset
);
6327 str
= "{ S3[i,j] }";
6328 uset
= isl_union_set_read_from_str(ctx
, str
);
6329 filters
= isl_union_set_list_add(filters
, uset
);
6330 node
= isl_schedule_node_insert_sequence(node
, filters
);
6332 schedule
= isl_schedule_node_get_schedule(node
);
6333 umap1
= isl_schedule_get_map(schedule
);
6334 uset
= isl_schedule_get_domain(schedule
);
6335 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
6336 isl_schedule_free(schedule
);
6338 node
= isl_schedule_node_parent(node
);
6339 node
= isl_schedule_node_parent(node
);
6340 id
= isl_id_alloc(ctx
, "group1", NULL
);
6341 node
= isl_schedule_node_group(node
, id
);
6342 node
= isl_schedule_node_child(node
, 1);
6343 node
= isl_schedule_node_child(node
, 0);
6344 id
= isl_id_alloc(ctx
, "group2", NULL
);
6345 node
= isl_schedule_node_group(node
, id
);
6347 schedule
= isl_schedule_node_get_schedule(node
);
6348 umap2
= isl_schedule_get_map(schedule
);
6349 isl_schedule_free(schedule
);
6351 node
= isl_schedule_node_root(node
);
6352 node
= isl_schedule_node_child(node
, 0);
6353 expansion1
= isl_schedule_node_get_subtree_expansion(node
);
6354 isl_schedule_node_free(node
);
6356 str
= "{ group1[i] -> S1[i,j] : 0 <= i,j < 10; "
6357 "group1[i] -> S2[i,j] : 0 <= i,j < 10; "
6358 "group1[i] -> S3[i,j] : 0 <= i,j < 10 }";
6360 expansion2
= isl_union_map_read_from_str(ctx
, str
);
6362 equal
= isl_union_map_is_equal(umap1
, umap2
);
6363 equal_expansion
= isl_union_map_is_equal(expansion1
, expansion2
);
6365 isl_union_map_free(umap1
);
6366 isl_union_map_free(umap2
);
6367 isl_union_map_free(expansion1
);
6368 isl_union_map_free(expansion2
);
6370 if (equal
< 0 || equal_expansion
< 0)
6373 isl_die(ctx
, isl_error_unknown
,
6374 "expressions not equal", return -1);
6375 if (!equal_expansion
)
6376 isl_die(ctx
, isl_error_unknown
,
6377 "unexpected expansion", return -1);
6382 /* Some tests for the isl_schedule_node_group function.
6384 static int test_schedule_tree_group(isl_ctx
*ctx
)
6386 if (test_schedule_tree_group_1(ctx
) < 0)
6388 if (test_schedule_tree_group_2(ctx
) < 0)
6397 { "{ rat: [i] : 0 <= i <= 10 }",
6398 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
6399 { "{ rat: [i] : FALSE }",
6400 "{ rat: coefficients[[cst] -> [a]] }" },
6402 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
6409 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
6410 "{ rat: [i] : 0 <= i <= 10 }" },
6411 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
6413 { "{ rat: coefficients[[cst] -> [a]] }",
6414 "{ rat: [i] : FALSE }" },
6417 /* Test the basic functionality of isl_basic_set_coefficients and
6418 * isl_basic_set_solutions.
6420 static int test_dual(isl_ctx
*ctx
)
6424 for (i
= 0; i
< ARRAY_SIZE(coef_tests
); ++i
) {
6426 isl_basic_set
*bset1
, *bset2
;
6428 bset1
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].set
);
6429 bset2
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].dual
);
6430 bset1
= isl_basic_set_coefficients(bset1
);
6431 equal
= isl_basic_set_is_equal(bset1
, bset2
);
6432 isl_basic_set_free(bset1
);
6433 isl_basic_set_free(bset2
);
6437 isl_die(ctx
, isl_error_unknown
,
6438 "incorrect dual", return -1);
6441 for (i
= 0; i
< ARRAY_SIZE(sol_tests
); ++i
) {
6443 isl_basic_set
*bset1
, *bset2
;
6445 bset1
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].set
);
6446 bset2
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].dual
);
6447 bset1
= isl_basic_set_solutions(bset1
);
6448 equal
= isl_basic_set_is_equal(bset1
, bset2
);
6449 isl_basic_set_free(bset1
);
6450 isl_basic_set_free(bset2
);
6454 isl_die(ctx
, isl_error_unknown
,
6455 "incorrect dual", return -1);
6465 const char *schedule
;
6470 { 0, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
6471 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6473 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
6474 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6476 { 1, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
6477 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6479 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
6480 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6482 { 0, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
6483 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6485 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
6486 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
6488 { 1, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
6489 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6491 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
6492 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
6496 /* Basic tiling tests. Create a schedule tree with a domain and a band node,
6497 * tile the band and then check if the tile and point bands have the
6498 * expected partial schedule.
6500 static int test_tile(isl_ctx
*ctx
)
6506 scale
= isl_options_get_tile_scale_tile_loops(ctx
);
6507 shift
= isl_options_get_tile_shift_point_loops(ctx
);
6509 for (i
= 0; i
< ARRAY_SIZE(tile_tests
); ++i
) {
6513 isl_union_set
*domain
;
6514 isl_multi_union_pw_aff
*mupa
, *mupa2
;
6515 isl_schedule_node
*node
;
6516 isl_multi_val
*sizes
;
6518 opt
= tile_tests
[i
].scale_tile
;
6519 isl_options_set_tile_scale_tile_loops(ctx
, opt
);
6520 opt
= tile_tests
[i
].shift_point
;
6521 isl_options_set_tile_shift_point_loops(ctx
, opt
);
6523 str
= tile_tests
[i
].domain
;
6524 domain
= isl_union_set_read_from_str(ctx
, str
);
6525 node
= isl_schedule_node_from_domain(domain
);
6526 node
= isl_schedule_node_child(node
, 0);
6527 str
= tile_tests
[i
].schedule
;
6528 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6529 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6530 str
= tile_tests
[i
].sizes
;
6531 sizes
= isl_multi_val_read_from_str(ctx
, str
);
6532 node
= isl_schedule_node_band_tile(node
, sizes
);
6534 str
= tile_tests
[i
].tile
;
6535 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6536 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
6537 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
, mupa2
);
6538 isl_multi_union_pw_aff_free(mupa
);
6539 isl_multi_union_pw_aff_free(mupa2
);
6541 node
= isl_schedule_node_child(node
, 0);
6543 str
= tile_tests
[i
].point
;
6544 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6545 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
6546 if (equal
>= 0 && equal
)
6547 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
,
6549 isl_multi_union_pw_aff_free(mupa
);
6550 isl_multi_union_pw_aff_free(mupa2
);
6552 isl_schedule_node_free(node
);
6557 isl_die(ctx
, isl_error_unknown
,
6558 "unexpected result", return -1);
6561 isl_options_set_tile_scale_tile_loops(ctx
, scale
);
6562 isl_options_set_tile_shift_point_loops(ctx
, shift
);
6567 /* Check that the domain hash of a space is equal to the hash
6568 * of the domain of the space.
6570 static int test_domain_hash(isl_ctx
*ctx
)
6574 uint32_t hash1
, hash2
;
6576 map
= isl_map_read_from_str(ctx
, "[n] -> { A[B[x] -> C[]] -> D[] }");
6577 space
= isl_map_get_space(map
);
6579 hash1
= isl_space_get_domain_hash(space
);
6580 space
= isl_space_domain(space
);
6581 hash2
= isl_space_get_hash(space
);
6582 isl_space_free(space
);
6587 isl_die(ctx
, isl_error_unknown
,
6588 "domain hash not equal to hash of domain", return -1);
6593 /* Check that a universe basic set that is not obviously equal to the universe
6594 * is still recognized as being equal to the universe.
6596 static int test_universe(isl_ctx
*ctx
)
6599 isl_basic_set
*bset
;
6602 s
= "{ [] : exists x, y : 3y <= 2x and y >= -3 + 2x and 2y >= 2 - x }";
6603 bset
= isl_basic_set_read_from_str(ctx
, s
);
6604 is_univ
= isl_basic_set_is_universe(bset
);
6605 isl_basic_set_free(bset
);
6610 isl_die(ctx
, isl_error_unknown
,
6611 "not recognized as universe set", return -1);
6618 int (*fn
)(isl_ctx
*ctx
);
6620 { "universe", &test_universe
},
6621 { "domain hash", &test_domain_hash
},
6622 { "dual", &test_dual
},
6623 { "dependence analysis", &test_flow
},
6624 { "val", &test_val
},
6625 { "compute divs", &test_compute_divs
},
6626 { "partial lexmin", &test_partial_lexmin
},
6627 { "simplify", &test_simplify
},
6628 { "curry", &test_curry
},
6629 { "piecewise multi affine expressions", &test_pw_multi_aff
},
6630 { "multi piecewise affine expressions", &test_multi_pw_aff
},
6631 { "conversion", &test_conversion
},
6632 { "list", &test_list
},
6633 { "align parameters", &test_align_parameters
},
6634 { "preimage", &test_preimage
},
6635 { "pullback", &test_pullback
},
6636 { "AST", &test_ast
},
6637 { "AST build", &test_ast_build
},
6638 { "AST generation", &test_ast_gen
},
6639 { "eliminate", &test_eliminate
},
6640 { "residue class", &test_residue_class
},
6641 { "div", &test_div
},
6642 { "slice", &test_slice
},
6643 { "fixed power", &test_fixed_power
},
6644 { "sample", &test_sample
},
6645 { "output", &test_output
},
6646 { "vertices", &test_vertices
},
6647 { "fixed", &test_fixed
},
6648 { "equal", &test_equal
},
6649 { "disjoint", &test_disjoint
},
6650 { "product", &test_product
},
6651 { "dim_max", &test_dim_max
},
6652 { "affine", &test_aff
},
6653 { "injective", &test_injective
},
6654 { "schedule (whole component)", &test_schedule_whole
},
6655 { "schedule (incremental)", &test_schedule_incremental
},
6656 { "schedule tree grouping", &test_schedule_tree_group
},
6657 { "tile", &test_tile
},
6658 { "union_pw", &test_union_pw
},
6659 { "eval", &test_eval
},
6660 { "parse", &test_parse
},
6661 { "single-valued", &test_sv
},
6662 { "affine hull", &test_affine_hull
},
6663 { "simple_hull", &test_simple_hull
},
6664 { "coalesce", &test_coalesce
},
6665 { "factorize", &test_factorize
},
6666 { "subset", &test_subset
},
6667 { "subtract", &test_subtract
},
6668 { "intersect", &test_intersect
},
6669 { "lexmin", &test_lexmin
},
6670 { "min", &test_min
},
6671 { "gist", &test_gist
},
6672 { "piecewise quasi-polynomials", &test_pwqp
},
6673 { "lift", &test_lift
},
6674 { "bound", &test_bound
},
6675 { "union", &test_union
},
6676 { "split periods", &test_split_periods
},
6677 { "lexicographic order", &test_lex
},
6678 { "bijectivity", &test_bijective
},
6679 { "dataflow analysis", &test_dep
},
6680 { "reading", &test_read
},
6681 { "bounded", &test_bounded
},
6682 { "construction", &test_construction
},
6683 { "dimension manipulation", &test_dim
},
6684 { "map application", &test_application
},
6685 { "convex hull", &test_convex_hull
},
6686 { "transitive closure", &test_closure
},
6689 int main(int argc
, char **argv
)
6692 struct isl_ctx
*ctx
;
6693 struct isl_options
*options
;
6695 srcdir
= getenv("srcdir");
6698 options
= isl_options_new_with_defaults();
6700 argc
= isl_options_parse(options
, argc
, argv
, ISL_ARG_ALL
);
6702 ctx
= isl_ctx_alloc_with_options(&isl_options_args
, options
);
6703 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
6704 printf("%s\n", tests
[i
].name
);
6705 if (tests
[i
].fn(ctx
) < 0)