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_private.h>
36 #include <isl/ast_build.h>
39 #include <isl_ast_build_expr.h>
40 #include <isl/options.h>
42 #include "isl_srcdir.c"
44 #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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
347 isl_int_set_si(v
, 1);
348 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
354 isl_int_set_si(v
, -5);
355 c
= 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 c
= isl_constraint_set_constant(c
, v
);
689 isl_int_set_si(v
, 1);
690 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
691 isl_int_set_si(v
, 3);
692 c
= 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 c
= isl_constraint_set_constant(c
, v
);
698 isl_int_set_si(v
, -1);
699 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
700 isl_int_set_si(v
, 3);
701 c
= 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 c
= isl_constraint_set_constant(c
, v
);
718 isl_int_set_si(v
, -1);
719 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
720 isl_int_set_si(v
, 3);
721 c
= 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 c
= isl_constraint_set_constant(c
, v
);
727 isl_int_set_si(v
, 1);
728 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
729 isl_int_set_si(v
, 3);
730 c
= 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 c
= isl_constraint_set_constant(c
, v
);
747 isl_int_set_si(v
, -1);
748 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
749 isl_int_set_si(v
, 3);
750 c
= 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 c
= isl_constraint_set_constant(c
, v
);
756 isl_int_set_si(v
, 1);
757 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
758 isl_int_set_si(v
, 4);
759 c
= 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 c
= isl_constraint_set_constant(c
, v
);
776 isl_int_set_si(v
, -1);
777 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
778 isl_int_set_si(v
, 3);
779 c
= 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 c
= isl_constraint_set_constant(c
, v
);
785 isl_int_set_si(v
, 1);
786 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
787 isl_int_set_si(v
, 6);
788 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
805 isl_int_set_si(v
, 3);
806 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
812 isl_int_set_si(v
, -3);
813 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
830 isl_int_set_si(v
, 6);
831 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
837 isl_int_set_si(v
, -3);
838 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
864 isl_int_set_si(v
, -3);
865 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
866 isl_int_set_si(v
, -3);
867 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
868 isl_int_set_si(v
, 6);
869 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
889 isl_int_set_si(v
, -3);
890 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
891 isl_int_set_si(v
, -3);
892 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
893 isl_int_set_si(v
, 6);
894 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
900 isl_int_set_si(v
, 1);
901 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
902 isl_int_set_si(v
, 1);
903 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
923 isl_int_set_si(v
, -1);
924 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
925 isl_int_set_si(v
, -2);
926 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
932 isl_int_set_si(v
, 3);
933 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
934 isl_int_set_si(v
, 2);
935 c
= 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 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
955 isl_int_set_si(v
, -2);
956 c
= 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 }" },
1266 { "{ [x, y, z] : 0 <= x, y, z <= 10; [x, y, 0] : x >= 0 and y > 0; "
1267 "[x, y, 0] : x >= 0 and y < 0 }",
1268 "{ [x, y, z] : x >= 0 and 0 <= z <= 10 }" },
1271 static int test_convex_hull_algo(isl_ctx
*ctx
, int convex
)
1274 int orig_convex
= ctx
->opt
->convex
;
1275 ctx
->opt
->convex
= convex
;
1277 test_convex_hull_case(ctx
, "convex0");
1278 test_convex_hull_case(ctx
, "convex1");
1279 test_convex_hull_case(ctx
, "convex2");
1280 test_convex_hull_case(ctx
, "convex3");
1281 test_convex_hull_case(ctx
, "convex4");
1282 test_convex_hull_case(ctx
, "convex5");
1283 test_convex_hull_case(ctx
, "convex6");
1284 test_convex_hull_case(ctx
, "convex7");
1285 test_convex_hull_case(ctx
, "convex8");
1286 test_convex_hull_case(ctx
, "convex9");
1287 test_convex_hull_case(ctx
, "convex10");
1288 test_convex_hull_case(ctx
, "convex11");
1289 test_convex_hull_case(ctx
, "convex12");
1290 test_convex_hull_case(ctx
, "convex13");
1291 test_convex_hull_case(ctx
, "convex14");
1292 test_convex_hull_case(ctx
, "convex15");
1294 for (i
= 0; i
< ARRAY_SIZE(convex_hull_tests
); ++i
) {
1295 isl_set
*set1
, *set2
;
1298 set1
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].set
);
1299 set2
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].hull
);
1300 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
1301 equal
= isl_set_is_equal(set1
, set2
);
1308 isl_die(ctx
, isl_error_unknown
,
1309 "unexpected convex hull", return -1);
1312 ctx
->opt
->convex
= orig_convex
;
1317 static int test_convex_hull(isl_ctx
*ctx
)
1319 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
) < 0)
1321 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
) < 0)
1326 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
1330 struct isl_basic_set
*bset1
, *bset2
;
1332 filename
= get_filename(ctx
, name
, "polylib");
1334 input
= fopen(filename
, "r");
1337 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1338 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1340 bset1
= isl_basic_set_gist(bset1
, bset2
);
1342 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1344 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1346 isl_basic_set_free(bset1
);
1347 isl_basic_set_free(bset2
);
1353 /* Inputs to isl_map_plain_gist_basic_map, along with the expected output.
1357 const char *context
;
1359 } plain_gist_tests
[] = {
1360 { "{ [i] -> [j] : i >= 1 and j >= 1 or i >= 2 and j <= 10 }",
1361 "{ [i] -> [j] : i >= 1 }",
1362 "{ [i] -> [j] : j >= 1 or i >= 2 and j <= 10 }" },
1363 { "{ [n] -> [i,j,k] : (i mod 3 = 2 and j mod 4 = 2) or "
1364 "(j mod 4 = 2 and k mod 6 = n) }",
1365 "{ [n] -> [i,j,k] : j mod 4 = 2 }",
1366 "{ [n] -> [i,j,k] : (i mod 3 = 2) or (k mod 6 = n) }" },
1367 { "{ [i] -> [j] : i > j and (exists a,b : i <= 2a + 5b <= 2) }",
1368 "{ [i] -> [j] : i > j }",
1369 "{ [i] -> [j] : exists a,b : i <= 2a + 5b <= 2 }" },
1372 /* Basic tests for isl_map_plain_gist_basic_map.
1374 static int test_plain_gist(isl_ctx
*ctx
)
1378 for (i
= 0; i
< ARRAY_SIZE(plain_gist_tests
); ++i
) {
1381 isl_map
*map
, *gist
;
1382 isl_basic_map
*context
;
1384 map
= isl_map_read_from_str(ctx
, plain_gist_tests
[i
].map
);
1385 str
= plain_gist_tests
[i
].context
;
1386 context
= isl_basic_map_read_from_str(ctx
, str
);
1387 map
= isl_map_plain_gist_basic_map(map
, context
);
1388 gist
= isl_map_read_from_str(ctx
, plain_gist_tests
[i
].gist
);
1389 equal
= isl_map_is_equal(map
, gist
);
1395 isl_die(ctx
, isl_error_unknown
,
1396 "incorrect gist result", return -1);
1404 const char *context
;
1407 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1408 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1409 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1410 "{ [a, b, c] : a <= 15 }" },
1411 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1412 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1413 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1414 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1415 { "{ [m, n, a, b] : a <= 2147 + n }",
1416 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1417 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1418 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1420 "{ [m, n, ku, kl] }" },
1421 { "{ [a, a, b] : a >= 10 }",
1422 "{ [a, b, c] : c >= a and c <= b and c >= 2 }",
1423 "{ [a, a, b] : a >= 10 }" },
1424 { "{ [i, j] : i >= 0 and i + j >= 0 }", "{ [i, j] : i <= 0 }",
1425 "{ [0, j] : j >= 0 }" },
1426 /* Check that no constraints on i6 are introduced in the gist */
1427 { "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1428 "20e0 <= 1530 - 4t1 - 5i4 and 20e0 >= 1511 - 4t1 - 5i4 and "
1429 "5e0 <= 381 - t1 and i4 <= 1) }",
1430 "[t1] -> { [i4, i6] : exists (e0 = floor((-t1 + i6)/5): "
1431 "5e0 = -t1 + i6 and i6 <= 6 and i6 >= 3) }",
1432 "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1433 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 <= 1530 - 4t1 - 5i4 and "
1434 "20e0 >= 1511 - 4t1 - 5i4) }" },
1435 /* Check that no constraints on i6 are introduced in the gist */
1436 { "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((1 + i4)/2), "
1437 "e1 = floor((1530 - 4t1 - 5i4)/20), "
1438 "e2 = floor((-4t1 - 5i4 + 10*floor((1 + i4)/2))/20), "
1439 "e3 = floor((-1 + i4)/2): t2 = 0 and 2e3 = -1 + i4 and "
1440 "20e2 >= -19 - 4t1 - 5i4 + 10e0 and 5e2 <= 1 - t1 and "
1441 "2e0 <= 1 + i4 and 2e0 >= i4 and "
1442 "20e1 <= 1530 - 4t1 - 5i4 and "
1443 "20e1 >= 1511 - 4t1 - 5i4 and i4 <= 1 and "
1444 "5e1 <= 381 - t1 and 20e2 <= -4t1 - 5i4 + 10e0) }",
1445 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((-17 + i4)/2), "
1446 "e1 = floor((-t1 + i6)/5): 5e1 = -t1 + i6 and "
1447 "2e0 <= -17 + i4 and 2e0 >= -18 + i4 and "
1448 "10e0 <= -91 + 5i4 + 4i6 and "
1449 "10e0 >= -105 + 5i4 + 4i6) }",
1450 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((381 - t1)/5), "
1451 "e1 = floor((-1 + i4)/2): t2 = 0 and 2e1 = -1 + i4 and "
1452 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 >= 1511 - 4t1 - 5i4) }" },
1453 { "{ [0, 0, q, p] : -5 <= q <= 5 and p >= 0 }",
1454 "{ [a, b, q, p] : b >= 1 + a }",
1455 "{ [a, b, q, p] : false }" },
1456 { "[n] -> { [x] : x = n && x mod 32 = 0 }",
1457 "[n] -> { [x] : x mod 32 = 0 }",
1458 "[n] -> { [x = n] }" },
1459 { "{ [x] : x mod 6 = 0 }", "{ [x] : x mod 3 = 0 }",
1460 "{ [x] : x mod 2 = 0 }" },
1461 { "{ [x] : x mod 3200 = 0 }", "{ [x] : x mod 10000 = 0 }",
1462 "{ [x] : x mod 128 = 0 }" },
1463 { "{ [x] : x mod 3200 = 0 }", "{ [x] : x mod 10 = 0 }",
1464 "{ [x] : x mod 3200 = 0 }" },
1465 { "{ [a, b, c] : a mod 2 = 0 and a = c }",
1466 "{ [a, b, c] : b mod 2 = 0 and b = c }",
1467 "{ [a, b, c = a] }" },
1468 { "{ [a, b, c] : a mod 6 = 0 and a = c }",
1469 "{ [a, b, c] : b mod 2 = 0 and b = c }",
1470 "{ [a, b, c = a] : a mod 3 = 0 }" },
1471 { "{ [x] : 0 <= x <= 4 or 6 <= x <= 9 }",
1472 "{ [x] : 1 <= x <= 3 or 7 <= x <= 8 }",
1474 { "{ [x,y] : x < 0 and 0 <= y <= 4 or x >= -2 and -x <= y <= 10 + x }",
1475 "{ [x,y] : 1 <= y <= 3 }",
1479 /* Check that isl_set_gist behaves as expected.
1481 * For the test cases in gist_tests, besides checking that the result
1482 * is as expected, also check that applying the gist operation does
1483 * not modify the input set (an earlier version of isl would do that) and
1484 * that the test case is consistent, i.e., that the gist has the same
1485 * intersection with the context as the input set.
1487 static int test_gist(struct isl_ctx
*ctx
)
1491 isl_basic_set
*bset1
, *bset2
;
1492 isl_map
*map1
, *map2
;
1495 for (i
= 0; i
< ARRAY_SIZE(gist_tests
); ++i
) {
1496 int equal_input
, equal_intersection
;
1497 isl_set
*set1
, *set2
, *copy
, *context
;
1499 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1500 context
= isl_set_read_from_str(ctx
, gist_tests
[i
].context
);
1501 copy
= isl_set_copy(set1
);
1502 set1
= isl_set_gist(set1
, isl_set_copy(context
));
1503 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].gist
);
1504 equal
= isl_set_is_equal(set1
, set2
);
1506 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1507 equal_input
= isl_set_is_equal(set1
, copy
);
1509 set1
= isl_set_intersect(set1
, isl_set_copy(context
));
1510 set2
= isl_set_intersect(set2
, context
);
1511 equal_intersection
= isl_set_is_equal(set1
, set2
);
1514 if (equal
< 0 || equal_input
< 0 || equal_intersection
< 0)
1517 isl_die(ctx
, isl_error_unknown
,
1518 "incorrect gist result", return -1);
1520 isl_die(ctx
, isl_error_unknown
,
1521 "gist modified input", return -1);
1523 isl_die(ctx
, isl_error_unknown
,
1524 "inconsistent gist test case", return -1);
1527 test_gist_case(ctx
, "gist1");
1529 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1530 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1531 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1532 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1533 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1534 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1535 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1536 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1537 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1538 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1539 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1540 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1541 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1542 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1543 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1544 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1545 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1546 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1547 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1548 bset1
= isl_basic_set_gist(bset1
, bset2
);
1549 assert(bset1
&& bset1
->n_div
== 0);
1550 isl_basic_set_free(bset1
);
1552 /* Check that the integer divisions of the second disjunct
1553 * do not spread to the first disjunct.
1555 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1556 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1557 "(exists (e0 = [(-1 + t1)/16], "
1558 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1559 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1560 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1561 "o0 <= 4294967295 and t1 <= -1)) }";
1562 map1
= isl_map_read_from_str(ctx
, str
);
1563 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1564 map2
= isl_map_read_from_str(ctx
, str
);
1565 map1
= isl_map_gist(map1
, map2
);
1569 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1570 isl_map_free(map1
); return -1);
1571 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1572 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1573 isl_map_free(map1
); return -1);
1576 if (test_plain_gist(ctx
) < 0)
1582 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1584 isl_set
*set
, *set2
;
1588 set
= isl_set_read_from_str(ctx
, str
);
1589 set
= isl_set_coalesce(set
);
1590 set2
= isl_set_read_from_str(ctx
, str
);
1591 equal
= isl_set_is_equal(set
, set2
);
1592 one
= set
&& set
->n
== 1;
1599 isl_die(ctx
, isl_error_unknown
,
1600 "coalesced set not equal to input", return -1);
1601 if (check_one
&& !one
)
1602 isl_die(ctx
, isl_error_unknown
,
1603 "coalesced set should not be a union", return -1);
1608 /* Inputs for coalescing tests with unbounded wrapping.
1609 * "str" is a string representation of the input set.
1610 * "single_disjunct" is set if we expect the result to consist of
1611 * a single disjunct.
1614 int single_disjunct
;
1616 } coalesce_unbounded_tests
[] = {
1617 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1618 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1619 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1620 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1622 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1623 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1624 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1625 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1628 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1629 * option turned off.
1631 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1637 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1638 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1640 for (i
= 0; i
< ARRAY_SIZE(coalesce_unbounded_tests
); ++i
) {
1641 const char *str
= coalesce_unbounded_tests
[i
].str
;
1642 int check_one
= coalesce_unbounded_tests
[i
].single_disjunct
;
1643 if (test_coalesce_set(ctx
, str
, check_one
) >= 0)
1649 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1654 /* Inputs for coalescing tests.
1655 * "str" is a string representation of the input set.
1656 * "single_disjunct" is set if we expect the result to consist of
1657 * a single disjunct.
1660 int single_disjunct
;
1662 } coalesce_tests
[] = {
1663 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1664 "y >= x & x >= 2 & 5 >= y }" },
1665 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1666 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1667 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1668 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1669 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1670 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1671 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1672 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1673 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1674 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1675 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1676 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1677 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1678 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1679 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1680 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1681 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1682 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1683 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1684 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1685 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1686 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1687 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1688 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1689 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1690 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1691 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1692 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1693 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1694 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1695 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1696 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1697 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1698 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1699 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1700 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1701 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1702 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1703 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1704 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1705 "[o0, o1, o2, o3, o4, o5, o6]] : "
1706 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1707 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1708 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1709 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1710 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1711 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1712 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1713 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1714 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1715 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1716 "o6 >= i3 + i6 - o3 and M >= 0 and "
1717 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1718 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1719 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1720 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1721 "(o0 = 0 and M >= 2 and N >= 3) or "
1722 "(M = 0 and o0 = 0 and N >= 3) }" },
1723 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1724 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1725 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1726 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1727 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1728 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1729 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1730 "(y = 3 and x = 1) }" },
1731 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1732 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1733 "i1 <= M and i3 <= M and i4 <= M) or "
1734 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1735 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1736 "i4 <= -1 + M) }" },
1737 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1738 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1739 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1740 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1741 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1742 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1743 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1744 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1745 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1746 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1747 { 0, "{ [a, b] : exists e : 2e = a and "
1748 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1749 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1750 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1751 "j >= 1 and j' <= i + j - i' and i >= 1; "
1753 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1754 "[i,j] : exists a : j = 3a }" },
1755 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1756 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1758 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1759 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1760 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1761 "c <= 6 + 8a and a >= 3; "
1762 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1763 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1764 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1765 "[x,0] : 3 <= x <= 4 }" },
1766 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1767 "[x,0] : 4 <= x <= 5 }" },
1768 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1769 "[x,0] : 3 <= x <= 5 }" },
1770 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1771 "[x,0] : 3 <= x <= 4 }" },
1772 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1774 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1775 { 1, "{ [0,0]; [1,1] }" },
1776 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1777 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1779 "[k, 0, k] : k <= 6 and k >= 1 }" },
1780 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1781 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1782 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1783 { 1, "[n] -> { [1] : n >= 0;"
1784 "[x] : exists (e0 = floor((x)/2): x >= 2 and "
1785 "2e0 >= -1 + x and 2e0 <= x and 2e0 <= n) }" },
1786 { 1, "[n] -> { [x, y] : exists (e0 = floor((x)/2), e1 = floor((y)/3): "
1787 "3e1 = y and x >= 2 and 2e0 >= -1 + x and "
1788 "2e0 <= x and 2e0 <= n);"
1789 "[1, y] : exists (e0 = floor((y)/3): 3e0 = y and "
1791 { 1, "[t1] -> { [i0] : (exists (e0 = floor((63t1)/64): "
1792 "128e0 >= -134 + 127t1 and t1 >= 2 and "
1793 "64e0 <= 63t1 and 64e0 >= -63 + 63t1)) or "
1795 { 1, "{ [i, i] : exists (e0 = floor((1 + 2i)/3): 3e0 <= 2i and "
1796 "3e0 >= -1 + 2i and i <= 9 and i >= 1);"
1798 { 1, "{ [t1] : exists (e0 = floor((-11 + t1)/2): 2e0 = -11 + t1 and "
1799 "t1 >= 13 and t1 <= 16);"
1800 "[t1] : t1 <= 15 and t1 >= 12 }" },
1801 { 1, "{ [x,y] : x = 3y and 0 <= y <= 2; [-3,-1] }" },
1802 { 1, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-2] }" },
1803 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-2,-2] }" },
1804 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-1] }" },
1805 { 1, "{ [i] : exists j : i = 4 j and 0 <= i <= 100;"
1806 "[i] : exists j : 1 <= i <= 100 and i >= 4j + 1 and "
1808 { 1, "{ [c0] : (exists (e0 : c0 - 1 <= 3e0 <= c0)) or "
1809 "(exists (e0 : 3e0 = -2 + c0)) }" },
1810 { 0, "[n, b0, t0] -> "
1811 "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1812 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1813 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1814 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1815 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 >= 8 + n and "
1816 "3i4 <= -96 + 3t0 + i0 and 3i4 >= -95 - n + 3t0 + i0 and "
1817 "i8 >= -157 + i0 - 4i4 and i8 >= 0 and "
1818 "i8 <= -33 + i0 - 4i4 and 3i8 <= -91 + 4n - i0)) or "
1819 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1820 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1821 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1822 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 <= 7 + n and "
1823 "4i4 <= -3 + i0 and 3i4 <= -96 + 3t0 + i0 and "
1824 "3i4 >= -95 - n + 3t0 + i0 and i8 >= -157 + i0 - 4i4 and "
1825 "i8 >= 0 and i8 <= -4 + i0 - 3i4 and i8 <= -41 + i0));"
1826 "[i0, i1, i2, i3, 0, i5, i6, i7, i8, i9, i10, i11, i12] : "
1827 "(exists (e0 = floor((i8)/32): b0 = 0 and 32e0 = i8 and "
1828 "n <= 2147483647 and t0 <= 31 and t0 >= 0 and i0 >= 11 and "
1829 "i0 >= 96 - 3t0 and i0 <= 95 + n - 3t0 and i0 <= 7 + n and "
1830 "i8 >= -40 + i0 and i8 <= -10 + i0)) }" },
1831 { 0, "{ [i0, i1, i2] : "
1832 "(exists (e0, e1 = floor((i0)/32), e2 = floor((i1)/32): "
1833 "32e1 = i0 and 32e2 = i1 and i1 >= -31 + i0 and "
1834 "i1 <= 31 + i0 and i2 >= -30 + i0 and i2 >= -30 + i1 and "
1835 "32e0 >= -30 + i0 and 32e0 >= -30 + i1 and "
1836 "32e0 >= -31 + i2 and 32e0 <= 30 + i2 and 32e0 <= 31 + i1 and "
1837 "32e0 <= 31 + i0)) or "
1839 { 1, "{ [a, b, c] : 2b = 1 + a and 2c = 2 + a; [0, 0, 0] }" },
1840 { 1, "{ [a, a, b, c] : 32*floor((a)/32) = a and 2*floor((b)/2) = b and "
1841 "2*floor((c)/2) = c and 0 <= a <= 192;"
1842 "[224, 224, b, c] : 2*floor((b)/2) = b and 2*floor((c)/2) = c }"
1844 { 1, "[n] -> { [a,b] : (exists e : 1 <= a <= 7e and 9e <= b <= n) or "
1845 "(0 <= a <= b <= n) }" },
1846 { 1, "{ [a, b] : 0 <= a <= 2 and b >= 0 and "
1847 "((0 < b <= 13) or (2*floor((a + b)/2) >= -5 + a + 2b)) }" },
1848 { 1, "{ [a] : (2 <= a <= 5) or (a mod 2 = 1 and 1 <= a <= 5) }" },
1849 { 1, "{ [a, b, c] : (b = -1 + a and 0 < a <= 3 and "
1850 "9*floor((-4a + 2c)/9) <= -3 - 4a + 2c) or "
1851 "(exists (e0 = floor((-16 + 2c)/9): a = 4 and "
1852 "b = 3 and 9e0 <= -19 + 2c)) }" },
1853 { 0, "{ [a, b, c] : (b <= 2 and b <= -2 + a) or "
1854 "(b = -1 + a and 0 < a <= 3 and "
1855 "9*floor((-4a + 2c)/9) <= -3 - 4a + 2c) or "
1856 "(exists (e0 = floor((-16 + 2c)/9): a = 4 and "
1857 "b = 3 and 9e0 <= -19 + 2c)) }" },
1858 { 1, "{ [y, x] : (x - y) mod 3 = 2 and 2 <= y <= 200 and 0 <= x <= 2;"
1860 { 1, "{ [x, y] : (x - y) mod 3 = 2 and 2 <= y <= 200 and 0 <= x <= 2;"
1862 { 1, "{ [1, y] : -1 <= y <= 1; [x, -x] : 0 <= x <= 1 }" },
1863 { 1, "{ [1, y] : 0 <= y <= 1; [x, -x] : 0 <= x <= 1 }" },
1864 { 1, "{ [x, y] : 0 <= x <= 10 and x - 4*floor(x/4) <= 1 and y <= 0; "
1865 "[x, y] : 0 <= x <= 10 and x - 4*floor(x/4) > 1 and y <= 0; "
1866 "[x, y] : 0 <= x <= 10 and x - 5*floor(x/5) <= 1 and 0 < y; "
1867 "[x, y] : 0 <= x <= 10 and x - 5*floor(x/5) > 1 and 0 < y }" },
1868 { 1, "{ [x, 0] : 0 <= x <= 10 and x mod 2 = 0; "
1869 "[x, 0] : 0 <= x <= 10 and x mod 2 = 1; "
1870 "[x, y] : 0 <= x <= 10 and 1 <= y <= 10 }" },
1871 { 1, "{ [a] : a <= 8 and "
1872 "(a mod 10 = 7 or a mod 10 = 8 or a mod 10 = 9) }" },
1875 /* A specialized coalescing test case that would result
1876 * in a segmentation fault or a failed assertion in earlier versions of isl.
1878 static int test_coalesce_special(struct isl_ctx
*ctx
)
1881 isl_map
*map1
, *map2
;
1883 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1884 "[[S_L309_IN[] -> T11[]] -> ce_imag2[1, o1]] : "
1885 "(y = 201 and o1 <= 239 and o1 >= 212) or "
1886 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 198 and y >= 3 and "
1887 "o1 <= 239 and o1 >= 212)) or "
1888 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 201 and y >= 3 and "
1889 "o1 <= 241 and o1 >= 240));"
1890 "[S_L220_OUT[] -> T7[]] -> "
1891 "[[S_L309_IN[] -> T11[]] -> ce_imag2[0, o1]] : "
1892 "(y = 2 and o1 <= 241 and o1 >= 212) or "
1893 "(exists (e0 = [(-2 + y)/3]: 3e0 = -2 + y and y <= 200 and "
1894 "y >= 5 and o1 <= 241 and o1 >= 212)) }";
1895 map1
= isl_map_read_from_str(ctx
, str
);
1896 map1
= isl_map_align_divs(map1
);
1897 map1
= isl_map_coalesce(map1
);
1898 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1899 "[[S_L309_IN[] -> T11[]] -> ce_imag2[o0, o1]] : "
1900 "exists (e0 = [(-1 - y + o0)/3]: 3e0 = -1 - y + o0 and "
1901 "y <= 201 and o0 <= 2 and o1 >= 212 and o1 <= 241 and "
1902 "o0 >= 3 - y and o0 <= -2 + y and o0 >= 0) }";
1903 map2
= isl_map_read_from_str(ctx
, str
);
1904 map2
= isl_map_union(map2
, map1
);
1905 map2
= isl_map_align_divs(map2
);
1906 map2
= isl_map_coalesce(map2
);
1914 /* A specialized coalescing test case that would result in an assertion
1915 * in an earlier version of isl.
1916 * The explicit call to isl_basic_set_union prevents the implicit
1917 * equality constraints in the first basic map from being detected prior
1918 * to the call to isl_set_coalesce, at least at the point
1919 * where this test case was introduced.
1921 static int test_coalesce_special2(struct isl_ctx
*ctx
)
1924 isl_basic_set
*bset1
, *bset2
;
1927 str
= "{ [x, y] : x, y >= 0 and x + 2y <= 1 and 2x + y <= 1 }";
1928 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1929 str
= "{ [x,0] : -1 <= x <= 1 and x mod 2 = 1 }" ;
1930 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1931 set
= isl_basic_set_union(bset1
, bset2
);
1932 set
= isl_set_coalesce(set
);
1940 /* Check that calling isl_set_coalesce does not leave other sets
1941 * that may share some information with the input to isl_set_coalesce
1942 * in an inconsistent state.
1943 * In particular, older versions of isl would modify all copies
1944 * of the basic sets in the isl_set_coalesce input in a way
1945 * that could leave them in an inconsistent state.
1946 * The result of printing any other set containing one of these
1947 * basic sets would then result in an invalid set description.
1949 static int test_coalesce_special3(isl_ctx
*ctx
)
1953 isl_set
*set1
, *set2
;
1956 set1
= isl_set_read_from_str(ctx
, "{ [0, 0, 0] }");
1957 str
= "{ [a, b, a + b] : a >= 0 and b >= 0 and 0 < a + b }";
1958 set2
= isl_set_read_from_str(ctx
, str
);
1959 set1
= isl_set_union(set1
, isl_set_copy(set2
));
1960 set1
= isl_set_coalesce(set1
);
1963 p
= isl_printer_to_str(ctx
);
1964 p
= isl_printer_print_set(p
, set2
);
1966 s
= isl_printer_get_str(p
);
1967 isl_printer_free(p
);
1968 set1
= isl_set_read_from_str(ctx
, s
);
1978 /* Test the functionality of isl_set_coalesce.
1979 * That is, check that the output is always equal to the input
1980 * and in some cases that the result consists of a single disjunct.
1982 static int test_coalesce(struct isl_ctx
*ctx
)
1986 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
1987 const char *str
= coalesce_tests
[i
].str
;
1988 int check_one
= coalesce_tests
[i
].single_disjunct
;
1989 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
1993 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1995 if (test_coalesce_special(ctx
) < 0)
1997 if (test_coalesce_special2(ctx
) < 0)
1999 if (test_coalesce_special3(ctx
) < 0)
2005 /* Construct a representation of the graph on the right of Figure 1
2006 * in "Computing the Transitive Closure of a Union of
2007 * Affine Integer Tuple Relations".
2009 static __isl_give isl_map
*cocoa_fig_1_right_graph(isl_ctx
*ctx
)
2012 isl_map
*up
, *right
;
2014 dom
= isl_set_read_from_str(ctx
,
2015 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
2016 "2 x - 3 y + 3 >= 0 }");
2017 right
= isl_map_read_from_str(ctx
,
2018 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
2019 up
= isl_map_read_from_str(ctx
,
2020 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
2021 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
2022 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
2023 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
2024 up
= isl_map_intersect_range(up
, dom
);
2025 return isl_map_union(up
, right
);
2028 /* Construct a representation of the power of the graph
2029 * on the right of Figure 1 in "Computing the Transitive Closure of
2030 * a Union of Affine Integer Tuple Relations".
2032 static __isl_give isl_map
*cocoa_fig_1_right_power(isl_ctx
*ctx
)
2034 return isl_map_read_from_str(ctx
,
2035 "{ [1] -> [[0,0] -> [0,1]]; [2] -> [[0,0] -> [1,1]]; "
2036 " [1] -> [[0,1] -> [1,1]]; [1] -> [[2,2] -> [3,2]]; "
2037 " [2] -> [[2,2] -> [3,3]]; [1] -> [[3,2] -> [3,3]] }");
2040 /* Construct a representation of the transitive closure of the graph
2041 * on the right of Figure 1 in "Computing the Transitive Closure of
2042 * a Union of Affine Integer Tuple Relations".
2044 static __isl_give isl_map
*cocoa_fig_1_right_tc(isl_ctx
*ctx
)
2046 return isl_set_unwrap(isl_map_range(cocoa_fig_1_right_power(ctx
)));
2049 static int test_closure(isl_ctx
*ctx
)
2052 isl_map
*map
, *map2
;
2055 /* COCOA example 1 */
2056 map
= isl_map_read_from_str(ctx
,
2057 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
2058 "1 <= i and i < n and 1 <= j and j < n or "
2059 "i2 = i + 1 and j2 = j - 1 and "
2060 "1 <= i and i < n and 2 <= j and j <= n }");
2061 map
= isl_map_power(map
, &exact
);
2065 /* COCOA example 1 */
2066 map
= isl_map_read_from_str(ctx
,
2067 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
2068 "1 <= i and i < n and 1 <= j and j < n or "
2069 "i2 = i + 1 and j2 = j - 1 and "
2070 "1 <= i and i < n and 2 <= j and j <= n }");
2071 map
= isl_map_transitive_closure(map
, &exact
);
2073 map2
= isl_map_read_from_str(ctx
,
2074 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
2075 "1 <= i and i < n and 1 <= j and j <= n and "
2076 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
2077 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
2078 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
2079 assert(isl_map_is_equal(map
, map2
));
2083 map
= isl_map_read_from_str(ctx
,
2084 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
2085 " 0 <= y and y <= n }");
2086 map
= isl_map_transitive_closure(map
, &exact
);
2087 map2
= isl_map_read_from_str(ctx
,
2088 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
2089 " 0 <= y and y <= n }");
2090 assert(isl_map_is_equal(map
, map2
));
2094 /* COCOA example 2 */
2095 map
= isl_map_read_from_str(ctx
,
2096 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
2097 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
2098 "i2 = i + 2 and j2 = j - 2 and "
2099 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
2100 map
= isl_map_transitive_closure(map
, &exact
);
2102 map2
= isl_map_read_from_str(ctx
,
2103 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
2104 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
2105 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
2106 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
2107 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
2108 assert(isl_map_is_equal(map
, map2
));
2112 /* COCOA Fig.2 left */
2113 map
= isl_map_read_from_str(ctx
,
2114 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
2115 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
2117 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
2118 "j <= 2 i - 3 and j <= n - 2 or "
2119 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2120 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2121 map
= isl_map_transitive_closure(map
, &exact
);
2125 /* COCOA Fig.2 right */
2126 map
= isl_map_read_from_str(ctx
,
2127 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
2128 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
2130 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
2131 "j <= 2 i - 4 and j <= n - 3 or "
2132 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2133 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2134 map
= isl_map_power(map
, &exact
);
2138 /* COCOA Fig.2 right */
2139 map
= isl_map_read_from_str(ctx
,
2140 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
2141 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
2143 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
2144 "j <= 2 i - 4 and j <= n - 3 or "
2145 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2146 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2147 map
= isl_map_transitive_closure(map
, &exact
);
2149 map2
= isl_map_read_from_str(ctx
,
2150 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
2151 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
2152 "j <= n and 3 + i + 2 j <= 3 n and "
2153 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
2154 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
2155 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
2156 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
2157 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
2158 assert(isl_map_is_equal(map
, map2
));
2162 map
= cocoa_fig_1_right_graph(ctx
);
2163 map
= isl_map_transitive_closure(map
, &exact
);
2165 map2
= cocoa_fig_1_right_tc(ctx
);
2166 assert(isl_map_is_equal(map
, map2
));
2170 map
= cocoa_fig_1_right_graph(ctx
);
2171 map
= isl_map_power(map
, &exact
);
2172 map2
= cocoa_fig_1_right_power(ctx
);
2173 equal
= isl_map_is_equal(map
, map2
);
2179 isl_die(ctx
, isl_error_unknown
, "power not exact", return -1);
2181 isl_die(ctx
, isl_error_unknown
, "unexpected power", return -1);
2183 /* COCOA Theorem 1 counter example */
2184 map
= isl_map_read_from_str(ctx
,
2185 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
2186 "i2 = 1 and j2 = j or "
2187 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
2188 map
= isl_map_transitive_closure(map
, &exact
);
2192 map
= isl_map_read_from_str(ctx
,
2193 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
2194 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
2195 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
2196 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
2197 map
= isl_map_transitive_closure(map
, &exact
);
2201 /* Kelly et al 1996, fig 12 */
2202 map
= isl_map_read_from_str(ctx
,
2203 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
2204 "1 <= i,j,j+1 <= n or "
2205 "j = n and j2 = 1 and i2 = i + 1 and "
2206 "1 <= i,i+1 <= n }");
2207 map
= isl_map_transitive_closure(map
, &exact
);
2209 map2
= isl_map_read_from_str(ctx
,
2210 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
2211 "1 <= i <= n and i = i2 or "
2212 "1 <= i < i2 <= n and 1 <= j <= n and "
2214 assert(isl_map_is_equal(map
, map2
));
2218 /* Omega's closure4 */
2219 map
= isl_map_read_from_str(ctx
,
2220 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
2221 "1 <= x,y <= 10 or "
2222 "x2 = x + 1 and y2 = y and "
2223 "1 <= x <= 20 && 5 <= y <= 15 }");
2224 map
= isl_map_transitive_closure(map
, &exact
);
2228 map
= isl_map_read_from_str(ctx
,
2229 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
2230 map
= isl_map_transitive_closure(map
, &exact
);
2232 map2
= isl_map_read_from_str(ctx
,
2233 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
2234 assert(isl_map_is_equal(map
, map2
));
2238 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
2239 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
2240 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
2241 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
2242 map
= isl_map_read_from_str(ctx
, str
);
2243 map
= isl_map_transitive_closure(map
, &exact
);
2245 map2
= isl_map_read_from_str(ctx
, str
);
2246 assert(isl_map_is_equal(map
, map2
));
2250 str
= "{[0] -> [1]; [2] -> [3]}";
2251 map
= isl_map_read_from_str(ctx
, str
);
2252 map
= isl_map_transitive_closure(map
, &exact
);
2254 map2
= isl_map_read_from_str(ctx
, str
);
2255 assert(isl_map_is_equal(map
, map2
));
2259 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
2260 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
2261 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
2262 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2263 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2264 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
2265 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
2266 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
2267 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2268 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2269 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
2270 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
2271 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
2272 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2273 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2274 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
2275 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
2276 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
2277 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2278 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
2279 map
= isl_map_read_from_str(ctx
, str
);
2280 map
= isl_map_transitive_closure(map
, NULL
);
2287 static int test_lex(struct isl_ctx
*ctx
)
2293 dim
= isl_space_set_alloc(ctx
, 0, 0);
2294 map
= isl_map_lex_le(dim
);
2295 empty
= isl_map_is_empty(map
);
2301 isl_die(ctx
, isl_error_unknown
,
2302 "expecting non-empty result", return -1);
2307 /* Inputs for isl_map_lexmin tests.
2308 * "map" is the input and "lexmin" is the expected result.
2313 } lexmin_tests
[] = {
2314 { "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }",
2315 "{ [x] -> [5] : 6 <= x <= 8; "
2316 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }" },
2317 { "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }",
2318 "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }" },
2319 { "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }",
2320 "{ [x] -> [y] : (4y = x and x >= 0) or "
2321 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
2322 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
2323 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }" },
2324 { "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }",
2325 "{ T[a] -> S[b, c] : 2b = a and 2c = a }" },
2326 /* Check that empty pieces are properly combined. */
2327 { "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
2328 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
2329 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }",
2330 "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
2331 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
2333 { "{ [i, k, j] -> [a, b, c, d] : 8*floor((b)/8) = b and k <= 255 and "
2334 "a <= 255 and c <= 255 and d <= 255 - j and "
2335 "255 - j <= 7d <= 7 - i and 240d <= 239 + a and "
2336 "247d <= 247 + k - j and 247d <= 247 + k - b and "
2337 "247d <= 247 + i and 248 - b <= 248d <= c and "
2338 "254d >= i - a + b and 254d >= -a + b and "
2339 "255d >= -i + a - b and 1792d >= -63736 + 257b }",
2341 "[-127762 + i + 502j, -62992 + 248j, 63240 - 248j, 255 - j] : "
2342 "k <= 255 and 7j >= 1778 + i and 246j >= 62738 - k and "
2343 "247j >= 62738 - i and 509j <= 129795 + i and "
2344 "742j >= 188724 - i; "
2345 "[0, k, j] -> [1, 0, 248, 1] : k <= 255 and 248 <= j <= 254, k }" },
2346 { "{ [a] -> [b] : 0 <= b <= 255 and -509 + a <= 512b < a and "
2347 "16*floor((8 + b)/16) <= 7 + b; "
2349 "{ [a] -> [b = 1] : a >= 510 or a <= 0; "
2350 "[a] -> [b = 0] : 0 < a <= 509 }" },
2351 { "{ rat: [i] : 1 <= 2i <= 9 }", "{ rat: [i] : 2i = 1 }" },
2352 { "{ rat: [i] : 1 <= 2i <= 9 or i >= 10 }", "{ rat: [i] : 2i = 1 }" },
2355 static int test_lexmin(struct isl_ctx
*ctx
)
2360 isl_basic_map
*bmap
;
2361 isl_map
*map
, *map2
;
2364 isl_pw_multi_aff
*pma
;
2366 str
= "[p0, p1] -> { [] -> [] : "
2367 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
2368 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
2369 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
2370 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
2371 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
2372 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
2373 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
2374 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
2375 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
2376 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
2377 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
2378 map
= isl_map_read_from_str(ctx
, str
);
2379 map
= isl_map_lexmin(map
);
2382 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
2383 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
2384 set
= isl_set_read_from_str(ctx
, str
);
2385 set
= isl_set_lexmax(set
);
2386 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
2387 set2
= isl_set_read_from_str(ctx
, str
);
2388 set
= isl_set_intersect(set
, set2
);
2389 assert(!isl_set_is_empty(set
));
2392 for (i
= 0; i
< ARRAY_SIZE(lexmin_tests
); ++i
) {
2393 map
= isl_map_read_from_str(ctx
, lexmin_tests
[i
].map
);
2394 map
= isl_map_lexmin(map
);
2395 map2
= isl_map_read_from_str(ctx
, lexmin_tests
[i
].lexmin
);
2396 equal
= isl_map_is_equal(map
, map2
);
2403 isl_die(ctx
, isl_error_unknown
,
2404 "unexpected result", return -1);
2407 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2408 " 8i' <= i and 8i' >= -7 + i }";
2409 bmap
= isl_basic_map_read_from_str(ctx
, str
);
2410 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
2411 map2
= isl_map_from_pw_multi_aff(pma
);
2412 map
= isl_map_from_basic_map(bmap
);
2413 assert(isl_map_is_equal(map
, map2
));
2417 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2418 " 8i' <= i and 8i' >= -7 + i }";
2419 set
= isl_set_read_from_str(ctx
, str
);
2420 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
2421 set2
= isl_set_from_pw_multi_aff(pma
);
2422 equal
= isl_set_is_equal(set
, set2
);
2428 isl_die(ctx
, isl_error_unknown
,
2429 "unexpected difference between set and "
2430 "piecewise affine expression", return -1);
2435 /* A specialized isl_set_min_val test case that would return the wrong result
2436 * in earlier versions of isl.
2437 * The explicit call to isl_basic_set_union prevents the second basic set
2438 * from being determined to be empty prior to the call to isl_set_min_val,
2439 * at least at the point where this test case was introduced.
2441 static int test_min_special(isl_ctx
*ctx
)
2444 isl_basic_set
*bset1
, *bset2
;
2450 str
= "{ [a, b] : a >= 2 and b >= 0 and 14 - a <= b <= 9 }";
2451 bset1
= isl_basic_set_read_from_str(ctx
, str
);
2452 str
= "{ [a, b] : 1 <= a, b and a + b <= 1 }";
2453 bset2
= isl_basic_set_read_from_str(ctx
, str
);
2454 set
= isl_basic_set_union(bset1
, bset2
);
2455 obj
= isl_aff_read_from_str(ctx
, "{ [a, b] -> [a] }");
2457 res
= isl_set_min_val(set
, obj
);
2458 ok
= isl_val_cmp_si(res
, 5) == 0;
2467 isl_die(ctx
, isl_error_unknown
, "unexpected minimum",
2473 /* A specialized isl_set_min_val test case that would return an error
2474 * in earlier versions of isl.
2476 static int test_min_special2(isl_ctx
*ctx
)
2479 isl_basic_set
*bset
;
2483 str
= "{ [i, j, k] : 2j = i and 2k = i + 1 and i >= 2 }";
2484 bset
= isl_basic_set_read_from_str(ctx
, str
);
2486 obj
= isl_aff_read_from_str(ctx
, "{ [i, j, k] -> [i] }");
2488 res
= isl_basic_set_max_val(bset
, obj
);
2490 isl_basic_set_free(bset
);
2503 __isl_give isl_val
*(*fn
)(__isl_keep isl_set
*set
,
2504 __isl_keep isl_aff
*obj
);
2507 { "{ [-1]; [1] }", "{ [x] -> [x] }", &isl_set_min_val
, "-1" },
2508 { "{ [-1]; [1] }", "{ [x] -> [x] }", &isl_set_max_val
, "1" },
2509 { "{ [a, b] : 0 <= a, b <= 100 and b mod 2 = 0}",
2510 "{ [a, b] -> [floor((b - 2*floor((-a)/4))/5)] }",
2511 &isl_set_max_val
, "30" },
2515 /* Perform basic isl_set_min_val and isl_set_max_val tests.
2516 * In particular, check the results on non-convex inputs.
2518 static int test_min(struct isl_ctx
*ctx
)
2526 for (i
= 0; i
< ARRAY_SIZE(opt_tests
); ++i
) {
2527 set
= isl_set_read_from_str(ctx
, opt_tests
[i
].set
);
2528 obj
= isl_aff_read_from_str(ctx
, opt_tests
[i
].obj
);
2529 res
= isl_val_read_from_str(ctx
, opt_tests
[i
].res
);
2530 val
= opt_tests
[i
].fn(set
, obj
);
2531 ok
= isl_val_eq(res
, val
);
2540 isl_die(ctx
, isl_error_unknown
,
2541 "unexpected optimum", return -1);
2544 if (test_min_special(ctx
) < 0)
2546 if (test_min_special2(ctx
) < 0)
2557 static isl_stat
collect_must_may(__isl_take isl_map
*dep
, int must
,
2558 void *dep_user
, void *user
)
2560 struct must_may
*mm
= (struct must_may
*)user
;
2563 mm
->must
= isl_map_union(mm
->must
, dep
);
2565 mm
->may
= isl_map_union(mm
->may
, dep
);
2570 static int common_space(void *first
, void *second
)
2572 int depth
= *(int *)first
;
2576 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
2584 map2
= isl_map_read_from_str(map
->ctx
, str
);
2585 equal
= isl_map_is_equal(map
, map2
);
2591 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
2595 equal
= map_is_equal(map
, str
);
2599 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
2600 "result not as expected", return -1);
2604 static int test_dep(struct isl_ctx
*ctx
)
2609 isl_access_info
*ai
;
2616 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2617 map
= isl_map_read_from_str(ctx
, str
);
2618 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2620 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2621 map
= isl_map_read_from_str(ctx
, str
);
2622 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2624 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2625 map
= isl_map_read_from_str(ctx
, str
);
2626 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2628 flow
= isl_access_info_compute_flow(ai
);
2629 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2630 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2631 mm
.may
= isl_map_empty(dim
);
2633 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2635 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
2636 " [1,10,0] -> [2,5,0] }";
2637 assert(map_is_equal(mm
.must
, str
));
2638 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2639 assert(map_is_equal(mm
.may
, str
));
2641 isl_map_free(mm
.must
);
2642 isl_map_free(mm
.may
);
2643 isl_flow_free(flow
);
2646 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2647 map
= isl_map_read_from_str(ctx
, str
);
2648 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2650 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2651 map
= isl_map_read_from_str(ctx
, str
);
2652 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2654 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2655 map
= isl_map_read_from_str(ctx
, str
);
2656 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2658 flow
= isl_access_info_compute_flow(ai
);
2659 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2660 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2661 mm
.may
= isl_map_empty(dim
);
2663 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2665 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2666 assert(map_is_equal(mm
.must
, str
));
2667 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2668 assert(map_is_equal(mm
.may
, str
));
2670 isl_map_free(mm
.must
);
2671 isl_map_free(mm
.may
);
2672 isl_flow_free(flow
);
2675 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2676 map
= isl_map_read_from_str(ctx
, str
);
2677 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2679 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2680 map
= isl_map_read_from_str(ctx
, str
);
2681 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2683 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2684 map
= isl_map_read_from_str(ctx
, str
);
2685 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2687 flow
= isl_access_info_compute_flow(ai
);
2688 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2689 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2690 mm
.may
= isl_map_empty(dim
);
2692 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2694 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2695 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2696 assert(map_is_equal(mm
.may
, str
));
2697 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2698 assert(map_is_equal(mm
.must
, str
));
2700 isl_map_free(mm
.must
);
2701 isl_map_free(mm
.may
);
2702 isl_flow_free(flow
);
2705 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2706 map
= isl_map_read_from_str(ctx
, str
);
2707 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2709 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2710 map
= isl_map_read_from_str(ctx
, str
);
2711 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2713 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2714 map
= isl_map_read_from_str(ctx
, str
);
2715 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2717 flow
= isl_access_info_compute_flow(ai
);
2718 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2719 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2720 mm
.may
= isl_map_empty(dim
);
2722 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2724 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2725 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2726 assert(map_is_equal(mm
.may
, str
));
2727 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2728 assert(map_is_equal(mm
.must
, str
));
2730 isl_map_free(mm
.must
);
2731 isl_map_free(mm
.may
);
2732 isl_flow_free(flow
);
2735 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2736 map
= isl_map_read_from_str(ctx
, str
);
2737 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2739 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2740 map
= isl_map_read_from_str(ctx
, str
);
2741 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2743 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2744 map
= isl_map_read_from_str(ctx
, str
);
2745 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2747 flow
= isl_access_info_compute_flow(ai
);
2748 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2749 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2750 mm
.may
= isl_map_empty(dim
);
2752 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2754 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2755 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2756 assert(map_is_equal(mm
.may
, str
));
2757 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2758 assert(map_is_equal(mm
.must
, str
));
2760 isl_map_free(mm
.must
);
2761 isl_map_free(mm
.may
);
2762 isl_flow_free(flow
);
2767 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2768 map
= isl_map_read_from_str(ctx
, str
);
2769 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2771 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2772 map
= isl_map_read_from_str(ctx
, str
);
2773 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2775 flow
= isl_access_info_compute_flow(ai
);
2776 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2777 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2778 mm
.may
= isl_map_empty(dim
);
2780 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2782 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2783 assert(map_is_equal(mm
.must
, str
));
2784 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2785 assert(map_is_equal(mm
.may
, str
));
2787 isl_map_free(mm
.must
);
2788 isl_map_free(mm
.may
);
2789 isl_flow_free(flow
);
2794 /* Check that the dependence analysis proceeds without errors.
2795 * Earlier versions of isl would break down during the analysis
2796 * due to the use of the wrong spaces.
2798 static int test_flow(isl_ctx
*ctx
)
2801 isl_union_map
*access
, *schedule
;
2802 isl_union_map
*must_dep
, *may_dep
;
2805 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2806 access
= isl_union_map_read_from_str(ctx
, str
);
2807 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2808 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2809 "S2[] -> [1,0,0,0]; "
2810 "S3[] -> [-1,0,0,0] }";
2811 schedule
= isl_union_map_read_from_str(ctx
, str
);
2812 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2813 isl_union_map_copy(access
), schedule
,
2814 &must_dep
, &may_dep
, NULL
, NULL
);
2815 isl_union_map_free(may_dep
);
2816 isl_union_map_free(must_dep
);
2825 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2826 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2827 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2828 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2829 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2830 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2831 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2832 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2833 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2836 int test_sv(isl_ctx
*ctx
)
2838 isl_union_map
*umap
;
2842 for (i
= 0; i
< ARRAY_SIZE(sv_tests
); ++i
) {
2843 umap
= isl_union_map_read_from_str(ctx
, sv_tests
[i
].map
);
2844 sv
= isl_union_map_is_single_valued(umap
);
2845 isl_union_map_free(umap
);
2848 if (sv_tests
[i
].sv
&& !sv
)
2849 isl_die(ctx
, isl_error_internal
,
2850 "map not detected as single valued", return -1);
2851 if (!sv_tests
[i
].sv
&& sv
)
2852 isl_die(ctx
, isl_error_internal
,
2853 "map detected as single valued", return -1);
2862 } bijective_tests
[] = {
2863 { "[N,M]->{[i,j] -> [i]}", 0 },
2864 { "[N,M]->{[i,j] -> [i] : j=i}", 1 },
2865 { "[N,M]->{[i,j] -> [i] : j=0}", 1 },
2866 { "[N,M]->{[i,j] -> [i] : j=N}", 1 },
2867 { "[N,M]->{[i,j] -> [j,i]}", 1 },
2868 { "[N,M]->{[i,j] -> [i+j]}", 0 },
2869 { "[N,M]->{[i,j] -> []}", 0 },
2870 { "[N,M]->{[i,j] -> [i,j,N]}", 1 },
2871 { "[N,M]->{[i,j] -> [2i]}", 0 },
2872 { "[N,M]->{[i,j] -> [i,i]}", 0 },
2873 { "[N,M]->{[i,j] -> [2i,i]}", 0 },
2874 { "[N,M]->{[i,j] -> [2i,j]}", 1 },
2875 { "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1 },
2878 static int test_bijective(struct isl_ctx
*ctx
)
2884 for (i
= 0; i
< ARRAY_SIZE(bijective_tests
); ++i
) {
2885 map
= isl_map_read_from_str(ctx
, bijective_tests
[i
].str
);
2886 bijective
= isl_map_is_bijective(map
);
2890 if (bijective_tests
[i
].bijective
&& !bijective
)
2891 isl_die(ctx
, isl_error_internal
,
2892 "map not detected as bijective", return -1);
2893 if (!bijective_tests
[i
].bijective
&& bijective
)
2894 isl_die(ctx
, isl_error_internal
,
2895 "map detected as bijective", return -1);
2901 /* Inputs for isl_pw_qpolynomial_gist tests.
2902 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2908 } pwqp_gist_tests
[] = {
2909 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2910 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2911 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2912 "{ [i] -> -1/2 + 1/2 * i }" },
2913 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2916 static int test_pwqp(struct isl_ctx
*ctx
)
2921 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
2924 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2925 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2927 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
2930 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2931 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2933 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2935 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2937 isl_pw_qpolynomial_free(pwqp1
);
2939 for (i
= 0; i
< ARRAY_SIZE(pwqp_gist_tests
); ++i
) {
2940 str
= pwqp_gist_tests
[i
].pwqp
;
2941 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2942 str
= pwqp_gist_tests
[i
].set
;
2943 set
= isl_set_read_from_str(ctx
, str
);
2944 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2945 str
= pwqp_gist_tests
[i
].gist
;
2946 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2947 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2948 equal
= isl_pw_qpolynomial_is_zero(pwqp1
);
2949 isl_pw_qpolynomial_free(pwqp1
);
2954 isl_die(ctx
, isl_error_unknown
,
2955 "unexpected result", return -1);
2958 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
2959 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2960 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
2961 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2963 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2965 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2967 isl_pw_qpolynomial_free(pwqp1
);
2969 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
2970 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2971 str
= "{ [x] -> x }";
2972 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2974 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2976 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2978 isl_pw_qpolynomial_free(pwqp1
);
2980 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2981 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2982 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2983 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
2984 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2985 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2986 isl_pw_qpolynomial_free(pwqp1
);
2988 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2989 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2990 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2991 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2992 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
2993 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
2994 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2995 isl_pw_qpolynomial_free(pwqp1
);
2996 isl_pw_qpolynomial_free(pwqp2
);
3000 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3002 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
3003 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3004 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
3005 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3006 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
3008 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
3009 isl_pw_qpolynomial_free(pwqp1
);
3010 isl_pw_qpolynomial_free(pwqp2
);
3014 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3019 static int test_split_periods(isl_ctx
*ctx
)
3022 isl_pw_qpolynomial
*pwqp
;
3024 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
3025 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
3026 "U >= 0; [U,V] -> U^2 : U >= 100 }";
3027 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3029 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
3031 isl_pw_qpolynomial_free(pwqp
);
3039 static int test_union(isl_ctx
*ctx
)
3042 isl_union_set
*uset1
, *uset2
;
3043 isl_union_map
*umap1
, *umap2
;
3046 str
= "{ [i] : 0 <= i <= 1 }";
3047 uset1
= isl_union_set_read_from_str(ctx
, str
);
3048 str
= "{ [1] -> [0] }";
3049 umap1
= isl_union_map_read_from_str(ctx
, str
);
3051 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
3052 equal
= isl_union_map_is_equal(umap1
, umap2
);
3054 isl_union_map_free(umap1
);
3055 isl_union_map_free(umap2
);
3060 isl_die(ctx
, isl_error_unknown
, "union maps not equal",
3063 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
3064 umap1
= isl_union_map_read_from_str(ctx
, str
);
3065 str
= "{ A[i]; B[i] }";
3066 uset1
= isl_union_set_read_from_str(ctx
, str
);
3068 uset2
= isl_union_map_domain(umap1
);
3070 equal
= isl_union_set_is_equal(uset1
, uset2
);
3072 isl_union_set_free(uset1
);
3073 isl_union_set_free(uset2
);
3078 isl_die(ctx
, isl_error_unknown
, "union sets not equal",
3084 /* Check that computing a bound of a non-zero polynomial over an unbounded
3085 * domain does not produce a rational value.
3086 * In particular, check that the upper bound is infinity.
3088 static int test_bound_unbounded_domain(isl_ctx
*ctx
)
3091 isl_pw_qpolynomial
*pwqp
;
3092 isl_pw_qpolynomial_fold
*pwf
, *pwf2
;
3095 str
= "{ [m,n] -> -m * n }";
3096 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3097 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3099 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3100 pwf2
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3101 equal
= isl_pw_qpolynomial_fold_plain_is_equal(pwf
, pwf2
);
3102 isl_pw_qpolynomial_fold_free(pwf
);
3103 isl_pw_qpolynomial_fold_free(pwf2
);
3108 isl_die(ctx
, isl_error_unknown
,
3109 "expecting infinite polynomial bound", return -1);
3114 static int test_bound(isl_ctx
*ctx
)
3118 isl_pw_qpolynomial
*pwqp
;
3119 isl_pw_qpolynomial_fold
*pwf
;
3121 if (test_bound_unbounded_domain(ctx
) < 0)
3124 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
3125 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3126 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3127 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
3128 isl_pw_qpolynomial_fold_free(pwf
);
3130 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
3133 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
3134 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3135 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3136 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
3137 isl_pw_qpolynomial_fold_free(pwf
);
3139 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
3145 static int test_lift(isl_ctx
*ctx
)
3148 isl_basic_map
*bmap
;
3149 isl_basic_set
*bset
;
3151 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
3152 bset
= isl_basic_set_read_from_str(ctx
, str
);
3153 bset
= isl_basic_set_lift(bset
);
3154 bmap
= isl_basic_map_from_range(bset
);
3155 bset
= isl_basic_map_domain(bmap
);
3156 isl_basic_set_free(bset
);
3165 } subset_tests
[] = {
3167 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
3168 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
3169 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
3171 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
3172 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
3173 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
3174 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
3175 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
3176 "256e0 <= 255i and 256e0 >= -255 + 255i and "
3177 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
3178 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
3179 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
3180 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
3181 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
3182 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
3183 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
3184 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
3185 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
3186 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
3187 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
3188 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
3189 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
3190 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
3191 "4e0 <= -57 + i0 + i1)) or "
3192 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
3193 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
3194 "4e0 >= -61 + i0 + i1)) or "
3195 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
3196 { "[a, b] -> { : a = 0 and b = -1 }", "[b, a] -> { : b >= -10 }", 1 },
3199 static int test_subset(isl_ctx
*ctx
)
3202 isl_set
*set1
, *set2
;
3205 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
3206 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
3207 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
3208 subset
= isl_set_is_subset(set1
, set2
);
3213 if (subset
!= subset_tests
[i
].subset
)
3214 isl_die(ctx
, isl_error_unknown
,
3215 "incorrect subset result", return -1);
3222 const char *minuend
;
3223 const char *subtrahend
;
3224 const char *difference
;
3225 } subtract_domain_tests
[] = {
3226 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
3227 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
3228 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
3231 static int test_subtract(isl_ctx
*ctx
)
3234 isl_union_map
*umap1
, *umap2
;
3235 isl_union_pw_multi_aff
*upma1
, *upma2
;
3236 isl_union_set
*uset
;
3239 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
3240 umap1
= isl_union_map_read_from_str(ctx
,
3241 subtract_domain_tests
[i
].minuend
);
3242 uset
= isl_union_set_read_from_str(ctx
,
3243 subtract_domain_tests
[i
].subtrahend
);
3244 umap2
= isl_union_map_read_from_str(ctx
,
3245 subtract_domain_tests
[i
].difference
);
3246 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
3247 equal
= isl_union_map_is_equal(umap1
, umap2
);
3248 isl_union_map_free(umap1
);
3249 isl_union_map_free(umap2
);
3253 isl_die(ctx
, isl_error_unknown
,
3254 "incorrect subtract domain result", return -1);
3257 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
3258 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
3259 subtract_domain_tests
[i
].minuend
);
3260 uset
= isl_union_set_read_from_str(ctx
,
3261 subtract_domain_tests
[i
].subtrahend
);
3262 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
3263 subtract_domain_tests
[i
].difference
);
3264 upma1
= isl_union_pw_multi_aff_subtract_domain(upma1
, uset
);
3265 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
3266 isl_union_pw_multi_aff_free(upma1
);
3267 isl_union_pw_multi_aff_free(upma2
);
3271 isl_die(ctx
, isl_error_unknown
,
3272 "incorrect subtract domain result", return -1);
3278 /* Check that intersecting the empty basic set with another basic set
3279 * does not increase the number of constraints. In particular,
3280 * the empty basic set should maintain its canonical representation.
3282 static int test_intersect(isl_ctx
*ctx
)
3285 isl_basic_set
*bset1
, *bset2
;
3287 bset1
= isl_basic_set_read_from_str(ctx
, "{ [a,b,c] : 1 = 0 }");
3288 bset2
= isl_basic_set_read_from_str(ctx
, "{ [1,2,3] }");
3289 n1
= isl_basic_set_n_constraint(bset1
);
3290 bset1
= isl_basic_set_intersect(bset1
, bset2
);
3291 n2
= isl_basic_set_n_constraint(bset1
);
3292 isl_basic_set_free(bset1
);
3296 isl_die(ctx
, isl_error_unknown
,
3297 "number of constraints of empty set changed",
3303 int test_factorize(isl_ctx
*ctx
)
3306 isl_basic_set
*bset
;
3309 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
3310 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
3311 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
3312 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
3313 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
3314 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
3315 "3i5 >= -2i0 - i2 + 3i4 }";
3316 bset
= isl_basic_set_read_from_str(ctx
, str
);
3317 f
= isl_basic_set_factorizer(bset
);
3318 isl_basic_set_free(bset
);
3319 isl_factorizer_free(f
);
3321 isl_die(ctx
, isl_error_unknown
,
3322 "failed to construct factorizer", return -1);
3324 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
3325 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
3326 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
3327 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
3328 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
3329 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
3330 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
3331 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
3332 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
3333 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
3334 bset
= isl_basic_set_read_from_str(ctx
, str
);
3335 f
= isl_basic_set_factorizer(bset
);
3336 isl_basic_set_free(bset
);
3337 isl_factorizer_free(f
);
3339 isl_die(ctx
, isl_error_unknown
,
3340 "failed to construct factorizer", return -1);
3345 static isl_stat
check_injective(__isl_take isl_map
*map
, void *user
)
3347 int *injective
= user
;
3349 *injective
= isl_map_is_injective(map
);
3352 if (*injective
< 0 || !*injective
)
3353 return isl_stat_error
;
3358 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
3359 const char *r
, const char *s
, int tilable
, int parallel
)
3363 isl_union_map
*W
, *R
, *S
;
3364 isl_union_map
*empty
;
3365 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
3366 isl_union_map
*validity
, *proximity
, *coincidence
;
3367 isl_union_map
*schedule
;
3368 isl_union_map
*test
;
3369 isl_union_set
*delta
;
3370 isl_union_set
*domain
;
3374 isl_schedule_constraints
*sc
;
3375 isl_schedule
*sched
;
3376 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
3378 D
= isl_union_set_read_from_str(ctx
, d
);
3379 W
= isl_union_map_read_from_str(ctx
, w
);
3380 R
= isl_union_map_read_from_str(ctx
, r
);
3381 S
= isl_union_map_read_from_str(ctx
, s
);
3383 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
3384 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
3386 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
3387 isl_union_map_compute_flow(isl_union_map_copy(R
),
3388 isl_union_map_copy(W
), empty
,
3389 isl_union_map_copy(S
),
3390 &dep_raw
, NULL
, NULL
, NULL
);
3391 isl_union_map_compute_flow(isl_union_map_copy(W
),
3392 isl_union_map_copy(W
),
3393 isl_union_map_copy(R
),
3394 isl_union_map_copy(S
),
3395 &dep_waw
, &dep_war
, NULL
, NULL
);
3397 dep
= isl_union_map_union(dep_waw
, dep_war
);
3398 dep
= isl_union_map_union(dep
, dep_raw
);
3399 validity
= isl_union_map_copy(dep
);
3400 coincidence
= isl_union_map_copy(dep
);
3401 proximity
= isl_union_map_copy(dep
);
3403 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
3404 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3405 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
3406 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3407 sched
= isl_schedule_constraints_compute_schedule(sc
);
3408 schedule
= isl_schedule_get_map(sched
);
3409 isl_schedule_free(sched
);
3410 isl_union_map_free(W
);
3411 isl_union_map_free(R
);
3412 isl_union_map_free(S
);
3415 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
3417 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
3418 is_complete
= isl_union_set_is_subset(D
, domain
);
3419 isl_union_set_free(D
);
3420 isl_union_set_free(domain
);
3422 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
3423 test
= isl_union_map_apply_range(test
, dep
);
3424 test
= isl_union_map_apply_range(test
, schedule
);
3426 delta
= isl_union_map_deltas(test
);
3427 if (isl_union_set_n_set(delta
) == 0) {
3431 isl_union_set_free(delta
);
3433 delta_set
= isl_set_from_union_set(delta
);
3435 slice
= isl_set_universe(isl_set_get_space(delta_set
));
3436 for (i
= 0; i
< tilable
; ++i
)
3437 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
3438 is_tilable
= isl_set_is_subset(delta_set
, slice
);
3439 isl_set_free(slice
);
3441 slice
= isl_set_universe(isl_set_get_space(delta_set
));
3442 for (i
= 0; i
< parallel
; ++i
)
3443 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
3444 is_parallel
= isl_set_is_subset(delta_set
, slice
);
3445 isl_set_free(slice
);
3447 origin
= isl_set_universe(isl_set_get_space(delta_set
));
3448 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
3449 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
3451 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
3452 delta_set
= isl_set_lexmin(delta_set
);
3454 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
3456 isl_set_free(origin
);
3457 isl_set_free(delta_set
);
3460 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
3461 is_injection
< 0 || is_complete
< 0)
3464 isl_die(ctx
, isl_error_unknown
,
3465 "generated schedule incomplete", return -1);
3467 isl_die(ctx
, isl_error_unknown
,
3468 "generated schedule not injective on each statement",
3471 isl_die(ctx
, isl_error_unknown
,
3472 "negative dependences in generated schedule",
3475 isl_die(ctx
, isl_error_unknown
,
3476 "generated schedule not as tilable as expected",
3479 isl_die(ctx
, isl_error_unknown
,
3480 "generated schedule not as parallel as expected",
3486 /* Compute a schedule for the given instance set, validity constraints,
3487 * proximity constraints and context and return a corresponding union map
3490 static __isl_give isl_union_map
*compute_schedule_with_context(isl_ctx
*ctx
,
3491 const char *domain
, const char *validity
, const char *proximity
,
3492 const char *context
)
3497 isl_union_map
*prox
;
3498 isl_schedule_constraints
*sc
;
3499 isl_schedule
*schedule
;
3500 isl_union_map
*sched
;
3502 con
= isl_set_read_from_str(ctx
, context
);
3503 dom
= isl_union_set_read_from_str(ctx
, domain
);
3504 dep
= isl_union_map_read_from_str(ctx
, validity
);
3505 prox
= isl_union_map_read_from_str(ctx
, proximity
);
3506 sc
= isl_schedule_constraints_on_domain(dom
);
3507 sc
= isl_schedule_constraints_set_context(sc
, con
);
3508 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
3509 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
3510 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3511 sched
= isl_schedule_get_map(schedule
);
3512 isl_schedule_free(schedule
);
3517 /* Compute a schedule for the given instance set, validity constraints and
3518 * proximity constraints and return a corresponding union map representation.
3520 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
3521 const char *domain
, const char *validity
, const char *proximity
)
3523 return compute_schedule_with_context(ctx
, domain
, validity
, proximity
,
3527 /* Check that a schedule can be constructed on the given domain
3528 * with the given validity and proximity constraints.
3530 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
3531 const char *validity
, const char *proximity
)
3533 isl_union_map
*sched
;
3535 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
3539 isl_union_map_free(sched
);
3543 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
3544 const char *validity
, const char *proximity
, const char *expected_sched
)
3546 isl_union_map
*sched1
, *sched2
;
3549 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
3550 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
3552 equal
= isl_union_map_is_equal(sched1
, sched2
);
3553 isl_union_map_free(sched1
);
3554 isl_union_map_free(sched2
);
3559 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
3565 /* Check that the schedule map is properly padded, even after being
3566 * reconstructed from the band forest.
3568 static int test_padded_schedule(isl_ctx
*ctx
)
3572 isl_union_map
*validity
, *proximity
;
3573 isl_schedule_constraints
*sc
;
3574 isl_schedule
*sched
;
3575 isl_union_map
*map1
, *map2
;
3576 isl_band_list
*list
;
3579 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
3580 D
= isl_union_set_read_from_str(ctx
, str
);
3581 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
3582 proximity
= isl_union_map_copy(validity
);
3583 sc
= isl_schedule_constraints_on_domain(D
);
3584 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3585 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3586 sched
= isl_schedule_constraints_compute_schedule(sc
);
3587 map1
= isl_schedule_get_map(sched
);
3588 list
= isl_schedule_get_band_forest(sched
);
3589 isl_band_list_free(list
);
3590 map2
= isl_schedule_get_map(sched
);
3591 isl_schedule_free(sched
);
3592 equal
= isl_union_map_is_equal(map1
, map2
);
3593 isl_union_map_free(map1
);
3594 isl_union_map_free(map2
);
3599 isl_die(ctx
, isl_error_unknown
,
3600 "reconstructed schedule map not the same as original",
3606 /* Check that conditional validity constraints are also taken into
3607 * account across bands.
3608 * In particular, try to make sure that live ranges D[1,0]->C[2,1] and
3609 * D[2,0]->C[3,0] are not local in the outer band of the generated schedule
3610 * and then check that the adjacent order constraint C[2,1]->D[2,0]
3611 * is enforced by the rest of the schedule.
3613 static int test_special_conditional_schedule_constraints(isl_ctx
*ctx
)
3616 isl_union_set
*domain
;
3617 isl_union_map
*validity
, *proximity
, *condition
;
3618 isl_union_map
*sink
, *source
, *dep
;
3619 isl_schedule_constraints
*sc
;
3620 isl_schedule
*schedule
;
3621 isl_union_access_info
*access
;
3622 isl_union_flow
*flow
;
3625 str
= "[n] -> { C[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3626 "A[k] : k >= 1 and k <= -1 + n; "
3627 "B[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3628 "D[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k }";
3629 domain
= isl_union_set_read_from_str(ctx
, str
);
3630 sc
= isl_schedule_constraints_on_domain(domain
);
3631 str
= "[n] -> { D[k, i] -> C[1 + k, k - i] : "
3632 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3633 "D[k, i] -> C[1 + k, i] : "
3634 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3635 "D[k, 0] -> C[1 + k, k] : k >= 1 and k <= -2 + n; "
3636 "D[k, 0] -> C[1 + k, 0] : k >= 1 and k <= -2 + n }";
3637 validity
= isl_union_map_read_from_str(ctx
, str
);
3638 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3639 str
= "[n] -> { C[k, i] -> D[k, i] : "
3640 "0 <= i <= -1 + k and k <= -1 + n }";
3641 proximity
= isl_union_map_read_from_str(ctx
, str
);
3642 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3643 str
= "[n] -> { [D[k, i] -> a[]] -> [C[1 + k, k - i] -> b[]] : "
3644 "i <= -1 + k and i >= 1 and k <= -2 + n; "
3645 "[B[k, i] -> c[]] -> [B[k, 1 + i] -> c[]] : "
3646 "k <= -1 + n and i >= 0 and i <= -2 + k }";
3647 condition
= isl_union_map_read_from_str(ctx
, str
);
3648 str
= "[n] -> { [B[k, i] -> e[]] -> [D[k, i] -> a[]] : "
3649 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3650 "[C[k, i] -> b[]] -> [D[k', -1 + k - i] -> a[]] : "
3651 "i >= 0 and i <= -1 + k and k <= -1 + n and "
3652 "k' <= -1 + n and k' >= k - i and k' >= 1 + k; "
3653 "[C[k, i] -> b[]] -> [D[k, -1 + k - i] -> a[]] : "
3654 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3655 "[B[k, i] -> c[]] -> [A[k'] -> d[]] : "
3656 "k <= -1 + n and i >= 0 and i <= -1 + k and "
3657 "k' >= 1 and k' <= -1 + n and k' >= 1 + k }";
3658 validity
= isl_union_map_read_from_str(ctx
, str
);
3659 sc
= isl_schedule_constraints_set_conditional_validity(sc
, condition
,
3661 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3662 str
= "{ D[2,0] -> [] }";
3663 sink
= isl_union_map_read_from_str(ctx
, str
);
3664 access
= isl_union_access_info_from_sink(sink
);
3665 str
= "{ C[2,1] -> [] }";
3666 source
= isl_union_map_read_from_str(ctx
, str
);
3667 access
= isl_union_access_info_set_must_source(access
, source
);
3668 access
= isl_union_access_info_set_schedule(access
, schedule
);
3669 flow
= isl_union_access_info_compute_flow(access
);
3670 dep
= isl_union_flow_get_must_dependence(flow
);
3671 isl_union_flow_free(flow
);
3672 empty
= isl_union_map_is_empty(dep
);
3673 isl_union_map_free(dep
);
3678 isl_die(ctx
, isl_error_unknown
,
3679 "conditional validity not respected", return -1);
3684 /* Input for testing of schedule construction based on
3685 * conditional constraints.
3687 * domain is the iteration domain
3688 * flow are the flow dependences, which determine the validity and
3689 * proximity constraints
3690 * condition are the conditions on the conditional validity constraints
3691 * conditional_validity are the conditional validity constraints
3692 * outer_band_n is the expected number of members in the outer band
3697 const char *condition
;
3698 const char *conditional_validity
;
3700 } live_range_tests
[] = {
3701 /* Contrived example that illustrates that we need to keep
3702 * track of tagged condition dependences and
3703 * tagged conditional validity dependences
3704 * in isl_sched_edge separately.
3705 * In particular, the conditional validity constraints on A
3706 * cannot be satisfied,
3707 * but they can be ignored because there are no corresponding
3708 * condition constraints. However, we do have an additional
3709 * conditional validity constraint that maps to the same
3710 * dependence relation
3711 * as the condition constraint on B. If we did not make a distinction
3712 * between tagged condition and tagged conditional validity
3713 * dependences, then we
3714 * could end up treating this shared dependence as an condition
3715 * constraint on A, forcing a localization of the conditions,
3716 * which is impossible.
3718 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
3719 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
3720 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
3721 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3722 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3723 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
3726 /* TACO 2013 Fig. 7 */
3727 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3728 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3729 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3730 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
3731 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
3732 "0 <= i < n and 0 <= j < n - 1 }",
3733 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
3734 "0 <= i < n and 0 <= j < j' < n;"
3735 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
3736 "0 <= i < i' < n and 0 <= j,j' < n;"
3737 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
3738 "0 <= i,j,j' < n and j < j' }",
3741 /* TACO 2013 Fig. 7, without tags */
3742 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3743 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3744 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3745 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3746 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3747 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
3748 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
3749 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
3752 /* TACO 2013 Fig. 12 */
3753 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
3754 "S3[i,3] : 0 <= i <= 1 }",
3755 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
3756 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
3757 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
3758 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
3759 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3760 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
3761 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3762 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
3763 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
3764 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
3765 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
3770 /* Test schedule construction based on conditional constraints.
3771 * In particular, check the number of members in the outer band node
3772 * as an indication of whether tiling is possible or not.
3774 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
3777 isl_union_set
*domain
;
3778 isl_union_map
*condition
;
3779 isl_union_map
*flow
;
3780 isl_union_map
*validity
;
3781 isl_schedule_constraints
*sc
;
3782 isl_schedule
*schedule
;
3783 isl_schedule_node
*node
;
3786 if (test_special_conditional_schedule_constraints(ctx
) < 0)
3789 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
3790 domain
= isl_union_set_read_from_str(ctx
,
3791 live_range_tests
[i
].domain
);
3792 flow
= isl_union_map_read_from_str(ctx
,
3793 live_range_tests
[i
].flow
);
3794 condition
= isl_union_map_read_from_str(ctx
,
3795 live_range_tests
[i
].condition
);
3796 validity
= isl_union_map_read_from_str(ctx
,
3797 live_range_tests
[i
].conditional_validity
);
3798 sc
= isl_schedule_constraints_on_domain(domain
);
3799 sc
= isl_schedule_constraints_set_validity(sc
,
3800 isl_union_map_copy(flow
));
3801 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
3802 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
3803 condition
, validity
);
3804 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3805 node
= isl_schedule_get_root(schedule
);
3807 isl_schedule_node_get_type(node
) != isl_schedule_node_band
)
3808 node
= isl_schedule_node_first_child(node
);
3809 n_member
= isl_schedule_node_band_n_member(node
);
3810 isl_schedule_node_free(node
);
3811 isl_schedule_free(schedule
);
3815 if (n_member
!= live_range_tests
[i
].outer_band_n
)
3816 isl_die(ctx
, isl_error_unknown
,
3817 "unexpected number of members in outer band",
3823 /* Check that the schedule computed for the given instance set and
3824 * dependence relation strongly satisfies the dependences.
3825 * In particular, check that no instance is scheduled before
3826 * or together with an instance on which it depends.
3827 * Earlier versions of isl would produce a schedule that
3828 * only weakly satisfies the dependences.
3830 static int test_strongly_satisfying_schedule(isl_ctx
*ctx
)
3832 const char *domain
, *dep
;
3833 isl_union_map
*D
, *schedule
;
3837 domain
= "{ B[i0, i1] : 0 <= i0 <= 1 and 0 <= i1 <= 11; "
3838 "A[i0] : 0 <= i0 <= 1 }";
3839 dep
= "{ B[i0, i1] -> B[i0, 1 + i1] : 0 <= i0 <= 1 and 0 <= i1 <= 10; "
3840 "B[0, 11] -> A[1]; A[i0] -> B[i0, 0] : 0 <= i0 <= 1 }";
3841 schedule
= compute_schedule(ctx
, domain
, dep
, dep
);
3842 D
= isl_union_map_read_from_str(ctx
, dep
);
3843 D
= isl_union_map_apply_domain(D
, isl_union_map_copy(schedule
));
3844 D
= isl_union_map_apply_range(D
, schedule
);
3845 map
= isl_map_from_union_map(D
);
3846 ge
= isl_map_lex_ge(isl_space_domain(isl_map_get_space(map
)));
3847 map
= isl_map_intersect(map
, ge
);
3848 empty
= isl_map_is_empty(map
);
3854 isl_die(ctx
, isl_error_unknown
,
3855 "dependences not strongly satisfied", return -1);
3860 /* Compute a schedule for input where the instance set constraints
3861 * conflict with the context constraints.
3862 * Earlier versions of isl did not properly handle this situation.
3864 static int test_conflicting_context_schedule(isl_ctx
*ctx
)
3866 isl_union_map
*schedule
;
3867 const char *domain
, *context
;
3869 domain
= "[n] -> { A[] : n >= 0 }";
3870 context
= "[n] -> { : n < 0 }";
3871 schedule
= compute_schedule_with_context(ctx
,
3872 domain
, "{}", "{}", context
);
3873 isl_union_map_free(schedule
);
3881 /* Check that the dependence carrying step is not confused by
3882 * a bound on the coefficient size.
3883 * In particular, force the scheduler to move to a dependence carrying
3884 * step by demanding outer coincidence and bound the size of
3885 * the coefficients. Earlier versions of isl would take this
3886 * bound into account while carrying dependences, breaking
3887 * fundamental assumptions.
3888 * On the other hand, the dependence carrying step now tries
3889 * to prevent loop coalescing by default, so check that indeed
3890 * no loop coalescing occurs by comparing the computed schedule
3891 * to the expected non-coalescing schedule.
3893 static int test_bounded_coefficients_schedule(isl_ctx
*ctx
)
3895 const char *domain
, *dep
;
3898 isl_schedule_constraints
*sc
;
3899 isl_schedule
*schedule
;
3900 isl_union_map
*sched1
, *sched2
;
3903 domain
= "{ C[i0, i1] : 2 <= i0 <= 3999 and 0 <= i1 <= -1 + i0 }";
3904 dep
= "{ C[i0, i1] -> C[i0, 1 + i1] : i0 <= 3999 and i1 >= 0 and "
3906 "C[i0, -1 + i0] -> C[1 + i0, 0] : i0 <= 3998 and i0 >= 1 }";
3907 I
= isl_union_set_read_from_str(ctx
, domain
);
3908 D
= isl_union_map_read_from_str(ctx
, dep
);
3909 sc
= isl_schedule_constraints_on_domain(I
);
3910 sc
= isl_schedule_constraints_set_validity(sc
, isl_union_map_copy(D
));
3911 sc
= isl_schedule_constraints_set_coincidence(sc
, D
);
3912 isl_options_set_schedule_outer_coincidence(ctx
, 1);
3913 isl_options_set_schedule_max_coefficient(ctx
, 20);
3914 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3915 isl_options_set_schedule_max_coefficient(ctx
, -1);
3916 isl_options_set_schedule_outer_coincidence(ctx
, 0);
3917 sched1
= isl_schedule_get_map(schedule
);
3918 isl_schedule_free(schedule
);
3920 sched2
= isl_union_map_read_from_str(ctx
, "{ C[x,y] -> [x,y] }");
3921 equal
= isl_union_map_is_equal(sched1
, sched2
);
3922 isl_union_map_free(sched1
);
3923 isl_union_map_free(sched2
);
3928 isl_die(ctx
, isl_error_unknown
,
3929 "unexpected schedule", return -1);
3934 /* Check that a set of schedule constraints that only allow for
3935 * a coalescing schedule still produces a schedule even if the user
3936 * request a non-coalescing schedule. Earlier versions of isl
3937 * would not handle this case correctly.
3939 static int test_coalescing_schedule(isl_ctx
*ctx
)
3941 const char *domain
, *dep
;
3944 isl_schedule_constraints
*sc
;
3945 isl_schedule
*schedule
;
3946 int treat_coalescing
;
3948 domain
= "{ S[a, b] : 0 <= a <= 1 and 0 <= b <= 1 }";
3949 dep
= "{ S[a, b] -> S[a + b, 1 - b] }";
3950 I
= isl_union_set_read_from_str(ctx
, domain
);
3951 D
= isl_union_map_read_from_str(ctx
, dep
);
3952 sc
= isl_schedule_constraints_on_domain(I
);
3953 sc
= isl_schedule_constraints_set_validity(sc
, D
);
3954 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
3955 isl_options_set_schedule_treat_coalescing(ctx
, 1);
3956 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3957 isl_options_set_schedule_treat_coalescing(ctx
, treat_coalescing
);
3958 isl_schedule_free(schedule
);
3964 int test_schedule(isl_ctx
*ctx
)
3966 const char *D
, *W
, *R
, *V
, *P
, *S
;
3967 int max_coincidence
;
3968 int treat_coalescing
;
3970 /* Handle resulting schedule with zero bands. */
3971 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
3975 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
3976 W
= "{ S1[t,i] -> a[t,i] }";
3977 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
3978 "S1[t,i] -> a[t-1,i+1] }";
3979 S
= "{ S1[t,i] -> [t,i] }";
3980 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3983 /* Fig. 5 of CC2008 */
3984 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
3986 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
3987 "j >= 2 and j <= -1 + N }";
3988 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
3989 "j >= 2 and j <= -1 + N; "
3990 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
3991 "j >= 2 and j <= -1 + N }";
3992 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3993 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3996 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
3997 W
= "{ S1[i] -> a[i] }";
3998 R
= "{ S2[i] -> a[i+1] }";
3999 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
4000 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
4003 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
4004 W
= "{ S1[i] -> a[i] }";
4005 R
= "{ S2[i] -> a[9-i] }";
4006 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
4007 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
4010 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
4011 W
= "{ S1[i] -> a[i] }";
4012 R
= "[N] -> { S2[i] -> a[N-1-i] }";
4013 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
4014 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
4017 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
4018 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
4019 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
4020 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
4021 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4024 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
4025 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
4026 R
= "{ S2[i,j] -> a[i-1,j] }";
4027 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
4028 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
4031 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
4032 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
4033 R
= "{ S2[i,j] -> a[i,j-1] }";
4034 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
4035 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
4038 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
4039 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
4040 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
4041 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
4042 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
4043 "S_0[] -> [0, 0, 0] }";
4044 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
4046 ctx
->opt
->schedule_parametric
= 0;
4047 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4049 ctx
->opt
->schedule_parametric
= 1;
4051 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
4052 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
4053 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
4054 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
4055 "S4[i] -> a[i,N] }";
4056 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
4057 "S4[i] -> [4,i,0] }";
4058 max_coincidence
= isl_options_get_schedule_maximize_coincidence(ctx
);
4059 isl_options_set_schedule_maximize_coincidence(ctx
, 0);
4060 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
4062 isl_options_set_schedule_maximize_coincidence(ctx
, max_coincidence
);
4064 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
4065 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
4067 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
4069 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
4071 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
4072 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4075 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
4076 " S_2[t] : t >= 0 and t <= -1 + N; "
4077 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
4079 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
4080 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
4081 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
4082 "i >= 0 and i <= -1 + N }";
4083 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
4084 "i >= 0 and i <= -1 + N; "
4085 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
4086 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
4087 " S_0[t] -> [0, t, 0] }";
4089 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
4091 ctx
->opt
->schedule_parametric
= 0;
4092 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4094 ctx
->opt
->schedule_parametric
= 1;
4096 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
4097 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
4098 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
4101 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
4102 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
4103 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
4104 "j >= 0 and j <= -1 + N; "
4105 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
4106 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
4107 "j >= 0 and j <= -1 + N; "
4108 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
4109 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
4110 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4113 D
= "{ S_0[i] : i >= 0 }";
4114 W
= "{ S_0[i] -> a[i] : i >= 0 }";
4115 R
= "{ S_0[i] -> a[0] : i >= 0 }";
4116 S
= "{ S_0[i] -> [0, i, 0] }";
4117 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4120 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
4121 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
4122 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
4123 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
4124 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4127 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
4128 "k <= -1 + n and k >= 0 }";
4129 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
4130 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
4131 "k <= -1 + n and k >= 0; "
4132 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
4133 "k <= -1 + n and k >= 0; "
4134 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
4135 "k <= -1 + n and k >= 0 }";
4136 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
4137 ctx
->opt
->schedule_outer_coincidence
= 1;
4138 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4140 ctx
->opt
->schedule_outer_coincidence
= 0;
4142 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
4143 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
4144 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
4145 "Stmt_for_body24[i0, i1, 1, 0]:"
4146 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
4147 "Stmt_for_body7[i0, i1, i2]:"
4148 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
4151 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
4152 "Stmt_for_body24[1, i1, i2, i3]:"
4153 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
4155 "Stmt_for_body24[0, i1, i2, i3] -> "
4156 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
4157 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
4159 "Stmt_for_body24[0, i1, i2, i3] ->"
4160 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
4161 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
4162 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
4163 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
4164 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
4165 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
4166 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
4167 "i1 <= 6 and i1 >= 0;"
4168 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
4169 "Stmt_for_body7[i0, i1, i2] -> "
4170 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
4171 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
4172 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
4173 "Stmt_for_body7[i0, i1, i2] -> "
4174 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
4175 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
4176 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
4178 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
4179 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
4180 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
4182 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4183 isl_options_set_schedule_treat_coalescing(ctx
, 0);
4184 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4186 isl_options_set_schedule_treat_coalescing(ctx
, treat_coalescing
);
4188 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
4189 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
4190 "j >= 1 and j <= 7;"
4191 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
4192 "j >= 1 and j <= 8 }";
4194 S
= "{ S_0[i, j] -> [i + j, j] }";
4195 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4196 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4198 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4200 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
4201 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
4202 "j >= 0 and j <= -1 + i }";
4203 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
4204 "i <= -1 + N and j >= 0;"
4205 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
4208 S
= "{ S_0[i, j] -> [i, j] }";
4209 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4210 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4212 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4214 /* Test both algorithms on a case with only proximity dependences. */
4215 D
= "{ S[i,j] : 0 <= i <= 10 }";
4217 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
4218 S
= "{ S[i, j] -> [j, i] }";
4219 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4220 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4222 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4223 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4226 D
= "{ A[a]; B[] }";
4228 P
= "{ A[a] -> B[] }";
4229 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4232 if (test_padded_schedule(ctx
) < 0)
4235 /* Check that check for progress is not confused by rational
4238 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
4239 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
4241 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
4242 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
4244 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4245 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4247 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4249 /* Check that we allow schedule rows that are only non-trivial
4250 * on some full-dimensional domains.
4252 D
= "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
4253 V
= "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
4254 "S1[j] -> S2[1] : 0 <= j <= 1 }";
4256 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4257 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4259 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4261 if (test_conditional_schedule_constraints(ctx
) < 0)
4264 if (test_strongly_satisfying_schedule(ctx
) < 0)
4267 if (test_conflicting_context_schedule(ctx
) < 0)
4270 if (test_bounded_coefficients_schedule(ctx
) < 0)
4272 if (test_coalescing_schedule(ctx
) < 0)
4278 /* Perform scheduling tests using the whole component scheduler.
4280 static int test_schedule_whole(isl_ctx
*ctx
)
4285 whole
= isl_options_get_schedule_whole_component(ctx
);
4286 isl_options_set_schedule_whole_component(ctx
, 1);
4287 r
= test_schedule(ctx
);
4288 isl_options_set_schedule_whole_component(ctx
, whole
);
4293 /* Perform scheduling tests using the incremental scheduler.
4295 static int test_schedule_incremental(isl_ctx
*ctx
)
4300 whole
= isl_options_get_schedule_whole_component(ctx
);
4301 isl_options_set_schedule_whole_component(ctx
, 0);
4302 r
= test_schedule(ctx
);
4303 isl_options_set_schedule_whole_component(ctx
, whole
);
4308 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
4310 isl_union_map
*umap
;
4313 umap
= isl_union_map_read_from_str(ctx
, str
);
4314 test
= isl_union_map_plain_is_injective(umap
);
4315 isl_union_map_free(umap
);
4318 if (test
== injective
)
4321 isl_die(ctx
, isl_error_unknown
,
4322 "map not detected as injective", return -1);
4324 isl_die(ctx
, isl_error_unknown
,
4325 "map detected as injective", return -1);
4328 int test_injective(isl_ctx
*ctx
)
4332 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
4334 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
4336 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
4338 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
4340 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
4342 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
4344 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
4346 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
4349 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
4350 if (test_plain_injective(ctx
, str
, 1))
4352 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
4353 if (test_plain_injective(ctx
, str
, 0))
4359 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
4367 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
4368 equal
= isl_aff_plain_is_equal(aff
, aff2
);
4374 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
4378 equal
= aff_plain_is_equal(aff
, str
);
4382 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
4383 "result not as expected", return -1);
4388 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
4389 __isl_take isl_aff
*aff2
);
4391 ['+'] = { &isl_aff_add
},
4392 ['-'] = { &isl_aff_sub
},
4393 ['*'] = { &isl_aff_mul
},
4394 ['/'] = { &isl_aff_div
},
4402 } aff_bin_tests
[] = {
4403 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
4404 "{ [i] -> [2i] }" },
4405 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
4407 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
4408 "{ [i] -> [2i] }" },
4409 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
4410 "{ [i] -> [2i] }" },
4411 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
4412 "{ [i] -> [i/2] }" },
4413 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
4415 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
4416 "{ [i] -> [NaN] }" },
4417 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
4418 "{ [i] -> [NaN] }" },
4419 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
4420 "{ [i] -> [NaN] }" },
4421 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
4422 "{ [i] -> [NaN] }" },
4423 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
4424 "{ [i] -> [NaN] }" },
4425 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
4426 "{ [i] -> [NaN] }" },
4427 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
4428 "{ [i] -> [NaN] }" },
4429 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
4430 "{ [i] -> [NaN] }" },
4431 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
4432 "{ [i] -> [NaN] }" },
4433 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
4434 "{ [i] -> [NaN] }" },
4435 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
4436 "{ [i] -> [NaN] }" },
4437 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
4438 "{ [i] -> [NaN] }" },
4441 /* Perform some basic tests of binary operations on isl_aff objects.
4443 static int test_bin_aff(isl_ctx
*ctx
)
4446 isl_aff
*aff1
, *aff2
, *res
;
4447 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
4448 __isl_take isl_aff
*aff2
);
4451 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
4452 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
4453 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
4454 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
4455 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
4456 aff1
= fn(aff1
, aff2
);
4457 if (isl_aff_is_nan(res
))
4458 ok
= isl_aff_is_nan(aff1
);
4460 ok
= isl_aff_plain_is_equal(aff1
, res
);
4466 isl_die(ctx
, isl_error_unknown
,
4467 "unexpected result", return -1);
4474 __isl_give isl_pw_aff
*(*fn
)(__isl_take isl_pw_aff
*pa1
,
4475 __isl_take isl_pw_aff
*pa2
);
4476 } pw_aff_bin_op
[] = {
4477 ['m'] = { &isl_pw_aff_min
},
4478 ['M'] = { &isl_pw_aff_max
},
4481 /* Inputs for binary isl_pw_aff operation tests.
4482 * "arg1" and "arg2" are the two arguments, "op" identifies the operation
4483 * defined by pw_aff_bin_op, and "res" is the expected result.
4490 } pw_aff_bin_tests
[] = {
4491 { "{ [i] -> [i] }", 'm', "{ [i] -> [i] }",
4493 { "{ [i] -> [i] }", 'M', "{ [i] -> [i] }",
4495 { "{ [i] -> [i] }", 'm', "{ [i] -> [0] }",
4496 "{ [i] -> [i] : i <= 0; [i] -> [0] : i > 0 }" },
4497 { "{ [i] -> [i] }", 'M', "{ [i] -> [0] }",
4498 "{ [i] -> [i] : i >= 0; [i] -> [0] : i < 0 }" },
4499 { "{ [i] -> [i] }", 'm', "{ [i] -> [NaN] }",
4500 "{ [i] -> [NaN] }" },
4501 { "{ [i] -> [NaN] }", 'm', "{ [i] -> [i] }",
4502 "{ [i] -> [NaN] }" },
4505 /* Perform some basic tests of binary operations on isl_pw_aff objects.
4507 static int test_bin_pw_aff(isl_ctx
*ctx
)
4511 isl_pw_aff
*pa1
, *pa2
, *res
;
4513 for (i
= 0; i
< ARRAY_SIZE(pw_aff_bin_tests
); ++i
) {
4514 pa1
= isl_pw_aff_read_from_str(ctx
, pw_aff_bin_tests
[i
].arg1
);
4515 pa2
= isl_pw_aff_read_from_str(ctx
, pw_aff_bin_tests
[i
].arg2
);
4516 res
= isl_pw_aff_read_from_str(ctx
, pw_aff_bin_tests
[i
].res
);
4517 pa1
= pw_aff_bin_op
[pw_aff_bin_tests
[i
].op
].fn(pa1
, pa2
);
4518 if (isl_pw_aff_involves_nan(res
))
4519 ok
= isl_pw_aff_involves_nan(pa1
);
4521 ok
= isl_pw_aff_plain_is_equal(pa1
, res
);
4522 isl_pw_aff_free(pa1
);
4523 isl_pw_aff_free(res
);
4527 isl_die(ctx
, isl_error_unknown
,
4528 "unexpected result", return -1);
4535 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4536 __isl_take isl_union_pw_multi_aff
*upma1
,
4537 __isl_take isl_union_pw_multi_aff
*upma2
);
4541 } upma_bin_tests
[] = {
4542 { &isl_union_pw_multi_aff_add
, "{ A[] -> [0]; B[0] -> [1] }",
4543 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
4544 { &isl_union_pw_multi_aff_union_add
, "{ A[] -> [0]; B[0] -> [1] }",
4545 "{ B[x] -> [2] : x >= 0 }",
4546 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
4547 { &isl_union_pw_multi_aff_pullback_union_pw_multi_aff
,
4548 "{ A[] -> B[0]; C[x] -> B[1] : x < 10; C[y] -> B[2] : y >= 10 }",
4549 "{ D[i] -> A[] : i < 0; D[i] -> C[i + 5] : i >= 0 }",
4550 "{ D[i] -> B[0] : i < 0; D[i] -> B[1] : 0 <= i < 5; "
4551 "D[i] -> B[2] : i >= 5 }" },
4552 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4553 "{ B[x] -> C[2] : x > 0 }",
4554 "{ B[x] -> A[1] : x <= 0; B[x] -> C[2] : x > 0 }" },
4555 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4556 "{ B[x] -> A[2] : x >= 0 }",
4557 "{ B[x] -> A[1] : x < 0; B[x] -> A[2] : x > 0; B[0] -> A[3] }" },
4560 /* Perform some basic tests of binary operations on
4561 * isl_union_pw_multi_aff objects.
4563 static int test_bin_upma(isl_ctx
*ctx
)
4566 isl_union_pw_multi_aff
*upma1
, *upma2
, *res
;
4569 for (i
= 0; i
< ARRAY_SIZE(upma_bin_tests
); ++i
) {
4570 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4571 upma_bin_tests
[i
].arg1
);
4572 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4573 upma_bin_tests
[i
].arg2
);
4574 res
= isl_union_pw_multi_aff_read_from_str(ctx
,
4575 upma_bin_tests
[i
].res
);
4576 upma1
= upma_bin_tests
[i
].fn(upma1
, upma2
);
4577 ok
= isl_union_pw_multi_aff_plain_is_equal(upma1
, res
);
4578 isl_union_pw_multi_aff_free(upma1
);
4579 isl_union_pw_multi_aff_free(res
);
4583 isl_die(ctx
, isl_error_unknown
,
4584 "unexpected result", return -1);
4591 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4592 __isl_take isl_union_pw_multi_aff
*upma1
,
4593 __isl_take isl_union_pw_multi_aff
*upma2
);
4596 } upma_bin_fail_tests
[] = {
4597 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4598 "{ B[x] -> C[2] : x >= 0 }" },
4601 /* Perform some basic tests of binary operations on
4602 * isl_union_pw_multi_aff objects that are expected to fail.
4604 static int test_bin_upma_fail(isl_ctx
*ctx
)
4607 isl_union_pw_multi_aff
*upma1
, *upma2
;
4610 on_error
= isl_options_get_on_error(ctx
);
4611 isl_options_set_on_error(ctx
, ISL_ON_ERROR_CONTINUE
);
4612 n
= ARRAY_SIZE(upma_bin_fail_tests
);
4613 for (i
= 0; i
< n
; ++i
) {
4614 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4615 upma_bin_fail_tests
[i
].arg1
);
4616 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4617 upma_bin_fail_tests
[i
].arg2
);
4618 upma1
= upma_bin_fail_tests
[i
].fn(upma1
, upma2
);
4619 isl_union_pw_multi_aff_free(upma1
);
4623 isl_options_set_on_error(ctx
, on_error
);
4625 isl_die(ctx
, isl_error_unknown
,
4626 "operation not expected to succeed", return -1);
4631 int test_aff(isl_ctx
*ctx
)
4636 isl_local_space
*ls
;
4640 if (test_bin_aff(ctx
) < 0)
4642 if (test_bin_pw_aff(ctx
) < 0)
4644 if (test_bin_upma(ctx
) < 0)
4646 if (test_bin_upma_fail(ctx
) < 0)
4649 space
= isl_space_set_alloc(ctx
, 0, 1);
4650 ls
= isl_local_space_from_space(space
);
4651 aff
= isl_aff_zero_on_domain(ls
);
4653 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4654 aff
= isl_aff_scale_down_ui(aff
, 3);
4655 aff
= isl_aff_floor(aff
);
4656 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4657 aff
= isl_aff_scale_down_ui(aff
, 2);
4658 aff
= isl_aff_floor(aff
);
4659 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4662 set
= isl_set_read_from_str(ctx
, str
);
4663 aff
= isl_aff_gist(aff
, set
);
4665 aff
= isl_aff_add_constant_si(aff
, -16);
4666 zero
= isl_aff_plain_is_zero(aff
);
4672 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4674 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
4675 aff
= isl_aff_scale_down_ui(aff
, 64);
4676 aff
= isl_aff_floor(aff
);
4677 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
4685 /* Check that the computation below results in a single expression.
4686 * One or two expressions may result depending on which constraint
4687 * ends up being considered as redundant with respect to the other
4688 * constraints after the projection that is performed internally
4689 * by isl_set_dim_min.
4691 static int test_dim_max_1(isl_ctx
*ctx
)
4698 str
= "[n] -> { [a, b] : n >= 0 and 4a >= -4 + n and b >= 0 and "
4699 "-4a <= b <= 3 and b < n - 4a }";
4700 set
= isl_set_read_from_str(ctx
, str
);
4701 pa
= isl_set_dim_min(set
, 0);
4702 n
= isl_pw_aff_n_piece(pa
);
4703 isl_pw_aff_free(pa
);
4708 isl_die(ctx
, isl_error_unknown
, "expecting single expression",
4714 int test_dim_max(isl_ctx
*ctx
)
4718 isl_set
*set1
, *set2
;
4723 if (test_dim_max_1(ctx
) < 0)
4726 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
4727 set
= isl_set_read_from_str(ctx
, str
);
4728 pwaff
= isl_set_dim_max(set
, 0);
4729 set1
= isl_set_from_pw_aff(pwaff
);
4730 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
4731 set2
= isl_set_read_from_str(ctx
, str
);
4732 equal
= isl_set_is_equal(set1
, set2
);
4738 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4740 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
4741 set
= isl_set_read_from_str(ctx
, str
);
4742 pwaff
= isl_set_dim_max(set
, 0);
4743 set1
= isl_set_from_pw_aff(pwaff
);
4744 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4745 set2
= isl_set_read_from_str(ctx
, str
);
4746 equal
= isl_set_is_equal(set1
, set2
);
4752 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4754 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
4755 set
= isl_set_read_from_str(ctx
, str
);
4756 pwaff
= isl_set_dim_max(set
, 0);
4757 set1
= isl_set_from_pw_aff(pwaff
);
4758 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4759 set2
= isl_set_read_from_str(ctx
, str
);
4760 equal
= isl_set_is_equal(set1
, set2
);
4766 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4768 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
4769 "0 <= i < N and 0 <= j < M }";
4770 map
= isl_map_read_from_str(ctx
, str
);
4771 set
= isl_map_range(map
);
4773 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
4774 set1
= isl_set_from_pw_aff(pwaff
);
4775 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
4776 set2
= isl_set_read_from_str(ctx
, str
);
4777 equal
= isl_set_is_equal(set1
, set2
);
4781 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
4782 set1
= isl_set_from_pw_aff(pwaff
);
4783 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
4784 set2
= isl_set_read_from_str(ctx
, str
);
4785 if (equal
>= 0 && equal
)
4786 equal
= isl_set_is_equal(set1
, set2
);
4795 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4797 /* Check that solutions are properly merged. */
4798 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
4799 "c <= -1 + n - 4a - 2b and c >= -2b and "
4800 "4a >= -4 + n and c >= 0 }";
4801 set
= isl_set_read_from_str(ctx
, str
);
4802 pwaff
= isl_set_dim_min(set
, 2);
4803 set1
= isl_set_from_pw_aff(pwaff
);
4804 str
= "[n] -> { [(0)] : n >= 1 }";
4805 set2
= isl_set_read_from_str(ctx
, str
);
4806 equal
= isl_set_is_equal(set1
, set2
);
4813 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4815 /* Check that empty solution lie in the right space. */
4816 str
= "[n] -> { [t,a] : 1 = 0 }";
4817 set
= isl_set_read_from_str(ctx
, str
);
4818 pwaff
= isl_set_dim_max(set
, 0);
4819 set1
= isl_set_from_pw_aff(pwaff
);
4820 str
= "[n] -> { [t] : 1 = 0 }";
4821 set2
= isl_set_read_from_str(ctx
, str
);
4822 equal
= isl_set_is_equal(set1
, set2
);
4829 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4834 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
4836 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
4840 isl_pw_multi_aff
*pma2
;
4846 ctx
= isl_pw_multi_aff_get_ctx(pma
);
4847 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4848 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
4849 isl_pw_multi_aff_free(pma2
);
4854 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
4855 * represented by "str".
4857 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
4862 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
4866 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
4867 "result not as expected", return -1);
4871 /* Basic test for isl_pw_multi_aff_product.
4873 * Check that multiple pieces are properly handled.
4875 static int test_product_pma(isl_ctx
*ctx
)
4879 isl_pw_multi_aff
*pma1
, *pma2
;
4881 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
4882 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4883 str
= "{ C[] -> D[] }";
4884 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4885 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
4886 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
4887 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
4888 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
4889 isl_pw_multi_aff_free(pma1
);
4896 int test_product(isl_ctx
*ctx
)
4900 isl_union_set
*uset1
, *uset2
;
4904 set
= isl_set_read_from_str(ctx
, str
);
4905 set
= isl_set_product(set
, isl_set_copy(set
));
4906 ok
= isl_set_is_wrapping(set
);
4911 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4914 uset1
= isl_union_set_read_from_str(ctx
, str
);
4915 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
4916 str
= "{ [[] -> []] }";
4917 uset2
= isl_union_set_read_from_str(ctx
, str
);
4918 ok
= isl_union_set_is_equal(uset1
, uset2
);
4919 isl_union_set_free(uset1
);
4920 isl_union_set_free(uset2
);
4924 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4926 if (test_product_pma(ctx
) < 0)
4932 /* Check that two sets are not considered disjoint just because
4933 * they have a different set of (named) parameters.
4935 static int test_disjoint(isl_ctx
*ctx
)
4938 isl_set
*set
, *set2
;
4941 str
= "[n] -> { [[]->[]] }";
4942 set
= isl_set_read_from_str(ctx
, str
);
4943 str
= "{ [[]->[]] }";
4944 set2
= isl_set_read_from_str(ctx
, str
);
4945 disjoint
= isl_set_is_disjoint(set
, set2
);
4951 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4956 int test_equal(isl_ctx
*ctx
)
4959 isl_set
*set
, *set2
;
4963 set
= isl_set_read_from_str(ctx
, str
);
4965 set2
= isl_set_read_from_str(ctx
, str
);
4966 equal
= isl_set_is_equal(set
, set2
);
4972 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4977 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
4978 enum isl_dim_type type
, unsigned pos
, int fixed
)
4982 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
4989 isl_die(ctx
, isl_error_unknown
,
4990 "map not detected as fixed", return -1);
4992 isl_die(ctx
, isl_error_unknown
,
4993 "map detected as fixed", return -1);
4996 int test_fixed(isl_ctx
*ctx
)
5001 str
= "{ [i] -> [i] }";
5002 map
= isl_map_read_from_str(ctx
, str
);
5003 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
5005 str
= "{ [i] -> [1] }";
5006 map
= isl_map_read_from_str(ctx
, str
);
5007 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
5009 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
5010 map
= isl_map_read_from_str(ctx
, str
);
5011 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
5013 map
= isl_map_read_from_str(ctx
, str
);
5014 map
= isl_map_neg(map
);
5015 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
5021 struct isl_vertices_test_data
{
5024 const char *vertex
[6];
5025 } vertices_tests
[] = {
5026 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
5027 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
5028 { "{ A[t, i] : t = 14 and i = 1 }",
5029 1, { "{ A[14, 1] }" } },
5030 { "[n, m] -> { [a, b, c] : b <= a and a <= n and b > 0 and c >= b and "
5031 "c <= m and m <= n and m > 0 }",
5033 "[n, m] -> { [n, m, m] : 0 < m <= n }",
5034 "[n, m] -> { [n, 1, m] : 0 < m <= n }",
5035 "[n, m] -> { [n, 1, 1] : 0 < m <= n }",
5036 "[n, m] -> { [m, m, m] : 0 < m <= n }",
5037 "[n, m] -> { [1, 1, m] : 0 < m <= n }",
5038 "[n, m] -> { [1, 1, 1] : 0 < m <= n }"
5042 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
5044 static isl_stat
find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
5046 struct isl_vertices_test_data
*data
= user
;
5049 isl_basic_set
*bset
;
5050 isl_pw_multi_aff
*pma
;
5054 ctx
= isl_vertex_get_ctx(vertex
);
5055 bset
= isl_vertex_get_domain(vertex
);
5056 ma
= isl_vertex_get_expr(vertex
);
5057 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
5059 for (i
= 0; i
< data
->n
; ++i
) {
5060 isl_pw_multi_aff
*pma_i
;
5062 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
5063 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
5064 isl_pw_multi_aff_free(pma_i
);
5066 if (equal
< 0 || equal
)
5070 isl_pw_multi_aff_free(pma
);
5071 isl_vertex_free(vertex
);
5074 return isl_stat_error
;
5076 return equal
? isl_stat_ok
: isl_stat_error
;
5079 int test_vertices(isl_ctx
*ctx
)
5083 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
5084 isl_basic_set
*bset
;
5085 isl_vertices
*vertices
;
5089 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
5090 vertices
= isl_basic_set_compute_vertices(bset
);
5091 n
= isl_vertices_get_n_vertices(vertices
);
5092 if (vertices_tests
[i
].n
!= n
)
5094 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
5095 &vertices_tests
[i
]) < 0)
5097 isl_vertices_free(vertices
);
5098 isl_basic_set_free(bset
);
5103 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
5110 int test_union_pw(isl_ctx
*ctx
)
5114 isl_union_set
*uset
;
5115 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
5117 str
= "{ [x] -> x^2 }";
5118 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
5119 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
5120 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
5121 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
5122 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
5123 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
5124 isl_union_pw_qpolynomial_free(upwqp1
);
5125 isl_union_pw_qpolynomial_free(upwqp2
);
5129 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5134 /* Test that isl_union_pw_qpolynomial_eval picks up the function
5135 * defined over the correct domain space.
5137 static int test_eval_1(isl_ctx
*ctx
)
5142 isl_union_pw_qpolynomial
*upwqp
;
5146 str
= "{ A[x] -> x^2; B[x] -> -x^2 }";
5147 upwqp
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
5149 set
= isl_set_read_from_str(ctx
, str
);
5150 pnt
= isl_set_sample_point(set
);
5151 v
= isl_union_pw_qpolynomial_eval(upwqp
, pnt
);
5152 cmp
= isl_val_cmp_si(v
, 36);
5158 isl_die(ctx
, isl_error_unknown
, "unexpected value", return -1);
5163 /* Check that isl_qpolynomial_eval handles getting called on a void point.
5165 static int test_eval_2(isl_ctx
*ctx
)
5170 isl_qpolynomial
*qp
;
5174 str
= "{ A[x] -> [x] }";
5175 qp
= isl_qpolynomial_from_aff(isl_aff_read_from_str(ctx
, str
));
5176 str
= "{ A[x] : false }";
5177 set
= isl_set_read_from_str(ctx
, str
);
5178 pnt
= isl_set_sample_point(set
);
5179 v
= isl_qpolynomial_eval(qp
, pnt
);
5180 ok
= isl_val_is_nan(v
);
5186 isl_die(ctx
, isl_error_unknown
, "expecting NaN", return -1);
5191 /* Perform basic polynomial evaluation tests.
5193 static int test_eval(isl_ctx
*ctx
)
5195 if (test_eval_1(ctx
) < 0)
5197 if (test_eval_2(ctx
) < 0)
5202 /* Descriptions of sets that are tested for reparsing after printing.
5204 const char *output_tests
[] = {
5205 "{ [1, y] : 0 <= y <= 1; [x, -x] : 0 <= x <= 1 }",
5208 /* Check that printing a set and reparsing a set from the printed output
5209 * results in the same set.
5211 static int test_output_set(isl_ctx
*ctx
)
5215 isl_set
*set1
, *set2
;
5218 for (i
= 0; i
< ARRAY_SIZE(output_tests
); ++i
) {
5219 set1
= isl_set_read_from_str(ctx
, output_tests
[i
]);
5220 str
= isl_set_to_str(set1
);
5221 set2
= isl_set_read_from_str(ctx
, str
);
5223 equal
= isl_set_is_equal(set1
, set2
);
5229 isl_die(ctx
, isl_error_unknown
,
5230 "parsed output not the same", return -1);
5236 int test_output(isl_ctx
*ctx
)
5244 if (test_output_set(ctx
) < 0)
5247 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
5248 pa
= isl_pw_aff_read_from_str(ctx
, str
);
5250 p
= isl_printer_to_str(ctx
);
5251 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
5252 p
= isl_printer_print_pw_aff(p
, pa
);
5253 s
= isl_printer_get_str(p
);
5254 isl_printer_free(p
);
5255 isl_pw_aff_free(pa
);
5259 equal
= !strcmp(s
, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
5264 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5269 int test_sample(isl_ctx
*ctx
)
5272 isl_basic_set
*bset1
, *bset2
;
5275 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
5276 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
5277 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
5278 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
5279 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
5280 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
5281 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
5282 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
5283 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
5284 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
5285 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
5286 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
5287 "d - 1073741821e and "
5288 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
5289 "3j >= 1 - a + b + 2e and "
5290 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
5291 "3i <= 4 - a + 4b - e and "
5292 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
5293 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
5294 "c <= -1 + a and 3i >= -2 - a + 3e and "
5295 "1073741822e <= 1073741823 - a + 1073741822b + c and "
5296 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
5297 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
5298 "1073741823e >= 1 + 1073741823b - d and "
5299 "3i >= 1073741823b + c - 1073741823e - f and "
5300 "3i >= 1 + 2b + e + 3g }";
5301 bset1
= isl_basic_set_read_from_str(ctx
, str
);
5302 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
5303 empty
= isl_basic_set_is_empty(bset2
);
5304 subset
= isl_basic_set_is_subset(bset2
, bset1
);
5305 isl_basic_set_free(bset1
);
5306 isl_basic_set_free(bset2
);
5307 if (empty
< 0 || subset
< 0)
5310 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
5312 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
5317 int test_fixed_power(isl_ctx
*ctx
)
5325 str
= "{ [i] -> [i + 1] }";
5326 map
= isl_map_read_from_str(ctx
, str
);
5327 isl_int_set_si(exp
, 23);
5328 map
= isl_map_fixed_power(map
, exp
);
5329 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
5338 int test_slice(isl_ctx
*ctx
)
5344 str
= "{ [i] -> [j] }";
5345 map
= isl_map_read_from_str(ctx
, str
);
5346 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5347 equal
= map_check_equal(map
, "{ [i] -> [i] }");
5352 str
= "{ [i] -> [j] }";
5353 map
= isl_map_read_from_str(ctx
, str
);
5354 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5355 equal
= map_check_equal(map
, "{ [i] -> [j] }");
5360 str
= "{ [i] -> [j] }";
5361 map
= isl_map_read_from_str(ctx
, str
);
5362 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5363 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
5368 str
= "{ [i] -> [j] }";
5369 map
= isl_map_read_from_str(ctx
, str
);
5370 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5371 equal
= map_check_equal(map
, "{ [0] -> [j] }");
5376 str
= "{ [i] -> [j] }";
5377 map
= isl_map_read_from_str(ctx
, str
);
5378 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5379 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
5384 str
= "{ [i] -> [j] }";
5385 map
= isl_map_read_from_str(ctx
, str
);
5386 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5387 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
5395 int test_eliminate(isl_ctx
*ctx
)
5401 str
= "{ [i] -> [j] : i = 2j }";
5402 map
= isl_map_read_from_str(ctx
, str
);
5403 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
5404 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
5412 /* Check that isl_set_dim_residue_class detects that the values of j
5413 * in the set below are all odd and that it does not detect any spurious
5416 static int test_residue_class(isl_ctx
*ctx
)
5423 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
5424 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
5425 set
= isl_set_read_from_str(ctx
, str
);
5428 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
5430 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
5431 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
5440 int test_align_parameters(isl_ctx
*ctx
)
5444 isl_multi_aff
*ma1
, *ma2
;
5447 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
5448 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
5450 space
= isl_space_params_alloc(ctx
, 1);
5451 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
5452 ma1
= isl_multi_aff_align_params(ma1
, space
);
5454 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
5455 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
5457 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
5459 isl_multi_aff_free(ma1
);
5460 isl_multi_aff_free(ma2
);
5465 isl_die(ctx
, isl_error_unknown
,
5466 "result not as expected", return -1);
5471 static int test_list(isl_ctx
*ctx
)
5473 isl_id
*a
, *b
, *c
, *d
, *id
;
5477 a
= isl_id_alloc(ctx
, "a", NULL
);
5478 b
= isl_id_alloc(ctx
, "b", NULL
);
5479 c
= isl_id_alloc(ctx
, "c", NULL
);
5480 d
= isl_id_alloc(ctx
, "d", NULL
);
5482 list
= isl_id_list_alloc(ctx
, 4);
5483 list
= isl_id_list_add(list
, b
);
5484 list
= isl_id_list_insert(list
, 0, a
);
5485 list
= isl_id_list_add(list
, c
);
5486 list
= isl_id_list_add(list
, d
);
5487 list
= isl_id_list_drop(list
, 1, 1);
5489 if (isl_id_list_n_id(list
) != 3) {
5490 isl_id_list_free(list
);
5491 isl_die(ctx
, isl_error_unknown
,
5492 "unexpected number of elements in list", return -1);
5495 id
= isl_id_list_get_id(list
, 0);
5498 id
= isl_id_list_get_id(list
, 1);
5501 id
= isl_id_list_get_id(list
, 2);
5505 isl_id_list_free(list
);
5508 isl_die(ctx
, isl_error_unknown
,
5509 "unexpected elements in list", return -1);
5514 const char *set_conversion_tests
[] = {
5515 "[N] -> { [i] : N - 1 <= 2 i <= N }",
5516 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
5517 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
5518 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
5519 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
5520 "[a, b] -> { [c, d] : (4*floor((-a + c)/4) = -a + c and "
5521 "32*floor((-b + d)/32) = -b + d and 5 <= c <= 8 and "
5522 "-3 + c <= d <= 28 + c) }",
5525 /* Check that converting from isl_set to isl_pw_multi_aff and back
5526 * to isl_set produces the original isl_set.
5528 static int test_set_conversion(isl_ctx
*ctx
)
5532 isl_set
*set1
, *set2
;
5533 isl_pw_multi_aff
*pma
;
5536 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
5537 str
= set_conversion_tests
[i
];
5538 set1
= isl_set_read_from_str(ctx
, str
);
5539 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
5540 set2
= isl_set_from_pw_multi_aff(pma
);
5541 equal
= isl_set_is_equal(set1
, set2
);
5548 isl_die(ctx
, isl_error_unknown
, "bad conversion",
5555 const char *conversion_tests
[] = {
5556 "{ [a, b, c, d] -> s0[a, b, e, f] : "
5557 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
5558 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
5559 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
5561 "{ [a, b] -> [c] : exists (e0 = floor((-a - b + c)/5): "
5562 "5e0 = -a - b + c and c >= -a and c <= 4 - a) }",
5563 "{ [a, b] -> [c] : exists d : 18 * d = -3 - a + 2c and 1 <= c <= 3 }",
5566 /* Check that converting from isl_map to isl_pw_multi_aff and back
5567 * to isl_map produces the original isl_map.
5569 static int test_map_conversion(isl_ctx
*ctx
)
5572 isl_map
*map1
, *map2
;
5573 isl_pw_multi_aff
*pma
;
5576 for (i
= 0; i
< ARRAY_SIZE(conversion_tests
); ++i
) {
5577 map1
= isl_map_read_from_str(ctx
, conversion_tests
[i
]);
5578 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
5579 map2
= isl_map_from_pw_multi_aff(pma
);
5580 equal
= isl_map_is_equal(map1
, map2
);
5587 isl_die(ctx
, isl_error_unknown
, "bad conversion",
5594 static int test_conversion(isl_ctx
*ctx
)
5596 if (test_set_conversion(ctx
) < 0)
5598 if (test_map_conversion(ctx
) < 0)
5603 /* Check that isl_basic_map_curry does not modify input.
5605 static int test_curry(isl_ctx
*ctx
)
5608 isl_basic_map
*bmap1
, *bmap2
;
5611 str
= "{ [A[] -> B[]] -> C[] }";
5612 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
5613 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
5614 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
5615 isl_basic_map_free(bmap1
);
5616 isl_basic_map_free(bmap2
);
5621 isl_die(ctx
, isl_error_unknown
,
5622 "curried map should not be equal to original",
5632 } preimage_tests
[] = {
5633 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
5634 "{ A[j,i] -> B[i,j] }",
5635 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
5636 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
5637 "{ A[a,b] -> B[a/2,b/6] }",
5638 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
5639 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
5640 "{ A[a,b] -> B[a/2,b/6] }",
5641 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
5642 "exists i,j : a = 2 i and b = 6 j }" },
5643 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
5644 "[n] -> { : 0 <= n <= 100 }" },
5645 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
5646 "{ A[a] -> B[2a] }",
5647 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
5648 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
5649 "{ A[a] -> B[([a/2])] }",
5650 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
5651 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
5652 "{ A[a] -> B[a,a,a/3] }",
5653 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
5654 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
5655 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
5658 static int test_preimage_basic_set(isl_ctx
*ctx
)
5661 isl_basic_set
*bset1
, *bset2
;
5665 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
5666 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
5667 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
5668 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
5669 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
5670 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5671 isl_basic_set_free(bset1
);
5672 isl_basic_set_free(bset2
);
5676 isl_die(ctx
, isl_error_unknown
, "bad preimage",
5687 } preimage_domain_tests
[] = {
5688 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
5689 "{ A[j,i] -> B[i,j] }",
5690 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
5691 { "{ B[i] -> C[i]; D[i] -> E[i] }",
5692 "{ A[i] -> B[i + 1] }",
5693 "{ A[i] -> C[i + 1] }" },
5694 { "{ B[i] -> C[i]; B[i] -> E[i] }",
5695 "{ A[i] -> B[i + 1] }",
5696 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
5697 { "{ B[i] -> C[([i/2])] }",
5698 "{ A[i] -> B[2i] }",
5699 "{ A[i] -> C[i] }" },
5700 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
5701 "{ A[i] -> B[([i/5]), ([i/7])] }",
5702 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
5703 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
5704 "[N] -> { A[] -> B[([N/5])] }",
5705 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
5706 { "{ B[i] -> C[i] : exists a : i = 5 a }",
5707 "{ A[i] -> B[2i] }",
5708 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
5709 { "{ B[i] -> C[i] : exists a : i = 2 a; "
5710 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
5711 "{ A[i] -> B[2i] }",
5712 "{ A[i] -> C[2i] }" },
5713 { "{ A[i] -> B[i] }", "{ C[i] -> A[(i + floor(i/3))/2] }",
5714 "{ C[i] -> B[j] : 2j = i + floor(i/3) }" },
5717 static int test_preimage_union_map(isl_ctx
*ctx
)
5720 isl_union_map
*umap1
, *umap2
;
5724 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
5725 umap1
= isl_union_map_read_from_str(ctx
,
5726 preimage_domain_tests
[i
].map
);
5727 ma
= isl_multi_aff_read_from_str(ctx
,
5728 preimage_domain_tests
[i
].ma
);
5729 umap2
= isl_union_map_read_from_str(ctx
,
5730 preimage_domain_tests
[i
].res
);
5731 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
5732 equal
= isl_union_map_is_equal(umap1
, umap2
);
5733 isl_union_map_free(umap1
);
5734 isl_union_map_free(umap2
);
5738 isl_die(ctx
, isl_error_unknown
, "bad preimage",
5745 static int test_preimage(isl_ctx
*ctx
)
5747 if (test_preimage_basic_set(ctx
) < 0)
5749 if (test_preimage_union_map(ctx
) < 0)
5759 } pullback_tests
[] = {
5760 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
5761 "{ A[a,b] -> C[b + 2a] }" },
5762 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
5763 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
5764 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
5765 "{ A[a] -> C[(a)/6] }" },
5766 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
5767 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
5768 "{ A[a] -> C[(2a)/3] }" },
5769 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
5770 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
5771 "{ A[i,j] -> C[i + j, i + j] }"},
5772 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
5773 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
5774 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
5775 { "{ [i, j] -> [floor((i)/4) + floor((2*i+j)/5)] }",
5776 "{ [i, j] -> [floor((i)/3), j] }",
5777 "{ [i, j] -> [(floor((i)/12) + floor((j + 2*floor((i)/3))/5))] }" },
5780 static int test_pullback(isl_ctx
*ctx
)
5783 isl_multi_aff
*ma1
, *ma2
;
5787 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
5788 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
5789 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
5790 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
5791 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
5792 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
5793 isl_multi_aff_free(ma1
);
5794 isl_multi_aff_free(ma2
);
5798 isl_die(ctx
, isl_error_unknown
, "bad pullback",
5805 /* Check that negation is printed correctly and that equal expressions
5806 * are correctly identified.
5808 static int test_ast(isl_ctx
*ctx
)
5810 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
5814 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
5815 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
5816 expr
= isl_ast_expr_add(expr1
, expr2
);
5817 expr2
= isl_ast_expr_copy(expr
);
5818 expr
= isl_ast_expr_neg(expr
);
5819 expr2
= isl_ast_expr_neg(expr2
);
5820 equal
= isl_ast_expr_is_equal(expr
, expr2
);
5821 str
= isl_ast_expr_to_C_str(expr
);
5822 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
5824 isl_ast_expr_free(expr
);
5825 isl_ast_expr_free(expr2
);
5827 if (ok
< 0 || equal
< 0)
5830 isl_die(ctx
, isl_error_unknown
,
5831 "equal expressions not considered equal", return -1);
5833 isl_die(ctx
, isl_error_unknown
,
5834 "isl_ast_expr printed incorrectly", return -1);
5836 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
5837 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
5838 expr
= isl_ast_expr_add(expr1
, expr2
);
5839 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
5840 expr
= isl_ast_expr_sub(expr3
, expr
);
5841 str
= isl_ast_expr_to_C_str(expr
);
5842 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
5844 isl_ast_expr_free(expr
);
5849 isl_die(ctx
, isl_error_unknown
,
5850 "isl_ast_expr printed incorrectly", return -1);
5855 /* Check that isl_ast_build_expr_from_set returns a valid expression
5856 * for an empty set. Note that isl_ast_build_expr_from_set getting
5857 * called on an empty set probably indicates a bug in the caller.
5859 static int test_ast_build(isl_ctx
*ctx
)
5862 isl_ast_build
*build
;
5865 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5866 build
= isl_ast_build_from_context(set
);
5868 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
5869 expr
= isl_ast_build_expr_from_set(build
, set
);
5871 isl_ast_expr_free(expr
);
5872 isl_ast_build_free(build
);
5880 /* Internal data structure for before_for and after_for callbacks.
5882 * depth is the current depth
5883 * before is the number of times before_for has been called
5884 * after is the number of times after_for has been called
5886 struct isl_test_codegen_data
{
5892 /* This function is called before each for loop in the AST generated
5893 * from test_ast_gen1.
5895 * Increment the number of calls and the depth.
5896 * Check that the space returned by isl_ast_build_get_schedule_space
5897 * matches the target space of the schedule returned by
5898 * isl_ast_build_get_schedule.
5899 * Return an isl_id that is checked by the corresponding call
5902 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
5905 struct isl_test_codegen_data
*data
= user
;
5908 isl_union_map
*schedule
;
5909 isl_union_set
*uset
;
5914 ctx
= isl_ast_build_get_ctx(build
);
5916 if (data
->before
>= 3)
5917 isl_die(ctx
, isl_error_unknown
,
5918 "unexpected number of for nodes", return NULL
);
5919 if (data
->depth
>= 2)
5920 isl_die(ctx
, isl_error_unknown
,
5921 "unexpected depth", return NULL
);
5923 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
5927 schedule
= isl_ast_build_get_schedule(build
);
5928 uset
= isl_union_map_range(schedule
);
5931 if (isl_union_set_n_set(uset
) != 1) {
5932 isl_union_set_free(uset
);
5933 isl_die(ctx
, isl_error_unknown
,
5934 "expecting single range space", return NULL
);
5937 space
= isl_ast_build_get_schedule_space(build
);
5938 set
= isl_union_set_extract_set(uset
, space
);
5939 isl_union_set_free(uset
);
5940 empty
= isl_set_is_empty(set
);
5946 isl_die(ctx
, isl_error_unknown
,
5947 "spaces don't match", return NULL
);
5949 return isl_id_alloc(ctx
, name
, NULL
);
5952 /* This function is called after each for loop in the AST generated
5953 * from test_ast_gen1.
5955 * Increment the number of calls and decrement the depth.
5956 * Check that the annotation attached to the node matches
5957 * the isl_id returned by the corresponding call to before_for.
5959 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
5960 __isl_keep isl_ast_build
*build
, void *user
)
5962 struct isl_test_codegen_data
*data
= user
;
5970 if (data
->after
> data
->before
)
5971 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5972 "mismatch in number of for nodes",
5973 return isl_ast_node_free(node
));
5975 id
= isl_ast_node_get_annotation(node
);
5977 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5978 "missing annotation", return isl_ast_node_free(node
));
5980 name
= isl_id_get_name(id
);
5981 valid
= name
&& atoi(name
+ 1) == data
->depth
;
5985 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5986 "wrong annotation", return isl_ast_node_free(node
));
5991 /* Check that the before_each_for and after_each_for callbacks
5992 * are called for each for loop in the generated code,
5993 * that they are called in the right order and that the isl_id
5994 * returned from the before_each_for callback is attached to
5995 * the isl_ast_node passed to the corresponding after_each_for call.
5997 static int test_ast_gen1(isl_ctx
*ctx
)
6001 isl_union_map
*schedule
;
6002 isl_ast_build
*build
;
6004 struct isl_test_codegen_data data
;
6006 str
= "[N] -> { : N >= 10 }";
6007 set
= isl_set_read_from_str(ctx
, str
);
6008 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
6009 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
6010 schedule
= isl_union_map_read_from_str(ctx
, str
);
6015 build
= isl_ast_build_from_context(set
);
6016 build
= isl_ast_build_set_before_each_for(build
,
6017 &before_for
, &data
);
6018 build
= isl_ast_build_set_after_each_for(build
,
6020 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6021 isl_ast_build_free(build
);
6025 isl_ast_node_free(tree
);
6027 if (data
.before
!= 3 || data
.after
!= 3)
6028 isl_die(ctx
, isl_error_unknown
,
6029 "unexpected number of for nodes", return -1);
6034 /* Check that the AST generator handles domains that are integrally disjoint
6035 * but not rationally disjoint.
6037 static int test_ast_gen2(isl_ctx
*ctx
)
6041 isl_union_map
*schedule
;
6042 isl_union_map
*options
;
6043 isl_ast_build
*build
;
6046 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
6047 schedule
= isl_union_map_read_from_str(ctx
, str
);
6048 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6049 build
= isl_ast_build_from_context(set
);
6051 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
6052 options
= isl_union_map_read_from_str(ctx
, str
);
6053 build
= isl_ast_build_set_options(build
, options
);
6054 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6055 isl_ast_build_free(build
);
6058 isl_ast_node_free(tree
);
6063 /* Increment *user on each call.
6065 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
6066 __isl_keep isl_ast_build
*build
, void *user
)
6075 /* Test that unrolling tries to minimize the number of instances.
6076 * In particular, for the schedule given below, make sure it generates
6077 * 3 nodes (rather than 101).
6079 static int test_ast_gen3(isl_ctx
*ctx
)
6083 isl_union_map
*schedule
;
6084 isl_union_map
*options
;
6085 isl_ast_build
*build
;
6089 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
6090 schedule
= isl_union_map_read_from_str(ctx
, str
);
6091 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6093 str
= "{ [i] -> unroll[0] }";
6094 options
= isl_union_map_read_from_str(ctx
, str
);
6096 build
= isl_ast_build_from_context(set
);
6097 build
= isl_ast_build_set_options(build
, options
);
6098 build
= isl_ast_build_set_at_each_domain(build
,
6099 &count_domains
, &n_domain
);
6100 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6101 isl_ast_build_free(build
);
6105 isl_ast_node_free(tree
);
6108 isl_die(ctx
, isl_error_unknown
,
6109 "unexpected number of for nodes", return -1);
6114 /* Check that if the ast_build_exploit_nested_bounds options is set,
6115 * we do not get an outer if node in the generated AST,
6116 * while we do get such an outer if node if the options is not set.
6118 static int test_ast_gen4(isl_ctx
*ctx
)
6122 isl_union_map
*schedule
;
6123 isl_ast_build
*build
;
6125 enum isl_ast_node_type type
;
6128 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
6129 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
6131 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
6133 schedule
= isl_union_map_read_from_str(ctx
, str
);
6134 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6135 build
= isl_ast_build_from_context(set
);
6136 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6137 isl_ast_build_free(build
);
6141 type
= isl_ast_node_get_type(tree
);
6142 isl_ast_node_free(tree
);
6144 if (type
== isl_ast_node_if
)
6145 isl_die(ctx
, isl_error_unknown
,
6146 "not expecting if node", return -1);
6148 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
6150 schedule
= isl_union_map_read_from_str(ctx
, str
);
6151 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6152 build
= isl_ast_build_from_context(set
);
6153 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6154 isl_ast_build_free(build
);
6158 type
= isl_ast_node_get_type(tree
);
6159 isl_ast_node_free(tree
);
6161 if (type
!= isl_ast_node_if
)
6162 isl_die(ctx
, isl_error_unknown
,
6163 "expecting if node", return -1);
6165 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
6170 /* This function is called for each leaf in the AST generated
6171 * from test_ast_gen5.
6173 * We finalize the AST generation by extending the outer schedule
6174 * with a zero-dimensional schedule. If this results in any for loops,
6175 * then this means that we did not pass along enough information
6176 * about the outer schedule to the inner AST generation.
6178 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
6181 isl_union_map
*schedule
, *extra
;
6184 schedule
= isl_ast_build_get_schedule(build
);
6185 extra
= isl_union_map_copy(schedule
);
6186 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
6187 schedule
= isl_union_map_range_product(schedule
, extra
);
6188 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6189 isl_ast_build_free(build
);
6194 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
6195 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
6196 "code should not contain any for loop",
6197 return isl_ast_node_free(tree
));
6202 /* Check that we do not lose any information when going back and
6203 * forth between internal and external schedule.
6205 * In particular, we create an AST where we unroll the only
6206 * non-constant dimension in the schedule. We therefore do
6207 * not expect any for loops in the AST. However, older versions
6208 * of isl would not pass along enough information about the outer
6209 * schedule when performing an inner code generation from a create_leaf
6210 * callback, resulting in the inner code generation producing a for loop.
6212 static int test_ast_gen5(isl_ctx
*ctx
)
6216 isl_union_map
*schedule
, *options
;
6217 isl_ast_build
*build
;
6220 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
6221 schedule
= isl_union_map_read_from_str(ctx
, str
);
6223 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
6224 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
6225 options
= isl_union_map_read_from_str(ctx
, str
);
6227 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6228 build
= isl_ast_build_from_context(set
);
6229 build
= isl_ast_build_set_options(build
, options
);
6230 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
6231 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6232 isl_ast_build_free(build
);
6233 isl_ast_node_free(tree
);
6240 /* Check that the expression
6242 * [n] -> { [n/2] : n <= 0 and n % 2 = 0; [0] : n > 0 }
6244 * is not combined into
6248 * as this would result in n/2 being evaluated in parts of
6249 * the definition domain where n is not a multiple of 2.
6251 static int test_ast_expr(isl_ctx
*ctx
)
6255 isl_ast_build
*build
;
6260 min_max
= isl_options_get_ast_build_detect_min_max(ctx
);
6261 isl_options_set_ast_build_detect_min_max(ctx
, 1);
6263 str
= "[n] -> { [n/2] : n <= 0 and n % 2 = 0; [0] : n > 0 }";
6264 pa
= isl_pw_aff_read_from_str(ctx
, str
);
6265 build
= isl_ast_build_alloc(ctx
);
6266 expr
= isl_ast_build_expr_from_pw_aff(build
, pa
);
6267 is_min
= isl_ast_expr_get_type(expr
) == isl_ast_expr_op
&&
6268 isl_ast_expr_get_op_type(expr
) == isl_ast_op_min
;
6269 isl_ast_build_free(build
);
6270 isl_ast_expr_free(expr
);
6272 isl_options_set_ast_build_detect_min_max(ctx
, min_max
);
6277 isl_die(ctx
, isl_error_unknown
,
6278 "expressions should not be combined", return -1);
6283 static int test_ast_gen(isl_ctx
*ctx
)
6285 if (test_ast_gen1(ctx
) < 0)
6287 if (test_ast_gen2(ctx
) < 0)
6289 if (test_ast_gen3(ctx
) < 0)
6291 if (test_ast_gen4(ctx
) < 0)
6293 if (test_ast_gen5(ctx
) < 0)
6295 if (test_ast_expr(ctx
) < 0)
6300 /* Check if dropping output dimensions from an isl_pw_multi_aff
6303 static int test_pw_multi_aff(isl_ctx
*ctx
)
6306 isl_pw_multi_aff
*pma1
, *pma2
;
6309 str
= "{ [i,j] -> [i+j, 4i-j] }";
6310 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
6311 str
= "{ [i,j] -> [4i-j] }";
6312 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
6314 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
6316 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
6318 isl_pw_multi_aff_free(pma1
);
6319 isl_pw_multi_aff_free(pma2
);
6323 isl_die(ctx
, isl_error_unknown
,
6324 "expressions not equal", return -1);
6329 /* Check that we can properly parse multi piecewise affine expressions
6330 * where the piecewise affine expressions have different domains.
6332 static int test_multi_pw_aff(isl_ctx
*ctx
)
6335 isl_set
*dom
, *dom2
;
6336 isl_multi_pw_aff
*mpa1
, *mpa2
;
6341 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
6342 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
6343 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
6344 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
6345 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
6346 str
= "{ [i] -> [(i : i > 0), 2i] }";
6347 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
6349 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
6351 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
6352 dom
= isl_pw_aff_domain(pa
);
6353 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
6354 dom2
= isl_pw_aff_domain(pa
);
6355 equal_domain
= isl_set_is_equal(dom
, dom2
);
6359 isl_multi_pw_aff_free(mpa1
);
6360 isl_multi_pw_aff_free(mpa2
);
6365 isl_die(ctx
, isl_error_unknown
,
6366 "expressions not equal", return -1);
6368 if (equal_domain
< 0)
6371 isl_die(ctx
, isl_error_unknown
,
6372 "domains unexpectedly equal", return -1);
6377 /* This is a regression test for a bug where isl_basic_map_simplify
6378 * would end up in an infinite loop. In particular, we construct
6379 * an empty basic set that is not obviously empty.
6380 * isl_basic_set_is_empty marks the basic set as empty.
6381 * After projecting out i3, the variable can be dropped completely,
6382 * but isl_basic_map_simplify refrains from doing so if the basic set
6383 * is empty and would end up in an infinite loop if it didn't test
6384 * explicitly for empty basic maps in the outer loop.
6386 static int test_simplify_1(isl_ctx
*ctx
)
6389 isl_basic_set
*bset
;
6392 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
6393 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
6394 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
6396 bset
= isl_basic_set_read_from_str(ctx
, str
);
6397 empty
= isl_basic_set_is_empty(bset
);
6398 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
6399 isl_basic_set_free(bset
);
6403 isl_die(ctx
, isl_error_unknown
,
6404 "basic set should be empty", return -1);
6409 /* Check that the equality in the set description below
6410 * is simplified away.
6412 static int test_simplify_2(isl_ctx
*ctx
)
6415 isl_basic_set
*bset
;
6418 str
= "{ [a] : exists e0, e1: 32e1 = 31 + 31a + 31e0 }";
6419 bset
= isl_basic_set_read_from_str(ctx
, str
);
6420 universe
= isl_basic_set_plain_is_universe(bset
);
6421 isl_basic_set_free(bset
);
6426 isl_die(ctx
, isl_error_unknown
,
6427 "equality not simplified away", return -1);
6431 /* Some simplification tests.
6433 static int test_simplify(isl_ctx
*ctx
)
6435 if (test_simplify_1(ctx
) < 0)
6437 if (test_simplify_2(ctx
) < 0)
6442 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
6443 * with gbr context would fail to disable the use of the shifted tableau
6444 * when transferring equalities for the input to the context, resulting
6445 * in invalid sample values.
6447 static int test_partial_lexmin(isl_ctx
*ctx
)
6450 isl_basic_set
*bset
;
6451 isl_basic_map
*bmap
;
6454 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
6455 bmap
= isl_basic_map_read_from_str(ctx
, str
);
6456 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
6457 bset
= isl_basic_set_read_from_str(ctx
, str
);
6458 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
6467 /* Check that the variable compression performed on the existentially
6468 * quantified variables inside isl_basic_set_compute_divs is not confused
6469 * by the implicit equalities among the parameters.
6471 static int test_compute_divs(isl_ctx
*ctx
)
6474 isl_basic_set
*bset
;
6477 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
6478 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
6479 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
6480 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
6481 bset
= isl_basic_set_read_from_str(ctx
, str
);
6482 set
= isl_basic_set_compute_divs(bset
);
6490 /* Check that the reaching domain elements and the prefix schedule
6491 * at a leaf node are the same before and after grouping.
6493 static int test_schedule_tree_group_1(isl_ctx
*ctx
)
6498 isl_union_set
*uset
;
6499 isl_multi_union_pw_aff
*mupa
;
6500 isl_union_pw_multi_aff
*upma1
, *upma2
;
6501 isl_union_set
*domain1
, *domain2
;
6502 isl_union_map
*umap1
, *umap2
;
6503 isl_schedule_node
*node
;
6505 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10 }";
6506 uset
= isl_union_set_read_from_str(ctx
, str
);
6507 node
= isl_schedule_node_from_domain(uset
);
6508 node
= isl_schedule_node_child(node
, 0);
6509 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [9 - i] }]";
6510 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6511 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6512 node
= isl_schedule_node_child(node
, 0);
6513 str
= "[{ S1[i,j] -> [j]; S2[i,j] -> [j] }]";
6514 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6515 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6516 node
= isl_schedule_node_child(node
, 0);
6517 umap1
= isl_schedule_node_get_prefix_schedule_union_map(node
);
6518 upma1
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
6519 domain1
= isl_schedule_node_get_domain(node
);
6520 id
= isl_id_alloc(ctx
, "group", NULL
);
6521 node
= isl_schedule_node_parent(node
);
6522 node
= isl_schedule_node_group(node
, id
);
6523 node
= isl_schedule_node_child(node
, 0);
6524 umap2
= isl_schedule_node_get_prefix_schedule_union_map(node
);
6525 upma2
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
6526 domain2
= isl_schedule_node_get_domain(node
);
6527 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
6528 if (equal
>= 0 && equal
)
6529 equal
= isl_union_set_is_equal(domain1
, domain2
);
6530 if (equal
>= 0 && equal
)
6531 equal
= isl_union_map_is_equal(umap1
, umap2
);
6532 isl_union_map_free(umap1
);
6533 isl_union_map_free(umap2
);
6534 isl_union_set_free(domain1
);
6535 isl_union_set_free(domain2
);
6536 isl_union_pw_multi_aff_free(upma1
);
6537 isl_union_pw_multi_aff_free(upma2
);
6538 isl_schedule_node_free(node
);
6543 isl_die(ctx
, isl_error_unknown
,
6544 "expressions not equal", return -1);
6549 /* Check that we can have nested groupings and that the union map
6550 * schedule representation is the same before and after the grouping.
6551 * Note that after the grouping, the union map representation contains
6552 * the domain constraints from the ranges of the expansion nodes,
6553 * while they are missing from the union map representation of
6554 * the tree without expansion nodes.
6556 * Also check that the global expansion is as expected.
6558 static int test_schedule_tree_group_2(isl_ctx
*ctx
)
6560 int equal
, equal_expansion
;
6563 isl_union_set
*uset
;
6564 isl_union_map
*umap1
, *umap2
;
6565 isl_union_map
*expansion1
, *expansion2
;
6566 isl_union_set_list
*filters
;
6567 isl_multi_union_pw_aff
*mupa
;
6568 isl_schedule
*schedule
;
6569 isl_schedule_node
*node
;
6571 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10; "
6572 "S3[i,j] : 0 <= i,j < 10 }";
6573 uset
= isl_union_set_read_from_str(ctx
, str
);
6574 node
= isl_schedule_node_from_domain(uset
);
6575 node
= isl_schedule_node_child(node
, 0);
6576 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [i]; S3[i,j] -> [i] }]";
6577 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6578 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6579 node
= isl_schedule_node_child(node
, 0);
6580 str
= "{ S1[i,j] }";
6581 uset
= isl_union_set_read_from_str(ctx
, str
);
6582 filters
= isl_union_set_list_from_union_set(uset
);
6583 str
= "{ S2[i,j]; S3[i,j] }";
6584 uset
= isl_union_set_read_from_str(ctx
, str
);
6585 filters
= isl_union_set_list_add(filters
, uset
);
6586 node
= isl_schedule_node_insert_sequence(node
, filters
);
6587 node
= isl_schedule_node_child(node
, 1);
6588 node
= isl_schedule_node_child(node
, 0);
6589 str
= "{ S2[i,j] }";
6590 uset
= isl_union_set_read_from_str(ctx
, str
);
6591 filters
= isl_union_set_list_from_union_set(uset
);
6592 str
= "{ S3[i,j] }";
6593 uset
= isl_union_set_read_from_str(ctx
, str
);
6594 filters
= isl_union_set_list_add(filters
, uset
);
6595 node
= isl_schedule_node_insert_sequence(node
, filters
);
6597 schedule
= isl_schedule_node_get_schedule(node
);
6598 umap1
= isl_schedule_get_map(schedule
);
6599 uset
= isl_schedule_get_domain(schedule
);
6600 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
6601 isl_schedule_free(schedule
);
6603 node
= isl_schedule_node_parent(node
);
6604 node
= isl_schedule_node_parent(node
);
6605 id
= isl_id_alloc(ctx
, "group1", NULL
);
6606 node
= isl_schedule_node_group(node
, id
);
6607 node
= isl_schedule_node_child(node
, 1);
6608 node
= isl_schedule_node_child(node
, 0);
6609 id
= isl_id_alloc(ctx
, "group2", NULL
);
6610 node
= isl_schedule_node_group(node
, id
);
6612 schedule
= isl_schedule_node_get_schedule(node
);
6613 umap2
= isl_schedule_get_map(schedule
);
6614 isl_schedule_free(schedule
);
6616 node
= isl_schedule_node_root(node
);
6617 node
= isl_schedule_node_child(node
, 0);
6618 expansion1
= isl_schedule_node_get_subtree_expansion(node
);
6619 isl_schedule_node_free(node
);
6621 str
= "{ group1[i] -> S1[i,j] : 0 <= i,j < 10; "
6622 "group1[i] -> S2[i,j] : 0 <= i,j < 10; "
6623 "group1[i] -> S3[i,j] : 0 <= i,j < 10 }";
6625 expansion2
= isl_union_map_read_from_str(ctx
, str
);
6627 equal
= isl_union_map_is_equal(umap1
, umap2
);
6628 equal_expansion
= isl_union_map_is_equal(expansion1
, expansion2
);
6630 isl_union_map_free(umap1
);
6631 isl_union_map_free(umap2
);
6632 isl_union_map_free(expansion1
);
6633 isl_union_map_free(expansion2
);
6635 if (equal
< 0 || equal_expansion
< 0)
6638 isl_die(ctx
, isl_error_unknown
,
6639 "expressions not equal", return -1);
6640 if (!equal_expansion
)
6641 isl_die(ctx
, isl_error_unknown
,
6642 "unexpected expansion", return -1);
6647 /* Some tests for the isl_schedule_node_group function.
6649 static int test_schedule_tree_group(isl_ctx
*ctx
)
6651 if (test_schedule_tree_group_1(ctx
) < 0)
6653 if (test_schedule_tree_group_2(ctx
) < 0)
6662 { "{ rat: [i] : 0 <= i <= 10 }",
6663 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
6664 { "{ rat: [i] : FALSE }",
6665 "{ rat: coefficients[[cst] -> [a]] }" },
6667 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
6674 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
6675 "{ rat: [i] : 0 <= i <= 10 }" },
6676 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
6678 { "{ rat: coefficients[[cst] -> [a]] }",
6679 "{ rat: [i] : FALSE }" },
6682 /* Test the basic functionality of isl_basic_set_coefficients and
6683 * isl_basic_set_solutions.
6685 static int test_dual(isl_ctx
*ctx
)
6689 for (i
= 0; i
< ARRAY_SIZE(coef_tests
); ++i
) {
6691 isl_basic_set
*bset1
, *bset2
;
6693 bset1
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].set
);
6694 bset2
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].dual
);
6695 bset1
= isl_basic_set_coefficients(bset1
);
6696 equal
= isl_basic_set_is_equal(bset1
, bset2
);
6697 isl_basic_set_free(bset1
);
6698 isl_basic_set_free(bset2
);
6702 isl_die(ctx
, isl_error_unknown
,
6703 "incorrect dual", return -1);
6706 for (i
= 0; i
< ARRAY_SIZE(sol_tests
); ++i
) {
6708 isl_basic_set
*bset1
, *bset2
;
6710 bset1
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].set
);
6711 bset2
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].dual
);
6712 bset1
= isl_basic_set_solutions(bset1
);
6713 equal
= isl_basic_set_is_equal(bset1
, bset2
);
6714 isl_basic_set_free(bset1
);
6715 isl_basic_set_free(bset2
);
6719 isl_die(ctx
, isl_error_unknown
,
6720 "incorrect dual", return -1);
6730 const char *schedule
;
6735 { 0, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
6736 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6738 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
6739 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6741 { 1, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
6742 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6744 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
6745 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6747 { 0, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
6748 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6750 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
6751 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
6753 { 1, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
6754 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6756 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
6757 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
6761 /* Basic tiling tests. Create a schedule tree with a domain and a band node,
6762 * tile the band and then check if the tile and point bands have the
6763 * expected partial schedule.
6765 static int test_tile(isl_ctx
*ctx
)
6771 scale
= isl_options_get_tile_scale_tile_loops(ctx
);
6772 shift
= isl_options_get_tile_shift_point_loops(ctx
);
6774 for (i
= 0; i
< ARRAY_SIZE(tile_tests
); ++i
) {
6778 isl_union_set
*domain
;
6779 isl_multi_union_pw_aff
*mupa
, *mupa2
;
6780 isl_schedule_node
*node
;
6781 isl_multi_val
*sizes
;
6783 opt
= tile_tests
[i
].scale_tile
;
6784 isl_options_set_tile_scale_tile_loops(ctx
, opt
);
6785 opt
= tile_tests
[i
].shift_point
;
6786 isl_options_set_tile_shift_point_loops(ctx
, opt
);
6788 str
= tile_tests
[i
].domain
;
6789 domain
= isl_union_set_read_from_str(ctx
, str
);
6790 node
= isl_schedule_node_from_domain(domain
);
6791 node
= isl_schedule_node_child(node
, 0);
6792 str
= tile_tests
[i
].schedule
;
6793 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6794 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6795 str
= tile_tests
[i
].sizes
;
6796 sizes
= isl_multi_val_read_from_str(ctx
, str
);
6797 node
= isl_schedule_node_band_tile(node
, sizes
);
6799 str
= tile_tests
[i
].tile
;
6800 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6801 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
6802 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
, mupa2
);
6803 isl_multi_union_pw_aff_free(mupa
);
6804 isl_multi_union_pw_aff_free(mupa2
);
6806 node
= isl_schedule_node_child(node
, 0);
6808 str
= tile_tests
[i
].point
;
6809 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6810 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
6811 if (equal
>= 0 && equal
)
6812 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
,
6814 isl_multi_union_pw_aff_free(mupa
);
6815 isl_multi_union_pw_aff_free(mupa2
);
6817 isl_schedule_node_free(node
);
6822 isl_die(ctx
, isl_error_unknown
,
6823 "unexpected result", return -1);
6826 isl_options_set_tile_scale_tile_loops(ctx
, scale
);
6827 isl_options_set_tile_shift_point_loops(ctx
, shift
);
6832 /* Check that the domain hash of a space is equal to the hash
6833 * of the domain of the space.
6835 static int test_domain_hash(isl_ctx
*ctx
)
6839 uint32_t hash1
, hash2
;
6841 map
= isl_map_read_from_str(ctx
, "[n] -> { A[B[x] -> C[]] -> D[] }");
6842 space
= isl_map_get_space(map
);
6844 hash1
= isl_space_get_domain_hash(space
);
6845 space
= isl_space_domain(space
);
6846 hash2
= isl_space_get_hash(space
);
6847 isl_space_free(space
);
6852 isl_die(ctx
, isl_error_unknown
,
6853 "domain hash not equal to hash of domain", return -1);
6858 /* Check that a universe basic set that is not obviously equal to the universe
6859 * is still recognized as being equal to the universe.
6861 static int test_universe(isl_ctx
*ctx
)
6864 isl_basic_set
*bset
;
6867 s
= "{ [] : exists x, y : 3y <= 2x and y >= -3 + 2x and 2y >= 2 - x }";
6868 bset
= isl_basic_set_read_from_str(ctx
, s
);
6869 is_univ
= isl_basic_set_is_universe(bset
);
6870 isl_basic_set_free(bset
);
6875 isl_die(ctx
, isl_error_unknown
,
6876 "not recognized as universe set", return -1);
6881 /* Sets for which chambers are computed and checked.
6883 const char *chambers_tests
[] = {
6884 "[A, B, C] -> { [x, y, z] : x >= 0 and y >= 0 and y <= A - x and "
6885 "z >= 0 and z <= C - y and z <= B - x - y }",
6888 /* Add the domain of "cell" to "cells".
6890 static int add_cell(__isl_take isl_cell
*cell
, void *user
)
6892 isl_basic_set_list
**cells
= user
;
6895 dom
= isl_cell_get_domain(cell
);
6896 isl_cell_free(cell
);
6897 *cells
= isl_basic_set_list_add(*cells
, dom
);
6899 return *cells
? 0 : -1;
6902 /* Check that the elements of "list" are pairwise disjoint.
6904 static isl_stat
check_pairwise_disjoint(__isl_keep isl_basic_set_list
*list
)
6909 return isl_stat_error
;
6911 n
= isl_basic_set_list_n_basic_set(list
);
6912 for (i
= 0; i
< n
; ++i
) {
6913 isl_basic_set
*bset_i
;
6915 bset_i
= isl_basic_set_list_get_basic_set(list
, i
);
6916 for (j
= i
+ 1; j
< n
; ++j
) {
6917 isl_basic_set
*bset_j
;
6920 bset_j
= isl_basic_set_list_get_basic_set(list
, j
);
6921 disjoint
= isl_basic_set_is_disjoint(bset_i
, bset_j
);
6922 isl_basic_set_free(bset_j
);
6924 isl_die(isl_basic_set_list_get_ctx(list
),
6925 isl_error_unknown
, "not disjoint",
6927 if (disjoint
< 0 || !disjoint
)
6930 isl_basic_set_free(bset_i
);
6932 return isl_stat_error
;
6938 /* Check that the chambers computed by isl_vertices_foreach_disjoint_cell
6939 * are pairwise disjoint.
6941 static int test_chambers(isl_ctx
*ctx
)
6945 for (i
= 0; i
< ARRAY_SIZE(chambers_tests
); ++i
) {
6946 isl_basic_set
*bset
;
6947 isl_vertices
*vertices
;
6948 isl_basic_set_list
*cells
;
6951 bset
= isl_basic_set_read_from_str(ctx
, chambers_tests
[i
]);
6952 vertices
= isl_basic_set_compute_vertices(bset
);
6953 cells
= isl_basic_set_list_alloc(ctx
, 0);
6954 if (isl_vertices_foreach_disjoint_cell(vertices
, &add_cell
,
6956 cells
= isl_basic_set_list_free(cells
);
6957 ok
= check_pairwise_disjoint(cells
);
6958 isl_basic_set_list_free(cells
);
6959 isl_vertices_free(vertices
);
6960 isl_basic_set_free(bset
);
6971 int (*fn
)(isl_ctx
*ctx
);
6973 { "universe", &test_universe
},
6974 { "domain hash", &test_domain_hash
},
6975 { "dual", &test_dual
},
6976 { "dependence analysis", &test_flow
},
6977 { "val", &test_val
},
6978 { "compute divs", &test_compute_divs
},
6979 { "partial lexmin", &test_partial_lexmin
},
6980 { "simplify", &test_simplify
},
6981 { "curry", &test_curry
},
6982 { "piecewise multi affine expressions", &test_pw_multi_aff
},
6983 { "multi piecewise affine expressions", &test_multi_pw_aff
},
6984 { "conversion", &test_conversion
},
6985 { "list", &test_list
},
6986 { "align parameters", &test_align_parameters
},
6987 { "preimage", &test_preimage
},
6988 { "pullback", &test_pullback
},
6989 { "AST", &test_ast
},
6990 { "AST build", &test_ast_build
},
6991 { "AST generation", &test_ast_gen
},
6992 { "eliminate", &test_eliminate
},
6993 { "residue class", &test_residue_class
},
6994 { "div", &test_div
},
6995 { "slice", &test_slice
},
6996 { "fixed power", &test_fixed_power
},
6997 { "sample", &test_sample
},
6998 { "output", &test_output
},
6999 { "vertices", &test_vertices
},
7000 { "chambers", &test_chambers
},
7001 { "fixed", &test_fixed
},
7002 { "equal", &test_equal
},
7003 { "disjoint", &test_disjoint
},
7004 { "product", &test_product
},
7005 { "dim_max", &test_dim_max
},
7006 { "affine", &test_aff
},
7007 { "injective", &test_injective
},
7008 { "schedule (whole component)", &test_schedule_whole
},
7009 { "schedule (incremental)", &test_schedule_incremental
},
7010 { "schedule tree grouping", &test_schedule_tree_group
},
7011 { "tile", &test_tile
},
7012 { "union_pw", &test_union_pw
},
7013 { "eval", &test_eval
},
7014 { "parse", &test_parse
},
7015 { "single-valued", &test_sv
},
7016 { "affine hull", &test_affine_hull
},
7017 { "simple_hull", &test_simple_hull
},
7018 { "coalesce", &test_coalesce
},
7019 { "factorize", &test_factorize
},
7020 { "subset", &test_subset
},
7021 { "subtract", &test_subtract
},
7022 { "intersect", &test_intersect
},
7023 { "lexmin", &test_lexmin
},
7024 { "min", &test_min
},
7025 { "gist", &test_gist
},
7026 { "piecewise quasi-polynomials", &test_pwqp
},
7027 { "lift", &test_lift
},
7028 { "bound", &test_bound
},
7029 { "union", &test_union
},
7030 { "split periods", &test_split_periods
},
7031 { "lexicographic order", &test_lex
},
7032 { "bijectivity", &test_bijective
},
7033 { "dataflow analysis", &test_dep
},
7034 { "reading", &test_read
},
7035 { "bounded", &test_bounded
},
7036 { "construction", &test_construction
},
7037 { "dimension manipulation", &test_dim
},
7038 { "map application", &test_application
},
7039 { "convex hull", &test_convex_hull
},
7040 { "transitive closure", &test_closure
},
7043 int main(int argc
, char **argv
)
7046 struct isl_ctx
*ctx
;
7047 struct isl_options
*options
;
7049 options
= isl_options_new_with_defaults();
7051 argc
= isl_options_parse(options
, argc
, argv
, ISL_ARG_ALL
);
7053 ctx
= isl_ctx_alloc_with_options(&isl_options_args
, options
);
7054 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
7055 printf("%s\n", tests
[i
].name
);
7056 if (tests
[i
].fn(ctx
) < 0)