2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
12 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
15 * B.P. 105 - 78153 Le Chesnay, France
21 #include <isl_ctx_private.h>
22 #include <isl_map_private.h>
23 #include <isl_aff_private.h>
24 #include <isl_space_private.h>
27 #include <isl_constraint_private.h>
28 #include <isl/polynomial.h>
29 #include <isl/union_set.h>
30 #include <isl/union_map.h>
31 #include <isl_factorization.h>
32 #include <isl/schedule.h>
33 #include <isl/schedule_node.h>
34 #include <isl_options_private.h>
35 #include <isl/vertices.h>
36 #include <isl/ast_build.h>
39 #include <isl_ast_build_expr.h>
40 #include <isl/options.h>
42 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
46 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
49 char *pattern
= "%s/test_inputs/%s.%s";
51 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
53 filename
= isl_alloc_array(ctx
, char, length
);
58 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
63 void test_parse_map(isl_ctx
*ctx
, const char *str
)
67 map
= isl_map_read_from_str(ctx
, str
);
72 int test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
77 map
= isl_map_read_from_str(ctx
, str
);
78 map2
= isl_map_read_from_str(ctx
, str2
);
79 equal
= isl_map_is_equal(map
, map2
);
86 isl_die(ctx
, isl_error_unknown
, "maps not equal",
92 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
94 isl_pw_qpolynomial
*pwqp
;
96 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
98 isl_pw_qpolynomial_free(pwqp
);
101 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
105 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
107 isl_pw_aff_free(pwaff
);
110 /* Check that we can read an isl_multi_val from "str" without errors.
112 static int test_parse_multi_val(isl_ctx
*ctx
, const char *str
)
116 mv
= isl_multi_val_read_from_str(ctx
, str
);
117 isl_multi_val_free(mv
);
122 /* Pairs of binary relation representations that should represent
123 * the same binary relations.
128 } parse_map_equal_tests
[] = {
129 { "{ [x,y] : [([x/2]+y)/3] >= 1 }",
130 "{ [x, y] : 2y >= 6 - x }" },
131 { "{ [x,y] : x <= min(y, 2*y+3) }",
132 "{ [x,y] : x <= y, 2*y + 3 }" },
133 { "{ [x,y] : x >= min(y, 2*y+3) }",
134 "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }" },
135 { "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }",
136 "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }" },
137 { "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }",
138 "{ [i,j] -> [min(i,j)] }" },
139 { "{ [i,j] : i != j }",
140 "{ [i,j] : i < j or i > j }" },
141 { "{ [i,j] : (i+1)*2 >= j }",
142 "{ [i, j] : j <= 2 + 2i }" },
143 { "{ [i] -> [i > 0 ? 4 : 5] }",
144 "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }" },
145 { "[N=2,M] -> { [i=[(M+N)/4]] }",
146 "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }" },
147 { "{ [x] : x >= 0 }",
148 "{ [x] : x-0 >= 0 }" },
149 { "{ [i] : ((i > 10)) }",
150 "{ [i] : i >= 11 }" },
152 "{ [i] -> [0 * i] }" },
153 { "{ [a] -> [b] : (not false) }",
154 "{ [a] -> [b] : true }" },
155 { "{ [i] : i/2 <= 5 }",
156 "{ [i] : i <= 10 }" },
157 { "{Sym=[n] [i] : i <= n }",
158 "[n] -> { [i] : i <= n }" },
161 { "{ [i] : 2*floor(i/2) = i }",
162 "{ [i] : exists a : i = 2 a }" },
163 { "{ [a] -> [b] : a = 5 implies b = 5 }",
164 "{ [a] -> [b] : a != 5 or b = 5 }" },
165 { "{ [a] -> [a - 1 : a > 0] }",
166 "{ [a] -> [a - 1] : a > 0 }" },
167 { "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
168 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }" },
169 { "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
170 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
171 { "{ [a] -> [(a * 2) : a >= 0; 0 : a < 0] }",
172 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
173 { "{ [a] -> [(a * 2 : a >= 0); 0 : a < 0] }",
174 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
175 { "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
176 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
177 { "{ [a,b] -> [i,j] : a,b << i,j }",
178 "{ [a,b] -> [i,j] : a < i or (a = i and b < j) }" },
179 { "{ [a,b] -> [i,j] : a,b <<= i,j }",
180 "{ [a,b] -> [i,j] : a < i or (a = i and b <= j) }" },
181 { "{ [a,b] -> [i,j] : a,b >> i,j }",
182 "{ [a,b] -> [i,j] : a > i or (a = i and b > j) }" },
183 { "{ [a,b] -> [i,j] : a,b >>= i,j }",
184 "{ [a,b] -> [i,j] : a > i or (a = i and b >= j) }" },
185 { "{ [n] -> [i] : exists (a, b, c: 8b <= i - 32a and "
186 "8b >= -7 + i - 32 a and b >= 0 and b <= 3 and "
187 "8c < n - 32a and i < n and c >= 0 and "
188 "c <= 3 and c >= -4a) }",
189 "{ [n] -> [i] : 0 <= i < n }" },
190 { "{ [x] -> [] : exists (a, b: 0 <= a <= 1 and 0 <= b <= 3 and "
191 "2b <= x - 8a and 2b >= -1 + x - 8a) }",
192 "{ [x] -> [] : 0 <= x <= 15 }" },
195 int test_parse(struct isl_ctx
*ctx
)
199 const char *str
, *str2
;
201 if (test_parse_multi_val(ctx
, "{ A[B[2] -> C[5, 7]] }") < 0)
203 if (test_parse_multi_val(ctx
, "[n] -> { [2] }") < 0)
205 if (test_parse_multi_val(ctx
, "{ A[4, infty, NaN, -1/2, 2/3] }") < 0)
208 str
= "{ [i] -> [-i] }";
209 map
= isl_map_read_from_str(ctx
, str
);
213 str
= "{ A[i] -> L[([i/3])] }";
214 map
= isl_map_read_from_str(ctx
, str
);
218 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
219 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
220 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
222 for (i
= 0; i
< ARRAY_SIZE(parse_map_equal_tests
); ++i
) {
223 str
= parse_map_equal_tests
[i
].map1
;
224 str2
= parse_map_equal_tests
[i
].map2
;
225 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
229 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
230 map
= isl_map_read_from_str(ctx
, str
);
231 str
= "{ [new, old] -> [o0, o1] : "
232 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
233 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
234 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
235 map2
= isl_map_read_from_str(ctx
, str
);
236 assert(isl_map_is_equal(map
, map2
));
240 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
241 map
= isl_map_read_from_str(ctx
, str
);
242 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
243 map2
= isl_map_read_from_str(ctx
, str
);
244 assert(isl_map_is_equal(map
, map2
));
248 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
249 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
250 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
251 test_parse_pwqp(ctx
, "{ [x] -> ([(x)/2] * [(x)/3]) }");
256 static int test_read(isl_ctx
*ctx
)
260 isl_basic_set
*bset1
, *bset2
;
261 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
264 filename
= get_filename(ctx
, "set", "omega");
266 input
= fopen(filename
, "r");
269 bset1
= isl_basic_set_read_from_file(ctx
, input
);
270 bset2
= isl_basic_set_read_from_str(ctx
, str
);
272 equal
= isl_basic_set_is_equal(bset1
, bset2
);
274 isl_basic_set_free(bset1
);
275 isl_basic_set_free(bset2
);
283 isl_die(ctx
, isl_error_unknown
,
284 "read sets not equal", return -1);
289 static int test_bounded(isl_ctx
*ctx
)
294 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
295 bounded
= isl_set_is_bounded(set
);
301 isl_die(ctx
, isl_error_unknown
,
302 "set not considered bounded", return -1);
304 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
305 bounded
= isl_set_is_bounded(set
);
312 isl_die(ctx
, isl_error_unknown
,
313 "set considered bounded", return -1);
315 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
316 bounded
= isl_set_is_bounded(set
);
322 isl_die(ctx
, isl_error_unknown
,
323 "set considered bounded", return -1);
328 /* Construct the basic set { [i] : 5 <= i <= N } */
329 static int test_construction(isl_ctx
*ctx
)
339 dim
= isl_space_set_alloc(ctx
, 1, 1);
340 bset
= isl_basic_set_universe(isl_space_copy(dim
));
341 ls
= isl_local_space_from_space(dim
);
343 c
= isl_constraint_alloc_inequality(isl_local_space_copy(ls
));
344 isl_int_set_si(v
, -1);
345 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
346 isl_int_set_si(v
, 1);
347 isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
348 bset
= isl_basic_set_add_constraint(bset
, c
);
350 c
= isl_constraint_alloc_inequality(isl_local_space_copy(ls
));
351 isl_int_set_si(v
, 1);
352 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
353 isl_int_set_si(v
, -5);
354 isl_constraint_set_constant(c
, v
);
355 bset
= isl_basic_set_add_constraint(bset
, c
);
357 isl_local_space_free(ls
);
358 isl_basic_set_free(bset
);
365 static int test_dim(isl_ctx
*ctx
)
368 isl_map
*map1
, *map2
;
371 map1
= isl_map_read_from_str(ctx
,
372 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
373 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
374 map2
= isl_map_read_from_str(ctx
,
375 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
376 equal
= isl_map_is_equal(map1
, map2
);
379 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
380 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
381 if (equal
>= 0 && equal
)
382 equal
= isl_map_is_equal(map1
, map2
);
390 isl_die(ctx
, isl_error_unknown
,
391 "unexpected result", return -1);
393 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
394 map1
= isl_map_read_from_str(ctx
, str
);
395 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
396 map2
= isl_map_read_from_str(ctx
, str
);
397 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
398 equal
= isl_map_is_equal(map1
, map2
);
405 isl_die(ctx
, isl_error_unknown
,
406 "unexpected result", return -1);
412 __isl_give isl_val
*(*op
)(__isl_take isl_val
*v
);
416 { &isl_val_neg
, "0", "0" },
417 { &isl_val_abs
, "0", "0" },
418 { &isl_val_2exp
, "0", "1" },
419 { &isl_val_floor
, "0", "0" },
420 { &isl_val_ceil
, "0", "0" },
421 { &isl_val_neg
, "1", "-1" },
422 { &isl_val_neg
, "-1", "1" },
423 { &isl_val_neg
, "1/2", "-1/2" },
424 { &isl_val_neg
, "-1/2", "1/2" },
425 { &isl_val_neg
, "infty", "-infty" },
426 { &isl_val_neg
, "-infty", "infty" },
427 { &isl_val_neg
, "NaN", "NaN" },
428 { &isl_val_abs
, "1", "1" },
429 { &isl_val_abs
, "-1", "1" },
430 { &isl_val_abs
, "1/2", "1/2" },
431 { &isl_val_abs
, "-1/2", "1/2" },
432 { &isl_val_abs
, "infty", "infty" },
433 { &isl_val_abs
, "-infty", "infty" },
434 { &isl_val_abs
, "NaN", "NaN" },
435 { &isl_val_floor
, "1", "1" },
436 { &isl_val_floor
, "-1", "-1" },
437 { &isl_val_floor
, "1/2", "0" },
438 { &isl_val_floor
, "-1/2", "-1" },
439 { &isl_val_floor
, "infty", "infty" },
440 { &isl_val_floor
, "-infty", "-infty" },
441 { &isl_val_floor
, "NaN", "NaN" },
442 { &isl_val_ceil
, "1", "1" },
443 { &isl_val_ceil
, "-1", "-1" },
444 { &isl_val_ceil
, "1/2", "1" },
445 { &isl_val_ceil
, "-1/2", "0" },
446 { &isl_val_ceil
, "infty", "infty" },
447 { &isl_val_ceil
, "-infty", "-infty" },
448 { &isl_val_ceil
, "NaN", "NaN" },
449 { &isl_val_2exp
, "-3", "1/8" },
450 { &isl_val_2exp
, "-1", "1/2" },
451 { &isl_val_2exp
, "1", "2" },
452 { &isl_val_2exp
, "2", "4" },
453 { &isl_val_2exp
, "3", "8" },
454 { &isl_val_inv
, "1", "1" },
455 { &isl_val_inv
, "2", "1/2" },
456 { &isl_val_inv
, "1/2", "2" },
457 { &isl_val_inv
, "-2", "-1/2" },
458 { &isl_val_inv
, "-1/2", "-2" },
459 { &isl_val_inv
, "0", "NaN" },
460 { &isl_val_inv
, "NaN", "NaN" },
461 { &isl_val_inv
, "infty", "0" },
462 { &isl_val_inv
, "-infty", "0" },
465 /* Perform some basic tests of unary operations on isl_val objects.
467 static int test_un_val(isl_ctx
*ctx
)
471 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v
);
474 for (i
= 0; i
< ARRAY_SIZE(val_un_tests
); ++i
) {
475 v
= isl_val_read_from_str(ctx
, val_un_tests
[i
].arg
);
476 res
= isl_val_read_from_str(ctx
, val_un_tests
[i
].res
);
477 fn
= val_un_tests
[i
].op
;
479 if (isl_val_is_nan(res
))
480 ok
= isl_val_is_nan(v
);
482 ok
= isl_val_eq(v
, res
);
488 isl_die(ctx
, isl_error_unknown
,
489 "unexpected result", return -1);
496 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
497 __isl_take isl_val
*v2
);
499 ['+'] = { &isl_val_add
},
500 ['-'] = { &isl_val_sub
},
501 ['*'] = { &isl_val_mul
},
502 ['/'] = { &isl_val_div
},
503 ['g'] = { &isl_val_gcd
},
504 ['m'] = { &isl_val_min
},
505 ['M'] = { &isl_val_max
},
513 } val_bin_tests
[] = {
514 { "0", '+', "0", "0" },
515 { "1", '+', "0", "1" },
516 { "1", '+', "1", "2" },
517 { "1", '-', "1", "0" },
518 { "1", '*', "1", "1" },
519 { "1", '/', "1", "1" },
520 { "2", '*', "3", "6" },
521 { "2", '*', "1/2", "1" },
522 { "2", '*', "1/3", "2/3" },
523 { "2/3", '*', "3/5", "2/5" },
524 { "2/3", '*', "7/5", "14/15" },
525 { "2", '/', "1/2", "4" },
526 { "-2", '/', "-1/2", "4" },
527 { "-2", '/', "1/2", "-4" },
528 { "2", '/', "-1/2", "-4" },
529 { "2", '/', "2", "1" },
530 { "2", '/', "3", "2/3" },
531 { "2/3", '/', "5/3", "2/5" },
532 { "2/3", '/', "5/7", "14/15" },
533 { "0", '/', "0", "NaN" },
534 { "42", '/', "0", "NaN" },
535 { "-42", '/', "0", "NaN" },
536 { "infty", '/', "0", "NaN" },
537 { "-infty", '/', "0", "NaN" },
538 { "NaN", '/', "0", "NaN" },
539 { "0", '/', "NaN", "NaN" },
540 { "42", '/', "NaN", "NaN" },
541 { "-42", '/', "NaN", "NaN" },
542 { "infty", '/', "NaN", "NaN" },
543 { "-infty", '/', "NaN", "NaN" },
544 { "NaN", '/', "NaN", "NaN" },
545 { "0", '/', "infty", "0" },
546 { "42", '/', "infty", "0" },
547 { "-42", '/', "infty", "0" },
548 { "infty", '/', "infty", "NaN" },
549 { "-infty", '/', "infty", "NaN" },
550 { "NaN", '/', "infty", "NaN" },
551 { "0", '/', "-infty", "0" },
552 { "42", '/', "-infty", "0" },
553 { "-42", '/', "-infty", "0" },
554 { "infty", '/', "-infty", "NaN" },
555 { "-infty", '/', "-infty", "NaN" },
556 { "NaN", '/', "-infty", "NaN" },
557 { "1", '-', "1/3", "2/3" },
558 { "1/3", '+', "1/2", "5/6" },
559 { "1/2", '+', "1/2", "1" },
560 { "3/4", '-', "1/4", "1/2" },
561 { "1/2", '-', "1/3", "1/6" },
562 { "infty", '+', "42", "infty" },
563 { "infty", '+', "infty", "infty" },
564 { "42", '+', "infty", "infty" },
565 { "infty", '-', "infty", "NaN" },
566 { "infty", '*', "infty", "infty" },
567 { "infty", '*', "-infty", "-infty" },
568 { "-infty", '*', "infty", "-infty" },
569 { "-infty", '*', "-infty", "infty" },
570 { "0", '*', "infty", "NaN" },
571 { "1", '*', "infty", "infty" },
572 { "infty", '*', "0", "NaN" },
573 { "infty", '*', "42", "infty" },
574 { "42", '-', "infty", "-infty" },
575 { "infty", '+', "-infty", "NaN" },
576 { "4", 'g', "6", "2" },
577 { "5", 'g', "6", "1" },
578 { "42", 'm', "3", "3" },
579 { "42", 'M', "3", "42" },
580 { "3", 'm', "42", "3" },
581 { "3", 'M', "42", "42" },
582 { "42", 'm', "infty", "42" },
583 { "42", 'M', "infty", "infty" },
584 { "42", 'm', "-infty", "-infty" },
585 { "42", 'M', "-infty", "42" },
586 { "42", 'm', "NaN", "NaN" },
587 { "42", 'M', "NaN", "NaN" },
588 { "infty", 'm', "-infty", "-infty" },
589 { "infty", 'M', "-infty", "infty" },
592 /* Perform some basic tests of binary operations on isl_val objects.
594 static int test_bin_val(isl_ctx
*ctx
)
597 isl_val
*v1
, *v2
, *res
;
598 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
599 __isl_take isl_val
*v2
);
602 for (i
= 0; i
< ARRAY_SIZE(val_bin_tests
); ++i
) {
603 v1
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg1
);
604 v2
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg2
);
605 res
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].res
);
606 fn
= val_bin_op
[val_bin_tests
[i
].op
].fn
;
608 if (isl_val_is_nan(res
))
609 ok
= isl_val_is_nan(v1
);
611 ok
= isl_val_eq(v1
, res
);
617 isl_die(ctx
, isl_error_unknown
,
618 "unexpected result", return -1);
624 /* Perform some basic tests on isl_val objects.
626 static int test_val(isl_ctx
*ctx
)
628 if (test_un_val(ctx
) < 0)
630 if (test_bin_val(ctx
) < 0)
635 /* Sets described using existentially quantified variables that
636 * can also be described without.
638 static const char *elimination_tests
[] = {
639 "{ [i,j] : 2 * [i/2] + 3 * [j/4] <= 10 and 2 i = j }",
640 "{ [m, w] : exists a : w - 2m - 5 <= 3a <= m - 2w }",
641 "{ [m, w] : exists a : w >= 0 and a < m and -1 + w <= a <= 2m - w }",
644 /* Check that redundant existentially quantified variables are
647 static int test_elimination(isl_ctx
*ctx
)
653 for (i
= 0; i
< ARRAY_SIZE(elimination_tests
); ++i
) {
654 bset
= isl_basic_set_read_from_str(ctx
, elimination_tests
[i
]);
655 n
= isl_basic_set_dim(bset
, isl_dim_div
);
656 isl_basic_set_free(bset
);
660 isl_die(ctx
, isl_error_unknown
,
661 "expecting no existentials", return -1);
667 static int test_div(isl_ctx
*ctx
)
675 struct isl_basic_set
*bset
;
676 struct isl_constraint
*c
;
681 dim
= isl_space_set_alloc(ctx
, 0, 3);
682 bset
= isl_basic_set_universe(isl_space_copy(dim
));
683 ls
= isl_local_space_from_space(dim
);
685 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
686 isl_int_set_si(v
, -1);
687 isl_constraint_set_constant(c
, v
);
688 isl_int_set_si(v
, 1);
689 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
690 isl_int_set_si(v
, 3);
691 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
692 bset
= isl_basic_set_add_constraint(bset
, c
);
694 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
695 isl_int_set_si(v
, 1);
696 isl_constraint_set_constant(c
, v
);
697 isl_int_set_si(v
, -1);
698 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
699 isl_int_set_si(v
, 3);
700 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
701 bset
= isl_basic_set_add_constraint(bset
, c
);
703 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
705 assert(bset
&& bset
->n_div
== 1);
706 isl_local_space_free(ls
);
707 isl_basic_set_free(bset
);
710 dim
= isl_space_set_alloc(ctx
, 0, 3);
711 bset
= isl_basic_set_universe(isl_space_copy(dim
));
712 ls
= isl_local_space_from_space(dim
);
714 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
715 isl_int_set_si(v
, 1);
716 isl_constraint_set_constant(c
, v
);
717 isl_int_set_si(v
, -1);
718 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
719 isl_int_set_si(v
, 3);
720 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
721 bset
= isl_basic_set_add_constraint(bset
, c
);
723 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
724 isl_int_set_si(v
, -1);
725 isl_constraint_set_constant(c
, v
);
726 isl_int_set_si(v
, 1);
727 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
728 isl_int_set_si(v
, 3);
729 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
730 bset
= isl_basic_set_add_constraint(bset
, c
);
732 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
734 assert(bset
&& bset
->n_div
== 1);
735 isl_local_space_free(ls
);
736 isl_basic_set_free(bset
);
739 dim
= isl_space_set_alloc(ctx
, 0, 3);
740 bset
= isl_basic_set_universe(isl_space_copy(dim
));
741 ls
= isl_local_space_from_space(dim
);
743 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
744 isl_int_set_si(v
, 1);
745 isl_constraint_set_constant(c
, v
);
746 isl_int_set_si(v
, -1);
747 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
748 isl_int_set_si(v
, 3);
749 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
750 bset
= isl_basic_set_add_constraint(bset
, c
);
752 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
753 isl_int_set_si(v
, -3);
754 isl_constraint_set_constant(c
, v
);
755 isl_int_set_si(v
, 1);
756 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
757 isl_int_set_si(v
, 4);
758 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
759 bset
= isl_basic_set_add_constraint(bset
, c
);
761 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
763 assert(bset
&& bset
->n_div
== 1);
764 isl_local_space_free(ls
);
765 isl_basic_set_free(bset
);
768 dim
= isl_space_set_alloc(ctx
, 0, 3);
769 bset
= isl_basic_set_universe(isl_space_copy(dim
));
770 ls
= isl_local_space_from_space(dim
);
772 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
773 isl_int_set_si(v
, 2);
774 isl_constraint_set_constant(c
, v
);
775 isl_int_set_si(v
, -1);
776 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
777 isl_int_set_si(v
, 3);
778 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
779 bset
= isl_basic_set_add_constraint(bset
, c
);
781 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
782 isl_int_set_si(v
, -1);
783 isl_constraint_set_constant(c
, v
);
784 isl_int_set_si(v
, 1);
785 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
786 isl_int_set_si(v
, 6);
787 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
788 bset
= isl_basic_set_add_constraint(bset
, c
);
790 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
792 assert(isl_basic_set_is_empty(bset
));
793 isl_local_space_free(ls
);
794 isl_basic_set_free(bset
);
797 dim
= isl_space_set_alloc(ctx
, 0, 3);
798 bset
= isl_basic_set_universe(isl_space_copy(dim
));
799 ls
= isl_local_space_from_space(dim
);
801 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
802 isl_int_set_si(v
, -1);
803 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
804 isl_int_set_si(v
, 3);
805 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
806 bset
= isl_basic_set_add_constraint(bset
, c
);
808 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
809 isl_int_set_si(v
, 1);
810 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
811 isl_int_set_si(v
, -3);
812 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
813 bset
= isl_basic_set_add_constraint(bset
, c
);
815 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
817 assert(bset
&& bset
->n_div
== 0);
818 isl_basic_set_free(bset
);
819 isl_local_space_free(ls
);
822 dim
= isl_space_set_alloc(ctx
, 0, 3);
823 bset
= isl_basic_set_universe(isl_space_copy(dim
));
824 ls
= isl_local_space_from_space(dim
);
826 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
827 isl_int_set_si(v
, -1);
828 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
829 isl_int_set_si(v
, 6);
830 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
831 bset
= isl_basic_set_add_constraint(bset
, c
);
833 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
834 isl_int_set_si(v
, 1);
835 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
836 isl_int_set_si(v
, -3);
837 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
838 bset
= isl_basic_set_add_constraint(bset
, c
);
840 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
842 assert(bset
&& bset
->n_div
== 1);
843 isl_basic_set_free(bset
);
844 isl_local_space_free(ls
);
847 /* This test is a bit tricky. We set up an equality
849 * Normalization of divs creates _two_ divs
852 * Afterwards e0 is removed again because it has coefficient -1
853 * and we end up with the original equality and div again.
854 * Perhaps we can avoid the introduction of this temporary div.
856 dim
= isl_space_set_alloc(ctx
, 0, 4);
857 bset
= isl_basic_set_universe(isl_space_copy(dim
));
858 ls
= isl_local_space_from_space(dim
);
860 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
861 isl_int_set_si(v
, -1);
862 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
863 isl_int_set_si(v
, -3);
864 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
865 isl_int_set_si(v
, -3);
866 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
867 isl_int_set_si(v
, 6);
868 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
869 bset
= isl_basic_set_add_constraint(bset
, c
);
871 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
873 /* Test disabled for now */
875 assert(bset && bset->n_div == 1);
877 isl_local_space_free(ls
);
878 isl_basic_set_free(bset
);
881 dim
= isl_space_set_alloc(ctx
, 0, 5);
882 bset
= isl_basic_set_universe(isl_space_copy(dim
));
883 ls
= isl_local_space_from_space(dim
);
885 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
886 isl_int_set_si(v
, -1);
887 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
888 isl_int_set_si(v
, -3);
889 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
890 isl_int_set_si(v
, -3);
891 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
892 isl_int_set_si(v
, 6);
893 isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
894 bset
= isl_basic_set_add_constraint(bset
, c
);
896 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
897 isl_int_set_si(v
, -1);
898 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
899 isl_int_set_si(v
, 1);
900 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
901 isl_int_set_si(v
, 1);
902 isl_constraint_set_constant(c
, v
);
903 bset
= isl_basic_set_add_constraint(bset
, c
);
905 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
907 /* Test disabled for now */
909 assert(bset && bset->n_div == 1);
911 isl_local_space_free(ls
);
912 isl_basic_set_free(bset
);
915 dim
= isl_space_set_alloc(ctx
, 0, 4);
916 bset
= isl_basic_set_universe(isl_space_copy(dim
));
917 ls
= isl_local_space_from_space(dim
);
919 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
920 isl_int_set_si(v
, 1);
921 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
922 isl_int_set_si(v
, -1);
923 isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
924 isl_int_set_si(v
, -2);
925 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
926 bset
= isl_basic_set_add_constraint(bset
, c
);
928 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
929 isl_int_set_si(v
, -1);
930 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
931 isl_int_set_si(v
, 3);
932 isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
933 isl_int_set_si(v
, 2);
934 isl_constraint_set_constant(c
, v
);
935 bset
= isl_basic_set_add_constraint(bset
, c
);
937 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
939 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
941 assert(!isl_basic_set_is_empty(bset
));
943 isl_local_space_free(ls
);
944 isl_basic_set_free(bset
);
947 dim
= isl_space_set_alloc(ctx
, 0, 3);
948 bset
= isl_basic_set_universe(isl_space_copy(dim
));
949 ls
= isl_local_space_from_space(dim
);
951 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
952 isl_int_set_si(v
, 1);
953 isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
954 isl_int_set_si(v
, -2);
955 isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
956 bset
= isl_basic_set_add_constraint(bset
, c
);
958 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
960 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
962 isl_local_space_free(ls
);
963 isl_basic_set_free(bset
);
967 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
968 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
969 set
= isl_set_read_from_str(ctx
, str
);
970 set
= isl_set_compute_divs(set
);
975 if (test_elimination(ctx
) < 0)
978 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
979 set
= isl_set_read_from_str(ctx
, str
);
980 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
981 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
982 empty
= isl_set_is_empty(set
);
987 isl_die(ctx
, isl_error_unknown
,
988 "result not as accurate as expected", return -1);
993 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
997 struct isl_basic_set
*bset1
, *bset2
;
998 struct isl_basic_map
*bmap
;
1000 filename
= get_filename(ctx
, name
, "omega");
1002 input
= fopen(filename
, "r");
1005 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1006 bmap
= isl_basic_map_read_from_file(ctx
, input
);
1008 bset1
= isl_basic_set_apply(bset1
, bmap
);
1010 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1012 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1014 isl_basic_set_free(bset1
);
1015 isl_basic_set_free(bset2
);
1021 static int test_application(isl_ctx
*ctx
)
1023 test_application_case(ctx
, "application");
1024 test_application_case(ctx
, "application2");
1029 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
1033 struct isl_basic_set
*bset1
, *bset2
;
1035 filename
= get_filename(ctx
, name
, "polylib");
1037 input
= fopen(filename
, "r");
1040 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1041 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1043 bset1
= isl_basic_set_affine_hull(bset1
);
1045 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1047 isl_basic_set_free(bset1
);
1048 isl_basic_set_free(bset2
);
1054 int test_affine_hull(struct isl_ctx
*ctx
)
1058 isl_basic_set
*bset
, *bset2
;
1062 test_affine_hull_case(ctx
, "affine2");
1063 test_affine_hull_case(ctx
, "affine");
1064 test_affine_hull_case(ctx
, "affine3");
1066 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
1067 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
1068 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
1069 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
1070 set
= isl_set_read_from_str(ctx
, str
);
1071 bset
= isl_set_affine_hull(set
);
1072 n
= isl_basic_set_dim(bset
, isl_dim_div
);
1073 isl_basic_set_free(bset
);
1075 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
1078 /* Check that isl_map_affine_hull is not confused by
1079 * the reordering of divs in isl_map_align_divs.
1081 str
= "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1082 "32e0 = b and 32e1 = c); "
1083 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1084 set
= isl_set_read_from_str(ctx
, str
);
1085 bset
= isl_set_affine_hull(set
);
1086 isl_basic_set_free(bset
);
1090 str
= "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1091 "32e2 = 31 + 31e0 }";
1092 set
= isl_set_read_from_str(ctx
, str
);
1093 bset
= isl_set_affine_hull(set
);
1094 str
= "{ [a] : exists e : a = 32 e }";
1095 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1096 subset
= isl_basic_set_is_subset(bset
, bset2
);
1097 isl_basic_set_free(bset
);
1098 isl_basic_set_free(bset2
);
1102 isl_die(ctx
, isl_error_unknown
, "not as accurate as expected",
1108 /* Pairs of maps and the corresponding expected results of
1109 * isl_map_plain_unshifted_simple_hull.
1114 } plain_unshifted_simple_hull_tests
[] = {
1115 { "{ [i] -> [j] : i >= 1 and j >= 1 or i >= 2 and j <= 10 }",
1116 "{ [i] -> [j] : i >= 1 }" },
1117 { "{ [n] -> [i,j,k] : (i mod 3 = 2 and j mod 4 = 2) or "
1118 "(j mod 4 = 2 and k mod 6 = n) }",
1119 "{ [n] -> [i,j,k] : j mod 4 = 2 }" },
1122 /* Basic tests for isl_map_plain_unshifted_simple_hull.
1124 static int test_plain_unshifted_simple_hull(isl_ctx
*ctx
)
1128 isl_basic_map
*hull
, *expected
;
1131 for (i
= 0; i
< ARRAY_SIZE(plain_unshifted_simple_hull_tests
); ++i
) {
1133 str
= plain_unshifted_simple_hull_tests
[i
].map
;
1134 map
= isl_map_read_from_str(ctx
, str
);
1135 str
= plain_unshifted_simple_hull_tests
[i
].hull
;
1136 expected
= isl_basic_map_read_from_str(ctx
, str
);
1137 hull
= isl_map_plain_unshifted_simple_hull(map
);
1138 equal
= isl_basic_map_is_equal(hull
, expected
);
1139 isl_basic_map_free(hull
);
1140 isl_basic_map_free(expected
);
1144 isl_die(ctx
, isl_error_unknown
, "unexpected hull",
1151 /* Pairs of sets and the corresponding expected results of
1152 * isl_set_unshifted_simple_hull.
1157 } unshifted_simple_hull_tests
[] = {
1158 { "{ [0,x,y] : x <= -1; [1,x,y] : x <= y <= -x; [2,x,y] : x <= 1 }",
1159 "{ [t,x,y] : 0 <= t <= 2 and x <= 1 }" },
1162 /* Basic tests for isl_set_unshifted_simple_hull.
1164 static int test_unshifted_simple_hull(isl_ctx
*ctx
)
1168 isl_basic_set
*hull
, *expected
;
1171 for (i
= 0; i
< ARRAY_SIZE(unshifted_simple_hull_tests
); ++i
) {
1173 str
= unshifted_simple_hull_tests
[i
].set
;
1174 set
= isl_set_read_from_str(ctx
, str
);
1175 str
= unshifted_simple_hull_tests
[i
].hull
;
1176 expected
= isl_basic_set_read_from_str(ctx
, str
);
1177 hull
= isl_set_unshifted_simple_hull(set
);
1178 equal
= isl_basic_set_is_equal(hull
, expected
);
1179 isl_basic_set_free(hull
);
1180 isl_basic_set_free(expected
);
1184 isl_die(ctx
, isl_error_unknown
, "unexpected hull",
1191 static int test_simple_hull(struct isl_ctx
*ctx
)
1195 isl_basic_set
*bset
;
1198 str
= "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x;"
1199 "[y, x] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }";
1200 set
= isl_set_read_from_str(ctx
, str
);
1201 bset
= isl_set_simple_hull(set
);
1202 is_empty
= isl_basic_set_is_empty(bset
);
1203 isl_basic_set_free(bset
);
1205 if (is_empty
== isl_bool_error
)
1208 if (is_empty
== isl_bool_false
)
1209 isl_die(ctx
, isl_error_unknown
, "Empty set should be detected",
1212 if (test_plain_unshifted_simple_hull(ctx
) < 0)
1214 if (test_unshifted_simple_hull(ctx
) < 0)
1220 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
1224 struct isl_basic_set
*bset1
, *bset2
;
1225 struct isl_set
*set
;
1227 filename
= get_filename(ctx
, name
, "polylib");
1229 input
= fopen(filename
, "r");
1232 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1233 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1235 set
= isl_basic_set_union(bset1
, bset2
);
1236 bset1
= isl_set_convex_hull(set
);
1238 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1240 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1242 isl_basic_set_free(bset1
);
1243 isl_basic_set_free(bset2
);
1252 } convex_hull_tests
[] = {
1253 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1254 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1255 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1256 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1257 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1258 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1259 "i2 <= 5 and i2 >= 4; "
1260 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1261 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1262 "i2 <= 5 + i0 and i2 >= i0 }" },
1263 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1264 "{ [x, y] : 1 = 0 }" },
1267 static int test_convex_hull_algo(isl_ctx
*ctx
, int convex
)
1270 int orig_convex
= ctx
->opt
->convex
;
1271 ctx
->opt
->convex
= convex
;
1273 test_convex_hull_case(ctx
, "convex0");
1274 test_convex_hull_case(ctx
, "convex1");
1275 test_convex_hull_case(ctx
, "convex2");
1276 test_convex_hull_case(ctx
, "convex3");
1277 test_convex_hull_case(ctx
, "convex4");
1278 test_convex_hull_case(ctx
, "convex5");
1279 test_convex_hull_case(ctx
, "convex6");
1280 test_convex_hull_case(ctx
, "convex7");
1281 test_convex_hull_case(ctx
, "convex8");
1282 test_convex_hull_case(ctx
, "convex9");
1283 test_convex_hull_case(ctx
, "convex10");
1284 test_convex_hull_case(ctx
, "convex11");
1285 test_convex_hull_case(ctx
, "convex12");
1286 test_convex_hull_case(ctx
, "convex13");
1287 test_convex_hull_case(ctx
, "convex14");
1288 test_convex_hull_case(ctx
, "convex15");
1290 for (i
= 0; i
< ARRAY_SIZE(convex_hull_tests
); ++i
) {
1291 isl_set
*set1
, *set2
;
1294 set1
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].set
);
1295 set2
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].hull
);
1296 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
1297 equal
= isl_set_is_equal(set1
, set2
);
1304 isl_die(ctx
, isl_error_unknown
,
1305 "unexpected convex hull", return -1);
1308 ctx
->opt
->convex
= orig_convex
;
1313 static int test_convex_hull(isl_ctx
*ctx
)
1315 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
) < 0)
1317 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
) < 0)
1322 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
1326 struct isl_basic_set
*bset1
, *bset2
;
1328 filename
= get_filename(ctx
, name
, "polylib");
1330 input
= fopen(filename
, "r");
1333 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1334 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1336 bset1
= isl_basic_set_gist(bset1
, bset2
);
1338 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1340 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1342 isl_basic_set_free(bset1
);
1343 isl_basic_set_free(bset2
);
1349 /* Inputs to isl_map_plain_gist_basic_map, along with the expected output.
1353 const char *context
;
1355 } plain_gist_tests
[] = {
1356 { "{ [i] -> [j] : i >= 1 and j >= 1 or i >= 2 and j <= 10 }",
1357 "{ [i] -> [j] : i >= 1 }",
1358 "{ [i] -> [j] : j >= 1 or i >= 2 and j <= 10 }" },
1359 { "{ [n] -> [i,j,k] : (i mod 3 = 2 and j mod 4 = 2) or "
1360 "(j mod 4 = 2 and k mod 6 = n) }",
1361 "{ [n] -> [i,j,k] : j mod 4 = 2 }",
1362 "{ [n] -> [i,j,k] : (i mod 3 = 2) or (k mod 6 = n) }" },
1363 { "{ [i] -> [j] : i > j and (exists a,b : i <= 2a + 5b <= 2) }",
1364 "{ [i] -> [j] : i > j }",
1365 "{ [i] -> [j] : exists a,b : i <= 2a + 5b <= 2 }" },
1368 /* Basic tests for isl_map_plain_gist_basic_map.
1370 static int test_plain_gist(isl_ctx
*ctx
)
1374 for (i
= 0; i
< ARRAY_SIZE(plain_gist_tests
); ++i
) {
1377 isl_map
*map
, *gist
;
1378 isl_basic_map
*context
;
1380 map
= isl_map_read_from_str(ctx
, plain_gist_tests
[i
].map
);
1381 str
= plain_gist_tests
[i
].context
;
1382 context
= isl_basic_map_read_from_str(ctx
, str
);
1383 map
= isl_map_plain_gist_basic_map(map
, context
);
1384 gist
= isl_map_read_from_str(ctx
, plain_gist_tests
[i
].gist
);
1385 equal
= isl_map_is_equal(map
, gist
);
1391 isl_die(ctx
, isl_error_unknown
,
1392 "incorrect gist result", return -1);
1400 const char *context
;
1403 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1404 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1405 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1406 "{ [a, b, c] : a <= 15 }" },
1407 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1408 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1409 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1410 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1411 { "{ [m, n, a, b] : a <= 2147 + n }",
1412 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1413 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1414 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1416 "{ [m, n, ku, kl] }" },
1417 { "{ [a, a, b] : a >= 10 }",
1418 "{ [a, b, c] : c >= a and c <= b and c >= 2 }",
1419 "{ [a, a, b] : a >= 10 }" },
1420 { "{ [i, j] : i >= 0 and i + j >= 0 }", "{ [i, j] : i <= 0 }",
1421 "{ [0, j] : j >= 0 }" },
1422 /* Check that no constraints on i6 are introduced in the gist */
1423 { "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1424 "20e0 <= 1530 - 4t1 - 5i4 and 20e0 >= 1511 - 4t1 - 5i4 and "
1425 "5e0 <= 381 - t1 and i4 <= 1) }",
1426 "[t1] -> { [i4, i6] : exists (e0 = floor((-t1 + i6)/5): "
1427 "5e0 = -t1 + i6 and i6 <= 6 and i6 >= 3) }",
1428 "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1429 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 <= 1530 - 4t1 - 5i4 and "
1430 "20e0 >= 1511 - 4t1 - 5i4) }" },
1431 /* Check that no constraints on i6 are introduced in the gist */
1432 { "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((1 + i4)/2), "
1433 "e1 = floor((1530 - 4t1 - 5i4)/20), "
1434 "e2 = floor((-4t1 - 5i4 + 10*floor((1 + i4)/2))/20), "
1435 "e3 = floor((-1 + i4)/2): t2 = 0 and 2e3 = -1 + i4 and "
1436 "20e2 >= -19 - 4t1 - 5i4 + 10e0 and 5e2 <= 1 - t1 and "
1437 "2e0 <= 1 + i4 and 2e0 >= i4 and "
1438 "20e1 <= 1530 - 4t1 - 5i4 and "
1439 "20e1 >= 1511 - 4t1 - 5i4 and i4 <= 1 and "
1440 "5e1 <= 381 - t1 and 20e2 <= -4t1 - 5i4 + 10e0) }",
1441 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((-17 + i4)/2), "
1442 "e1 = floor((-t1 + i6)/5): 5e1 = -t1 + i6 and "
1443 "2e0 <= -17 + i4 and 2e0 >= -18 + i4 and "
1444 "10e0 <= -91 + 5i4 + 4i6 and "
1445 "10e0 >= -105 + 5i4 + 4i6) }",
1446 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((381 - t1)/5), "
1447 "e1 = floor((-1 + i4)/2): t2 = 0 and 2e1 = -1 + i4 and "
1448 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 >= 1511 - 4t1 - 5i4) }" },
1449 { "{ [0, 0, q, p] : -5 <= q <= 5 and p >= 0 }",
1450 "{ [a, b, q, p] : b >= 1 + a }",
1451 "{ [a, b, q, p] : false }" },
1452 { "[n] -> { [x] : x = n && x mod 32 = 0 }",
1453 "[n] -> { [x] : x mod 32 = 0 }",
1454 "[n] -> { [x = n] }" },
1455 { "{ [x] : x mod 6 = 0 }", "{ [x] : x mod 3 = 0 }",
1456 "{ [x] : x mod 2 = 0 }" },
1457 { "{ [x] : x mod 3200 = 0 }", "{ [x] : x mod 10000 = 0 }",
1458 "{ [x] : x mod 128 = 0 }" },
1459 { "{ [x] : x mod 3200 = 0 }", "{ [x] : x mod 10 = 0 }",
1460 "{ [x] : x mod 3200 = 0 }" },
1461 { "{ [a, b, c] : a mod 2 = 0 and a = c }",
1462 "{ [a, b, c] : b mod 2 = 0 and b = c }",
1463 "{ [a, b, c = a] }" },
1464 { "{ [a, b, c] : a mod 6 = 0 and a = c }",
1465 "{ [a, b, c] : b mod 2 = 0 and b = c }",
1466 "{ [a, b, c = a] : a mod 3 = 0 }" },
1467 { "{ [x] : 0 <= x <= 4 or 6 <= x <= 9 }",
1468 "{ [x] : 1 <= x <= 3 or 7 <= x <= 8 }",
1470 { "{ [x,y] : x < 0 and 0 <= y <= 4 or x >= -2 and -x <= y <= 10 + x }",
1471 "{ [x,y] : 1 <= y <= 3 }",
1475 /* Check that isl_set_gist behaves as expected.
1477 * For the test cases in gist_tests, besides checking that the result
1478 * is as expected, also check that applying the gist operation does
1479 * not modify the input set (an earlier version of isl would do that) and
1480 * that the test case is consistent, i.e., that the gist has the same
1481 * intersection with the context as the input set.
1483 static int test_gist(struct isl_ctx
*ctx
)
1487 isl_basic_set
*bset1
, *bset2
;
1488 isl_map
*map1
, *map2
;
1491 for (i
= 0; i
< ARRAY_SIZE(gist_tests
); ++i
) {
1492 int equal_input
, equal_intersection
;
1493 isl_set
*set1
, *set2
, *copy
, *context
;
1495 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1496 context
= isl_set_read_from_str(ctx
, gist_tests
[i
].context
);
1497 copy
= isl_set_copy(set1
);
1498 set1
= isl_set_gist(set1
, isl_set_copy(context
));
1499 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].gist
);
1500 equal
= isl_set_is_equal(set1
, set2
);
1502 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1503 equal_input
= isl_set_is_equal(set1
, copy
);
1505 set1
= isl_set_intersect(set1
, isl_set_copy(context
));
1506 set2
= isl_set_intersect(set2
, context
);
1507 equal_intersection
= isl_set_is_equal(set1
, set2
);
1510 if (equal
< 0 || equal_input
< 0 || equal_intersection
< 0)
1513 isl_die(ctx
, isl_error_unknown
,
1514 "incorrect gist result", return -1);
1516 isl_die(ctx
, isl_error_unknown
,
1517 "gist modified input", return -1);
1519 isl_die(ctx
, isl_error_unknown
,
1520 "inconsistent gist test case", return -1);
1523 test_gist_case(ctx
, "gist1");
1525 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1526 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1527 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1528 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1529 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1530 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1531 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1532 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1533 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1534 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1535 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1536 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1537 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1538 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1539 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1540 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1541 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1542 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1543 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1544 bset1
= isl_basic_set_gist(bset1
, bset2
);
1545 assert(bset1
&& bset1
->n_div
== 0);
1546 isl_basic_set_free(bset1
);
1548 /* Check that the integer divisions of the second disjunct
1549 * do not spread to the first disjunct.
1551 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1552 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1553 "(exists (e0 = [(-1 + t1)/16], "
1554 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1555 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1556 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1557 "o0 <= 4294967295 and t1 <= -1)) }";
1558 map1
= isl_map_read_from_str(ctx
, str
);
1559 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1560 map2
= isl_map_read_from_str(ctx
, str
);
1561 map1
= isl_map_gist(map1
, map2
);
1565 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1566 isl_map_free(map1
); return -1);
1567 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1568 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1569 isl_map_free(map1
); return -1);
1572 if (test_plain_gist(ctx
) < 0)
1578 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1580 isl_set
*set
, *set2
;
1584 set
= isl_set_read_from_str(ctx
, str
);
1585 set
= isl_set_coalesce(set
);
1586 set2
= isl_set_read_from_str(ctx
, str
);
1587 equal
= isl_set_is_equal(set
, set2
);
1588 one
= set
&& set
->n
== 1;
1595 isl_die(ctx
, isl_error_unknown
,
1596 "coalesced set not equal to input", return -1);
1597 if (check_one
&& !one
)
1598 isl_die(ctx
, isl_error_unknown
,
1599 "coalesced set should not be a union", return -1);
1604 /* Inputs for coalescing tests with unbounded wrapping.
1605 * "str" is a string representation of the input set.
1606 * "single_disjunct" is set if we expect the result to consist of
1607 * a single disjunct.
1610 int single_disjunct
;
1612 } coalesce_unbounded_tests
[] = {
1613 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1614 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1615 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1616 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1618 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1619 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1620 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1621 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1624 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1625 * option turned off.
1627 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1633 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1634 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1636 for (i
= 0; i
< ARRAY_SIZE(coalesce_unbounded_tests
); ++i
) {
1637 const char *str
= coalesce_unbounded_tests
[i
].str
;
1638 int check_one
= coalesce_unbounded_tests
[i
].single_disjunct
;
1639 if (test_coalesce_set(ctx
, str
, check_one
) >= 0)
1645 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1650 /* Inputs for coalescing tests.
1651 * "str" is a string representation of the input set.
1652 * "single_disjunct" is set if we expect the result to consist of
1653 * a single disjunct.
1656 int single_disjunct
;
1658 } coalesce_tests
[] = {
1659 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1660 "y >= x & x >= 2 & 5 >= y }" },
1661 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1662 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1663 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1664 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1665 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1666 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1667 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1668 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1669 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1670 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1671 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1672 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1673 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1674 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1675 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1676 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1677 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1678 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1679 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1680 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1681 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1682 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1683 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1684 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1685 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1686 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1687 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1688 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1689 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1690 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1691 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1692 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1693 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1694 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1695 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1696 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1697 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1698 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1699 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1700 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1701 "[o0, o1, o2, o3, o4, o5, o6]] : "
1702 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1703 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1704 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1705 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1706 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1707 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1708 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1709 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1710 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1711 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1712 "o6 >= i3 + i6 - o3 and M >= 0 and "
1713 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1714 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1715 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1716 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1717 "(o0 = 0 and M >= 2 and N >= 3) or "
1718 "(M = 0 and o0 = 0 and N >= 3) }" },
1719 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1720 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1721 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1722 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1723 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1724 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1725 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1726 "(y = 3 and x = 1) }" },
1727 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1728 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1729 "i1 <= M and i3 <= M and i4 <= M) or "
1730 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1731 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1732 "i4 <= -1 + M) }" },
1733 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1734 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1735 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1736 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1737 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1738 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1739 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1740 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1741 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1742 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1743 { 0, "{ [a, b] : exists e : 2e = a and "
1744 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1745 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1746 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1747 "j >= 1 and j' <= i + j - i' and i >= 1; "
1749 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1750 "[i,j] : exists a : j = 3a }" },
1751 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1752 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1754 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1755 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1756 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1757 "c <= 6 + 8a and a >= 3; "
1758 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1759 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1760 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1761 "[x,0] : 3 <= x <= 4 }" },
1762 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1763 "[x,0] : 4 <= x <= 5 }" },
1764 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1765 "[x,0] : 3 <= x <= 5 }" },
1766 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1767 "[x,0] : 3 <= x <= 4 }" },
1768 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1770 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1771 { 1, "{ [0,0]; [1,1] }" },
1772 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1773 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1775 "[k, 0, k] : k <= 6 and k >= 1 }" },
1776 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1777 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1778 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1779 { 1, "[n] -> { [1] : n >= 0;"
1780 "[x] : exists (e0 = floor((x)/2): x >= 2 and "
1781 "2e0 >= -1 + x and 2e0 <= x and 2e0 <= n) }" },
1782 { 1, "[n] -> { [x, y] : exists (e0 = floor((x)/2), e1 = floor((y)/3): "
1783 "3e1 = y and x >= 2 and 2e0 >= -1 + x and "
1784 "2e0 <= x and 2e0 <= n);"
1785 "[1, y] : exists (e0 = floor((y)/3): 3e0 = y and "
1787 { 1, "[t1] -> { [i0] : (exists (e0 = floor((63t1)/64): "
1788 "128e0 >= -134 + 127t1 and t1 >= 2 and "
1789 "64e0 <= 63t1 and 64e0 >= -63 + 63t1)) or "
1791 { 1, "{ [i, i] : exists (e0 = floor((1 + 2i)/3): 3e0 <= 2i and "
1792 "3e0 >= -1 + 2i and i <= 9 and i >= 1);"
1794 { 1, "{ [t1] : exists (e0 = floor((-11 + t1)/2): 2e0 = -11 + t1 and "
1795 "t1 >= 13 and t1 <= 16);"
1796 "[t1] : t1 <= 15 and t1 >= 12 }" },
1797 { 1, "{ [x,y] : x = 3y and 0 <= y <= 2; [-3,-1] }" },
1798 { 1, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-2] }" },
1799 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-2,-2] }" },
1800 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-1] }" },
1801 { 1, "{ [i] : exists j : i = 4 j and 0 <= i <= 100;"
1802 "[i] : exists j : 1 <= i <= 100 and i >= 4j + 1 and "
1804 { 1, "{ [c0] : (exists (e0 : c0 - 1 <= 3e0 <= c0)) or "
1805 "(exists (e0 : 3e0 = -2 + c0)) }" },
1806 { 0, "[n, b0, t0] -> "
1807 "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1808 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1809 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1810 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1811 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 >= 8 + n and "
1812 "3i4 <= -96 + 3t0 + i0 and 3i4 >= -95 - n + 3t0 + i0 and "
1813 "i8 >= -157 + i0 - 4i4 and i8 >= 0 and "
1814 "i8 <= -33 + i0 - 4i4 and 3i8 <= -91 + 4n - i0)) or "
1815 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1816 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1817 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1818 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 <= 7 + n and "
1819 "4i4 <= -3 + i0 and 3i4 <= -96 + 3t0 + i0 and "
1820 "3i4 >= -95 - n + 3t0 + i0 and i8 >= -157 + i0 - 4i4 and "
1821 "i8 >= 0 and i8 <= -4 + i0 - 3i4 and i8 <= -41 + i0));"
1822 "[i0, i1, i2, i3, 0, i5, i6, i7, i8, i9, i10, i11, i12] : "
1823 "(exists (e0 = floor((i8)/32): b0 = 0 and 32e0 = i8 and "
1824 "n <= 2147483647 and t0 <= 31 and t0 >= 0 and i0 >= 11 and "
1825 "i0 >= 96 - 3t0 and i0 <= 95 + n - 3t0 and i0 <= 7 + n and "
1826 "i8 >= -40 + i0 and i8 <= -10 + i0)) }" },
1827 { 0, "{ [i0, i1, i2] : "
1828 "(exists (e0, e1 = floor((i0)/32), e2 = floor((i1)/32): "
1829 "32e1 = i0 and 32e2 = i1 and i1 >= -31 + i0 and "
1830 "i1 <= 31 + i0 and i2 >= -30 + i0 and i2 >= -30 + i1 and "
1831 "32e0 >= -30 + i0 and 32e0 >= -30 + i1 and "
1832 "32e0 >= -31 + i2 and 32e0 <= 30 + i2 and 32e0 <= 31 + i1 and "
1833 "32e0 <= 31 + i0)) or "
1835 { 1, "{ [a, b, c] : 2b = 1 + a and 2c = 2 + a; [0, 0, 0] }" },
1836 { 1, "{ [a, a, b, c] : 32*floor((a)/32) = a and 2*floor((b)/2) = b and "
1837 "2*floor((c)/2) = c and 0 <= a <= 192;"
1838 "[224, 224, b, c] : 2*floor((b)/2) = b and 2*floor((c)/2) = c }"
1840 { 1, "[n] -> { [a,b] : (exists e : 1 <= a <= 7e and 9e <= b <= n) or "
1841 "(0 <= a <= b <= n) }" },
1844 /* A specialized coalescing test case that would result
1845 * in a segmentation fault or a failed assertion in earlier versions of isl.
1847 static int test_coalesce_special(struct isl_ctx
*ctx
)
1850 isl_map
*map1
, *map2
;
1852 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1853 "[[S_L309_IN[] -> T11[]] -> ce_imag2[1, o1]] : "
1854 "(y = 201 and o1 <= 239 and o1 >= 212) or "
1855 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 198 and y >= 3 and "
1856 "o1 <= 239 and o1 >= 212)) or "
1857 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 201 and y >= 3 and "
1858 "o1 <= 241 and o1 >= 240));"
1859 "[S_L220_OUT[] -> T7[]] -> "
1860 "[[S_L309_IN[] -> T11[]] -> ce_imag2[0, o1]] : "
1861 "(y = 2 and o1 <= 241 and o1 >= 212) or "
1862 "(exists (e0 = [(-2 + y)/3]: 3e0 = -2 + y and y <= 200 and "
1863 "y >= 5 and o1 <= 241 and o1 >= 212)) }";
1864 map1
= isl_map_read_from_str(ctx
, str
);
1865 map1
= isl_map_align_divs(map1
);
1866 map1
= isl_map_coalesce(map1
);
1867 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1868 "[[S_L309_IN[] -> T11[]] -> ce_imag2[o0, o1]] : "
1869 "exists (e0 = [(-1 - y + o0)/3]: 3e0 = -1 - y + o0 and "
1870 "y <= 201 and o0 <= 2 and o1 >= 212 and o1 <= 241 and "
1871 "o0 >= 3 - y and o0 <= -2 + y and o0 >= 0) }";
1872 map2
= isl_map_read_from_str(ctx
, str
);
1873 map2
= isl_map_union(map2
, map1
);
1874 map2
= isl_map_align_divs(map2
);
1875 map2
= isl_map_coalesce(map2
);
1883 /* Test the functionality of isl_set_coalesce.
1884 * That is, check that the output is always equal to the input
1885 * and in some cases that the result consists of a single disjunct.
1887 static int test_coalesce(struct isl_ctx
*ctx
)
1891 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
1892 const char *str
= coalesce_tests
[i
].str
;
1893 int check_one
= coalesce_tests
[i
].single_disjunct
;
1894 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
1898 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
1900 if (test_coalesce_special(ctx
) < 0)
1906 /* Construct a representation of the graph on the right of Figure 1
1907 * in "Computing the Transitive Closure of a Union of
1908 * Affine Integer Tuple Relations".
1910 static __isl_give isl_map
*cocoa_fig_1_right_graph(isl_ctx
*ctx
)
1913 isl_map
*up
, *right
;
1915 dom
= isl_set_read_from_str(ctx
,
1916 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
1917 "2 x - 3 y + 3 >= 0 }");
1918 right
= isl_map_read_from_str(ctx
,
1919 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
1920 up
= isl_map_read_from_str(ctx
,
1921 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
1922 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
1923 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
1924 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
1925 up
= isl_map_intersect_range(up
, dom
);
1926 return isl_map_union(up
, right
);
1929 /* Construct a representation of the power of the graph
1930 * on the right of Figure 1 in "Computing the Transitive Closure of
1931 * a Union of Affine Integer Tuple Relations".
1933 static __isl_give isl_map
*cocoa_fig_1_right_power(isl_ctx
*ctx
)
1935 return isl_map_read_from_str(ctx
,
1936 "{ [1] -> [[0,0] -> [0,1]]; [2] -> [[0,0] -> [1,1]]; "
1937 " [1] -> [[0,1] -> [1,1]]; [1] -> [[2,2] -> [3,2]]; "
1938 " [2] -> [[2,2] -> [3,3]]; [1] -> [[3,2] -> [3,3]] }");
1941 /* Construct a representation of the transitive closure of the graph
1942 * on the right of Figure 1 in "Computing the Transitive Closure of
1943 * a Union of Affine Integer Tuple Relations".
1945 static __isl_give isl_map
*cocoa_fig_1_right_tc(isl_ctx
*ctx
)
1947 return isl_set_unwrap(isl_map_range(cocoa_fig_1_right_power(ctx
)));
1950 static int test_closure(isl_ctx
*ctx
)
1953 isl_map
*map
, *map2
;
1956 /* COCOA example 1 */
1957 map
= isl_map_read_from_str(ctx
,
1958 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1959 "1 <= i and i < n and 1 <= j and j < n or "
1960 "i2 = i + 1 and j2 = j - 1 and "
1961 "1 <= i and i < n and 2 <= j and j <= n }");
1962 map
= isl_map_power(map
, &exact
);
1966 /* COCOA example 1 */
1967 map
= isl_map_read_from_str(ctx
,
1968 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
1969 "1 <= i and i < n and 1 <= j and j < n or "
1970 "i2 = i + 1 and j2 = j - 1 and "
1971 "1 <= i and i < n and 2 <= j and j <= n }");
1972 map
= isl_map_transitive_closure(map
, &exact
);
1974 map2
= isl_map_read_from_str(ctx
,
1975 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
1976 "1 <= i and i < n and 1 <= j and j <= n and "
1977 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
1978 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
1979 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
1980 assert(isl_map_is_equal(map
, map2
));
1984 map
= isl_map_read_from_str(ctx
,
1985 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
1986 " 0 <= y and y <= n }");
1987 map
= isl_map_transitive_closure(map
, &exact
);
1988 map2
= isl_map_read_from_str(ctx
,
1989 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
1990 " 0 <= y and y <= n }");
1991 assert(isl_map_is_equal(map
, map2
));
1995 /* COCOA example 2 */
1996 map
= isl_map_read_from_str(ctx
,
1997 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
1998 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
1999 "i2 = i + 2 and j2 = j - 2 and "
2000 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
2001 map
= isl_map_transitive_closure(map
, &exact
);
2003 map2
= isl_map_read_from_str(ctx
,
2004 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
2005 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
2006 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
2007 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
2008 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
2009 assert(isl_map_is_equal(map
, map2
));
2013 /* COCOA Fig.2 left */
2014 map
= isl_map_read_from_str(ctx
,
2015 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
2016 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
2018 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
2019 "j <= 2 i - 3 and j <= n - 2 or "
2020 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2021 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2022 map
= isl_map_transitive_closure(map
, &exact
);
2026 /* COCOA Fig.2 right */
2027 map
= isl_map_read_from_str(ctx
,
2028 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
2029 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
2031 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
2032 "j <= 2 i - 4 and j <= n - 3 or "
2033 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2034 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2035 map
= isl_map_power(map
, &exact
);
2039 /* COCOA Fig.2 right */
2040 map
= isl_map_read_from_str(ctx
,
2041 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
2042 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
2044 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
2045 "j <= 2 i - 4 and j <= n - 3 or "
2046 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2047 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2048 map
= isl_map_transitive_closure(map
, &exact
);
2050 map2
= isl_map_read_from_str(ctx
,
2051 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
2052 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
2053 "j <= n and 3 + i + 2 j <= 3 n and "
2054 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
2055 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
2056 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
2057 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
2058 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
2059 assert(isl_map_is_equal(map
, map2
));
2063 map
= cocoa_fig_1_right_graph(ctx
);
2064 map
= isl_map_transitive_closure(map
, &exact
);
2066 map2
= cocoa_fig_1_right_tc(ctx
);
2067 assert(isl_map_is_equal(map
, map2
));
2071 map
= cocoa_fig_1_right_graph(ctx
);
2072 map
= isl_map_power(map
, &exact
);
2073 map2
= cocoa_fig_1_right_power(ctx
);
2074 equal
= isl_map_is_equal(map
, map2
);
2080 isl_die(ctx
, isl_error_unknown
, "power not exact", return -1);
2082 isl_die(ctx
, isl_error_unknown
, "unexpected power", return -1);
2084 /* COCOA Theorem 1 counter example */
2085 map
= isl_map_read_from_str(ctx
,
2086 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
2087 "i2 = 1 and j2 = j or "
2088 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
2089 map
= isl_map_transitive_closure(map
, &exact
);
2093 map
= isl_map_read_from_str(ctx
,
2094 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
2095 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
2096 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
2097 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
2098 map
= isl_map_transitive_closure(map
, &exact
);
2102 /* Kelly et al 1996, fig 12 */
2103 map
= isl_map_read_from_str(ctx
,
2104 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
2105 "1 <= i,j,j+1 <= n or "
2106 "j = n and j2 = 1 and i2 = i + 1 and "
2107 "1 <= i,i+1 <= n }");
2108 map
= isl_map_transitive_closure(map
, &exact
);
2110 map2
= isl_map_read_from_str(ctx
,
2111 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
2112 "1 <= i <= n and i = i2 or "
2113 "1 <= i < i2 <= n and 1 <= j <= n and "
2115 assert(isl_map_is_equal(map
, map2
));
2119 /* Omega's closure4 */
2120 map
= isl_map_read_from_str(ctx
,
2121 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
2122 "1 <= x,y <= 10 or "
2123 "x2 = x + 1 and y2 = y and "
2124 "1 <= x <= 20 && 5 <= y <= 15 }");
2125 map
= isl_map_transitive_closure(map
, &exact
);
2129 map
= isl_map_read_from_str(ctx
,
2130 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
2131 map
= isl_map_transitive_closure(map
, &exact
);
2133 map2
= isl_map_read_from_str(ctx
,
2134 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
2135 assert(isl_map_is_equal(map
, map2
));
2139 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
2140 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
2141 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
2142 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
2143 map
= isl_map_read_from_str(ctx
, str
);
2144 map
= isl_map_transitive_closure(map
, &exact
);
2146 map2
= isl_map_read_from_str(ctx
, str
);
2147 assert(isl_map_is_equal(map
, map2
));
2151 str
= "{[0] -> [1]; [2] -> [3]}";
2152 map
= isl_map_read_from_str(ctx
, str
);
2153 map
= isl_map_transitive_closure(map
, &exact
);
2155 map2
= isl_map_read_from_str(ctx
, str
);
2156 assert(isl_map_is_equal(map
, map2
));
2160 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
2161 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
2162 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
2163 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2164 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2165 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
2166 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
2167 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
2168 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2169 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2170 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
2171 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
2172 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
2173 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2174 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2175 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
2176 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
2177 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
2178 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2179 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
2180 map
= isl_map_read_from_str(ctx
, str
);
2181 map
= isl_map_transitive_closure(map
, NULL
);
2188 static int test_lex(struct isl_ctx
*ctx
)
2194 dim
= isl_space_set_alloc(ctx
, 0, 0);
2195 map
= isl_map_lex_le(dim
);
2196 empty
= isl_map_is_empty(map
);
2202 isl_die(ctx
, isl_error_unknown
,
2203 "expecting non-empty result", return -1);
2208 static int test_lexmin(struct isl_ctx
*ctx
)
2212 isl_basic_map
*bmap
;
2213 isl_map
*map
, *map2
;
2216 isl_pw_multi_aff
*pma
;
2218 str
= "[p0, p1] -> { [] -> [] : "
2219 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
2220 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
2221 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
2222 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
2223 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
2224 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
2225 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
2226 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
2227 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
2228 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
2229 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
2230 map
= isl_map_read_from_str(ctx
, str
);
2231 map
= isl_map_lexmin(map
);
2234 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
2235 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
2236 set
= isl_set_read_from_str(ctx
, str
);
2237 set
= isl_set_lexmax(set
);
2238 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
2239 set2
= isl_set_read_from_str(ctx
, str
);
2240 set
= isl_set_intersect(set
, set2
);
2241 assert(!isl_set_is_empty(set
));
2244 str
= "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }";
2245 map
= isl_map_read_from_str(ctx
, str
);
2246 map
= isl_map_lexmin(map
);
2247 str
= "{ [x] -> [5] : 6 <= x <= 8; "
2248 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }";
2249 map2
= isl_map_read_from_str(ctx
, str
);
2250 assert(isl_map_is_equal(map
, map2
));
2254 str
= "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }";
2255 map
= isl_map_read_from_str(ctx
, str
);
2256 map2
= isl_map_copy(map
);
2257 map
= isl_map_lexmin(map
);
2258 assert(isl_map_is_equal(map
, map2
));
2262 str
= "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }";
2263 map
= isl_map_read_from_str(ctx
, str
);
2264 map
= isl_map_lexmin(map
);
2265 str
= "{ [x] -> [y] : (4y = x and x >= 0) or "
2266 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
2267 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
2268 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }";
2269 map2
= isl_map_read_from_str(ctx
, str
);
2270 assert(isl_map_is_equal(map
, map2
));
2274 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2275 " 8i' <= i and 8i' >= -7 + i }";
2276 bmap
= isl_basic_map_read_from_str(ctx
, str
);
2277 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
2278 map2
= isl_map_from_pw_multi_aff(pma
);
2279 map
= isl_map_from_basic_map(bmap
);
2280 assert(isl_map_is_equal(map
, map2
));
2284 str
= "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }";
2285 map
= isl_map_read_from_str(ctx
, str
);
2286 map
= isl_map_lexmin(map
);
2287 str
= "{ T[a] -> S[b, c] : 2b = a and 2c = a }";
2288 map2
= isl_map_read_from_str(ctx
, str
);
2289 assert(isl_map_is_equal(map
, map2
));
2293 /* Check that empty pieces are properly combined. */
2294 str
= "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
2295 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
2296 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }";
2297 map
= isl_map_read_from_str(ctx
, str
);
2298 map
= isl_map_lexmin(map
);
2299 str
= "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
2300 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
2302 map2
= isl_map_read_from_str(ctx
, str
);
2303 assert(isl_map_is_equal(map
, map2
));
2307 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2308 " 8i' <= i and 8i' >= -7 + i }";
2309 set
= isl_set_read_from_str(ctx
, str
);
2310 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
2311 set2
= isl_set_from_pw_multi_aff(pma
);
2312 equal
= isl_set_is_equal(set
, set2
);
2318 isl_die(ctx
, isl_error_unknown
,
2319 "unexpected difference between set and "
2320 "piecewise affine expression", return -1);
2328 __isl_give isl_val
*(*fn
)(__isl_keep isl_set
*set
,
2329 __isl_keep isl_aff
*obj
);
2332 { "{ [-1]; [1] }", "{ [x] -> [x] }", &isl_set_min_val
, "-1" },
2333 { "{ [-1]; [1] }", "{ [x] -> [x] }", &isl_set_max_val
, "1" },
2334 { "{ [a, b] : 0 <= a, b <= 100 and b mod 2 = 0}",
2335 "{ [a, b] -> [floor((b - 2*floor((-a)/4))/5)] }",
2336 &isl_set_max_val
, "30" },
2340 /* Perform basic isl_set_min_val and isl_set_max_val tests.
2341 * In particular, check the results on non-convex inputs.
2343 static int test_min(struct isl_ctx
*ctx
)
2351 for (i
= 0; i
< ARRAY_SIZE(opt_tests
); ++i
) {
2352 set
= isl_set_read_from_str(ctx
, opt_tests
[i
].set
);
2353 obj
= isl_aff_read_from_str(ctx
, opt_tests
[i
].obj
);
2354 res
= isl_val_read_from_str(ctx
, opt_tests
[i
].res
);
2355 val
= opt_tests
[i
].fn(set
, obj
);
2356 ok
= isl_val_eq(res
, val
);
2365 isl_die(ctx
, isl_error_unknown
,
2366 "unexpected optimum", return -1);
2377 static isl_stat
collect_must_may(__isl_take isl_map
*dep
, int must
,
2378 void *dep_user
, void *user
)
2380 struct must_may
*mm
= (struct must_may
*)user
;
2383 mm
->must
= isl_map_union(mm
->must
, dep
);
2385 mm
->may
= isl_map_union(mm
->may
, dep
);
2390 static int common_space(void *first
, void *second
)
2392 int depth
= *(int *)first
;
2396 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
2404 map2
= isl_map_read_from_str(map
->ctx
, str
);
2405 equal
= isl_map_is_equal(map
, map2
);
2411 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
2415 equal
= map_is_equal(map
, str
);
2419 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
2420 "result not as expected", return -1);
2424 static int test_dep(struct isl_ctx
*ctx
)
2429 isl_access_info
*ai
;
2436 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2437 map
= isl_map_read_from_str(ctx
, str
);
2438 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2440 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2441 map
= isl_map_read_from_str(ctx
, str
);
2442 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2444 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2445 map
= isl_map_read_from_str(ctx
, str
);
2446 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2448 flow
= isl_access_info_compute_flow(ai
);
2449 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2450 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2451 mm
.may
= isl_map_empty(dim
);
2453 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2455 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
2456 " [1,10,0] -> [2,5,0] }";
2457 assert(map_is_equal(mm
.must
, str
));
2458 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2459 assert(map_is_equal(mm
.may
, str
));
2461 isl_map_free(mm
.must
);
2462 isl_map_free(mm
.may
);
2463 isl_flow_free(flow
);
2466 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2467 map
= isl_map_read_from_str(ctx
, str
);
2468 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2470 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2471 map
= isl_map_read_from_str(ctx
, str
);
2472 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2474 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2475 map
= isl_map_read_from_str(ctx
, str
);
2476 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2478 flow
= isl_access_info_compute_flow(ai
);
2479 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2480 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2481 mm
.may
= isl_map_empty(dim
);
2483 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2485 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2486 assert(map_is_equal(mm
.must
, str
));
2487 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2488 assert(map_is_equal(mm
.may
, str
));
2490 isl_map_free(mm
.must
);
2491 isl_map_free(mm
.may
);
2492 isl_flow_free(flow
);
2495 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2496 map
= isl_map_read_from_str(ctx
, str
);
2497 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2499 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2500 map
= isl_map_read_from_str(ctx
, str
);
2501 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2503 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2504 map
= isl_map_read_from_str(ctx
, str
);
2505 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2507 flow
= isl_access_info_compute_flow(ai
);
2508 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2509 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2510 mm
.may
= isl_map_empty(dim
);
2512 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2514 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2515 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2516 assert(map_is_equal(mm
.may
, str
));
2517 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2518 assert(map_is_equal(mm
.must
, str
));
2520 isl_map_free(mm
.must
);
2521 isl_map_free(mm
.may
);
2522 isl_flow_free(flow
);
2525 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2526 map
= isl_map_read_from_str(ctx
, str
);
2527 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2529 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2530 map
= isl_map_read_from_str(ctx
, str
);
2531 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2533 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2534 map
= isl_map_read_from_str(ctx
, str
);
2535 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2537 flow
= isl_access_info_compute_flow(ai
);
2538 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2539 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2540 mm
.may
= isl_map_empty(dim
);
2542 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2544 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2545 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2546 assert(map_is_equal(mm
.may
, str
));
2547 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2548 assert(map_is_equal(mm
.must
, str
));
2550 isl_map_free(mm
.must
);
2551 isl_map_free(mm
.may
);
2552 isl_flow_free(flow
);
2555 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2556 map
= isl_map_read_from_str(ctx
, str
);
2557 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2559 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2560 map
= isl_map_read_from_str(ctx
, str
);
2561 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2563 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2564 map
= isl_map_read_from_str(ctx
, str
);
2565 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2567 flow
= isl_access_info_compute_flow(ai
);
2568 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2569 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2570 mm
.may
= isl_map_empty(dim
);
2572 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2574 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2575 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2576 assert(map_is_equal(mm
.may
, str
));
2577 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2578 assert(map_is_equal(mm
.must
, str
));
2580 isl_map_free(mm
.must
);
2581 isl_map_free(mm
.may
);
2582 isl_flow_free(flow
);
2587 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2588 map
= isl_map_read_from_str(ctx
, str
);
2589 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2591 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2592 map
= isl_map_read_from_str(ctx
, str
);
2593 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2595 flow
= isl_access_info_compute_flow(ai
);
2596 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2597 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2598 mm
.may
= isl_map_empty(dim
);
2600 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2602 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2603 assert(map_is_equal(mm
.must
, str
));
2604 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2605 assert(map_is_equal(mm
.may
, str
));
2607 isl_map_free(mm
.must
);
2608 isl_map_free(mm
.may
);
2609 isl_flow_free(flow
);
2614 /* Check that the dependence analysis proceeds without errors.
2615 * Earlier versions of isl would break down during the analysis
2616 * due to the use of the wrong spaces.
2618 static int test_flow(isl_ctx
*ctx
)
2621 isl_union_map
*access
, *schedule
;
2622 isl_union_map
*must_dep
, *may_dep
;
2625 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2626 access
= isl_union_map_read_from_str(ctx
, str
);
2627 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2628 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2629 "S2[] -> [1,0,0,0]; "
2630 "S3[] -> [-1,0,0,0] }";
2631 schedule
= isl_union_map_read_from_str(ctx
, str
);
2632 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2633 isl_union_map_copy(access
), schedule
,
2634 &must_dep
, &may_dep
, NULL
, NULL
);
2635 isl_union_map_free(may_dep
);
2636 isl_union_map_free(must_dep
);
2645 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2646 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2647 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2648 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2649 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2650 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2651 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2652 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2653 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2656 int test_sv(isl_ctx
*ctx
)
2658 isl_union_map
*umap
;
2662 for (i
= 0; i
< ARRAY_SIZE(sv_tests
); ++i
) {
2663 umap
= isl_union_map_read_from_str(ctx
, sv_tests
[i
].map
);
2664 sv
= isl_union_map_is_single_valued(umap
);
2665 isl_union_map_free(umap
);
2668 if (sv_tests
[i
].sv
&& !sv
)
2669 isl_die(ctx
, isl_error_internal
,
2670 "map not detected as single valued", return -1);
2671 if (!sv_tests
[i
].sv
&& sv
)
2672 isl_die(ctx
, isl_error_internal
,
2673 "map detected as single valued", return -1);
2682 } bijective_tests
[] = {
2683 { "[N,M]->{[i,j] -> [i]}", 0 },
2684 { "[N,M]->{[i,j] -> [i] : j=i}", 1 },
2685 { "[N,M]->{[i,j] -> [i] : j=0}", 1 },
2686 { "[N,M]->{[i,j] -> [i] : j=N}", 1 },
2687 { "[N,M]->{[i,j] -> [j,i]}", 1 },
2688 { "[N,M]->{[i,j] -> [i+j]}", 0 },
2689 { "[N,M]->{[i,j] -> []}", 0 },
2690 { "[N,M]->{[i,j] -> [i,j,N]}", 1 },
2691 { "[N,M]->{[i,j] -> [2i]}", 0 },
2692 { "[N,M]->{[i,j] -> [i,i]}", 0 },
2693 { "[N,M]->{[i,j] -> [2i,i]}", 0 },
2694 { "[N,M]->{[i,j] -> [2i,j]}", 1 },
2695 { "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1 },
2698 static int test_bijective(struct isl_ctx
*ctx
)
2704 for (i
= 0; i
< ARRAY_SIZE(bijective_tests
); ++i
) {
2705 map
= isl_map_read_from_str(ctx
, bijective_tests
[i
].str
);
2706 bijective
= isl_map_is_bijective(map
);
2710 if (bijective_tests
[i
].bijective
&& !bijective
)
2711 isl_die(ctx
, isl_error_internal
,
2712 "map not detected as bijective", return -1);
2713 if (!bijective_tests
[i
].bijective
&& bijective
)
2714 isl_die(ctx
, isl_error_internal
,
2715 "map detected as bijective", return -1);
2721 /* Inputs for isl_pw_qpolynomial_gist tests.
2722 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2728 } pwqp_gist_tests
[] = {
2729 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2730 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2731 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2732 "{ [i] -> -1/2 + 1/2 * i }" },
2733 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2736 static int test_pwqp(struct isl_ctx
*ctx
)
2741 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
2744 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2745 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2747 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
2750 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2751 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2753 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2755 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2757 isl_pw_qpolynomial_free(pwqp1
);
2759 for (i
= 0; i
< ARRAY_SIZE(pwqp_gist_tests
); ++i
) {
2760 str
= pwqp_gist_tests
[i
].pwqp
;
2761 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2762 str
= pwqp_gist_tests
[i
].set
;
2763 set
= isl_set_read_from_str(ctx
, str
);
2764 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2765 str
= pwqp_gist_tests
[i
].gist
;
2766 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2767 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2768 equal
= isl_pw_qpolynomial_is_zero(pwqp1
);
2769 isl_pw_qpolynomial_free(pwqp1
);
2774 isl_die(ctx
, isl_error_unknown
,
2775 "unexpected result", return -1);
2778 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
2779 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2780 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
2781 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2783 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2785 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2787 isl_pw_qpolynomial_free(pwqp1
);
2789 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
2790 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2791 str
= "{ [x] -> x }";
2792 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2794 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2796 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2798 isl_pw_qpolynomial_free(pwqp1
);
2800 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
2801 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2802 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2803 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
2804 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2805 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2806 isl_pw_qpolynomial_free(pwqp1
);
2808 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
2809 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2810 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2811 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2812 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
2813 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
2814 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2815 isl_pw_qpolynomial_free(pwqp1
);
2816 isl_pw_qpolynomial_free(pwqp2
);
2820 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2822 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
2823 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2824 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
2825 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2826 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
2828 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
2829 isl_pw_qpolynomial_free(pwqp1
);
2830 isl_pw_qpolynomial_free(pwqp2
);
2834 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
2839 static int test_split_periods(isl_ctx
*ctx
)
2842 isl_pw_qpolynomial
*pwqp
;
2844 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
2845 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
2846 "U >= 0; [U,V] -> U^2 : U >= 100 }";
2847 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2849 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
2851 isl_pw_qpolynomial_free(pwqp
);
2859 static int test_union(isl_ctx
*ctx
)
2862 isl_union_set
*uset1
, *uset2
;
2863 isl_union_map
*umap1
, *umap2
;
2866 str
= "{ [i] : 0 <= i <= 1 }";
2867 uset1
= isl_union_set_read_from_str(ctx
, str
);
2868 str
= "{ [1] -> [0] }";
2869 umap1
= isl_union_map_read_from_str(ctx
, str
);
2871 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
2872 equal
= isl_union_map_is_equal(umap1
, umap2
);
2874 isl_union_map_free(umap1
);
2875 isl_union_map_free(umap2
);
2880 isl_die(ctx
, isl_error_unknown
, "union maps not equal",
2883 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
2884 umap1
= isl_union_map_read_from_str(ctx
, str
);
2885 str
= "{ A[i]; B[i] }";
2886 uset1
= isl_union_set_read_from_str(ctx
, str
);
2888 uset2
= isl_union_map_domain(umap1
);
2890 equal
= isl_union_set_is_equal(uset1
, uset2
);
2892 isl_union_set_free(uset1
);
2893 isl_union_set_free(uset2
);
2898 isl_die(ctx
, isl_error_unknown
, "union sets not equal",
2904 /* Check that computing a bound of a non-zero polynomial over an unbounded
2905 * domain does not produce a rational value.
2906 * In particular, check that the upper bound is infinity.
2908 static int test_bound_unbounded_domain(isl_ctx
*ctx
)
2911 isl_pw_qpolynomial
*pwqp
;
2912 isl_pw_qpolynomial_fold
*pwf
, *pwf2
;
2915 str
= "{ [m,n] -> -m * n }";
2916 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2917 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2919 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2920 pwf2
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2921 equal
= isl_pw_qpolynomial_fold_plain_is_equal(pwf
, pwf2
);
2922 isl_pw_qpolynomial_fold_free(pwf
);
2923 isl_pw_qpolynomial_fold_free(pwf2
);
2928 isl_die(ctx
, isl_error_unknown
,
2929 "expecting infinite polynomial bound", return -1);
2934 static int test_bound(isl_ctx
*ctx
)
2938 isl_pw_qpolynomial
*pwqp
;
2939 isl_pw_qpolynomial_fold
*pwf
;
2941 if (test_bound_unbounded_domain(ctx
) < 0)
2944 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
2945 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2946 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2947 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
2948 isl_pw_qpolynomial_fold_free(pwf
);
2950 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
2953 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
2954 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2955 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
2956 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
2957 isl_pw_qpolynomial_fold_free(pwf
);
2959 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
2965 static int test_lift(isl_ctx
*ctx
)
2968 isl_basic_map
*bmap
;
2969 isl_basic_set
*bset
;
2971 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
2972 bset
= isl_basic_set_read_from_str(ctx
, str
);
2973 bset
= isl_basic_set_lift(bset
);
2974 bmap
= isl_basic_map_from_range(bset
);
2975 bset
= isl_basic_map_domain(bmap
);
2976 isl_basic_set_free(bset
);
2985 } subset_tests
[] = {
2987 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
2988 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
2989 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
2991 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
2992 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
2993 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
2994 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
2995 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
2996 "256e0 <= 255i and 256e0 >= -255 + 255i and "
2997 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
2998 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
2999 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
3000 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
3001 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
3002 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
3003 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
3004 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
3005 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
3006 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
3007 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
3008 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
3009 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
3010 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
3011 "4e0 <= -57 + i0 + i1)) or "
3012 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
3013 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
3014 "4e0 >= -61 + i0 + i1)) or "
3015 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
3016 { "[a, b] -> { : a = 0 and b = -1 }", "[b, a] -> { : b >= -10 }", 1 },
3019 static int test_subset(isl_ctx
*ctx
)
3022 isl_set
*set1
, *set2
;
3025 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
3026 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
3027 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
3028 subset
= isl_set_is_subset(set1
, set2
);
3033 if (subset
!= subset_tests
[i
].subset
)
3034 isl_die(ctx
, isl_error_unknown
,
3035 "incorrect subset result", return -1);
3042 const char *minuend
;
3043 const char *subtrahend
;
3044 const char *difference
;
3045 } subtract_domain_tests
[] = {
3046 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
3047 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
3048 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
3051 static int test_subtract(isl_ctx
*ctx
)
3054 isl_union_map
*umap1
, *umap2
;
3055 isl_union_pw_multi_aff
*upma1
, *upma2
;
3056 isl_union_set
*uset
;
3059 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
3060 umap1
= isl_union_map_read_from_str(ctx
,
3061 subtract_domain_tests
[i
].minuend
);
3062 uset
= isl_union_set_read_from_str(ctx
,
3063 subtract_domain_tests
[i
].subtrahend
);
3064 umap2
= isl_union_map_read_from_str(ctx
,
3065 subtract_domain_tests
[i
].difference
);
3066 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
3067 equal
= isl_union_map_is_equal(umap1
, umap2
);
3068 isl_union_map_free(umap1
);
3069 isl_union_map_free(umap2
);
3073 isl_die(ctx
, isl_error_unknown
,
3074 "incorrect subtract domain result", return -1);
3077 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
3078 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
3079 subtract_domain_tests
[i
].minuend
);
3080 uset
= isl_union_set_read_from_str(ctx
,
3081 subtract_domain_tests
[i
].subtrahend
);
3082 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
3083 subtract_domain_tests
[i
].difference
);
3084 upma1
= isl_union_pw_multi_aff_subtract_domain(upma1
, uset
);
3085 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
3086 isl_union_pw_multi_aff_free(upma1
);
3087 isl_union_pw_multi_aff_free(upma2
);
3091 isl_die(ctx
, isl_error_unknown
,
3092 "incorrect subtract domain result", return -1);
3098 /* Check that intersecting the empty basic set with another basic set
3099 * does not increase the number of constraints. In particular,
3100 * the empty basic set should maintain its canonical representation.
3102 static int test_intersect(isl_ctx
*ctx
)
3105 isl_basic_set
*bset1
, *bset2
;
3107 bset1
= isl_basic_set_read_from_str(ctx
, "{ [a,b,c] : 1 = 0 }");
3108 bset2
= isl_basic_set_read_from_str(ctx
, "{ [1,2,3] }");
3109 n1
= isl_basic_set_n_constraint(bset1
);
3110 bset1
= isl_basic_set_intersect(bset1
, bset2
);
3111 n2
= isl_basic_set_n_constraint(bset1
);
3112 isl_basic_set_free(bset1
);
3116 isl_die(ctx
, isl_error_unknown
,
3117 "number of constraints of empty set changed",
3123 int test_factorize(isl_ctx
*ctx
)
3126 isl_basic_set
*bset
;
3129 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
3130 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
3131 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
3132 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
3133 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
3134 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
3135 "3i5 >= -2i0 - i2 + 3i4 }";
3136 bset
= isl_basic_set_read_from_str(ctx
, str
);
3137 f
= isl_basic_set_factorizer(bset
);
3138 isl_basic_set_free(bset
);
3139 isl_factorizer_free(f
);
3141 isl_die(ctx
, isl_error_unknown
,
3142 "failed to construct factorizer", return -1);
3144 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
3145 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
3146 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
3147 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
3148 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
3149 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
3150 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
3151 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
3152 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
3153 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
3154 bset
= isl_basic_set_read_from_str(ctx
, str
);
3155 f
= isl_basic_set_factorizer(bset
);
3156 isl_basic_set_free(bset
);
3157 isl_factorizer_free(f
);
3159 isl_die(ctx
, isl_error_unknown
,
3160 "failed to construct factorizer", return -1);
3165 static isl_stat
check_injective(__isl_take isl_map
*map
, void *user
)
3167 int *injective
= user
;
3169 *injective
= isl_map_is_injective(map
);
3172 if (*injective
< 0 || !*injective
)
3173 return isl_stat_error
;
3178 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
3179 const char *r
, const char *s
, int tilable
, int parallel
)
3183 isl_union_map
*W
, *R
, *S
;
3184 isl_union_map
*empty
;
3185 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
3186 isl_union_map
*validity
, *proximity
, *coincidence
;
3187 isl_union_map
*schedule
;
3188 isl_union_map
*test
;
3189 isl_union_set
*delta
;
3190 isl_union_set
*domain
;
3194 isl_schedule_constraints
*sc
;
3195 isl_schedule
*sched
;
3196 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
3198 D
= isl_union_set_read_from_str(ctx
, d
);
3199 W
= isl_union_map_read_from_str(ctx
, w
);
3200 R
= isl_union_map_read_from_str(ctx
, r
);
3201 S
= isl_union_map_read_from_str(ctx
, s
);
3203 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
3204 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
3206 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
3207 isl_union_map_compute_flow(isl_union_map_copy(R
),
3208 isl_union_map_copy(W
), empty
,
3209 isl_union_map_copy(S
),
3210 &dep_raw
, NULL
, NULL
, NULL
);
3211 isl_union_map_compute_flow(isl_union_map_copy(W
),
3212 isl_union_map_copy(W
),
3213 isl_union_map_copy(R
),
3214 isl_union_map_copy(S
),
3215 &dep_waw
, &dep_war
, NULL
, NULL
);
3217 dep
= isl_union_map_union(dep_waw
, dep_war
);
3218 dep
= isl_union_map_union(dep
, dep_raw
);
3219 validity
= isl_union_map_copy(dep
);
3220 coincidence
= isl_union_map_copy(dep
);
3221 proximity
= isl_union_map_copy(dep
);
3223 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
3224 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3225 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
3226 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3227 sched
= isl_schedule_constraints_compute_schedule(sc
);
3228 schedule
= isl_schedule_get_map(sched
);
3229 isl_schedule_free(sched
);
3230 isl_union_map_free(W
);
3231 isl_union_map_free(R
);
3232 isl_union_map_free(S
);
3235 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
3237 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
3238 is_complete
= isl_union_set_is_subset(D
, domain
);
3239 isl_union_set_free(D
);
3240 isl_union_set_free(domain
);
3242 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
3243 test
= isl_union_map_apply_range(test
, dep
);
3244 test
= isl_union_map_apply_range(test
, schedule
);
3246 delta
= isl_union_map_deltas(test
);
3247 if (isl_union_set_n_set(delta
) == 0) {
3251 isl_union_set_free(delta
);
3253 delta_set
= isl_set_from_union_set(delta
);
3255 slice
= isl_set_universe(isl_set_get_space(delta_set
));
3256 for (i
= 0; i
< tilable
; ++i
)
3257 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
3258 is_tilable
= isl_set_is_subset(delta_set
, slice
);
3259 isl_set_free(slice
);
3261 slice
= isl_set_universe(isl_set_get_space(delta_set
));
3262 for (i
= 0; i
< parallel
; ++i
)
3263 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
3264 is_parallel
= isl_set_is_subset(delta_set
, slice
);
3265 isl_set_free(slice
);
3267 origin
= isl_set_universe(isl_set_get_space(delta_set
));
3268 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
3269 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
3271 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
3272 delta_set
= isl_set_lexmin(delta_set
);
3274 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
3276 isl_set_free(origin
);
3277 isl_set_free(delta_set
);
3280 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
3281 is_injection
< 0 || is_complete
< 0)
3284 isl_die(ctx
, isl_error_unknown
,
3285 "generated schedule incomplete", return -1);
3287 isl_die(ctx
, isl_error_unknown
,
3288 "generated schedule not injective on each statement",
3291 isl_die(ctx
, isl_error_unknown
,
3292 "negative dependences in generated schedule",
3295 isl_die(ctx
, isl_error_unknown
,
3296 "generated schedule not as tilable as expected",
3299 isl_die(ctx
, isl_error_unknown
,
3300 "generated schedule not as parallel as expected",
3306 /* Compute a schedule for the given instance set, validity constraints,
3307 * proximity constraints and context and return a corresponding union map
3310 static __isl_give isl_union_map
*compute_schedule_with_context(isl_ctx
*ctx
,
3311 const char *domain
, const char *validity
, const char *proximity
,
3312 const char *context
)
3317 isl_union_map
*prox
;
3318 isl_schedule_constraints
*sc
;
3319 isl_schedule
*schedule
;
3320 isl_union_map
*sched
;
3322 con
= isl_set_read_from_str(ctx
, context
);
3323 dom
= isl_union_set_read_from_str(ctx
, domain
);
3324 dep
= isl_union_map_read_from_str(ctx
, validity
);
3325 prox
= isl_union_map_read_from_str(ctx
, proximity
);
3326 sc
= isl_schedule_constraints_on_domain(dom
);
3327 sc
= isl_schedule_constraints_set_context(sc
, con
);
3328 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
3329 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
3330 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3331 sched
= isl_schedule_get_map(schedule
);
3332 isl_schedule_free(schedule
);
3337 /* Compute a schedule for the given instance set, validity constraints and
3338 * proximity constraints and return a corresponding union map representation.
3340 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
3341 const char *domain
, const char *validity
, const char *proximity
)
3343 return compute_schedule_with_context(ctx
, domain
, validity
, proximity
,
3347 /* Check that a schedule can be constructed on the given domain
3348 * with the given validity and proximity constraints.
3350 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
3351 const char *validity
, const char *proximity
)
3353 isl_union_map
*sched
;
3355 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
3359 isl_union_map_free(sched
);
3363 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
3364 const char *validity
, const char *proximity
, const char *expected_sched
)
3366 isl_union_map
*sched1
, *sched2
;
3369 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
3370 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
3372 equal
= isl_union_map_is_equal(sched1
, sched2
);
3373 isl_union_map_free(sched1
);
3374 isl_union_map_free(sched2
);
3379 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
3385 /* Check that the schedule map is properly padded, even after being
3386 * reconstructed from the band forest.
3388 static int test_padded_schedule(isl_ctx
*ctx
)
3392 isl_union_map
*validity
, *proximity
;
3393 isl_schedule_constraints
*sc
;
3394 isl_schedule
*sched
;
3395 isl_union_map
*map1
, *map2
;
3396 isl_band_list
*list
;
3399 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
3400 D
= isl_union_set_read_from_str(ctx
, str
);
3401 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
3402 proximity
= isl_union_map_copy(validity
);
3403 sc
= isl_schedule_constraints_on_domain(D
);
3404 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3405 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3406 sched
= isl_schedule_constraints_compute_schedule(sc
);
3407 map1
= isl_schedule_get_map(sched
);
3408 list
= isl_schedule_get_band_forest(sched
);
3409 isl_band_list_free(list
);
3410 map2
= isl_schedule_get_map(sched
);
3411 isl_schedule_free(sched
);
3412 equal
= isl_union_map_is_equal(map1
, map2
);
3413 isl_union_map_free(map1
);
3414 isl_union_map_free(map2
);
3419 isl_die(ctx
, isl_error_unknown
,
3420 "reconstructed schedule map not the same as original",
3426 /* Check that conditional validity constraints are also taken into
3427 * account across bands.
3428 * In particular, try to make sure that live ranges D[1,0]->C[2,1] and
3429 * D[2,0]->C[3,0] are not local in the outer band of the generated schedule
3430 * and then check that the adjacent order constraint C[2,1]->D[2,0]
3431 * is enforced by the rest of the schedule.
3433 static int test_special_conditional_schedule_constraints(isl_ctx
*ctx
)
3436 isl_union_set
*domain
;
3437 isl_union_map
*validity
, *proximity
, *condition
;
3438 isl_union_map
*sink
, *source
, *dep
;
3439 isl_schedule_constraints
*sc
;
3440 isl_schedule
*schedule
;
3441 isl_union_access_info
*access
;
3442 isl_union_flow
*flow
;
3445 str
= "[n] -> { C[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3446 "A[k] : k >= 1 and k <= -1 + n; "
3447 "B[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3448 "D[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k }";
3449 domain
= isl_union_set_read_from_str(ctx
, str
);
3450 sc
= isl_schedule_constraints_on_domain(domain
);
3451 str
= "[n] -> { D[k, i] -> C[1 + k, k - i] : "
3452 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3453 "D[k, i] -> C[1 + k, i] : "
3454 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3455 "D[k, 0] -> C[1 + k, k] : k >= 1 and k <= -2 + n; "
3456 "D[k, 0] -> C[1 + k, 0] : k >= 1 and k <= -2 + n }";
3457 validity
= isl_union_map_read_from_str(ctx
, str
);
3458 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3459 str
= "[n] -> { C[k, i] -> D[k, i] : "
3460 "0 <= i <= -1 + k and k <= -1 + n }";
3461 proximity
= isl_union_map_read_from_str(ctx
, str
);
3462 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3463 str
= "[n] -> { [D[k, i] -> a[]] -> [C[1 + k, k - i] -> b[]] : "
3464 "i <= -1 + k and i >= 1 and k <= -2 + n; "
3465 "[B[k, i] -> c[]] -> [B[k, 1 + i] -> c[]] : "
3466 "k <= -1 + n and i >= 0 and i <= -2 + k }";
3467 condition
= isl_union_map_read_from_str(ctx
, str
);
3468 str
= "[n] -> { [B[k, i] -> e[]] -> [D[k, i] -> a[]] : "
3469 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3470 "[C[k, i] -> b[]] -> [D[k', -1 + k - i] -> a[]] : "
3471 "i >= 0 and i <= -1 + k and k <= -1 + n and "
3472 "k' <= -1 + n and k' >= k - i and k' >= 1 + k; "
3473 "[C[k, i] -> b[]] -> [D[k, -1 + k - i] -> a[]] : "
3474 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3475 "[B[k, i] -> c[]] -> [A[k'] -> d[]] : "
3476 "k <= -1 + n and i >= 0 and i <= -1 + k and "
3477 "k' >= 1 and k' <= -1 + n and k' >= 1 + k }";
3478 validity
= isl_union_map_read_from_str(ctx
, str
);
3479 sc
= isl_schedule_constraints_set_conditional_validity(sc
, condition
,
3481 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3482 str
= "{ D[2,0] -> [] }";
3483 sink
= isl_union_map_read_from_str(ctx
, str
);
3484 access
= isl_union_access_info_from_sink(sink
);
3485 str
= "{ C[2,1] -> [] }";
3486 source
= isl_union_map_read_from_str(ctx
, str
);
3487 access
= isl_union_access_info_set_must_source(access
, source
);
3488 access
= isl_union_access_info_set_schedule(access
, schedule
);
3489 flow
= isl_union_access_info_compute_flow(access
);
3490 dep
= isl_union_flow_get_must_dependence(flow
);
3491 isl_union_flow_free(flow
);
3492 empty
= isl_union_map_is_empty(dep
);
3493 isl_union_map_free(dep
);
3498 isl_die(ctx
, isl_error_unknown
,
3499 "conditional validity not respected", return -1);
3504 /* Input for testing of schedule construction based on
3505 * conditional constraints.
3507 * domain is the iteration domain
3508 * flow are the flow dependences, which determine the validity and
3509 * proximity constraints
3510 * condition are the conditions on the conditional validity constraints
3511 * conditional_validity are the conditional validity constraints
3512 * outer_band_n is the expected number of members in the outer band
3517 const char *condition
;
3518 const char *conditional_validity
;
3520 } live_range_tests
[] = {
3521 /* Contrived example that illustrates that we need to keep
3522 * track of tagged condition dependences and
3523 * tagged conditional validity dependences
3524 * in isl_sched_edge separately.
3525 * In particular, the conditional validity constraints on A
3526 * cannot be satisfied,
3527 * but they can be ignored because there are no corresponding
3528 * condition constraints. However, we do have an additional
3529 * conditional validity constraint that maps to the same
3530 * dependence relation
3531 * as the condition constraint on B. If we did not make a distinction
3532 * between tagged condition and tagged conditional validity
3533 * dependences, then we
3534 * could end up treating this shared dependence as an condition
3535 * constraint on A, forcing a localization of the conditions,
3536 * which is impossible.
3538 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
3539 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
3540 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
3541 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3542 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3543 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
3546 /* TACO 2013 Fig. 7 */
3547 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3548 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3549 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3550 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
3551 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
3552 "0 <= i < n and 0 <= j < n - 1 }",
3553 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
3554 "0 <= i < n and 0 <= j < j' < n;"
3555 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
3556 "0 <= i < i' < n and 0 <= j,j' < n;"
3557 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
3558 "0 <= i,j,j' < n and j < j' }",
3561 /* TACO 2013 Fig. 7, without tags */
3562 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3563 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3564 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3565 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3566 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3567 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
3568 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
3569 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
3572 /* TACO 2013 Fig. 12 */
3573 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
3574 "S3[i,3] : 0 <= i <= 1 }",
3575 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
3576 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
3577 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
3578 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
3579 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3580 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
3581 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3582 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
3583 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
3584 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
3585 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
3590 /* Test schedule construction based on conditional constraints.
3591 * In particular, check the number of members in the outer band node
3592 * as an indication of whether tiling is possible or not.
3594 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
3597 isl_union_set
*domain
;
3598 isl_union_map
*condition
;
3599 isl_union_map
*flow
;
3600 isl_union_map
*validity
;
3601 isl_schedule_constraints
*sc
;
3602 isl_schedule
*schedule
;
3603 isl_schedule_node
*node
;
3606 if (test_special_conditional_schedule_constraints(ctx
) < 0)
3609 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
3610 domain
= isl_union_set_read_from_str(ctx
,
3611 live_range_tests
[i
].domain
);
3612 flow
= isl_union_map_read_from_str(ctx
,
3613 live_range_tests
[i
].flow
);
3614 condition
= isl_union_map_read_from_str(ctx
,
3615 live_range_tests
[i
].condition
);
3616 validity
= isl_union_map_read_from_str(ctx
,
3617 live_range_tests
[i
].conditional_validity
);
3618 sc
= isl_schedule_constraints_on_domain(domain
);
3619 sc
= isl_schedule_constraints_set_validity(sc
,
3620 isl_union_map_copy(flow
));
3621 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
3622 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
3623 condition
, validity
);
3624 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3625 node
= isl_schedule_get_root(schedule
);
3627 isl_schedule_node_get_type(node
) != isl_schedule_node_band
)
3628 node
= isl_schedule_node_first_child(node
);
3629 n_member
= isl_schedule_node_band_n_member(node
);
3630 isl_schedule_node_free(node
);
3631 isl_schedule_free(schedule
);
3635 if (n_member
!= live_range_tests
[i
].outer_band_n
)
3636 isl_die(ctx
, isl_error_unknown
,
3637 "unexpected number of members in outer band",
3643 /* Check that the schedule computed for the given instance set and
3644 * dependence relation strongly satisfies the dependences.
3645 * In particular, check that no instance is scheduled before
3646 * or together with an instance on which it depends.
3647 * Earlier versions of isl would produce a schedule that
3648 * only weakly satisfies the dependences.
3650 static int test_strongly_satisfying_schedule(isl_ctx
*ctx
)
3652 const char *domain
, *dep
;
3653 isl_union_map
*D
, *schedule
;
3657 domain
= "{ B[i0, i1] : 0 <= i0 <= 1 and 0 <= i1 <= 11; "
3658 "A[i0] : 0 <= i0 <= 1 }";
3659 dep
= "{ B[i0, i1] -> B[i0, 1 + i1] : 0 <= i0 <= 1 and 0 <= i1 <= 10; "
3660 "B[0, 11] -> A[1]; A[i0] -> B[i0, 0] : 0 <= i0 <= 1 }";
3661 schedule
= compute_schedule(ctx
, domain
, dep
, dep
);
3662 D
= isl_union_map_read_from_str(ctx
, dep
);
3663 D
= isl_union_map_apply_domain(D
, isl_union_map_copy(schedule
));
3664 D
= isl_union_map_apply_range(D
, schedule
);
3665 map
= isl_map_from_union_map(D
);
3666 ge
= isl_map_lex_ge(isl_space_domain(isl_map_get_space(map
)));
3667 map
= isl_map_intersect(map
, ge
);
3668 empty
= isl_map_is_empty(map
);
3674 isl_die(ctx
, isl_error_unknown
,
3675 "dependences not strongly satisfied", return -1);
3680 /* Compute a schedule for input where the instance set constraints
3681 * conflict with the context constraints.
3682 * Earlier versions of isl did not properly handle this situation.
3684 static int test_conflicting_context_schedule(isl_ctx
*ctx
)
3686 isl_union_map
*schedule
;
3687 const char *domain
, *context
;
3689 domain
= "[n] -> { A[] : n >= 0 }";
3690 context
= "[n] -> { : n < 0 }";
3691 schedule
= compute_schedule_with_context(ctx
,
3692 domain
, "{}", "{}", context
);
3693 isl_union_map_free(schedule
);
3701 /* Check that the dependence carrying step is not confused by
3702 * a bound on the coefficient size.
3703 * In particular, force the scheduler to move to a dependence carrying
3704 * step by demanding outer coincidence and bound the size of
3705 * the coefficients. Earlier versions of isl would take this
3706 * bound into account while carrying dependences, breaking
3707 * fundamental assumptions.
3708 * On the other hand, the dependence carrying step now tries
3709 * to prevent loop coalescing by default, so check that indeed
3710 * no loop coalescing occurs by comparing the computed schedule
3711 * to the expected non-coalescing schedule.
3713 static int test_bounded_coefficients_schedule(isl_ctx
*ctx
)
3715 const char *domain
, *dep
;
3718 isl_schedule_constraints
*sc
;
3719 isl_schedule
*schedule
;
3720 isl_union_map
*sched1
, *sched2
;
3723 domain
= "{ C[i0, i1] : 2 <= i0 <= 3999 and 0 <= i1 <= -1 + i0 }";
3724 dep
= "{ C[i0, i1] -> C[i0, 1 + i1] : i0 <= 3999 and i1 >= 0 and "
3726 "C[i0, -1 + i0] -> C[1 + i0, 0] : i0 <= 3998 and i0 >= 1 }";
3727 I
= isl_union_set_read_from_str(ctx
, domain
);
3728 D
= isl_union_map_read_from_str(ctx
, dep
);
3729 sc
= isl_schedule_constraints_on_domain(I
);
3730 sc
= isl_schedule_constraints_set_validity(sc
, isl_union_map_copy(D
));
3731 sc
= isl_schedule_constraints_set_coincidence(sc
, D
);
3732 isl_options_set_schedule_outer_coincidence(ctx
, 1);
3733 isl_options_set_schedule_max_coefficient(ctx
, 20);
3734 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3735 isl_options_set_schedule_max_coefficient(ctx
, -1);
3736 isl_options_set_schedule_outer_coincidence(ctx
, 0);
3737 sched1
= isl_schedule_get_map(schedule
);
3738 isl_schedule_free(schedule
);
3740 sched2
= isl_union_map_read_from_str(ctx
, "{ C[x,y] -> [x,y] }");
3741 equal
= isl_union_map_is_equal(sched1
, sched2
);
3742 isl_union_map_free(sched1
);
3743 isl_union_map_free(sched2
);
3748 isl_die(ctx
, isl_error_unknown
,
3749 "unexpected schedule", return -1);
3754 /* Check that a set of schedule constraints that only allow for
3755 * a coalescing schedule still produces a schedule even if the user
3756 * request a non-coalescing schedule. Earlier versions of isl
3757 * would not handle this case correctly.
3759 static int test_coalescing_schedule(isl_ctx
*ctx
)
3761 const char *domain
, *dep
;
3764 isl_schedule_constraints
*sc
;
3765 isl_schedule
*schedule
;
3766 int treat_coalescing
;
3768 domain
= "{ S[a, b] : 0 <= a <= 1 and 0 <= b <= 1 }";
3769 dep
= "{ S[a, b] -> S[a + b, 1 - b] }";
3770 I
= isl_union_set_read_from_str(ctx
, domain
);
3771 D
= isl_union_map_read_from_str(ctx
, dep
);
3772 sc
= isl_schedule_constraints_on_domain(I
);
3773 sc
= isl_schedule_constraints_set_validity(sc
, D
);
3774 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
3775 isl_options_set_schedule_treat_coalescing(ctx
, 1);
3776 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3777 isl_options_set_schedule_treat_coalescing(ctx
, treat_coalescing
);
3778 isl_schedule_free(schedule
);
3784 int test_schedule(isl_ctx
*ctx
)
3786 const char *D
, *W
, *R
, *V
, *P
, *S
;
3787 int max_coincidence
;
3788 int treat_coalescing
;
3790 /* Handle resulting schedule with zero bands. */
3791 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
3795 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
3796 W
= "{ S1[t,i] -> a[t,i] }";
3797 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
3798 "S1[t,i] -> a[t-1,i+1] }";
3799 S
= "{ S1[t,i] -> [t,i] }";
3800 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3803 /* Fig. 5 of CC2008 */
3804 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
3806 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
3807 "j >= 2 and j <= -1 + N }";
3808 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
3809 "j >= 2 and j <= -1 + N; "
3810 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
3811 "j >= 2 and j <= -1 + N }";
3812 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3813 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3816 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
3817 W
= "{ S1[i] -> a[i] }";
3818 R
= "{ S2[i] -> a[i+1] }";
3819 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3820 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3823 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
3824 W
= "{ S1[i] -> a[i] }";
3825 R
= "{ S2[i] -> a[9-i] }";
3826 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3827 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3830 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
3831 W
= "{ S1[i] -> a[i] }";
3832 R
= "[N] -> { S2[i] -> a[N-1-i] }";
3833 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
3834 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
3837 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
3838 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
3839 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
3840 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
3841 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3844 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3845 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
3846 R
= "{ S2[i,j] -> a[i-1,j] }";
3847 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3848 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3851 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
3852 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
3853 R
= "{ S2[i,j] -> a[i,j-1] }";
3854 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
3855 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3858 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
3859 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
3860 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
3861 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
3862 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
3863 "S_0[] -> [0, 0, 0] }";
3864 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
3866 ctx
->opt
->schedule_parametric
= 0;
3867 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3869 ctx
->opt
->schedule_parametric
= 1;
3871 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
3872 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
3873 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
3874 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
3875 "S4[i] -> a[i,N] }";
3876 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
3877 "S4[i] -> [4,i,0] }";
3878 max_coincidence
= isl_options_get_schedule_maximize_coincidence(ctx
);
3879 isl_options_set_schedule_maximize_coincidence(ctx
, 0);
3880 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
3882 isl_options_set_schedule_maximize_coincidence(ctx
, max_coincidence
);
3884 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
3885 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3887 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
3889 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
3891 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
3892 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3895 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
3896 " S_2[t] : t >= 0 and t <= -1 + N; "
3897 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
3899 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
3900 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
3901 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
3902 "i >= 0 and i <= -1 + N }";
3903 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
3904 "i >= 0 and i <= -1 + N; "
3905 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
3906 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
3907 " S_0[t] -> [0, t, 0] }";
3909 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
3911 ctx
->opt
->schedule_parametric
= 0;
3912 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3914 ctx
->opt
->schedule_parametric
= 1;
3916 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
3917 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
3918 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
3921 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
3922 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
3923 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
3924 "j >= 0 and j <= -1 + N; "
3925 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3926 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
3927 "j >= 0 and j <= -1 + N; "
3928 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
3929 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
3930 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3933 D
= "{ S_0[i] : i >= 0 }";
3934 W
= "{ S_0[i] -> a[i] : i >= 0 }";
3935 R
= "{ S_0[i] -> a[0] : i >= 0 }";
3936 S
= "{ S_0[i] -> [0, i, 0] }";
3937 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3940 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
3941 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
3942 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
3943 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
3944 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3947 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
3948 "k <= -1 + n and k >= 0 }";
3949 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
3950 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
3951 "k <= -1 + n and k >= 0; "
3952 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
3953 "k <= -1 + n and k >= 0; "
3954 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
3955 "k <= -1 + n and k >= 0 }";
3956 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
3957 ctx
->opt
->schedule_outer_coincidence
= 1;
3958 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
3960 ctx
->opt
->schedule_outer_coincidence
= 0;
3962 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
3963 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
3964 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
3965 "Stmt_for_body24[i0, i1, 1, 0]:"
3966 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
3967 "Stmt_for_body7[i0, i1, i2]:"
3968 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
3971 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
3972 "Stmt_for_body24[1, i1, i2, i3]:"
3973 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
3975 "Stmt_for_body24[0, i1, i2, i3] -> "
3976 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
3977 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
3979 "Stmt_for_body24[0, i1, i2, i3] ->"
3980 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
3981 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
3982 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
3983 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
3984 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
3985 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
3986 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
3987 "i1 <= 6 and i1 >= 0;"
3988 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
3989 "Stmt_for_body7[i0, i1, i2] -> "
3990 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
3991 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
3992 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
3993 "Stmt_for_body7[i0, i1, i2] -> "
3994 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
3995 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
3996 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
3998 S
= "{ Stmt_for_body24[i0, i1, i2, i3] -> "
3999 "[i0, 5i0 + i1, 6i0 + i1 + i2, 1 + 6i0 + i1 + i2 + i3, 1];"
4000 "Stmt_for_body7[i0, i1, i2] -> [0, 5i0, 6i0 + i1, 6i0 + i2, 0] }";
4002 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4003 isl_options_set_schedule_treat_coalescing(ctx
, 0);
4004 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4006 isl_options_set_schedule_treat_coalescing(ctx
, treat_coalescing
);
4008 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
4009 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
4010 "j >= 1 and j <= 7;"
4011 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
4012 "j >= 1 and j <= 8 }";
4014 S
= "{ S_0[i, j] -> [i + j, j] }";
4015 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4016 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4018 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4020 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
4021 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
4022 "j >= 0 and j <= -1 + i }";
4023 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
4024 "i <= -1 + N and j >= 0;"
4025 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
4028 S
= "{ S_0[i, j] -> [i, j] }";
4029 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4030 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4032 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4034 /* Test both algorithms on a case with only proximity dependences. */
4035 D
= "{ S[i,j] : 0 <= i <= 10 }";
4037 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
4038 S
= "{ S[i, j] -> [j, i] }";
4039 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4040 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4042 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4043 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4046 D
= "{ A[a]; B[] }";
4048 P
= "{ A[a] -> B[] }";
4049 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4052 if (test_padded_schedule(ctx
) < 0)
4055 /* Check that check for progress is not confused by rational
4058 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
4059 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
4061 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
4062 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
4064 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4065 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4067 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4069 /* Check that we allow schedule rows that are only non-trivial
4070 * on some full-dimensional domains.
4072 D
= "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
4073 V
= "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
4074 "S1[j] -> S2[1] : 0 <= j <= 1 }";
4076 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4077 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4079 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4081 if (test_conditional_schedule_constraints(ctx
) < 0)
4084 if (test_strongly_satisfying_schedule(ctx
) < 0)
4087 if (test_conflicting_context_schedule(ctx
) < 0)
4090 if (test_bounded_coefficients_schedule(ctx
) < 0)
4092 if (test_coalescing_schedule(ctx
) < 0)
4098 /* Perform scheduling tests using the whole component scheduler.
4100 static int test_schedule_whole(isl_ctx
*ctx
)
4105 whole
= isl_options_get_schedule_whole_component(ctx
);
4106 isl_options_set_schedule_whole_component(ctx
, 1);
4107 r
= test_schedule(ctx
);
4108 isl_options_set_schedule_whole_component(ctx
, whole
);
4113 /* Perform scheduling tests using the incremental scheduler.
4115 static int test_schedule_incremental(isl_ctx
*ctx
)
4120 whole
= isl_options_get_schedule_whole_component(ctx
);
4121 isl_options_set_schedule_whole_component(ctx
, 0);
4122 r
= test_schedule(ctx
);
4123 isl_options_set_schedule_whole_component(ctx
, whole
);
4128 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
4130 isl_union_map
*umap
;
4133 umap
= isl_union_map_read_from_str(ctx
, str
);
4134 test
= isl_union_map_plain_is_injective(umap
);
4135 isl_union_map_free(umap
);
4138 if (test
== injective
)
4141 isl_die(ctx
, isl_error_unknown
,
4142 "map not detected as injective", return -1);
4144 isl_die(ctx
, isl_error_unknown
,
4145 "map detected as injective", return -1);
4148 int test_injective(isl_ctx
*ctx
)
4152 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
4154 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
4156 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
4158 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
4160 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
4162 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
4164 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
4166 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
4169 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
4170 if (test_plain_injective(ctx
, str
, 1))
4172 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
4173 if (test_plain_injective(ctx
, str
, 0))
4179 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
4187 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
4188 equal
= isl_aff_plain_is_equal(aff
, aff2
);
4194 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
4198 equal
= aff_plain_is_equal(aff
, str
);
4202 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
4203 "result not as expected", return -1);
4208 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
4209 __isl_take isl_aff
*aff2
);
4211 ['+'] = { &isl_aff_add
},
4212 ['-'] = { &isl_aff_sub
},
4213 ['*'] = { &isl_aff_mul
},
4214 ['/'] = { &isl_aff_div
},
4222 } aff_bin_tests
[] = {
4223 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
4224 "{ [i] -> [2i] }" },
4225 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
4227 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
4228 "{ [i] -> [2i] }" },
4229 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
4230 "{ [i] -> [2i] }" },
4231 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
4232 "{ [i] -> [i/2] }" },
4233 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
4235 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
4236 "{ [i] -> [NaN] }" },
4237 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
4238 "{ [i] -> [NaN] }" },
4239 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
4240 "{ [i] -> [NaN] }" },
4241 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
4242 "{ [i] -> [NaN] }" },
4243 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
4244 "{ [i] -> [NaN] }" },
4245 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
4246 "{ [i] -> [NaN] }" },
4247 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
4248 "{ [i] -> [NaN] }" },
4249 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
4250 "{ [i] -> [NaN] }" },
4251 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
4252 "{ [i] -> [NaN] }" },
4253 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
4254 "{ [i] -> [NaN] }" },
4255 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
4256 "{ [i] -> [NaN] }" },
4257 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
4258 "{ [i] -> [NaN] }" },
4261 /* Perform some basic tests of binary operations on isl_aff objects.
4263 static int test_bin_aff(isl_ctx
*ctx
)
4266 isl_aff
*aff1
, *aff2
, *res
;
4267 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
4268 __isl_take isl_aff
*aff2
);
4271 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
4272 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
4273 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
4274 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
4275 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
4276 aff1
= fn(aff1
, aff2
);
4277 if (isl_aff_is_nan(res
))
4278 ok
= isl_aff_is_nan(aff1
);
4280 ok
= isl_aff_plain_is_equal(aff1
, res
);
4286 isl_die(ctx
, isl_error_unknown
,
4287 "unexpected result", return -1);
4294 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4295 __isl_take isl_union_pw_multi_aff
*upma1
,
4296 __isl_take isl_union_pw_multi_aff
*upma2
);
4300 } upma_bin_tests
[] = {
4301 { &isl_union_pw_multi_aff_add
, "{ A[] -> [0]; B[0] -> [1] }",
4302 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
4303 { &isl_union_pw_multi_aff_union_add
, "{ A[] -> [0]; B[0] -> [1] }",
4304 "{ B[x] -> [2] : x >= 0 }",
4305 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
4306 { &isl_union_pw_multi_aff_pullback_union_pw_multi_aff
,
4307 "{ A[] -> B[0]; C[x] -> B[1] : x < 10; C[y] -> B[2] : y >= 10 }",
4308 "{ D[i] -> A[] : i < 0; D[i] -> C[i + 5] : i >= 0 }",
4309 "{ D[i] -> B[0] : i < 0; D[i] -> B[1] : 0 <= i < 5; "
4310 "D[i] -> B[2] : i >= 5 }" },
4311 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4312 "{ B[x] -> C[2] : x > 0 }",
4313 "{ B[x] -> A[1] : x <= 0; B[x] -> C[2] : x > 0 }" },
4314 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4315 "{ B[x] -> A[2] : x >= 0 }",
4316 "{ B[x] -> A[1] : x < 0; B[x] -> A[2] : x > 0; B[0] -> A[3] }" },
4319 /* Perform some basic tests of binary operations on
4320 * isl_union_pw_multi_aff objects.
4322 static int test_bin_upma(isl_ctx
*ctx
)
4325 isl_union_pw_multi_aff
*upma1
, *upma2
, *res
;
4328 for (i
= 0; i
< ARRAY_SIZE(upma_bin_tests
); ++i
) {
4329 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4330 upma_bin_tests
[i
].arg1
);
4331 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4332 upma_bin_tests
[i
].arg2
);
4333 res
= isl_union_pw_multi_aff_read_from_str(ctx
,
4334 upma_bin_tests
[i
].res
);
4335 upma1
= upma_bin_tests
[i
].fn(upma1
, upma2
);
4336 ok
= isl_union_pw_multi_aff_plain_is_equal(upma1
, res
);
4337 isl_union_pw_multi_aff_free(upma1
);
4338 isl_union_pw_multi_aff_free(res
);
4342 isl_die(ctx
, isl_error_unknown
,
4343 "unexpected result", return -1);
4350 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4351 __isl_take isl_union_pw_multi_aff
*upma1
,
4352 __isl_take isl_union_pw_multi_aff
*upma2
);
4355 } upma_bin_fail_tests
[] = {
4356 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4357 "{ B[x] -> C[2] : x >= 0 }" },
4360 /* Perform some basic tests of binary operations on
4361 * isl_union_pw_multi_aff objects that are expected to fail.
4363 static int test_bin_upma_fail(isl_ctx
*ctx
)
4366 isl_union_pw_multi_aff
*upma1
, *upma2
;
4369 on_error
= isl_options_get_on_error(ctx
);
4370 isl_options_set_on_error(ctx
, ISL_ON_ERROR_CONTINUE
);
4371 n
= ARRAY_SIZE(upma_bin_fail_tests
);
4372 for (i
= 0; i
< n
; ++i
) {
4373 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4374 upma_bin_fail_tests
[i
].arg1
);
4375 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4376 upma_bin_fail_tests
[i
].arg2
);
4377 upma1
= upma_bin_fail_tests
[i
].fn(upma1
, upma2
);
4378 isl_union_pw_multi_aff_free(upma1
);
4382 isl_options_set_on_error(ctx
, on_error
);
4384 isl_die(ctx
, isl_error_unknown
,
4385 "operation not expected to succeed", return -1);
4390 int test_aff(isl_ctx
*ctx
)
4395 isl_local_space
*ls
;
4399 if (test_bin_aff(ctx
) < 0)
4401 if (test_bin_upma(ctx
) < 0)
4403 if (test_bin_upma_fail(ctx
) < 0)
4406 space
= isl_space_set_alloc(ctx
, 0, 1);
4407 ls
= isl_local_space_from_space(space
);
4408 aff
= isl_aff_zero_on_domain(ls
);
4410 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4411 aff
= isl_aff_scale_down_ui(aff
, 3);
4412 aff
= isl_aff_floor(aff
);
4413 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4414 aff
= isl_aff_scale_down_ui(aff
, 2);
4415 aff
= isl_aff_floor(aff
);
4416 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4419 set
= isl_set_read_from_str(ctx
, str
);
4420 aff
= isl_aff_gist(aff
, set
);
4422 aff
= isl_aff_add_constant_si(aff
, -16);
4423 zero
= isl_aff_plain_is_zero(aff
);
4429 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4431 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
4432 aff
= isl_aff_scale_down_ui(aff
, 64);
4433 aff
= isl_aff_floor(aff
);
4434 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
4442 int test_dim_max(isl_ctx
*ctx
)
4446 isl_set
*set1
, *set2
;
4451 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
4452 set
= isl_set_read_from_str(ctx
, str
);
4453 pwaff
= isl_set_dim_max(set
, 0);
4454 set1
= isl_set_from_pw_aff(pwaff
);
4455 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
4456 set2
= isl_set_read_from_str(ctx
, str
);
4457 equal
= isl_set_is_equal(set1
, set2
);
4463 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4465 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
4466 set
= isl_set_read_from_str(ctx
, str
);
4467 pwaff
= isl_set_dim_max(set
, 0);
4468 set1
= isl_set_from_pw_aff(pwaff
);
4469 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4470 set2
= isl_set_read_from_str(ctx
, str
);
4471 equal
= isl_set_is_equal(set1
, set2
);
4477 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4479 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
4480 set
= isl_set_read_from_str(ctx
, str
);
4481 pwaff
= isl_set_dim_max(set
, 0);
4482 set1
= isl_set_from_pw_aff(pwaff
);
4483 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4484 set2
= isl_set_read_from_str(ctx
, str
);
4485 equal
= isl_set_is_equal(set1
, set2
);
4491 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4493 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
4494 "0 <= i < N and 0 <= j < M }";
4495 map
= isl_map_read_from_str(ctx
, str
);
4496 set
= isl_map_range(map
);
4498 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
4499 set1
= isl_set_from_pw_aff(pwaff
);
4500 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
4501 set2
= isl_set_read_from_str(ctx
, str
);
4502 equal
= isl_set_is_equal(set1
, set2
);
4506 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
4507 set1
= isl_set_from_pw_aff(pwaff
);
4508 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
4509 set2
= isl_set_read_from_str(ctx
, str
);
4510 if (equal
>= 0 && equal
)
4511 equal
= isl_set_is_equal(set1
, set2
);
4520 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4522 /* Check that solutions are properly merged. */
4523 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
4524 "c <= -1 + n - 4a - 2b and c >= -2b and "
4525 "4a >= -4 + n and c >= 0 }";
4526 set
= isl_set_read_from_str(ctx
, str
);
4527 pwaff
= isl_set_dim_min(set
, 2);
4528 set1
= isl_set_from_pw_aff(pwaff
);
4529 str
= "[n] -> { [(0)] : n >= 1 }";
4530 set2
= isl_set_read_from_str(ctx
, str
);
4531 equal
= isl_set_is_equal(set1
, set2
);
4538 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4540 /* Check that empty solution lie in the right space. */
4541 str
= "[n] -> { [t,a] : 1 = 0 }";
4542 set
= isl_set_read_from_str(ctx
, str
);
4543 pwaff
= isl_set_dim_max(set
, 0);
4544 set1
= isl_set_from_pw_aff(pwaff
);
4545 str
= "[n] -> { [t] : 1 = 0 }";
4546 set2
= isl_set_read_from_str(ctx
, str
);
4547 equal
= isl_set_is_equal(set1
, set2
);
4554 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4559 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
4561 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
4565 isl_pw_multi_aff
*pma2
;
4571 ctx
= isl_pw_multi_aff_get_ctx(pma
);
4572 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4573 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
4574 isl_pw_multi_aff_free(pma2
);
4579 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
4580 * represented by "str".
4582 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
4587 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
4591 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
4592 "result not as expected", return -1);
4596 /* Basic test for isl_pw_multi_aff_product.
4598 * Check that multiple pieces are properly handled.
4600 static int test_product_pma(isl_ctx
*ctx
)
4604 isl_pw_multi_aff
*pma1
, *pma2
;
4606 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
4607 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4608 str
= "{ C[] -> D[] }";
4609 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
4610 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
4611 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
4612 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
4613 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
4614 isl_pw_multi_aff_free(pma1
);
4621 int test_product(isl_ctx
*ctx
)
4625 isl_union_set
*uset1
, *uset2
;
4629 set
= isl_set_read_from_str(ctx
, str
);
4630 set
= isl_set_product(set
, isl_set_copy(set
));
4631 ok
= isl_set_is_wrapping(set
);
4636 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4639 uset1
= isl_union_set_read_from_str(ctx
, str
);
4640 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
4641 str
= "{ [[] -> []] }";
4642 uset2
= isl_union_set_read_from_str(ctx
, str
);
4643 ok
= isl_union_set_is_equal(uset1
, uset2
);
4644 isl_union_set_free(uset1
);
4645 isl_union_set_free(uset2
);
4649 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4651 if (test_product_pma(ctx
) < 0)
4657 /* Check that two sets are not considered disjoint just because
4658 * they have a different set of (named) parameters.
4660 static int test_disjoint(isl_ctx
*ctx
)
4663 isl_set
*set
, *set2
;
4666 str
= "[n] -> { [[]->[]] }";
4667 set
= isl_set_read_from_str(ctx
, str
);
4668 str
= "{ [[]->[]] }";
4669 set2
= isl_set_read_from_str(ctx
, str
);
4670 disjoint
= isl_set_is_disjoint(set
, set2
);
4676 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4681 int test_equal(isl_ctx
*ctx
)
4684 isl_set
*set
, *set2
;
4688 set
= isl_set_read_from_str(ctx
, str
);
4690 set2
= isl_set_read_from_str(ctx
, str
);
4691 equal
= isl_set_is_equal(set
, set2
);
4697 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4702 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
4703 enum isl_dim_type type
, unsigned pos
, int fixed
)
4707 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
4714 isl_die(ctx
, isl_error_unknown
,
4715 "map not detected as fixed", return -1);
4717 isl_die(ctx
, isl_error_unknown
,
4718 "map detected as fixed", return -1);
4721 int test_fixed(isl_ctx
*ctx
)
4726 str
= "{ [i] -> [i] }";
4727 map
= isl_map_read_from_str(ctx
, str
);
4728 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
4730 str
= "{ [i] -> [1] }";
4731 map
= isl_map_read_from_str(ctx
, str
);
4732 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4734 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
4735 map
= isl_map_read_from_str(ctx
, str
);
4736 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4738 map
= isl_map_read_from_str(ctx
, str
);
4739 map
= isl_map_neg(map
);
4740 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
4746 struct isl_vertices_test_data
{
4749 const char *vertex
[2];
4750 } vertices_tests
[] = {
4751 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
4752 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
4753 { "{ A[t, i] : t = 14 and i = 1 }",
4754 1, { "{ A[14, 1] }" } },
4757 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
4759 static isl_stat
find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
4761 struct isl_vertices_test_data
*data
= user
;
4764 isl_basic_set
*bset
;
4765 isl_pw_multi_aff
*pma
;
4769 ctx
= isl_vertex_get_ctx(vertex
);
4770 bset
= isl_vertex_get_domain(vertex
);
4771 ma
= isl_vertex_get_expr(vertex
);
4772 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
4774 for (i
= 0; i
< data
->n
; ++i
) {
4775 isl_pw_multi_aff
*pma_i
;
4777 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
4778 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
4779 isl_pw_multi_aff_free(pma_i
);
4781 if (equal
< 0 || equal
)
4785 isl_pw_multi_aff_free(pma
);
4786 isl_vertex_free(vertex
);
4789 return isl_stat_error
;
4791 return equal
? isl_stat_ok
: isl_stat_error
;
4794 int test_vertices(isl_ctx
*ctx
)
4798 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
4799 isl_basic_set
*bset
;
4800 isl_vertices
*vertices
;
4804 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
4805 vertices
= isl_basic_set_compute_vertices(bset
);
4806 n
= isl_vertices_get_n_vertices(vertices
);
4807 if (vertices_tests
[i
].n
!= n
)
4809 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
4810 &vertices_tests
[i
]) < 0)
4812 isl_vertices_free(vertices
);
4813 isl_basic_set_free(bset
);
4818 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
4825 int test_union_pw(isl_ctx
*ctx
)
4829 isl_union_set
*uset
;
4830 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
4832 str
= "{ [x] -> x^2 }";
4833 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
4834 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
4835 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
4836 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
4837 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
4838 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
4839 isl_union_pw_qpolynomial_free(upwqp1
);
4840 isl_union_pw_qpolynomial_free(upwqp2
);
4844 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4849 /* Test that isl_union_pw_qpolynomial_eval picks up the function
4850 * defined over the correct domain space.
4852 static int test_eval(isl_ctx
*ctx
)
4857 isl_union_pw_qpolynomial
*upwqp
;
4861 str
= "{ A[x] -> x^2; B[x] -> -x^2 }";
4862 upwqp
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
4864 set
= isl_set_read_from_str(ctx
, str
);
4865 pnt
= isl_set_sample_point(set
);
4866 v
= isl_union_pw_qpolynomial_eval(upwqp
, pnt
);
4867 cmp
= isl_val_cmp_si(v
, 36);
4873 isl_die(ctx
, isl_error_unknown
, "unexpected value", return -1);
4878 /* Descriptions of sets that are tested for reparsing after printing.
4880 const char *output_tests
[] = {
4881 "{ [1, y] : 0 <= y <= 1; [x, -x] : 0 <= x <= 1 }",
4884 /* Check that printing a set and reparsing a set from the printed output
4885 * results in the same set.
4887 static int test_output_set(isl_ctx
*ctx
)
4891 isl_set
*set1
, *set2
;
4894 for (i
= 0; i
< ARRAY_SIZE(output_tests
); ++i
) {
4895 set1
= isl_set_read_from_str(ctx
, output_tests
[i
]);
4896 str
= isl_set_to_str(set1
);
4897 set2
= isl_set_read_from_str(ctx
, str
);
4899 equal
= isl_set_is_equal(set1
, set2
);
4905 isl_die(ctx
, isl_error_unknown
,
4906 "parsed output not the same", return -1);
4912 int test_output(isl_ctx
*ctx
)
4920 if (test_output_set(ctx
) < 0)
4923 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
4924 pa
= isl_pw_aff_read_from_str(ctx
, str
);
4926 p
= isl_printer_to_str(ctx
);
4927 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
4928 p
= isl_printer_print_pw_aff(p
, pa
);
4929 s
= isl_printer_get_str(p
);
4930 isl_printer_free(p
);
4931 isl_pw_aff_free(pa
);
4935 equal
= !strcmp(s
, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
4940 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4945 int test_sample(isl_ctx
*ctx
)
4948 isl_basic_set
*bset1
, *bset2
;
4951 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
4952 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
4953 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
4954 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
4955 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
4956 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
4957 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
4958 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
4959 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
4960 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
4961 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
4962 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
4963 "d - 1073741821e and "
4964 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
4965 "3j >= 1 - a + b + 2e and "
4966 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
4967 "3i <= 4 - a + 4b - e and "
4968 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
4969 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
4970 "c <= -1 + a and 3i >= -2 - a + 3e and "
4971 "1073741822e <= 1073741823 - a + 1073741822b + c and "
4972 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
4973 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
4974 "1073741823e >= 1 + 1073741823b - d and "
4975 "3i >= 1073741823b + c - 1073741823e - f and "
4976 "3i >= 1 + 2b + e + 3g }";
4977 bset1
= isl_basic_set_read_from_str(ctx
, str
);
4978 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
4979 empty
= isl_basic_set_is_empty(bset2
);
4980 subset
= isl_basic_set_is_subset(bset2
, bset1
);
4981 isl_basic_set_free(bset1
);
4982 isl_basic_set_free(bset2
);
4983 if (empty
< 0 || subset
< 0)
4986 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
4988 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
4993 int test_fixed_power(isl_ctx
*ctx
)
5001 str
= "{ [i] -> [i + 1] }";
5002 map
= isl_map_read_from_str(ctx
, str
);
5003 isl_int_set_si(exp
, 23);
5004 map
= isl_map_fixed_power(map
, exp
);
5005 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
5014 int test_slice(isl_ctx
*ctx
)
5020 str
= "{ [i] -> [j] }";
5021 map
= isl_map_read_from_str(ctx
, str
);
5022 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5023 equal
= map_check_equal(map
, "{ [i] -> [i] }");
5028 str
= "{ [i] -> [j] }";
5029 map
= isl_map_read_from_str(ctx
, str
);
5030 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5031 equal
= map_check_equal(map
, "{ [i] -> [j] }");
5036 str
= "{ [i] -> [j] }";
5037 map
= isl_map_read_from_str(ctx
, str
);
5038 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5039 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
5044 str
= "{ [i] -> [j] }";
5045 map
= isl_map_read_from_str(ctx
, str
);
5046 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5047 equal
= map_check_equal(map
, "{ [0] -> [j] }");
5052 str
= "{ [i] -> [j] }";
5053 map
= isl_map_read_from_str(ctx
, str
);
5054 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5055 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
5060 str
= "{ [i] -> [j] }";
5061 map
= isl_map_read_from_str(ctx
, str
);
5062 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5063 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
5071 int test_eliminate(isl_ctx
*ctx
)
5077 str
= "{ [i] -> [j] : i = 2j }";
5078 map
= isl_map_read_from_str(ctx
, str
);
5079 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
5080 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
5088 /* Check that isl_set_dim_residue_class detects that the values of j
5089 * in the set below are all odd and that it does not detect any spurious
5092 static int test_residue_class(isl_ctx
*ctx
)
5099 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
5100 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
5101 set
= isl_set_read_from_str(ctx
, str
);
5104 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
5106 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
5107 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
5116 int test_align_parameters(isl_ctx
*ctx
)
5120 isl_multi_aff
*ma1
, *ma2
;
5123 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
5124 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
5126 space
= isl_space_params_alloc(ctx
, 1);
5127 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
5128 ma1
= isl_multi_aff_align_params(ma1
, space
);
5130 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
5131 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
5133 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
5135 isl_multi_aff_free(ma1
);
5136 isl_multi_aff_free(ma2
);
5141 isl_die(ctx
, isl_error_unknown
,
5142 "result not as expected", return -1);
5147 static int test_list(isl_ctx
*ctx
)
5149 isl_id
*a
, *b
, *c
, *d
, *id
;
5153 a
= isl_id_alloc(ctx
, "a", NULL
);
5154 b
= isl_id_alloc(ctx
, "b", NULL
);
5155 c
= isl_id_alloc(ctx
, "c", NULL
);
5156 d
= isl_id_alloc(ctx
, "d", NULL
);
5158 list
= isl_id_list_alloc(ctx
, 4);
5159 list
= isl_id_list_add(list
, a
);
5160 list
= isl_id_list_add(list
, b
);
5161 list
= isl_id_list_add(list
, c
);
5162 list
= isl_id_list_add(list
, d
);
5163 list
= isl_id_list_drop(list
, 1, 1);
5165 if (isl_id_list_n_id(list
) != 3) {
5166 isl_id_list_free(list
);
5167 isl_die(ctx
, isl_error_unknown
,
5168 "unexpected number of elements in list", return -1);
5171 id
= isl_id_list_get_id(list
, 0);
5174 id
= isl_id_list_get_id(list
, 1);
5177 id
= isl_id_list_get_id(list
, 2);
5181 isl_id_list_free(list
);
5184 isl_die(ctx
, isl_error_unknown
,
5185 "unexpected elements in list", return -1);
5190 const char *set_conversion_tests
[] = {
5191 "[N] -> { [i] : N - 1 <= 2 i <= N }",
5192 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
5193 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
5194 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
5195 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
5196 "[a, b] -> { [c, d] : (4*floor((-a + c)/4) = -a + c and "
5197 "32*floor((-b + d)/32) = -b + d and 5 <= c <= 8 and "
5198 "-3 + c <= d <= 28 + c) }",
5201 /* Check that converting from isl_set to isl_pw_multi_aff and back
5202 * to isl_set produces the original isl_set.
5204 static int test_set_conversion(isl_ctx
*ctx
)
5208 isl_set
*set1
, *set2
;
5209 isl_pw_multi_aff
*pma
;
5212 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
5213 str
= set_conversion_tests
[i
];
5214 set1
= isl_set_read_from_str(ctx
, str
);
5215 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
5216 set2
= isl_set_from_pw_multi_aff(pma
);
5217 equal
= isl_set_is_equal(set1
, set2
);
5224 isl_die(ctx
, isl_error_unknown
, "bad conversion",
5231 const char *conversion_tests
[] = {
5232 "{ [a, b, c, d] -> s0[a, b, e, f] : "
5233 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
5234 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
5235 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
5237 "{ [a, b] -> [c] : exists (e0 = floor((-a - b + c)/5): "
5238 "5e0 = -a - b + c and c >= -a and c <= 4 - a) }",
5239 "{ [a, b] -> [c] : exists d : 18 * d = -3 - a + 2c and 1 <= c <= 3 }",
5242 /* Check that converting from isl_map to isl_pw_multi_aff and back
5243 * to isl_map produces the original isl_map.
5245 static int test_map_conversion(isl_ctx
*ctx
)
5248 isl_map
*map1
, *map2
;
5249 isl_pw_multi_aff
*pma
;
5252 for (i
= 0; i
< ARRAY_SIZE(conversion_tests
); ++i
) {
5253 map1
= isl_map_read_from_str(ctx
, conversion_tests
[i
]);
5254 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
5255 map2
= isl_map_from_pw_multi_aff(pma
);
5256 equal
= isl_map_is_equal(map1
, map2
);
5263 isl_die(ctx
, isl_error_unknown
, "bad conversion",
5270 static int test_conversion(isl_ctx
*ctx
)
5272 if (test_set_conversion(ctx
) < 0)
5274 if (test_map_conversion(ctx
) < 0)
5279 /* Check that isl_basic_map_curry does not modify input.
5281 static int test_curry(isl_ctx
*ctx
)
5284 isl_basic_map
*bmap1
, *bmap2
;
5287 str
= "{ [A[] -> B[]] -> C[] }";
5288 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
5289 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
5290 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
5291 isl_basic_map_free(bmap1
);
5292 isl_basic_map_free(bmap2
);
5297 isl_die(ctx
, isl_error_unknown
,
5298 "curried map should not be equal to original",
5308 } preimage_tests
[] = {
5309 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
5310 "{ A[j,i] -> B[i,j] }",
5311 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
5312 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
5313 "{ A[a,b] -> B[a/2,b/6] }",
5314 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
5315 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
5316 "{ A[a,b] -> B[a/2,b/6] }",
5317 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
5318 "exists i,j : a = 2 i and b = 6 j }" },
5319 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
5320 "[n] -> { : 0 <= n <= 100 }" },
5321 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
5322 "{ A[a] -> B[2a] }",
5323 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
5324 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
5325 "{ A[a] -> B[([a/2])] }",
5326 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
5327 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
5328 "{ A[a] -> B[a,a,a/3] }",
5329 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
5330 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
5331 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
5334 static int test_preimage_basic_set(isl_ctx
*ctx
)
5337 isl_basic_set
*bset1
, *bset2
;
5341 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
5342 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
5343 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
5344 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
5345 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
5346 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5347 isl_basic_set_free(bset1
);
5348 isl_basic_set_free(bset2
);
5352 isl_die(ctx
, isl_error_unknown
, "bad preimage",
5363 } preimage_domain_tests
[] = {
5364 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
5365 "{ A[j,i] -> B[i,j] }",
5366 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
5367 { "{ B[i] -> C[i]; D[i] -> E[i] }",
5368 "{ A[i] -> B[i + 1] }",
5369 "{ A[i] -> C[i + 1] }" },
5370 { "{ B[i] -> C[i]; B[i] -> E[i] }",
5371 "{ A[i] -> B[i + 1] }",
5372 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
5373 { "{ B[i] -> C[([i/2])] }",
5374 "{ A[i] -> B[2i] }",
5375 "{ A[i] -> C[i] }" },
5376 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
5377 "{ A[i] -> B[([i/5]), ([i/7])] }",
5378 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
5379 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
5380 "[N] -> { A[] -> B[([N/5])] }",
5381 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
5382 { "{ B[i] -> C[i] : exists a : i = 5 a }",
5383 "{ A[i] -> B[2i] }",
5384 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
5385 { "{ B[i] -> C[i] : exists a : i = 2 a; "
5386 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
5387 "{ A[i] -> B[2i] }",
5388 "{ A[i] -> C[2i] }" },
5389 { "{ A[i] -> B[i] }", "{ C[i] -> A[(i + floor(i/3))/2] }",
5390 "{ C[i] -> B[j] : 2j = i + floor(i/3) }" },
5393 static int test_preimage_union_map(isl_ctx
*ctx
)
5396 isl_union_map
*umap1
, *umap2
;
5400 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
5401 umap1
= isl_union_map_read_from_str(ctx
,
5402 preimage_domain_tests
[i
].map
);
5403 ma
= isl_multi_aff_read_from_str(ctx
,
5404 preimage_domain_tests
[i
].ma
);
5405 umap2
= isl_union_map_read_from_str(ctx
,
5406 preimage_domain_tests
[i
].res
);
5407 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
5408 equal
= isl_union_map_is_equal(umap1
, umap2
);
5409 isl_union_map_free(umap1
);
5410 isl_union_map_free(umap2
);
5414 isl_die(ctx
, isl_error_unknown
, "bad preimage",
5421 static int test_preimage(isl_ctx
*ctx
)
5423 if (test_preimage_basic_set(ctx
) < 0)
5425 if (test_preimage_union_map(ctx
) < 0)
5435 } pullback_tests
[] = {
5436 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
5437 "{ A[a,b] -> C[b + 2a] }" },
5438 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
5439 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
5440 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
5441 "{ A[a] -> C[(a)/6] }" },
5442 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
5443 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
5444 "{ A[a] -> C[(2a)/3] }" },
5445 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
5446 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
5447 "{ A[i,j] -> C[i + j, i + j] }"},
5448 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
5449 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
5450 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
5451 { "{ [i, j] -> [floor((i)/4) + floor((2*i+j)/5)] }",
5452 "{ [i, j] -> [floor((i)/3), j] }",
5453 "{ [i, j] -> [(floor((i)/12) + floor((j + 2*floor((i)/3))/5))] }" },
5456 static int test_pullback(isl_ctx
*ctx
)
5459 isl_multi_aff
*ma1
, *ma2
;
5463 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
5464 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
5465 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
5466 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
5467 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
5468 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
5469 isl_multi_aff_free(ma1
);
5470 isl_multi_aff_free(ma2
);
5474 isl_die(ctx
, isl_error_unknown
, "bad pullback",
5481 /* Check that negation is printed correctly and that equal expressions
5482 * are correctly identified.
5484 static int test_ast(isl_ctx
*ctx
)
5486 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
5490 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
5491 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
5492 expr
= isl_ast_expr_add(expr1
, expr2
);
5493 expr2
= isl_ast_expr_copy(expr
);
5494 expr
= isl_ast_expr_neg(expr
);
5495 expr2
= isl_ast_expr_neg(expr2
);
5496 equal
= isl_ast_expr_is_equal(expr
, expr2
);
5497 str
= isl_ast_expr_to_str(expr
);
5498 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
5500 isl_ast_expr_free(expr
);
5501 isl_ast_expr_free(expr2
);
5503 if (ok
< 0 || equal
< 0)
5506 isl_die(ctx
, isl_error_unknown
,
5507 "equal expressions not considered equal", return -1);
5509 isl_die(ctx
, isl_error_unknown
,
5510 "isl_ast_expr printed incorrectly", return -1);
5512 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
5513 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
5514 expr
= isl_ast_expr_add(expr1
, expr2
);
5515 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
5516 expr
= isl_ast_expr_sub(expr3
, expr
);
5517 str
= isl_ast_expr_to_str(expr
);
5518 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
5520 isl_ast_expr_free(expr
);
5525 isl_die(ctx
, isl_error_unknown
,
5526 "isl_ast_expr printed incorrectly", return -1);
5531 /* Check that isl_ast_build_expr_from_set returns a valid expression
5532 * for an empty set. Note that isl_ast_build_expr_from_set getting
5533 * called on an empty set probably indicates a bug in the caller.
5535 static int test_ast_build(isl_ctx
*ctx
)
5538 isl_ast_build
*build
;
5541 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5542 build
= isl_ast_build_from_context(set
);
5544 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
5545 expr
= isl_ast_build_expr_from_set(build
, set
);
5547 isl_ast_expr_free(expr
);
5548 isl_ast_build_free(build
);
5556 /* Internal data structure for before_for and after_for callbacks.
5558 * depth is the current depth
5559 * before is the number of times before_for has been called
5560 * after is the number of times after_for has been called
5562 struct isl_test_codegen_data
{
5568 /* This function is called before each for loop in the AST generated
5569 * from test_ast_gen1.
5571 * Increment the number of calls and the depth.
5572 * Check that the space returned by isl_ast_build_get_schedule_space
5573 * matches the target space of the schedule returned by
5574 * isl_ast_build_get_schedule.
5575 * Return an isl_id that is checked by the corresponding call
5578 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
5581 struct isl_test_codegen_data
*data
= user
;
5584 isl_union_map
*schedule
;
5585 isl_union_set
*uset
;
5590 ctx
= isl_ast_build_get_ctx(build
);
5592 if (data
->before
>= 3)
5593 isl_die(ctx
, isl_error_unknown
,
5594 "unexpected number of for nodes", return NULL
);
5595 if (data
->depth
>= 2)
5596 isl_die(ctx
, isl_error_unknown
,
5597 "unexpected depth", return NULL
);
5599 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
5603 schedule
= isl_ast_build_get_schedule(build
);
5604 uset
= isl_union_map_range(schedule
);
5607 if (isl_union_set_n_set(uset
) != 1) {
5608 isl_union_set_free(uset
);
5609 isl_die(ctx
, isl_error_unknown
,
5610 "expecting single range space", return NULL
);
5613 space
= isl_ast_build_get_schedule_space(build
);
5614 set
= isl_union_set_extract_set(uset
, space
);
5615 isl_union_set_free(uset
);
5616 empty
= isl_set_is_empty(set
);
5622 isl_die(ctx
, isl_error_unknown
,
5623 "spaces don't match", return NULL
);
5625 return isl_id_alloc(ctx
, name
, NULL
);
5628 /* This function is called after each for loop in the AST generated
5629 * from test_ast_gen1.
5631 * Increment the number of calls and decrement the depth.
5632 * Check that the annotation attached to the node matches
5633 * the isl_id returned by the corresponding call to before_for.
5635 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
5636 __isl_keep isl_ast_build
*build
, void *user
)
5638 struct isl_test_codegen_data
*data
= user
;
5646 if (data
->after
> data
->before
)
5647 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5648 "mismatch in number of for nodes",
5649 return isl_ast_node_free(node
));
5651 id
= isl_ast_node_get_annotation(node
);
5653 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5654 "missing annotation", return isl_ast_node_free(node
));
5656 name
= isl_id_get_name(id
);
5657 valid
= name
&& atoi(name
+ 1) == data
->depth
;
5661 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
5662 "wrong annotation", return isl_ast_node_free(node
));
5667 /* Check that the before_each_for and after_each_for callbacks
5668 * are called for each for loop in the generated code,
5669 * that they are called in the right order and that the isl_id
5670 * returned from the before_each_for callback is attached to
5671 * the isl_ast_node passed to the corresponding after_each_for call.
5673 static int test_ast_gen1(isl_ctx
*ctx
)
5677 isl_union_map
*schedule
;
5678 isl_ast_build
*build
;
5680 struct isl_test_codegen_data data
;
5682 str
= "[N] -> { : N >= 10 }";
5683 set
= isl_set_read_from_str(ctx
, str
);
5684 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
5685 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
5686 schedule
= isl_union_map_read_from_str(ctx
, str
);
5691 build
= isl_ast_build_from_context(set
);
5692 build
= isl_ast_build_set_before_each_for(build
,
5693 &before_for
, &data
);
5694 build
= isl_ast_build_set_after_each_for(build
,
5696 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5697 isl_ast_build_free(build
);
5701 isl_ast_node_free(tree
);
5703 if (data
.before
!= 3 || data
.after
!= 3)
5704 isl_die(ctx
, isl_error_unknown
,
5705 "unexpected number of for nodes", return -1);
5710 /* Check that the AST generator handles domains that are integrally disjoint
5711 * but not rationally disjoint.
5713 static int test_ast_gen2(isl_ctx
*ctx
)
5717 isl_union_map
*schedule
;
5718 isl_union_map
*options
;
5719 isl_ast_build
*build
;
5722 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
5723 schedule
= isl_union_map_read_from_str(ctx
, str
);
5724 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5725 build
= isl_ast_build_from_context(set
);
5727 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
5728 options
= isl_union_map_read_from_str(ctx
, str
);
5729 build
= isl_ast_build_set_options(build
, options
);
5730 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5731 isl_ast_build_free(build
);
5734 isl_ast_node_free(tree
);
5739 /* Increment *user on each call.
5741 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
5742 __isl_keep isl_ast_build
*build
, void *user
)
5751 /* Test that unrolling tries to minimize the number of instances.
5752 * In particular, for the schedule given below, make sure it generates
5753 * 3 nodes (rather than 101).
5755 static int test_ast_gen3(isl_ctx
*ctx
)
5759 isl_union_map
*schedule
;
5760 isl_union_map
*options
;
5761 isl_ast_build
*build
;
5765 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
5766 schedule
= isl_union_map_read_from_str(ctx
, str
);
5767 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5769 str
= "{ [i] -> unroll[0] }";
5770 options
= isl_union_map_read_from_str(ctx
, str
);
5772 build
= isl_ast_build_from_context(set
);
5773 build
= isl_ast_build_set_options(build
, options
);
5774 build
= isl_ast_build_set_at_each_domain(build
,
5775 &count_domains
, &n_domain
);
5776 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5777 isl_ast_build_free(build
);
5781 isl_ast_node_free(tree
);
5784 isl_die(ctx
, isl_error_unknown
,
5785 "unexpected number of for nodes", return -1);
5790 /* Check that if the ast_build_exploit_nested_bounds options is set,
5791 * we do not get an outer if node in the generated AST,
5792 * while we do get such an outer if node if the options is not set.
5794 static int test_ast_gen4(isl_ctx
*ctx
)
5798 isl_union_map
*schedule
;
5799 isl_ast_build
*build
;
5801 enum isl_ast_node_type type
;
5804 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
5805 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
5807 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
5809 schedule
= isl_union_map_read_from_str(ctx
, str
);
5810 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5811 build
= isl_ast_build_from_context(set
);
5812 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5813 isl_ast_build_free(build
);
5817 type
= isl_ast_node_get_type(tree
);
5818 isl_ast_node_free(tree
);
5820 if (type
== isl_ast_node_if
)
5821 isl_die(ctx
, isl_error_unknown
,
5822 "not expecting if node", return -1);
5824 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
5826 schedule
= isl_union_map_read_from_str(ctx
, str
);
5827 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5828 build
= isl_ast_build_from_context(set
);
5829 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5830 isl_ast_build_free(build
);
5834 type
= isl_ast_node_get_type(tree
);
5835 isl_ast_node_free(tree
);
5837 if (type
!= isl_ast_node_if
)
5838 isl_die(ctx
, isl_error_unknown
,
5839 "expecting if node", return -1);
5841 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
5846 /* This function is called for each leaf in the AST generated
5847 * from test_ast_gen5.
5849 * We finalize the AST generation by extending the outer schedule
5850 * with a zero-dimensional schedule. If this results in any for loops,
5851 * then this means that we did not pass along enough information
5852 * about the outer schedule to the inner AST generation.
5854 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
5857 isl_union_map
*schedule
, *extra
;
5860 schedule
= isl_ast_build_get_schedule(build
);
5861 extra
= isl_union_map_copy(schedule
);
5862 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
5863 schedule
= isl_union_map_range_product(schedule
, extra
);
5864 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5865 isl_ast_build_free(build
);
5870 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
5871 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
5872 "code should not contain any for loop",
5873 return isl_ast_node_free(tree
));
5878 /* Check that we do not lose any information when going back and
5879 * forth between internal and external schedule.
5881 * In particular, we create an AST where we unroll the only
5882 * non-constant dimension in the schedule. We therefore do
5883 * not expect any for loops in the AST. However, older versions
5884 * of isl would not pass along enough information about the outer
5885 * schedule when performing an inner code generation from a create_leaf
5886 * callback, resulting in the inner code generation producing a for loop.
5888 static int test_ast_gen5(isl_ctx
*ctx
)
5892 isl_union_map
*schedule
, *options
;
5893 isl_ast_build
*build
;
5896 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
5897 schedule
= isl_union_map_read_from_str(ctx
, str
);
5899 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
5900 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
5901 options
= isl_union_map_read_from_str(ctx
, str
);
5903 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
5904 build
= isl_ast_build_from_context(set
);
5905 build
= isl_ast_build_set_options(build
, options
);
5906 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
5907 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
5908 isl_ast_build_free(build
);
5909 isl_ast_node_free(tree
);
5916 static int test_ast_gen(isl_ctx
*ctx
)
5918 if (test_ast_gen1(ctx
) < 0)
5920 if (test_ast_gen2(ctx
) < 0)
5922 if (test_ast_gen3(ctx
) < 0)
5924 if (test_ast_gen4(ctx
) < 0)
5926 if (test_ast_gen5(ctx
) < 0)
5931 /* Check if dropping output dimensions from an isl_pw_multi_aff
5934 static int test_pw_multi_aff(isl_ctx
*ctx
)
5937 isl_pw_multi_aff
*pma1
, *pma2
;
5940 str
= "{ [i,j] -> [i+j, 4i-j] }";
5941 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5942 str
= "{ [i,j] -> [4i-j] }";
5943 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5945 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
5947 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
5949 isl_pw_multi_aff_free(pma1
);
5950 isl_pw_multi_aff_free(pma2
);
5954 isl_die(ctx
, isl_error_unknown
,
5955 "expressions not equal", return -1);
5960 /* Check that we can properly parse multi piecewise affine expressions
5961 * where the piecewise affine expressions have different domains.
5963 static int test_multi_pw_aff(isl_ctx
*ctx
)
5966 isl_set
*dom
, *dom2
;
5967 isl_multi_pw_aff
*mpa1
, *mpa2
;
5972 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
5973 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
5974 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
5975 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
5976 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
5977 str
= "{ [i] -> [(i : i > 0), 2i] }";
5978 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
5980 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
5982 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
5983 dom
= isl_pw_aff_domain(pa
);
5984 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
5985 dom2
= isl_pw_aff_domain(pa
);
5986 equal_domain
= isl_set_is_equal(dom
, dom2
);
5990 isl_multi_pw_aff_free(mpa1
);
5991 isl_multi_pw_aff_free(mpa2
);
5996 isl_die(ctx
, isl_error_unknown
,
5997 "expressions not equal", return -1);
5999 if (equal_domain
< 0)
6002 isl_die(ctx
, isl_error_unknown
,
6003 "domains unexpectedly equal", return -1);
6008 /* This is a regression test for a bug where isl_basic_map_simplify
6009 * would end up in an infinite loop. In particular, we construct
6010 * an empty basic set that is not obviously empty.
6011 * isl_basic_set_is_empty marks the basic set as empty.
6012 * After projecting out i3, the variable can be dropped completely,
6013 * but isl_basic_map_simplify refrains from doing so if the basic set
6014 * is empty and would end up in an infinite loop if it didn't test
6015 * explicitly for empty basic maps in the outer loop.
6017 static int test_simplify_1(isl_ctx
*ctx
)
6020 isl_basic_set
*bset
;
6023 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
6024 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
6025 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
6027 bset
= isl_basic_set_read_from_str(ctx
, str
);
6028 empty
= isl_basic_set_is_empty(bset
);
6029 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
6030 isl_basic_set_free(bset
);
6034 isl_die(ctx
, isl_error_unknown
,
6035 "basic set should be empty", return -1);
6040 /* Check that the equality in the set description below
6041 * is simplified away.
6043 static int test_simplify_2(isl_ctx
*ctx
)
6046 isl_basic_set
*bset
;
6049 str
= "{ [a] : exists e0, e1: 32e1 = 31 + 31a + 31e0 }";
6050 bset
= isl_basic_set_read_from_str(ctx
, str
);
6051 universe
= isl_basic_set_plain_is_universe(bset
);
6052 isl_basic_set_free(bset
);
6057 isl_die(ctx
, isl_error_unknown
,
6058 "equality not simplified away", return -1);
6062 /* Some simplification tests.
6064 static int test_simplify(isl_ctx
*ctx
)
6066 if (test_simplify_1(ctx
) < 0)
6068 if (test_simplify_2(ctx
) < 0)
6073 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
6074 * with gbr context would fail to disable the use of the shifted tableau
6075 * when transferring equalities for the input to the context, resulting
6076 * in invalid sample values.
6078 static int test_partial_lexmin(isl_ctx
*ctx
)
6081 isl_basic_set
*bset
;
6082 isl_basic_map
*bmap
;
6085 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
6086 bmap
= isl_basic_map_read_from_str(ctx
, str
);
6087 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
6088 bset
= isl_basic_set_read_from_str(ctx
, str
);
6089 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
6098 /* Check that the variable compression performed on the existentially
6099 * quantified variables inside isl_basic_set_compute_divs is not confused
6100 * by the implicit equalities among the parameters.
6102 static int test_compute_divs(isl_ctx
*ctx
)
6105 isl_basic_set
*bset
;
6108 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
6109 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
6110 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
6111 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
6112 bset
= isl_basic_set_read_from_str(ctx
, str
);
6113 set
= isl_basic_set_compute_divs(bset
);
6121 /* Check that the reaching domain elements and the prefix schedule
6122 * at a leaf node are the same before and after grouping.
6124 static int test_schedule_tree_group_1(isl_ctx
*ctx
)
6129 isl_union_set
*uset
;
6130 isl_multi_union_pw_aff
*mupa
;
6131 isl_union_pw_multi_aff
*upma1
, *upma2
;
6132 isl_union_set
*domain1
, *domain2
;
6133 isl_union_map
*umap1
, *umap2
;
6134 isl_schedule_node
*node
;
6136 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10 }";
6137 uset
= isl_union_set_read_from_str(ctx
, str
);
6138 node
= isl_schedule_node_from_domain(uset
);
6139 node
= isl_schedule_node_child(node
, 0);
6140 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [9 - i] }]";
6141 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6142 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6143 node
= isl_schedule_node_child(node
, 0);
6144 str
= "[{ S1[i,j] -> [j]; S2[i,j] -> [j] }]";
6145 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6146 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6147 node
= isl_schedule_node_child(node
, 0);
6148 umap1
= isl_schedule_node_get_prefix_schedule_union_map(node
);
6149 upma1
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
6150 domain1
= isl_schedule_node_get_domain(node
);
6151 id
= isl_id_alloc(ctx
, "group", NULL
);
6152 node
= isl_schedule_node_parent(node
);
6153 node
= isl_schedule_node_group(node
, id
);
6154 node
= isl_schedule_node_child(node
, 0);
6155 umap2
= isl_schedule_node_get_prefix_schedule_union_map(node
);
6156 upma2
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
6157 domain2
= isl_schedule_node_get_domain(node
);
6158 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
6159 if (equal
>= 0 && equal
)
6160 equal
= isl_union_set_is_equal(domain1
, domain2
);
6161 if (equal
>= 0 && equal
)
6162 equal
= isl_union_map_is_equal(umap1
, umap2
);
6163 isl_union_map_free(umap1
);
6164 isl_union_map_free(umap2
);
6165 isl_union_set_free(domain1
);
6166 isl_union_set_free(domain2
);
6167 isl_union_pw_multi_aff_free(upma1
);
6168 isl_union_pw_multi_aff_free(upma2
);
6169 isl_schedule_node_free(node
);
6174 isl_die(ctx
, isl_error_unknown
,
6175 "expressions not equal", return -1);
6180 /* Check that we can have nested groupings and that the union map
6181 * schedule representation is the same before and after the grouping.
6182 * Note that after the grouping, the union map representation contains
6183 * the domain constraints from the ranges of the expansion nodes,
6184 * while they are missing from the union map representation of
6185 * the tree without expansion nodes.
6187 * Also check that the global expansion is as expected.
6189 static int test_schedule_tree_group_2(isl_ctx
*ctx
)
6191 int equal
, equal_expansion
;
6194 isl_union_set
*uset
;
6195 isl_union_map
*umap1
, *umap2
;
6196 isl_union_map
*expansion1
, *expansion2
;
6197 isl_union_set_list
*filters
;
6198 isl_multi_union_pw_aff
*mupa
;
6199 isl_schedule
*schedule
;
6200 isl_schedule_node
*node
;
6202 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10; "
6203 "S3[i,j] : 0 <= i,j < 10 }";
6204 uset
= isl_union_set_read_from_str(ctx
, str
);
6205 node
= isl_schedule_node_from_domain(uset
);
6206 node
= isl_schedule_node_child(node
, 0);
6207 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [i]; S3[i,j] -> [i] }]";
6208 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6209 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6210 node
= isl_schedule_node_child(node
, 0);
6211 str
= "{ S1[i,j] }";
6212 uset
= isl_union_set_read_from_str(ctx
, str
);
6213 filters
= isl_union_set_list_from_union_set(uset
);
6214 str
= "{ S2[i,j]; S3[i,j] }";
6215 uset
= isl_union_set_read_from_str(ctx
, str
);
6216 filters
= isl_union_set_list_add(filters
, uset
);
6217 node
= isl_schedule_node_insert_sequence(node
, filters
);
6218 node
= isl_schedule_node_child(node
, 1);
6219 node
= isl_schedule_node_child(node
, 0);
6220 str
= "{ S2[i,j] }";
6221 uset
= isl_union_set_read_from_str(ctx
, str
);
6222 filters
= isl_union_set_list_from_union_set(uset
);
6223 str
= "{ S3[i,j] }";
6224 uset
= isl_union_set_read_from_str(ctx
, str
);
6225 filters
= isl_union_set_list_add(filters
, uset
);
6226 node
= isl_schedule_node_insert_sequence(node
, filters
);
6228 schedule
= isl_schedule_node_get_schedule(node
);
6229 umap1
= isl_schedule_get_map(schedule
);
6230 uset
= isl_schedule_get_domain(schedule
);
6231 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
6232 isl_schedule_free(schedule
);
6234 node
= isl_schedule_node_parent(node
);
6235 node
= isl_schedule_node_parent(node
);
6236 id
= isl_id_alloc(ctx
, "group1", NULL
);
6237 node
= isl_schedule_node_group(node
, id
);
6238 node
= isl_schedule_node_child(node
, 1);
6239 node
= isl_schedule_node_child(node
, 0);
6240 id
= isl_id_alloc(ctx
, "group2", NULL
);
6241 node
= isl_schedule_node_group(node
, id
);
6243 schedule
= isl_schedule_node_get_schedule(node
);
6244 umap2
= isl_schedule_get_map(schedule
);
6245 isl_schedule_free(schedule
);
6247 node
= isl_schedule_node_root(node
);
6248 node
= isl_schedule_node_child(node
, 0);
6249 expansion1
= isl_schedule_node_get_subtree_expansion(node
);
6250 isl_schedule_node_free(node
);
6252 str
= "{ group1[i] -> S1[i,j] : 0 <= i,j < 10; "
6253 "group1[i] -> S2[i,j] : 0 <= i,j < 10; "
6254 "group1[i] -> S3[i,j] : 0 <= i,j < 10 }";
6256 expansion2
= isl_union_map_read_from_str(ctx
, str
);
6258 equal
= isl_union_map_is_equal(umap1
, umap2
);
6259 equal_expansion
= isl_union_map_is_equal(expansion1
, expansion2
);
6261 isl_union_map_free(umap1
);
6262 isl_union_map_free(umap2
);
6263 isl_union_map_free(expansion1
);
6264 isl_union_map_free(expansion2
);
6266 if (equal
< 0 || equal_expansion
< 0)
6269 isl_die(ctx
, isl_error_unknown
,
6270 "expressions not equal", return -1);
6271 if (!equal_expansion
)
6272 isl_die(ctx
, isl_error_unknown
,
6273 "unexpected expansion", return -1);
6278 /* Some tests for the isl_schedule_node_group function.
6280 static int test_schedule_tree_group(isl_ctx
*ctx
)
6282 if (test_schedule_tree_group_1(ctx
) < 0)
6284 if (test_schedule_tree_group_2(ctx
) < 0)
6293 { "{ rat: [i] : 0 <= i <= 10 }",
6294 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
6295 { "{ rat: [i] : FALSE }",
6296 "{ rat: coefficients[[cst] -> [a]] }" },
6298 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
6305 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
6306 "{ rat: [i] : 0 <= i <= 10 }" },
6307 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
6309 { "{ rat: coefficients[[cst] -> [a]] }",
6310 "{ rat: [i] : FALSE }" },
6313 /* Test the basic functionality of isl_basic_set_coefficients and
6314 * isl_basic_set_solutions.
6316 static int test_dual(isl_ctx
*ctx
)
6320 for (i
= 0; i
< ARRAY_SIZE(coef_tests
); ++i
) {
6322 isl_basic_set
*bset1
, *bset2
;
6324 bset1
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].set
);
6325 bset2
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].dual
);
6326 bset1
= isl_basic_set_coefficients(bset1
);
6327 equal
= isl_basic_set_is_equal(bset1
, bset2
);
6328 isl_basic_set_free(bset1
);
6329 isl_basic_set_free(bset2
);
6333 isl_die(ctx
, isl_error_unknown
,
6334 "incorrect dual", return -1);
6337 for (i
= 0; i
< ARRAY_SIZE(sol_tests
); ++i
) {
6339 isl_basic_set
*bset1
, *bset2
;
6341 bset1
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].set
);
6342 bset2
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].dual
);
6343 bset1
= isl_basic_set_solutions(bset1
);
6344 equal
= isl_basic_set_is_equal(bset1
, bset2
);
6345 isl_basic_set_free(bset1
);
6346 isl_basic_set_free(bset2
);
6350 isl_die(ctx
, isl_error_unknown
,
6351 "incorrect dual", return -1);
6361 const char *schedule
;
6366 { 0, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
6367 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6369 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
6370 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6372 { 1, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
6373 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6375 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
6376 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6378 { 0, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
6379 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6381 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
6382 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
6384 { 1, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
6385 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6387 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
6388 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
6392 /* Basic tiling tests. Create a schedule tree with a domain and a band node,
6393 * tile the band and then check if the tile and point bands have the
6394 * expected partial schedule.
6396 static int test_tile(isl_ctx
*ctx
)
6402 scale
= isl_options_get_tile_scale_tile_loops(ctx
);
6403 shift
= isl_options_get_tile_shift_point_loops(ctx
);
6405 for (i
= 0; i
< ARRAY_SIZE(tile_tests
); ++i
) {
6409 isl_union_set
*domain
;
6410 isl_multi_union_pw_aff
*mupa
, *mupa2
;
6411 isl_schedule_node
*node
;
6412 isl_multi_val
*sizes
;
6414 opt
= tile_tests
[i
].scale_tile
;
6415 isl_options_set_tile_scale_tile_loops(ctx
, opt
);
6416 opt
= tile_tests
[i
].shift_point
;
6417 isl_options_set_tile_shift_point_loops(ctx
, opt
);
6419 str
= tile_tests
[i
].domain
;
6420 domain
= isl_union_set_read_from_str(ctx
, str
);
6421 node
= isl_schedule_node_from_domain(domain
);
6422 node
= isl_schedule_node_child(node
, 0);
6423 str
= tile_tests
[i
].schedule
;
6424 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6425 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6426 str
= tile_tests
[i
].sizes
;
6427 sizes
= isl_multi_val_read_from_str(ctx
, str
);
6428 node
= isl_schedule_node_band_tile(node
, sizes
);
6430 str
= tile_tests
[i
].tile
;
6431 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6432 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
6433 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
, mupa2
);
6434 isl_multi_union_pw_aff_free(mupa
);
6435 isl_multi_union_pw_aff_free(mupa2
);
6437 node
= isl_schedule_node_child(node
, 0);
6439 str
= tile_tests
[i
].point
;
6440 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6441 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
6442 if (equal
>= 0 && equal
)
6443 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
,
6445 isl_multi_union_pw_aff_free(mupa
);
6446 isl_multi_union_pw_aff_free(mupa2
);
6448 isl_schedule_node_free(node
);
6453 isl_die(ctx
, isl_error_unknown
,
6454 "unexpected result", return -1);
6457 isl_options_set_tile_scale_tile_loops(ctx
, scale
);
6458 isl_options_set_tile_shift_point_loops(ctx
, shift
);
6463 /* Check that the domain hash of a space is equal to the hash
6464 * of the domain of the space.
6466 static int test_domain_hash(isl_ctx
*ctx
)
6470 uint32_t hash1
, hash2
;
6472 map
= isl_map_read_from_str(ctx
, "[n] -> { A[B[x] -> C[]] -> D[] }");
6473 space
= isl_map_get_space(map
);
6475 hash1
= isl_space_get_domain_hash(space
);
6476 space
= isl_space_domain(space
);
6477 hash2
= isl_space_get_hash(space
);
6478 isl_space_free(space
);
6483 isl_die(ctx
, isl_error_unknown
,
6484 "domain hash not equal to hash of domain", return -1);
6489 /* Check that a universe basic set that is not obviously equal to the universe
6490 * is still recognized as being equal to the universe.
6492 static int test_universe(isl_ctx
*ctx
)
6495 isl_basic_set
*bset
;
6498 s
= "{ [] : exists x, y : 3y <= 2x and y >= -3 + 2x and 2y >= 2 - x }";
6499 bset
= isl_basic_set_read_from_str(ctx
, s
);
6500 is_univ
= isl_basic_set_is_universe(bset
);
6501 isl_basic_set_free(bset
);
6506 isl_die(ctx
, isl_error_unknown
,
6507 "not recognized as universe set", return -1);
6514 int (*fn
)(isl_ctx
*ctx
);
6516 { "universe", &test_universe
},
6517 { "domain hash", &test_domain_hash
},
6518 { "dual", &test_dual
},
6519 { "dependence analysis", &test_flow
},
6520 { "val", &test_val
},
6521 { "compute divs", &test_compute_divs
},
6522 { "partial lexmin", &test_partial_lexmin
},
6523 { "simplify", &test_simplify
},
6524 { "curry", &test_curry
},
6525 { "piecewise multi affine expressions", &test_pw_multi_aff
},
6526 { "multi piecewise affine expressions", &test_multi_pw_aff
},
6527 { "conversion", &test_conversion
},
6528 { "list", &test_list
},
6529 { "align parameters", &test_align_parameters
},
6530 { "preimage", &test_preimage
},
6531 { "pullback", &test_pullback
},
6532 { "AST", &test_ast
},
6533 { "AST build", &test_ast_build
},
6534 { "AST generation", &test_ast_gen
},
6535 { "eliminate", &test_eliminate
},
6536 { "residue class", &test_residue_class
},
6537 { "div", &test_div
},
6538 { "slice", &test_slice
},
6539 { "fixed power", &test_fixed_power
},
6540 { "sample", &test_sample
},
6541 { "output", &test_output
},
6542 { "vertices", &test_vertices
},
6543 { "fixed", &test_fixed
},
6544 { "equal", &test_equal
},
6545 { "disjoint", &test_disjoint
},
6546 { "product", &test_product
},
6547 { "dim_max", &test_dim_max
},
6548 { "affine", &test_aff
},
6549 { "injective", &test_injective
},
6550 { "schedule (whole component)", &test_schedule_whole
},
6551 { "schedule (incremental)", &test_schedule_incremental
},
6552 { "schedule tree grouping", &test_schedule_tree_group
},
6553 { "tile", &test_tile
},
6554 { "union_pw", &test_union_pw
},
6555 { "eval", &test_eval
},
6556 { "parse", &test_parse
},
6557 { "single-valued", &test_sv
},
6558 { "affine hull", &test_affine_hull
},
6559 { "simple_hull", &test_simple_hull
},
6560 { "coalesce", &test_coalesce
},
6561 { "factorize", &test_factorize
},
6562 { "subset", &test_subset
},
6563 { "subtract", &test_subtract
},
6564 { "intersect", &test_intersect
},
6565 { "lexmin", &test_lexmin
},
6566 { "min", &test_min
},
6567 { "gist", &test_gist
},
6568 { "piecewise quasi-polynomials", &test_pwqp
},
6569 { "lift", &test_lift
},
6570 { "bound", &test_bound
},
6571 { "union", &test_union
},
6572 { "split periods", &test_split_periods
},
6573 { "lexicographic order", &test_lex
},
6574 { "bijectivity", &test_bijective
},
6575 { "dataflow analysis", &test_dep
},
6576 { "reading", &test_read
},
6577 { "bounded", &test_bounded
},
6578 { "construction", &test_construction
},
6579 { "dimension manipulation", &test_dim
},
6580 { "map application", &test_application
},
6581 { "convex hull", &test_convex_hull
},
6582 { "transitive closure", &test_closure
},
6585 int main(int argc
, char **argv
)
6588 struct isl_ctx
*ctx
;
6589 struct isl_options
*options
;
6591 srcdir
= getenv("srcdir");
6594 options
= isl_options_new_with_defaults();
6596 argc
= isl_options_parse(options
, argc
, argv
, ISL_ARG_ALL
);
6598 ctx
= isl_ctx_alloc_with_options(&isl_options_args
, options
);
6599 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
6600 printf("%s\n", tests
[i
].name
);
6601 if (tests
[i
].fn(ctx
) < 0)