2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2012-2013 Ecole Normale Superieure
5 * Copyright 2014 INRIA Rocquencourt
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
12 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
14 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
15 * B.P. 105 - 78153 Le Chesnay, France
21 #include <isl_ctx_private.h>
22 #include <isl_map_private.h>
23 #include <isl_aff_private.h>
24 #include <isl_space_private.h>
27 #include <isl_constraint_private.h>
28 #include <isl/polynomial.h>
29 #include <isl/union_set.h>
30 #include <isl/union_map.h>
31 #include <isl_factorization.h>
32 #include <isl/schedule.h>
33 #include <isl/schedule_node.h>
34 #include <isl_options_private.h>
35 #include <isl_vertices_private.h>
36 #include <isl/ast_build.h>
39 #include <isl_ast_build_expr.h>
40 #include <isl/options.h>
42 #include "isl_srcdir.c"
44 #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array))
46 static char *get_filename(isl_ctx
*ctx
, const char *name
, const char *suffix
) {
49 char *pattern
= "%s/test_inputs/%s.%s";
51 length
= strlen(pattern
) - 6 + strlen(srcdir
) + strlen(name
)
53 filename
= isl_alloc_array(ctx
, char, length
);
58 sprintf(filename
, pattern
, srcdir
, name
, suffix
);
63 void test_parse_map(isl_ctx
*ctx
, const char *str
)
67 map
= isl_map_read_from_str(ctx
, str
);
72 int test_parse_map_equal(isl_ctx
*ctx
, const char *str
, const char *str2
)
77 map
= isl_map_read_from_str(ctx
, str
);
78 map2
= isl_map_read_from_str(ctx
, str2
);
79 equal
= isl_map_is_equal(map
, map2
);
86 isl_die(ctx
, isl_error_unknown
, "maps not equal",
92 void test_parse_pwqp(isl_ctx
*ctx
, const char *str
)
94 isl_pw_qpolynomial
*pwqp
;
96 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
98 isl_pw_qpolynomial_free(pwqp
);
101 static void test_parse_pwaff(isl_ctx
*ctx
, const char *str
)
105 pwaff
= isl_pw_aff_read_from_str(ctx
, str
);
107 isl_pw_aff_free(pwaff
);
110 /* Check that we can read an isl_multi_val from "str" without errors.
112 static int test_parse_multi_val(isl_ctx
*ctx
, const char *str
)
116 mv
= isl_multi_val_read_from_str(ctx
, str
);
117 isl_multi_val_free(mv
);
122 /* Pairs of binary relation representations that should represent
123 * the same binary relations.
128 } parse_map_equal_tests
[] = {
129 { "{ [x,y] : [([x/2]+y)/3] >= 1 }",
130 "{ [x, y] : 2y >= 6 - x }" },
131 { "{ [x,y] : x <= min(y, 2*y+3) }",
132 "{ [x,y] : x <= y, 2*y + 3 }" },
133 { "{ [x,y] : x >= min(y, 2*y+3) }",
134 "{ [x, y] : (y <= x and y >= -3) or (2y <= -3 + x and y <= -4) }" },
135 { "[n] -> { [c1] : c1>=0 and c1<=floord(n-4,3) }",
136 "[n] -> { [c1] : c1 >= 0 and 3c1 <= -4 + n }" },
137 { "{ [i,j] -> [i] : i < j; [i,j] -> [j] : j <= i }",
138 "{ [i,j] -> [min(i,j)] }" },
139 { "{ [i,j] : i != j }",
140 "{ [i,j] : i < j or i > j }" },
141 { "{ [i,j] : (i+1)*2 >= j }",
142 "{ [i, j] : j <= 2 + 2i }" },
143 { "{ [i] -> [i > 0 ? 4 : 5] }",
144 "{ [i] -> [5] : i <= 0; [i] -> [4] : i >= 1 }" },
145 { "[N=2,M] -> { [i=[(M+N)/4]] }",
146 "[N, M] -> { [i] : N = 2 and 4i <= 2 + M and 4i >= -1 + M }" },
147 { "{ [x] : x >= 0 }",
148 "{ [x] : x-0 >= 0 }" },
149 { "{ [i] : ((i > 10)) }",
150 "{ [i] : i >= 11 }" },
152 "{ [i] -> [0 * i] }" },
153 { "{ [a] -> [b] : (not false) }",
154 "{ [a] -> [b] : true }" },
155 { "{ [i] : i/2 <= 5 }",
156 "{ [i] : i <= 10 }" },
157 { "{Sym=[n] [i] : i <= n }",
158 "[n] -> { [i] : i <= n }" },
161 { "{ [i] : 2*floor(i/2) = i }",
162 "{ [i] : exists a : i = 2 a }" },
163 { "{ [a] -> [b] : a = 5 implies b = 5 }",
164 "{ [a] -> [b] : a != 5 or b = 5 }" },
165 { "{ [a] -> [a - 1 : a > 0] }",
166 "{ [a] -> [a - 1] : a > 0 }" },
167 { "{ [a] -> [a - 1 : a > 0; a : a <= 0] }",
168 "{ [a] -> [a - 1] : a > 0; [a] -> [a] : a <= 0 }" },
169 { "{ [a] -> [(a) * 2 : a >= 0; 0 : a < 0] }",
170 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
171 { "{ [a] -> [(a * 2) : a >= 0; 0 : a < 0] }",
172 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
173 { "{ [a] -> [(a * 2 : a >= 0); 0 : a < 0] }",
174 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
175 { "{ [a] -> [(a * 2 : a >= 0; 0 : a < 0)] }",
176 "{ [a] -> [2a] : a >= 0; [a] -> [0] : a < 0 }" },
177 { "{ [a,b] -> [i,j] : a,b << i,j }",
178 "{ [a,b] -> [i,j] : a < i or (a = i and b < j) }" },
179 { "{ [a,b] -> [i,j] : a,b <<= i,j }",
180 "{ [a,b] -> [i,j] : a < i or (a = i and b <= j) }" },
181 { "{ [a,b] -> [i,j] : a,b >> i,j }",
182 "{ [a,b] -> [i,j] : a > i or (a = i and b > j) }" },
183 { "{ [a,b] -> [i,j] : a,b >>= i,j }",
184 "{ [a,b] -> [i,j] : a > i or (a = i and b >= j) }" },
185 { "{ [n] -> [i] : exists (a, b, c: 8b <= i - 32a and "
186 "8b >= -7 + i - 32 a and b >= 0 and b <= 3 and "
187 "8c < n - 32a and i < n and c >= 0 and "
188 "c <= 3 and c >= -4a) }",
189 "{ [n] -> [i] : 0 <= i < n }" },
190 { "{ [x] -> [] : exists (a, b: 0 <= a <= 1 and 0 <= b <= 3 and "
191 "2b <= x - 8a and 2b >= -1 + x - 8a) }",
192 "{ [x] -> [] : 0 <= x <= 15 }" },
193 { "{ [x] -> [x] : }",
197 int test_parse(struct isl_ctx
*ctx
)
201 const char *str
, *str2
;
203 if (test_parse_multi_val(ctx
, "{ A[B[2] -> C[5, 7]] }") < 0)
205 if (test_parse_multi_val(ctx
, "[n] -> { [2] }") < 0)
207 if (test_parse_multi_val(ctx
, "{ A[4, infty, NaN, -1/2, 2/3] }") < 0)
210 str
= "{ [i] -> [-i] }";
211 map
= isl_map_read_from_str(ctx
, str
);
215 str
= "{ A[i] -> L[([i/3])] }";
216 map
= isl_map_read_from_str(ctx
, str
);
220 test_parse_map(ctx
, "{[[s] -> A[i]] -> [[s+1] -> A[i]]}");
221 test_parse_map(ctx
, "{ [p1, y1, y2] -> [2, y1, y2] : "
222 "p1 = 1 && (y1 <= y2 || y2 = 0) }");
224 for (i
= 0; i
< ARRAY_SIZE(parse_map_equal_tests
); ++i
) {
225 str
= parse_map_equal_tests
[i
].map1
;
226 str2
= parse_map_equal_tests
[i
].map2
;
227 if (test_parse_map_equal(ctx
, str
, str2
) < 0)
231 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
232 map
= isl_map_read_from_str(ctx
, str
);
233 str
= "{ [new, old] -> [o0, o1] : "
234 "exists (e0 = [(-1 - new + o0)/2], e1 = [(-1 - old + o1)/2]: "
235 "2e0 = -1 - new + o0 and 2e1 = -1 - old + o1 and o0 >= 0 and "
236 "o0 <= 1 and o1 >= 0 and o1 <= 1) }";
237 map2
= isl_map_read_from_str(ctx
, str
);
238 assert(isl_map_is_equal(map
, map2
));
242 str
= "{[new,old] -> [new+1-2*[(new+1)/2],old+1-2*[(old+1)/2]]}";
243 map
= isl_map_read_from_str(ctx
, str
);
244 str
= "{[new,old] -> [(new+1)%2,(old+1)%2]}";
245 map2
= isl_map_read_from_str(ctx
, str
);
246 assert(isl_map_is_equal(map
, map2
));
250 test_parse_pwqp(ctx
, "{ [i] -> i + [ (i + [i/3])/2 ] }");
251 test_parse_map(ctx
, "{ S1[i] -> [([i/10]),i%10] : 0 <= i <= 45 }");
252 test_parse_pwaff(ctx
, "{ [i] -> [i + 1] : i > 0; [a] -> [a] : a < 0 }");
253 test_parse_pwqp(ctx
, "{ [x] -> ([(x)/2] * [(x)/3]) }");
254 test_parse_pwaff(ctx
, "{ [] -> [(100)] }");
259 static int test_read(isl_ctx
*ctx
)
263 isl_basic_set
*bset1
, *bset2
;
264 const char *str
= "{[y]: Exists ( alpha : 2alpha = y)}";
267 filename
= get_filename(ctx
, "set", "omega");
269 input
= fopen(filename
, "r");
272 bset1
= isl_basic_set_read_from_file(ctx
, input
);
273 bset2
= isl_basic_set_read_from_str(ctx
, str
);
275 equal
= isl_basic_set_is_equal(bset1
, bset2
);
277 isl_basic_set_free(bset1
);
278 isl_basic_set_free(bset2
);
286 isl_die(ctx
, isl_error_unknown
,
287 "read sets not equal", return -1);
292 static int test_bounded(isl_ctx
*ctx
)
297 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : 0 <= i <= n }");
298 bounded
= isl_set_is_bounded(set
);
304 isl_die(ctx
, isl_error_unknown
,
305 "set not considered bounded", return -1);
307 set
= isl_set_read_from_str(ctx
, "{[n, i] : 0 <= i <= n }");
308 bounded
= isl_set_is_bounded(set
);
315 isl_die(ctx
, isl_error_unknown
,
316 "set considered bounded", return -1);
318 set
= isl_set_read_from_str(ctx
, "[n] -> {[i] : i <= n }");
319 bounded
= isl_set_is_bounded(set
);
325 isl_die(ctx
, isl_error_unknown
,
326 "set considered bounded", return -1);
331 /* Construct the basic set { [i] : 5 <= i <= N } */
332 static int test_construction_1(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 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
345 c
= isl_constraint_set_coefficient_si(c
, isl_dim_param
, 0, 1);
346 bset
= isl_basic_set_add_constraint(bset
, c
);
348 c
= isl_constraint_alloc_inequality(isl_local_space_copy(ls
));
349 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, 1);
350 c
= isl_constraint_set_constant_si(c
, -5);
351 bset
= isl_basic_set_add_constraint(bset
, c
);
353 isl_local_space_free(ls
);
354 isl_basic_set_free(bset
);
359 /* Construct the basic set { [x] : -100 <= x <= 100 }
360 * using isl_basic_set_{lower,upper}_bound_val and
361 * check that it is equal the same basic set parsed from a string.
363 static int test_construction_2(isl_ctx
*ctx
)
368 isl_basic_set
*bset1
, *bset2
;
370 v
= isl_val_int_from_si(ctx
, 100);
371 space
= isl_space_set_alloc(ctx
, 0, 1);
372 bset1
= isl_basic_set_universe(space
);
373 bset1
= isl_basic_set_upper_bound_val(bset1
, isl_dim_set
, 0,
375 bset1
= isl_basic_set_lower_bound_val(bset1
, isl_dim_set
, 0,
377 bset2
= isl_basic_set_read_from_str(ctx
, "{ [x] : -100 <= x <= 100 }");
378 equal
= isl_basic_set_is_equal(bset1
, bset2
);
379 isl_basic_set_free(bset1
);
380 isl_basic_set_free(bset2
);
385 isl_die(ctx
, isl_error_unknown
,
386 "failed construction", return -1);
391 /* Basic tests for constructing basic sets.
393 static int test_construction(isl_ctx
*ctx
)
395 if (test_construction_1(ctx
) < 0)
397 if (test_construction_2(ctx
) < 0)
402 static int test_dim(isl_ctx
*ctx
)
405 isl_map
*map1
, *map2
;
408 map1
= isl_map_read_from_str(ctx
,
409 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
410 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
411 map2
= isl_map_read_from_str(ctx
,
412 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
413 equal
= isl_map_is_equal(map1
, map2
);
416 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
417 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
418 if (equal
>= 0 && equal
)
419 equal
= isl_map_is_equal(map1
, map2
);
427 isl_die(ctx
, isl_error_unknown
,
428 "unexpected result", return -1);
430 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
431 map1
= isl_map_read_from_str(ctx
, str
);
432 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
433 map2
= isl_map_read_from_str(ctx
, str
);
434 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
435 equal
= isl_map_is_equal(map1
, map2
);
442 isl_die(ctx
, isl_error_unknown
,
443 "unexpected result", return -1);
449 __isl_give isl_val
*(*op
)(__isl_take isl_val
*v
);
453 { &isl_val_neg
, "0", "0" },
454 { &isl_val_abs
, "0", "0" },
455 { &isl_val_2exp
, "0", "1" },
456 { &isl_val_floor
, "0", "0" },
457 { &isl_val_ceil
, "0", "0" },
458 { &isl_val_neg
, "1", "-1" },
459 { &isl_val_neg
, "-1", "1" },
460 { &isl_val_neg
, "1/2", "-1/2" },
461 { &isl_val_neg
, "-1/2", "1/2" },
462 { &isl_val_neg
, "infty", "-infty" },
463 { &isl_val_neg
, "-infty", "infty" },
464 { &isl_val_neg
, "NaN", "NaN" },
465 { &isl_val_abs
, "1", "1" },
466 { &isl_val_abs
, "-1", "1" },
467 { &isl_val_abs
, "1/2", "1/2" },
468 { &isl_val_abs
, "-1/2", "1/2" },
469 { &isl_val_abs
, "infty", "infty" },
470 { &isl_val_abs
, "-infty", "infty" },
471 { &isl_val_abs
, "NaN", "NaN" },
472 { &isl_val_floor
, "1", "1" },
473 { &isl_val_floor
, "-1", "-1" },
474 { &isl_val_floor
, "1/2", "0" },
475 { &isl_val_floor
, "-1/2", "-1" },
476 { &isl_val_floor
, "infty", "infty" },
477 { &isl_val_floor
, "-infty", "-infty" },
478 { &isl_val_floor
, "NaN", "NaN" },
479 { &isl_val_ceil
, "1", "1" },
480 { &isl_val_ceil
, "-1", "-1" },
481 { &isl_val_ceil
, "1/2", "1" },
482 { &isl_val_ceil
, "-1/2", "0" },
483 { &isl_val_ceil
, "infty", "infty" },
484 { &isl_val_ceil
, "-infty", "-infty" },
485 { &isl_val_ceil
, "NaN", "NaN" },
486 { &isl_val_2exp
, "-3", "1/8" },
487 { &isl_val_2exp
, "-1", "1/2" },
488 { &isl_val_2exp
, "1", "2" },
489 { &isl_val_2exp
, "2", "4" },
490 { &isl_val_2exp
, "3", "8" },
491 { &isl_val_inv
, "1", "1" },
492 { &isl_val_inv
, "2", "1/2" },
493 { &isl_val_inv
, "1/2", "2" },
494 { &isl_val_inv
, "-2", "-1/2" },
495 { &isl_val_inv
, "-1/2", "-2" },
496 { &isl_val_inv
, "0", "NaN" },
497 { &isl_val_inv
, "NaN", "NaN" },
498 { &isl_val_inv
, "infty", "0" },
499 { &isl_val_inv
, "-infty", "0" },
502 /* Perform some basic tests of unary operations on isl_val objects.
504 static int test_un_val(isl_ctx
*ctx
)
508 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v
);
511 for (i
= 0; i
< ARRAY_SIZE(val_un_tests
); ++i
) {
512 v
= isl_val_read_from_str(ctx
, val_un_tests
[i
].arg
);
513 res
= isl_val_read_from_str(ctx
, val_un_tests
[i
].res
);
514 fn
= val_un_tests
[i
].op
;
516 is_nan
= isl_val_is_nan(res
);
520 ok
= isl_val_is_nan(v
);
522 ok
= isl_val_eq(v
, res
);
528 isl_die(ctx
, isl_error_unknown
,
529 "unexpected result", return -1);
536 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
537 __isl_take isl_val
*v2
);
539 ['+'] = { &isl_val_add
},
540 ['-'] = { &isl_val_sub
},
541 ['*'] = { &isl_val_mul
},
542 ['/'] = { &isl_val_div
},
543 ['g'] = { &isl_val_gcd
},
544 ['m'] = { &isl_val_min
},
545 ['M'] = { &isl_val_max
},
553 } val_bin_tests
[] = {
554 { "0", '+', "0", "0" },
555 { "1", '+', "0", "1" },
556 { "1", '+', "1", "2" },
557 { "1", '-', "1", "0" },
558 { "1", '*', "1", "1" },
559 { "1", '/', "1", "1" },
560 { "2", '*', "3", "6" },
561 { "2", '*', "1/2", "1" },
562 { "2", '*', "1/3", "2/3" },
563 { "2/3", '*', "3/5", "2/5" },
564 { "2/3", '*', "7/5", "14/15" },
565 { "2", '/', "1/2", "4" },
566 { "-2", '/', "-1/2", "4" },
567 { "-2", '/', "1/2", "-4" },
568 { "2", '/', "-1/2", "-4" },
569 { "2", '/', "2", "1" },
570 { "2", '/', "3", "2/3" },
571 { "2/3", '/', "5/3", "2/5" },
572 { "2/3", '/', "5/7", "14/15" },
573 { "0", '/', "0", "NaN" },
574 { "42", '/', "0", "NaN" },
575 { "-42", '/', "0", "NaN" },
576 { "infty", '/', "0", "NaN" },
577 { "-infty", '/', "0", "NaN" },
578 { "NaN", '/', "0", "NaN" },
579 { "0", '/', "NaN", "NaN" },
580 { "42", '/', "NaN", "NaN" },
581 { "-42", '/', "NaN", "NaN" },
582 { "infty", '/', "NaN", "NaN" },
583 { "-infty", '/', "NaN", "NaN" },
584 { "NaN", '/', "NaN", "NaN" },
585 { "0", '/', "infty", "0" },
586 { "42", '/', "infty", "0" },
587 { "-42", '/', "infty", "0" },
588 { "infty", '/', "infty", "NaN" },
589 { "-infty", '/', "infty", "NaN" },
590 { "NaN", '/', "infty", "NaN" },
591 { "0", '/', "-infty", "0" },
592 { "42", '/', "-infty", "0" },
593 { "-42", '/', "-infty", "0" },
594 { "infty", '/', "-infty", "NaN" },
595 { "-infty", '/', "-infty", "NaN" },
596 { "NaN", '/', "-infty", "NaN" },
597 { "1", '-', "1/3", "2/3" },
598 { "1/3", '+', "1/2", "5/6" },
599 { "1/2", '+', "1/2", "1" },
600 { "3/4", '-', "1/4", "1/2" },
601 { "1/2", '-', "1/3", "1/6" },
602 { "infty", '+', "42", "infty" },
603 { "infty", '+', "infty", "infty" },
604 { "42", '+', "infty", "infty" },
605 { "infty", '-', "infty", "NaN" },
606 { "infty", '*', "infty", "infty" },
607 { "infty", '*', "-infty", "-infty" },
608 { "-infty", '*', "infty", "-infty" },
609 { "-infty", '*', "-infty", "infty" },
610 { "0", '*', "infty", "NaN" },
611 { "1", '*', "infty", "infty" },
612 { "infty", '*', "0", "NaN" },
613 { "infty", '*', "42", "infty" },
614 { "42", '-', "infty", "-infty" },
615 { "infty", '+', "-infty", "NaN" },
616 { "4", 'g', "6", "2" },
617 { "5", 'g', "6", "1" },
618 { "42", 'm', "3", "3" },
619 { "42", 'M', "3", "42" },
620 { "3", 'm', "42", "3" },
621 { "3", 'M', "42", "42" },
622 { "42", 'm', "infty", "42" },
623 { "42", 'M', "infty", "infty" },
624 { "42", 'm', "-infty", "-infty" },
625 { "42", 'M', "-infty", "42" },
626 { "42", 'm', "NaN", "NaN" },
627 { "42", 'M', "NaN", "NaN" },
628 { "infty", 'm', "-infty", "-infty" },
629 { "infty", 'M', "-infty", "infty" },
632 /* Perform some basic tests of binary operations on isl_val objects.
634 static int test_bin_val(isl_ctx
*ctx
)
637 isl_val
*v1
, *v2
, *res
;
638 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
639 __isl_take isl_val
*v2
);
642 for (i
= 0; i
< ARRAY_SIZE(val_bin_tests
); ++i
) {
643 v1
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg1
);
644 v2
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg2
);
645 res
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].res
);
646 fn
= val_bin_op
[val_bin_tests
[i
].op
].fn
;
648 if (isl_val_is_nan(res
))
649 ok
= isl_val_is_nan(v1
);
651 ok
= isl_val_eq(v1
, res
);
657 isl_die(ctx
, isl_error_unknown
,
658 "unexpected result", return -1);
664 /* Perform some basic tests on isl_val objects.
666 static int test_val(isl_ctx
*ctx
)
668 if (test_un_val(ctx
) < 0)
670 if (test_bin_val(ctx
) < 0)
675 /* Sets described using existentially quantified variables that
676 * can also be described without.
678 static const char *elimination_tests
[] = {
679 "{ [i,j] : 2 * [i/2] + 3 * [j/4] <= 10 and 2 i = j }",
680 "{ [m, w] : exists a : w - 2m - 5 <= 3a <= m - 2w }",
681 "{ [m, w] : exists a : w >= 0 and a < m and -1 + w <= a <= 2m - w }",
684 /* Check that redundant existentially quantified variables are
687 static int test_elimination(isl_ctx
*ctx
)
693 for (i
= 0; i
< ARRAY_SIZE(elimination_tests
); ++i
) {
694 bset
= isl_basic_set_read_from_str(ctx
, elimination_tests
[i
]);
695 n
= isl_basic_set_dim(bset
, isl_dim_div
);
696 isl_basic_set_free(bset
);
700 isl_die(ctx
, isl_error_unknown
,
701 "expecting no existentials", return -1);
707 static int test_div(isl_ctx
*ctx
)
714 struct isl_basic_set
*bset
;
715 struct isl_constraint
*c
;
718 dim
= isl_space_set_alloc(ctx
, 0, 3);
719 bset
= isl_basic_set_universe(isl_space_copy(dim
));
720 ls
= isl_local_space_from_space(dim
);
722 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
723 c
= isl_constraint_set_constant_si(c
, -1);
724 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, 1);
725 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 1, 3);
726 bset
= isl_basic_set_add_constraint(bset
, c
);
728 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
729 c
= isl_constraint_set_constant_si(c
, 1);
730 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
731 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 2, 3);
732 bset
= isl_basic_set_add_constraint(bset
, c
);
734 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
736 assert(bset
&& bset
->n_div
== 1);
737 isl_local_space_free(ls
);
738 isl_basic_set_free(bset
);
741 dim
= isl_space_set_alloc(ctx
, 0, 3);
742 bset
= isl_basic_set_universe(isl_space_copy(dim
));
743 ls
= isl_local_space_from_space(dim
);
745 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
746 c
= isl_constraint_set_constant_si(c
, 1);
747 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
748 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 1, 3);
749 bset
= isl_basic_set_add_constraint(bset
, c
);
751 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
752 c
= isl_constraint_set_constant_si(c
, -1);
753 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, 1);
754 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 2, 3);
755 bset
= isl_basic_set_add_constraint(bset
, c
);
757 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
759 assert(bset
&& bset
->n_div
== 1);
760 isl_local_space_free(ls
);
761 isl_basic_set_free(bset
);
764 dim
= isl_space_set_alloc(ctx
, 0, 3);
765 bset
= isl_basic_set_universe(isl_space_copy(dim
));
766 ls
= isl_local_space_from_space(dim
);
768 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
769 c
= isl_constraint_set_constant_si(c
, 1);
770 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
771 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 1, 3);
772 bset
= isl_basic_set_add_constraint(bset
, c
);
774 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
775 c
= isl_constraint_set_constant_si(c
, -3);
776 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, 1);
777 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 2, 4);
778 bset
= isl_basic_set_add_constraint(bset
, c
);
780 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
782 assert(bset
&& bset
->n_div
== 1);
783 isl_local_space_free(ls
);
784 isl_basic_set_free(bset
);
787 dim
= isl_space_set_alloc(ctx
, 0, 3);
788 bset
= isl_basic_set_universe(isl_space_copy(dim
));
789 ls
= isl_local_space_from_space(dim
);
791 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
792 c
= isl_constraint_set_constant_si(c
, 2);
793 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
794 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 1, 3);
795 bset
= isl_basic_set_add_constraint(bset
, c
);
797 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
798 c
= isl_constraint_set_constant_si(c
, -1);
799 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, 1);
800 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 2, 6);
801 bset
= isl_basic_set_add_constraint(bset
, c
);
803 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
805 assert(isl_basic_set_is_empty(bset
));
806 isl_local_space_free(ls
);
807 isl_basic_set_free(bset
);
810 dim
= isl_space_set_alloc(ctx
, 0, 3);
811 bset
= isl_basic_set_universe(isl_space_copy(dim
));
812 ls
= isl_local_space_from_space(dim
);
814 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
815 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
816 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 2, 3);
817 bset
= isl_basic_set_add_constraint(bset
, c
);
819 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
820 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, 1);
821 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 1, -3);
822 bset
= isl_basic_set_add_constraint(bset
, c
);
824 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
826 assert(bset
&& bset
->n_div
== 0);
827 isl_basic_set_free(bset
);
828 isl_local_space_free(ls
);
831 dim
= isl_space_set_alloc(ctx
, 0, 3);
832 bset
= isl_basic_set_universe(isl_space_copy(dim
));
833 ls
= isl_local_space_from_space(dim
);
835 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
836 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
837 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 2, 6);
838 bset
= isl_basic_set_add_constraint(bset
, c
);
840 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
841 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, 1);
842 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 1, -3);
843 bset
= isl_basic_set_add_constraint(bset
, c
);
845 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
847 assert(bset
&& bset
->n_div
== 1);
848 isl_basic_set_free(bset
);
849 isl_local_space_free(ls
);
852 /* This test is a bit tricky. We set up an equality
854 * Normalization of divs creates _two_ divs
857 * Afterwards e0 is removed again because it has coefficient -1
858 * and we end up with the original equality and div again.
859 * Perhaps we can avoid the introduction of this temporary div.
861 dim
= isl_space_set_alloc(ctx
, 0, 4);
862 bset
= isl_basic_set_universe(isl_space_copy(dim
));
863 ls
= isl_local_space_from_space(dim
);
865 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
866 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
867 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 1, -3);
868 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 2, -3);
869 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 3, 6);
870 bset
= isl_basic_set_add_constraint(bset
, c
);
872 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
874 /* Test disabled for now */
876 assert(bset && bset->n_div == 1);
878 isl_local_space_free(ls
);
879 isl_basic_set_free(bset
);
882 dim
= isl_space_set_alloc(ctx
, 0, 5);
883 bset
= isl_basic_set_universe(isl_space_copy(dim
));
884 ls
= isl_local_space_from_space(dim
);
886 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
887 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
888 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 1, -3);
889 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 3, -3);
890 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 4, 6);
891 bset
= isl_basic_set_add_constraint(bset
, c
);
893 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
894 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
895 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 2, 1);
896 c
= isl_constraint_set_constant_si(c
, 1);
897 bset
= isl_basic_set_add_constraint(bset
, c
);
899 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
901 /* Test disabled for now */
903 assert(bset && bset->n_div == 1);
905 isl_local_space_free(ls
);
906 isl_basic_set_free(bset
);
909 dim
= isl_space_set_alloc(ctx
, 0, 4);
910 bset
= isl_basic_set_universe(isl_space_copy(dim
));
911 ls
= isl_local_space_from_space(dim
);
913 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
914 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, 1);
915 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 1, -1);
916 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 2, -2);
917 bset
= isl_basic_set_add_constraint(bset
, c
);
919 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
920 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, -1);
921 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 3, 3);
922 c
= isl_constraint_set_constant_si(c
, 2);
923 bset
= isl_basic_set_add_constraint(bset
, c
);
925 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
927 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
929 assert(!isl_basic_set_is_empty(bset
));
931 isl_local_space_free(ls
);
932 isl_basic_set_free(bset
);
935 dim
= isl_space_set_alloc(ctx
, 0, 3);
936 bset
= isl_basic_set_universe(isl_space_copy(dim
));
937 ls
= isl_local_space_from_space(dim
);
939 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
940 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 0, 1);
941 c
= isl_constraint_set_coefficient_si(c
, isl_dim_set
, 2, -2);
942 bset
= isl_basic_set_add_constraint(bset
, c
);
944 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
946 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
948 isl_local_space_free(ls
);
949 isl_basic_set_free(bset
);
951 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
952 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
953 set
= isl_set_read_from_str(ctx
, str
);
954 set
= isl_set_compute_divs(set
);
959 if (test_elimination(ctx
) < 0)
962 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
963 set
= isl_set_read_from_str(ctx
, str
);
964 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
965 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
966 empty
= isl_set_is_empty(set
);
971 isl_die(ctx
, isl_error_unknown
,
972 "result not as accurate as expected", return -1);
977 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
981 struct isl_basic_set
*bset1
, *bset2
;
982 struct isl_basic_map
*bmap
;
984 filename
= get_filename(ctx
, name
, "omega");
986 input
= fopen(filename
, "r");
989 bset1
= isl_basic_set_read_from_file(ctx
, input
);
990 bmap
= isl_basic_map_read_from_file(ctx
, input
);
992 bset1
= isl_basic_set_apply(bset1
, bmap
);
994 bset2
= isl_basic_set_read_from_file(ctx
, input
);
996 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
998 isl_basic_set_free(bset1
);
999 isl_basic_set_free(bset2
);
1005 static int test_application(isl_ctx
*ctx
)
1007 test_application_case(ctx
, "application");
1008 test_application_case(ctx
, "application2");
1013 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
1017 struct isl_basic_set
*bset1
, *bset2
;
1019 filename
= get_filename(ctx
, name
, "polylib");
1021 input
= fopen(filename
, "r");
1024 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1025 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1027 bset1
= isl_basic_set_affine_hull(bset1
);
1029 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1031 isl_basic_set_free(bset1
);
1032 isl_basic_set_free(bset2
);
1038 int test_affine_hull(struct isl_ctx
*ctx
)
1042 isl_basic_set
*bset
, *bset2
;
1046 test_affine_hull_case(ctx
, "affine2");
1047 test_affine_hull_case(ctx
, "affine");
1048 test_affine_hull_case(ctx
, "affine3");
1050 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
1051 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
1052 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
1053 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
1054 set
= isl_set_read_from_str(ctx
, str
);
1055 bset
= isl_set_affine_hull(set
);
1056 n
= isl_basic_set_dim(bset
, isl_dim_div
);
1057 isl_basic_set_free(bset
);
1059 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
1062 /* Check that isl_map_affine_hull is not confused by
1063 * the reordering of divs in isl_map_align_divs.
1065 str
= "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1066 "32e0 = b and 32e1 = c); "
1067 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1068 set
= isl_set_read_from_str(ctx
, str
);
1069 bset
= isl_set_affine_hull(set
);
1070 isl_basic_set_free(bset
);
1074 str
= "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1075 "32e2 = 31 + 31e0 }";
1076 set
= isl_set_read_from_str(ctx
, str
);
1077 bset
= isl_set_affine_hull(set
);
1078 str
= "{ [a] : exists e : a = 32 e }";
1079 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1080 subset
= isl_basic_set_is_subset(bset
, bset2
);
1081 isl_basic_set_free(bset
);
1082 isl_basic_set_free(bset2
);
1086 isl_die(ctx
, isl_error_unknown
, "not as accurate as expected",
1092 /* Pairs of maps and the corresponding expected results of
1093 * isl_map_plain_unshifted_simple_hull.
1098 } plain_unshifted_simple_hull_tests
[] = {
1099 { "{ [i] -> [j] : i >= 1 and j >= 1 or i >= 2 and j <= 10 }",
1100 "{ [i] -> [j] : i >= 1 }" },
1101 { "{ [n] -> [i,j,k] : (i mod 3 = 2 and j mod 4 = 2) or "
1102 "(j mod 4 = 2 and k mod 6 = n) }",
1103 "{ [n] -> [i,j,k] : j mod 4 = 2 }" },
1106 /* Basic tests for isl_map_plain_unshifted_simple_hull.
1108 static int test_plain_unshifted_simple_hull(isl_ctx
*ctx
)
1112 isl_basic_map
*hull
, *expected
;
1115 for (i
= 0; i
< ARRAY_SIZE(plain_unshifted_simple_hull_tests
); ++i
) {
1117 str
= plain_unshifted_simple_hull_tests
[i
].map
;
1118 map
= isl_map_read_from_str(ctx
, str
);
1119 str
= plain_unshifted_simple_hull_tests
[i
].hull
;
1120 expected
= isl_basic_map_read_from_str(ctx
, str
);
1121 hull
= isl_map_plain_unshifted_simple_hull(map
);
1122 equal
= isl_basic_map_is_equal(hull
, expected
);
1123 isl_basic_map_free(hull
);
1124 isl_basic_map_free(expected
);
1128 isl_die(ctx
, isl_error_unknown
, "unexpected hull",
1135 /* Pairs of sets and the corresponding expected results of
1136 * isl_set_unshifted_simple_hull.
1141 } unshifted_simple_hull_tests
[] = {
1142 { "{ [0,x,y] : x <= -1; [1,x,y] : x <= y <= -x; [2,x,y] : x <= 1 }",
1143 "{ [t,x,y] : 0 <= t <= 2 and x <= 1 }" },
1146 /* Basic tests for isl_set_unshifted_simple_hull.
1148 static int test_unshifted_simple_hull(isl_ctx
*ctx
)
1152 isl_basic_set
*hull
, *expected
;
1155 for (i
= 0; i
< ARRAY_SIZE(unshifted_simple_hull_tests
); ++i
) {
1157 str
= unshifted_simple_hull_tests
[i
].set
;
1158 set
= isl_set_read_from_str(ctx
, str
);
1159 str
= unshifted_simple_hull_tests
[i
].hull
;
1160 expected
= isl_basic_set_read_from_str(ctx
, str
);
1161 hull
= isl_set_unshifted_simple_hull(set
);
1162 equal
= isl_basic_set_is_equal(hull
, expected
);
1163 isl_basic_set_free(hull
);
1164 isl_basic_set_free(expected
);
1168 isl_die(ctx
, isl_error_unknown
, "unexpected hull",
1175 static int test_simple_hull(struct isl_ctx
*ctx
)
1179 isl_basic_set
*bset
;
1182 str
= "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x;"
1183 "[y, x] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }";
1184 set
= isl_set_read_from_str(ctx
, str
);
1185 bset
= isl_set_simple_hull(set
);
1186 is_empty
= isl_basic_set_is_empty(bset
);
1187 isl_basic_set_free(bset
);
1189 if (is_empty
== isl_bool_error
)
1192 if (is_empty
== isl_bool_false
)
1193 isl_die(ctx
, isl_error_unknown
, "Empty set should be detected",
1196 if (test_plain_unshifted_simple_hull(ctx
) < 0)
1198 if (test_unshifted_simple_hull(ctx
) < 0)
1204 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
1208 struct isl_basic_set
*bset1
, *bset2
;
1209 struct isl_set
*set
;
1211 filename
= get_filename(ctx
, name
, "polylib");
1213 input
= fopen(filename
, "r");
1216 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1217 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1219 set
= isl_basic_set_union(bset1
, bset2
);
1220 bset1
= isl_set_convex_hull(set
);
1222 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1224 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1226 isl_basic_set_free(bset1
);
1227 isl_basic_set_free(bset2
);
1236 } convex_hull_tests
[] = {
1237 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1238 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1239 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1240 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1241 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1242 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1243 "i2 <= 5 and i2 >= 4; "
1244 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1245 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1246 "i2 <= 5 + i0 and i2 >= i0 }" },
1247 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1248 "{ [x, y] : 1 = 0 }" },
1249 { "{ [x, y, z] : 0 <= x, y, z <= 10; [x, y, 0] : x >= 0 and y > 0; "
1250 "[x, y, 0] : x >= 0 and y < 0 }",
1251 "{ [x, y, z] : x >= 0 and 0 <= z <= 10 }" },
1254 static int test_convex_hull_algo(isl_ctx
*ctx
, int convex
)
1257 int orig_convex
= ctx
->opt
->convex
;
1258 ctx
->opt
->convex
= convex
;
1260 test_convex_hull_case(ctx
, "convex0");
1261 test_convex_hull_case(ctx
, "convex1");
1262 test_convex_hull_case(ctx
, "convex2");
1263 test_convex_hull_case(ctx
, "convex3");
1264 test_convex_hull_case(ctx
, "convex4");
1265 test_convex_hull_case(ctx
, "convex5");
1266 test_convex_hull_case(ctx
, "convex6");
1267 test_convex_hull_case(ctx
, "convex7");
1268 test_convex_hull_case(ctx
, "convex8");
1269 test_convex_hull_case(ctx
, "convex9");
1270 test_convex_hull_case(ctx
, "convex10");
1271 test_convex_hull_case(ctx
, "convex11");
1272 test_convex_hull_case(ctx
, "convex12");
1273 test_convex_hull_case(ctx
, "convex13");
1274 test_convex_hull_case(ctx
, "convex14");
1275 test_convex_hull_case(ctx
, "convex15");
1277 for (i
= 0; i
< ARRAY_SIZE(convex_hull_tests
); ++i
) {
1278 isl_set
*set1
, *set2
;
1281 set1
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].set
);
1282 set2
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].hull
);
1283 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
1284 equal
= isl_set_is_equal(set1
, set2
);
1291 isl_die(ctx
, isl_error_unknown
,
1292 "unexpected convex hull", return -1);
1295 ctx
->opt
->convex
= orig_convex
;
1300 static int test_convex_hull(isl_ctx
*ctx
)
1302 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
) < 0)
1304 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
) < 0)
1309 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
1313 struct isl_basic_set
*bset1
, *bset2
;
1315 filename
= get_filename(ctx
, name
, "polylib");
1317 input
= fopen(filename
, "r");
1320 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1321 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1323 bset1
= isl_basic_set_gist(bset1
, bset2
);
1325 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1327 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1329 isl_basic_set_free(bset1
);
1330 isl_basic_set_free(bset2
);
1336 /* Inputs to isl_map_plain_gist_basic_map, along with the expected output.
1340 const char *context
;
1342 } plain_gist_tests
[] = {
1343 { "{ [i] -> [j] : i >= 1 and j >= 1 or i >= 2 and j <= 10 }",
1344 "{ [i] -> [j] : i >= 1 }",
1345 "{ [i] -> [j] : j >= 1 or i >= 2 and j <= 10 }" },
1346 { "{ [n] -> [i,j,k] : (i mod 3 = 2 and j mod 4 = 2) or "
1347 "(j mod 4 = 2 and k mod 6 = n) }",
1348 "{ [n] -> [i,j,k] : j mod 4 = 2 }",
1349 "{ [n] -> [i,j,k] : (i mod 3 = 2) or (k mod 6 = n) }" },
1350 { "{ [i] -> [j] : i > j and (exists a,b : i <= 2a + 5b <= 2) }",
1351 "{ [i] -> [j] : i > j }",
1352 "{ [i] -> [j] : exists a,b : i <= 2a + 5b <= 2 }" },
1355 /* Basic tests for isl_map_plain_gist_basic_map.
1357 static int test_plain_gist(isl_ctx
*ctx
)
1361 for (i
= 0; i
< ARRAY_SIZE(plain_gist_tests
); ++i
) {
1364 isl_map
*map
, *gist
;
1365 isl_basic_map
*context
;
1367 map
= isl_map_read_from_str(ctx
, plain_gist_tests
[i
].map
);
1368 str
= plain_gist_tests
[i
].context
;
1369 context
= isl_basic_map_read_from_str(ctx
, str
);
1370 map
= isl_map_plain_gist_basic_map(map
, context
);
1371 gist
= isl_map_read_from_str(ctx
, plain_gist_tests
[i
].gist
);
1372 equal
= isl_map_is_equal(map
, gist
);
1378 isl_die(ctx
, isl_error_unknown
,
1379 "incorrect gist result", return -1);
1387 const char *context
;
1390 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1391 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1392 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1393 "{ [a, b, c] : a <= 15 }" },
1394 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1395 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1396 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1397 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1398 { "{ [m, n, a, b] : a <= 2147 + n }",
1399 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1400 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1401 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1403 "{ [m, n, ku, kl] }" },
1404 { "{ [a, a, b] : a >= 10 }",
1405 "{ [a, b, c] : c >= a and c <= b and c >= 2 }",
1406 "{ [a, a, b] : a >= 10 }" },
1407 { "{ [i, j] : i >= 0 and i + j >= 0 }", "{ [i, j] : i <= 0 }",
1408 "{ [0, j] : j >= 0 }" },
1409 /* Check that no constraints on i6 are introduced in the gist */
1410 { "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1411 "20e0 <= 1530 - 4t1 - 5i4 and 20e0 >= 1511 - 4t1 - 5i4 and "
1412 "5e0 <= 381 - t1 and i4 <= 1) }",
1413 "[t1] -> { [i4, i6] : exists (e0 = floor((-t1 + i6)/5): "
1414 "5e0 = -t1 + i6 and i6 <= 6 and i6 >= 3) }",
1415 "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1416 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 <= 1530 - 4t1 - 5i4 and "
1417 "20e0 >= 1511 - 4t1 - 5i4) }" },
1418 /* Check that no constraints on i6 are introduced in the gist */
1419 { "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((1 + i4)/2), "
1420 "e1 = floor((1530 - 4t1 - 5i4)/20), "
1421 "e2 = floor((-4t1 - 5i4 + 10*floor((1 + i4)/2))/20), "
1422 "e3 = floor((-1 + i4)/2): t2 = 0 and 2e3 = -1 + i4 and "
1423 "20e2 >= -19 - 4t1 - 5i4 + 10e0 and 5e2 <= 1 - t1 and "
1424 "2e0 <= 1 + i4 and 2e0 >= i4 and "
1425 "20e1 <= 1530 - 4t1 - 5i4 and "
1426 "20e1 >= 1511 - 4t1 - 5i4 and i4 <= 1 and "
1427 "5e1 <= 381 - t1 and 20e2 <= -4t1 - 5i4 + 10e0) }",
1428 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((-17 + i4)/2), "
1429 "e1 = floor((-t1 + i6)/5): 5e1 = -t1 + i6 and "
1430 "2e0 <= -17 + i4 and 2e0 >= -18 + i4 and "
1431 "10e0 <= -91 + 5i4 + 4i6 and "
1432 "10e0 >= -105 + 5i4 + 4i6) }",
1433 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((381 - t1)/5), "
1434 "e1 = floor((-1 + i4)/2): t2 = 0 and 2e1 = -1 + i4 and "
1435 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 >= 1511 - 4t1 - 5i4) }" },
1436 { "{ [0, 0, q, p] : -5 <= q <= 5 and p >= 0 }",
1437 "{ [a, b, q, p] : b >= 1 + a }",
1438 "{ [a, b, q, p] : false }" },
1439 { "[n] -> { [x] : x = n && x mod 32 = 0 }",
1440 "[n] -> { [x] : x mod 32 = 0 }",
1441 "[n] -> { [x = n] }" },
1442 { "{ [x] : x mod 6 = 0 }", "{ [x] : x mod 3 = 0 }",
1443 "{ [x] : x mod 2 = 0 }" },
1444 { "{ [x] : x mod 3200 = 0 }", "{ [x] : x mod 10000 = 0 }",
1445 "{ [x] : x mod 128 = 0 }" },
1446 { "{ [x] : x mod 3200 = 0 }", "{ [x] : x mod 10 = 0 }",
1447 "{ [x] : x mod 3200 = 0 }" },
1448 { "{ [a, b, c] : a mod 2 = 0 and a = c }",
1449 "{ [a, b, c] : b mod 2 = 0 and b = c }",
1450 "{ [a, b, c = a] }" },
1451 { "{ [a, b, c] : a mod 6 = 0 and a = c }",
1452 "{ [a, b, c] : b mod 2 = 0 and b = c }",
1453 "{ [a, b, c = a] : a mod 3 = 0 }" },
1454 { "{ [x] : 0 <= x <= 4 or 6 <= x <= 9 }",
1455 "{ [x] : 1 <= x <= 3 or 7 <= x <= 8 }",
1457 { "{ [x,y] : x < 0 and 0 <= y <= 4 or x >= -2 and -x <= y <= 10 + x }",
1458 "{ [x,y] : 1 <= y <= 3 }",
1462 /* Check that isl_set_gist behaves as expected.
1464 * For the test cases in gist_tests, besides checking that the result
1465 * is as expected, also check that applying the gist operation does
1466 * not modify the input set (an earlier version of isl would do that) and
1467 * that the test case is consistent, i.e., that the gist has the same
1468 * intersection with the context as the input set.
1470 static int test_gist(struct isl_ctx
*ctx
)
1474 isl_basic_set
*bset1
, *bset2
;
1475 isl_map
*map1
, *map2
;
1478 for (i
= 0; i
< ARRAY_SIZE(gist_tests
); ++i
) {
1479 int equal_input
, equal_intersection
;
1480 isl_set
*set1
, *set2
, *copy
, *context
;
1482 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1483 context
= isl_set_read_from_str(ctx
, gist_tests
[i
].context
);
1484 copy
= isl_set_copy(set1
);
1485 set1
= isl_set_gist(set1
, isl_set_copy(context
));
1486 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].gist
);
1487 equal
= isl_set_is_equal(set1
, set2
);
1489 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1490 equal_input
= isl_set_is_equal(set1
, copy
);
1492 set1
= isl_set_intersect(set1
, isl_set_copy(context
));
1493 set2
= isl_set_intersect(set2
, context
);
1494 equal_intersection
= isl_set_is_equal(set1
, set2
);
1497 if (equal
< 0 || equal_input
< 0 || equal_intersection
< 0)
1500 isl_die(ctx
, isl_error_unknown
,
1501 "incorrect gist result", return -1);
1503 isl_die(ctx
, isl_error_unknown
,
1504 "gist modified input", return -1);
1506 isl_die(ctx
, isl_error_unknown
,
1507 "inconsistent gist test case", return -1);
1510 test_gist_case(ctx
, "gist1");
1512 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1513 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1514 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1515 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1516 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1517 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1518 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1519 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1520 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1521 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1522 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1523 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1524 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1525 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1526 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1527 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1528 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1529 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1530 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1531 bset1
= isl_basic_set_gist(bset1
, bset2
);
1532 assert(bset1
&& bset1
->n_div
== 0);
1533 isl_basic_set_free(bset1
);
1535 /* Check that the integer divisions of the second disjunct
1536 * do not spread to the first disjunct.
1538 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1539 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1540 "(exists (e0 = [(-1 + t1)/16], "
1541 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1542 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1543 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1544 "o0 <= 4294967295 and t1 <= -1)) }";
1545 map1
= isl_map_read_from_str(ctx
, str
);
1546 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1547 map2
= isl_map_read_from_str(ctx
, str
);
1548 map1
= isl_map_gist(map1
, map2
);
1552 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1553 isl_map_free(map1
); return -1);
1554 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1555 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1556 isl_map_free(map1
); return -1);
1559 if (test_plain_gist(ctx
) < 0)
1565 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1567 isl_set
*set
, *set2
;
1571 set
= isl_set_read_from_str(ctx
, str
);
1572 set
= isl_set_coalesce(set
);
1573 set2
= isl_set_read_from_str(ctx
, str
);
1574 equal
= isl_set_is_equal(set
, set2
);
1575 one
= set
&& set
->n
== 1;
1582 isl_die(ctx
, isl_error_unknown
,
1583 "coalesced set not equal to input", return -1);
1584 if (check_one
&& !one
)
1585 isl_die(ctx
, isl_error_unknown
,
1586 "coalesced set should not be a union", return -1);
1591 /* Inputs for coalescing tests with unbounded wrapping.
1592 * "str" is a string representation of the input set.
1593 * "single_disjunct" is set if we expect the result to consist of
1594 * a single disjunct.
1597 int single_disjunct
;
1599 } coalesce_unbounded_tests
[] = {
1600 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1601 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1602 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1603 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1605 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1606 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1607 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1608 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1611 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1612 * option turned off.
1614 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1620 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1621 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1623 for (i
= 0; i
< ARRAY_SIZE(coalesce_unbounded_tests
); ++i
) {
1624 const char *str
= coalesce_unbounded_tests
[i
].str
;
1625 int check_one
= coalesce_unbounded_tests
[i
].single_disjunct
;
1626 if (test_coalesce_set(ctx
, str
, check_one
) >= 0)
1632 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1637 /* Inputs for coalescing tests.
1638 * "str" is a string representation of the input set.
1639 * "single_disjunct" is set if we expect the result to consist of
1640 * a single disjunct.
1643 int single_disjunct
;
1645 } coalesce_tests
[] = {
1646 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1647 "y >= x & x >= 2 & 5 >= y }" },
1648 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1649 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1650 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1651 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1652 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1653 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1654 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1655 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1656 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1657 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1658 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1659 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1660 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1661 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1662 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1663 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1664 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1665 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1666 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1667 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1668 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1669 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1670 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1671 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1672 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1673 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1674 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1675 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1676 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1677 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1678 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1679 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1680 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1681 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1682 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1683 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1684 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1685 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1686 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1687 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1688 "[o0, o1, o2, o3, o4, o5, o6]] : "
1689 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1690 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1691 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1692 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1693 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1694 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1695 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1696 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1697 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1698 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1699 "o6 >= i3 + i6 - o3 and M >= 0 and "
1700 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1701 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1702 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1703 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1704 "(o0 = 0 and M >= 2 and N >= 3) or "
1705 "(M = 0 and o0 = 0 and N >= 3) }" },
1706 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1707 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1708 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1709 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1710 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1711 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1712 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1713 "(y = 3 and x = 1) }" },
1714 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1715 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1716 "i1 <= M and i3 <= M and i4 <= M) or "
1717 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1718 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1719 "i4 <= -1 + M) }" },
1720 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1721 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1722 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1723 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1724 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1725 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1726 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1727 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1728 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1729 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1730 { 0, "{ [a, b] : exists e : 2e = a and "
1731 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1732 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1733 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1734 "j >= 1 and j' <= i + j - i' and i >= 1; "
1736 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1737 "[i,j] : exists a : j = 3a }" },
1738 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1739 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1741 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1742 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1743 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1744 "c <= 6 + 8a and a >= 3; "
1745 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1746 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1747 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1748 "[x,0] : 3 <= x <= 4 }" },
1749 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1750 "[x,0] : 4 <= x <= 5 }" },
1751 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1752 "[x,0] : 3 <= x <= 5 }" },
1753 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1754 "[x,0] : 3 <= x <= 4 }" },
1755 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1757 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1758 { 1, "{ [0,0]; [1,1] }" },
1759 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1760 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1762 "[k, 0, k] : k <= 6 and k >= 1 }" },
1763 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1764 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1765 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1766 { 1, "[n] -> { [1] : n >= 0;"
1767 "[x] : exists (e0 = floor((x)/2): x >= 2 and "
1768 "2e0 >= -1 + x and 2e0 <= x and 2e0 <= n) }" },
1769 { 1, "[n] -> { [x, y] : exists (e0 = floor((x)/2), e1 = floor((y)/3): "
1770 "3e1 = y and x >= 2 and 2e0 >= -1 + x and "
1771 "2e0 <= x and 2e0 <= n);"
1772 "[1, y] : exists (e0 = floor((y)/3): 3e0 = y and "
1774 { 1, "[t1] -> { [i0] : (exists (e0 = floor((63t1)/64): "
1775 "128e0 >= -134 + 127t1 and t1 >= 2 and "
1776 "64e0 <= 63t1 and 64e0 >= -63 + 63t1)) or "
1778 { 1, "{ [i, i] : exists (e0 = floor((1 + 2i)/3): 3e0 <= 2i and "
1779 "3e0 >= -1 + 2i and i <= 9 and i >= 1);"
1781 { 1, "{ [t1] : exists (e0 = floor((-11 + t1)/2): 2e0 = -11 + t1 and "
1782 "t1 >= 13 and t1 <= 16);"
1783 "[t1] : t1 <= 15 and t1 >= 12 }" },
1784 { 1, "{ [x,y] : x = 3y and 0 <= y <= 2; [-3,-1] }" },
1785 { 1, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-2] }" },
1786 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-2,-2] }" },
1787 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-1] }" },
1788 { 1, "{ [i] : exists j : i = 4 j and 0 <= i <= 100;"
1789 "[i] : exists j : 1 <= i <= 100 and i >= 4j + 1 and "
1791 { 1, "{ [c0] : (exists (e0 : c0 - 1 <= 3e0 <= c0)) or "
1792 "(exists (e0 : 3e0 = -2 + c0)) }" },
1793 { 0, "[n, b0, t0] -> "
1794 "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1795 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1796 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1797 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1798 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 >= 8 + n and "
1799 "3i4 <= -96 + 3t0 + i0 and 3i4 >= -95 - n + 3t0 + i0 and "
1800 "i8 >= -157 + i0 - 4i4 and i8 >= 0 and "
1801 "i8 <= -33 + i0 - 4i4 and 3i8 <= -91 + 4n - i0)) or "
1802 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1803 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1804 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1805 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 <= 7 + n and "
1806 "4i4 <= -3 + i0 and 3i4 <= -96 + 3t0 + i0 and "
1807 "3i4 >= -95 - n + 3t0 + i0 and i8 >= -157 + i0 - 4i4 and "
1808 "i8 >= 0 and i8 <= -4 + i0 - 3i4 and i8 <= -41 + i0));"
1809 "[i0, i1, i2, i3, 0, i5, i6, i7, i8, i9, i10, i11, i12] : "
1810 "(exists (e0 = floor((i8)/32): b0 = 0 and 32e0 = i8 and "
1811 "n <= 2147483647 and t0 <= 31 and t0 >= 0 and i0 >= 11 and "
1812 "i0 >= 96 - 3t0 and i0 <= 95 + n - 3t0 and i0 <= 7 + n and "
1813 "i8 >= -40 + i0 and i8 <= -10 + i0)) }" },
1814 { 0, "{ [i0, i1, i2] : "
1815 "(exists (e0, e1 = floor((i0)/32), e2 = floor((i1)/32): "
1816 "32e1 = i0 and 32e2 = i1 and i1 >= -31 + i0 and "
1817 "i1 <= 31 + i0 and i2 >= -30 + i0 and i2 >= -30 + i1 and "
1818 "32e0 >= -30 + i0 and 32e0 >= -30 + i1 and "
1819 "32e0 >= -31 + i2 and 32e0 <= 30 + i2 and 32e0 <= 31 + i1 and "
1820 "32e0 <= 31 + i0)) or "
1822 { 1, "{ [a, b, c] : 2b = 1 + a and 2c = 2 + a; [0, 0, 0] }" },
1823 { 1, "{ [a, a, b, c] : 32*floor((a)/32) = a and 2*floor((b)/2) = b and "
1824 "2*floor((c)/2) = c and 0 <= a <= 192;"
1825 "[224, 224, b, c] : 2*floor((b)/2) = b and 2*floor((c)/2) = c }"
1827 { 1, "[n] -> { [a,b] : (exists e : 1 <= a <= 7e and 9e <= b <= n) or "
1828 "(0 <= a <= b <= n) }" },
1829 { 1, "{ [a, b] : 0 <= a <= 2 and b >= 0 and "
1830 "((0 < b <= 13) or (2*floor((a + b)/2) >= -5 + a + 2b)) }" },
1831 { 1, "{ [a] : (2 <= a <= 5) or (a mod 2 = 1 and 1 <= a <= 5) }" },
1832 { 1, "{ [a, b, c] : (b = -1 + a and 0 < a <= 3 and "
1833 "9*floor((-4a + 2c)/9) <= -3 - 4a + 2c) or "
1834 "(exists (e0 = floor((-16 + 2c)/9): a = 4 and "
1835 "b = 3 and 9e0 <= -19 + 2c)) }" },
1836 { 1, "{ [a, b, c] : (b = -1 + a and 0 < a <= 3 and "
1837 "9*floor((-4a + 2c)/9) <= -3 - 4a + 2c) or "
1838 "(a = 4 and b = 3 and "
1839 "9*floor((-16 + 2c)/9) <= -19 + 2c) }" },
1840 { 0, "{ [a, b, c] : (b <= 2 and b <= -2 + a) or "
1841 "(b = -1 + a and 0 < a <= 3 and "
1842 "9*floor((-4a + 2c)/9) <= -3 - 4a + 2c) or "
1843 "(exists (e0 = floor((-16 + 2c)/9): a = 4 and "
1844 "b = 3 and 9e0 <= -19 + 2c)) }" },
1845 { 1, "{ [y, x] : (x - y) mod 3 = 2 and 2 <= y <= 200 and 0 <= x <= 2;"
1847 { 1, "{ [x, y] : (x - y) mod 3 = 2 and 2 <= y <= 200 and 0 <= x <= 2;"
1849 { 1, "{ [1, y] : -1 <= y <= 1; [x, -x] : 0 <= x <= 1 }" },
1850 { 1, "{ [1, y] : 0 <= y <= 1; [x, -x] : 0 <= x <= 1 }" },
1851 { 1, "{ [x, y] : 0 <= x <= 10 and x - 4*floor(x/4) <= 1 and y <= 0; "
1852 "[x, y] : 0 <= x <= 10 and x - 4*floor(x/4) > 1 and y <= 0; "
1853 "[x, y] : 0 <= x <= 10 and x - 5*floor(x/5) <= 1 and 0 < y; "
1854 "[x, y] : 0 <= x <= 10 and x - 5*floor(x/5) > 1 and 0 < y }" },
1855 { 1, "{ [x, 0] : 0 <= x <= 10 and x mod 2 = 0; "
1856 "[x, 0] : 0 <= x <= 10 and x mod 2 = 1; "
1857 "[x, y] : 0 <= x <= 10 and 1 <= y <= 10 }" },
1858 { 1, "{ [a] : a <= 8 and "
1859 "(a mod 10 = 7 or a mod 10 = 8 or a mod 10 = 9) }" },
1860 { 1, "{ [x, y] : 2y = -x and x <= 0 or "
1861 "x <= -1 and 2y <= -x - 1 and 2y >= x - 1 }" },
1862 { 0, "{ [x, y] : 2y = -x and x <= 0 or "
1863 "x <= -2 and 2y <= -x - 1 and 2y >= x - 1 }" },
1864 { 1, "{ [a] : (a <= 0 and 3*floor((a)/3) = a) or "
1865 "(a < 0 and 3*floor((a)/3) < a) }" },
1866 { 1, "{ [a] : (a <= 0 and 3*floor((a)/3) = a) or "
1867 "(a < -1 and 3*floor((a)/3) < a) }" },
1868 { 1, "{ [a, b] : a <= 1024 and b >= 0 and "
1869 "((-31 - a + b <= 32*floor((-1 - a)/32) <= -33 + b and "
1870 "32*floor((-1 - a)/32) <= -16 + b + 16*floor((-1 - a)/16))"
1871 "or (2 <= a <= 15 and b < a)) }" },
1872 { 1, "{ [a] : a > 0 and ((16*floor((a)/16) < a and "
1873 "32*floor((a)/32) < a) or a <= 15) }" },
1874 { 1, "{ [a, b, c, d] : (-a + d) mod 64 = 0 and a <= 8 and b <= 1 and "
1875 "10 - a <= c <= 3 and d >= 5 and 9 - 64b <= d <= 70;"
1876 "[a, b = 1, c, d] : (-a + d) mod 64 = 0 and a <= 8 and c >= 4 and "
1877 "10 - a <= c <= 5 and 5 <= d <= 73 - c }" },
1878 { 1, "[n, m] -> { S_0[i] : (-n + i) mod 3 = 0 and m >= 3 + n and "
1879 "i >= n and 3*floor((2 + n + 2m)/3) <= n + 3m - i; "
1880 "S_0[n] : n <= m <= 2 + n }" },
1881 { 1, "{ [a, b] : exists (e0: 0 <= a <= 1 and b >= 0 and "
1882 "2e0 >= -5 + a + 2b and 2e0 >= -1 + a + b and "
1884 "[a, b] : exists (e0: 0 <= a <= 1 and 2e0 >= -5 + a + 2b and "
1885 "2e0 >= -1 - a + b and 2e0 <= -a + b and "
1886 "2e0 < -a + 2b) }" },
1887 { 1, "{ [i, j, i - 8j] : 8 <= i <= 63 and -7 + i <= 8j <= i; "
1888 "[i, 0, i] : 0 <= i <= 7 }" },
1889 { 1, "{ [a, b] : a >= 0 and 0 <= b <= 1 - a; [1, 1] }" },
1890 { 0, "{ [a, b] : a >= 0 and 0 <= b <= 1 - a; [0, 2] }" },
1891 { 0, "{ [a, b] : a >= 0 and 0 <= b <= 1 - a; [-1, 3] }" },
1892 { 1, "{ [a, b] : a, b >= 0 and a + 2b <= 2; [1, 1] }" },
1893 { 0, "{ [a, b] : a, b >= 0 and a + 2b <= 2; [2, 1] }" },
1894 { 0, "{ [a, c] : (2 + a) mod 4 = 0 or "
1895 "(c = 4 + a and 4 * floor((a)/4) = a and a >= 0 and a <= 4) or "
1896 "(c = 3 + a and 4 * floor((-1 + a)/4) = -1 + a and "
1897 "a > 0 and a <= 5) }" },
1900 /* A specialized coalescing test case that would result
1901 * in a segmentation fault or a failed assertion in earlier versions of isl.
1903 static int test_coalesce_special(struct isl_ctx
*ctx
)
1906 isl_map
*map1
, *map2
;
1908 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1909 "[[S_L309_IN[] -> T11[]] -> ce_imag2[1, o1]] : "
1910 "(y = 201 and o1 <= 239 and o1 >= 212) or "
1911 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 198 and y >= 3 and "
1912 "o1 <= 239 and o1 >= 212)) or "
1913 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 201 and y >= 3 and "
1914 "o1 <= 241 and o1 >= 240));"
1915 "[S_L220_OUT[] -> T7[]] -> "
1916 "[[S_L309_IN[] -> T11[]] -> ce_imag2[0, o1]] : "
1917 "(y = 2 and o1 <= 241 and o1 >= 212) or "
1918 "(exists (e0 = [(-2 + y)/3]: 3e0 = -2 + y and y <= 200 and "
1919 "y >= 5 and o1 <= 241 and o1 >= 212)) }";
1920 map1
= isl_map_read_from_str(ctx
, str
);
1921 map1
= isl_map_align_divs_internal(map1
);
1922 map1
= isl_map_coalesce(map1
);
1923 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1924 "[[S_L309_IN[] -> T11[]] -> ce_imag2[o0, o1]] : "
1925 "exists (e0 = [(-1 - y + o0)/3]: 3e0 = -1 - y + o0 and "
1926 "y <= 201 and o0 <= 2 and o1 >= 212 and o1 <= 241 and "
1927 "o0 >= 3 - y and o0 <= -2 + y and o0 >= 0) }";
1928 map2
= isl_map_read_from_str(ctx
, str
);
1929 map2
= isl_map_union(map2
, map1
);
1930 map2
= isl_map_align_divs_internal(map2
);
1931 map2
= isl_map_coalesce(map2
);
1939 /* A specialized coalescing test case that would result in an assertion
1940 * in an earlier version of isl.
1941 * The explicit call to isl_basic_set_union prevents the implicit
1942 * equality constraints in the first basic map from being detected prior
1943 * to the call to isl_set_coalesce, at least at the point
1944 * where this test case was introduced.
1946 static int test_coalesce_special2(struct isl_ctx
*ctx
)
1949 isl_basic_set
*bset1
, *bset2
;
1952 str
= "{ [x, y] : x, y >= 0 and x + 2y <= 1 and 2x + y <= 1 }";
1953 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1954 str
= "{ [x,0] : -1 <= x <= 1 and x mod 2 = 1 }" ;
1955 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1956 set
= isl_basic_set_union(bset1
, bset2
);
1957 set
= isl_set_coalesce(set
);
1965 /* Check that calling isl_set_coalesce does not leave other sets
1966 * that may share some information with the input to isl_set_coalesce
1967 * in an inconsistent state.
1968 * In particular, older versions of isl would modify all copies
1969 * of the basic sets in the isl_set_coalesce input in a way
1970 * that could leave them in an inconsistent state.
1971 * The result of printing any other set containing one of these
1972 * basic sets would then result in an invalid set description.
1974 static int test_coalesce_special3(isl_ctx
*ctx
)
1978 isl_set
*set1
, *set2
;
1981 set1
= isl_set_read_from_str(ctx
, "{ [0, 0, 0] }");
1982 str
= "{ [a, b, a + b] : a >= 0 and b >= 0 and 0 < a + b }";
1983 set2
= isl_set_read_from_str(ctx
, str
);
1984 set1
= isl_set_union(set1
, isl_set_copy(set2
));
1985 set1
= isl_set_coalesce(set1
);
1988 p
= isl_printer_to_str(ctx
);
1989 p
= isl_printer_print_set(p
, set2
);
1991 s
= isl_printer_get_str(p
);
1992 isl_printer_free(p
);
1993 set1
= isl_set_read_from_str(ctx
, s
);
2003 /* Test the functionality of isl_set_coalesce.
2004 * That is, check that the output is always equal to the input
2005 * and in some cases that the result consists of a single disjunct.
2007 static int test_coalesce(struct isl_ctx
*ctx
)
2011 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
2012 const char *str
= coalesce_tests
[i
].str
;
2013 int check_one
= coalesce_tests
[i
].single_disjunct
;
2014 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
2018 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
2020 if (test_coalesce_special(ctx
) < 0)
2022 if (test_coalesce_special2(ctx
) < 0)
2024 if (test_coalesce_special3(ctx
) < 0)
2030 /* Construct a representation of the graph on the right of Figure 1
2031 * in "Computing the Transitive Closure of a Union of
2032 * Affine Integer Tuple Relations".
2034 static __isl_give isl_map
*cocoa_fig_1_right_graph(isl_ctx
*ctx
)
2037 isl_map
*up
, *right
;
2039 dom
= isl_set_read_from_str(ctx
,
2040 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
2041 "2 x - 3 y + 3 >= 0 }");
2042 right
= isl_map_read_from_str(ctx
,
2043 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
2044 up
= isl_map_read_from_str(ctx
,
2045 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
2046 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
2047 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
2048 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
2049 up
= isl_map_intersect_range(up
, dom
);
2050 return isl_map_union(up
, right
);
2053 /* Construct a representation of the power of the graph
2054 * on the right of Figure 1 in "Computing the Transitive Closure of
2055 * a Union of Affine Integer Tuple Relations".
2057 static __isl_give isl_map
*cocoa_fig_1_right_power(isl_ctx
*ctx
)
2059 return isl_map_read_from_str(ctx
,
2060 "{ [1] -> [[0,0] -> [0,1]]; [2] -> [[0,0] -> [1,1]]; "
2061 " [1] -> [[0,1] -> [1,1]]; [1] -> [[2,2] -> [3,2]]; "
2062 " [2] -> [[2,2] -> [3,3]]; [1] -> [[3,2] -> [3,3]] }");
2065 /* Construct a representation of the transitive closure of the graph
2066 * on the right of Figure 1 in "Computing the Transitive Closure of
2067 * a Union of Affine Integer Tuple Relations".
2069 static __isl_give isl_map
*cocoa_fig_1_right_tc(isl_ctx
*ctx
)
2071 return isl_set_unwrap(isl_map_range(cocoa_fig_1_right_power(ctx
)));
2074 static int test_closure(isl_ctx
*ctx
)
2077 isl_map
*map
, *map2
;
2080 /* COCOA example 1 */
2081 map
= isl_map_read_from_str(ctx
,
2082 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
2083 "1 <= i and i < n and 1 <= j and j < n or "
2084 "i2 = i + 1 and j2 = j - 1 and "
2085 "1 <= i and i < n and 2 <= j and j <= n }");
2086 map
= isl_map_power(map
, &exact
);
2090 /* COCOA example 1 */
2091 map
= isl_map_read_from_str(ctx
,
2092 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
2093 "1 <= i and i < n and 1 <= j and j < n or "
2094 "i2 = i + 1 and j2 = j - 1 and "
2095 "1 <= i and i < n and 2 <= j and j <= n }");
2096 map
= isl_map_transitive_closure(map
, &exact
);
2098 map2
= isl_map_read_from_str(ctx
,
2099 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
2100 "1 <= i and i < n and 1 <= j and j <= n and "
2101 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
2102 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
2103 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
2104 assert(isl_map_is_equal(map
, map2
));
2108 map
= isl_map_read_from_str(ctx
,
2109 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
2110 " 0 <= y and y <= n }");
2111 map
= isl_map_transitive_closure(map
, &exact
);
2112 map2
= isl_map_read_from_str(ctx
,
2113 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
2114 " 0 <= y and y <= n }");
2115 assert(isl_map_is_equal(map
, map2
));
2119 /* COCOA example 2 */
2120 map
= isl_map_read_from_str(ctx
,
2121 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
2122 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
2123 "i2 = i + 2 and j2 = j - 2 and "
2124 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
2125 map
= isl_map_transitive_closure(map
, &exact
);
2127 map2
= isl_map_read_from_str(ctx
,
2128 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
2129 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
2130 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
2131 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
2132 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
2133 assert(isl_map_is_equal(map
, map2
));
2137 /* COCOA Fig.2 left */
2138 map
= isl_map_read_from_str(ctx
,
2139 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
2140 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
2142 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
2143 "j <= 2 i - 3 and j <= n - 2 or "
2144 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2145 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2146 map
= isl_map_transitive_closure(map
, &exact
);
2150 /* COCOA Fig.2 right */
2151 map
= isl_map_read_from_str(ctx
,
2152 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
2153 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
2155 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
2156 "j <= 2 i - 4 and j <= n - 3 or "
2157 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2158 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2159 map
= isl_map_power(map
, &exact
);
2163 /* COCOA Fig.2 right */
2164 map
= isl_map_read_from_str(ctx
,
2165 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
2166 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
2168 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
2169 "j <= 2 i - 4 and j <= n - 3 or "
2170 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2171 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2172 map
= isl_map_transitive_closure(map
, &exact
);
2174 map2
= isl_map_read_from_str(ctx
,
2175 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
2176 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
2177 "j <= n and 3 + i + 2 j <= 3 n and "
2178 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
2179 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
2180 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
2181 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
2182 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
2183 assert(isl_map_is_equal(map
, map2
));
2187 map
= cocoa_fig_1_right_graph(ctx
);
2188 map
= isl_map_transitive_closure(map
, &exact
);
2190 map2
= cocoa_fig_1_right_tc(ctx
);
2191 assert(isl_map_is_equal(map
, map2
));
2195 map
= cocoa_fig_1_right_graph(ctx
);
2196 map
= isl_map_power(map
, &exact
);
2197 map2
= cocoa_fig_1_right_power(ctx
);
2198 equal
= isl_map_is_equal(map
, map2
);
2204 isl_die(ctx
, isl_error_unknown
, "power not exact", return -1);
2206 isl_die(ctx
, isl_error_unknown
, "unexpected power", return -1);
2208 /* COCOA Theorem 1 counter example */
2209 map
= isl_map_read_from_str(ctx
,
2210 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
2211 "i2 = 1 and j2 = j or "
2212 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
2213 map
= isl_map_transitive_closure(map
, &exact
);
2217 map
= isl_map_read_from_str(ctx
,
2218 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
2219 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
2220 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
2221 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
2222 map
= isl_map_transitive_closure(map
, &exact
);
2226 /* Kelly et al 1996, fig 12 */
2227 map
= isl_map_read_from_str(ctx
,
2228 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
2229 "1 <= i,j,j+1 <= n or "
2230 "j = n and j2 = 1 and i2 = i + 1 and "
2231 "1 <= i,i+1 <= n }");
2232 map
= isl_map_transitive_closure(map
, &exact
);
2234 map2
= isl_map_read_from_str(ctx
,
2235 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
2236 "1 <= i <= n and i = i2 or "
2237 "1 <= i < i2 <= n and 1 <= j <= n and "
2239 assert(isl_map_is_equal(map
, map2
));
2243 /* Omega's closure4 */
2244 map
= isl_map_read_from_str(ctx
,
2245 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
2246 "1 <= x,y <= 10 or "
2247 "x2 = x + 1 and y2 = y and "
2248 "1 <= x <= 20 && 5 <= y <= 15 }");
2249 map
= isl_map_transitive_closure(map
, &exact
);
2253 map
= isl_map_read_from_str(ctx
,
2254 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
2255 map
= isl_map_transitive_closure(map
, &exact
);
2257 map2
= isl_map_read_from_str(ctx
,
2258 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
2259 assert(isl_map_is_equal(map
, map2
));
2263 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
2264 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
2265 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
2266 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
2267 map
= isl_map_read_from_str(ctx
, str
);
2268 map
= isl_map_transitive_closure(map
, &exact
);
2270 map2
= isl_map_read_from_str(ctx
, str
);
2271 assert(isl_map_is_equal(map
, map2
));
2275 str
= "{[0] -> [1]; [2] -> [3]}";
2276 map
= isl_map_read_from_str(ctx
, str
);
2277 map
= isl_map_transitive_closure(map
, &exact
);
2279 map2
= isl_map_read_from_str(ctx
, str
);
2280 assert(isl_map_is_equal(map
, map2
));
2284 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
2285 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
2286 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
2287 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2288 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2289 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
2290 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
2291 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
2292 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2293 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2294 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
2295 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
2296 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
2297 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2298 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2299 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
2300 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
2301 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
2302 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2303 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
2304 map
= isl_map_read_from_str(ctx
, str
);
2305 map
= isl_map_transitive_closure(map
, NULL
);
2312 static int test_lex(struct isl_ctx
*ctx
)
2318 dim
= isl_space_set_alloc(ctx
, 0, 0);
2319 map
= isl_map_lex_le(dim
);
2320 empty
= isl_map_is_empty(map
);
2326 isl_die(ctx
, isl_error_unknown
,
2327 "expecting non-empty result", return -1);
2332 /* Inputs for isl_map_lexmin tests.
2333 * "map" is the input and "lexmin" is the expected result.
2338 } lexmin_tests
[] = {
2339 { "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }",
2340 "{ [x] -> [5] : 6 <= x <= 8; "
2341 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }" },
2342 { "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }",
2343 "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }" },
2344 { "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }",
2345 "{ [x] -> [y] : (4y = x and x >= 0) or "
2346 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
2347 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
2348 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }" },
2349 { "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }",
2350 "{ T[a] -> S[b, c] : 2b = a and 2c = a }" },
2351 /* Check that empty pieces are properly combined. */
2352 { "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
2353 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
2354 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }",
2355 "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
2356 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
2358 { "{ [i, k, j] -> [a, b, c, d] : 8*floor((b)/8) = b and k <= 255 and "
2359 "a <= 255 and c <= 255 and d <= 255 - j and "
2360 "255 - j <= 7d <= 7 - i and 240d <= 239 + a and "
2361 "247d <= 247 + k - j and 247d <= 247 + k - b and "
2362 "247d <= 247 + i and 248 - b <= 248d <= c and "
2363 "254d >= i - a + b and 254d >= -a + b and "
2364 "255d >= -i + a - b and 1792d >= -63736 + 257b }",
2366 "[-127762 + i + 502j, -62992 + 248j, 63240 - 248j, 255 - j] : "
2367 "k <= 255 and 7j >= 1778 + i and 246j >= 62738 - k and "
2368 "247j >= 62738 - i and 509j <= 129795 + i and "
2369 "742j >= 188724 - i; "
2370 "[0, k, j] -> [1, 0, 248, 1] : k <= 255 and 248 <= j <= 254, k }" },
2371 { "{ [a] -> [b] : 0 <= b <= 255 and -509 + a <= 512b < a and "
2372 "16*floor((8 + b)/16) <= 7 + b; "
2374 "{ [a] -> [b = 1] : a >= 510 or a <= 0; "
2375 "[a] -> [b = 0] : 0 < a <= 509 }" },
2376 { "{ rat: [i] : 1 <= 2i <= 9 }", "{ rat: [i] : 2i = 1 }" },
2377 { "{ rat: [i] : 1 <= 2i <= 9 or i >= 10 }", "{ rat: [i] : 2i = 1 }" },
2380 static int test_lexmin(struct isl_ctx
*ctx
)
2385 isl_basic_map
*bmap
;
2386 isl_map
*map
, *map2
;
2389 isl_pw_multi_aff
*pma
;
2391 str
= "[p0, p1] -> { [] -> [] : "
2392 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
2393 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
2394 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
2395 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
2396 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
2397 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
2398 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
2399 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
2400 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
2401 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
2402 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
2403 map
= isl_map_read_from_str(ctx
, str
);
2404 map
= isl_map_lexmin(map
);
2407 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
2408 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
2409 set
= isl_set_read_from_str(ctx
, str
);
2410 set
= isl_set_lexmax(set
);
2411 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
2412 set2
= isl_set_read_from_str(ctx
, str
);
2413 set
= isl_set_intersect(set
, set2
);
2414 assert(!isl_set_is_empty(set
));
2417 for (i
= 0; i
< ARRAY_SIZE(lexmin_tests
); ++i
) {
2418 map
= isl_map_read_from_str(ctx
, lexmin_tests
[i
].map
);
2419 map
= isl_map_lexmin(map
);
2420 map2
= isl_map_read_from_str(ctx
, lexmin_tests
[i
].lexmin
);
2421 equal
= isl_map_is_equal(map
, map2
);
2428 isl_die(ctx
, isl_error_unknown
,
2429 "unexpected result", return -1);
2432 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2433 " 8i' <= i and 8i' >= -7 + i }";
2434 bmap
= isl_basic_map_read_from_str(ctx
, str
);
2435 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
2436 map2
= isl_map_from_pw_multi_aff(pma
);
2437 map
= isl_map_from_basic_map(bmap
);
2438 assert(isl_map_is_equal(map
, map2
));
2442 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2443 " 8i' <= i and 8i' >= -7 + i }";
2444 set
= isl_set_read_from_str(ctx
, str
);
2445 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
2446 set2
= isl_set_from_pw_multi_aff(pma
);
2447 equal
= isl_set_is_equal(set
, set2
);
2453 isl_die(ctx
, isl_error_unknown
,
2454 "unexpected difference between set and "
2455 "piecewise affine expression", return -1);
2460 /* A specialized isl_set_min_val test case that would return the wrong result
2461 * in earlier versions of isl.
2462 * The explicit call to isl_basic_set_union prevents the second basic set
2463 * from being determined to be empty prior to the call to isl_set_min_val,
2464 * at least at the point where this test case was introduced.
2466 static int test_min_special(isl_ctx
*ctx
)
2469 isl_basic_set
*bset1
, *bset2
;
2475 str
= "{ [a, b] : a >= 2 and b >= 0 and 14 - a <= b <= 9 }";
2476 bset1
= isl_basic_set_read_from_str(ctx
, str
);
2477 str
= "{ [a, b] : 1 <= a, b and a + b <= 1 }";
2478 bset2
= isl_basic_set_read_from_str(ctx
, str
);
2479 set
= isl_basic_set_union(bset1
, bset2
);
2480 obj
= isl_aff_read_from_str(ctx
, "{ [a, b] -> [a] }");
2482 res
= isl_set_min_val(set
, obj
);
2483 ok
= isl_val_cmp_si(res
, 5) == 0;
2492 isl_die(ctx
, isl_error_unknown
, "unexpected minimum",
2498 /* A specialized isl_set_min_val test case that would return an error
2499 * in earlier versions of isl.
2501 static int test_min_special2(isl_ctx
*ctx
)
2504 isl_basic_set
*bset
;
2508 str
= "{ [i, j, k] : 2j = i and 2k = i + 1 and i >= 2 }";
2509 bset
= isl_basic_set_read_from_str(ctx
, str
);
2511 obj
= isl_aff_read_from_str(ctx
, "{ [i, j, k] -> [i] }");
2513 res
= isl_basic_set_max_val(bset
, obj
);
2515 isl_basic_set_free(bset
);
2528 __isl_give isl_val
*(*fn
)(__isl_keep isl_set
*set
,
2529 __isl_keep isl_aff
*obj
);
2532 { "{ [-1]; [1] }", "{ [x] -> [x] }", &isl_set_min_val
, "-1" },
2533 { "{ [-1]; [1] }", "{ [x] -> [x] }", &isl_set_max_val
, "1" },
2534 { "{ [a, b] : 0 <= a, b <= 100 and b mod 2 = 0}",
2535 "{ [a, b] -> [floor((b - 2*floor((-a)/4))/5)] }",
2536 &isl_set_max_val
, "30" },
2540 /* Perform basic isl_set_min_val and isl_set_max_val tests.
2541 * In particular, check the results on non-convex inputs.
2543 static int test_min(struct isl_ctx
*ctx
)
2551 for (i
= 0; i
< ARRAY_SIZE(opt_tests
); ++i
) {
2552 set
= isl_set_read_from_str(ctx
, opt_tests
[i
].set
);
2553 obj
= isl_aff_read_from_str(ctx
, opt_tests
[i
].obj
);
2554 res
= isl_val_read_from_str(ctx
, opt_tests
[i
].res
);
2555 val
= opt_tests
[i
].fn(set
, obj
);
2556 ok
= isl_val_eq(res
, val
);
2565 isl_die(ctx
, isl_error_unknown
,
2566 "unexpected optimum", return -1);
2569 if (test_min_special(ctx
) < 0)
2571 if (test_min_special2(ctx
) < 0)
2582 static isl_stat
collect_must_may(__isl_take isl_map
*dep
, int must
,
2583 void *dep_user
, void *user
)
2585 struct must_may
*mm
= (struct must_may
*)user
;
2588 mm
->must
= isl_map_union(mm
->must
, dep
);
2590 mm
->may
= isl_map_union(mm
->may
, dep
);
2595 static int common_space(void *first
, void *second
)
2597 int depth
= *(int *)first
;
2601 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
2609 map2
= isl_map_read_from_str(map
->ctx
, str
);
2610 equal
= isl_map_is_equal(map
, map2
);
2616 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
2620 equal
= map_is_equal(map
, str
);
2624 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
2625 "result not as expected", return -1);
2629 static int test_dep(struct isl_ctx
*ctx
)
2634 isl_access_info
*ai
;
2641 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2642 map
= isl_map_read_from_str(ctx
, str
);
2643 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2645 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2646 map
= isl_map_read_from_str(ctx
, str
);
2647 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2649 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2650 map
= isl_map_read_from_str(ctx
, str
);
2651 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2653 flow
= isl_access_info_compute_flow(ai
);
2654 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2655 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2656 mm
.may
= isl_map_empty(dim
);
2658 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2660 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
2661 " [1,10,0] -> [2,5,0] }";
2662 assert(map_is_equal(mm
.must
, str
));
2663 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2664 assert(map_is_equal(mm
.may
, str
));
2666 isl_map_free(mm
.must
);
2667 isl_map_free(mm
.may
);
2668 isl_flow_free(flow
);
2671 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2672 map
= isl_map_read_from_str(ctx
, str
);
2673 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2675 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2676 map
= isl_map_read_from_str(ctx
, str
);
2677 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2679 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2680 map
= isl_map_read_from_str(ctx
, str
);
2681 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2683 flow
= isl_access_info_compute_flow(ai
);
2684 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2685 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2686 mm
.may
= isl_map_empty(dim
);
2688 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2690 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2691 assert(map_is_equal(mm
.must
, str
));
2692 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2693 assert(map_is_equal(mm
.may
, str
));
2695 isl_map_free(mm
.must
);
2696 isl_map_free(mm
.may
);
2697 isl_flow_free(flow
);
2700 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2701 map
= isl_map_read_from_str(ctx
, str
);
2702 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2704 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2705 map
= isl_map_read_from_str(ctx
, str
);
2706 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2708 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2709 map
= isl_map_read_from_str(ctx
, str
);
2710 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2712 flow
= isl_access_info_compute_flow(ai
);
2713 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2714 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2715 mm
.may
= isl_map_empty(dim
);
2717 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2719 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2720 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2721 assert(map_is_equal(mm
.may
, str
));
2722 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2723 assert(map_is_equal(mm
.must
, str
));
2725 isl_map_free(mm
.must
);
2726 isl_map_free(mm
.may
);
2727 isl_flow_free(flow
);
2730 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2731 map
= isl_map_read_from_str(ctx
, str
);
2732 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2734 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2735 map
= isl_map_read_from_str(ctx
, str
);
2736 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2738 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2739 map
= isl_map_read_from_str(ctx
, str
);
2740 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2742 flow
= isl_access_info_compute_flow(ai
);
2743 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2744 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2745 mm
.may
= isl_map_empty(dim
);
2747 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2749 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2750 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2751 assert(map_is_equal(mm
.may
, str
));
2752 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2753 assert(map_is_equal(mm
.must
, str
));
2755 isl_map_free(mm
.must
);
2756 isl_map_free(mm
.may
);
2757 isl_flow_free(flow
);
2760 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2761 map
= isl_map_read_from_str(ctx
, str
);
2762 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2764 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2765 map
= isl_map_read_from_str(ctx
, str
);
2766 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2768 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2769 map
= isl_map_read_from_str(ctx
, str
);
2770 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2772 flow
= isl_access_info_compute_flow(ai
);
2773 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2774 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2775 mm
.may
= isl_map_empty(dim
);
2777 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2779 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2780 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2781 assert(map_is_equal(mm
.may
, str
));
2782 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2783 assert(map_is_equal(mm
.must
, str
));
2785 isl_map_free(mm
.must
);
2786 isl_map_free(mm
.may
);
2787 isl_flow_free(flow
);
2792 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2793 map
= isl_map_read_from_str(ctx
, str
);
2794 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2796 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2797 map
= isl_map_read_from_str(ctx
, str
);
2798 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2800 flow
= isl_access_info_compute_flow(ai
);
2801 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2802 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2803 mm
.may
= isl_map_empty(dim
);
2805 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2807 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2808 assert(map_is_equal(mm
.must
, str
));
2809 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2810 assert(map_is_equal(mm
.may
, str
));
2812 isl_map_free(mm
.must
);
2813 isl_map_free(mm
.may
);
2814 isl_flow_free(flow
);
2819 /* Check that the dependence analysis proceeds without errors.
2820 * Earlier versions of isl would break down during the analysis
2821 * due to the use of the wrong spaces.
2823 static int test_flow(isl_ctx
*ctx
)
2826 isl_union_map
*access
, *schedule
;
2827 isl_union_map
*must_dep
, *may_dep
;
2830 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2831 access
= isl_union_map_read_from_str(ctx
, str
);
2832 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2833 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2834 "S2[] -> [1,0,0,0]; "
2835 "S3[] -> [-1,0,0,0] }";
2836 schedule
= isl_union_map_read_from_str(ctx
, str
);
2837 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2838 isl_union_map_copy(access
), schedule
,
2839 &must_dep
, &may_dep
, NULL
, NULL
);
2840 isl_union_map_free(may_dep
);
2841 isl_union_map_free(must_dep
);
2850 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2851 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2852 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2853 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2854 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2855 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2856 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2857 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2858 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2861 int test_sv(isl_ctx
*ctx
)
2863 isl_union_map
*umap
;
2867 for (i
= 0; i
< ARRAY_SIZE(sv_tests
); ++i
) {
2868 umap
= isl_union_map_read_from_str(ctx
, sv_tests
[i
].map
);
2869 sv
= isl_union_map_is_single_valued(umap
);
2870 isl_union_map_free(umap
);
2873 if (sv_tests
[i
].sv
&& !sv
)
2874 isl_die(ctx
, isl_error_internal
,
2875 "map not detected as single valued", return -1);
2876 if (!sv_tests
[i
].sv
&& sv
)
2877 isl_die(ctx
, isl_error_internal
,
2878 "map detected as single valued", return -1);
2887 } bijective_tests
[] = {
2888 { "[N,M]->{[i,j] -> [i]}", 0 },
2889 { "[N,M]->{[i,j] -> [i] : j=i}", 1 },
2890 { "[N,M]->{[i,j] -> [i] : j=0}", 1 },
2891 { "[N,M]->{[i,j] -> [i] : j=N}", 1 },
2892 { "[N,M]->{[i,j] -> [j,i]}", 1 },
2893 { "[N,M]->{[i,j] -> [i+j]}", 0 },
2894 { "[N,M]->{[i,j] -> []}", 0 },
2895 { "[N,M]->{[i,j] -> [i,j,N]}", 1 },
2896 { "[N,M]->{[i,j] -> [2i]}", 0 },
2897 { "[N,M]->{[i,j] -> [i,i]}", 0 },
2898 { "[N,M]->{[i,j] -> [2i,i]}", 0 },
2899 { "[N,M]->{[i,j] -> [2i,j]}", 1 },
2900 { "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1 },
2903 static int test_bijective(struct isl_ctx
*ctx
)
2909 for (i
= 0; i
< ARRAY_SIZE(bijective_tests
); ++i
) {
2910 map
= isl_map_read_from_str(ctx
, bijective_tests
[i
].str
);
2911 bijective
= isl_map_is_bijective(map
);
2915 if (bijective_tests
[i
].bijective
&& !bijective
)
2916 isl_die(ctx
, isl_error_internal
,
2917 "map not detected as bijective", return -1);
2918 if (!bijective_tests
[i
].bijective
&& bijective
)
2919 isl_die(ctx
, isl_error_internal
,
2920 "map detected as bijective", return -1);
2926 /* Inputs for isl_pw_qpolynomial_gist tests.
2927 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2933 } pwqp_gist_tests
[] = {
2934 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2935 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2936 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2937 "{ [i] -> -1/2 + 1/2 * i }" },
2938 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
2941 static int test_pwqp(struct isl_ctx
*ctx
)
2946 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
2949 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2950 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2952 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
2955 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
2956 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2958 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2960 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2962 isl_pw_qpolynomial_free(pwqp1
);
2964 for (i
= 0; i
< ARRAY_SIZE(pwqp_gist_tests
); ++i
) {
2965 str
= pwqp_gist_tests
[i
].pwqp
;
2966 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2967 str
= pwqp_gist_tests
[i
].set
;
2968 set
= isl_set_read_from_str(ctx
, str
);
2969 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
2970 str
= pwqp_gist_tests
[i
].gist
;
2971 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2972 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2973 equal
= isl_pw_qpolynomial_is_zero(pwqp1
);
2974 isl_pw_qpolynomial_free(pwqp1
);
2979 isl_die(ctx
, isl_error_unknown
,
2980 "unexpected result", return -1);
2983 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
2984 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2985 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
2986 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2988 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
2990 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
2992 isl_pw_qpolynomial_free(pwqp1
);
2994 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
2995 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2996 str
= "{ [x] -> x }";
2997 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
2999 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
3001 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
3003 isl_pw_qpolynomial_free(pwqp1
);
3005 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
3006 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3007 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3008 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
3009 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
3010 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
3011 isl_pw_qpolynomial_free(pwqp1
);
3013 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
3014 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3015 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
3016 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3017 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
3018 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
3019 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
3020 isl_pw_qpolynomial_free(pwqp1
);
3021 isl_pw_qpolynomial_free(pwqp2
);
3025 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3027 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
3028 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3029 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
3030 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3031 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
3033 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
3034 isl_pw_qpolynomial_free(pwqp1
);
3035 isl_pw_qpolynomial_free(pwqp2
);
3039 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3044 static int test_split_periods(isl_ctx
*ctx
)
3047 isl_pw_qpolynomial
*pwqp
;
3049 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
3050 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
3051 "U >= 0; [U,V] -> U^2 : U >= 100 }";
3052 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3054 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
3056 isl_pw_qpolynomial_free(pwqp
);
3064 static int test_union(isl_ctx
*ctx
)
3067 isl_union_set
*uset1
, *uset2
;
3068 isl_union_map
*umap1
, *umap2
;
3071 str
= "{ [i] : 0 <= i <= 1 }";
3072 uset1
= isl_union_set_read_from_str(ctx
, str
);
3073 str
= "{ [1] -> [0] }";
3074 umap1
= isl_union_map_read_from_str(ctx
, str
);
3076 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
3077 equal
= isl_union_map_is_equal(umap1
, umap2
);
3079 isl_union_map_free(umap1
);
3080 isl_union_map_free(umap2
);
3085 isl_die(ctx
, isl_error_unknown
, "union maps not equal",
3088 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
3089 umap1
= isl_union_map_read_from_str(ctx
, str
);
3090 str
= "{ A[i]; B[i] }";
3091 uset1
= isl_union_set_read_from_str(ctx
, str
);
3093 uset2
= isl_union_map_domain(umap1
);
3095 equal
= isl_union_set_is_equal(uset1
, uset2
);
3097 isl_union_set_free(uset1
);
3098 isl_union_set_free(uset2
);
3103 isl_die(ctx
, isl_error_unknown
, "union sets not equal",
3109 /* Check that computing a bound of a non-zero polynomial over an unbounded
3110 * domain does not produce a rational value.
3111 * In particular, check that the upper bound is infinity.
3113 static int test_bound_unbounded_domain(isl_ctx
*ctx
)
3116 isl_pw_qpolynomial
*pwqp
;
3117 isl_pw_qpolynomial_fold
*pwf
, *pwf2
;
3120 str
= "{ [m,n] -> -m * n }";
3121 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3122 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3124 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3125 pwf2
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3126 equal
= isl_pw_qpolynomial_fold_plain_is_equal(pwf
, pwf2
);
3127 isl_pw_qpolynomial_fold_free(pwf
);
3128 isl_pw_qpolynomial_fold_free(pwf2
);
3133 isl_die(ctx
, isl_error_unknown
,
3134 "expecting infinite polynomial bound", return -1);
3139 static int test_bound(isl_ctx
*ctx
)
3143 isl_pw_qpolynomial
*pwqp
;
3144 isl_pw_qpolynomial_fold
*pwf
;
3146 if (test_bound_unbounded_domain(ctx
) < 0)
3149 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
3150 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3151 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3152 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
3153 isl_pw_qpolynomial_fold_free(pwf
);
3155 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
3158 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
3159 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3160 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3161 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
3162 isl_pw_qpolynomial_fold_free(pwf
);
3164 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
3170 static int test_lift(isl_ctx
*ctx
)
3173 isl_basic_map
*bmap
;
3174 isl_basic_set
*bset
;
3176 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
3177 bset
= isl_basic_set_read_from_str(ctx
, str
);
3178 bset
= isl_basic_set_lift(bset
);
3179 bmap
= isl_basic_map_from_range(bset
);
3180 bset
= isl_basic_map_domain(bmap
);
3181 isl_basic_set_free(bset
);
3190 } subset_tests
[] = {
3192 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
3193 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
3194 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
3196 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
3197 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
3198 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
3199 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
3200 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
3201 "256e0 <= 255i and 256e0 >= -255 + 255i and "
3202 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
3203 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
3204 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
3205 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
3206 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
3207 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
3208 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
3209 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
3210 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
3211 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
3212 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
3213 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
3214 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
3215 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
3216 "4e0 <= -57 + i0 + i1)) or "
3217 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
3218 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
3219 "4e0 >= -61 + i0 + i1)) or "
3220 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
3221 { "[a, b] -> { : a = 0 and b = -1 }", "[b, a] -> { : b >= -10 }", 1 },
3224 static int test_subset(isl_ctx
*ctx
)
3227 isl_set
*set1
, *set2
;
3230 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
3231 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
3232 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
3233 subset
= isl_set_is_subset(set1
, set2
);
3238 if (subset
!= subset_tests
[i
].subset
)
3239 isl_die(ctx
, isl_error_unknown
,
3240 "incorrect subset result", return -1);
3247 const char *minuend
;
3248 const char *subtrahend
;
3249 const char *difference
;
3250 } subtract_domain_tests
[] = {
3251 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
3252 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
3253 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
3256 static int test_subtract(isl_ctx
*ctx
)
3259 isl_union_map
*umap1
, *umap2
;
3260 isl_union_pw_multi_aff
*upma1
, *upma2
;
3261 isl_union_set
*uset
;
3264 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
3265 umap1
= isl_union_map_read_from_str(ctx
,
3266 subtract_domain_tests
[i
].minuend
);
3267 uset
= isl_union_set_read_from_str(ctx
,
3268 subtract_domain_tests
[i
].subtrahend
);
3269 umap2
= isl_union_map_read_from_str(ctx
,
3270 subtract_domain_tests
[i
].difference
);
3271 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
3272 equal
= isl_union_map_is_equal(umap1
, umap2
);
3273 isl_union_map_free(umap1
);
3274 isl_union_map_free(umap2
);
3278 isl_die(ctx
, isl_error_unknown
,
3279 "incorrect subtract domain result", return -1);
3282 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
3283 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
3284 subtract_domain_tests
[i
].minuend
);
3285 uset
= isl_union_set_read_from_str(ctx
,
3286 subtract_domain_tests
[i
].subtrahend
);
3287 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
3288 subtract_domain_tests
[i
].difference
);
3289 upma1
= isl_union_pw_multi_aff_subtract_domain(upma1
, uset
);
3290 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
3291 isl_union_pw_multi_aff_free(upma1
);
3292 isl_union_pw_multi_aff_free(upma2
);
3296 isl_die(ctx
, isl_error_unknown
,
3297 "incorrect subtract domain result", return -1);
3303 /* Check that intersecting the empty basic set with another basic set
3304 * does not increase the number of constraints. In particular,
3305 * the empty basic set should maintain its canonical representation.
3307 static int test_intersect(isl_ctx
*ctx
)
3310 isl_basic_set
*bset1
, *bset2
;
3312 bset1
= isl_basic_set_read_from_str(ctx
, "{ [a,b,c] : 1 = 0 }");
3313 bset2
= isl_basic_set_read_from_str(ctx
, "{ [1,2,3] }");
3314 n1
= isl_basic_set_n_constraint(bset1
);
3315 bset1
= isl_basic_set_intersect(bset1
, bset2
);
3316 n2
= isl_basic_set_n_constraint(bset1
);
3317 isl_basic_set_free(bset1
);
3321 isl_die(ctx
, isl_error_unknown
,
3322 "number of constraints of empty set changed",
3328 int test_factorize(isl_ctx
*ctx
)
3331 isl_basic_set
*bset
;
3334 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
3335 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
3336 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
3337 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
3338 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
3339 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
3340 "3i5 >= -2i0 - i2 + 3i4 }";
3341 bset
= isl_basic_set_read_from_str(ctx
, str
);
3342 f
= isl_basic_set_factorizer(bset
);
3343 isl_basic_set_free(bset
);
3344 isl_factorizer_free(f
);
3346 isl_die(ctx
, isl_error_unknown
,
3347 "failed to construct factorizer", return -1);
3349 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
3350 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
3351 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
3352 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
3353 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
3354 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
3355 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
3356 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
3357 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
3358 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
3359 bset
= isl_basic_set_read_from_str(ctx
, str
);
3360 f
= isl_basic_set_factorizer(bset
);
3361 isl_basic_set_free(bset
);
3362 isl_factorizer_free(f
);
3364 isl_die(ctx
, isl_error_unknown
,
3365 "failed to construct factorizer", return -1);
3370 static isl_stat
check_injective(__isl_take isl_map
*map
, void *user
)
3372 int *injective
= user
;
3374 *injective
= isl_map_is_injective(map
);
3377 if (*injective
< 0 || !*injective
)
3378 return isl_stat_error
;
3383 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
3384 const char *r
, const char *s
, int tilable
, int parallel
)
3388 isl_union_map
*W
, *R
, *S
;
3389 isl_union_map
*empty
;
3390 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
3391 isl_union_map
*validity
, *proximity
, *coincidence
;
3392 isl_union_map
*schedule
;
3393 isl_union_map
*test
;
3394 isl_union_set
*delta
;
3395 isl_union_set
*domain
;
3399 isl_schedule_constraints
*sc
;
3400 isl_schedule
*sched
;
3401 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
3403 D
= isl_union_set_read_from_str(ctx
, d
);
3404 W
= isl_union_map_read_from_str(ctx
, w
);
3405 R
= isl_union_map_read_from_str(ctx
, r
);
3406 S
= isl_union_map_read_from_str(ctx
, s
);
3408 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
3409 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
3411 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
3412 isl_union_map_compute_flow(isl_union_map_copy(R
),
3413 isl_union_map_copy(W
), empty
,
3414 isl_union_map_copy(S
),
3415 &dep_raw
, NULL
, NULL
, NULL
);
3416 isl_union_map_compute_flow(isl_union_map_copy(W
),
3417 isl_union_map_copy(W
),
3418 isl_union_map_copy(R
),
3419 isl_union_map_copy(S
),
3420 &dep_waw
, &dep_war
, NULL
, NULL
);
3422 dep
= isl_union_map_union(dep_waw
, dep_war
);
3423 dep
= isl_union_map_union(dep
, dep_raw
);
3424 validity
= isl_union_map_copy(dep
);
3425 coincidence
= isl_union_map_copy(dep
);
3426 proximity
= isl_union_map_copy(dep
);
3428 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
3429 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3430 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
3431 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3432 sched
= isl_schedule_constraints_compute_schedule(sc
);
3433 schedule
= isl_schedule_get_map(sched
);
3434 isl_schedule_free(sched
);
3435 isl_union_map_free(W
);
3436 isl_union_map_free(R
);
3437 isl_union_map_free(S
);
3440 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
3442 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
3443 is_complete
= isl_union_set_is_subset(D
, domain
);
3444 isl_union_set_free(D
);
3445 isl_union_set_free(domain
);
3447 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
3448 test
= isl_union_map_apply_range(test
, dep
);
3449 test
= isl_union_map_apply_range(test
, schedule
);
3451 delta
= isl_union_map_deltas(test
);
3452 if (isl_union_set_n_set(delta
) == 0) {
3456 isl_union_set_free(delta
);
3458 delta_set
= isl_set_from_union_set(delta
);
3460 slice
= isl_set_universe(isl_set_get_space(delta_set
));
3461 for (i
= 0; i
< tilable
; ++i
)
3462 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
3463 is_tilable
= isl_set_is_subset(delta_set
, slice
);
3464 isl_set_free(slice
);
3466 slice
= isl_set_universe(isl_set_get_space(delta_set
));
3467 for (i
= 0; i
< parallel
; ++i
)
3468 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
3469 is_parallel
= isl_set_is_subset(delta_set
, slice
);
3470 isl_set_free(slice
);
3472 origin
= isl_set_universe(isl_set_get_space(delta_set
));
3473 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
3474 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
3476 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
3477 delta_set
= isl_set_lexmin(delta_set
);
3479 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
3481 isl_set_free(origin
);
3482 isl_set_free(delta_set
);
3485 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
3486 is_injection
< 0 || is_complete
< 0)
3489 isl_die(ctx
, isl_error_unknown
,
3490 "generated schedule incomplete", return -1);
3492 isl_die(ctx
, isl_error_unknown
,
3493 "generated schedule not injective on each statement",
3496 isl_die(ctx
, isl_error_unknown
,
3497 "negative dependences in generated schedule",
3500 isl_die(ctx
, isl_error_unknown
,
3501 "generated schedule not as tilable as expected",
3504 isl_die(ctx
, isl_error_unknown
,
3505 "generated schedule not as parallel as expected",
3511 /* Compute a schedule for the given instance set, validity constraints,
3512 * proximity constraints and context and return a corresponding union map
3515 static __isl_give isl_union_map
*compute_schedule_with_context(isl_ctx
*ctx
,
3516 const char *domain
, const char *validity
, const char *proximity
,
3517 const char *context
)
3522 isl_union_map
*prox
;
3523 isl_schedule_constraints
*sc
;
3524 isl_schedule
*schedule
;
3525 isl_union_map
*sched
;
3527 con
= isl_set_read_from_str(ctx
, context
);
3528 dom
= isl_union_set_read_from_str(ctx
, domain
);
3529 dep
= isl_union_map_read_from_str(ctx
, validity
);
3530 prox
= isl_union_map_read_from_str(ctx
, proximity
);
3531 sc
= isl_schedule_constraints_on_domain(dom
);
3532 sc
= isl_schedule_constraints_set_context(sc
, con
);
3533 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
3534 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
3535 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3536 sched
= isl_schedule_get_map(schedule
);
3537 isl_schedule_free(schedule
);
3542 /* Compute a schedule for the given instance set, validity constraints and
3543 * proximity constraints and return a corresponding union map representation.
3545 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
3546 const char *domain
, const char *validity
, const char *proximity
)
3548 return compute_schedule_with_context(ctx
, domain
, validity
, proximity
,
3552 /* Check that a schedule can be constructed on the given domain
3553 * with the given validity and proximity constraints.
3555 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
3556 const char *validity
, const char *proximity
)
3558 isl_union_map
*sched
;
3560 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
3564 isl_union_map_free(sched
);
3568 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
3569 const char *validity
, const char *proximity
, const char *expected_sched
)
3571 isl_union_map
*sched1
, *sched2
;
3574 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
3575 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
3577 equal
= isl_union_map_is_equal(sched1
, sched2
);
3578 isl_union_map_free(sched1
);
3579 isl_union_map_free(sched2
);
3584 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
3590 /* Check that the schedule map is properly padded, i.e., that the range
3591 * lives in a single space.
3593 static int test_padded_schedule(isl_ctx
*ctx
)
3597 isl_union_map
*validity
, *proximity
;
3598 isl_schedule_constraints
*sc
;
3599 isl_schedule
*sched
;
3600 isl_union_map
*umap
;
3601 isl_union_set
*range
;
3604 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
3605 D
= isl_union_set_read_from_str(ctx
, str
);
3606 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
3607 proximity
= isl_union_map_copy(validity
);
3608 sc
= isl_schedule_constraints_on_domain(D
);
3609 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3610 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3611 sched
= isl_schedule_constraints_compute_schedule(sc
);
3612 umap
= isl_schedule_get_map(sched
);
3613 isl_schedule_free(sched
);
3614 range
= isl_union_map_range(umap
);
3615 set
= isl_set_from_union_set(range
);
3624 /* Check that conditional validity constraints are also taken into
3625 * account across bands.
3626 * In particular, try to make sure that live ranges D[1,0]->C[2,1] and
3627 * D[2,0]->C[3,0] are not local in the outer band of the generated schedule
3628 * and then check that the adjacent order constraint C[2,1]->D[2,0]
3629 * is enforced by the rest of the schedule.
3631 static int test_special_conditional_schedule_constraints(isl_ctx
*ctx
)
3634 isl_union_set
*domain
;
3635 isl_union_map
*validity
, *proximity
, *condition
;
3636 isl_union_map
*sink
, *source
, *dep
;
3637 isl_schedule_constraints
*sc
;
3638 isl_schedule
*schedule
;
3639 isl_union_access_info
*access
;
3640 isl_union_flow
*flow
;
3643 str
= "[n] -> { C[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3644 "A[k] : k >= 1 and k <= -1 + n; "
3645 "B[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3646 "D[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k }";
3647 domain
= isl_union_set_read_from_str(ctx
, str
);
3648 sc
= isl_schedule_constraints_on_domain(domain
);
3649 str
= "[n] -> { D[k, i] -> C[1 + k, k - i] : "
3650 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3651 "D[k, i] -> C[1 + k, i] : "
3652 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3653 "D[k, 0] -> C[1 + k, k] : k >= 1 and k <= -2 + n; "
3654 "D[k, 0] -> C[1 + k, 0] : k >= 1 and k <= -2 + n }";
3655 validity
= isl_union_map_read_from_str(ctx
, str
);
3656 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3657 str
= "[n] -> { C[k, i] -> D[k, i] : "
3658 "0 <= i <= -1 + k and k <= -1 + n }";
3659 proximity
= isl_union_map_read_from_str(ctx
, str
);
3660 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3661 str
= "[n] -> { [D[k, i] -> a[]] -> [C[1 + k, k - i] -> b[]] : "
3662 "i <= -1 + k and i >= 1 and k <= -2 + n; "
3663 "[B[k, i] -> c[]] -> [B[k, 1 + i] -> c[]] : "
3664 "k <= -1 + n and i >= 0 and i <= -2 + k }";
3665 condition
= isl_union_map_read_from_str(ctx
, str
);
3666 str
= "[n] -> { [B[k, i] -> e[]] -> [D[k, i] -> a[]] : "
3667 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3668 "[C[k, i] -> b[]] -> [D[k', -1 + k - i] -> a[]] : "
3669 "i >= 0 and i <= -1 + k and k <= -1 + n and "
3670 "k' <= -1 + n and k' >= k - i and k' >= 1 + k; "
3671 "[C[k, i] -> b[]] -> [D[k, -1 + k - i] -> a[]] : "
3672 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3673 "[B[k, i] -> c[]] -> [A[k'] -> d[]] : "
3674 "k <= -1 + n and i >= 0 and i <= -1 + k and "
3675 "k' >= 1 and k' <= -1 + n and k' >= 1 + k }";
3676 validity
= isl_union_map_read_from_str(ctx
, str
);
3677 sc
= isl_schedule_constraints_set_conditional_validity(sc
, condition
,
3679 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3680 str
= "{ D[2,0] -> [] }";
3681 sink
= isl_union_map_read_from_str(ctx
, str
);
3682 access
= isl_union_access_info_from_sink(sink
);
3683 str
= "{ C[2,1] -> [] }";
3684 source
= isl_union_map_read_from_str(ctx
, str
);
3685 access
= isl_union_access_info_set_must_source(access
, source
);
3686 access
= isl_union_access_info_set_schedule(access
, schedule
);
3687 flow
= isl_union_access_info_compute_flow(access
);
3688 dep
= isl_union_flow_get_must_dependence(flow
);
3689 isl_union_flow_free(flow
);
3690 empty
= isl_union_map_is_empty(dep
);
3691 isl_union_map_free(dep
);
3696 isl_die(ctx
, isl_error_unknown
,
3697 "conditional validity not respected", return -1);
3702 /* Check that the test for violated conditional validity constraints
3703 * is not confused by domain compression.
3704 * In particular, earlier versions of isl would apply
3705 * a schedule on the compressed domains to the original domains,
3706 * resulting in a failure to detect that the default schedule
3707 * violates the conditional validity constraints.
3709 static int test_special_conditional_schedule_constraints_2(isl_ctx
*ctx
)
3713 isl_union_set
*domain
;
3714 isl_union_map
*validity
, *condition
;
3715 isl_schedule_constraints
*sc
;
3716 isl_schedule
*schedule
;
3717 isl_union_map
*umap
;
3720 str
= "{ A[0, i] : 0 <= i <= 10; B[1, i] : 0 <= i <= 10 }";
3721 domain
= isl_union_set_read_from_str(ctx
, str
);
3722 sc
= isl_schedule_constraints_on_domain(domain
);
3723 str
= "{ B[1, i] -> A[0, i + 1] }";
3724 condition
= isl_union_map_read_from_str(ctx
, str
);
3725 str
= "{ A[0, i] -> B[1, i - 1] }";
3726 validity
= isl_union_map_read_from_str(ctx
, str
);
3727 sc
= isl_schedule_constraints_set_conditional_validity(sc
, condition
,
3728 isl_union_map_copy(validity
));
3729 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3730 umap
= isl_schedule_get_map(schedule
);
3731 isl_schedule_free(schedule
);
3732 validity
= isl_union_map_apply_domain(validity
,
3733 isl_union_map_copy(umap
));
3734 validity
= isl_union_map_apply_range(validity
, umap
);
3735 map
= isl_map_from_union_map(validity
);
3736 ge
= isl_map_lex_ge(isl_space_domain(isl_map_get_space(map
)));
3737 map
= isl_map_intersect(map
, ge
);
3738 empty
= isl_map_is_empty(map
);
3744 isl_die(ctx
, isl_error_unknown
,
3745 "conditional validity constraints not satisfied",
3751 /* Input for testing of schedule construction based on
3752 * conditional constraints.
3754 * domain is the iteration domain
3755 * flow are the flow dependences, which determine the validity and
3756 * proximity constraints
3757 * condition are the conditions on the conditional validity constraints
3758 * conditional_validity are the conditional validity constraints
3759 * outer_band_n is the expected number of members in the outer band
3764 const char *condition
;
3765 const char *conditional_validity
;
3767 } live_range_tests
[] = {
3768 /* Contrived example that illustrates that we need to keep
3769 * track of tagged condition dependences and
3770 * tagged conditional validity dependences
3771 * in isl_sched_edge separately.
3772 * In particular, the conditional validity constraints on A
3773 * cannot be satisfied,
3774 * but they can be ignored because there are no corresponding
3775 * condition constraints. However, we do have an additional
3776 * conditional validity constraint that maps to the same
3777 * dependence relation
3778 * as the condition constraint on B. If we did not make a distinction
3779 * between tagged condition and tagged conditional validity
3780 * dependences, then we
3781 * could end up treating this shared dependence as an condition
3782 * constraint on A, forcing a localization of the conditions,
3783 * which is impossible.
3785 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
3786 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
3787 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
3788 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3789 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3790 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
3793 /* TACO 2013 Fig. 7 */
3794 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3795 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3796 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3797 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
3798 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
3799 "0 <= i < n and 0 <= j < n - 1 }",
3800 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
3801 "0 <= i < n and 0 <= j < j' < n;"
3802 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
3803 "0 <= i < i' < n and 0 <= j,j' < n;"
3804 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
3805 "0 <= i,j,j' < n and j < j' }",
3808 /* TACO 2013 Fig. 7, without tags */
3809 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3810 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3811 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3812 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3813 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3814 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
3815 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
3816 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
3819 /* TACO 2013 Fig. 12 */
3820 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
3821 "S3[i,3] : 0 <= i <= 1 }",
3822 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
3823 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
3824 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
3825 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
3826 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3827 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
3828 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3829 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
3830 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
3831 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
3832 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
3837 /* Test schedule construction based on conditional constraints.
3838 * In particular, check the number of members in the outer band node
3839 * as an indication of whether tiling is possible or not.
3841 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
3844 isl_union_set
*domain
;
3845 isl_union_map
*condition
;
3846 isl_union_map
*flow
;
3847 isl_union_map
*validity
;
3848 isl_schedule_constraints
*sc
;
3849 isl_schedule
*schedule
;
3850 isl_schedule_node
*node
;
3853 if (test_special_conditional_schedule_constraints(ctx
) < 0)
3855 if (test_special_conditional_schedule_constraints_2(ctx
) < 0)
3858 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
3859 domain
= isl_union_set_read_from_str(ctx
,
3860 live_range_tests
[i
].domain
);
3861 flow
= isl_union_map_read_from_str(ctx
,
3862 live_range_tests
[i
].flow
);
3863 condition
= isl_union_map_read_from_str(ctx
,
3864 live_range_tests
[i
].condition
);
3865 validity
= isl_union_map_read_from_str(ctx
,
3866 live_range_tests
[i
].conditional_validity
);
3867 sc
= isl_schedule_constraints_on_domain(domain
);
3868 sc
= isl_schedule_constraints_set_validity(sc
,
3869 isl_union_map_copy(flow
));
3870 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
3871 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
3872 condition
, validity
);
3873 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3874 node
= isl_schedule_get_root(schedule
);
3876 isl_schedule_node_get_type(node
) != isl_schedule_node_band
)
3877 node
= isl_schedule_node_first_child(node
);
3878 n_member
= isl_schedule_node_band_n_member(node
);
3879 isl_schedule_node_free(node
);
3880 isl_schedule_free(schedule
);
3884 if (n_member
!= live_range_tests
[i
].outer_band_n
)
3885 isl_die(ctx
, isl_error_unknown
,
3886 "unexpected number of members in outer band",
3892 /* Check that the schedule computed for the given instance set and
3893 * dependence relation strongly satisfies the dependences.
3894 * In particular, check that no instance is scheduled before
3895 * or together with an instance on which it depends.
3896 * Earlier versions of isl would produce a schedule that
3897 * only weakly satisfies the dependences.
3899 static int test_strongly_satisfying_schedule(isl_ctx
*ctx
)
3901 const char *domain
, *dep
;
3902 isl_union_map
*D
, *schedule
;
3906 domain
= "{ B[i0, i1] : 0 <= i0 <= 1 and 0 <= i1 <= 11; "
3907 "A[i0] : 0 <= i0 <= 1 }";
3908 dep
= "{ B[i0, i1] -> B[i0, 1 + i1] : 0 <= i0 <= 1 and 0 <= i1 <= 10; "
3909 "B[0, 11] -> A[1]; A[i0] -> B[i0, 0] : 0 <= i0 <= 1 }";
3910 schedule
= compute_schedule(ctx
, domain
, dep
, dep
);
3911 D
= isl_union_map_read_from_str(ctx
, dep
);
3912 D
= isl_union_map_apply_domain(D
, isl_union_map_copy(schedule
));
3913 D
= isl_union_map_apply_range(D
, schedule
);
3914 map
= isl_map_from_union_map(D
);
3915 ge
= isl_map_lex_ge(isl_space_domain(isl_map_get_space(map
)));
3916 map
= isl_map_intersect(map
, ge
);
3917 empty
= isl_map_is_empty(map
);
3923 isl_die(ctx
, isl_error_unknown
,
3924 "dependences not strongly satisfied", return -1);
3929 /* Compute a schedule for input where the instance set constraints
3930 * conflict with the context constraints.
3931 * Earlier versions of isl did not properly handle this situation.
3933 static int test_conflicting_context_schedule(isl_ctx
*ctx
)
3935 isl_union_map
*schedule
;
3936 const char *domain
, *context
;
3938 domain
= "[n] -> { A[] : n >= 0 }";
3939 context
= "[n] -> { : n < 0 }";
3940 schedule
= compute_schedule_with_context(ctx
,
3941 domain
, "{}", "{}", context
);
3942 isl_union_map_free(schedule
);
3950 /* Check that the dependence carrying step is not confused by
3951 * a bound on the coefficient size.
3952 * In particular, force the scheduler to move to a dependence carrying
3953 * step by demanding outer coincidence and bound the size of
3954 * the coefficients. Earlier versions of isl would take this
3955 * bound into account while carrying dependences, breaking
3956 * fundamental assumptions.
3957 * On the other hand, the dependence carrying step now tries
3958 * to prevent loop coalescing by default, so check that indeed
3959 * no loop coalescing occurs by comparing the computed schedule
3960 * to the expected non-coalescing schedule.
3962 static int test_bounded_coefficients_schedule(isl_ctx
*ctx
)
3964 const char *domain
, *dep
;
3967 isl_schedule_constraints
*sc
;
3968 isl_schedule
*schedule
;
3969 isl_union_map
*sched1
, *sched2
;
3972 domain
= "{ C[i0, i1] : 2 <= i0 <= 3999 and 0 <= i1 <= -1 + i0 }";
3973 dep
= "{ C[i0, i1] -> C[i0, 1 + i1] : i0 <= 3999 and i1 >= 0 and "
3975 "C[i0, -1 + i0] -> C[1 + i0, 0] : i0 <= 3998 and i0 >= 1 }";
3976 I
= isl_union_set_read_from_str(ctx
, domain
);
3977 D
= isl_union_map_read_from_str(ctx
, dep
);
3978 sc
= isl_schedule_constraints_on_domain(I
);
3979 sc
= isl_schedule_constraints_set_validity(sc
, isl_union_map_copy(D
));
3980 sc
= isl_schedule_constraints_set_coincidence(sc
, D
);
3981 isl_options_set_schedule_outer_coincidence(ctx
, 1);
3982 isl_options_set_schedule_max_coefficient(ctx
, 20);
3983 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3984 isl_options_set_schedule_max_coefficient(ctx
, -1);
3985 isl_options_set_schedule_outer_coincidence(ctx
, 0);
3986 sched1
= isl_schedule_get_map(schedule
);
3987 isl_schedule_free(schedule
);
3989 sched2
= isl_union_map_read_from_str(ctx
, "{ C[x,y] -> [x,y] }");
3990 equal
= isl_union_map_is_equal(sched1
, sched2
);
3991 isl_union_map_free(sched1
);
3992 isl_union_map_free(sched2
);
3997 isl_die(ctx
, isl_error_unknown
,
3998 "unexpected schedule", return -1);
4003 /* Check that the bounds on the coefficients are respected.
4004 * This function checks for a particular output schedule,
4005 * but the exact output is not important, only that it does
4006 * not contain any coefficients greater than 4.
4007 * It is, however, easier to check for a particular output.
4008 * This test is only run for the whole component scheduler
4009 * because the incremental scheduler produces a slightly different schedule.
4011 static int test_bounded_coefficients_schedule_whole(isl_ctx
*ctx
)
4013 const char *domain
, *dep
, *str
;
4016 isl_schedule_constraints
*sc
;
4017 isl_schedule
*schedule
;
4018 isl_union_map
*sched1
, *sched2
;
4021 domain
= "{ S_4[i, j, k] : 0 <= i < j <= 10 and 0 <= k <= 100; "
4022 "S_2[i, j] : 0 <= i < j <= 10; S_6[i, j] : 0 <= i < j <= 10 }";
4023 dep
= "{ S_2[0, j] -> S_4[0, j, 0] : 0 < j <= 10; "
4024 "S_4[0, j, 100] -> S_6[0, j] : 0 < j <= 10 }";
4025 I
= isl_union_set_read_from_str(ctx
, domain
);
4026 D
= isl_union_map_read_from_str(ctx
, dep
);
4027 sc
= isl_schedule_constraints_on_domain(I
);
4028 sc
= isl_schedule_constraints_set_validity(sc
, D
);
4029 isl_options_set_schedule_max_constant_term(ctx
, 10);
4030 isl_options_set_schedule_max_coefficient(ctx
, 4);
4031 schedule
= isl_schedule_constraints_compute_schedule(sc
);
4032 isl_options_set_schedule_max_coefficient(ctx
, -1);
4033 isl_options_set_schedule_max_constant_term(ctx
, -1);
4034 sched1
= isl_schedule_get_map(schedule
);
4035 isl_schedule_free(schedule
);
4037 str
= "{ S_4[i, j, k] -> [i, j, 10 - k]; "
4038 "S_2[i, j] -> [0, i, j]; S_6[i, j] -> [0, 10 + i, j] }";
4039 sched2
= isl_union_map_read_from_str(ctx
, str
);
4040 equal
= isl_union_map_is_equal(sched1
, sched2
);
4041 isl_union_map_free(sched1
);
4042 isl_union_map_free(sched2
);
4047 isl_die(ctx
, isl_error_unknown
,
4048 "unexpected schedule", return -1);
4053 /* Check that a set of schedule constraints that only allow for
4054 * a coalescing schedule still produces a schedule even if the user
4055 * request a non-coalescing schedule. Earlier versions of isl
4056 * would not handle this case correctly.
4058 static int test_coalescing_schedule(isl_ctx
*ctx
)
4060 const char *domain
, *dep
;
4063 isl_schedule_constraints
*sc
;
4064 isl_schedule
*schedule
;
4065 int treat_coalescing
;
4067 domain
= "{ S[a, b] : 0 <= a <= 1 and 0 <= b <= 1 }";
4068 dep
= "{ S[a, b] -> S[a + b, 1 - b] }";
4069 I
= isl_union_set_read_from_str(ctx
, domain
);
4070 D
= isl_union_map_read_from_str(ctx
, dep
);
4071 sc
= isl_schedule_constraints_on_domain(I
);
4072 sc
= isl_schedule_constraints_set_validity(sc
, D
);
4073 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4074 isl_options_set_schedule_treat_coalescing(ctx
, 1);
4075 schedule
= isl_schedule_constraints_compute_schedule(sc
);
4076 isl_options_set_schedule_treat_coalescing(ctx
, treat_coalescing
);
4077 isl_schedule_free(schedule
);
4083 /* Check that the scheduler does not perform any needless
4084 * compound skewing. Earlier versions of isl would compute
4085 * schedules in terms of transformed schedule coefficients and
4086 * would not accurately keep track of the sum of the original
4087 * schedule coefficients. It could then produce the schedule
4088 * S[t,i,j,k] -> [t, 2t + i, 2t + i + j, 2t + i + j + k]
4089 * for the input below instead of the schedule below.
4091 static int test_skewing_schedule(isl_ctx
*ctx
)
4093 const char *D
, *V
, *P
, *S
;
4095 D
= "[n] -> { S[t,i,j,k] : 0 <= t,i,j,k < n }";
4096 V
= "[n] -> { S[t,i,j,k] -> S[t+1,a,b,c] : 0 <= t,i,j,k,a,b,c < n and "
4097 "-2 <= a-i <= 2 and -1 <= a-i + b-j <= 1 and "
4098 "-1 <= a-i + b-j + c-k <= 1 }";
4100 S
= "{ S[t,i,j,k] -> [t, 2t + i, t + i + j, 2t + k] }";
4102 return test_special_schedule(ctx
, D
, V
, P
, S
);
4105 int test_schedule(isl_ctx
*ctx
)
4107 const char *D
, *W
, *R
, *V
, *P
, *S
;
4108 int max_coincidence
;
4109 int treat_coalescing
;
4111 /* Handle resulting schedule with zero bands. */
4112 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
4116 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
4117 W
= "{ S1[t,i] -> a[t,i] }";
4118 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
4119 "S1[t,i] -> a[t-1,i+1] }";
4120 S
= "{ S1[t,i] -> [t,i] }";
4121 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
4124 /* Fig. 5 of CC2008 */
4125 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
4127 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
4128 "j >= 2 and j <= -1 + N }";
4129 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
4130 "j >= 2 and j <= -1 + N; "
4131 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
4132 "j >= 2 and j <= -1 + N }";
4133 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
4134 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
4137 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
4138 W
= "{ S1[i] -> a[i] }";
4139 R
= "{ S2[i] -> a[i+1] }";
4140 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
4141 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
4144 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
4145 W
= "{ S1[i] -> a[i] }";
4146 R
= "{ S2[i] -> a[9-i] }";
4147 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
4148 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
4151 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
4152 W
= "{ S1[i] -> a[i] }";
4153 R
= "[N] -> { S2[i] -> a[N-1-i] }";
4154 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
4155 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
4158 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
4159 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
4160 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
4161 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
4162 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4165 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
4166 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
4167 R
= "{ S2[i,j] -> a[i-1,j] }";
4168 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
4169 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
4172 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
4173 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
4174 R
= "{ S2[i,j] -> a[i,j-1] }";
4175 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
4176 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
4179 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
4180 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
4181 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
4182 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
4183 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
4184 "S_0[] -> [0, 0, 0] }";
4185 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
4187 ctx
->opt
->schedule_parametric
= 0;
4188 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4190 ctx
->opt
->schedule_parametric
= 1;
4192 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
4193 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
4194 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
4195 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
4196 "S4[i] -> a[i,N] }";
4197 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
4198 "S4[i] -> [4,i,0] }";
4199 max_coincidence
= isl_options_get_schedule_maximize_coincidence(ctx
);
4200 isl_options_set_schedule_maximize_coincidence(ctx
, 0);
4201 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
4203 isl_options_set_schedule_maximize_coincidence(ctx
, max_coincidence
);
4205 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
4206 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
4208 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
4210 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
4212 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
4213 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4216 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
4217 " S_2[t] : t >= 0 and t <= -1 + N; "
4218 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
4220 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
4221 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
4222 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
4223 "i >= 0 and i <= -1 + N }";
4224 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
4225 "i >= 0 and i <= -1 + N; "
4226 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
4227 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
4228 " S_0[t] -> [0, t, 0] }";
4230 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
4232 ctx
->opt
->schedule_parametric
= 0;
4233 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4235 ctx
->opt
->schedule_parametric
= 1;
4237 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
4238 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
4239 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
4242 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
4243 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
4244 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
4245 "j >= 0 and j <= -1 + N; "
4246 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
4247 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
4248 "j >= 0 and j <= -1 + N; "
4249 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
4250 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
4251 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4254 D
= "{ S_0[i] : i >= 0 }";
4255 W
= "{ S_0[i] -> a[i] : i >= 0 }";
4256 R
= "{ S_0[i] -> a[0] : i >= 0 }";
4257 S
= "{ S_0[i] -> [0, i, 0] }";
4258 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4261 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
4262 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
4263 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
4264 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
4265 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4268 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
4269 "k <= -1 + n and k >= 0 }";
4270 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
4271 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
4272 "k <= -1 + n and k >= 0; "
4273 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
4274 "k <= -1 + n and k >= 0; "
4275 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
4276 "k <= -1 + n and k >= 0 }";
4277 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
4278 ctx
->opt
->schedule_outer_coincidence
= 1;
4279 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4281 ctx
->opt
->schedule_outer_coincidence
= 0;
4283 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
4284 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
4285 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
4286 "Stmt_for_body24[i0, i1, 1, 0]:"
4287 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
4288 "Stmt_for_body7[i0, i1, i2]:"
4289 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
4292 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
4293 "Stmt_for_body24[1, i1, i2, i3]:"
4294 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
4296 "Stmt_for_body24[0, i1, i2, i3] -> "
4297 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
4298 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
4300 "Stmt_for_body24[0, i1, i2, i3] ->"
4301 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
4302 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
4303 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
4304 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
4305 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
4306 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
4307 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
4308 "i1 <= 6 and i1 >= 0;"
4309 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
4310 "Stmt_for_body7[i0, i1, i2] -> "
4311 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
4312 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
4313 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
4314 "Stmt_for_body7[i0, i1, i2] -> "
4315 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
4316 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
4317 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
4320 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4321 isl_options_set_schedule_treat_coalescing(ctx
, 0);
4322 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4324 isl_options_set_schedule_treat_coalescing(ctx
, treat_coalescing
);
4326 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
4327 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
4328 "j >= 1 and j <= 7;"
4329 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
4330 "j >= 1 and j <= 8 }";
4332 S
= "{ S_0[i, j] -> [i + j, i] }";
4333 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4334 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4336 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4338 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
4339 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
4340 "j >= 0 and j <= -1 + i }";
4341 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
4342 "i <= -1 + N and j >= 0;"
4343 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
4346 S
= "{ S_0[i, j] -> [i, j] }";
4347 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4348 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4350 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4352 /* Test both algorithms on a case with only proximity dependences. */
4353 D
= "{ S[i,j] : 0 <= i <= 10 }";
4355 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
4356 S
= "{ S[i, j] -> [j, i] }";
4357 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4358 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4360 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4361 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4364 D
= "{ A[a]; B[] }";
4366 P
= "{ A[a] -> B[] }";
4367 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4370 if (test_padded_schedule(ctx
) < 0)
4373 /* Check that check for progress is not confused by rational
4376 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
4377 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
4379 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
4380 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
4382 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4383 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4385 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4387 /* Check that we allow schedule rows that are only non-trivial
4388 * on some full-dimensional domains.
4390 D
= "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
4391 V
= "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
4392 "S1[j] -> S2[1] : 0 <= j <= 1 }";
4394 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4395 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4397 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4399 if (test_conditional_schedule_constraints(ctx
) < 0)
4402 if (test_strongly_satisfying_schedule(ctx
) < 0)
4405 if (test_conflicting_context_schedule(ctx
) < 0)
4408 if (test_bounded_coefficients_schedule(ctx
) < 0)
4410 if (test_coalescing_schedule(ctx
) < 0)
4412 if (test_skewing_schedule(ctx
) < 0)
4418 /* Perform scheduling tests using the whole component scheduler.
4420 static int test_schedule_whole(isl_ctx
*ctx
)
4425 whole
= isl_options_get_schedule_whole_component(ctx
);
4426 isl_options_set_schedule_whole_component(ctx
, 1);
4427 r
= test_schedule(ctx
);
4429 r
= test_bounded_coefficients_schedule_whole(ctx
);
4430 isl_options_set_schedule_whole_component(ctx
, whole
);
4435 /* Perform scheduling tests using the incremental scheduler.
4437 static int test_schedule_incremental(isl_ctx
*ctx
)
4442 whole
= isl_options_get_schedule_whole_component(ctx
);
4443 isl_options_set_schedule_whole_component(ctx
, 0);
4444 r
= test_schedule(ctx
);
4445 isl_options_set_schedule_whole_component(ctx
, whole
);
4450 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
4452 isl_union_map
*umap
;
4455 umap
= isl_union_map_read_from_str(ctx
, str
);
4456 test
= isl_union_map_plain_is_injective(umap
);
4457 isl_union_map_free(umap
);
4460 if (test
== injective
)
4463 isl_die(ctx
, isl_error_unknown
,
4464 "map not detected as injective", return -1);
4466 isl_die(ctx
, isl_error_unknown
,
4467 "map detected as injective", return -1);
4470 int test_injective(isl_ctx
*ctx
)
4474 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
4476 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
4478 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
4480 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
4482 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
4484 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
4486 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
4488 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
4491 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
4492 if (test_plain_injective(ctx
, str
, 1))
4494 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
4495 if (test_plain_injective(ctx
, str
, 0))
4501 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
4509 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
4510 equal
= isl_aff_plain_is_equal(aff
, aff2
);
4516 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
4520 equal
= aff_plain_is_equal(aff
, str
);
4524 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
4525 "result not as expected", return -1);
4529 /* Is "upa" obviously equal to the isl_union_pw_aff represented by "str"?
4531 static isl_bool
union_pw_aff_plain_is_equal(__isl_keep isl_union_pw_aff
*upa
,
4535 isl_union_pw_aff
*upa2
;
4539 return isl_bool_error
;
4541 ctx
= isl_union_pw_aff_get_ctx(upa
);
4542 upa2
= isl_union_pw_aff_read_from_str(ctx
, str
);
4543 equal
= isl_union_pw_aff_plain_is_equal(upa
, upa2
);
4544 isl_union_pw_aff_free(upa2
);
4549 /* Check that "upa" is obviously equal to the isl_union_pw_aff
4550 * represented by "str".
4552 static isl_stat
union_pw_aff_check_plain_equal(__isl_keep isl_union_pw_aff
*upa
,
4557 equal
= union_pw_aff_plain_is_equal(upa
, str
);
4559 return isl_stat_error
;
4561 isl_die(isl_union_pw_aff_get_ctx(upa
), isl_error_unknown
,
4562 "result not as expected", return isl_stat_error
);
4566 /* Basic tests on isl_union_pw_aff.
4568 * In particular, check that isl_union_pw_aff_aff_on_domain
4569 * aligns the parameters of the input objects and
4570 * that isl_union_pw_aff_param_on_domain_id properly
4571 * introduces the parameter.
4573 static int test_upa(isl_ctx
*ctx
)
4578 isl_union_set
*domain
;
4579 isl_union_pw_aff
*upa
;
4582 aff
= isl_aff_read_from_str(ctx
, "[N] -> { [N] }");
4583 str
= "[M] -> { A[i] : 0 <= i < M; B[] }";
4584 domain
= isl_union_set_read_from_str(ctx
, str
);
4585 upa
= isl_union_pw_aff_aff_on_domain(domain
, aff
);
4586 str
= "[N, M] -> { A[i] -> [N] : 0 <= i < M; B[] -> [N] }";
4587 ok
= union_pw_aff_check_plain_equal(upa
, str
);
4588 isl_union_pw_aff_free(upa
);
4592 id
= isl_id_alloc(ctx
, "N", NULL
);
4593 str
= "[M] -> { A[i] : 0 <= i < M; B[] }";
4594 domain
= isl_union_set_read_from_str(ctx
, str
);
4595 upa
= isl_union_pw_aff_param_on_domain_id(domain
, id
);
4596 str
= "[N, M] -> { A[i] -> [N] : 0 <= i < M; B[] -> [N] }";
4597 ok
= union_pw_aff_check_plain_equal(upa
, str
);
4598 isl_union_pw_aff_free(upa
);
4606 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
4607 __isl_take isl_aff
*aff2
);
4609 ['+'] = { &isl_aff_add
},
4610 ['-'] = { &isl_aff_sub
},
4611 ['*'] = { &isl_aff_mul
},
4612 ['/'] = { &isl_aff_div
},
4620 } aff_bin_tests
[] = {
4621 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
4622 "{ [i] -> [2i] }" },
4623 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
4625 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
4626 "{ [i] -> [2i] }" },
4627 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
4628 "{ [i] -> [2i] }" },
4629 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
4630 "{ [i] -> [i/2] }" },
4631 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
4633 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
4634 "{ [i] -> [NaN] }" },
4635 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
4636 "{ [i] -> [NaN] }" },
4637 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
4638 "{ [i] -> [NaN] }" },
4639 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
4640 "{ [i] -> [NaN] }" },
4641 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
4642 "{ [i] -> [NaN] }" },
4643 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
4644 "{ [i] -> [NaN] }" },
4645 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
4646 "{ [i] -> [NaN] }" },
4647 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
4648 "{ [i] -> [NaN] }" },
4649 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
4650 "{ [i] -> [NaN] }" },
4651 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
4652 "{ [i] -> [NaN] }" },
4653 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
4654 "{ [i] -> [NaN] }" },
4655 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
4656 "{ [i] -> [NaN] }" },
4659 /* Perform some basic tests of binary operations on isl_aff objects.
4661 static int test_bin_aff(isl_ctx
*ctx
)
4664 isl_aff
*aff1
, *aff2
, *res
;
4665 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
4666 __isl_take isl_aff
*aff2
);
4669 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
4670 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
4671 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
4672 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
4673 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
4674 aff1
= fn(aff1
, aff2
);
4675 if (isl_aff_is_nan(res
))
4676 ok
= isl_aff_is_nan(aff1
);
4678 ok
= isl_aff_plain_is_equal(aff1
, res
);
4684 isl_die(ctx
, isl_error_unknown
,
4685 "unexpected result", return -1);
4692 __isl_give isl_pw_aff
*(*fn
)(__isl_take isl_pw_aff
*pa1
,
4693 __isl_take isl_pw_aff
*pa2
);
4694 } pw_aff_bin_op
[] = {
4695 ['m'] = { &isl_pw_aff_min
},
4696 ['M'] = { &isl_pw_aff_max
},
4699 /* Inputs for binary isl_pw_aff operation tests.
4700 * "arg1" and "arg2" are the two arguments, "op" identifies the operation
4701 * defined by pw_aff_bin_op, and "res" is the expected result.
4708 } pw_aff_bin_tests
[] = {
4709 { "{ [i] -> [i] }", 'm', "{ [i] -> [i] }",
4711 { "{ [i] -> [i] }", 'M', "{ [i] -> [i] }",
4713 { "{ [i] -> [i] }", 'm', "{ [i] -> [0] }",
4714 "{ [i] -> [i] : i <= 0; [i] -> [0] : i > 0 }" },
4715 { "{ [i] -> [i] }", 'M', "{ [i] -> [0] }",
4716 "{ [i] -> [i] : i >= 0; [i] -> [0] : i < 0 }" },
4717 { "{ [i] -> [i] }", 'm', "{ [i] -> [NaN] }",
4718 "{ [i] -> [NaN] }" },
4719 { "{ [i] -> [NaN] }", 'm', "{ [i] -> [i] }",
4720 "{ [i] -> [NaN] }" },
4723 /* Perform some basic tests of binary operations on isl_pw_aff objects.
4725 static int test_bin_pw_aff(isl_ctx
*ctx
)
4729 isl_pw_aff
*pa1
, *pa2
, *res
;
4731 for (i
= 0; i
< ARRAY_SIZE(pw_aff_bin_tests
); ++i
) {
4732 pa1
= isl_pw_aff_read_from_str(ctx
, pw_aff_bin_tests
[i
].arg1
);
4733 pa2
= isl_pw_aff_read_from_str(ctx
, pw_aff_bin_tests
[i
].arg2
);
4734 res
= isl_pw_aff_read_from_str(ctx
, pw_aff_bin_tests
[i
].res
);
4735 pa1
= pw_aff_bin_op
[pw_aff_bin_tests
[i
].op
].fn(pa1
, pa2
);
4736 if (isl_pw_aff_involves_nan(res
))
4737 ok
= isl_pw_aff_involves_nan(pa1
);
4739 ok
= isl_pw_aff_plain_is_equal(pa1
, res
);
4740 isl_pw_aff_free(pa1
);
4741 isl_pw_aff_free(res
);
4745 isl_die(ctx
, isl_error_unknown
,
4746 "unexpected result", return -1);
4753 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4754 __isl_take isl_union_pw_multi_aff
*upma1
,
4755 __isl_take isl_union_pw_multi_aff
*upma2
);
4759 } upma_bin_tests
[] = {
4760 { &isl_union_pw_multi_aff_add
, "{ A[] -> [0]; B[0] -> [1] }",
4761 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
4762 { &isl_union_pw_multi_aff_union_add
, "{ A[] -> [0]; B[0] -> [1] }",
4763 "{ B[x] -> [2] : x >= 0 }",
4764 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
4765 { &isl_union_pw_multi_aff_pullback_union_pw_multi_aff
,
4766 "{ A[] -> B[0]; C[x] -> B[1] : x < 10; C[y] -> B[2] : y >= 10 }",
4767 "{ D[i] -> A[] : i < 0; D[i] -> C[i + 5] : i >= 0 }",
4768 "{ D[i] -> B[0] : i < 0; D[i] -> B[1] : 0 <= i < 5; "
4769 "D[i] -> B[2] : i >= 5 }" },
4770 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4771 "{ B[x] -> C[2] : x > 0 }",
4772 "{ B[x] -> A[1] : x <= 0; B[x] -> C[2] : x > 0 }" },
4773 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4774 "{ B[x] -> A[2] : x >= 0 }",
4775 "{ B[x] -> A[1] : x < 0; B[x] -> A[2] : x > 0; B[0] -> A[3] }" },
4778 /* Perform some basic tests of binary operations on
4779 * isl_union_pw_multi_aff objects.
4781 static int test_bin_upma(isl_ctx
*ctx
)
4784 isl_union_pw_multi_aff
*upma1
, *upma2
, *res
;
4787 for (i
= 0; i
< ARRAY_SIZE(upma_bin_tests
); ++i
) {
4788 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4789 upma_bin_tests
[i
].arg1
);
4790 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4791 upma_bin_tests
[i
].arg2
);
4792 res
= isl_union_pw_multi_aff_read_from_str(ctx
,
4793 upma_bin_tests
[i
].res
);
4794 upma1
= upma_bin_tests
[i
].fn(upma1
, upma2
);
4795 ok
= isl_union_pw_multi_aff_plain_is_equal(upma1
, res
);
4796 isl_union_pw_multi_aff_free(upma1
);
4797 isl_union_pw_multi_aff_free(res
);
4801 isl_die(ctx
, isl_error_unknown
,
4802 "unexpected result", return -1);
4809 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4810 __isl_take isl_union_pw_multi_aff
*upma1
,
4811 __isl_take isl_union_pw_multi_aff
*upma2
);
4814 } upma_bin_fail_tests
[] = {
4815 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4816 "{ B[x] -> C[2] : x >= 0 }" },
4819 /* Perform some basic tests of binary operations on
4820 * isl_union_pw_multi_aff objects that are expected to fail.
4822 static int test_bin_upma_fail(isl_ctx
*ctx
)
4825 isl_union_pw_multi_aff
*upma1
, *upma2
;
4828 on_error
= isl_options_get_on_error(ctx
);
4829 isl_options_set_on_error(ctx
, ISL_ON_ERROR_CONTINUE
);
4830 n
= ARRAY_SIZE(upma_bin_fail_tests
);
4831 for (i
= 0; i
< n
; ++i
) {
4832 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4833 upma_bin_fail_tests
[i
].arg1
);
4834 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4835 upma_bin_fail_tests
[i
].arg2
);
4836 upma1
= upma_bin_fail_tests
[i
].fn(upma1
, upma2
);
4837 isl_union_pw_multi_aff_free(upma1
);
4841 isl_options_set_on_error(ctx
, on_error
);
4843 isl_die(ctx
, isl_error_unknown
,
4844 "operation not expected to succeed", return -1);
4849 /* Inputs for basic tests of binary operations on
4850 * pairs of isl_multi_union_pw_aff and isl_union_set objects.
4851 * "fn" is the function that is tested.
4852 * "arg1" and "arg2" are string descriptions of the inputs.
4853 * "res" is a string description of the expected result.
4856 __isl_give isl_multi_union_pw_aff
*(*fn
)(
4857 __isl_take isl_multi_union_pw_aff
*mupa
,
4858 __isl_take isl_union_set
*uset
);
4862 } mupa_uset_tests
[] = {
4863 { &isl_multi_union_pw_aff_intersect_domain
,
4864 "C[{ B[i,j] -> [i + 2j] }]", "{ B[i,i] }",
4865 "C[{ B[i,i] -> [3i] }]" },
4868 /* Perform some basic tests of binary operations on
4869 * pairs of isl_multi_union_pw_aff and isl_union_set objects.
4871 static int test_mupa_uset(isl_ctx
*ctx
)
4875 isl_multi_union_pw_aff
*mupa
, *res
;
4876 isl_union_set
*uset
;
4878 for (i
= 0; i
< ARRAY_SIZE(mupa_uset_tests
); ++i
) {
4879 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
,
4880 mupa_uset_tests
[i
].arg1
);
4881 uset
= isl_union_set_read_from_str(ctx
,
4882 mupa_uset_tests
[i
].arg2
);
4883 res
= isl_multi_union_pw_aff_read_from_str(ctx
,
4884 mupa_uset_tests
[i
].res
);
4885 mupa
= mupa_uset_tests
[i
].fn(mupa
, uset
);
4886 ok
= isl_multi_union_pw_aff_plain_is_equal(mupa
, res
);
4887 isl_multi_union_pw_aff_free(mupa
);
4888 isl_multi_union_pw_aff_free(res
);
4892 isl_die(ctx
, isl_error_unknown
,
4893 "unexpected result", return -1);
4899 /* Check that the input tuple of an isl_aff can be set properly.
4901 static isl_stat
test_aff_set_tuple_id(isl_ctx
*ctx
)
4907 aff
= isl_aff_read_from_str(ctx
, "{ [x] -> [x + 1] }");
4908 id
= isl_id_alloc(ctx
, "A", NULL
);
4909 aff
= isl_aff_set_tuple_id(aff
, isl_dim_in
, id
);
4910 equal
= aff_check_plain_equal(aff
, "{ A[x] -> [x + 1] }");
4913 return isl_stat_error
;
4918 int test_aff(isl_ctx
*ctx
)
4923 isl_local_space
*ls
;
4927 if (test_upa(ctx
) < 0)
4929 if (test_bin_aff(ctx
) < 0)
4931 if (test_bin_pw_aff(ctx
) < 0)
4933 if (test_bin_upma(ctx
) < 0)
4935 if (test_bin_upma_fail(ctx
) < 0)
4937 if (test_mupa_uset(ctx
) < 0)
4940 space
= isl_space_set_alloc(ctx
, 0, 1);
4941 ls
= isl_local_space_from_space(space
);
4942 aff
= isl_aff_zero_on_domain(ls
);
4944 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4945 aff
= isl_aff_scale_down_ui(aff
, 3);
4946 aff
= isl_aff_floor(aff
);
4947 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4948 aff
= isl_aff_scale_down_ui(aff
, 2);
4949 aff
= isl_aff_floor(aff
);
4950 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4953 set
= isl_set_read_from_str(ctx
, str
);
4954 aff
= isl_aff_gist(aff
, set
);
4956 aff
= isl_aff_add_constant_si(aff
, -16);
4957 zero
= isl_aff_plain_is_zero(aff
);
4963 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4965 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
4966 aff
= isl_aff_scale_down_ui(aff
, 64);
4967 aff
= isl_aff_floor(aff
);
4968 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
4973 if (test_aff_set_tuple_id(ctx
) < 0)
4979 /* Check that "pa" consists of a single expression.
4981 static int check_single_piece(isl_ctx
*ctx
, __isl_take isl_pw_aff
*pa
)
4985 n
= isl_pw_aff_n_piece(pa
);
4986 isl_pw_aff_free(pa
);
4991 isl_die(ctx
, isl_error_unknown
, "expecting single expression",
4997 /* Check that the computation below results in a single expression.
4998 * One or two expressions may result depending on which constraint
4999 * ends up being considered as redundant with respect to the other
5000 * constraints after the projection that is performed internally
5001 * by isl_set_dim_min.
5003 static int test_dim_max_1(isl_ctx
*ctx
)
5009 str
= "[n] -> { [a, b] : n >= 0 and 4a >= -4 + n and b >= 0 and "
5010 "-4a <= b <= 3 and b < n - 4a }";
5011 set
= isl_set_read_from_str(ctx
, str
);
5012 pa
= isl_set_dim_min(set
, 0);
5013 return check_single_piece(ctx
, pa
);
5016 /* Check that the computation below results in a single expression.
5017 * The PIP problem corresponding to these constraints has a row
5018 * that causes a split of the solution domain. The solver should
5019 * first pick rows that split off empty parts such that the actual
5020 * solution domain does not get split.
5021 * Note that the description contains some redundant constraints.
5022 * If these constraints get removed first, then the row mentioned
5023 * above does not appear in the PIP problem.
5025 static int test_dim_max_2(isl_ctx
*ctx
)
5031 str
= "[P, N] -> { [a] : a < N and a >= 0 and N > P and a <= P and "
5032 "N > 0 and P >= 0 }";
5033 set
= isl_set_read_from_str(ctx
, str
);
5034 pa
= isl_set_dim_max(set
, 0);
5035 return check_single_piece(ctx
, pa
);
5038 int test_dim_max(isl_ctx
*ctx
)
5042 isl_set
*set1
, *set2
;
5047 if (test_dim_max_1(ctx
) < 0)
5049 if (test_dim_max_2(ctx
) < 0)
5052 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
5053 set
= isl_set_read_from_str(ctx
, str
);
5054 pwaff
= isl_set_dim_max(set
, 0);
5055 set1
= isl_set_from_pw_aff(pwaff
);
5056 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
5057 set2
= isl_set_read_from_str(ctx
, str
);
5058 equal
= isl_set_is_equal(set1
, set2
);
5064 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5066 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
5067 set
= isl_set_read_from_str(ctx
, str
);
5068 pwaff
= isl_set_dim_max(set
, 0);
5069 set1
= isl_set_from_pw_aff(pwaff
);
5070 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
5071 set2
= isl_set_read_from_str(ctx
, str
);
5072 equal
= isl_set_is_equal(set1
, set2
);
5078 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5080 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
5081 set
= isl_set_read_from_str(ctx
, str
);
5082 pwaff
= isl_set_dim_max(set
, 0);
5083 set1
= isl_set_from_pw_aff(pwaff
);
5084 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
5085 set2
= isl_set_read_from_str(ctx
, str
);
5086 equal
= isl_set_is_equal(set1
, set2
);
5092 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5094 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
5095 "0 <= i < N and 0 <= j < M }";
5096 map
= isl_map_read_from_str(ctx
, str
);
5097 set
= isl_map_range(map
);
5099 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
5100 set1
= isl_set_from_pw_aff(pwaff
);
5101 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
5102 set2
= isl_set_read_from_str(ctx
, str
);
5103 equal
= isl_set_is_equal(set1
, set2
);
5107 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
5108 set1
= isl_set_from_pw_aff(pwaff
);
5109 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
5110 set2
= isl_set_read_from_str(ctx
, str
);
5111 if (equal
>= 0 && equal
)
5112 equal
= isl_set_is_equal(set1
, set2
);
5121 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5123 /* Check that solutions are properly merged. */
5124 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
5125 "c <= -1 + n - 4a - 2b and c >= -2b and "
5126 "4a >= -4 + n and c >= 0 }";
5127 set
= isl_set_read_from_str(ctx
, str
);
5128 pwaff
= isl_set_dim_min(set
, 2);
5129 set1
= isl_set_from_pw_aff(pwaff
);
5130 str
= "[n] -> { [(0)] : n >= 1 }";
5131 set2
= isl_set_read_from_str(ctx
, str
);
5132 equal
= isl_set_is_equal(set1
, set2
);
5139 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5141 /* Check that empty solution lie in the right space. */
5142 str
= "[n] -> { [t,a] : 1 = 0 }";
5143 set
= isl_set_read_from_str(ctx
, str
);
5144 pwaff
= isl_set_dim_max(set
, 0);
5145 set1
= isl_set_from_pw_aff(pwaff
);
5146 str
= "[n] -> { [t] : 1 = 0 }";
5147 set2
= isl_set_read_from_str(ctx
, str
);
5148 equal
= isl_set_is_equal(set1
, set2
);
5155 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5160 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
5162 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
5166 isl_pw_multi_aff
*pma2
;
5172 ctx
= isl_pw_multi_aff_get_ctx(pma
);
5173 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5174 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
5175 isl_pw_multi_aff_free(pma2
);
5180 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
5181 * represented by "str".
5183 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
5188 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
5192 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
5193 "result not as expected", return -1);
5197 /* Basic test for isl_pw_multi_aff_product.
5199 * Check that multiple pieces are properly handled.
5201 static int test_product_pma(isl_ctx
*ctx
)
5205 isl_pw_multi_aff
*pma1
, *pma2
;
5207 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
5208 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5209 str
= "{ C[] -> D[] }";
5210 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5211 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
5212 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
5213 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
5214 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
5215 isl_pw_multi_aff_free(pma1
);
5222 int test_product(isl_ctx
*ctx
)
5226 isl_union_set
*uset1
, *uset2
;
5230 set
= isl_set_read_from_str(ctx
, str
);
5231 set
= isl_set_product(set
, isl_set_copy(set
));
5232 ok
= isl_set_is_wrapping(set
);
5237 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5240 uset1
= isl_union_set_read_from_str(ctx
, str
);
5241 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
5242 str
= "{ [[] -> []] }";
5243 uset2
= isl_union_set_read_from_str(ctx
, str
);
5244 ok
= isl_union_set_is_equal(uset1
, uset2
);
5245 isl_union_set_free(uset1
);
5246 isl_union_set_free(uset2
);
5250 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5252 if (test_product_pma(ctx
) < 0)
5258 /* Check that two sets are not considered disjoint just because
5259 * they have a different set of (named) parameters.
5261 static int test_disjoint(isl_ctx
*ctx
)
5264 isl_set
*set
, *set2
;
5267 str
= "[n] -> { [[]->[]] }";
5268 set
= isl_set_read_from_str(ctx
, str
);
5269 str
= "{ [[]->[]] }";
5270 set2
= isl_set_read_from_str(ctx
, str
);
5271 disjoint
= isl_set_is_disjoint(set
, set2
);
5277 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5282 /* Inputs for isl_pw_multi_aff_is_equal tests.
5283 * "f1" and "f2" are the two function that need to be compared.
5284 * "equal" is the expected result.
5290 } pma_equal_tests
[] = {
5291 { 1, "[N] -> { [floor(N/2)] : 0 <= N <= 1 }",
5292 "[N] -> { [0] : 0 <= N <= 1 }" },
5293 { 1, "[N] -> { [floor(N/2)] : 0 <= N <= 2 }",
5294 "[N] -> { [0] : 0 <= N <= 1; [1] : N = 2 }" },
5295 { 0, "[N] -> { [floor(N/2)] : 0 <= N <= 2 }",
5296 "[N] -> { [0] : 0 <= N <= 1 }" },
5297 { 0, "{ [NaN] }", "{ [NaN] }" },
5300 int test_equal(isl_ctx
*ctx
)
5304 isl_set
*set
, *set2
;
5308 set
= isl_set_read_from_str(ctx
, str
);
5310 set2
= isl_set_read_from_str(ctx
, str
);
5311 equal
= isl_set_is_equal(set
, set2
);
5317 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5319 for (i
= 0; i
< ARRAY_SIZE(pma_equal_tests
); ++i
) {
5320 int expected
= pma_equal_tests
[i
].equal
;
5321 isl_pw_multi_aff
*f1
, *f2
;
5323 f1
= isl_pw_multi_aff_read_from_str(ctx
, pma_equal_tests
[i
].f1
);
5324 f2
= isl_pw_multi_aff_read_from_str(ctx
, pma_equal_tests
[i
].f2
);
5325 equal
= isl_pw_multi_aff_is_equal(f1
, f2
);
5326 isl_pw_multi_aff_free(f1
);
5327 isl_pw_multi_aff_free(f2
);
5330 if (equal
!= expected
)
5331 isl_die(ctx
, isl_error_unknown
,
5332 "unexpected equality result", return -1);
5338 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
5339 enum isl_dim_type type
, unsigned pos
, int fixed
)
5343 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
5350 isl_die(ctx
, isl_error_unknown
,
5351 "map not detected as fixed", return -1);
5353 isl_die(ctx
, isl_error_unknown
,
5354 "map detected as fixed", return -1);
5357 int test_fixed(isl_ctx
*ctx
)
5362 str
= "{ [i] -> [i] }";
5363 map
= isl_map_read_from_str(ctx
, str
);
5364 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
5366 str
= "{ [i] -> [1] }";
5367 map
= isl_map_read_from_str(ctx
, str
);
5368 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
5370 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
5371 map
= isl_map_read_from_str(ctx
, str
);
5372 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
5374 map
= isl_map_read_from_str(ctx
, str
);
5375 map
= isl_map_neg(map
);
5376 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
5382 struct isl_vertices_test_data
{
5385 const char *vertex
[6];
5386 } vertices_tests
[] = {
5387 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
5388 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
5389 { "{ A[t, i] : t = 14 and i = 1 }",
5390 1, { "{ A[14, 1] }" } },
5391 { "[n, m] -> { [a, b, c] : b <= a and a <= n and b > 0 and c >= b and "
5392 "c <= m and m <= n and m > 0 }",
5394 "[n, m] -> { [n, m, m] : 0 < m <= n }",
5395 "[n, m] -> { [n, 1, m] : 0 < m <= n }",
5396 "[n, m] -> { [n, 1, 1] : 0 < m <= n }",
5397 "[n, m] -> { [m, m, m] : 0 < m <= n }",
5398 "[n, m] -> { [1, 1, m] : 0 < m <= n }",
5399 "[n, m] -> { [1, 1, 1] : 0 < m <= n }"
5403 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
5405 static isl_stat
find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
5407 struct isl_vertices_test_data
*data
= user
;
5410 isl_basic_set
*bset
;
5411 isl_pw_multi_aff
*pma
;
5415 ctx
= isl_vertex_get_ctx(vertex
);
5416 bset
= isl_vertex_get_domain(vertex
);
5417 ma
= isl_vertex_get_expr(vertex
);
5418 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
5420 for (i
= 0; i
< data
->n
; ++i
) {
5421 isl_pw_multi_aff
*pma_i
;
5423 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
5424 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
5425 isl_pw_multi_aff_free(pma_i
);
5427 if (equal
< 0 || equal
)
5431 isl_pw_multi_aff_free(pma
);
5432 isl_vertex_free(vertex
);
5435 return isl_stat_error
;
5437 return equal
? isl_stat_ok
: isl_stat_error
;
5440 int test_vertices(isl_ctx
*ctx
)
5444 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
5445 isl_basic_set
*bset
;
5446 isl_vertices
*vertices
;
5450 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
5451 vertices
= isl_basic_set_compute_vertices(bset
);
5452 n
= isl_vertices_get_n_vertices(vertices
);
5453 if (vertices_tests
[i
].n
!= n
)
5455 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
5456 &vertices_tests
[i
]) < 0)
5458 isl_vertices_free(vertices
);
5459 isl_basic_set_free(bset
);
5464 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
5471 int test_union_pw(isl_ctx
*ctx
)
5475 isl_union_set
*uset
;
5476 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
5478 str
= "{ [x] -> x^2 }";
5479 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
5480 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
5481 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
5482 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
5483 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
5484 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
5485 isl_union_pw_qpolynomial_free(upwqp1
);
5486 isl_union_pw_qpolynomial_free(upwqp2
);
5490 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5495 /* Test that isl_union_pw_qpolynomial_eval picks up the function
5496 * defined over the correct domain space.
5498 static int test_eval_1(isl_ctx
*ctx
)
5503 isl_union_pw_qpolynomial
*upwqp
;
5507 str
= "{ A[x] -> x^2; B[x] -> -x^2 }";
5508 upwqp
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
5510 set
= isl_set_read_from_str(ctx
, str
);
5511 pnt
= isl_set_sample_point(set
);
5512 v
= isl_union_pw_qpolynomial_eval(upwqp
, pnt
);
5513 cmp
= isl_val_cmp_si(v
, 36);
5519 isl_die(ctx
, isl_error_unknown
, "unexpected value", return -1);
5524 /* Check that isl_qpolynomial_eval handles getting called on a void point.
5526 static int test_eval_2(isl_ctx
*ctx
)
5531 isl_qpolynomial
*qp
;
5535 str
= "{ A[x] -> [x] }";
5536 qp
= isl_qpolynomial_from_aff(isl_aff_read_from_str(ctx
, str
));
5537 str
= "{ A[x] : false }";
5538 set
= isl_set_read_from_str(ctx
, str
);
5539 pnt
= isl_set_sample_point(set
);
5540 v
= isl_qpolynomial_eval(qp
, pnt
);
5541 ok
= isl_val_is_nan(v
);
5547 isl_die(ctx
, isl_error_unknown
, "expecting NaN", return -1);
5552 /* Perform basic polynomial evaluation tests.
5554 static int test_eval(isl_ctx
*ctx
)
5556 if (test_eval_1(ctx
) < 0)
5558 if (test_eval_2(ctx
) < 0)
5563 /* Descriptions of sets that are tested for reparsing after printing.
5565 const char *output_tests
[] = {
5566 "{ [1, y] : 0 <= y <= 1; [x, -x] : 0 <= x <= 1 }",
5569 "{ [x] : x mod 2 = 0 }",
5570 "{ [x] : x mod 2 = 1 }",
5571 "{ [x, y] : x mod 2 = 0 and 3*floor(y/2) < x }",
5572 "{ [y, x] : x mod 2 = 0 and 3*floor(y/2) < x }",
5573 "{ [x, y] : x mod 2 = 0 and 3*floor(y/2) = x + y }",
5574 "{ [y, x] : x mod 2 = 0 and 3*floor(y/2) = x + y }",
5575 "[n] -> { [y, x] : 2*((x + 2y) mod 3) = n }",
5576 "{ [x, y] : (2*floor(x/3) + 3*floor(y/4)) mod 5 = x }",
5579 /* Check that printing a set and reparsing a set from the printed output
5580 * results in the same set.
5582 static int test_output_set(isl_ctx
*ctx
)
5586 isl_set
*set1
, *set2
;
5589 for (i
= 0; i
< ARRAY_SIZE(output_tests
); ++i
) {
5590 set1
= isl_set_read_from_str(ctx
, output_tests
[i
]);
5591 str
= isl_set_to_str(set1
);
5592 set2
= isl_set_read_from_str(ctx
, str
);
5594 equal
= isl_set_is_equal(set1
, set2
);
5600 isl_die(ctx
, isl_error_unknown
,
5601 "parsed output not the same", return -1);
5607 int test_output(isl_ctx
*ctx
)
5615 if (test_output_set(ctx
) < 0)
5618 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
5619 pa
= isl_pw_aff_read_from_str(ctx
, str
);
5621 p
= isl_printer_to_str(ctx
);
5622 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
5623 p
= isl_printer_print_pw_aff(p
, pa
);
5624 s
= isl_printer_get_str(p
);
5625 isl_printer_free(p
);
5626 isl_pw_aff_free(pa
);
5630 equal
= !strcmp(s
, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
5635 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5640 int test_sample(isl_ctx
*ctx
)
5643 isl_basic_set
*bset1
, *bset2
;
5646 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
5647 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
5648 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
5649 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
5650 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
5651 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
5652 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
5653 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
5654 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
5655 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
5656 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
5657 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
5658 "d - 1073741821e and "
5659 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
5660 "3j >= 1 - a + b + 2e and "
5661 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
5662 "3i <= 4 - a + 4b - e and "
5663 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
5664 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
5665 "c <= -1 + a and 3i >= -2 - a + 3e and "
5666 "1073741822e <= 1073741823 - a + 1073741822b + c and "
5667 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
5668 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
5669 "1073741823e >= 1 + 1073741823b - d and "
5670 "3i >= 1073741823b + c - 1073741823e - f and "
5671 "3i >= 1 + 2b + e + 3g }";
5672 bset1
= isl_basic_set_read_from_str(ctx
, str
);
5673 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
5674 empty
= isl_basic_set_is_empty(bset2
);
5675 subset
= isl_basic_set_is_subset(bset2
, bset1
);
5676 isl_basic_set_free(bset1
);
5677 isl_basic_set_free(bset2
);
5678 if (empty
< 0 || subset
< 0)
5681 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
5683 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
5688 int test_fixed_power(isl_ctx
*ctx
)
5695 str
= "{ [i] -> [i + 1] }";
5696 map
= isl_map_read_from_str(ctx
, str
);
5697 exp
= isl_val_int_from_si(ctx
, 23);
5698 map
= isl_map_fixed_power_val(map
, exp
);
5699 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
5707 int test_slice(isl_ctx
*ctx
)
5713 str
= "{ [i] -> [j] }";
5714 map
= isl_map_read_from_str(ctx
, str
);
5715 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5716 equal
= map_check_equal(map
, "{ [i] -> [i] }");
5721 str
= "{ [i] -> [j] }";
5722 map
= isl_map_read_from_str(ctx
, str
);
5723 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5724 equal
= map_check_equal(map
, "{ [i] -> [j] }");
5729 str
= "{ [i] -> [j] }";
5730 map
= isl_map_read_from_str(ctx
, str
);
5731 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5732 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
5737 str
= "{ [i] -> [j] }";
5738 map
= isl_map_read_from_str(ctx
, str
);
5739 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5740 equal
= map_check_equal(map
, "{ [0] -> [j] }");
5745 str
= "{ [i] -> [j] }";
5746 map
= isl_map_read_from_str(ctx
, str
);
5747 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5748 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
5753 str
= "{ [i] -> [j] }";
5754 map
= isl_map_read_from_str(ctx
, str
);
5755 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5756 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
5764 int test_eliminate(isl_ctx
*ctx
)
5770 str
= "{ [i] -> [j] : i = 2j }";
5771 map
= isl_map_read_from_str(ctx
, str
);
5772 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
5773 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
5781 /* Check that isl_set_dim_residue_class detects that the values of j
5782 * in the set below are all odd and that it does not detect any spurious
5785 static int test_residue_class(isl_ctx
*ctx
)
5792 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
5793 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
5794 set
= isl_set_read_from_str(ctx
, str
);
5797 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
5799 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
5800 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
5801 res
= isl_stat_error
);
5809 static int test_align_parameters_1(isl_ctx
*ctx
)
5813 isl_multi_aff
*ma1
, *ma2
;
5816 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
5817 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
5819 space
= isl_space_params_alloc(ctx
, 1);
5820 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
5821 ma1
= isl_multi_aff_align_params(ma1
, space
);
5823 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
5824 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
5826 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
5828 isl_multi_aff_free(ma1
);
5829 isl_multi_aff_free(ma2
);
5834 isl_die(ctx
, isl_error_unknown
,
5835 "result not as expected", return -1);
5840 /* Check the isl_multi_*_from_*_list operation in case inputs
5841 * have unaligned parameters.
5842 * In particular, older versions of isl would simply fail
5843 * (without printing any error message).
5845 static isl_stat
test_align_parameters_2(isl_ctx
*ctx
)
5852 map
= isl_map_read_from_str(ctx
, "{ A[] -> M[x] }");
5853 space
= isl_map_get_space(map
);
5856 aff
= isl_aff_read_from_str(ctx
, "[N] -> { A[] -> [N] }");
5857 ma
= isl_multi_aff_from_aff_list(space
, isl_aff_list_from_aff(aff
));
5858 isl_multi_aff_free(ma
);
5861 return isl_stat_error
;
5865 /* Perform basic parameter alignment tests.
5867 static int test_align_parameters(isl_ctx
*ctx
)
5869 if (test_align_parameters_1(ctx
) < 0)
5871 if (test_align_parameters_2(ctx
) < 0)
5877 static int test_list(isl_ctx
*ctx
)
5879 isl_id
*a
, *b
, *c
, *d
, *id
;
5883 a
= isl_id_alloc(ctx
, "a", NULL
);
5884 b
= isl_id_alloc(ctx
, "b", NULL
);
5885 c
= isl_id_alloc(ctx
, "c", NULL
);
5886 d
= isl_id_alloc(ctx
, "d", NULL
);
5888 list
= isl_id_list_alloc(ctx
, 4);
5889 list
= isl_id_list_add(list
, b
);
5890 list
= isl_id_list_insert(list
, 0, a
);
5891 list
= isl_id_list_add(list
, c
);
5892 list
= isl_id_list_add(list
, d
);
5893 list
= isl_id_list_drop(list
, 1, 1);
5897 if (isl_id_list_n_id(list
) != 3) {
5898 isl_id_list_free(list
);
5899 isl_die(ctx
, isl_error_unknown
,
5900 "unexpected number of elements in list", return -1);
5903 id
= isl_id_list_get_id(list
, 0);
5906 id
= isl_id_list_get_id(list
, 1);
5909 id
= isl_id_list_get_id(list
, 2);
5913 isl_id_list_free(list
);
5916 isl_die(ctx
, isl_error_unknown
,
5917 "unexpected elements in list", return -1);
5922 const char *set_conversion_tests
[] = {
5923 "[N] -> { [i] : N - 1 <= 2 i <= N }",
5924 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
5925 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
5926 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
5927 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
5928 "[a, b] -> { [c, d] : (4*floor((-a + c)/4) = -a + c and "
5929 "32*floor((-b + d)/32) = -b + d and 5 <= c <= 8 and "
5930 "-3 + c <= d <= 28 + c) }",
5933 /* Check that converting from isl_set to isl_pw_multi_aff and back
5934 * to isl_set produces the original isl_set.
5936 static int test_set_conversion(isl_ctx
*ctx
)
5940 isl_set
*set1
, *set2
;
5941 isl_pw_multi_aff
*pma
;
5944 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
5945 str
= set_conversion_tests
[i
];
5946 set1
= isl_set_read_from_str(ctx
, str
);
5947 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
5948 set2
= isl_set_from_pw_multi_aff(pma
);
5949 equal
= isl_set_is_equal(set1
, set2
);
5956 isl_die(ctx
, isl_error_unknown
, "bad conversion",
5963 const char *conversion_tests
[] = {
5964 "{ [a, b, c, d] -> s0[a, b, e, f] : "
5965 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
5966 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
5967 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
5969 "{ [a, b] -> [c] : exists (e0 = floor((-a - b + c)/5): "
5970 "5e0 = -a - b + c and c >= -a and c <= 4 - a) }",
5971 "{ [a, b] -> [c] : exists d : 18 * d = -3 - a + 2c and 1 <= c <= 3 }",
5974 /* Check that converting from isl_map to isl_pw_multi_aff and back
5975 * to isl_map produces the original isl_map.
5977 static int test_map_conversion(isl_ctx
*ctx
)
5980 isl_map
*map1
, *map2
;
5981 isl_pw_multi_aff
*pma
;
5984 for (i
= 0; i
< ARRAY_SIZE(conversion_tests
); ++i
) {
5985 map1
= isl_map_read_from_str(ctx
, conversion_tests
[i
]);
5986 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
5987 map2
= isl_map_from_pw_multi_aff(pma
);
5988 equal
= isl_map_is_equal(map1
, map2
);
5995 isl_die(ctx
, isl_error_unknown
, "bad conversion",
6002 static int test_conversion(isl_ctx
*ctx
)
6004 if (test_set_conversion(ctx
) < 0)
6006 if (test_map_conversion(ctx
) < 0)
6011 /* Check that isl_basic_map_curry does not modify input.
6013 static int test_curry(isl_ctx
*ctx
)
6016 isl_basic_map
*bmap1
, *bmap2
;
6019 str
= "{ [A[] -> B[]] -> C[] }";
6020 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
6021 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
6022 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
6023 isl_basic_map_free(bmap1
);
6024 isl_basic_map_free(bmap2
);
6029 isl_die(ctx
, isl_error_unknown
,
6030 "curried map should not be equal to original",
6040 } preimage_tests
[] = {
6041 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
6042 "{ A[j,i] -> B[i,j] }",
6043 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
6044 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
6045 "{ A[a,b] -> B[a/2,b/6] }",
6046 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
6047 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
6048 "{ A[a,b] -> B[a/2,b/6] }",
6049 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
6050 "exists i,j : a = 2 i and b = 6 j }" },
6051 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
6052 "[n] -> { : 0 <= n <= 100 }" },
6053 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
6054 "{ A[a] -> B[2a] }",
6055 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
6056 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
6057 "{ A[a] -> B[([a/2])] }",
6058 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
6059 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
6060 "{ A[a] -> B[a,a,a/3] }",
6061 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
6062 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
6063 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
6066 static int test_preimage_basic_set(isl_ctx
*ctx
)
6069 isl_basic_set
*bset1
, *bset2
;
6073 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
6074 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
6075 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
6076 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
6077 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
6078 equal
= isl_basic_set_is_equal(bset1
, bset2
);
6079 isl_basic_set_free(bset1
);
6080 isl_basic_set_free(bset2
);
6084 isl_die(ctx
, isl_error_unknown
, "bad preimage",
6095 } preimage_domain_tests
[] = {
6096 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
6097 "{ A[j,i] -> B[i,j] }",
6098 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
6099 { "{ B[i] -> C[i]; D[i] -> E[i] }",
6100 "{ A[i] -> B[i + 1] }",
6101 "{ A[i] -> C[i + 1] }" },
6102 { "{ B[i] -> C[i]; B[i] -> E[i] }",
6103 "{ A[i] -> B[i + 1] }",
6104 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
6105 { "{ B[i] -> C[([i/2])] }",
6106 "{ A[i] -> B[2i] }",
6107 "{ A[i] -> C[i] }" },
6108 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
6109 "{ A[i] -> B[([i/5]), ([i/7])] }",
6110 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
6111 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
6112 "[N] -> { A[] -> B[([N/5])] }",
6113 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
6114 { "{ B[i] -> C[i] : exists a : i = 5 a }",
6115 "{ A[i] -> B[2i] }",
6116 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
6117 { "{ B[i] -> C[i] : exists a : i = 2 a; "
6118 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
6119 "{ A[i] -> B[2i] }",
6120 "{ A[i] -> C[2i] }" },
6121 { "{ A[i] -> B[i] }", "{ C[i] -> A[(i + floor(i/3))/2] }",
6122 "{ C[i] -> B[j] : 2j = i + floor(i/3) }" },
6125 static int test_preimage_union_map(isl_ctx
*ctx
)
6128 isl_union_map
*umap1
, *umap2
;
6132 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
6133 umap1
= isl_union_map_read_from_str(ctx
,
6134 preimage_domain_tests
[i
].map
);
6135 ma
= isl_multi_aff_read_from_str(ctx
,
6136 preimage_domain_tests
[i
].ma
);
6137 umap2
= isl_union_map_read_from_str(ctx
,
6138 preimage_domain_tests
[i
].res
);
6139 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
6140 equal
= isl_union_map_is_equal(umap1
, umap2
);
6141 isl_union_map_free(umap1
);
6142 isl_union_map_free(umap2
);
6146 isl_die(ctx
, isl_error_unknown
, "bad preimage",
6153 static int test_preimage(isl_ctx
*ctx
)
6155 if (test_preimage_basic_set(ctx
) < 0)
6157 if (test_preimage_union_map(ctx
) < 0)
6167 } pullback_tests
[] = {
6168 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
6169 "{ A[a,b] -> C[b + 2a] }" },
6170 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
6171 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
6172 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
6173 "{ A[a] -> C[(a)/6] }" },
6174 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
6175 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
6176 "{ A[a] -> C[(2a)/3] }" },
6177 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
6178 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
6179 "{ A[i,j] -> C[i + j, i + j] }"},
6180 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
6181 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
6182 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
6183 { "{ [i, j] -> [floor((i)/4) + floor((2*i+j)/5)] }",
6184 "{ [i, j] -> [floor((i)/3), j] }",
6185 "{ [i, j] -> [(floor((i)/12) + floor((j + 2*floor((i)/3))/5))] }" },
6188 static int test_pullback(isl_ctx
*ctx
)
6191 isl_multi_aff
*ma1
, *ma2
;
6195 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
6196 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
6197 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
6198 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
6199 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
6200 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
6201 isl_multi_aff_free(ma1
);
6202 isl_multi_aff_free(ma2
);
6206 isl_die(ctx
, isl_error_unknown
, "bad pullback",
6213 /* Check that negation is printed correctly and that equal expressions
6214 * are correctly identified.
6216 static int test_ast(isl_ctx
*ctx
)
6218 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
6222 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
6223 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
6224 expr
= isl_ast_expr_add(expr1
, expr2
);
6225 expr2
= isl_ast_expr_copy(expr
);
6226 expr
= isl_ast_expr_neg(expr
);
6227 expr2
= isl_ast_expr_neg(expr2
);
6228 equal
= isl_ast_expr_is_equal(expr
, expr2
);
6229 str
= isl_ast_expr_to_C_str(expr
);
6230 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
6232 isl_ast_expr_free(expr
);
6233 isl_ast_expr_free(expr2
);
6235 if (ok
< 0 || equal
< 0)
6238 isl_die(ctx
, isl_error_unknown
,
6239 "equal expressions not considered equal", return -1);
6241 isl_die(ctx
, isl_error_unknown
,
6242 "isl_ast_expr printed incorrectly", return -1);
6244 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
6245 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
6246 expr
= isl_ast_expr_add(expr1
, expr2
);
6247 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
6248 expr
= isl_ast_expr_sub(expr3
, expr
);
6249 str
= isl_ast_expr_to_C_str(expr
);
6250 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
6252 isl_ast_expr_free(expr
);
6257 isl_die(ctx
, isl_error_unknown
,
6258 "isl_ast_expr printed incorrectly", return -1);
6263 /* Check that isl_ast_build_expr_from_set returns a valid expression
6264 * for an empty set. Note that isl_ast_build_expr_from_set getting
6265 * called on an empty set probably indicates a bug in the caller.
6267 static int test_ast_build(isl_ctx
*ctx
)
6270 isl_ast_build
*build
;
6273 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6274 build
= isl_ast_build_from_context(set
);
6276 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
6277 expr
= isl_ast_build_expr_from_set(build
, set
);
6279 isl_ast_expr_free(expr
);
6280 isl_ast_build_free(build
);
6288 /* Internal data structure for before_for and after_for callbacks.
6290 * depth is the current depth
6291 * before is the number of times before_for has been called
6292 * after is the number of times after_for has been called
6294 struct isl_test_codegen_data
{
6300 /* This function is called before each for loop in the AST generated
6301 * from test_ast_gen1.
6303 * Increment the number of calls and the depth.
6304 * Check that the space returned by isl_ast_build_get_schedule_space
6305 * matches the target space of the schedule returned by
6306 * isl_ast_build_get_schedule.
6307 * Return an isl_id that is checked by the corresponding call
6310 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
6313 struct isl_test_codegen_data
*data
= user
;
6316 isl_union_map
*schedule
;
6317 isl_union_set
*uset
;
6322 ctx
= isl_ast_build_get_ctx(build
);
6324 if (data
->before
>= 3)
6325 isl_die(ctx
, isl_error_unknown
,
6326 "unexpected number of for nodes", return NULL
);
6327 if (data
->depth
>= 2)
6328 isl_die(ctx
, isl_error_unknown
,
6329 "unexpected depth", return NULL
);
6331 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
6335 schedule
= isl_ast_build_get_schedule(build
);
6336 uset
= isl_union_map_range(schedule
);
6339 if (isl_union_set_n_set(uset
) != 1) {
6340 isl_union_set_free(uset
);
6341 isl_die(ctx
, isl_error_unknown
,
6342 "expecting single range space", return NULL
);
6345 space
= isl_ast_build_get_schedule_space(build
);
6346 set
= isl_union_set_extract_set(uset
, space
);
6347 isl_union_set_free(uset
);
6348 empty
= isl_set_is_empty(set
);
6354 isl_die(ctx
, isl_error_unknown
,
6355 "spaces don't match", return NULL
);
6357 return isl_id_alloc(ctx
, name
, NULL
);
6360 /* This function is called after each for loop in the AST generated
6361 * from test_ast_gen1.
6363 * Increment the number of calls and decrement the depth.
6364 * Check that the annotation attached to the node matches
6365 * the isl_id returned by the corresponding call to before_for.
6367 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
6368 __isl_keep isl_ast_build
*build
, void *user
)
6370 struct isl_test_codegen_data
*data
= user
;
6378 if (data
->after
> data
->before
)
6379 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
6380 "mismatch in number of for nodes",
6381 return isl_ast_node_free(node
));
6383 id
= isl_ast_node_get_annotation(node
);
6385 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
6386 "missing annotation", return isl_ast_node_free(node
));
6388 name
= isl_id_get_name(id
);
6389 valid
= name
&& atoi(name
+ 1) == data
->depth
;
6393 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
6394 "wrong annotation", return isl_ast_node_free(node
));
6399 /* Check that the before_each_for and after_each_for callbacks
6400 * are called for each for loop in the generated code,
6401 * that they are called in the right order and that the isl_id
6402 * returned from the before_each_for callback is attached to
6403 * the isl_ast_node passed to the corresponding after_each_for call.
6405 static int test_ast_gen1(isl_ctx
*ctx
)
6409 isl_union_map
*schedule
;
6410 isl_ast_build
*build
;
6412 struct isl_test_codegen_data data
;
6414 str
= "[N] -> { : N >= 10 }";
6415 set
= isl_set_read_from_str(ctx
, str
);
6416 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
6417 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
6418 schedule
= isl_union_map_read_from_str(ctx
, str
);
6423 build
= isl_ast_build_from_context(set
);
6424 build
= isl_ast_build_set_before_each_for(build
,
6425 &before_for
, &data
);
6426 build
= isl_ast_build_set_after_each_for(build
,
6428 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6429 isl_ast_build_free(build
);
6433 isl_ast_node_free(tree
);
6435 if (data
.before
!= 3 || data
.after
!= 3)
6436 isl_die(ctx
, isl_error_unknown
,
6437 "unexpected number of for nodes", return -1);
6442 /* Check that the AST generator handles domains that are integrally disjoint
6443 * but not rationally disjoint.
6445 static int test_ast_gen2(isl_ctx
*ctx
)
6449 isl_union_map
*schedule
;
6450 isl_union_map
*options
;
6451 isl_ast_build
*build
;
6454 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
6455 schedule
= isl_union_map_read_from_str(ctx
, str
);
6456 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6457 build
= isl_ast_build_from_context(set
);
6459 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
6460 options
= isl_union_map_read_from_str(ctx
, str
);
6461 build
= isl_ast_build_set_options(build
, options
);
6462 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6463 isl_ast_build_free(build
);
6466 isl_ast_node_free(tree
);
6471 /* Increment *user on each call.
6473 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
6474 __isl_keep isl_ast_build
*build
, void *user
)
6483 /* Test that unrolling tries to minimize the number of instances.
6484 * In particular, for the schedule given below, make sure it generates
6485 * 3 nodes (rather than 101).
6487 static int test_ast_gen3(isl_ctx
*ctx
)
6491 isl_union_map
*schedule
;
6492 isl_union_map
*options
;
6493 isl_ast_build
*build
;
6497 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
6498 schedule
= isl_union_map_read_from_str(ctx
, str
);
6499 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6501 str
= "{ [i] -> unroll[0] }";
6502 options
= isl_union_map_read_from_str(ctx
, str
);
6504 build
= isl_ast_build_from_context(set
);
6505 build
= isl_ast_build_set_options(build
, options
);
6506 build
= isl_ast_build_set_at_each_domain(build
,
6507 &count_domains
, &n_domain
);
6508 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6509 isl_ast_build_free(build
);
6513 isl_ast_node_free(tree
);
6516 isl_die(ctx
, isl_error_unknown
,
6517 "unexpected number of for nodes", return -1);
6522 /* Check that if the ast_build_exploit_nested_bounds options is set,
6523 * we do not get an outer if node in the generated AST,
6524 * while we do get such an outer if node if the options is not set.
6526 static int test_ast_gen4(isl_ctx
*ctx
)
6530 isl_union_map
*schedule
;
6531 isl_ast_build
*build
;
6533 enum isl_ast_node_type type
;
6536 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
6537 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
6539 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
6541 schedule
= isl_union_map_read_from_str(ctx
, str
);
6542 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6543 build
= isl_ast_build_from_context(set
);
6544 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6545 isl_ast_build_free(build
);
6549 type
= isl_ast_node_get_type(tree
);
6550 isl_ast_node_free(tree
);
6552 if (type
== isl_ast_node_if
)
6553 isl_die(ctx
, isl_error_unknown
,
6554 "not expecting if node", return -1);
6556 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
6558 schedule
= isl_union_map_read_from_str(ctx
, str
);
6559 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6560 build
= isl_ast_build_from_context(set
);
6561 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6562 isl_ast_build_free(build
);
6566 type
= isl_ast_node_get_type(tree
);
6567 isl_ast_node_free(tree
);
6569 if (type
!= isl_ast_node_if
)
6570 isl_die(ctx
, isl_error_unknown
,
6571 "expecting if node", return -1);
6573 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
6578 /* This function is called for each leaf in the AST generated
6579 * from test_ast_gen5.
6581 * We finalize the AST generation by extending the outer schedule
6582 * with a zero-dimensional schedule. If this results in any for loops,
6583 * then this means that we did not pass along enough information
6584 * about the outer schedule to the inner AST generation.
6586 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
6589 isl_union_map
*schedule
, *extra
;
6592 schedule
= isl_ast_build_get_schedule(build
);
6593 extra
= isl_union_map_copy(schedule
);
6594 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
6595 schedule
= isl_union_map_range_product(schedule
, extra
);
6596 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6597 isl_ast_build_free(build
);
6602 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
6603 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
6604 "code should not contain any for loop",
6605 return isl_ast_node_free(tree
));
6610 /* Check that we do not lose any information when going back and
6611 * forth between internal and external schedule.
6613 * In particular, we create an AST where we unroll the only
6614 * non-constant dimension in the schedule. We therefore do
6615 * not expect any for loops in the AST. However, older versions
6616 * of isl would not pass along enough information about the outer
6617 * schedule when performing an inner code generation from a create_leaf
6618 * callback, resulting in the inner code generation producing a for loop.
6620 static int test_ast_gen5(isl_ctx
*ctx
)
6624 isl_union_map
*schedule
, *options
;
6625 isl_ast_build
*build
;
6628 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
6629 schedule
= isl_union_map_read_from_str(ctx
, str
);
6631 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
6632 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
6633 options
= isl_union_map_read_from_str(ctx
, str
);
6635 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6636 build
= isl_ast_build_from_context(set
);
6637 build
= isl_ast_build_set_options(build
, options
);
6638 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
6639 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6640 isl_ast_build_free(build
);
6641 isl_ast_node_free(tree
);
6648 /* Check that the expression
6650 * [n] -> { [n/2] : n <= 0 and n % 2 = 0; [0] : n > 0 }
6652 * is not combined into
6656 * as this would result in n/2 being evaluated in parts of
6657 * the definition domain where n is not a multiple of 2.
6659 static int test_ast_expr(isl_ctx
*ctx
)
6663 isl_ast_build
*build
;
6668 min_max
= isl_options_get_ast_build_detect_min_max(ctx
);
6669 isl_options_set_ast_build_detect_min_max(ctx
, 1);
6671 str
= "[n] -> { [n/2] : n <= 0 and n % 2 = 0; [0] : n > 0 }";
6672 pa
= isl_pw_aff_read_from_str(ctx
, str
);
6673 build
= isl_ast_build_alloc(ctx
);
6674 expr
= isl_ast_build_expr_from_pw_aff(build
, pa
);
6675 is_min
= isl_ast_expr_get_type(expr
) == isl_ast_expr_op
&&
6676 isl_ast_expr_get_op_type(expr
) == isl_ast_op_min
;
6677 isl_ast_build_free(build
);
6678 isl_ast_expr_free(expr
);
6680 isl_options_set_ast_build_detect_min_max(ctx
, min_max
);
6685 isl_die(ctx
, isl_error_unknown
,
6686 "expressions should not be combined", return -1);
6691 static int test_ast_gen(isl_ctx
*ctx
)
6693 if (test_ast_gen1(ctx
) < 0)
6695 if (test_ast_gen2(ctx
) < 0)
6697 if (test_ast_gen3(ctx
) < 0)
6699 if (test_ast_gen4(ctx
) < 0)
6701 if (test_ast_gen5(ctx
) < 0)
6703 if (test_ast_expr(ctx
) < 0)
6708 /* Check if dropping output dimensions from an isl_pw_multi_aff
6711 static int test_pw_multi_aff(isl_ctx
*ctx
)
6714 isl_pw_multi_aff
*pma1
, *pma2
;
6717 str
= "{ [i,j] -> [i+j, 4i-j] }";
6718 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
6719 str
= "{ [i,j] -> [4i-j] }";
6720 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
6722 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
6724 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
6726 isl_pw_multi_aff_free(pma1
);
6727 isl_pw_multi_aff_free(pma2
);
6731 isl_die(ctx
, isl_error_unknown
,
6732 "expressions not equal", return -1);
6737 /* Check that we can properly parse multi piecewise affine expressions
6738 * where the piecewise affine expressions have different domains.
6740 static int test_multi_pw_aff(isl_ctx
*ctx
)
6743 isl_set
*dom
, *dom2
;
6744 isl_multi_pw_aff
*mpa1
, *mpa2
;
6749 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
6750 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
6751 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
6752 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
6753 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
6754 str
= "{ [i] -> [(i : i > 0), 2i] }";
6755 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
6757 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
6759 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
6760 dom
= isl_pw_aff_domain(pa
);
6761 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
6762 dom2
= isl_pw_aff_domain(pa
);
6763 equal_domain
= isl_set_is_equal(dom
, dom2
);
6767 isl_multi_pw_aff_free(mpa1
);
6768 isl_multi_pw_aff_free(mpa2
);
6773 isl_die(ctx
, isl_error_unknown
,
6774 "expressions not equal", return -1);
6776 if (equal_domain
< 0)
6779 isl_die(ctx
, isl_error_unknown
,
6780 "domains unexpectedly equal", return -1);
6785 /* This is a regression test for a bug where isl_basic_map_simplify
6786 * would end up in an infinite loop. In particular, we construct
6787 * an empty basic set that is not obviously empty.
6788 * isl_basic_set_is_empty marks the basic set as empty.
6789 * After projecting out i3, the variable can be dropped completely,
6790 * but isl_basic_map_simplify refrains from doing so if the basic set
6791 * is empty and would end up in an infinite loop if it didn't test
6792 * explicitly for empty basic maps in the outer loop.
6794 static int test_simplify_1(isl_ctx
*ctx
)
6797 isl_basic_set
*bset
;
6800 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
6801 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
6802 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
6804 bset
= isl_basic_set_read_from_str(ctx
, str
);
6805 empty
= isl_basic_set_is_empty(bset
);
6806 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
6807 isl_basic_set_free(bset
);
6811 isl_die(ctx
, isl_error_unknown
,
6812 "basic set should be empty", return -1);
6817 /* Check that the equality in the set description below
6818 * is simplified away.
6820 static int test_simplify_2(isl_ctx
*ctx
)
6823 isl_basic_set
*bset
;
6826 str
= "{ [a] : exists e0, e1: 32e1 = 31 + 31a + 31e0 }";
6827 bset
= isl_basic_set_read_from_str(ctx
, str
);
6828 universe
= isl_basic_set_plain_is_universe(bset
);
6829 isl_basic_set_free(bset
);
6834 isl_die(ctx
, isl_error_unknown
,
6835 "equality not simplified away", return -1);
6839 /* Some simplification tests.
6841 static int test_simplify(isl_ctx
*ctx
)
6843 if (test_simplify_1(ctx
) < 0)
6845 if (test_simplify_2(ctx
) < 0)
6850 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
6851 * with gbr context would fail to disable the use of the shifted tableau
6852 * when transferring equalities for the input to the context, resulting
6853 * in invalid sample values.
6855 static int test_partial_lexmin(isl_ctx
*ctx
)
6858 isl_basic_set
*bset
;
6859 isl_basic_map
*bmap
;
6862 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
6863 bmap
= isl_basic_map_read_from_str(ctx
, str
);
6864 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
6865 bset
= isl_basic_set_read_from_str(ctx
, str
);
6866 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
6875 /* Check that the variable compression performed on the existentially
6876 * quantified variables inside isl_basic_set_compute_divs is not confused
6877 * by the implicit equalities among the parameters.
6879 static int test_compute_divs(isl_ctx
*ctx
)
6882 isl_basic_set
*bset
;
6885 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
6886 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
6887 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
6888 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
6889 bset
= isl_basic_set_read_from_str(ctx
, str
);
6890 set
= isl_basic_set_compute_divs(bset
);
6898 /* Check that isl_schedule_get_map is not confused by a schedule tree
6899 * with divergent filter node parameters, as can result from a call
6900 * to isl_schedule_intersect_domain.
6902 static int test_schedule_tree(isl_ctx
*ctx
)
6905 isl_union_set
*uset
;
6906 isl_schedule
*sched1
, *sched2
;
6907 isl_union_map
*umap
;
6909 uset
= isl_union_set_read_from_str(ctx
, "{ A[i] }");
6910 sched1
= isl_schedule_from_domain(uset
);
6911 uset
= isl_union_set_read_from_str(ctx
, "{ B[] }");
6912 sched2
= isl_schedule_from_domain(uset
);
6914 sched1
= isl_schedule_sequence(sched1
, sched2
);
6915 str
= "[n] -> { A[i] : 0 <= i < n; B[] }";
6916 uset
= isl_union_set_read_from_str(ctx
, str
);
6917 sched1
= isl_schedule_intersect_domain(sched1
, uset
);
6918 umap
= isl_schedule_get_map(sched1
);
6919 isl_schedule_free(sched1
);
6920 isl_union_map_free(umap
);
6927 /* Check that the reaching domain elements and the prefix schedule
6928 * at a leaf node are the same before and after grouping.
6930 static int test_schedule_tree_group_1(isl_ctx
*ctx
)
6935 isl_union_set
*uset
;
6936 isl_multi_union_pw_aff
*mupa
;
6937 isl_union_pw_multi_aff
*upma1
, *upma2
;
6938 isl_union_set
*domain1
, *domain2
;
6939 isl_union_map
*umap1
, *umap2
;
6940 isl_schedule_node
*node
;
6942 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10 }";
6943 uset
= isl_union_set_read_from_str(ctx
, str
);
6944 node
= isl_schedule_node_from_domain(uset
);
6945 node
= isl_schedule_node_child(node
, 0);
6946 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [9 - i] }]";
6947 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6948 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6949 node
= isl_schedule_node_child(node
, 0);
6950 str
= "[{ S1[i,j] -> [j]; S2[i,j] -> [j] }]";
6951 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6952 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6953 node
= isl_schedule_node_child(node
, 0);
6954 umap1
= isl_schedule_node_get_prefix_schedule_union_map(node
);
6955 upma1
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
6956 domain1
= isl_schedule_node_get_domain(node
);
6957 id
= isl_id_alloc(ctx
, "group", NULL
);
6958 node
= isl_schedule_node_parent(node
);
6959 node
= isl_schedule_node_group(node
, id
);
6960 node
= isl_schedule_node_child(node
, 0);
6961 umap2
= isl_schedule_node_get_prefix_schedule_union_map(node
);
6962 upma2
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
6963 domain2
= isl_schedule_node_get_domain(node
);
6964 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
6965 if (equal
>= 0 && equal
)
6966 equal
= isl_union_set_is_equal(domain1
, domain2
);
6967 if (equal
>= 0 && equal
)
6968 equal
= isl_union_map_is_equal(umap1
, umap2
);
6969 isl_union_map_free(umap1
);
6970 isl_union_map_free(umap2
);
6971 isl_union_set_free(domain1
);
6972 isl_union_set_free(domain2
);
6973 isl_union_pw_multi_aff_free(upma1
);
6974 isl_union_pw_multi_aff_free(upma2
);
6975 isl_schedule_node_free(node
);
6980 isl_die(ctx
, isl_error_unknown
,
6981 "expressions not equal", return -1);
6986 /* Check that we can have nested groupings and that the union map
6987 * schedule representation is the same before and after the grouping.
6988 * Note that after the grouping, the union map representation contains
6989 * the domain constraints from the ranges of the expansion nodes,
6990 * while they are missing from the union map representation of
6991 * the tree without expansion nodes.
6993 * Also check that the global expansion is as expected.
6995 static int test_schedule_tree_group_2(isl_ctx
*ctx
)
6997 int equal
, equal_expansion
;
7000 isl_union_set
*uset
;
7001 isl_union_map
*umap1
, *umap2
;
7002 isl_union_map
*expansion1
, *expansion2
;
7003 isl_union_set_list
*filters
;
7004 isl_multi_union_pw_aff
*mupa
;
7005 isl_schedule
*schedule
;
7006 isl_schedule_node
*node
;
7008 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10; "
7009 "S3[i,j] : 0 <= i,j < 10 }";
7010 uset
= isl_union_set_read_from_str(ctx
, str
);
7011 node
= isl_schedule_node_from_domain(uset
);
7012 node
= isl_schedule_node_child(node
, 0);
7013 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [i]; S3[i,j] -> [i] }]";
7014 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
7015 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
7016 node
= isl_schedule_node_child(node
, 0);
7017 str
= "{ S1[i,j] }";
7018 uset
= isl_union_set_read_from_str(ctx
, str
);
7019 filters
= isl_union_set_list_from_union_set(uset
);
7020 str
= "{ S2[i,j]; S3[i,j] }";
7021 uset
= isl_union_set_read_from_str(ctx
, str
);
7022 filters
= isl_union_set_list_add(filters
, uset
);
7023 node
= isl_schedule_node_insert_sequence(node
, filters
);
7024 node
= isl_schedule_node_child(node
, 1);
7025 node
= isl_schedule_node_child(node
, 0);
7026 str
= "{ S2[i,j] }";
7027 uset
= isl_union_set_read_from_str(ctx
, str
);
7028 filters
= isl_union_set_list_from_union_set(uset
);
7029 str
= "{ S3[i,j] }";
7030 uset
= isl_union_set_read_from_str(ctx
, str
);
7031 filters
= isl_union_set_list_add(filters
, uset
);
7032 node
= isl_schedule_node_insert_sequence(node
, filters
);
7034 schedule
= isl_schedule_node_get_schedule(node
);
7035 umap1
= isl_schedule_get_map(schedule
);
7036 uset
= isl_schedule_get_domain(schedule
);
7037 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
7038 isl_schedule_free(schedule
);
7040 node
= isl_schedule_node_parent(node
);
7041 node
= isl_schedule_node_parent(node
);
7042 id
= isl_id_alloc(ctx
, "group1", NULL
);
7043 node
= isl_schedule_node_group(node
, id
);
7044 node
= isl_schedule_node_child(node
, 1);
7045 node
= isl_schedule_node_child(node
, 0);
7046 id
= isl_id_alloc(ctx
, "group2", NULL
);
7047 node
= isl_schedule_node_group(node
, id
);
7049 schedule
= isl_schedule_node_get_schedule(node
);
7050 umap2
= isl_schedule_get_map(schedule
);
7051 isl_schedule_free(schedule
);
7053 node
= isl_schedule_node_root(node
);
7054 node
= isl_schedule_node_child(node
, 0);
7055 expansion1
= isl_schedule_node_get_subtree_expansion(node
);
7056 isl_schedule_node_free(node
);
7058 str
= "{ group1[i] -> S1[i,j] : 0 <= i,j < 10; "
7059 "group1[i] -> S2[i,j] : 0 <= i,j < 10; "
7060 "group1[i] -> S3[i,j] : 0 <= i,j < 10 }";
7062 expansion2
= isl_union_map_read_from_str(ctx
, str
);
7064 equal
= isl_union_map_is_equal(umap1
, umap2
);
7065 equal_expansion
= isl_union_map_is_equal(expansion1
, expansion2
);
7067 isl_union_map_free(umap1
);
7068 isl_union_map_free(umap2
);
7069 isl_union_map_free(expansion1
);
7070 isl_union_map_free(expansion2
);
7072 if (equal
< 0 || equal_expansion
< 0)
7075 isl_die(ctx
, isl_error_unknown
,
7076 "expressions not equal", return -1);
7077 if (!equal_expansion
)
7078 isl_die(ctx
, isl_error_unknown
,
7079 "unexpected expansion", return -1);
7084 /* Some tests for the isl_schedule_node_group function.
7086 static int test_schedule_tree_group(isl_ctx
*ctx
)
7088 if (test_schedule_tree_group_1(ctx
) < 0)
7090 if (test_schedule_tree_group_2(ctx
) < 0)
7099 { "{ rat: [i] : 0 <= i <= 10 }",
7100 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
7101 { "{ rat: [i] : FALSE }",
7102 "{ rat: coefficients[[cst] -> [a]] }" },
7104 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
7111 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
7112 "{ rat: [i] : 0 <= i <= 10 }" },
7113 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
7115 { "{ rat: coefficients[[cst] -> [a]] }",
7116 "{ rat: [i] : FALSE }" },
7119 /* Test the basic functionality of isl_basic_set_coefficients and
7120 * isl_basic_set_solutions.
7122 static int test_dual(isl_ctx
*ctx
)
7126 for (i
= 0; i
< ARRAY_SIZE(coef_tests
); ++i
) {
7128 isl_basic_set
*bset1
, *bset2
;
7130 bset1
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].set
);
7131 bset2
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].dual
);
7132 bset1
= isl_basic_set_coefficients(bset1
);
7133 equal
= isl_basic_set_is_equal(bset1
, bset2
);
7134 isl_basic_set_free(bset1
);
7135 isl_basic_set_free(bset2
);
7139 isl_die(ctx
, isl_error_unknown
,
7140 "incorrect dual", return -1);
7143 for (i
= 0; i
< ARRAY_SIZE(sol_tests
); ++i
) {
7145 isl_basic_set
*bset1
, *bset2
;
7147 bset1
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].set
);
7148 bset2
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].dual
);
7149 bset1
= isl_basic_set_solutions(bset1
);
7150 equal
= isl_basic_set_is_equal(bset1
, bset2
);
7151 isl_basic_set_free(bset1
);
7152 isl_basic_set_free(bset2
);
7156 isl_die(ctx
, isl_error_unknown
,
7157 "incorrect dual", return -1);
7167 const char *schedule
;
7172 { 0, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
7173 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
7175 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
7176 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
7178 { 1, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
7179 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
7181 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
7182 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
7184 { 0, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
7185 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
7187 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
7188 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
7190 { 1, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
7191 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
7193 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
7194 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
7198 /* Basic tiling tests. Create a schedule tree with a domain and a band node,
7199 * tile the band and then check if the tile and point bands have the
7200 * expected partial schedule.
7202 static int test_tile(isl_ctx
*ctx
)
7208 scale
= isl_options_get_tile_scale_tile_loops(ctx
);
7209 shift
= isl_options_get_tile_shift_point_loops(ctx
);
7211 for (i
= 0; i
< ARRAY_SIZE(tile_tests
); ++i
) {
7215 isl_union_set
*domain
;
7216 isl_multi_union_pw_aff
*mupa
, *mupa2
;
7217 isl_schedule_node
*node
;
7218 isl_multi_val
*sizes
;
7220 opt
= tile_tests
[i
].scale_tile
;
7221 isl_options_set_tile_scale_tile_loops(ctx
, opt
);
7222 opt
= tile_tests
[i
].shift_point
;
7223 isl_options_set_tile_shift_point_loops(ctx
, opt
);
7225 str
= tile_tests
[i
].domain
;
7226 domain
= isl_union_set_read_from_str(ctx
, str
);
7227 node
= isl_schedule_node_from_domain(domain
);
7228 node
= isl_schedule_node_child(node
, 0);
7229 str
= tile_tests
[i
].schedule
;
7230 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
7231 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
7232 str
= tile_tests
[i
].sizes
;
7233 sizes
= isl_multi_val_read_from_str(ctx
, str
);
7234 node
= isl_schedule_node_band_tile(node
, sizes
);
7236 str
= tile_tests
[i
].tile
;
7237 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
7238 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
7239 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
, mupa2
);
7240 isl_multi_union_pw_aff_free(mupa
);
7241 isl_multi_union_pw_aff_free(mupa2
);
7243 node
= isl_schedule_node_child(node
, 0);
7245 str
= tile_tests
[i
].point
;
7246 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
7247 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
7248 if (equal
>= 0 && equal
)
7249 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
,
7251 isl_multi_union_pw_aff_free(mupa
);
7252 isl_multi_union_pw_aff_free(mupa2
);
7254 isl_schedule_node_free(node
);
7259 isl_die(ctx
, isl_error_unknown
,
7260 "unexpected result", return -1);
7263 isl_options_set_tile_scale_tile_loops(ctx
, scale
);
7264 isl_options_set_tile_shift_point_loops(ctx
, shift
);
7269 /* Check that the domain hash of a space is equal to the hash
7270 * of the domain of the space.
7272 static int test_domain_hash(isl_ctx
*ctx
)
7276 uint32_t hash1
, hash2
;
7278 map
= isl_map_read_from_str(ctx
, "[n] -> { A[B[x] -> C[]] -> D[] }");
7279 space
= isl_map_get_space(map
);
7281 hash1
= isl_space_get_domain_hash(space
);
7282 space
= isl_space_domain(space
);
7283 hash2
= isl_space_get_hash(space
);
7284 isl_space_free(space
);
7289 isl_die(ctx
, isl_error_unknown
,
7290 "domain hash not equal to hash of domain", return -1);
7295 /* Check that a universe basic set that is not obviously equal to the universe
7296 * is still recognized as being equal to the universe.
7298 static int test_universe(isl_ctx
*ctx
)
7301 isl_basic_set
*bset
;
7304 s
= "{ [] : exists x, y : 3y <= 2x and y >= -3 + 2x and 2y >= 2 - x }";
7305 bset
= isl_basic_set_read_from_str(ctx
, s
);
7306 is_univ
= isl_basic_set_is_universe(bset
);
7307 isl_basic_set_free(bset
);
7312 isl_die(ctx
, isl_error_unknown
,
7313 "not recognized as universe set", return -1);
7318 /* Sets for which chambers are computed and checked.
7320 const char *chambers_tests
[] = {
7321 "[A, B, C] -> { [x, y, z] : x >= 0 and y >= 0 and y <= A - x and "
7322 "z >= 0 and z <= C - y and z <= B - x - y }",
7325 /* Add the domain of "cell" to "cells".
7327 static isl_stat
add_cell(__isl_take isl_cell
*cell
, void *user
)
7329 isl_basic_set_list
**cells
= user
;
7332 dom
= isl_cell_get_domain(cell
);
7333 isl_cell_free(cell
);
7334 *cells
= isl_basic_set_list_add(*cells
, dom
);
7336 return *cells
? isl_stat_ok
: isl_stat_error
;
7339 /* Check that the elements of "list" are pairwise disjoint.
7341 static isl_stat
check_pairwise_disjoint(__isl_keep isl_basic_set_list
*list
)
7346 return isl_stat_error
;
7348 n
= isl_basic_set_list_n_basic_set(list
);
7349 for (i
= 0; i
< n
; ++i
) {
7350 isl_basic_set
*bset_i
;
7352 bset_i
= isl_basic_set_list_get_basic_set(list
, i
);
7353 for (j
= i
+ 1; j
< n
; ++j
) {
7354 isl_basic_set
*bset_j
;
7357 bset_j
= isl_basic_set_list_get_basic_set(list
, j
);
7358 disjoint
= isl_basic_set_is_disjoint(bset_i
, bset_j
);
7359 isl_basic_set_free(bset_j
);
7361 isl_die(isl_basic_set_list_get_ctx(list
),
7362 isl_error_unknown
, "not disjoint",
7364 if (disjoint
< 0 || !disjoint
)
7367 isl_basic_set_free(bset_i
);
7369 return isl_stat_error
;
7375 /* Check that the chambers computed by isl_vertices_foreach_disjoint_cell
7376 * are pairwise disjoint.
7378 static int test_chambers(isl_ctx
*ctx
)
7382 for (i
= 0; i
< ARRAY_SIZE(chambers_tests
); ++i
) {
7383 isl_basic_set
*bset
;
7384 isl_vertices
*vertices
;
7385 isl_basic_set_list
*cells
;
7388 bset
= isl_basic_set_read_from_str(ctx
, chambers_tests
[i
]);
7389 vertices
= isl_basic_set_compute_vertices(bset
);
7390 cells
= isl_basic_set_list_alloc(ctx
, 0);
7391 if (isl_vertices_foreach_disjoint_cell(vertices
, &add_cell
,
7393 cells
= isl_basic_set_list_free(cells
);
7394 ok
= check_pairwise_disjoint(cells
);
7395 isl_basic_set_list_free(cells
);
7396 isl_vertices_free(vertices
);
7397 isl_basic_set_free(bset
);
7408 int (*fn
)(isl_ctx
*ctx
);
7410 { "universe", &test_universe
},
7411 { "domain hash", &test_domain_hash
},
7412 { "dual", &test_dual
},
7413 { "dependence analysis", &test_flow
},
7414 { "val", &test_val
},
7415 { "compute divs", &test_compute_divs
},
7416 { "partial lexmin", &test_partial_lexmin
},
7417 { "simplify", &test_simplify
},
7418 { "curry", &test_curry
},
7419 { "piecewise multi affine expressions", &test_pw_multi_aff
},
7420 { "multi piecewise affine expressions", &test_multi_pw_aff
},
7421 { "conversion", &test_conversion
},
7422 { "list", &test_list
},
7423 { "align parameters", &test_align_parameters
},
7424 { "preimage", &test_preimage
},
7425 { "pullback", &test_pullback
},
7426 { "AST", &test_ast
},
7427 { "AST build", &test_ast_build
},
7428 { "AST generation", &test_ast_gen
},
7429 { "eliminate", &test_eliminate
},
7430 { "residue class", &test_residue_class
},
7431 { "div", &test_div
},
7432 { "slice", &test_slice
},
7433 { "fixed power", &test_fixed_power
},
7434 { "sample", &test_sample
},
7435 { "output", &test_output
},
7436 { "vertices", &test_vertices
},
7437 { "chambers", &test_chambers
},
7438 { "fixed", &test_fixed
},
7439 { "equal", &test_equal
},
7440 { "disjoint", &test_disjoint
},
7441 { "product", &test_product
},
7442 { "dim_max", &test_dim_max
},
7443 { "affine", &test_aff
},
7444 { "injective", &test_injective
},
7445 { "schedule (whole component)", &test_schedule_whole
},
7446 { "schedule (incremental)", &test_schedule_incremental
},
7447 { "schedule tree", &test_schedule_tree
},
7448 { "schedule tree grouping", &test_schedule_tree_group
},
7449 { "tile", &test_tile
},
7450 { "union_pw", &test_union_pw
},
7451 { "eval", &test_eval
},
7452 { "parse", &test_parse
},
7453 { "single-valued", &test_sv
},
7454 { "affine hull", &test_affine_hull
},
7455 { "simple_hull", &test_simple_hull
},
7456 { "coalesce", &test_coalesce
},
7457 { "factorize", &test_factorize
},
7458 { "subset", &test_subset
},
7459 { "subtract", &test_subtract
},
7460 { "intersect", &test_intersect
},
7461 { "lexmin", &test_lexmin
},
7462 { "min", &test_min
},
7463 { "gist", &test_gist
},
7464 { "piecewise quasi-polynomials", &test_pwqp
},
7465 { "lift", &test_lift
},
7466 { "bound", &test_bound
},
7467 { "union", &test_union
},
7468 { "split periods", &test_split_periods
},
7469 { "lexicographic order", &test_lex
},
7470 { "bijectivity", &test_bijective
},
7471 { "dataflow analysis", &test_dep
},
7472 { "reading", &test_read
},
7473 { "bounded", &test_bounded
},
7474 { "construction", &test_construction
},
7475 { "dimension manipulation", &test_dim
},
7476 { "map application", &test_application
},
7477 { "convex hull", &test_convex_hull
},
7478 { "transitive closure", &test_closure
},
7481 int main(int argc
, char **argv
)
7484 struct isl_ctx
*ctx
;
7485 struct isl_options
*options
;
7487 options
= isl_options_new_with_defaults();
7489 argc
= isl_options_parse(options
, argc
, argv
, ISL_ARG_ALL
);
7491 ctx
= isl_ctx_alloc_with_options(&isl_options_args
, options
);
7492 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
7493 printf("%s\n", tests
[i
].name
);
7494 if (tests
[i
].fn(ctx
) < 0)