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
)
342 dim
= isl_space_set_alloc(ctx
, 1, 1);
343 bset
= isl_basic_set_universe(isl_space_copy(dim
));
344 ls
= isl_local_space_from_space(dim
);
346 c
= isl_constraint_alloc_inequality(isl_local_space_copy(ls
));
347 isl_int_set_si(v
, -1);
348 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
349 isl_int_set_si(v
, 1);
350 c
= isl_constraint_set_coefficient(c
, isl_dim_param
, 0, v
);
351 bset
= isl_basic_set_add_constraint(bset
, c
);
353 c
= isl_constraint_alloc_inequality(isl_local_space_copy(ls
));
354 isl_int_set_si(v
, 1);
355 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
356 isl_int_set_si(v
, -5);
357 c
= isl_constraint_set_constant(c
, v
);
358 bset
= isl_basic_set_add_constraint(bset
, c
);
360 isl_local_space_free(ls
);
361 isl_basic_set_free(bset
);
368 /* Construct the basic set { [x] : -100 <= x <= 100 }
369 * using isl_basic_set_{lower,upper}_bound_val and
370 * check that it is equal the same basic set parsed from a string.
372 static int test_construction_2(isl_ctx
*ctx
)
377 isl_basic_set
*bset1
, *bset2
;
379 v
= isl_val_int_from_si(ctx
, 100);
380 space
= isl_space_set_alloc(ctx
, 0, 1);
381 bset1
= isl_basic_set_universe(space
);
382 bset1
= isl_basic_set_upper_bound_val(bset1
, isl_dim_set
, 0,
384 bset1
= isl_basic_set_lower_bound_val(bset1
, isl_dim_set
, 0,
386 bset2
= isl_basic_set_read_from_str(ctx
, "{ [x] : -100 <= x <= 100 }");
387 equal
= isl_basic_set_is_equal(bset1
, bset2
);
388 isl_basic_set_free(bset1
);
389 isl_basic_set_free(bset2
);
394 isl_die(ctx
, isl_error_unknown
,
395 "failed construction", return -1);
400 /* Basic tests for constructing basic sets.
402 static int test_construction(isl_ctx
*ctx
)
404 if (test_construction_1(ctx
) < 0)
406 if (test_construction_2(ctx
) < 0)
411 static int test_dim(isl_ctx
*ctx
)
414 isl_map
*map1
, *map2
;
417 map1
= isl_map_read_from_str(ctx
,
418 "[n] -> { [i] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
419 map1
= isl_map_add_dims(map1
, isl_dim_in
, 1);
420 map2
= isl_map_read_from_str(ctx
,
421 "[n] -> { [i,k] -> [j] : exists (a = [i/10] : i - 10a <= n ) }");
422 equal
= isl_map_is_equal(map1
, map2
);
425 map1
= isl_map_project_out(map1
, isl_dim_in
, 0, 1);
426 map2
= isl_map_read_from_str(ctx
, "[n] -> { [i] -> [j] : n >= 0 }");
427 if (equal
>= 0 && equal
)
428 equal
= isl_map_is_equal(map1
, map2
);
436 isl_die(ctx
, isl_error_unknown
,
437 "unexpected result", return -1);
439 str
= "[n] -> { [i] -> [] : exists a : 0 <= i <= n and i = 2 a }";
440 map1
= isl_map_read_from_str(ctx
, str
);
441 str
= "{ [i] -> [j] : exists a : 0 <= i <= j and i = 2 a }";
442 map2
= isl_map_read_from_str(ctx
, str
);
443 map1
= isl_map_move_dims(map1
, isl_dim_out
, 0, isl_dim_param
, 0, 1);
444 equal
= isl_map_is_equal(map1
, map2
);
451 isl_die(ctx
, isl_error_unknown
,
452 "unexpected result", return -1);
458 __isl_give isl_val
*(*op
)(__isl_take isl_val
*v
);
462 { &isl_val_neg
, "0", "0" },
463 { &isl_val_abs
, "0", "0" },
464 { &isl_val_2exp
, "0", "1" },
465 { &isl_val_floor
, "0", "0" },
466 { &isl_val_ceil
, "0", "0" },
467 { &isl_val_neg
, "1", "-1" },
468 { &isl_val_neg
, "-1", "1" },
469 { &isl_val_neg
, "1/2", "-1/2" },
470 { &isl_val_neg
, "-1/2", "1/2" },
471 { &isl_val_neg
, "infty", "-infty" },
472 { &isl_val_neg
, "-infty", "infty" },
473 { &isl_val_neg
, "NaN", "NaN" },
474 { &isl_val_abs
, "1", "1" },
475 { &isl_val_abs
, "-1", "1" },
476 { &isl_val_abs
, "1/2", "1/2" },
477 { &isl_val_abs
, "-1/2", "1/2" },
478 { &isl_val_abs
, "infty", "infty" },
479 { &isl_val_abs
, "-infty", "infty" },
480 { &isl_val_abs
, "NaN", "NaN" },
481 { &isl_val_floor
, "1", "1" },
482 { &isl_val_floor
, "-1", "-1" },
483 { &isl_val_floor
, "1/2", "0" },
484 { &isl_val_floor
, "-1/2", "-1" },
485 { &isl_val_floor
, "infty", "infty" },
486 { &isl_val_floor
, "-infty", "-infty" },
487 { &isl_val_floor
, "NaN", "NaN" },
488 { &isl_val_ceil
, "1", "1" },
489 { &isl_val_ceil
, "-1", "-1" },
490 { &isl_val_ceil
, "1/2", "1" },
491 { &isl_val_ceil
, "-1/2", "0" },
492 { &isl_val_ceil
, "infty", "infty" },
493 { &isl_val_ceil
, "-infty", "-infty" },
494 { &isl_val_ceil
, "NaN", "NaN" },
495 { &isl_val_2exp
, "-3", "1/8" },
496 { &isl_val_2exp
, "-1", "1/2" },
497 { &isl_val_2exp
, "1", "2" },
498 { &isl_val_2exp
, "2", "4" },
499 { &isl_val_2exp
, "3", "8" },
500 { &isl_val_inv
, "1", "1" },
501 { &isl_val_inv
, "2", "1/2" },
502 { &isl_val_inv
, "1/2", "2" },
503 { &isl_val_inv
, "-2", "-1/2" },
504 { &isl_val_inv
, "-1/2", "-2" },
505 { &isl_val_inv
, "0", "NaN" },
506 { &isl_val_inv
, "NaN", "NaN" },
507 { &isl_val_inv
, "infty", "0" },
508 { &isl_val_inv
, "-infty", "0" },
511 /* Perform some basic tests of unary operations on isl_val objects.
513 static int test_un_val(isl_ctx
*ctx
)
517 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v
);
520 for (i
= 0; i
< ARRAY_SIZE(val_un_tests
); ++i
) {
521 v
= isl_val_read_from_str(ctx
, val_un_tests
[i
].arg
);
522 res
= isl_val_read_from_str(ctx
, val_un_tests
[i
].res
);
523 fn
= val_un_tests
[i
].op
;
525 is_nan
= isl_val_is_nan(res
);
529 ok
= isl_val_is_nan(v
);
531 ok
= isl_val_eq(v
, res
);
537 isl_die(ctx
, isl_error_unknown
,
538 "unexpected result", return -1);
545 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
546 __isl_take isl_val
*v2
);
548 ['+'] = { &isl_val_add
},
549 ['-'] = { &isl_val_sub
},
550 ['*'] = { &isl_val_mul
},
551 ['/'] = { &isl_val_div
},
552 ['g'] = { &isl_val_gcd
},
553 ['m'] = { &isl_val_min
},
554 ['M'] = { &isl_val_max
},
562 } val_bin_tests
[] = {
563 { "0", '+', "0", "0" },
564 { "1", '+', "0", "1" },
565 { "1", '+', "1", "2" },
566 { "1", '-', "1", "0" },
567 { "1", '*', "1", "1" },
568 { "1", '/', "1", "1" },
569 { "2", '*', "3", "6" },
570 { "2", '*', "1/2", "1" },
571 { "2", '*', "1/3", "2/3" },
572 { "2/3", '*', "3/5", "2/5" },
573 { "2/3", '*', "7/5", "14/15" },
574 { "2", '/', "1/2", "4" },
575 { "-2", '/', "-1/2", "4" },
576 { "-2", '/', "1/2", "-4" },
577 { "2", '/', "-1/2", "-4" },
578 { "2", '/', "2", "1" },
579 { "2", '/', "3", "2/3" },
580 { "2/3", '/', "5/3", "2/5" },
581 { "2/3", '/', "5/7", "14/15" },
582 { "0", '/', "0", "NaN" },
583 { "42", '/', "0", "NaN" },
584 { "-42", '/', "0", "NaN" },
585 { "infty", '/', "0", "NaN" },
586 { "-infty", '/', "0", "NaN" },
587 { "NaN", '/', "0", "NaN" },
588 { "0", '/', "NaN", "NaN" },
589 { "42", '/', "NaN", "NaN" },
590 { "-42", '/', "NaN", "NaN" },
591 { "infty", '/', "NaN", "NaN" },
592 { "-infty", '/', "NaN", "NaN" },
593 { "NaN", '/', "NaN", "NaN" },
594 { "0", '/', "infty", "0" },
595 { "42", '/', "infty", "0" },
596 { "-42", '/', "infty", "0" },
597 { "infty", '/', "infty", "NaN" },
598 { "-infty", '/', "infty", "NaN" },
599 { "NaN", '/', "infty", "NaN" },
600 { "0", '/', "-infty", "0" },
601 { "42", '/', "-infty", "0" },
602 { "-42", '/', "-infty", "0" },
603 { "infty", '/', "-infty", "NaN" },
604 { "-infty", '/', "-infty", "NaN" },
605 { "NaN", '/', "-infty", "NaN" },
606 { "1", '-', "1/3", "2/3" },
607 { "1/3", '+', "1/2", "5/6" },
608 { "1/2", '+', "1/2", "1" },
609 { "3/4", '-', "1/4", "1/2" },
610 { "1/2", '-', "1/3", "1/6" },
611 { "infty", '+', "42", "infty" },
612 { "infty", '+', "infty", "infty" },
613 { "42", '+', "infty", "infty" },
614 { "infty", '-', "infty", "NaN" },
615 { "infty", '*', "infty", "infty" },
616 { "infty", '*', "-infty", "-infty" },
617 { "-infty", '*', "infty", "-infty" },
618 { "-infty", '*', "-infty", "infty" },
619 { "0", '*', "infty", "NaN" },
620 { "1", '*', "infty", "infty" },
621 { "infty", '*', "0", "NaN" },
622 { "infty", '*', "42", "infty" },
623 { "42", '-', "infty", "-infty" },
624 { "infty", '+', "-infty", "NaN" },
625 { "4", 'g', "6", "2" },
626 { "5", 'g', "6", "1" },
627 { "42", 'm', "3", "3" },
628 { "42", 'M', "3", "42" },
629 { "3", 'm', "42", "3" },
630 { "3", 'M', "42", "42" },
631 { "42", 'm', "infty", "42" },
632 { "42", 'M', "infty", "infty" },
633 { "42", 'm', "-infty", "-infty" },
634 { "42", 'M', "-infty", "42" },
635 { "42", 'm', "NaN", "NaN" },
636 { "42", 'M', "NaN", "NaN" },
637 { "infty", 'm', "-infty", "-infty" },
638 { "infty", 'M', "-infty", "infty" },
641 /* Perform some basic tests of binary operations on isl_val objects.
643 static int test_bin_val(isl_ctx
*ctx
)
646 isl_val
*v1
, *v2
, *res
;
647 __isl_give isl_val
*(*fn
)(__isl_take isl_val
*v1
,
648 __isl_take isl_val
*v2
);
651 for (i
= 0; i
< ARRAY_SIZE(val_bin_tests
); ++i
) {
652 v1
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg1
);
653 v2
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].arg2
);
654 res
= isl_val_read_from_str(ctx
, val_bin_tests
[i
].res
);
655 fn
= val_bin_op
[val_bin_tests
[i
].op
].fn
;
657 if (isl_val_is_nan(res
))
658 ok
= isl_val_is_nan(v1
);
660 ok
= isl_val_eq(v1
, res
);
666 isl_die(ctx
, isl_error_unknown
,
667 "unexpected result", return -1);
673 /* Perform some basic tests on isl_val objects.
675 static int test_val(isl_ctx
*ctx
)
677 if (test_un_val(ctx
) < 0)
679 if (test_bin_val(ctx
) < 0)
684 /* Sets described using existentially quantified variables that
685 * can also be described without.
687 static const char *elimination_tests
[] = {
688 "{ [i,j] : 2 * [i/2] + 3 * [j/4] <= 10 and 2 i = j }",
689 "{ [m, w] : exists a : w - 2m - 5 <= 3a <= m - 2w }",
690 "{ [m, w] : exists a : w >= 0 and a < m and -1 + w <= a <= 2m - w }",
693 /* Check that redundant existentially quantified variables are
696 static int test_elimination(isl_ctx
*ctx
)
702 for (i
= 0; i
< ARRAY_SIZE(elimination_tests
); ++i
) {
703 bset
= isl_basic_set_read_from_str(ctx
, elimination_tests
[i
]);
704 n
= isl_basic_set_dim(bset
, isl_dim_div
);
705 isl_basic_set_free(bset
);
709 isl_die(ctx
, isl_error_unknown
,
710 "expecting no existentials", return -1);
716 static int test_div(isl_ctx
*ctx
)
724 struct isl_basic_set
*bset
;
725 struct isl_constraint
*c
;
730 dim
= isl_space_set_alloc(ctx
, 0, 3);
731 bset
= isl_basic_set_universe(isl_space_copy(dim
));
732 ls
= isl_local_space_from_space(dim
);
734 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
735 isl_int_set_si(v
, -1);
736 c
= isl_constraint_set_constant(c
, v
);
737 isl_int_set_si(v
, 1);
738 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
739 isl_int_set_si(v
, 3);
740 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
741 bset
= isl_basic_set_add_constraint(bset
, c
);
743 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
744 isl_int_set_si(v
, 1);
745 c
= isl_constraint_set_constant(c
, v
);
746 isl_int_set_si(v
, -1);
747 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
748 isl_int_set_si(v
, 3);
749 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
750 bset
= isl_basic_set_add_constraint(bset
, c
);
752 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
754 assert(bset
&& bset
->n_div
== 1);
755 isl_local_space_free(ls
);
756 isl_basic_set_free(bset
);
759 dim
= isl_space_set_alloc(ctx
, 0, 3);
760 bset
= isl_basic_set_universe(isl_space_copy(dim
));
761 ls
= isl_local_space_from_space(dim
);
763 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
764 isl_int_set_si(v
, 1);
765 c
= isl_constraint_set_constant(c
, v
);
766 isl_int_set_si(v
, -1);
767 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
768 isl_int_set_si(v
, 3);
769 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
770 bset
= isl_basic_set_add_constraint(bset
, c
);
772 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
773 isl_int_set_si(v
, -1);
774 c
= isl_constraint_set_constant(c
, v
);
775 isl_int_set_si(v
, 1);
776 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
777 isl_int_set_si(v
, 3);
778 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
779 bset
= isl_basic_set_add_constraint(bset
, c
);
781 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
783 assert(bset
&& bset
->n_div
== 1);
784 isl_local_space_free(ls
);
785 isl_basic_set_free(bset
);
788 dim
= isl_space_set_alloc(ctx
, 0, 3);
789 bset
= isl_basic_set_universe(isl_space_copy(dim
));
790 ls
= isl_local_space_from_space(dim
);
792 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
793 isl_int_set_si(v
, 1);
794 c
= isl_constraint_set_constant(c
, v
);
795 isl_int_set_si(v
, -1);
796 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
797 isl_int_set_si(v
, 3);
798 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
799 bset
= isl_basic_set_add_constraint(bset
, c
);
801 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
802 isl_int_set_si(v
, -3);
803 c
= isl_constraint_set_constant(c
, v
);
804 isl_int_set_si(v
, 1);
805 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
806 isl_int_set_si(v
, 4);
807 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
808 bset
= isl_basic_set_add_constraint(bset
, c
);
810 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
812 assert(bset
&& bset
->n_div
== 1);
813 isl_local_space_free(ls
);
814 isl_basic_set_free(bset
);
817 dim
= isl_space_set_alloc(ctx
, 0, 3);
818 bset
= isl_basic_set_universe(isl_space_copy(dim
));
819 ls
= isl_local_space_from_space(dim
);
821 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
822 isl_int_set_si(v
, 2);
823 c
= isl_constraint_set_constant(c
, v
);
824 isl_int_set_si(v
, -1);
825 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
826 isl_int_set_si(v
, 3);
827 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
828 bset
= isl_basic_set_add_constraint(bset
, c
);
830 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
831 isl_int_set_si(v
, -1);
832 c
= isl_constraint_set_constant(c
, v
);
833 isl_int_set_si(v
, 1);
834 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
835 isl_int_set_si(v
, 6);
836 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
837 bset
= isl_basic_set_add_constraint(bset
, c
);
839 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 1, 2);
841 assert(isl_basic_set_is_empty(bset
));
842 isl_local_space_free(ls
);
843 isl_basic_set_free(bset
);
846 dim
= isl_space_set_alloc(ctx
, 0, 3);
847 bset
= isl_basic_set_universe(isl_space_copy(dim
));
848 ls
= isl_local_space_from_space(dim
);
850 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
851 isl_int_set_si(v
, -1);
852 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
853 isl_int_set_si(v
, 3);
854 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
855 bset
= isl_basic_set_add_constraint(bset
, c
);
857 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
858 isl_int_set_si(v
, 1);
859 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
860 isl_int_set_si(v
, -3);
861 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
862 bset
= isl_basic_set_add_constraint(bset
, c
);
864 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
866 assert(bset
&& bset
->n_div
== 0);
867 isl_basic_set_free(bset
);
868 isl_local_space_free(ls
);
871 dim
= isl_space_set_alloc(ctx
, 0, 3);
872 bset
= isl_basic_set_universe(isl_space_copy(dim
));
873 ls
= isl_local_space_from_space(dim
);
875 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
876 isl_int_set_si(v
, -1);
877 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
878 isl_int_set_si(v
, 6);
879 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
880 bset
= isl_basic_set_add_constraint(bset
, c
);
882 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
883 isl_int_set_si(v
, 1);
884 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
885 isl_int_set_si(v
, -3);
886 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
887 bset
= isl_basic_set_add_constraint(bset
, c
);
889 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
891 assert(bset
&& bset
->n_div
== 1);
892 isl_basic_set_free(bset
);
893 isl_local_space_free(ls
);
896 /* This test is a bit tricky. We set up an equality
898 * Normalization of divs creates _two_ divs
901 * Afterwards e0 is removed again because it has coefficient -1
902 * and we end up with the original equality and div again.
903 * Perhaps we can avoid the introduction of this temporary div.
905 dim
= isl_space_set_alloc(ctx
, 0, 4);
906 bset
= isl_basic_set_universe(isl_space_copy(dim
));
907 ls
= isl_local_space_from_space(dim
);
909 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
910 isl_int_set_si(v
, -1);
911 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
912 isl_int_set_si(v
, -3);
913 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
914 isl_int_set_si(v
, -3);
915 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
916 isl_int_set_si(v
, 6);
917 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
918 bset
= isl_basic_set_add_constraint(bset
, c
);
920 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
922 /* Test disabled for now */
924 assert(bset && bset->n_div == 1);
926 isl_local_space_free(ls
);
927 isl_basic_set_free(bset
);
930 dim
= isl_space_set_alloc(ctx
, 0, 5);
931 bset
= isl_basic_set_universe(isl_space_copy(dim
));
932 ls
= isl_local_space_from_space(dim
);
934 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
935 isl_int_set_si(v
, -1);
936 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
937 isl_int_set_si(v
, -3);
938 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
939 isl_int_set_si(v
, -3);
940 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
941 isl_int_set_si(v
, 6);
942 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 4, v
);
943 bset
= isl_basic_set_add_constraint(bset
, c
);
945 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
946 isl_int_set_si(v
, -1);
947 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
948 isl_int_set_si(v
, 1);
949 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
950 isl_int_set_si(v
, 1);
951 c
= isl_constraint_set_constant(c
, v
);
952 bset
= isl_basic_set_add_constraint(bset
, c
);
954 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 4, 1);
956 /* Test disabled for now */
958 assert(bset && bset->n_div == 1);
960 isl_local_space_free(ls
);
961 isl_basic_set_free(bset
);
964 dim
= isl_space_set_alloc(ctx
, 0, 4);
965 bset
= isl_basic_set_universe(isl_space_copy(dim
));
966 ls
= isl_local_space_from_space(dim
);
968 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
969 isl_int_set_si(v
, 1);
970 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
971 isl_int_set_si(v
, -1);
972 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 1, v
);
973 isl_int_set_si(v
, -2);
974 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
975 bset
= isl_basic_set_add_constraint(bset
, c
);
977 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
978 isl_int_set_si(v
, -1);
979 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
980 isl_int_set_si(v
, 3);
981 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 3, v
);
982 isl_int_set_si(v
, 2);
983 c
= isl_constraint_set_constant(c
, v
);
984 bset
= isl_basic_set_add_constraint(bset
, c
);
986 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 2);
988 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
990 assert(!isl_basic_set_is_empty(bset
));
992 isl_local_space_free(ls
);
993 isl_basic_set_free(bset
);
996 dim
= isl_space_set_alloc(ctx
, 0, 3);
997 bset
= isl_basic_set_universe(isl_space_copy(dim
));
998 ls
= isl_local_space_from_space(dim
);
1000 c
= isl_constraint_alloc_equality(isl_local_space_copy(ls
));
1001 isl_int_set_si(v
, 1);
1002 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 0, v
);
1003 isl_int_set_si(v
, -2);
1004 c
= isl_constraint_set_coefficient(c
, isl_dim_set
, 2, v
);
1005 bset
= isl_basic_set_add_constraint(bset
, c
);
1007 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 2, 1);
1009 bset
= isl_basic_set_fix_si(bset
, isl_dim_set
, 0, 2);
1011 isl_local_space_free(ls
);
1012 isl_basic_set_free(bset
);
1016 str
= "{ [i] : exists (e0, e1: 3e1 >= 1 + 2e0 and "
1017 "8e1 <= -1 + 5i - 5e0 and 2e1 >= 1 + 2i - 5e0) }";
1018 set
= isl_set_read_from_str(ctx
, str
);
1019 set
= isl_set_compute_divs(set
);
1024 if (test_elimination(ctx
) < 0)
1027 str
= "{ [i,j,k] : 3 + i + 2j >= 0 and 2 * [(i+2j)/4] <= k }";
1028 set
= isl_set_read_from_str(ctx
, str
);
1029 set
= isl_set_remove_divs_involving_dims(set
, isl_dim_set
, 0, 2);
1030 set
= isl_set_fix_si(set
, isl_dim_set
, 2, -3);
1031 empty
= isl_set_is_empty(set
);
1036 isl_die(ctx
, isl_error_unknown
,
1037 "result not as accurate as expected", return -1);
1042 void test_application_case(struct isl_ctx
*ctx
, const char *name
)
1046 struct isl_basic_set
*bset1
, *bset2
;
1047 struct isl_basic_map
*bmap
;
1049 filename
= get_filename(ctx
, name
, "omega");
1051 input
= fopen(filename
, "r");
1054 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1055 bmap
= isl_basic_map_read_from_file(ctx
, input
);
1057 bset1
= isl_basic_set_apply(bset1
, bmap
);
1059 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1061 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1063 isl_basic_set_free(bset1
);
1064 isl_basic_set_free(bset2
);
1070 static int test_application(isl_ctx
*ctx
)
1072 test_application_case(ctx
, "application");
1073 test_application_case(ctx
, "application2");
1078 void test_affine_hull_case(struct isl_ctx
*ctx
, const char *name
)
1082 struct isl_basic_set
*bset1
, *bset2
;
1084 filename
= get_filename(ctx
, name
, "polylib");
1086 input
= fopen(filename
, "r");
1089 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1090 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1092 bset1
= isl_basic_set_affine_hull(bset1
);
1094 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1096 isl_basic_set_free(bset1
);
1097 isl_basic_set_free(bset2
);
1103 int test_affine_hull(struct isl_ctx
*ctx
)
1107 isl_basic_set
*bset
, *bset2
;
1111 test_affine_hull_case(ctx
, "affine2");
1112 test_affine_hull_case(ctx
, "affine");
1113 test_affine_hull_case(ctx
, "affine3");
1115 str
= "[m] -> { [i0] : exists (e0, e1: e1 <= 1 + i0 and "
1116 "m >= 3 and 4i0 <= 2 + m and e1 >= i0 and "
1117 "e1 >= 0 and e1 <= 2 and e1 >= 1 + 2e0 and "
1118 "2e1 <= 1 + m + 4e0 and 2e1 >= 2 - m + 4i0 - 4e0) }";
1119 set
= isl_set_read_from_str(ctx
, str
);
1120 bset
= isl_set_affine_hull(set
);
1121 n
= isl_basic_set_dim(bset
, isl_dim_div
);
1122 isl_basic_set_free(bset
);
1124 isl_die(ctx
, isl_error_unknown
, "not expecting any divs",
1127 /* Check that isl_map_affine_hull is not confused by
1128 * the reordering of divs in isl_map_align_divs.
1130 str
= "{ [a, b, c, 0] : exists (e0 = [(b)/32], e1 = [(c)/32]: "
1131 "32e0 = b and 32e1 = c); "
1132 "[a, 0, c, 0] : exists (e0 = [(c)/32]: 32e0 = c) }";
1133 set
= isl_set_read_from_str(ctx
, str
);
1134 bset
= isl_set_affine_hull(set
);
1135 isl_basic_set_free(bset
);
1139 str
= "{ [a] : exists e0, e1, e2: 32e1 = 31 + 31a + 31e0 and "
1140 "32e2 = 31 + 31e0 }";
1141 set
= isl_set_read_from_str(ctx
, str
);
1142 bset
= isl_set_affine_hull(set
);
1143 str
= "{ [a] : exists e : a = 32 e }";
1144 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1145 subset
= isl_basic_set_is_subset(bset
, bset2
);
1146 isl_basic_set_free(bset
);
1147 isl_basic_set_free(bset2
);
1151 isl_die(ctx
, isl_error_unknown
, "not as accurate as expected",
1157 /* Pairs of maps and the corresponding expected results of
1158 * isl_map_plain_unshifted_simple_hull.
1163 } plain_unshifted_simple_hull_tests
[] = {
1164 { "{ [i] -> [j] : i >= 1 and j >= 1 or i >= 2 and j <= 10 }",
1165 "{ [i] -> [j] : i >= 1 }" },
1166 { "{ [n] -> [i,j,k] : (i mod 3 = 2 and j mod 4 = 2) or "
1167 "(j mod 4 = 2 and k mod 6 = n) }",
1168 "{ [n] -> [i,j,k] : j mod 4 = 2 }" },
1171 /* Basic tests for isl_map_plain_unshifted_simple_hull.
1173 static int test_plain_unshifted_simple_hull(isl_ctx
*ctx
)
1177 isl_basic_map
*hull
, *expected
;
1180 for (i
= 0; i
< ARRAY_SIZE(plain_unshifted_simple_hull_tests
); ++i
) {
1182 str
= plain_unshifted_simple_hull_tests
[i
].map
;
1183 map
= isl_map_read_from_str(ctx
, str
);
1184 str
= plain_unshifted_simple_hull_tests
[i
].hull
;
1185 expected
= isl_basic_map_read_from_str(ctx
, str
);
1186 hull
= isl_map_plain_unshifted_simple_hull(map
);
1187 equal
= isl_basic_map_is_equal(hull
, expected
);
1188 isl_basic_map_free(hull
);
1189 isl_basic_map_free(expected
);
1193 isl_die(ctx
, isl_error_unknown
, "unexpected hull",
1200 /* Pairs of sets and the corresponding expected results of
1201 * isl_set_unshifted_simple_hull.
1206 } unshifted_simple_hull_tests
[] = {
1207 { "{ [0,x,y] : x <= -1; [1,x,y] : x <= y <= -x; [2,x,y] : x <= 1 }",
1208 "{ [t,x,y] : 0 <= t <= 2 and x <= 1 }" },
1211 /* Basic tests for isl_set_unshifted_simple_hull.
1213 static int test_unshifted_simple_hull(isl_ctx
*ctx
)
1217 isl_basic_set
*hull
, *expected
;
1220 for (i
= 0; i
< ARRAY_SIZE(unshifted_simple_hull_tests
); ++i
) {
1222 str
= unshifted_simple_hull_tests
[i
].set
;
1223 set
= isl_set_read_from_str(ctx
, str
);
1224 str
= unshifted_simple_hull_tests
[i
].hull
;
1225 expected
= isl_basic_set_read_from_str(ctx
, str
);
1226 hull
= isl_set_unshifted_simple_hull(set
);
1227 equal
= isl_basic_set_is_equal(hull
, expected
);
1228 isl_basic_set_free(hull
);
1229 isl_basic_set_free(expected
);
1233 isl_die(ctx
, isl_error_unknown
, "unexpected hull",
1240 static int test_simple_hull(struct isl_ctx
*ctx
)
1244 isl_basic_set
*bset
;
1247 str
= "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x;"
1248 "[y, x] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }";
1249 set
= isl_set_read_from_str(ctx
, str
);
1250 bset
= isl_set_simple_hull(set
);
1251 is_empty
= isl_basic_set_is_empty(bset
);
1252 isl_basic_set_free(bset
);
1254 if (is_empty
== isl_bool_error
)
1257 if (is_empty
== isl_bool_false
)
1258 isl_die(ctx
, isl_error_unknown
, "Empty set should be detected",
1261 if (test_plain_unshifted_simple_hull(ctx
) < 0)
1263 if (test_unshifted_simple_hull(ctx
) < 0)
1269 void test_convex_hull_case(struct isl_ctx
*ctx
, const char *name
)
1273 struct isl_basic_set
*bset1
, *bset2
;
1274 struct isl_set
*set
;
1276 filename
= get_filename(ctx
, name
, "polylib");
1278 input
= fopen(filename
, "r");
1281 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1282 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1284 set
= isl_basic_set_union(bset1
, bset2
);
1285 bset1
= isl_set_convex_hull(set
);
1287 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1289 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1291 isl_basic_set_free(bset1
);
1292 isl_basic_set_free(bset2
);
1301 } convex_hull_tests
[] = {
1302 { "{ [i0, i1, i2] : (i2 = 1 and i0 = 0 and i1 >= 0) or "
1303 "(i0 = 1 and i1 = 0 and i2 = 1) or "
1304 "(i0 = 0 and i1 = 0 and i2 = 0) }",
1305 "{ [i0, i1, i2] : i0 >= 0 and i2 >= i0 and i2 <= 1 and i1 >= 0 }" },
1306 { "[n] -> { [i0, i1, i0] : i0 <= -4 + n; "
1307 "[i0, i0, i2] : n = 6 and i0 >= 0 and i2 <= 7 - i0 and "
1308 "i2 <= 5 and i2 >= 4; "
1309 "[3, i1, 3] : n = 5 and i1 <= 2 and i1 >= 0 }",
1310 "[n] -> { [i0, i1, i2] : i2 <= -1 + n and 2i2 <= -6 + 3n - i0 and "
1311 "i2 <= 5 + i0 and i2 >= i0 }" },
1312 { "{ [x, y] : 3y <= 2x and y >= -2 + 2x and 2y >= 2 - x }",
1313 "{ [x, y] : 1 = 0 }" },
1314 { "{ [x, y, z] : 0 <= x, y, z <= 10; [x, y, 0] : x >= 0 and y > 0; "
1315 "[x, y, 0] : x >= 0 and y < 0 }",
1316 "{ [x, y, z] : x >= 0 and 0 <= z <= 10 }" },
1319 static int test_convex_hull_algo(isl_ctx
*ctx
, int convex
)
1322 int orig_convex
= ctx
->opt
->convex
;
1323 ctx
->opt
->convex
= convex
;
1325 test_convex_hull_case(ctx
, "convex0");
1326 test_convex_hull_case(ctx
, "convex1");
1327 test_convex_hull_case(ctx
, "convex2");
1328 test_convex_hull_case(ctx
, "convex3");
1329 test_convex_hull_case(ctx
, "convex4");
1330 test_convex_hull_case(ctx
, "convex5");
1331 test_convex_hull_case(ctx
, "convex6");
1332 test_convex_hull_case(ctx
, "convex7");
1333 test_convex_hull_case(ctx
, "convex8");
1334 test_convex_hull_case(ctx
, "convex9");
1335 test_convex_hull_case(ctx
, "convex10");
1336 test_convex_hull_case(ctx
, "convex11");
1337 test_convex_hull_case(ctx
, "convex12");
1338 test_convex_hull_case(ctx
, "convex13");
1339 test_convex_hull_case(ctx
, "convex14");
1340 test_convex_hull_case(ctx
, "convex15");
1342 for (i
= 0; i
< ARRAY_SIZE(convex_hull_tests
); ++i
) {
1343 isl_set
*set1
, *set2
;
1346 set1
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].set
);
1347 set2
= isl_set_read_from_str(ctx
, convex_hull_tests
[i
].hull
);
1348 set1
= isl_set_from_basic_set(isl_set_convex_hull(set1
));
1349 equal
= isl_set_is_equal(set1
, set2
);
1356 isl_die(ctx
, isl_error_unknown
,
1357 "unexpected convex hull", return -1);
1360 ctx
->opt
->convex
= orig_convex
;
1365 static int test_convex_hull(isl_ctx
*ctx
)
1367 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_FM
) < 0)
1369 if (test_convex_hull_algo(ctx
, ISL_CONVEX_HULL_WRAP
) < 0)
1374 void test_gist_case(struct isl_ctx
*ctx
, const char *name
)
1378 struct isl_basic_set
*bset1
, *bset2
;
1380 filename
= get_filename(ctx
, name
, "polylib");
1382 input
= fopen(filename
, "r");
1385 bset1
= isl_basic_set_read_from_file(ctx
, input
);
1386 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1388 bset1
= isl_basic_set_gist(bset1
, bset2
);
1390 bset2
= isl_basic_set_read_from_file(ctx
, input
);
1392 assert(isl_basic_set_is_equal(bset1
, bset2
) == 1);
1394 isl_basic_set_free(bset1
);
1395 isl_basic_set_free(bset2
);
1401 /* Inputs to isl_map_plain_gist_basic_map, along with the expected output.
1405 const char *context
;
1407 } plain_gist_tests
[] = {
1408 { "{ [i] -> [j] : i >= 1 and j >= 1 or i >= 2 and j <= 10 }",
1409 "{ [i] -> [j] : i >= 1 }",
1410 "{ [i] -> [j] : j >= 1 or i >= 2 and j <= 10 }" },
1411 { "{ [n] -> [i,j,k] : (i mod 3 = 2 and j mod 4 = 2) or "
1412 "(j mod 4 = 2 and k mod 6 = n) }",
1413 "{ [n] -> [i,j,k] : j mod 4 = 2 }",
1414 "{ [n] -> [i,j,k] : (i mod 3 = 2) or (k mod 6 = n) }" },
1415 { "{ [i] -> [j] : i > j and (exists a,b : i <= 2a + 5b <= 2) }",
1416 "{ [i] -> [j] : i > j }",
1417 "{ [i] -> [j] : exists a,b : i <= 2a + 5b <= 2 }" },
1420 /* Basic tests for isl_map_plain_gist_basic_map.
1422 static int test_plain_gist(isl_ctx
*ctx
)
1426 for (i
= 0; i
< ARRAY_SIZE(plain_gist_tests
); ++i
) {
1429 isl_map
*map
, *gist
;
1430 isl_basic_map
*context
;
1432 map
= isl_map_read_from_str(ctx
, plain_gist_tests
[i
].map
);
1433 str
= plain_gist_tests
[i
].context
;
1434 context
= isl_basic_map_read_from_str(ctx
, str
);
1435 map
= isl_map_plain_gist_basic_map(map
, context
);
1436 gist
= isl_map_read_from_str(ctx
, plain_gist_tests
[i
].gist
);
1437 equal
= isl_map_is_equal(map
, gist
);
1443 isl_die(ctx
, isl_error_unknown
,
1444 "incorrect gist result", return -1);
1452 const char *context
;
1455 { "{ [a, b, c] : a <= 15 and a >= 1 }",
1456 "{ [a, b, c] : exists (e0 = floor((-1 + a)/16): a >= 1 and "
1457 "c <= 30 and 32e0 >= -62 + 2a + 2b - c and b >= 0) }",
1458 "{ [a, b, c] : a <= 15 }" },
1459 { "{ : }", "{ : 1 = 0 }", "{ : }" },
1460 { "{ : 1 = 0 }", "{ : 1 = 0 }", "{ : }" },
1461 { "[M] -> { [x] : exists (e0 = floor((-2 + x)/3): 3e0 = -2 + x) }",
1462 "[M] -> { [3M] }" , "[M] -> { [x] : 1 = 0 }" },
1463 { "{ [m, n, a, b] : a <= 2147 + n }",
1464 "{ [m, n, a, b] : (m >= 1 and n >= 1 and a <= 2148 - m and "
1465 "b <= 2148 - n and b >= 0 and b >= 2149 - n - a) or "
1466 "(n >= 1 and a >= 0 and b <= 2148 - n - a and "
1468 "{ [m, n, ku, kl] }" },
1469 { "{ [a, a, b] : a >= 10 }",
1470 "{ [a, b, c] : c >= a and c <= b and c >= 2 }",
1471 "{ [a, a, b] : a >= 10 }" },
1472 { "{ [i, j] : i >= 0 and i + j >= 0 }", "{ [i, j] : i <= 0 }",
1473 "{ [0, j] : j >= 0 }" },
1474 /* Check that no constraints on i6 are introduced in the gist */
1475 { "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1476 "20e0 <= 1530 - 4t1 - 5i4 and 20e0 >= 1511 - 4t1 - 5i4 and "
1477 "5e0 <= 381 - t1 and i4 <= 1) }",
1478 "[t1] -> { [i4, i6] : exists (e0 = floor((-t1 + i6)/5): "
1479 "5e0 = -t1 + i6 and i6 <= 6 and i6 >= 3) }",
1480 "[t1] -> { [i4, i6] : exists (e0 = floor((1530 - 4t1 - 5i4)/20): "
1481 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 <= 1530 - 4t1 - 5i4 and "
1482 "20e0 >= 1511 - 4t1 - 5i4) }" },
1483 /* Check that no constraints on i6 are introduced in the gist */
1484 { "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((1 + i4)/2), "
1485 "e1 = floor((1530 - 4t1 - 5i4)/20), "
1486 "e2 = floor((-4t1 - 5i4 + 10*floor((1 + i4)/2))/20), "
1487 "e3 = floor((-1 + i4)/2): t2 = 0 and 2e3 = -1 + i4 and "
1488 "20e2 >= -19 - 4t1 - 5i4 + 10e0 and 5e2 <= 1 - t1 and "
1489 "2e0 <= 1 + i4 and 2e0 >= i4 and "
1490 "20e1 <= 1530 - 4t1 - 5i4 and "
1491 "20e1 >= 1511 - 4t1 - 5i4 and i4 <= 1 and "
1492 "5e1 <= 381 - t1 and 20e2 <= -4t1 - 5i4 + 10e0) }",
1493 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((-17 + i4)/2), "
1494 "e1 = floor((-t1 + i6)/5): 5e1 = -t1 + i6 and "
1495 "2e0 <= -17 + i4 and 2e0 >= -18 + i4 and "
1496 "10e0 <= -91 + 5i4 + 4i6 and "
1497 "10e0 >= -105 + 5i4 + 4i6) }",
1498 "[t1, t2] -> { [i4, i5, i6] : exists (e0 = floor((381 - t1)/5), "
1499 "e1 = floor((-1 + i4)/2): t2 = 0 and 2e1 = -1 + i4 and "
1500 "i4 <= 1 and 5e0 <= 381 - t1 and 20e0 >= 1511 - 4t1 - 5i4) }" },
1501 { "{ [0, 0, q, p] : -5 <= q <= 5 and p >= 0 }",
1502 "{ [a, b, q, p] : b >= 1 + a }",
1503 "{ [a, b, q, p] : false }" },
1504 { "[n] -> { [x] : x = n && x mod 32 = 0 }",
1505 "[n] -> { [x] : x mod 32 = 0 }",
1506 "[n] -> { [x = n] }" },
1507 { "{ [x] : x mod 6 = 0 }", "{ [x] : x mod 3 = 0 }",
1508 "{ [x] : x mod 2 = 0 }" },
1509 { "{ [x] : x mod 3200 = 0 }", "{ [x] : x mod 10000 = 0 }",
1510 "{ [x] : x mod 128 = 0 }" },
1511 { "{ [x] : x mod 3200 = 0 }", "{ [x] : x mod 10 = 0 }",
1512 "{ [x] : x mod 3200 = 0 }" },
1513 { "{ [a, b, c] : a mod 2 = 0 and a = c }",
1514 "{ [a, b, c] : b mod 2 = 0 and b = c }",
1515 "{ [a, b, c = a] }" },
1516 { "{ [a, b, c] : a mod 6 = 0 and a = c }",
1517 "{ [a, b, c] : b mod 2 = 0 and b = c }",
1518 "{ [a, b, c = a] : a mod 3 = 0 }" },
1519 { "{ [x] : 0 <= x <= 4 or 6 <= x <= 9 }",
1520 "{ [x] : 1 <= x <= 3 or 7 <= x <= 8 }",
1522 { "{ [x,y] : x < 0 and 0 <= y <= 4 or x >= -2 and -x <= y <= 10 + x }",
1523 "{ [x,y] : 1 <= y <= 3 }",
1527 /* Check that isl_set_gist behaves as expected.
1529 * For the test cases in gist_tests, besides checking that the result
1530 * is as expected, also check that applying the gist operation does
1531 * not modify the input set (an earlier version of isl would do that) and
1532 * that the test case is consistent, i.e., that the gist has the same
1533 * intersection with the context as the input set.
1535 static int test_gist(struct isl_ctx
*ctx
)
1539 isl_basic_set
*bset1
, *bset2
;
1540 isl_map
*map1
, *map2
;
1543 for (i
= 0; i
< ARRAY_SIZE(gist_tests
); ++i
) {
1544 int equal_input
, equal_intersection
;
1545 isl_set
*set1
, *set2
, *copy
, *context
;
1547 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1548 context
= isl_set_read_from_str(ctx
, gist_tests
[i
].context
);
1549 copy
= isl_set_copy(set1
);
1550 set1
= isl_set_gist(set1
, isl_set_copy(context
));
1551 set2
= isl_set_read_from_str(ctx
, gist_tests
[i
].gist
);
1552 equal
= isl_set_is_equal(set1
, set2
);
1554 set1
= isl_set_read_from_str(ctx
, gist_tests
[i
].set
);
1555 equal_input
= isl_set_is_equal(set1
, copy
);
1557 set1
= isl_set_intersect(set1
, isl_set_copy(context
));
1558 set2
= isl_set_intersect(set2
, context
);
1559 equal_intersection
= isl_set_is_equal(set1
, set2
);
1562 if (equal
< 0 || equal_input
< 0 || equal_intersection
< 0)
1565 isl_die(ctx
, isl_error_unknown
,
1566 "incorrect gist result", return -1);
1568 isl_die(ctx
, isl_error_unknown
,
1569 "gist modified input", return -1);
1571 isl_die(ctx
, isl_error_unknown
,
1572 "inconsistent gist test case", return -1);
1575 test_gist_case(ctx
, "gist1");
1577 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : "
1578 "exists (e0 = [(15 + p0 + 15p6 + 15p10)/16], e1 = [(p5)/8], "
1579 "e2 = [(p6)/128], e3 = [(8p2 - p5)/128], "
1580 "e4 = [(128p3 - p6)/4096]: 8e1 = p5 and 128e2 = p6 and "
1581 "128e3 = 8p2 - p5 and 4096e4 = 128p3 - p6 and p2 >= 0 and "
1582 "16e0 >= 16 + 16p6 + 15p10 and p2 <= 15 and p3 >= 0 and "
1583 "p3 <= 31 and p6 >= 128p3 and p5 >= 8p2 and p10 >= 0 and "
1584 "16e0 <= 15 + p0 + 15p6 + 15p10 and 16e0 >= p0 + 15p6 + 15p10 and "
1585 "p10 <= 15 and p10 <= -1 + p0 - p6) }";
1586 bset1
= isl_basic_set_read_from_str(ctx
, str
);
1587 str
= "[p0, p2, p3, p5, p6, p10] -> { [] : exists (e0 = [(p5)/8], "
1588 "e1 = [(p6)/128], e2 = [(8p2 - p5)/128], "
1589 "e3 = [(128p3 - p6)/4096]: 8e0 = p5 and 128e1 = p6 and "
1590 "128e2 = 8p2 - p5 and 4096e3 = 128p3 - p6 and p5 >= -7 and "
1591 "p2 >= 0 and 8p2 <= -1 + p0 and p2 <= 15 and p3 >= 0 and "
1592 "p3 <= 31 and 128p3 <= -1 + p0 and p6 >= -127 and "
1593 "p5 <= -1 + p0 and p6 <= -1 + p0 and p6 >= 128p3 and "
1594 "p0 >= 1 and p5 >= 8p2 and p10 >= 0 and p10 <= 15 ) }";
1595 bset2
= isl_basic_set_read_from_str(ctx
, str
);
1596 bset1
= isl_basic_set_gist(bset1
, bset2
);
1597 assert(bset1
&& bset1
->n_div
== 0);
1598 isl_basic_set_free(bset1
);
1600 /* Check that the integer divisions of the second disjunct
1601 * do not spread to the first disjunct.
1603 str
= "[t1] -> { S_0[] -> A[o0] : (exists (e0 = [(-t1 + o0)/16]: "
1604 "16e0 = -t1 + o0 and o0 >= 0 and o0 <= 15 and t1 >= 0)) or "
1605 "(exists (e0 = [(-1 + t1)/16], "
1606 "e1 = [(-16 + t1 - 16e0)/4294967296]: "
1607 "4294967296e1 = -16 + t1 - o0 - 16e0 and "
1608 "16e0 <= -1 + t1 and 16e0 >= -16 + t1 and o0 >= 0 and "
1609 "o0 <= 4294967295 and t1 <= -1)) }";
1610 map1
= isl_map_read_from_str(ctx
, str
);
1611 str
= "[t1] -> { S_0[] -> A[o0] : t1 >= 0 and t1 <= 4294967295 }";
1612 map2
= isl_map_read_from_str(ctx
, str
);
1613 map1
= isl_map_gist(map1
, map2
);
1617 isl_die(ctx
, isl_error_unknown
, "expecting single disjunct",
1618 isl_map_free(map1
); return -1);
1619 if (isl_basic_map_dim(map1
->p
[0], isl_dim_div
) != 1)
1620 isl_die(ctx
, isl_error_unknown
, "expecting single div",
1621 isl_map_free(map1
); return -1);
1624 if (test_plain_gist(ctx
) < 0)
1630 int test_coalesce_set(isl_ctx
*ctx
, const char *str
, int check_one
)
1632 isl_set
*set
, *set2
;
1636 set
= isl_set_read_from_str(ctx
, str
);
1637 set
= isl_set_coalesce(set
);
1638 set2
= isl_set_read_from_str(ctx
, str
);
1639 equal
= isl_set_is_equal(set
, set2
);
1640 one
= set
&& set
->n
== 1;
1647 isl_die(ctx
, isl_error_unknown
,
1648 "coalesced set not equal to input", return -1);
1649 if (check_one
&& !one
)
1650 isl_die(ctx
, isl_error_unknown
,
1651 "coalesced set should not be a union", return -1);
1656 /* Inputs for coalescing tests with unbounded wrapping.
1657 * "str" is a string representation of the input set.
1658 * "single_disjunct" is set if we expect the result to consist of
1659 * a single disjunct.
1662 int single_disjunct
;
1664 } coalesce_unbounded_tests
[] = {
1665 { 1, "{ [x,y,z] : y + 2 >= 0 and x - y + 1 >= 0 and "
1666 "-x - y + 1 >= 0 and -3 <= z <= 3;"
1667 "[x,y,z] : -x+z + 20 >= 0 and -x-z + 20 >= 0 and "
1668 "x-z + 20 >= 0 and x+z + 20 >= 0 and "
1670 { 1, "{ [x,y] : 0 <= x,y <= 10; [5,y]: 4 <= y <= 11 }" },
1671 { 1, "{ [x,0,0] : -5 <= x <= 5; [0,y,1] : -5 <= y <= 5 }" },
1672 { 1, "{ [x,y] : 0 <= x <= 10 and 0 >= y >= -1 and x+y >= 0; [0,1] }" },
1673 { 1, "{ [x,y] : (0 <= x,y <= 4) or (2 <= x,y <= 5 and x + y <= 9) }" },
1676 /* Test the functionality of isl_set_coalesce with the bounded wrapping
1677 * option turned off.
1679 int test_coalesce_unbounded_wrapping(isl_ctx
*ctx
)
1685 bounded
= isl_options_get_coalesce_bounded_wrapping(ctx
);
1686 isl_options_set_coalesce_bounded_wrapping(ctx
, 0);
1688 for (i
= 0; i
< ARRAY_SIZE(coalesce_unbounded_tests
); ++i
) {
1689 const char *str
= coalesce_unbounded_tests
[i
].str
;
1690 int check_one
= coalesce_unbounded_tests
[i
].single_disjunct
;
1691 if (test_coalesce_set(ctx
, str
, check_one
) >= 0)
1697 isl_options_set_coalesce_bounded_wrapping(ctx
, bounded
);
1702 /* Inputs for coalescing tests.
1703 * "str" is a string representation of the input set.
1704 * "single_disjunct" is set if we expect the result to consist of
1705 * a single disjunct.
1708 int single_disjunct
;
1710 } coalesce_tests
[] = {
1711 { 1, "{[x,y]: x >= 0 & x <= 10 & y >= 0 & y <= 10 or "
1712 "y >= x & x >= 2 & 5 >= y }" },
1713 { 1, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1714 "x + y >= 10 & y <= x & x + y <= 20 & y >= 0}" },
1715 { 0, "{[x,y]: y >= 0 & 2x + y <= 30 & y <= 10 & x >= 0 or "
1716 "x + y >= 10 & y <= x & x + y <= 19 & y >= 0}" },
1717 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1718 "y >= 0 & x >= 6 & x <= 10 & y <= x}" },
1719 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1720 "y >= 0 & x >= 7 & x <= 10 & y <= x}" },
1721 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or "
1722 "y >= 0 & x >= 6 & x <= 10 & y + 1 <= x}" },
1723 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 6}" },
1724 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 7 & y <= 6}" },
1725 { 1, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 5}" },
1726 { 0, "{[x,y]: y >= 0 & x <= 5 & y <= x or y >= 0 & x = 6 & y <= 7}" },
1727 { 1, "[n] -> { [i] : i = 1 and n >= 2 or 2 <= i and i <= n }" },
1728 { 0, "{[x,y] : x >= 0 and y >= 0 or 0 <= y and y <= 5 and x = -1}" },
1729 { 1, "[n] -> { [i] : 1 <= i and i <= n - 1 or 2 <= i and i <= n }" },
1730 { 0, "[n] -> { [[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1731 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1732 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1733 "4e4 = -2 + o0 and i0 >= 8 + 2n and o0 >= 2 + i0 and "
1734 "o0 <= 56 + 2n and o0 <= -12 + 4n and i0 <= 57 + 2n and "
1735 "i0 <= -11 + 4n and o0 >= 6 + 2n and 4e0 <= i0 and "
1736 "4e0 >= -3 + i0 and 4e1 <= o0 and 4e1 >= -3 + o0 and "
1737 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0);"
1738 "[[i0] -> [o0]] : exists (e0 = [(i0)/4], e1 = [(o0)/4], "
1739 "e2 = [(n)/2], e3 = [(-2 + i0)/4], e4 = [(-2 + o0)/4], "
1740 "e5 = [(-2n + i0)/4]: 2e2 = n and 4e3 = -2 + i0 and "
1741 "4e4 = -2 + o0 and 2e0 >= 3 + n and e0 <= -4 + n and "
1742 "2e0 <= 27 + n and e1 <= -4 + n and 2e1 <= 27 + n and "
1743 "2e1 >= 2 + n and e1 >= 1 + e0 and i0 >= 7 + 2n and "
1744 "i0 <= -11 + 4n and i0 <= 57 + 2n and 4e0 <= -2 + i0 and "
1745 "4e0 >= -3 + i0 and o0 >= 6 + 2n and o0 <= -11 + 4n and "
1746 "o0 <= 57 + 2n and 4e1 <= -2 + o0 and 4e1 >= -3 + o0 and "
1747 "4e5 <= -2n + i0 and 4e5 >= -3 - 2n + i0 ) }" },
1748 { 0, "[n, m] -> { [o0, o2, o3] : (o3 = 1 and o0 >= 1 + m and "
1749 "o0 <= n + m and o2 <= m and o0 >= 2 + n and o2 >= 3) or "
1750 "(o0 >= 2 + n and o0 >= 1 + m and o0 <= n + m and n >= 1 and "
1751 "o3 <= -1 + o2 and o3 >= 1 - m + o2 and o3 >= 2 and o3 <= n) }" },
1752 { 0, "[M, N] -> { [[i0, i1, i2, i3, i4, i5, i6] -> "
1753 "[o0, o1, o2, o3, o4, o5, o6]] : "
1754 "(o6 <= -4 + 2M - 2N + i0 + i1 - i2 + i6 - o0 - o1 + o2 and "
1755 "o3 <= -2 + i3 and o6 >= 2 + i0 + i3 + i6 - o0 - o3 and "
1756 "o6 >= 2 - M + N + i3 + i4 + i6 - o3 - o4 and o0 <= -1 + i0 and "
1757 "o4 >= 4 - 3M + 3N - i0 - i1 + i2 + 2i3 + i4 + o0 + o1 - o2 - 2o3 "
1758 "and o6 <= -3 + 2M - 2N + i3 + i4 - i5 + i6 - o3 - o4 + o5 and "
1759 "2o6 <= -5 + 5M - 5N + 2i0 + i1 - i2 - i5 + 2i6 - 2o0 - o1 + o2 + o5 "
1760 "and o6 >= 2i0 + i1 + i6 - 2o0 - o1 and "
1761 "3o6 <= -5 + 4M - 4N + 2i0 + i1 - i2 + 2i3 + i4 - i5 + 3i6 "
1762 "- 2o0 - o1 + o2 - 2o3 - o4 + o5) or "
1763 "(N >= 2 and o3 <= -1 + i3 and o0 <= -1 + i0 and "
1764 "o6 >= i3 + i6 - o3 and M >= 0 and "
1765 "2o6 >= 1 + i0 + i3 + 2i6 - o0 - o3 and "
1766 "o6 >= 1 - M + i0 + i6 - o0 and N >= 2M and o6 >= i0 + i6 - o0) }" },
1767 { 0, "[M, N] -> { [o0] : (o0 = 0 and M >= 1 and N >= 2) or "
1768 "(o0 = 0 and M >= 1 and N >= 2M and N >= 2 + M) or "
1769 "(o0 = 0 and M >= 2 and N >= 3) or "
1770 "(M = 0 and o0 = 0 and N >= 3) }" },
1771 { 0, "{ [i0, i1, i2, i3] : (i1 = 10i0 and i0 >= 1 and 10i0 <= 100 and "
1772 "i3 <= 9 + 10 i2 and i3 >= 1 + 10i2 and i3 >= 0) or "
1773 "(i1 <= 9 + 10i0 and i1 >= 1 + 10i0 and i2 >= 0 and "
1774 "i0 >= 0 and i1 <= 100 and i3 <= 9 + 10i2 and i3 >= 1 + 10i2) }" },
1775 { 0, "[M] -> { [i1] : (i1 >= 2 and i1 <= M) or (i1 = M and M >= 1) }" },
1776 { 0, "{[x,y] : x,y >= 0; [x,y] : 10 <= x <= 20 and y >= -1 }" },
1777 { 1, "{ [x, y] : (x >= 1 and y >= 1 and x <= 2 and y <= 2) or "
1778 "(y = 3 and x = 1) }" },
1779 { 1, "[M] -> { [i0, i1, i2, i3, i4] : (i1 >= 3 and i4 >= 2 + i2 and "
1780 "i2 >= 2 and i0 >= 2 and i3 >= 1 + i2 and i0 <= M and "
1781 "i1 <= M and i3 <= M and i4 <= M) or "
1782 "(i1 >= 2 and i4 >= 1 + i2 and i2 >= 2 and i0 >= 2 and "
1783 "i3 >= 1 + i2 and i0 <= M and i1 <= -1 + M and i3 <= M and "
1784 "i4 <= -1 + M) }" },
1785 { 1, "{ [x, y] : (x >= 0 and y >= 0 and x <= 10 and y <= 10) or "
1786 "(x >= 1 and y >= 1 and x <= 11 and y <= 11) }" },
1787 { 0, "{[x,0] : x >= 0; [x,1] : x <= 20}" },
1788 { 1, "{ [x, 1 - x] : 0 <= x <= 1; [0,0] }" },
1789 { 1, "{ [0,0]; [i,i] : 1 <= i <= 10 }" },
1790 { 0, "{ [0,0]; [i,j] : 1 <= i,j <= 10 }" },
1791 { 1, "{ [0,0]; [i,2i] : 1 <= i <= 10 }" },
1792 { 0, "{ [0,0]; [i,2i] : 2 <= i <= 10 }" },
1793 { 0, "{ [1,0]; [i,2i] : 1 <= i <= 10 }" },
1794 { 0, "{ [0,1]; [i,2i] : 1 <= i <= 10 }" },
1795 { 0, "{ [a, b] : exists e : 2e = a and "
1796 "a >= 0 and (a <= 3 or (b <= 0 and b >= -4 + a)) }" },
1797 { 0, "{ [i, j, i', j'] : i <= 2 and j <= 2 and "
1798 "j' >= -1 + 2i + j - 2i' and i' <= -1 + i and "
1799 "j >= 1 and j' <= i + j - i' and i >= 1; "
1801 { 1, "{ [i,j] : exists a,b : i = 2a and j = 3b; "
1802 "[i,j] : exists a : j = 3a }" },
1803 { 1, "{ [a, b, c] : (c <= 7 - b and b <= 1 and b >= 0 and "
1804 "c >= 3 + b and b <= 3 + 8a and b >= -26 + 8a and "
1806 "(b <= 1 and c <= 7 and b >= 0 and c >= 4 + b and "
1807 "b <= 3 + 8a and b >= -26 + 8a and a >= 3) }" },
1808 { 1, "{ [a, 0, c] : c >= 1 and c <= 29 and c >= -1 + 8a and "
1809 "c <= 6 + 8a and a >= 3; "
1810 "[a, -1, c] : c >= 1 and c <= 30 and c >= 8a and "
1811 "c <= 7 + 8a and a >= 3 and a <= 4 }" },
1812 { 1, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1813 "[x,0] : 3 <= x <= 4 }" },
1814 { 1, "{ [x,y] : 0 <= x <= 3 and y >= 0 and x + 3y <= 6; "
1815 "[x,0] : 4 <= x <= 5 }" },
1816 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + 2y <= 4; "
1817 "[x,0] : 3 <= x <= 5 }" },
1818 { 0, "{ [x,y] : 0 <= x <= 2 and y >= 0 and x + y <= 4; "
1819 "[x,0] : 3 <= x <= 4 }" },
1820 { 1, "{ [i0, i1] : i0 <= 122 and i0 >= 1 and 128i1 >= -249 + i0 and "
1822 "[i0, 0] : i0 >= 123 and i0 <= 124 }" },
1823 { 1, "{ [0,0]; [1,1] }" },
1824 { 1, "[n] -> { [k] : 16k <= -1 + n and k >= 1; [0] : n >= 2 }" },
1825 { 1, "{ [k, ii, k - ii] : ii >= -6 + k and ii <= 6 and ii >= 1 and "
1827 "[k, 0, k] : k <= 6 and k >= 1 }" },
1828 { 1, "{ [i,j] : i = 4 j and 0 <= i <= 100;"
1829 "[i,j] : 1 <= i <= 100 and i >= 4j + 1 and i <= 4j + 2 }" },
1830 { 1, "{ [x,y] : x % 2 = 0 and y % 2 = 0; [x,x] : x % 2 = 0 }" },
1831 { 1, "[n] -> { [1] : n >= 0;"
1832 "[x] : exists (e0 = floor((x)/2): x >= 2 and "
1833 "2e0 >= -1 + x and 2e0 <= x and 2e0 <= n) }" },
1834 { 1, "[n] -> { [x, y] : exists (e0 = floor((x)/2), e1 = floor((y)/3): "
1835 "3e1 = y and x >= 2 and 2e0 >= -1 + x and "
1836 "2e0 <= x and 2e0 <= n);"
1837 "[1, y] : exists (e0 = floor((y)/3): 3e0 = y and "
1839 { 1, "[t1] -> { [i0] : (exists (e0 = floor((63t1)/64): "
1840 "128e0 >= -134 + 127t1 and t1 >= 2 and "
1841 "64e0 <= 63t1 and 64e0 >= -63 + 63t1)) or "
1843 { 1, "{ [i, i] : exists (e0 = floor((1 + 2i)/3): 3e0 <= 2i and "
1844 "3e0 >= -1 + 2i and i <= 9 and i >= 1);"
1846 { 1, "{ [t1] : exists (e0 = floor((-11 + t1)/2): 2e0 = -11 + t1 and "
1847 "t1 >= 13 and t1 <= 16);"
1848 "[t1] : t1 <= 15 and t1 >= 12 }" },
1849 { 1, "{ [x,y] : x = 3y and 0 <= y <= 2; [-3,-1] }" },
1850 { 1, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-2] }" },
1851 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-2,-2] }" },
1852 { 0, "{ [x,y] : 2x = 3y and 0 <= y <= 4; [-3,-1] }" },
1853 { 1, "{ [i] : exists j : i = 4 j and 0 <= i <= 100;"
1854 "[i] : exists j : 1 <= i <= 100 and i >= 4j + 1 and "
1856 { 1, "{ [c0] : (exists (e0 : c0 - 1 <= 3e0 <= c0)) or "
1857 "(exists (e0 : 3e0 = -2 + c0)) }" },
1858 { 0, "[n, b0, t0] -> "
1859 "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
1860 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1861 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1862 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1863 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 >= 8 + n and "
1864 "3i4 <= -96 + 3t0 + i0 and 3i4 >= -95 - n + 3t0 + i0 and "
1865 "i8 >= -157 + i0 - 4i4 and i8 >= 0 and "
1866 "i8 <= -33 + i0 - 4i4 and 3i8 <= -91 + 4n - i0)) or "
1867 "(exists (e0 = floor((-32b0 + i4)/1048576), "
1868 "e1 = floor((i8)/32): 1048576e0 = -32b0 + i4 and 32e1 = i8 and "
1869 "n <= 2147483647 and b0 <= 32767 and b0 >= 0 and "
1870 "32b0 <= -2 + n and t0 <= 31 and t0 >= 0 and i0 <= 7 + n and "
1871 "4i4 <= -3 + i0 and 3i4 <= -96 + 3t0 + i0 and "
1872 "3i4 >= -95 - n + 3t0 + i0 and i8 >= -157 + i0 - 4i4 and "
1873 "i8 >= 0 and i8 <= -4 + i0 - 3i4 and i8 <= -41 + i0));"
1874 "[i0, i1, i2, i3, 0, i5, i6, i7, i8, i9, i10, i11, i12] : "
1875 "(exists (e0 = floor((i8)/32): b0 = 0 and 32e0 = i8 and "
1876 "n <= 2147483647 and t0 <= 31 and t0 >= 0 and i0 >= 11 and "
1877 "i0 >= 96 - 3t0 and i0 <= 95 + n - 3t0 and i0 <= 7 + n and "
1878 "i8 >= -40 + i0 and i8 <= -10 + i0)) }" },
1879 { 0, "{ [i0, i1, i2] : "
1880 "(exists (e0, e1 = floor((i0)/32), e2 = floor((i1)/32): "
1881 "32e1 = i0 and 32e2 = i1 and i1 >= -31 + i0 and "
1882 "i1 <= 31 + i0 and i2 >= -30 + i0 and i2 >= -30 + i1 and "
1883 "32e0 >= -30 + i0 and 32e0 >= -30 + i1 and "
1884 "32e0 >= -31 + i2 and 32e0 <= 30 + i2 and 32e0 <= 31 + i1 and "
1885 "32e0 <= 31 + i0)) or "
1887 { 1, "{ [a, b, c] : 2b = 1 + a and 2c = 2 + a; [0, 0, 0] }" },
1888 { 1, "{ [a, a, b, c] : 32*floor((a)/32) = a and 2*floor((b)/2) = b and "
1889 "2*floor((c)/2) = c and 0 <= a <= 192;"
1890 "[224, 224, b, c] : 2*floor((b)/2) = b and 2*floor((c)/2) = c }"
1892 { 1, "[n] -> { [a,b] : (exists e : 1 <= a <= 7e and 9e <= b <= n) or "
1893 "(0 <= a <= b <= n) }" },
1894 { 1, "{ [a, b] : 0 <= a <= 2 and b >= 0 and "
1895 "((0 < b <= 13) or (2*floor((a + b)/2) >= -5 + a + 2b)) }" },
1896 { 1, "{ [a] : (2 <= a <= 5) or (a mod 2 = 1 and 1 <= a <= 5) }" },
1897 { 1, "{ [a, b, c] : (b = -1 + a and 0 < a <= 3 and "
1898 "9*floor((-4a + 2c)/9) <= -3 - 4a + 2c) or "
1899 "(exists (e0 = floor((-16 + 2c)/9): a = 4 and "
1900 "b = 3 and 9e0 <= -19 + 2c)) }" },
1901 { 1, "{ [a, b, c] : (b = -1 + a and 0 < a <= 3 and "
1902 "9*floor((-4a + 2c)/9) <= -3 - 4a + 2c) or "
1903 "(a = 4 and b = 3 and "
1904 "9*floor((-16 + 2c)/9) <= -19 + 2c) }" },
1905 { 0, "{ [a, b, c] : (b <= 2 and b <= -2 + a) or "
1906 "(b = -1 + a and 0 < a <= 3 and "
1907 "9*floor((-4a + 2c)/9) <= -3 - 4a + 2c) or "
1908 "(exists (e0 = floor((-16 + 2c)/9): a = 4 and "
1909 "b = 3 and 9e0 <= -19 + 2c)) }" },
1910 { 1, "{ [y, x] : (x - y) mod 3 = 2 and 2 <= y <= 200 and 0 <= x <= 2;"
1912 { 1, "{ [x, y] : (x - y) mod 3 = 2 and 2 <= y <= 200 and 0 <= x <= 2;"
1914 { 1, "{ [1, y] : -1 <= y <= 1; [x, -x] : 0 <= x <= 1 }" },
1915 { 1, "{ [1, y] : 0 <= y <= 1; [x, -x] : 0 <= x <= 1 }" },
1916 { 1, "{ [x, y] : 0 <= x <= 10 and x - 4*floor(x/4) <= 1 and y <= 0; "
1917 "[x, y] : 0 <= x <= 10 and x - 4*floor(x/4) > 1 and y <= 0; "
1918 "[x, y] : 0 <= x <= 10 and x - 5*floor(x/5) <= 1 and 0 < y; "
1919 "[x, y] : 0 <= x <= 10 and x - 5*floor(x/5) > 1 and 0 < y }" },
1920 { 1, "{ [x, 0] : 0 <= x <= 10 and x mod 2 = 0; "
1921 "[x, 0] : 0 <= x <= 10 and x mod 2 = 1; "
1922 "[x, y] : 0 <= x <= 10 and 1 <= y <= 10 }" },
1923 { 1, "{ [a] : a <= 8 and "
1924 "(a mod 10 = 7 or a mod 10 = 8 or a mod 10 = 9) }" },
1925 { 1, "{ [x, y] : 2y = -x and x <= 0 or "
1926 "x <= -1 and 2y <= -x - 1 and 2y >= x - 1 }" },
1927 { 0, "{ [x, y] : 2y = -x and x <= 0 or "
1928 "x <= -2 and 2y <= -x - 1 and 2y >= x - 1 }" },
1929 { 1, "{ [a] : (a <= 0 and 3*floor((a)/3) = a) or "
1930 "(a < 0 and 3*floor((a)/3) < a) }" },
1931 { 1, "{ [a] : (a <= 0 and 3*floor((a)/3) = a) or "
1932 "(a < -1 and 3*floor((a)/3) < a) }" },
1933 { 1, "{ [a, b] : a <= 1024 and b >= 0 and "
1934 "((-31 - a + b <= 32*floor((-1 - a)/32) <= -33 + b and "
1935 "32*floor((-1 - a)/32) <= -16 + b + 16*floor((-1 - a)/16))"
1936 "or (2 <= a <= 15 and b < a)) }" },
1937 { 1, "{ [a] : a > 0 and ((16*floor((a)/16) < a and "
1938 "32*floor((a)/32) < a) or a <= 15) }" },
1939 { 1, "{ [a, b, c, d] : (-a + d) mod 64 = 0 and a <= 8 and b <= 1 and "
1940 "10 - a <= c <= 3 and d >= 5 and 9 - 64b <= d <= 70;"
1941 "[a, b = 1, c, d] : (-a + d) mod 64 = 0 and a <= 8 and c >= 4 and "
1942 "10 - a <= c <= 5 and 5 <= d <= 73 - c }" },
1943 { 1, "[n, m] -> { S_0[i] : (-n + i) mod 3 = 0 and m >= 3 + n and "
1944 "i >= n and 3*floor((2 + n + 2m)/3) <= n + 3m - i; "
1945 "S_0[n] : n <= m <= 2 + n }" },
1946 { 1, "{ [a, b] : exists (e0: 0 <= a <= 1 and b >= 0 and "
1947 "2e0 >= -5 + a + 2b and 2e0 >= -1 + a + b and "
1949 "[a, b] : exists (e0: 0 <= a <= 1 and 2e0 >= -5 + a + 2b and "
1950 "2e0 >= -1 - a + b and 2e0 <= -a + b and "
1951 "2e0 < -a + 2b) }" },
1952 { 1, "{ [i, j, i - 8j] : 8 <= i <= 63 and -7 + i <= 8j <= i; "
1953 "[i, 0, i] : 0 <= i <= 7 }" },
1954 { 1, "{ [a, b] : a >= 0 and 0 <= b <= 1 - a; [1, 1] }" },
1955 { 0, "{ [a, b] : a >= 0 and 0 <= b <= 1 - a; [0, 2] }" },
1956 { 0, "{ [a, b] : a >= 0 and 0 <= b <= 1 - a; [-1, 3] }" },
1957 { 1, "{ [a, b] : a, b >= 0 and a + 2b <= 2; [1, 1] }" },
1958 { 0, "{ [a, b] : a, b >= 0 and a + 2b <= 2; [2, 1] }" },
1961 /* A specialized coalescing test case that would result
1962 * in a segmentation fault or a failed assertion in earlier versions of isl.
1964 static int test_coalesce_special(struct isl_ctx
*ctx
)
1967 isl_map
*map1
, *map2
;
1969 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1970 "[[S_L309_IN[] -> T11[]] -> ce_imag2[1, o1]] : "
1971 "(y = 201 and o1 <= 239 and o1 >= 212) or "
1972 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 198 and y >= 3 and "
1973 "o1 <= 239 and o1 >= 212)) or "
1974 "(exists (e0 = [(y)/3]: 3e0 = y and y <= 201 and y >= 3 and "
1975 "o1 <= 241 and o1 >= 240));"
1976 "[S_L220_OUT[] -> T7[]] -> "
1977 "[[S_L309_IN[] -> T11[]] -> ce_imag2[0, o1]] : "
1978 "(y = 2 and o1 <= 241 and o1 >= 212) or "
1979 "(exists (e0 = [(-2 + y)/3]: 3e0 = -2 + y and y <= 200 and "
1980 "y >= 5 and o1 <= 241 and o1 >= 212)) }";
1981 map1
= isl_map_read_from_str(ctx
, str
);
1982 map1
= isl_map_align_divs_internal(map1
);
1983 map1
= isl_map_coalesce(map1
);
1984 str
= "[y] -> { [S_L220_OUT[] -> T7[]] -> "
1985 "[[S_L309_IN[] -> T11[]] -> ce_imag2[o0, o1]] : "
1986 "exists (e0 = [(-1 - y + o0)/3]: 3e0 = -1 - y + o0 and "
1987 "y <= 201 and o0 <= 2 and o1 >= 212 and o1 <= 241 and "
1988 "o0 >= 3 - y and o0 <= -2 + y and o0 >= 0) }";
1989 map2
= isl_map_read_from_str(ctx
, str
);
1990 map2
= isl_map_union(map2
, map1
);
1991 map2
= isl_map_align_divs_internal(map2
);
1992 map2
= isl_map_coalesce(map2
);
2000 /* A specialized coalescing test case that would result in an assertion
2001 * in an earlier version of isl.
2002 * The explicit call to isl_basic_set_union prevents the implicit
2003 * equality constraints in the first basic map from being detected prior
2004 * to the call to isl_set_coalesce, at least at the point
2005 * where this test case was introduced.
2007 static int test_coalesce_special2(struct isl_ctx
*ctx
)
2010 isl_basic_set
*bset1
, *bset2
;
2013 str
= "{ [x, y] : x, y >= 0 and x + 2y <= 1 and 2x + y <= 1 }";
2014 bset1
= isl_basic_set_read_from_str(ctx
, str
);
2015 str
= "{ [x,0] : -1 <= x <= 1 and x mod 2 = 1 }" ;
2016 bset2
= isl_basic_set_read_from_str(ctx
, str
);
2017 set
= isl_basic_set_union(bset1
, bset2
);
2018 set
= isl_set_coalesce(set
);
2026 /* Check that calling isl_set_coalesce does not leave other sets
2027 * that may share some information with the input to isl_set_coalesce
2028 * in an inconsistent state.
2029 * In particular, older versions of isl would modify all copies
2030 * of the basic sets in the isl_set_coalesce input in a way
2031 * that could leave them in an inconsistent state.
2032 * The result of printing any other set containing one of these
2033 * basic sets would then result in an invalid set description.
2035 static int test_coalesce_special3(isl_ctx
*ctx
)
2039 isl_set
*set1
, *set2
;
2042 set1
= isl_set_read_from_str(ctx
, "{ [0, 0, 0] }");
2043 str
= "{ [a, b, a + b] : a >= 0 and b >= 0 and 0 < a + b }";
2044 set2
= isl_set_read_from_str(ctx
, str
);
2045 set1
= isl_set_union(set1
, isl_set_copy(set2
));
2046 set1
= isl_set_coalesce(set1
);
2049 p
= isl_printer_to_str(ctx
);
2050 p
= isl_printer_print_set(p
, set2
);
2052 s
= isl_printer_get_str(p
);
2053 isl_printer_free(p
);
2054 set1
= isl_set_read_from_str(ctx
, s
);
2064 /* Test the functionality of isl_set_coalesce.
2065 * That is, check that the output is always equal to the input
2066 * and in some cases that the result consists of a single disjunct.
2068 static int test_coalesce(struct isl_ctx
*ctx
)
2072 for (i
= 0; i
< ARRAY_SIZE(coalesce_tests
); ++i
) {
2073 const char *str
= coalesce_tests
[i
].str
;
2074 int check_one
= coalesce_tests
[i
].single_disjunct
;
2075 if (test_coalesce_set(ctx
, str
, check_one
) < 0)
2079 if (test_coalesce_unbounded_wrapping(ctx
) < 0)
2081 if (test_coalesce_special(ctx
) < 0)
2083 if (test_coalesce_special2(ctx
) < 0)
2085 if (test_coalesce_special3(ctx
) < 0)
2091 /* Construct a representation of the graph on the right of Figure 1
2092 * in "Computing the Transitive Closure of a Union of
2093 * Affine Integer Tuple Relations".
2095 static __isl_give isl_map
*cocoa_fig_1_right_graph(isl_ctx
*ctx
)
2098 isl_map
*up
, *right
;
2100 dom
= isl_set_read_from_str(ctx
,
2101 "{ [x,y] : x >= 0 and -2 x + 3 y >= 0 and x <= 3 and "
2102 "2 x - 3 y + 3 >= 0 }");
2103 right
= isl_map_read_from_str(ctx
,
2104 "{ [x,y] -> [x2,y2] : x2 = x + 1 and y2 = y }");
2105 up
= isl_map_read_from_str(ctx
,
2106 "{ [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 }");
2107 right
= isl_map_intersect_domain(right
, isl_set_copy(dom
));
2108 right
= isl_map_intersect_range(right
, isl_set_copy(dom
));
2109 up
= isl_map_intersect_domain(up
, isl_set_copy(dom
));
2110 up
= isl_map_intersect_range(up
, dom
);
2111 return isl_map_union(up
, right
);
2114 /* Construct a representation of the power of the graph
2115 * on the right of Figure 1 in "Computing the Transitive Closure of
2116 * a Union of Affine Integer Tuple Relations".
2118 static __isl_give isl_map
*cocoa_fig_1_right_power(isl_ctx
*ctx
)
2120 return isl_map_read_from_str(ctx
,
2121 "{ [1] -> [[0,0] -> [0,1]]; [2] -> [[0,0] -> [1,1]]; "
2122 " [1] -> [[0,1] -> [1,1]]; [1] -> [[2,2] -> [3,2]]; "
2123 " [2] -> [[2,2] -> [3,3]]; [1] -> [[3,2] -> [3,3]] }");
2126 /* Construct a representation of the transitive closure of the graph
2127 * on the right of Figure 1 in "Computing the Transitive Closure of
2128 * a Union of Affine Integer Tuple Relations".
2130 static __isl_give isl_map
*cocoa_fig_1_right_tc(isl_ctx
*ctx
)
2132 return isl_set_unwrap(isl_map_range(cocoa_fig_1_right_power(ctx
)));
2135 static int test_closure(isl_ctx
*ctx
)
2138 isl_map
*map
, *map2
;
2141 /* COCOA example 1 */
2142 map
= isl_map_read_from_str(ctx
,
2143 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
2144 "1 <= i and i < n and 1 <= j and j < n or "
2145 "i2 = i + 1 and j2 = j - 1 and "
2146 "1 <= i and i < n and 2 <= j and j <= n }");
2147 map
= isl_map_power(map
, &exact
);
2151 /* COCOA example 1 */
2152 map
= isl_map_read_from_str(ctx
,
2153 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 1 and j2 = j + 1 and "
2154 "1 <= i and i < n and 1 <= j and j < n or "
2155 "i2 = i + 1 and j2 = j - 1 and "
2156 "1 <= i and i < n and 2 <= j and j <= n }");
2157 map
= isl_map_transitive_closure(map
, &exact
);
2159 map2
= isl_map_read_from_str(ctx
,
2160 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
2161 "1 <= i and i < n and 1 <= j and j <= n and "
2162 "2 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
2163 "i2 = i + k1 + k2 and j2 = j + k1 - k2 and "
2164 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1 )}");
2165 assert(isl_map_is_equal(map
, map2
));
2169 map
= isl_map_read_from_str(ctx
,
2170 "[n] -> { [x] -> [y] : y = x + 1 and 0 <= x and x <= n and "
2171 " 0 <= y and y <= n }");
2172 map
= isl_map_transitive_closure(map
, &exact
);
2173 map2
= isl_map_read_from_str(ctx
,
2174 "[n] -> { [x] -> [y] : y > x and 0 <= x and x <= n and "
2175 " 0 <= y and y <= n }");
2176 assert(isl_map_is_equal(map
, map2
));
2180 /* COCOA example 2 */
2181 map
= isl_map_read_from_str(ctx
,
2182 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j + 2 and "
2183 "1 <= i and i < n - 1 and 1 <= j and j < n - 1 or "
2184 "i2 = i + 2 and j2 = j - 2 and "
2185 "1 <= i and i < n - 1 and 3 <= j and j <= n }");
2186 map
= isl_map_transitive_closure(map
, &exact
);
2188 map2
= isl_map_read_from_str(ctx
,
2189 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k : "
2190 "1 <= i and i < n - 1 and 1 <= j and j <= n and "
2191 "3 <= i2 and i2 <= n and 1 <= j2 and j2 <= n and "
2192 "i2 = i + 2 k1 + 2 k2 and j2 = j + 2 k1 - 2 k2 and "
2193 "k1 >= 0 and k2 >= 0 and k1 + k2 = k and k >= 1) }");
2194 assert(isl_map_is_equal(map
, map2
));
2198 /* COCOA Fig.2 left */
2199 map
= isl_map_read_from_str(ctx
,
2200 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 2 and j2 = j and "
2201 "i <= 2 j - 3 and i <= n - 2 and j <= 2 i - 1 and "
2203 "i2 = i and j2 = j + 2 and i <= 2 j - 1 and i <= n and "
2204 "j <= 2 i - 3 and j <= n - 2 or "
2205 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2206 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2207 map
= isl_map_transitive_closure(map
, &exact
);
2211 /* COCOA Fig.2 right */
2212 map
= isl_map_read_from_str(ctx
,
2213 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
2214 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
2216 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
2217 "j <= 2 i - 4 and j <= n - 3 or "
2218 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2219 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2220 map
= isl_map_power(map
, &exact
);
2224 /* COCOA Fig.2 right */
2225 map
= isl_map_read_from_str(ctx
,
2226 "[n] -> { [i,j] -> [i2,j2] : i2 = i + 3 and j2 = j and "
2227 "i <= 2 j - 4 and i <= n - 3 and j <= 2 i - 1 and "
2229 "i2 = i and j2 = j + 3 and i <= 2 j - 1 and i <= n and "
2230 "j <= 2 i - 4 and j <= n - 3 or "
2231 "i2 = i + 1 and j2 = j + 1 and i <= 2 j - 1 and "
2232 "i <= n - 1 and j <= 2 i - 1 and j <= n - 1 }");
2233 map
= isl_map_transitive_closure(map
, &exact
);
2235 map2
= isl_map_read_from_str(ctx
,
2236 "[n] -> { [i,j] -> [i2,j2] : exists (k1,k2,k3,k : "
2237 "i <= 2 j - 1 and i <= n and j <= 2 i - 1 and "
2238 "j <= n and 3 + i + 2 j <= 3 n and "
2239 "3 + 2 i + j <= 3n and i2 <= 2 j2 -1 and i2 <= n and "
2240 "i2 <= 3 j2 - 4 and j2 <= 2 i2 -1 and j2 <= n and "
2241 "13 + 4 j2 <= 11 i2 and i2 = i + 3 k1 + k3 and "
2242 "j2 = j + 3 k2 + k3 and k1 >= 0 and k2 >= 0 and "
2243 "k3 >= 0 and k1 + k2 + k3 = k and k > 0) }");
2244 assert(isl_map_is_equal(map
, map2
));
2248 map
= cocoa_fig_1_right_graph(ctx
);
2249 map
= isl_map_transitive_closure(map
, &exact
);
2251 map2
= cocoa_fig_1_right_tc(ctx
);
2252 assert(isl_map_is_equal(map
, map2
));
2256 map
= cocoa_fig_1_right_graph(ctx
);
2257 map
= isl_map_power(map
, &exact
);
2258 map2
= cocoa_fig_1_right_power(ctx
);
2259 equal
= isl_map_is_equal(map
, map2
);
2265 isl_die(ctx
, isl_error_unknown
, "power not exact", return -1);
2267 isl_die(ctx
, isl_error_unknown
, "unexpected power", return -1);
2269 /* COCOA Theorem 1 counter example */
2270 map
= isl_map_read_from_str(ctx
,
2271 "{ [i,j] -> [i2,j2] : i = 0 and 0 <= j and j <= 1 and "
2272 "i2 = 1 and j2 = j or "
2273 "i = 0 and j = 0 and i2 = 0 and j2 = 1 }");
2274 map
= isl_map_transitive_closure(map
, &exact
);
2278 map
= isl_map_read_from_str(ctx
,
2279 "[m,n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 2 and "
2280 "1 <= i,i2 <= n and 1 <= j,j2 <= m or "
2281 "i2 = i + 1 and 3 <= j2 - j <= 4 and "
2282 "1 <= i,i2 <= n and 1 <= j,j2 <= m }");
2283 map
= isl_map_transitive_closure(map
, &exact
);
2287 /* Kelly et al 1996, fig 12 */
2288 map
= isl_map_read_from_str(ctx
,
2289 "[n] -> { [i,j] -> [i2,j2] : i2 = i and j2 = j + 1 and "
2290 "1 <= i,j,j+1 <= n or "
2291 "j = n and j2 = 1 and i2 = i + 1 and "
2292 "1 <= i,i+1 <= n }");
2293 map
= isl_map_transitive_closure(map
, &exact
);
2295 map2
= isl_map_read_from_str(ctx
,
2296 "[n] -> { [i,j] -> [i2,j2] : 1 <= j < j2 <= n and "
2297 "1 <= i <= n and i = i2 or "
2298 "1 <= i < i2 <= n and 1 <= j <= n and "
2300 assert(isl_map_is_equal(map
, map2
));
2304 /* Omega's closure4 */
2305 map
= isl_map_read_from_str(ctx
,
2306 "[m,n] -> { [x,y] -> [x2,y2] : x2 = x and y2 = y + 1 and "
2307 "1 <= x,y <= 10 or "
2308 "x2 = x + 1 and y2 = y and "
2309 "1 <= x <= 20 && 5 <= y <= 15 }");
2310 map
= isl_map_transitive_closure(map
, &exact
);
2314 map
= isl_map_read_from_str(ctx
,
2315 "[n] -> { [x] -> [y]: 1 <= n <= y - x <= 10 }");
2316 map
= isl_map_transitive_closure(map
, &exact
);
2318 map2
= isl_map_read_from_str(ctx
,
2319 "[n] -> { [x] -> [y] : 1 <= n <= 10 and y >= n + x }");
2320 assert(isl_map_is_equal(map
, map2
));
2324 str
= "[n, m] -> { [i0, i1, i2, i3] -> [o0, o1, o2, o3] : "
2325 "i3 = 1 and o0 = i0 and o1 = -1 + i1 and o2 = -1 + i2 and "
2326 "o3 = -2 + i2 and i1 <= -1 + i0 and i1 >= 1 - m + i0 and "
2327 "i1 >= 2 and i1 <= n and i2 >= 3 and i2 <= 1 + n and i2 <= m }";
2328 map
= isl_map_read_from_str(ctx
, str
);
2329 map
= isl_map_transitive_closure(map
, &exact
);
2331 map2
= isl_map_read_from_str(ctx
, str
);
2332 assert(isl_map_is_equal(map
, map2
));
2336 str
= "{[0] -> [1]; [2] -> [3]}";
2337 map
= isl_map_read_from_str(ctx
, str
);
2338 map
= isl_map_transitive_closure(map
, &exact
);
2340 map2
= isl_map_read_from_str(ctx
, str
);
2341 assert(isl_map_is_equal(map
, map2
));
2345 str
= "[n] -> { [[i0, i1, 1, 0, i0] -> [i5, 1]] -> "
2346 "[[i0, -1 + i1, 2, 0, i0] -> [-1 + i5, 2]] : "
2347 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 2 and "
2348 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2349 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2350 "[[i0, i1, 2, 0, i0] -> [i5, 1]] -> "
2351 "[[i0, i1, 1, 0, i0] -> [-1 + i5, 2]] : "
2352 "exists (e0 = [(3 - n)/3]: i5 >= 2 and i1 >= 1 and "
2353 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2354 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2355 "[[i0, i1, 1, 0, i0] -> [i5, 2]] -> "
2356 "[[i0, -1 + i1, 2, 0, i0] -> [i5, 1]] : "
2357 "exists (e0 = [(3 - n)/3]: i1 >= 2 and i5 >= 1 and "
2358 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2359 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n); "
2360 "[[i0, i1, 2, 0, i0] -> [i5, 2]] -> "
2361 "[[i0, i1, 1, 0, i0] -> [i5, 1]] : "
2362 "exists (e0 = [(3 - n)/3]: i5 >= 1 and i1 >= 1 and "
2363 "3i0 <= -1 + n and i1 <= -1 + n and i5 <= -1 + n and "
2364 "3e0 >= 1 - n and 3e0 <= 2 - n and 3i0 >= -2 + n) }";
2365 map
= isl_map_read_from_str(ctx
, str
);
2366 map
= isl_map_transitive_closure(map
, NULL
);
2373 static int test_lex(struct isl_ctx
*ctx
)
2379 dim
= isl_space_set_alloc(ctx
, 0, 0);
2380 map
= isl_map_lex_le(dim
);
2381 empty
= isl_map_is_empty(map
);
2387 isl_die(ctx
, isl_error_unknown
,
2388 "expecting non-empty result", return -1);
2393 /* Inputs for isl_map_lexmin tests.
2394 * "map" is the input and "lexmin" is the expected result.
2399 } lexmin_tests
[] = {
2400 { "{ [x] -> [y] : x <= y <= 10; [x] -> [5] : -8 <= x <= 8 }",
2401 "{ [x] -> [5] : 6 <= x <= 8; "
2402 "[x] -> [x] : x <= 5 or (9 <= x <= 10) }" },
2403 { "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }",
2404 "{ [x] -> [y] : 4y = x or 4y = -1 + x or 4y = -2 + x }" },
2405 { "{ [x] -> [y] : x = 4y; [x] -> [y] : x = 2y }",
2406 "{ [x] -> [y] : (4y = x and x >= 0) or "
2407 "(exists (e0 = [(x)/4], e1 = [(-2 + x)/4]: 2y = x and "
2408 "4e1 = -2 + x and 4e0 <= -1 + x and 4e0 >= -3 + x)) or "
2409 "(exists (e0 = [(x)/4]: 2y = x and 4e0 = x and x <= -4)) }" },
2410 { "{ T[a] -> S[b, c] : a = 4b-2c and c >= b }",
2411 "{ T[a] -> S[b, c] : 2b = a and 2c = a }" },
2412 /* Check that empty pieces are properly combined. */
2413 { "[K, N] -> { [x, y] -> [a, b] : K+2<=N<=K+4 and x>=4 and "
2414 "2N-6<=x<K+N and N-1<=a<=K+N-1 and N+b-6<=a<=2N-4 and "
2415 "b<=2N-3K+a and 3b<=4N-K+1 and b>=N and a>=x+1 }",
2416 "[K, N] -> { [x, y] -> [1 + x, N] : x >= -6 + 2N and "
2417 "x <= -5 + 2N and x >= -1 + 3K - N and x <= -2 + K + N and "
2419 { "{ [i, k, j] -> [a, b, c, d] : 8*floor((b)/8) = b and k <= 255 and "
2420 "a <= 255 and c <= 255 and d <= 255 - j and "
2421 "255 - j <= 7d <= 7 - i and 240d <= 239 + a and "
2422 "247d <= 247 + k - j and 247d <= 247 + k - b and "
2423 "247d <= 247 + i and 248 - b <= 248d <= c and "
2424 "254d >= i - a + b and 254d >= -a + b and "
2425 "255d >= -i + a - b and 1792d >= -63736 + 257b }",
2427 "[-127762 + i + 502j, -62992 + 248j, 63240 - 248j, 255 - j] : "
2428 "k <= 255 and 7j >= 1778 + i and 246j >= 62738 - k and "
2429 "247j >= 62738 - i and 509j <= 129795 + i and "
2430 "742j >= 188724 - i; "
2431 "[0, k, j] -> [1, 0, 248, 1] : k <= 255 and 248 <= j <= 254, k }" },
2432 { "{ [a] -> [b] : 0 <= b <= 255 and -509 + a <= 512b < a and "
2433 "16*floor((8 + b)/16) <= 7 + b; "
2435 "{ [a] -> [b = 1] : a >= 510 or a <= 0; "
2436 "[a] -> [b = 0] : 0 < a <= 509 }" },
2437 { "{ rat: [i] : 1 <= 2i <= 9 }", "{ rat: [i] : 2i = 1 }" },
2438 { "{ rat: [i] : 1 <= 2i <= 9 or i >= 10 }", "{ rat: [i] : 2i = 1 }" },
2441 static int test_lexmin(struct isl_ctx
*ctx
)
2446 isl_basic_map
*bmap
;
2447 isl_map
*map
, *map2
;
2450 isl_pw_multi_aff
*pma
;
2452 str
= "[p0, p1] -> { [] -> [] : "
2453 "exists (e0 = [(2p1)/3], e1, e2, e3 = [(3 - p1 + 3e0)/3], "
2454 "e4 = [(p1)/3], e5 = [(p1 + 3e4)/3]: "
2455 "3e0 >= -2 + 2p1 and 3e0 >= p1 and 3e3 >= 1 - p1 + 3e0 and "
2456 "3e0 <= 2p1 and 3e3 >= -2 + p1 and 3e3 <= -1 + p1 and p1 >= 3 and "
2457 "3e5 >= -2 + 2p1 and 3e5 >= p1 and 3e5 <= -1 + p1 + 3e4 and "
2458 "3e4 <= p1 and 3e4 >= -2 + p1 and e3 <= -1 + e0 and "
2459 "3e4 >= 6 - p1 + 3e1 and 3e1 >= p1 and 3e5 >= -2 + p1 + 3e4 and "
2460 "2e4 >= 3 - p1 + 2e1 and e4 <= e1 and 3e3 <= 2 - p1 + 3e0 and "
2461 "e5 >= 1 + e1 and 3e4 >= 6 - 2p1 + 3e1 and "
2462 "p0 >= 2 and p1 >= p0 and 3e2 >= p1 and 3e4 >= 6 - p1 + 3e2 and "
2463 "e2 <= e1 and e3 >= 1 and e4 <= e2) }";
2464 map
= isl_map_read_from_str(ctx
, str
);
2465 map
= isl_map_lexmin(map
);
2468 str
= "[C] -> { [obj,a,b,c] : obj <= 38 a + 7 b + 10 c and "
2469 "a + b <= 1 and c <= 10 b and c <= C and a,b,c,C >= 0 }";
2470 set
= isl_set_read_from_str(ctx
, str
);
2471 set
= isl_set_lexmax(set
);
2472 str
= "[C] -> { [obj,a,b,c] : C = 8 }";
2473 set2
= isl_set_read_from_str(ctx
, str
);
2474 set
= isl_set_intersect(set
, set2
);
2475 assert(!isl_set_is_empty(set
));
2478 for (i
= 0; i
< ARRAY_SIZE(lexmin_tests
); ++i
) {
2479 map
= isl_map_read_from_str(ctx
, lexmin_tests
[i
].map
);
2480 map
= isl_map_lexmin(map
);
2481 map2
= isl_map_read_from_str(ctx
, lexmin_tests
[i
].lexmin
);
2482 equal
= isl_map_is_equal(map
, map2
);
2489 isl_die(ctx
, isl_error_unknown
,
2490 "unexpected result", return -1);
2493 str
= "{ [i] -> [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2494 " 8i' <= i and 8i' >= -7 + i }";
2495 bmap
= isl_basic_map_read_from_str(ctx
, str
);
2496 pma
= isl_basic_map_lexmin_pw_multi_aff(isl_basic_map_copy(bmap
));
2497 map2
= isl_map_from_pw_multi_aff(pma
);
2498 map
= isl_map_from_basic_map(bmap
);
2499 assert(isl_map_is_equal(map
, map2
));
2503 str
= "[i] -> { [i', j] : j = i - 8i' and i' >= 0 and i' <= 7 and "
2504 " 8i' <= i and 8i' >= -7 + i }";
2505 set
= isl_set_read_from_str(ctx
, str
);
2506 pma
= isl_set_lexmin_pw_multi_aff(isl_set_copy(set
));
2507 set2
= isl_set_from_pw_multi_aff(pma
);
2508 equal
= isl_set_is_equal(set
, set2
);
2514 isl_die(ctx
, isl_error_unknown
,
2515 "unexpected difference between set and "
2516 "piecewise affine expression", return -1);
2521 /* A specialized isl_set_min_val test case that would return the wrong result
2522 * in earlier versions of isl.
2523 * The explicit call to isl_basic_set_union prevents the second basic set
2524 * from being determined to be empty prior to the call to isl_set_min_val,
2525 * at least at the point where this test case was introduced.
2527 static int test_min_special(isl_ctx
*ctx
)
2530 isl_basic_set
*bset1
, *bset2
;
2536 str
= "{ [a, b] : a >= 2 and b >= 0 and 14 - a <= b <= 9 }";
2537 bset1
= isl_basic_set_read_from_str(ctx
, str
);
2538 str
= "{ [a, b] : 1 <= a, b and a + b <= 1 }";
2539 bset2
= isl_basic_set_read_from_str(ctx
, str
);
2540 set
= isl_basic_set_union(bset1
, bset2
);
2541 obj
= isl_aff_read_from_str(ctx
, "{ [a, b] -> [a] }");
2543 res
= isl_set_min_val(set
, obj
);
2544 ok
= isl_val_cmp_si(res
, 5) == 0;
2553 isl_die(ctx
, isl_error_unknown
, "unexpected minimum",
2559 /* A specialized isl_set_min_val test case that would return an error
2560 * in earlier versions of isl.
2562 static int test_min_special2(isl_ctx
*ctx
)
2565 isl_basic_set
*bset
;
2569 str
= "{ [i, j, k] : 2j = i and 2k = i + 1 and i >= 2 }";
2570 bset
= isl_basic_set_read_from_str(ctx
, str
);
2572 obj
= isl_aff_read_from_str(ctx
, "{ [i, j, k] -> [i] }");
2574 res
= isl_basic_set_max_val(bset
, obj
);
2576 isl_basic_set_free(bset
);
2589 __isl_give isl_val
*(*fn
)(__isl_keep isl_set
*set
,
2590 __isl_keep isl_aff
*obj
);
2593 { "{ [-1]; [1] }", "{ [x] -> [x] }", &isl_set_min_val
, "-1" },
2594 { "{ [-1]; [1] }", "{ [x] -> [x] }", &isl_set_max_val
, "1" },
2595 { "{ [a, b] : 0 <= a, b <= 100 and b mod 2 = 0}",
2596 "{ [a, b] -> [floor((b - 2*floor((-a)/4))/5)] }",
2597 &isl_set_max_val
, "30" },
2601 /* Perform basic isl_set_min_val and isl_set_max_val tests.
2602 * In particular, check the results on non-convex inputs.
2604 static int test_min(struct isl_ctx
*ctx
)
2612 for (i
= 0; i
< ARRAY_SIZE(opt_tests
); ++i
) {
2613 set
= isl_set_read_from_str(ctx
, opt_tests
[i
].set
);
2614 obj
= isl_aff_read_from_str(ctx
, opt_tests
[i
].obj
);
2615 res
= isl_val_read_from_str(ctx
, opt_tests
[i
].res
);
2616 val
= opt_tests
[i
].fn(set
, obj
);
2617 ok
= isl_val_eq(res
, val
);
2626 isl_die(ctx
, isl_error_unknown
,
2627 "unexpected optimum", return -1);
2630 if (test_min_special(ctx
) < 0)
2632 if (test_min_special2(ctx
) < 0)
2643 static isl_stat
collect_must_may(__isl_take isl_map
*dep
, int must
,
2644 void *dep_user
, void *user
)
2646 struct must_may
*mm
= (struct must_may
*)user
;
2649 mm
->must
= isl_map_union(mm
->must
, dep
);
2651 mm
->may
= isl_map_union(mm
->may
, dep
);
2656 static int common_space(void *first
, void *second
)
2658 int depth
= *(int *)first
;
2662 static int map_is_equal(__isl_keep isl_map
*map
, const char *str
)
2670 map2
= isl_map_read_from_str(map
->ctx
, str
);
2671 equal
= isl_map_is_equal(map
, map2
);
2677 static int map_check_equal(__isl_keep isl_map
*map
, const char *str
)
2681 equal
= map_is_equal(map
, str
);
2685 isl_die(isl_map_get_ctx(map
), isl_error_unknown
,
2686 "result not as expected", return -1);
2690 static int test_dep(struct isl_ctx
*ctx
)
2695 isl_access_info
*ai
;
2702 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2703 map
= isl_map_read_from_str(ctx
, str
);
2704 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2706 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2707 map
= isl_map_read_from_str(ctx
, str
);
2708 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2710 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2711 map
= isl_map_read_from_str(ctx
, str
);
2712 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2714 flow
= isl_access_info_compute_flow(ai
);
2715 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2716 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2717 mm
.may
= isl_map_empty(dim
);
2719 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2721 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10); "
2722 " [1,10,0] -> [2,5,0] }";
2723 assert(map_is_equal(mm
.must
, str
));
2724 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2725 assert(map_is_equal(mm
.may
, str
));
2727 isl_map_free(mm
.must
);
2728 isl_map_free(mm
.may
);
2729 isl_flow_free(flow
);
2732 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2733 map
= isl_map_read_from_str(ctx
, str
);
2734 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2736 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2737 map
= isl_map_read_from_str(ctx
, str
);
2738 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2740 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2741 map
= isl_map_read_from_str(ctx
, str
);
2742 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2744 flow
= isl_access_info_compute_flow(ai
);
2745 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2746 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2747 mm
.may
= isl_map_empty(dim
);
2749 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2751 str
= "{ [0,i,0] -> [2,i,0] : (0 <= i <= 4) or (6 <= i <= 10) }";
2752 assert(map_is_equal(mm
.must
, str
));
2753 str
= "{ [0,5,0] -> [2,5,0]; [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2754 assert(map_is_equal(mm
.may
, str
));
2756 isl_map_free(mm
.must
);
2757 isl_map_free(mm
.may
);
2758 isl_flow_free(flow
);
2761 str
= "{ [2,i,0] -> [i] : 0 <= i <= 10 }";
2762 map
= isl_map_read_from_str(ctx
, str
);
2763 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2765 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2766 map
= isl_map_read_from_str(ctx
, str
);
2767 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2769 str
= "{ [1,i,0] -> [5] : 0 <= i <= 10 }";
2770 map
= isl_map_read_from_str(ctx
, str
);
2771 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2773 flow
= isl_access_info_compute_flow(ai
);
2774 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2775 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2776 mm
.may
= isl_map_empty(dim
);
2778 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2780 str
= "{ [0,i,0] -> [2,i,0] : 0 <= i <= 10; "
2781 " [1,i,0] -> [2,5,0] : 0 <= i <= 10 }";
2782 assert(map_is_equal(mm
.may
, str
));
2783 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2784 assert(map_is_equal(mm
.must
, str
));
2786 isl_map_free(mm
.must
);
2787 isl_map_free(mm
.may
);
2788 isl_flow_free(flow
);
2791 str
= "{ [0,i,2] -> [i] : 0 <= i <= 10 }";
2792 map
= isl_map_read_from_str(ctx
, str
);
2793 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2795 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2796 map
= isl_map_read_from_str(ctx
, str
);
2797 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2799 str
= "{ [0,i,1] -> [5] : 0 <= i <= 10 }";
2800 map
= isl_map_read_from_str(ctx
, str
);
2801 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2803 flow
= isl_access_info_compute_flow(ai
);
2804 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2805 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2806 mm
.may
= isl_map_empty(dim
);
2808 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2810 str
= "{ [0,i,0] -> [0,i,2] : 0 <= i <= 10; "
2811 " [0,i,1] -> [0,5,2] : 0 <= i <= 5 }";
2812 assert(map_is_equal(mm
.may
, str
));
2813 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2814 assert(map_is_equal(mm
.must
, str
));
2816 isl_map_free(mm
.must
);
2817 isl_map_free(mm
.may
);
2818 isl_flow_free(flow
);
2821 str
= "{ [0,i,1] -> [i] : 0 <= i <= 10 }";
2822 map
= isl_map_read_from_str(ctx
, str
);
2823 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 2);
2825 str
= "{ [0,i,0] -> [i] : 0 <= i <= 10 }";
2826 map
= isl_map_read_from_str(ctx
, str
);
2827 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2829 str
= "{ [0,i,2] -> [5] : 0 <= i <= 10 }";
2830 map
= isl_map_read_from_str(ctx
, str
);
2831 ai
= isl_access_info_add_source(ai
, map
, 0, &depth
);
2833 flow
= isl_access_info_compute_flow(ai
);
2834 dim
= isl_space_alloc(ctx
, 0, 3, 3);
2835 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2836 mm
.may
= isl_map_empty(dim
);
2838 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2840 str
= "{ [0,i,0] -> [0,i,1] : 0 <= i <= 10; "
2841 " [0,i,2] -> [0,5,1] : 0 <= i <= 4 }";
2842 assert(map_is_equal(mm
.may
, str
));
2843 str
= "{ [i,j,k] -> [l,m,n] : 1 = 0 }";
2844 assert(map_is_equal(mm
.must
, str
));
2846 isl_map_free(mm
.must
);
2847 isl_map_free(mm
.may
);
2848 isl_flow_free(flow
);
2853 str
= "{ [1,i,0,0,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2854 map
= isl_map_read_from_str(ctx
, str
);
2855 ai
= isl_access_info_alloc(map
, &depth
, &common_space
, 1);
2857 str
= "{ [0,i,0,j,0] -> [i,j] : 0 <= i <= 10 and 0 <= j <= 10 }";
2858 map
= isl_map_read_from_str(ctx
, str
);
2859 ai
= isl_access_info_add_source(ai
, map
, 1, &depth
);
2861 flow
= isl_access_info_compute_flow(ai
);
2862 dim
= isl_space_alloc(ctx
, 0, 5, 5);
2863 mm
.must
= isl_map_empty(isl_space_copy(dim
));
2864 mm
.may
= isl_map_empty(dim
);
2866 isl_flow_foreach(flow
, collect_must_may
, &mm
);
2868 str
= "{ [0,i,0,j,0] -> [1,i,0,0,0] : 0 <= i,j <= 10 }";
2869 assert(map_is_equal(mm
.must
, str
));
2870 str
= "{ [0,0,0,0,0] -> [0,0,0,0,0] : 1 = 0 }";
2871 assert(map_is_equal(mm
.may
, str
));
2873 isl_map_free(mm
.must
);
2874 isl_map_free(mm
.may
);
2875 isl_flow_free(flow
);
2880 /* Check that the dependence analysis proceeds without errors.
2881 * Earlier versions of isl would break down during the analysis
2882 * due to the use of the wrong spaces.
2884 static int test_flow(isl_ctx
*ctx
)
2887 isl_union_map
*access
, *schedule
;
2888 isl_union_map
*must_dep
, *may_dep
;
2891 str
= "{ S0[j] -> i[]; S1[j,i] -> i[]; S2[] -> i[]; S3[] -> i[] }";
2892 access
= isl_union_map_read_from_str(ctx
, str
);
2893 str
= "{ S0[j] -> [0,j,0,0] : 0 <= j < 10; "
2894 "S1[j,i] -> [0,j,1,i] : 0 <= j < i < 10; "
2895 "S2[] -> [1,0,0,0]; "
2896 "S3[] -> [-1,0,0,0] }";
2897 schedule
= isl_union_map_read_from_str(ctx
, str
);
2898 r
= isl_union_map_compute_flow(access
, isl_union_map_copy(access
),
2899 isl_union_map_copy(access
), schedule
,
2900 &must_dep
, &may_dep
, NULL
, NULL
);
2901 isl_union_map_free(may_dep
);
2902 isl_union_map_free(must_dep
);
2911 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 9 }", 1 },
2912 { "[N] -> { [i] -> [f] : 0 <= i <= N and 0 <= i - 10 f <= 10 }", 0 },
2913 { "{ [i] -> [3*floor(i/2) + 5*floor(i/3)] }", 1 },
2914 { "{ S1[i] -> [i] : 0 <= i <= 9; S2[i] -> [i] : 0 <= i <= 9 }", 1 },
2915 { "{ [i] -> S1[i] : 0 <= i <= 9; [i] -> S2[i] : 0 <= i <= 9 }", 0 },
2916 { "{ A[i] -> [i]; B[i] -> [i]; B[i] -> [i + 1] }", 0 },
2917 { "{ A[i] -> [i]; B[i] -> [i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2918 { "{ A[i] -> [i]; B[i] -> A[i] : i < 0; B[i] -> [i + 1] : i > 0 }", 1 },
2919 { "{ A[i] -> [i]; B[i] -> [j] : i - 1 <= j <= i }", 0 },
2922 int test_sv(isl_ctx
*ctx
)
2924 isl_union_map
*umap
;
2928 for (i
= 0; i
< ARRAY_SIZE(sv_tests
); ++i
) {
2929 umap
= isl_union_map_read_from_str(ctx
, sv_tests
[i
].map
);
2930 sv
= isl_union_map_is_single_valued(umap
);
2931 isl_union_map_free(umap
);
2934 if (sv_tests
[i
].sv
&& !sv
)
2935 isl_die(ctx
, isl_error_internal
,
2936 "map not detected as single valued", return -1);
2937 if (!sv_tests
[i
].sv
&& sv
)
2938 isl_die(ctx
, isl_error_internal
,
2939 "map detected as single valued", return -1);
2948 } bijective_tests
[] = {
2949 { "[N,M]->{[i,j] -> [i]}", 0 },
2950 { "[N,M]->{[i,j] -> [i] : j=i}", 1 },
2951 { "[N,M]->{[i,j] -> [i] : j=0}", 1 },
2952 { "[N,M]->{[i,j] -> [i] : j=N}", 1 },
2953 { "[N,M]->{[i,j] -> [j,i]}", 1 },
2954 { "[N,M]->{[i,j] -> [i+j]}", 0 },
2955 { "[N,M]->{[i,j] -> []}", 0 },
2956 { "[N,M]->{[i,j] -> [i,j,N]}", 1 },
2957 { "[N,M]->{[i,j] -> [2i]}", 0 },
2958 { "[N,M]->{[i,j] -> [i,i]}", 0 },
2959 { "[N,M]->{[i,j] -> [2i,i]}", 0 },
2960 { "[N,M]->{[i,j] -> [2i,j]}", 1 },
2961 { "[N,M]->{[i,j] -> [x,y] : 2x=i & y =j}", 1 },
2964 static int test_bijective(struct isl_ctx
*ctx
)
2970 for (i
= 0; i
< ARRAY_SIZE(bijective_tests
); ++i
) {
2971 map
= isl_map_read_from_str(ctx
, bijective_tests
[i
].str
);
2972 bijective
= isl_map_is_bijective(map
);
2976 if (bijective_tests
[i
].bijective
&& !bijective
)
2977 isl_die(ctx
, isl_error_internal
,
2978 "map not detected as bijective", return -1);
2979 if (!bijective_tests
[i
].bijective
&& bijective
)
2980 isl_die(ctx
, isl_error_internal
,
2981 "map detected as bijective", return -1);
2987 /* Inputs for isl_pw_qpolynomial_gist tests.
2988 * "pwqp" is the input, "set" is the context and "gist" is the expected result.
2994 } pwqp_gist_tests
[] = {
2995 { "{ [i] -> i }", "{ [k] : exists a : k = 2a }", "{ [i] -> i }" },
2996 { "{ [i] -> i + [ (i + [i/3])/2 ] }", "{ [10] }", "{ [i] -> 16 }" },
2997 { "{ [i] -> ([(i)/2]) }", "{ [k] : exists a : k = 2a+1 }",
2998 "{ [i] -> -1/2 + 1/2 * i }" },
2999 { "{ [i] -> i^2 : i != 0 }", "{ [i] : i != 0 }", "{ [i] -> i^2 }" },
3002 static int test_pwqp(struct isl_ctx
*ctx
)
3007 isl_pw_qpolynomial
*pwqp1
, *pwqp2
;
3010 str
= "{ [i,j,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
3011 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3013 pwqp1
= isl_pw_qpolynomial_move_dims(pwqp1
, isl_dim_param
, 0,
3016 str
= "[j] -> { [i,k] -> 1 + 9 * [i/5] + 7 * [j/11] + 4 * [k/13] }";
3017 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3019 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
3021 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
3023 isl_pw_qpolynomial_free(pwqp1
);
3025 for (i
= 0; i
< ARRAY_SIZE(pwqp_gist_tests
); ++i
) {
3026 str
= pwqp_gist_tests
[i
].pwqp
;
3027 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3028 str
= pwqp_gist_tests
[i
].set
;
3029 set
= isl_set_read_from_str(ctx
, str
);
3030 pwqp1
= isl_pw_qpolynomial_gist(pwqp1
, set
);
3031 str
= pwqp_gist_tests
[i
].gist
;
3032 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3033 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
3034 equal
= isl_pw_qpolynomial_is_zero(pwqp1
);
3035 isl_pw_qpolynomial_free(pwqp1
);
3040 isl_die(ctx
, isl_error_unknown
,
3041 "unexpected result", return -1);
3044 str
= "{ [i] -> ([([i/2] + [i/2])/5]) }";
3045 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3046 str
= "{ [i] -> ([(2 * [i/2])/5]) }";
3047 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3049 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
3051 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
3053 isl_pw_qpolynomial_free(pwqp1
);
3055 str
= "{ [x] -> ([x/2] + [(x+1)/2]) }";
3056 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3057 str
= "{ [x] -> x }";
3058 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3060 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
3062 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
3064 isl_pw_qpolynomial_free(pwqp1
);
3066 str
= "{ [i] -> ([i/2]) : i >= 0; [i] -> ([i/3]) : i < 0 }";
3067 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3068 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3069 pwqp1
= isl_pw_qpolynomial_coalesce(pwqp1
);
3070 pwqp1
= isl_pw_qpolynomial_sub(pwqp1
, pwqp2
);
3071 assert(isl_pw_qpolynomial_is_zero(pwqp1
));
3072 isl_pw_qpolynomial_free(pwqp1
);
3074 str
= "{ [a,b,a] -> (([(2*[a/3]+b)/5]) * ([(2*[a/3]+b)/5])) }";
3075 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3076 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
3077 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3078 set
= isl_set_read_from_str(ctx
, "{ [a,b,a] }");
3079 pwqp1
= isl_pw_qpolynomial_intersect_domain(pwqp1
, set
);
3080 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
3081 isl_pw_qpolynomial_free(pwqp1
);
3082 isl_pw_qpolynomial_free(pwqp2
);
3086 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3088 str
= "{ [a,b,c] -> (([(2*[a/3]+1)/5]) * ([(2*[c/3]+1)/5])) : b = 1 }";
3089 pwqp2
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3090 str
= "{ [a,b,c] -> (([(2*[a/3]+b)/5]) * ([(2*[c/3]+b)/5])) }";
3091 pwqp1
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3092 pwqp1
= isl_pw_qpolynomial_fix_val(pwqp1
, isl_dim_set
, 1,
3094 equal
= isl_pw_qpolynomial_plain_is_equal(pwqp1
, pwqp2
);
3095 isl_pw_qpolynomial_free(pwqp1
);
3096 isl_pw_qpolynomial_free(pwqp2
);
3100 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
3105 static int test_split_periods(isl_ctx
*ctx
)
3108 isl_pw_qpolynomial
*pwqp
;
3110 str
= "{ [U,V] -> 1/3 * U + 2/3 * V - [(U + 2V)/3] + [U/2] : "
3111 "U + 2V + 3 >= 0 and - U -2V >= 0 and - U + 10 >= 0 and "
3112 "U >= 0; [U,V] -> U^2 : U >= 100 }";
3113 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3115 pwqp
= isl_pw_qpolynomial_split_periods(pwqp
, 2);
3117 isl_pw_qpolynomial_free(pwqp
);
3125 static int test_union(isl_ctx
*ctx
)
3128 isl_union_set
*uset1
, *uset2
;
3129 isl_union_map
*umap1
, *umap2
;
3132 str
= "{ [i] : 0 <= i <= 1 }";
3133 uset1
= isl_union_set_read_from_str(ctx
, str
);
3134 str
= "{ [1] -> [0] }";
3135 umap1
= isl_union_map_read_from_str(ctx
, str
);
3137 umap2
= isl_union_set_lex_gt_union_set(isl_union_set_copy(uset1
), uset1
);
3138 equal
= isl_union_map_is_equal(umap1
, umap2
);
3140 isl_union_map_free(umap1
);
3141 isl_union_map_free(umap2
);
3146 isl_die(ctx
, isl_error_unknown
, "union maps not equal",
3149 str
= "{ A[i] -> B[i]; B[i] -> C[i]; A[0] -> C[1] }";
3150 umap1
= isl_union_map_read_from_str(ctx
, str
);
3151 str
= "{ A[i]; B[i] }";
3152 uset1
= isl_union_set_read_from_str(ctx
, str
);
3154 uset2
= isl_union_map_domain(umap1
);
3156 equal
= isl_union_set_is_equal(uset1
, uset2
);
3158 isl_union_set_free(uset1
);
3159 isl_union_set_free(uset2
);
3164 isl_die(ctx
, isl_error_unknown
, "union sets not equal",
3170 /* Check that computing a bound of a non-zero polynomial over an unbounded
3171 * domain does not produce a rational value.
3172 * In particular, check that the upper bound is infinity.
3174 static int test_bound_unbounded_domain(isl_ctx
*ctx
)
3177 isl_pw_qpolynomial
*pwqp
;
3178 isl_pw_qpolynomial_fold
*pwf
, *pwf2
;
3181 str
= "{ [m,n] -> -m * n }";
3182 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3183 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3185 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3186 pwf2
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3187 equal
= isl_pw_qpolynomial_fold_plain_is_equal(pwf
, pwf2
);
3188 isl_pw_qpolynomial_fold_free(pwf
);
3189 isl_pw_qpolynomial_fold_free(pwf2
);
3194 isl_die(ctx
, isl_error_unknown
,
3195 "expecting infinite polynomial bound", return -1);
3200 static int test_bound(isl_ctx
*ctx
)
3204 isl_pw_qpolynomial
*pwqp
;
3205 isl_pw_qpolynomial_fold
*pwf
;
3207 if (test_bound_unbounded_domain(ctx
) < 0)
3210 str
= "{ [[a, b, c, d] -> [e]] -> 0 }";
3211 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3212 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3213 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
3214 isl_pw_qpolynomial_fold_free(pwf
);
3216 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
3219 str
= "{ [[x]->[x]] -> 1 : exists a : x = 2 a }";
3220 pwqp
= isl_pw_qpolynomial_read_from_str(ctx
, str
);
3221 pwf
= isl_pw_qpolynomial_bound(pwqp
, isl_fold_max
, NULL
);
3222 dim
= isl_pw_qpolynomial_fold_dim(pwf
, isl_dim_in
);
3223 isl_pw_qpolynomial_fold_free(pwf
);
3225 isl_die(ctx
, isl_error_unknown
, "unexpected input dimension",
3231 static int test_lift(isl_ctx
*ctx
)
3234 isl_basic_map
*bmap
;
3235 isl_basic_set
*bset
;
3237 str
= "{ [i0] : exists e0 : i0 = 4e0 }";
3238 bset
= isl_basic_set_read_from_str(ctx
, str
);
3239 bset
= isl_basic_set_lift(bset
);
3240 bmap
= isl_basic_map_from_range(bset
);
3241 bset
= isl_basic_map_domain(bmap
);
3242 isl_basic_set_free(bset
);
3251 } subset_tests
[] = {
3253 "{ [i0, i1] : exists (e0 = [(i0 - i1)/16], e1: "
3254 "16e0 <= i0 - i1 and 16e0 >= -15 + i0 - i1 and "
3255 "16e1 <= i1 and 16e0 >= -i1 and 16e1 >= -i0 + i1) }", 1 },
3257 "{ [i] : exists (e0 = [(255i)/256], e1 = [(127i + 65e0)/191], "
3258 "e2 = [(3i + 61e1)/65], e3 = [(52i + 12e2)/61], "
3259 "e4 = [(2i + e3)/3], e5 = [(4i + e3)/4], e6 = [(8i + e3)/12]: "
3260 "3e4 = 2i + e3 and 4e5 = 4i + e3 and 12e6 = 8i + e3 and "
3261 "i <= 255 and 64e3 >= -45 + 67i and i >= 0 and "
3262 "256e0 <= 255i and 256e0 >= -255 + 255i and "
3263 "191e1 <= 127i + 65e0 and 191e1 >= -190 + 127i + 65e0 and "
3264 "65e2 <= 3i + 61e1 and 65e2 >= -64 + 3i + 61e1 and "
3265 "61e3 <= 52i + 12e2 and 61e3 >= -60 + 52i + 12e2) }", 1 },
3266 { "{ [i] : 0 <= i <= 10 }", "{ rat: [i] : 0 <= i <= 10 }", 1 },
3267 { "{ rat: [i] : 0 <= i <= 10 }", "{ [i] : 0 <= i <= 10 }", 0 },
3268 { "{ rat: [0] }", "{ [i] : 0 <= i <= 10 }", 1 },
3269 { "{ rat: [(1)/2] }", "{ [i] : 0 <= i <= 10 }", 0 },
3270 { "{ [t, i] : (exists (e0 = [(2 + t)/4]: 4e0 <= 2 + t and "
3271 "4e0 >= -1 + t and i >= 57 and i <= 62 and "
3272 "4e0 <= 62 + t - i and 4e0 >= -61 + t + i and "
3273 "t >= 0 and t <= 511 and 4e0 <= -57 + t + i and "
3274 "4e0 >= 58 + t - i and i >= 58 + t and i >= 62 - t)) }",
3275 "{ [i0, i1] : (exists (e0 = [(4 + i0)/4]: 4e0 <= 62 + i0 - i1 and "
3276 "4e0 >= 1 + i0 and i0 >= 0 and i0 <= 511 and "
3277 "4e0 <= -57 + i0 + i1)) or "
3278 "(exists (e0 = [(2 + i0)/4]: 4e0 <= i0 and "
3279 "4e0 >= 58 + i0 - i1 and i0 >= 2 and i0 <= 511 and "
3280 "4e0 >= -61 + i0 + i1)) or "
3281 "(i1 <= 66 - i0 and i0 >= 2 and i1 >= 59 + i0) }", 1 },
3282 { "[a, b] -> { : a = 0 and b = -1 }", "[b, a] -> { : b >= -10 }", 1 },
3285 static int test_subset(isl_ctx
*ctx
)
3288 isl_set
*set1
, *set2
;
3291 for (i
= 0; i
< ARRAY_SIZE(subset_tests
); ++i
) {
3292 set1
= isl_set_read_from_str(ctx
, subset_tests
[i
].set1
);
3293 set2
= isl_set_read_from_str(ctx
, subset_tests
[i
].set2
);
3294 subset
= isl_set_is_subset(set1
, set2
);
3299 if (subset
!= subset_tests
[i
].subset
)
3300 isl_die(ctx
, isl_error_unknown
,
3301 "incorrect subset result", return -1);
3308 const char *minuend
;
3309 const char *subtrahend
;
3310 const char *difference
;
3311 } subtract_domain_tests
[] = {
3312 { "{ A[i] -> B[i] }", "{ A[i] }", "{ }" },
3313 { "{ A[i] -> B[i] }", "{ B[i] }", "{ A[i] -> B[i] }" },
3314 { "{ A[i] -> B[i] }", "{ A[i] : i > 0 }", "{ A[i] -> B[i] : i <= 0 }" },
3317 static int test_subtract(isl_ctx
*ctx
)
3320 isl_union_map
*umap1
, *umap2
;
3321 isl_union_pw_multi_aff
*upma1
, *upma2
;
3322 isl_union_set
*uset
;
3325 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
3326 umap1
= isl_union_map_read_from_str(ctx
,
3327 subtract_domain_tests
[i
].minuend
);
3328 uset
= isl_union_set_read_from_str(ctx
,
3329 subtract_domain_tests
[i
].subtrahend
);
3330 umap2
= isl_union_map_read_from_str(ctx
,
3331 subtract_domain_tests
[i
].difference
);
3332 umap1
= isl_union_map_subtract_domain(umap1
, uset
);
3333 equal
= isl_union_map_is_equal(umap1
, umap2
);
3334 isl_union_map_free(umap1
);
3335 isl_union_map_free(umap2
);
3339 isl_die(ctx
, isl_error_unknown
,
3340 "incorrect subtract domain result", return -1);
3343 for (i
= 0; i
< ARRAY_SIZE(subtract_domain_tests
); ++i
) {
3344 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
3345 subtract_domain_tests
[i
].minuend
);
3346 uset
= isl_union_set_read_from_str(ctx
,
3347 subtract_domain_tests
[i
].subtrahend
);
3348 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
3349 subtract_domain_tests
[i
].difference
);
3350 upma1
= isl_union_pw_multi_aff_subtract_domain(upma1
, uset
);
3351 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
3352 isl_union_pw_multi_aff_free(upma1
);
3353 isl_union_pw_multi_aff_free(upma2
);
3357 isl_die(ctx
, isl_error_unknown
,
3358 "incorrect subtract domain result", return -1);
3364 /* Check that intersecting the empty basic set with another basic set
3365 * does not increase the number of constraints. In particular,
3366 * the empty basic set should maintain its canonical representation.
3368 static int test_intersect(isl_ctx
*ctx
)
3371 isl_basic_set
*bset1
, *bset2
;
3373 bset1
= isl_basic_set_read_from_str(ctx
, "{ [a,b,c] : 1 = 0 }");
3374 bset2
= isl_basic_set_read_from_str(ctx
, "{ [1,2,3] }");
3375 n1
= isl_basic_set_n_constraint(bset1
);
3376 bset1
= isl_basic_set_intersect(bset1
, bset2
);
3377 n2
= isl_basic_set_n_constraint(bset1
);
3378 isl_basic_set_free(bset1
);
3382 isl_die(ctx
, isl_error_unknown
,
3383 "number of constraints of empty set changed",
3389 int test_factorize(isl_ctx
*ctx
)
3392 isl_basic_set
*bset
;
3395 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7] : 3i5 <= 2 - 2i0 and "
3396 "i0 >= -2 and i6 >= 1 + i3 and i7 >= 0 and 3i5 >= -2i0 and "
3397 "2i4 <= i2 and i6 >= 1 + 2i0 + 3i1 and i4 <= -1 and "
3398 "i6 >= 1 + 2i0 + 3i5 and i6 <= 2 + 2i0 + 3i5 and "
3399 "3i5 <= 2 - 2i0 - i2 + 3i4 and i6 <= 2 + 2i0 + 3i1 and "
3400 "i0 <= -1 and i7 <= i2 + i3 - 3i4 - i6 and "
3401 "3i5 >= -2i0 - i2 + 3i4 }";
3402 bset
= isl_basic_set_read_from_str(ctx
, str
);
3403 f
= isl_basic_set_factorizer(bset
);
3404 isl_basic_set_free(bset
);
3405 isl_factorizer_free(f
);
3407 isl_die(ctx
, isl_error_unknown
,
3408 "failed to construct factorizer", return -1);
3410 str
= "{ [i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12] : "
3411 "i12 <= 2 + i0 - i11 and 2i8 >= -i4 and i11 >= i1 and "
3412 "3i5 <= -i2 and 2i11 >= -i4 - 2i7 and i11 <= 3 + i0 + 3i9 and "
3413 "i11 <= -i4 - 2i7 and i12 >= -i10 and i2 >= -2 and "
3414 "i11 >= i1 + 3i10 and i11 >= 1 + i0 + 3i9 and "
3415 "i11 <= 1 - i4 - 2i8 and 6i6 <= 6 - i2 and 3i6 >= 1 - i2 and "
3416 "i11 <= 2 + i1 and i12 <= i4 + i11 and i12 >= i0 - i11 and "
3417 "3i5 >= -2 - i2 and i12 >= -1 + i4 + i11 and 3i3 <= 3 - i2 and "
3418 "9i6 <= 11 - i2 + 6i5 and 3i3 >= 1 - i2 and "
3419 "9i6 <= 5 - i2 + 6i3 and i12 <= -1 and i2 <= 0 }";
3420 bset
= isl_basic_set_read_from_str(ctx
, str
);
3421 f
= isl_basic_set_factorizer(bset
);
3422 isl_basic_set_free(bset
);
3423 isl_factorizer_free(f
);
3425 isl_die(ctx
, isl_error_unknown
,
3426 "failed to construct factorizer", return -1);
3431 static isl_stat
check_injective(__isl_take isl_map
*map
, void *user
)
3433 int *injective
= user
;
3435 *injective
= isl_map_is_injective(map
);
3438 if (*injective
< 0 || !*injective
)
3439 return isl_stat_error
;
3444 int test_one_schedule(isl_ctx
*ctx
, const char *d
, const char *w
,
3445 const char *r
, const char *s
, int tilable
, int parallel
)
3449 isl_union_map
*W
, *R
, *S
;
3450 isl_union_map
*empty
;
3451 isl_union_map
*dep_raw
, *dep_war
, *dep_waw
, *dep
;
3452 isl_union_map
*validity
, *proximity
, *coincidence
;
3453 isl_union_map
*schedule
;
3454 isl_union_map
*test
;
3455 isl_union_set
*delta
;
3456 isl_union_set
*domain
;
3460 isl_schedule_constraints
*sc
;
3461 isl_schedule
*sched
;
3462 int is_nonneg
, is_parallel
, is_tilable
, is_injection
, is_complete
;
3464 D
= isl_union_set_read_from_str(ctx
, d
);
3465 W
= isl_union_map_read_from_str(ctx
, w
);
3466 R
= isl_union_map_read_from_str(ctx
, r
);
3467 S
= isl_union_map_read_from_str(ctx
, s
);
3469 W
= isl_union_map_intersect_domain(W
, isl_union_set_copy(D
));
3470 R
= isl_union_map_intersect_domain(R
, isl_union_set_copy(D
));
3472 empty
= isl_union_map_empty(isl_union_map_get_space(S
));
3473 isl_union_map_compute_flow(isl_union_map_copy(R
),
3474 isl_union_map_copy(W
), empty
,
3475 isl_union_map_copy(S
),
3476 &dep_raw
, NULL
, NULL
, NULL
);
3477 isl_union_map_compute_flow(isl_union_map_copy(W
),
3478 isl_union_map_copy(W
),
3479 isl_union_map_copy(R
),
3480 isl_union_map_copy(S
),
3481 &dep_waw
, &dep_war
, NULL
, NULL
);
3483 dep
= isl_union_map_union(dep_waw
, dep_war
);
3484 dep
= isl_union_map_union(dep
, dep_raw
);
3485 validity
= isl_union_map_copy(dep
);
3486 coincidence
= isl_union_map_copy(dep
);
3487 proximity
= isl_union_map_copy(dep
);
3489 sc
= isl_schedule_constraints_on_domain(isl_union_set_copy(D
));
3490 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3491 sc
= isl_schedule_constraints_set_coincidence(sc
, coincidence
);
3492 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3493 sched
= isl_schedule_constraints_compute_schedule(sc
);
3494 schedule
= isl_schedule_get_map(sched
);
3495 isl_schedule_free(sched
);
3496 isl_union_map_free(W
);
3497 isl_union_map_free(R
);
3498 isl_union_map_free(S
);
3501 isl_union_map_foreach_map(schedule
, &check_injective
, &is_injection
);
3503 domain
= isl_union_map_domain(isl_union_map_copy(schedule
));
3504 is_complete
= isl_union_set_is_subset(D
, domain
);
3505 isl_union_set_free(D
);
3506 isl_union_set_free(domain
);
3508 test
= isl_union_map_reverse(isl_union_map_copy(schedule
));
3509 test
= isl_union_map_apply_range(test
, dep
);
3510 test
= isl_union_map_apply_range(test
, schedule
);
3512 delta
= isl_union_map_deltas(test
);
3513 if (isl_union_set_n_set(delta
) == 0) {
3517 isl_union_set_free(delta
);
3519 delta_set
= isl_set_from_union_set(delta
);
3521 slice
= isl_set_universe(isl_set_get_space(delta_set
));
3522 for (i
= 0; i
< tilable
; ++i
)
3523 slice
= isl_set_lower_bound_si(slice
, isl_dim_set
, i
, 0);
3524 is_tilable
= isl_set_is_subset(delta_set
, slice
);
3525 isl_set_free(slice
);
3527 slice
= isl_set_universe(isl_set_get_space(delta_set
));
3528 for (i
= 0; i
< parallel
; ++i
)
3529 slice
= isl_set_fix_si(slice
, isl_dim_set
, i
, 0);
3530 is_parallel
= isl_set_is_subset(delta_set
, slice
);
3531 isl_set_free(slice
);
3533 origin
= isl_set_universe(isl_set_get_space(delta_set
));
3534 for (i
= 0; i
< isl_set_dim(origin
, isl_dim_set
); ++i
)
3535 origin
= isl_set_fix_si(origin
, isl_dim_set
, i
, 0);
3537 delta_set
= isl_set_union(delta_set
, isl_set_copy(origin
));
3538 delta_set
= isl_set_lexmin(delta_set
);
3540 is_nonneg
= isl_set_is_equal(delta_set
, origin
);
3542 isl_set_free(origin
);
3543 isl_set_free(delta_set
);
3546 if (is_nonneg
< 0 || is_parallel
< 0 || is_tilable
< 0 ||
3547 is_injection
< 0 || is_complete
< 0)
3550 isl_die(ctx
, isl_error_unknown
,
3551 "generated schedule incomplete", return -1);
3553 isl_die(ctx
, isl_error_unknown
,
3554 "generated schedule not injective on each statement",
3557 isl_die(ctx
, isl_error_unknown
,
3558 "negative dependences in generated schedule",
3561 isl_die(ctx
, isl_error_unknown
,
3562 "generated schedule not as tilable as expected",
3565 isl_die(ctx
, isl_error_unknown
,
3566 "generated schedule not as parallel as expected",
3572 /* Compute a schedule for the given instance set, validity constraints,
3573 * proximity constraints and context and return a corresponding union map
3576 static __isl_give isl_union_map
*compute_schedule_with_context(isl_ctx
*ctx
,
3577 const char *domain
, const char *validity
, const char *proximity
,
3578 const char *context
)
3583 isl_union_map
*prox
;
3584 isl_schedule_constraints
*sc
;
3585 isl_schedule
*schedule
;
3586 isl_union_map
*sched
;
3588 con
= isl_set_read_from_str(ctx
, context
);
3589 dom
= isl_union_set_read_from_str(ctx
, domain
);
3590 dep
= isl_union_map_read_from_str(ctx
, validity
);
3591 prox
= isl_union_map_read_from_str(ctx
, proximity
);
3592 sc
= isl_schedule_constraints_on_domain(dom
);
3593 sc
= isl_schedule_constraints_set_context(sc
, con
);
3594 sc
= isl_schedule_constraints_set_validity(sc
, dep
);
3595 sc
= isl_schedule_constraints_set_proximity(sc
, prox
);
3596 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3597 sched
= isl_schedule_get_map(schedule
);
3598 isl_schedule_free(schedule
);
3603 /* Compute a schedule for the given instance set, validity constraints and
3604 * proximity constraints and return a corresponding union map representation.
3606 static __isl_give isl_union_map
*compute_schedule(isl_ctx
*ctx
,
3607 const char *domain
, const char *validity
, const char *proximity
)
3609 return compute_schedule_with_context(ctx
, domain
, validity
, proximity
,
3613 /* Check that a schedule can be constructed on the given domain
3614 * with the given validity and proximity constraints.
3616 static int test_has_schedule(isl_ctx
*ctx
, const char *domain
,
3617 const char *validity
, const char *proximity
)
3619 isl_union_map
*sched
;
3621 sched
= compute_schedule(ctx
, domain
, validity
, proximity
);
3625 isl_union_map_free(sched
);
3629 int test_special_schedule(isl_ctx
*ctx
, const char *domain
,
3630 const char *validity
, const char *proximity
, const char *expected_sched
)
3632 isl_union_map
*sched1
, *sched2
;
3635 sched1
= compute_schedule(ctx
, domain
, validity
, proximity
);
3636 sched2
= isl_union_map_read_from_str(ctx
, expected_sched
);
3638 equal
= isl_union_map_is_equal(sched1
, sched2
);
3639 isl_union_map_free(sched1
);
3640 isl_union_map_free(sched2
);
3645 isl_die(ctx
, isl_error_unknown
, "unexpected schedule",
3651 /* Check that the schedule map is properly padded, even after being
3652 * reconstructed from the band forest.
3654 static int test_padded_schedule(isl_ctx
*ctx
)
3658 isl_union_map
*validity
, *proximity
;
3659 isl_schedule_constraints
*sc
;
3660 isl_schedule
*sched
;
3661 isl_union_map
*map1
, *map2
;
3662 isl_band_list
*list
;
3665 str
= "[N] -> { S0[i] : 0 <= i <= N; S1[i, j] : 0 <= i, j <= N }";
3666 D
= isl_union_set_read_from_str(ctx
, str
);
3667 validity
= isl_union_map_empty(isl_union_set_get_space(D
));
3668 proximity
= isl_union_map_copy(validity
);
3669 sc
= isl_schedule_constraints_on_domain(D
);
3670 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3671 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3672 sched
= isl_schedule_constraints_compute_schedule(sc
);
3673 map1
= isl_schedule_get_map(sched
);
3674 list
= isl_schedule_get_band_forest(sched
);
3675 isl_band_list_free(list
);
3676 map2
= isl_schedule_get_map(sched
);
3677 isl_schedule_free(sched
);
3678 equal
= isl_union_map_is_equal(map1
, map2
);
3679 isl_union_map_free(map1
);
3680 isl_union_map_free(map2
);
3685 isl_die(ctx
, isl_error_unknown
,
3686 "reconstructed schedule map not the same as original",
3692 /* Check that conditional validity constraints are also taken into
3693 * account across bands.
3694 * In particular, try to make sure that live ranges D[1,0]->C[2,1] and
3695 * D[2,0]->C[3,0] are not local in the outer band of the generated schedule
3696 * and then check that the adjacent order constraint C[2,1]->D[2,0]
3697 * is enforced by the rest of the schedule.
3699 static int test_special_conditional_schedule_constraints(isl_ctx
*ctx
)
3702 isl_union_set
*domain
;
3703 isl_union_map
*validity
, *proximity
, *condition
;
3704 isl_union_map
*sink
, *source
, *dep
;
3705 isl_schedule_constraints
*sc
;
3706 isl_schedule
*schedule
;
3707 isl_union_access_info
*access
;
3708 isl_union_flow
*flow
;
3711 str
= "[n] -> { C[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3712 "A[k] : k >= 1 and k <= -1 + n; "
3713 "B[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k; "
3714 "D[k, i] : k <= -1 + n and i >= 0 and i <= -1 + k }";
3715 domain
= isl_union_set_read_from_str(ctx
, str
);
3716 sc
= isl_schedule_constraints_on_domain(domain
);
3717 str
= "[n] -> { D[k, i] -> C[1 + k, k - i] : "
3718 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3719 "D[k, i] -> C[1 + k, i] : "
3720 "k <= -2 + n and i >= 1 and i <= -1 + k; "
3721 "D[k, 0] -> C[1 + k, k] : k >= 1 and k <= -2 + n; "
3722 "D[k, 0] -> C[1 + k, 0] : k >= 1 and k <= -2 + n }";
3723 validity
= isl_union_map_read_from_str(ctx
, str
);
3724 sc
= isl_schedule_constraints_set_validity(sc
, validity
);
3725 str
= "[n] -> { C[k, i] -> D[k, i] : "
3726 "0 <= i <= -1 + k and k <= -1 + n }";
3727 proximity
= isl_union_map_read_from_str(ctx
, str
);
3728 sc
= isl_schedule_constraints_set_proximity(sc
, proximity
);
3729 str
= "[n] -> { [D[k, i] -> a[]] -> [C[1 + k, k - i] -> b[]] : "
3730 "i <= -1 + k and i >= 1 and k <= -2 + n; "
3731 "[B[k, i] -> c[]] -> [B[k, 1 + i] -> c[]] : "
3732 "k <= -1 + n and i >= 0 and i <= -2 + k }";
3733 condition
= isl_union_map_read_from_str(ctx
, str
);
3734 str
= "[n] -> { [B[k, i] -> e[]] -> [D[k, i] -> a[]] : "
3735 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3736 "[C[k, i] -> b[]] -> [D[k', -1 + k - i] -> a[]] : "
3737 "i >= 0 and i <= -1 + k and k <= -1 + n and "
3738 "k' <= -1 + n and k' >= k - i and k' >= 1 + k; "
3739 "[C[k, i] -> b[]] -> [D[k, -1 + k - i] -> a[]] : "
3740 "i >= 0 and i <= -1 + k and k <= -1 + n; "
3741 "[B[k, i] -> c[]] -> [A[k'] -> d[]] : "
3742 "k <= -1 + n and i >= 0 and i <= -1 + k and "
3743 "k' >= 1 and k' <= -1 + n and k' >= 1 + k }";
3744 validity
= isl_union_map_read_from_str(ctx
, str
);
3745 sc
= isl_schedule_constraints_set_conditional_validity(sc
, condition
,
3747 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3748 str
= "{ D[2,0] -> [] }";
3749 sink
= isl_union_map_read_from_str(ctx
, str
);
3750 access
= isl_union_access_info_from_sink(sink
);
3751 str
= "{ C[2,1] -> [] }";
3752 source
= isl_union_map_read_from_str(ctx
, str
);
3753 access
= isl_union_access_info_set_must_source(access
, source
);
3754 access
= isl_union_access_info_set_schedule(access
, schedule
);
3755 flow
= isl_union_access_info_compute_flow(access
);
3756 dep
= isl_union_flow_get_must_dependence(flow
);
3757 isl_union_flow_free(flow
);
3758 empty
= isl_union_map_is_empty(dep
);
3759 isl_union_map_free(dep
);
3764 isl_die(ctx
, isl_error_unknown
,
3765 "conditional validity not respected", return -1);
3770 /* Check that the test for violated conditional validity constraints
3771 * is not confused by domain compression.
3772 * In particular, earlier versions of isl would apply
3773 * a schedule on the compressed domains to the original domains,
3774 * resulting in a failure to detect that the default schedule
3775 * violates the conditional validity constraints.
3777 static int test_special_conditional_schedule_constraints_2(isl_ctx
*ctx
)
3781 isl_union_set
*domain
;
3782 isl_union_map
*validity
, *condition
;
3783 isl_schedule_constraints
*sc
;
3784 isl_schedule
*schedule
;
3785 isl_union_map
*umap
;
3788 str
= "{ A[0, i] : 0 <= i <= 10; B[1, i] : 0 <= i <= 10 }";
3789 domain
= isl_union_set_read_from_str(ctx
, str
);
3790 sc
= isl_schedule_constraints_on_domain(domain
);
3791 str
= "{ B[1, i] -> A[0, i + 1] }";
3792 condition
= isl_union_map_read_from_str(ctx
, str
);
3793 str
= "{ A[0, i] -> B[1, i - 1] }";
3794 validity
= isl_union_map_read_from_str(ctx
, str
);
3795 sc
= isl_schedule_constraints_set_conditional_validity(sc
, condition
,
3796 isl_union_map_copy(validity
));
3797 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3798 umap
= isl_schedule_get_map(schedule
);
3799 isl_schedule_free(schedule
);
3800 validity
= isl_union_map_apply_domain(validity
,
3801 isl_union_map_copy(umap
));
3802 validity
= isl_union_map_apply_range(validity
, umap
);
3803 map
= isl_map_from_union_map(validity
);
3804 ge
= isl_map_lex_ge(isl_space_domain(isl_map_get_space(map
)));
3805 map
= isl_map_intersect(map
, ge
);
3806 empty
= isl_map_is_empty(map
);
3812 isl_die(ctx
, isl_error_unknown
,
3813 "conditional validity constraints not satisfied",
3819 /* Input for testing of schedule construction based on
3820 * conditional constraints.
3822 * domain is the iteration domain
3823 * flow are the flow dependences, which determine the validity and
3824 * proximity constraints
3825 * condition are the conditions on the conditional validity constraints
3826 * conditional_validity are the conditional validity constraints
3827 * outer_band_n is the expected number of members in the outer band
3832 const char *condition
;
3833 const char *conditional_validity
;
3835 } live_range_tests
[] = {
3836 /* Contrived example that illustrates that we need to keep
3837 * track of tagged condition dependences and
3838 * tagged conditional validity dependences
3839 * in isl_sched_edge separately.
3840 * In particular, the conditional validity constraints on A
3841 * cannot be satisfied,
3842 * but they can be ignored because there are no corresponding
3843 * condition constraints. However, we do have an additional
3844 * conditional validity constraint that maps to the same
3845 * dependence relation
3846 * as the condition constraint on B. If we did not make a distinction
3847 * between tagged condition and tagged conditional validity
3848 * dependences, then we
3849 * could end up treating this shared dependence as an condition
3850 * constraint on A, forcing a localization of the conditions,
3851 * which is impossible.
3853 { "{ S[i] : 0 <= 1 < 100; T[i] : 0 <= 1 < 100 }",
3854 "{ S[i] -> S[i+1] : 0 <= i < 99 }",
3855 "{ [S[i] -> B[]] -> [S[i+1] -> B[]] : 0 <= i < 99 }",
3856 "{ [S[i] -> A[]] -> [T[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3857 "[T[i] -> A[]] -> [S[i'] -> A[]] : 0 <= i', i < 100 and i != i';"
3858 "[S[i] -> A[]] -> [S[i+1] -> A[]] : 0 <= i < 99 }",
3861 /* TACO 2013 Fig. 7 */
3862 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3863 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3864 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3865 "[n] -> { [S1[i,j] -> t[]] -> [S2[i,j] -> t[]] : 0 <= i,j < n;"
3866 "[S2[i,j] -> x1[]] -> [S2[i,j+1] -> x1[]] : "
3867 "0 <= i < n and 0 <= j < n - 1 }",
3868 "[n] -> { [S2[i,j] -> t[]] -> [S1[i,j'] -> t[]] : "
3869 "0 <= i < n and 0 <= j < j' < n;"
3870 "[S2[i,j] -> t[]] -> [S1[i',j'] -> t[]] : "
3871 "0 <= i < i' < n and 0 <= j,j' < n;"
3872 "[S2[i,j] -> x1[]] -> [S2[i,j'] -> x1[]] : "
3873 "0 <= i,j,j' < n and j < j' }",
3876 /* TACO 2013 Fig. 7, without tags */
3877 { "[n] -> { S1[i,j] : 0 <= i,j < n; S2[i,j] : 0 <= i,j < n }",
3878 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3879 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3880 "[n] -> { S1[i,j] -> S2[i,j] : 0 <= i,j < n;"
3881 "S2[i,j] -> S2[i,j+1] : 0 <= i < n and 0 <= j < n - 1 }",
3882 "[n] -> { S2[i,j] -> S1[i,j'] : 0 <= i < n and 0 <= j < j' < n;"
3883 "S2[i,j] -> S1[i',j'] : 0 <= i < i' < n and 0 <= j,j' < n;"
3884 "S2[i,j] -> S2[i,j'] : 0 <= i,j,j' < n and j < j' }",
3887 /* TACO 2013 Fig. 12 */
3888 { "{ S1[i,0] : 0 <= i <= 1; S2[i,j] : 0 <= i <= 1 and 1 <= j <= 2;"
3889 "S3[i,3] : 0 <= i <= 1 }",
3890 "{ S1[i,0] -> S2[i,1] : 0 <= i <= 1;"
3891 "S2[i,1] -> S2[i,2] : 0 <= i <= 1;"
3892 "S2[i,2] -> S3[i,3] : 0 <= i <= 1 }",
3893 "{ [S1[i,0]->t[]] -> [S2[i,1]->t[]] : 0 <= i <= 1;"
3894 "[S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3895 "[S2[i,2]->t[]] -> [S3[i,3]->t[]] : 0 <= i <= 1 }",
3896 "{ [S2[i,1]->t[]] -> [S2[i,2]->t[]] : 0 <= i <= 1;"
3897 "[S2[0,j]->t[]] -> [S2[1,j']->t[]] : 1 <= j,j' <= 2;"
3898 "[S2[0,j]->t[]] -> [S1[1,0]->t[]] : 1 <= j <= 2;"
3899 "[S3[0,3]->t[]] -> [S2[1,j]->t[]] : 1 <= j <= 2;"
3900 "[S3[0,3]->t[]] -> [S1[1,0]->t[]] }",
3905 /* Test schedule construction based on conditional constraints.
3906 * In particular, check the number of members in the outer band node
3907 * as an indication of whether tiling is possible or not.
3909 static int test_conditional_schedule_constraints(isl_ctx
*ctx
)
3912 isl_union_set
*domain
;
3913 isl_union_map
*condition
;
3914 isl_union_map
*flow
;
3915 isl_union_map
*validity
;
3916 isl_schedule_constraints
*sc
;
3917 isl_schedule
*schedule
;
3918 isl_schedule_node
*node
;
3921 if (test_special_conditional_schedule_constraints(ctx
) < 0)
3923 if (test_special_conditional_schedule_constraints_2(ctx
) < 0)
3926 for (i
= 0; i
< ARRAY_SIZE(live_range_tests
); ++i
) {
3927 domain
= isl_union_set_read_from_str(ctx
,
3928 live_range_tests
[i
].domain
);
3929 flow
= isl_union_map_read_from_str(ctx
,
3930 live_range_tests
[i
].flow
);
3931 condition
= isl_union_map_read_from_str(ctx
,
3932 live_range_tests
[i
].condition
);
3933 validity
= isl_union_map_read_from_str(ctx
,
3934 live_range_tests
[i
].conditional_validity
);
3935 sc
= isl_schedule_constraints_on_domain(domain
);
3936 sc
= isl_schedule_constraints_set_validity(sc
,
3937 isl_union_map_copy(flow
));
3938 sc
= isl_schedule_constraints_set_proximity(sc
, flow
);
3939 sc
= isl_schedule_constraints_set_conditional_validity(sc
,
3940 condition
, validity
);
3941 schedule
= isl_schedule_constraints_compute_schedule(sc
);
3942 node
= isl_schedule_get_root(schedule
);
3944 isl_schedule_node_get_type(node
) != isl_schedule_node_band
)
3945 node
= isl_schedule_node_first_child(node
);
3946 n_member
= isl_schedule_node_band_n_member(node
);
3947 isl_schedule_node_free(node
);
3948 isl_schedule_free(schedule
);
3952 if (n_member
!= live_range_tests
[i
].outer_band_n
)
3953 isl_die(ctx
, isl_error_unknown
,
3954 "unexpected number of members in outer band",
3960 /* Check that the schedule computed for the given instance set and
3961 * dependence relation strongly satisfies the dependences.
3962 * In particular, check that no instance is scheduled before
3963 * or together with an instance on which it depends.
3964 * Earlier versions of isl would produce a schedule that
3965 * only weakly satisfies the dependences.
3967 static int test_strongly_satisfying_schedule(isl_ctx
*ctx
)
3969 const char *domain
, *dep
;
3970 isl_union_map
*D
, *schedule
;
3974 domain
= "{ B[i0, i1] : 0 <= i0 <= 1 and 0 <= i1 <= 11; "
3975 "A[i0] : 0 <= i0 <= 1 }";
3976 dep
= "{ B[i0, i1] -> B[i0, 1 + i1] : 0 <= i0 <= 1 and 0 <= i1 <= 10; "
3977 "B[0, 11] -> A[1]; A[i0] -> B[i0, 0] : 0 <= i0 <= 1 }";
3978 schedule
= compute_schedule(ctx
, domain
, dep
, dep
);
3979 D
= isl_union_map_read_from_str(ctx
, dep
);
3980 D
= isl_union_map_apply_domain(D
, isl_union_map_copy(schedule
));
3981 D
= isl_union_map_apply_range(D
, schedule
);
3982 map
= isl_map_from_union_map(D
);
3983 ge
= isl_map_lex_ge(isl_space_domain(isl_map_get_space(map
)));
3984 map
= isl_map_intersect(map
, ge
);
3985 empty
= isl_map_is_empty(map
);
3991 isl_die(ctx
, isl_error_unknown
,
3992 "dependences not strongly satisfied", return -1);
3997 /* Compute a schedule for input where the instance set constraints
3998 * conflict with the context constraints.
3999 * Earlier versions of isl did not properly handle this situation.
4001 static int test_conflicting_context_schedule(isl_ctx
*ctx
)
4003 isl_union_map
*schedule
;
4004 const char *domain
, *context
;
4006 domain
= "[n] -> { A[] : n >= 0 }";
4007 context
= "[n] -> { : n < 0 }";
4008 schedule
= compute_schedule_with_context(ctx
,
4009 domain
, "{}", "{}", context
);
4010 isl_union_map_free(schedule
);
4018 /* Check that the dependence carrying step is not confused by
4019 * a bound on the coefficient size.
4020 * In particular, force the scheduler to move to a dependence carrying
4021 * step by demanding outer coincidence and bound the size of
4022 * the coefficients. Earlier versions of isl would take this
4023 * bound into account while carrying dependences, breaking
4024 * fundamental assumptions.
4025 * On the other hand, the dependence carrying step now tries
4026 * to prevent loop coalescing by default, so check that indeed
4027 * no loop coalescing occurs by comparing the computed schedule
4028 * to the expected non-coalescing schedule.
4030 static int test_bounded_coefficients_schedule(isl_ctx
*ctx
)
4032 const char *domain
, *dep
;
4035 isl_schedule_constraints
*sc
;
4036 isl_schedule
*schedule
;
4037 isl_union_map
*sched1
, *sched2
;
4040 domain
= "{ C[i0, i1] : 2 <= i0 <= 3999 and 0 <= i1 <= -1 + i0 }";
4041 dep
= "{ C[i0, i1] -> C[i0, 1 + i1] : i0 <= 3999 and i1 >= 0 and "
4043 "C[i0, -1 + i0] -> C[1 + i0, 0] : i0 <= 3998 and i0 >= 1 }";
4044 I
= isl_union_set_read_from_str(ctx
, domain
);
4045 D
= isl_union_map_read_from_str(ctx
, dep
);
4046 sc
= isl_schedule_constraints_on_domain(I
);
4047 sc
= isl_schedule_constraints_set_validity(sc
, isl_union_map_copy(D
));
4048 sc
= isl_schedule_constraints_set_coincidence(sc
, D
);
4049 isl_options_set_schedule_outer_coincidence(ctx
, 1);
4050 isl_options_set_schedule_max_coefficient(ctx
, 20);
4051 schedule
= isl_schedule_constraints_compute_schedule(sc
);
4052 isl_options_set_schedule_max_coefficient(ctx
, -1);
4053 isl_options_set_schedule_outer_coincidence(ctx
, 0);
4054 sched1
= isl_schedule_get_map(schedule
);
4055 isl_schedule_free(schedule
);
4057 sched2
= isl_union_map_read_from_str(ctx
, "{ C[x,y] -> [x,y] }");
4058 equal
= isl_union_map_is_equal(sched1
, sched2
);
4059 isl_union_map_free(sched1
);
4060 isl_union_map_free(sched2
);
4065 isl_die(ctx
, isl_error_unknown
,
4066 "unexpected schedule", return -1);
4071 /* Check that the bounds on the coefficients are respected.
4072 * This function checks for a particular output schedule,
4073 * but the exact output is not important, only that it does
4074 * not contain any coefficients greater than 4.
4075 * It is, however, easier to check for a particular output.
4076 * This test is only run for the whole component scheduler
4077 * because the incremental scheduler produces a slightly different schedule.
4079 static int test_bounded_coefficients_schedule_whole(isl_ctx
*ctx
)
4081 const char *domain
, *dep
, *str
;
4084 isl_schedule_constraints
*sc
;
4085 isl_schedule
*schedule
;
4086 isl_union_map
*sched1
, *sched2
;
4089 domain
= "{ S_4[i, j, k] : 0 <= i < j <= 10 and 0 <= k <= 100; "
4090 "S_2[i, j] : 0 <= i < j <= 10; S_6[i, j] : 0 <= i < j <= 10 }";
4091 dep
= "{ S_2[0, j] -> S_4[0, j, 0] : 0 < j <= 10; "
4092 "S_4[0, j, 100] -> S_6[0, j] : 0 < j <= 10 }";
4093 I
= isl_union_set_read_from_str(ctx
, domain
);
4094 D
= isl_union_map_read_from_str(ctx
, dep
);
4095 sc
= isl_schedule_constraints_on_domain(I
);
4096 sc
= isl_schedule_constraints_set_validity(sc
, D
);
4097 isl_options_set_schedule_max_constant_term(ctx
, 10);
4098 isl_options_set_schedule_max_coefficient(ctx
, 4);
4099 schedule
= isl_schedule_constraints_compute_schedule(sc
);
4100 isl_options_set_schedule_max_coefficient(ctx
, -1);
4101 isl_options_set_schedule_max_constant_term(ctx
, -1);
4102 sched1
= isl_schedule_get_map(schedule
);
4103 isl_schedule_free(schedule
);
4105 str
= "{ S_4[i, j, k] -> [i, j, 10 - k]; "
4106 "S_2[i, j] -> [0, i, j]; S_6[i, j] -> [0, 10 + i, j] }";
4107 sched2
= isl_union_map_read_from_str(ctx
, str
);
4108 equal
= isl_union_map_is_equal(sched1
, sched2
);
4109 isl_union_map_free(sched1
);
4110 isl_union_map_free(sched2
);
4115 isl_die(ctx
, isl_error_unknown
,
4116 "unexpected schedule", return -1);
4121 /* Check that a set of schedule constraints that only allow for
4122 * a coalescing schedule still produces a schedule even if the user
4123 * request a non-coalescing schedule. Earlier versions of isl
4124 * would not handle this case correctly.
4126 static int test_coalescing_schedule(isl_ctx
*ctx
)
4128 const char *domain
, *dep
;
4131 isl_schedule_constraints
*sc
;
4132 isl_schedule
*schedule
;
4133 int treat_coalescing
;
4135 domain
= "{ S[a, b] : 0 <= a <= 1 and 0 <= b <= 1 }";
4136 dep
= "{ S[a, b] -> S[a + b, 1 - b] }";
4137 I
= isl_union_set_read_from_str(ctx
, domain
);
4138 D
= isl_union_map_read_from_str(ctx
, dep
);
4139 sc
= isl_schedule_constraints_on_domain(I
);
4140 sc
= isl_schedule_constraints_set_validity(sc
, D
);
4141 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4142 isl_options_set_schedule_treat_coalescing(ctx
, 1);
4143 schedule
= isl_schedule_constraints_compute_schedule(sc
);
4144 isl_options_set_schedule_treat_coalescing(ctx
, treat_coalescing
);
4145 isl_schedule_free(schedule
);
4151 /* Check that the scheduler does not perform any needless
4152 * compound skewing. Earlier versions of isl would compute
4153 * schedules in terms of transformed schedule coefficients and
4154 * would not accurately keep track of the sum of the original
4155 * schedule coefficients. It could then produce the schedule
4156 * S[t,i,j,k] -> [t, 2t + i, 2t + i + j, 2t + i + j + k]
4157 * for the input below instead of the schedule below.
4159 static int test_skewing_schedule(isl_ctx
*ctx
)
4161 const char *D
, *V
, *P
, *S
;
4163 D
= "[n] -> { S[t,i,j,k] : 0 <= t,i,j,k < n }";
4164 V
= "[n] -> { S[t,i,j,k] -> S[t+1,a,b,c] : 0 <= t,i,j,k,a,b,c < n and "
4165 "-2 <= a-i <= 2 and -1 <= a-i + b-j <= 1 and "
4166 "-1 <= a-i + b-j + c-k <= 1 }";
4168 S
= "{ S[t,i,j,k] -> [t, 2t + i, t + i + j, 2t + k] }";
4170 return test_special_schedule(ctx
, D
, V
, P
, S
);
4173 int test_schedule(isl_ctx
*ctx
)
4175 const char *D
, *W
, *R
, *V
, *P
, *S
;
4176 int max_coincidence
;
4177 int treat_coalescing
;
4179 /* Handle resulting schedule with zero bands. */
4180 if (test_one_schedule(ctx
, "{[]}", "{}", "{}", "{[] -> []}", 0, 0) < 0)
4184 D
= "[T,N] -> { S1[t,i] : 1 <= t <= T and 2 <= i <= N - 1 }";
4185 W
= "{ S1[t,i] -> a[t,i] }";
4186 R
= "{ S1[t,i] -> a[t-1,i]; S1[t,i] -> a[t-1,i-1]; "
4187 "S1[t,i] -> a[t-1,i+1] }";
4188 S
= "{ S1[t,i] -> [t,i] }";
4189 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
4192 /* Fig. 5 of CC2008 */
4193 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and j >= 2 and "
4195 W
= "[N] -> { S_0[i, j] -> a[i, j] : i >= 0 and i <= -1 + N and "
4196 "j >= 2 and j <= -1 + N }";
4197 R
= "[N] -> { S_0[i, j] -> a[j, i] : i >= 0 and i <= -1 + N and "
4198 "j >= 2 and j <= -1 + N; "
4199 "S_0[i, j] -> a[i, -1 + j] : i >= 0 and i <= -1 + N and "
4200 "j >= 2 and j <= -1 + N }";
4201 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
4202 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
4205 D
= "{ S1[i] : 0 <= i <= 10; S2[i] : 0 <= i <= 9 }";
4206 W
= "{ S1[i] -> a[i] }";
4207 R
= "{ S2[i] -> a[i+1] }";
4208 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
4209 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
4212 D
= "{ S1[i] : 0 <= i < 10; S2[i] : 0 <= i < 10 }";
4213 W
= "{ S1[i] -> a[i] }";
4214 R
= "{ S2[i] -> a[9-i] }";
4215 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
4216 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
4219 D
= "[N] -> { S1[i] : 0 <= i < N; S2[i] : 0 <= i < N }";
4220 W
= "{ S1[i] -> a[i] }";
4221 R
= "[N] -> { S2[i] -> a[N-1-i] }";
4222 S
= "{ S1[i] -> [0,i]; S2[i] -> [1,i] }";
4223 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 1) < 0)
4226 D
= "{ S1[i] : 0 < i < 10; S2[i] : 0 <= i < 10 }";
4227 W
= "{ S1[i] -> a[i]; S2[i] -> b[i] }";
4228 R
= "{ S2[i] -> a[i]; S1[i] -> b[i-1] }";
4229 S
= "{ S1[i] -> [i,0]; S2[i] -> [i,1] }";
4230 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4233 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
4234 W
= "{ S1[i] -> a[0,i]; S2[i,j] -> a[i,j] }";
4235 R
= "{ S2[i,j] -> a[i-1,j] }";
4236 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
4237 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
4240 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i,j] : 1 <= i,j <= N }";
4241 W
= "{ S1[i] -> a[i,0]; S2[i,j] -> a[i,j] }";
4242 R
= "{ S2[i,j] -> a[i,j-1] }";
4243 S
= "{ S1[i] -> [0,i,0]; S2[i,j] -> [1,i,j] }";
4244 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
4247 D
= "[N] -> { S_0[]; S_1[i] : i >= 0 and i <= -1 + N; S_2[] }";
4248 W
= "[N] -> { S_0[] -> a[0]; S_2[] -> b[0]; "
4249 "S_1[i] -> a[1 + i] : i >= 0 and i <= -1 + N }";
4250 R
= "[N] -> { S_2[] -> a[N]; S_1[i] -> a[i] : i >= 0 and i <= -1 + N }";
4251 S
= "[N] -> { S_1[i] -> [1, i, 0]; S_2[] -> [2, 0, 1]; "
4252 "S_0[] -> [0, 0, 0] }";
4253 if (test_one_schedule(ctx
, D
, W
, R
, S
, 1, 0) < 0)
4255 ctx
->opt
->schedule_parametric
= 0;
4256 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4258 ctx
->opt
->schedule_parametric
= 1;
4260 D
= "[N] -> { S1[i] : 1 <= i <= N; S2[i] : 1 <= i <= N; "
4261 "S3[i,j] : 1 <= i,j <= N; S4[i] : 1 <= i <= N }";
4262 W
= "{ S1[i] -> a[i,0]; S2[i] -> a[0,i]; S3[i,j] -> a[i,j] }";
4263 R
= "[N] -> { S3[i,j] -> a[i-1,j]; S3[i,j] -> a[i,j-1]; "
4264 "S4[i] -> a[i,N] }";
4265 S
= "{ S1[i] -> [0,i,0]; S2[i] -> [1,i,0]; S3[i,j] -> [2,i,j]; "
4266 "S4[i] -> [4,i,0] }";
4267 max_coincidence
= isl_options_get_schedule_maximize_coincidence(ctx
);
4268 isl_options_set_schedule_maximize_coincidence(ctx
, 0);
4269 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 0) < 0)
4271 isl_options_set_schedule_maximize_coincidence(ctx
, max_coincidence
);
4273 D
= "[N] -> { S_0[i, j] : i >= 1 and i <= N and j >= 1 and j <= N }";
4274 W
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
4276 R
= "[N] -> { S_0[i, j] -> s[0] : i >= 1 and i <= N and j >= 1 and "
4278 "S_0[i, j] -> a[i, j] : i >= 1 and i <= N and j >= 1 and "
4280 S
= "[N] -> { S_0[i, j] -> [0, i, 0, j, 0] }";
4281 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4284 D
= "[N] -> { S_0[t] : t >= 0 and t <= -1 + N; "
4285 " S_2[t] : t >= 0 and t <= -1 + N; "
4286 " S_1[t, i] : t >= 0 and t <= -1 + N and i >= 0 and "
4288 W
= "[N] -> { S_0[t] -> a[t, 0] : t >= 0 and t <= -1 + N; "
4289 " S_2[t] -> b[t] : t >= 0 and t <= -1 + N; "
4290 " S_1[t, i] -> a[t, 1 + i] : t >= 0 and t <= -1 + N and "
4291 "i >= 0 and i <= -1 + N }";
4292 R
= "[N] -> { S_1[t, i] -> a[t, i] : t >= 0 and t <= -1 + N and "
4293 "i >= 0 and i <= -1 + N; "
4294 " S_2[t] -> a[t, N] : t >= 0 and t <= -1 + N }";
4295 S
= "[N] -> { S_2[t] -> [0, t, 2]; S_1[t, i] -> [0, t, 1, i, 0]; "
4296 " S_0[t] -> [0, t, 0] }";
4298 if (test_one_schedule(ctx
, D
, W
, R
, S
, 2, 1) < 0)
4300 ctx
->opt
->schedule_parametric
= 0;
4301 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4303 ctx
->opt
->schedule_parametric
= 1;
4305 D
= "[N] -> { S1[i,j] : 0 <= i,j < N; S2[i,j] : 0 <= i,j < N }";
4306 S
= "{ S1[i,j] -> [0,i,j]; S2[i,j] -> [1,i,j] }";
4307 if (test_one_schedule(ctx
, D
, "{}", "{}", S
, 2, 2) < 0)
4310 D
= "[M, N] -> { S_1[i] : i >= 0 and i <= -1 + M; "
4311 "S_0[i, j] : i >= 0 and i <= -1 + M and j >= 0 and j <= -1 + N }";
4312 W
= "[M, N] -> { S_0[i, j] -> a[j] : i >= 0 and i <= -1 + M and "
4313 "j >= 0 and j <= -1 + N; "
4314 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
4315 R
= "[M, N] -> { S_0[i, j] -> a[0] : i >= 0 and i <= -1 + M and "
4316 "j >= 0 and j <= -1 + N; "
4317 "S_1[i] -> b[0] : i >= 0 and i <= -1 + M }";
4318 S
= "[M, N] -> { S_1[i] -> [1, i, 0]; S_0[i, j] -> [0, i, 0, j, 0] }";
4319 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4322 D
= "{ S_0[i] : i >= 0 }";
4323 W
= "{ S_0[i] -> a[i] : i >= 0 }";
4324 R
= "{ S_0[i] -> a[0] : i >= 0 }";
4325 S
= "{ S_0[i] -> [0, i, 0] }";
4326 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4329 D
= "{ S_0[i] : i >= 0; S_1[i] : i >= 0 }";
4330 W
= "{ S_0[i] -> a[i] : i >= 0; S_1[i] -> b[i] : i >= 0 }";
4331 R
= "{ S_0[i] -> b[0] : i >= 0; S_1[i] -> a[i] : i >= 0 }";
4332 S
= "{ S_1[i] -> [0, i, 1]; S_0[i] -> [0, i, 0] }";
4333 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4336 D
= "[n] -> { S_0[j, k] : j <= -1 + n and j >= 0 and "
4337 "k <= -1 + n and k >= 0 }";
4338 W
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and " "k <= -1 + n and k >= 0 }";
4339 R
= "[n] -> { S_0[j, k] -> B[j] : j <= -1 + n and j >= 0 and "
4340 "k <= -1 + n and k >= 0; "
4341 "S_0[j, k] -> B[k] : j <= -1 + n and j >= 0 and "
4342 "k <= -1 + n and k >= 0; "
4343 "S_0[j, k] -> A[k] : j <= -1 + n and j >= 0 and "
4344 "k <= -1 + n and k >= 0 }";
4345 S
= "[n] -> { S_0[j, k] -> [2, j, k] }";
4346 ctx
->opt
->schedule_outer_coincidence
= 1;
4347 if (test_one_schedule(ctx
, D
, W
, R
, S
, 0, 0) < 0)
4349 ctx
->opt
->schedule_outer_coincidence
= 0;
4351 D
= "{Stmt_for_body24[i0, i1, i2, i3]:"
4352 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 6 and i2 >= 2 and "
4353 "i2 <= 6 - i1 and i3 >= 0 and i3 <= -1 + i2;"
4354 "Stmt_for_body24[i0, i1, 1, 0]:"
4355 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 5;"
4356 "Stmt_for_body7[i0, i1, i2]:"
4357 "i0 >= 0 and i0 <= 1 and i1 >= 0 and i1 <= 7 and i2 >= 0 and "
4360 V
= "{Stmt_for_body24[0, i1, i2, i3] -> "
4361 "Stmt_for_body24[1, i1, i2, i3]:"
4362 "i3 >= 0 and i3 <= -1 + i2 and i1 >= 0 and i2 <= 6 - i1 and "
4364 "Stmt_for_body24[0, i1, i2, i3] -> "
4365 "Stmt_for_body7[1, 1 + i1 + i3, 1 + i1 + i2]:"
4366 "i3 <= -1 + i2 and i2 <= 6 - i1 and i2 >= 1 and i1 >= 0 and "
4368 "Stmt_for_body24[0, i1, i2, i3] ->"
4369 "Stmt_for_body7[1, i1, 1 + i1 + i3]:"
4370 "i3 >= 0 and i2 <= 6 - i1 and i1 >= 0 and i3 <= -1 + i2;"
4371 "Stmt_for_body7[0, i1, i2] -> Stmt_for_body7[1, i1, i2]:"
4372 "(i2 >= 1 + i1 and i2 <= 6 and i1 >= 0 and i1 <= 4) or "
4373 "(i2 >= 3 and i2 <= 7 and i1 >= 1 and i2 >= 1 + i1) or "
4374 "(i2 >= 0 and i2 <= i1 and i2 >= -7 + i1 and i1 <= 7);"
4375 "Stmt_for_body7[0, i1, 1 + i1] -> Stmt_for_body7[1, i1, 1 + i1]:"
4376 "i1 <= 6 and i1 >= 0;"
4377 "Stmt_for_body7[0, 0, 7] -> Stmt_for_body7[1, 0, 7];"
4378 "Stmt_for_body7[i0, i1, i2] -> "
4379 "Stmt_for_body24[i0, o1, -1 + i2 - o1, -1 + i1 - o1]:"
4380 "i0 >= 0 and i0 <= 1 and o1 >= 0 and i2 >= 1 + i1 and "
4381 "o1 <= -2 + i2 and i2 <= 7 and o1 <= -1 + i1;"
4382 "Stmt_for_body7[i0, i1, i2] -> "
4383 "Stmt_for_body24[i0, i1, o2, -1 - i1 + i2]:"
4384 "i0 >= 0 and i0 <= 1 and i1 >= 0 and o2 >= -i1 + i2 and "
4385 "o2 >= 1 and o2 <= 6 - i1 and i2 >= 1 + i1 }";
4388 treat_coalescing
= isl_options_get_schedule_treat_coalescing(ctx
);
4389 isl_options_set_schedule_treat_coalescing(ctx
, 0);
4390 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4392 isl_options_set_schedule_treat_coalescing(ctx
, treat_coalescing
);
4394 D
= "{ S_0[i, j] : i >= 1 and i <= 10 and j >= 1 and j <= 8 }";
4395 V
= "{ S_0[i, j] -> S_0[i, 1 + j] : i >= 1 and i <= 10 and "
4396 "j >= 1 and j <= 7;"
4397 "S_0[i, j] -> S_0[1 + i, j] : i >= 1 and i <= 9 and "
4398 "j >= 1 and j <= 8 }";
4400 S
= "{ S_0[i, j] -> [i + j, i] }";
4401 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4402 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4404 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4406 /* Fig. 1 from Feautrier's "Some Efficient Solutions..." pt. 2, 1992 */
4407 D
= "[N] -> { S_0[i, j] : i >= 0 and i <= -1 + N and "
4408 "j >= 0 and j <= -1 + i }";
4409 V
= "[N] -> { S_0[i, j] -> S_0[i, 1 + j] : j <= -2 + i and "
4410 "i <= -1 + N and j >= 0;"
4411 "S_0[i, -1 + i] -> S_0[1 + i, 0] : i >= 1 and "
4414 S
= "{ S_0[i, j] -> [i, j] }";
4415 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4416 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4418 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4420 /* Test both algorithms on a case with only proximity dependences. */
4421 D
= "{ S[i,j] : 0 <= i <= 10 }";
4423 P
= "{ S[i,j] -> S[i+1,j] : 0 <= i,j <= 10 }";
4424 S
= "{ S[i, j] -> [j, i] }";
4425 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4426 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4428 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4429 if (test_special_schedule(ctx
, D
, V
, P
, S
) < 0)
4432 D
= "{ A[a]; B[] }";
4434 P
= "{ A[a] -> B[] }";
4435 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4438 if (test_padded_schedule(ctx
) < 0)
4441 /* Check that check for progress is not confused by rational
4444 D
= "[N] -> { S0[i, j] : i >= 0 and i <= N and j >= 0 and j <= N }";
4445 V
= "[N] -> { S0[i0, -1 + N] -> S0[2 + i0, 0] : i0 >= 0 and "
4447 "S0[i0, i1] -> S0[i0, 1 + i1] : i0 >= 0 and "
4448 "i0 <= N and i1 >= 0 and i1 <= -1 + N }";
4450 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4451 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4453 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4455 /* Check that we allow schedule rows that are only non-trivial
4456 * on some full-dimensional domains.
4458 D
= "{ S1[j] : 0 <= j <= 1; S0[]; S2[k] : 0 <= k <= 1 }";
4459 V
= "{ S0[] -> S1[j] : 0 <= j <= 1; S2[0] -> S0[];"
4460 "S1[j] -> S2[1] : 0 <= j <= 1 }";
4462 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_FEAUTRIER
;
4463 if (test_has_schedule(ctx
, D
, V
, P
) < 0)
4465 ctx
->opt
->schedule_algorithm
= ISL_SCHEDULE_ALGORITHM_ISL
;
4467 if (test_conditional_schedule_constraints(ctx
) < 0)
4470 if (test_strongly_satisfying_schedule(ctx
) < 0)
4473 if (test_conflicting_context_schedule(ctx
) < 0)
4476 if (test_bounded_coefficients_schedule(ctx
) < 0)
4478 if (test_coalescing_schedule(ctx
) < 0)
4480 if (test_skewing_schedule(ctx
) < 0)
4486 /* Perform scheduling tests using the whole component scheduler.
4488 static int test_schedule_whole(isl_ctx
*ctx
)
4493 whole
= isl_options_get_schedule_whole_component(ctx
);
4494 isl_options_set_schedule_whole_component(ctx
, 1);
4495 r
= test_schedule(ctx
);
4497 r
= test_bounded_coefficients_schedule_whole(ctx
);
4498 isl_options_set_schedule_whole_component(ctx
, whole
);
4503 /* Perform scheduling tests using the incremental scheduler.
4505 static int test_schedule_incremental(isl_ctx
*ctx
)
4510 whole
= isl_options_get_schedule_whole_component(ctx
);
4511 isl_options_set_schedule_whole_component(ctx
, 0);
4512 r
= test_schedule(ctx
);
4513 isl_options_set_schedule_whole_component(ctx
, whole
);
4518 int test_plain_injective(isl_ctx
*ctx
, const char *str
, int injective
)
4520 isl_union_map
*umap
;
4523 umap
= isl_union_map_read_from_str(ctx
, str
);
4524 test
= isl_union_map_plain_is_injective(umap
);
4525 isl_union_map_free(umap
);
4528 if (test
== injective
)
4531 isl_die(ctx
, isl_error_unknown
,
4532 "map not detected as injective", return -1);
4534 isl_die(ctx
, isl_error_unknown
,
4535 "map detected as injective", return -1);
4538 int test_injective(isl_ctx
*ctx
)
4542 if (test_plain_injective(ctx
, "{S[i,j] -> A[0]; T[i,j] -> B[1]}", 0))
4544 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> B[0]}", 1))
4546 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[1]}", 1))
4548 if (test_plain_injective(ctx
, "{S[] -> A[0]; T[] -> A[0]}", 0))
4550 if (test_plain_injective(ctx
, "{S[i] -> A[i,0]; T[i] -> A[i,1]}", 1))
4552 if (test_plain_injective(ctx
, "{S[i] -> A[i]; T[i] -> A[i]}", 0))
4554 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[0,1]}", 1))
4556 if (test_plain_injective(ctx
, "{S[] -> A[0,0]; T[] -> A[1,0]}", 1))
4559 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[1,0]}";
4560 if (test_plain_injective(ctx
, str
, 1))
4562 str
= "{S[] -> A[0,0]; T[] -> A[0,1]; U[] -> A[0,0]}";
4563 if (test_plain_injective(ctx
, str
, 0))
4569 static int aff_plain_is_equal(__isl_keep isl_aff
*aff
, const char *str
)
4577 aff2
= isl_aff_read_from_str(isl_aff_get_ctx(aff
), str
);
4578 equal
= isl_aff_plain_is_equal(aff
, aff2
);
4584 static int aff_check_plain_equal(__isl_keep isl_aff
*aff
, const char *str
)
4588 equal
= aff_plain_is_equal(aff
, str
);
4592 isl_die(isl_aff_get_ctx(aff
), isl_error_unknown
,
4593 "result not as expected", return -1);
4598 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
4599 __isl_take isl_aff
*aff2
);
4601 ['+'] = { &isl_aff_add
},
4602 ['-'] = { &isl_aff_sub
},
4603 ['*'] = { &isl_aff_mul
},
4604 ['/'] = { &isl_aff_div
},
4612 } aff_bin_tests
[] = {
4613 { "{ [i] -> [i] }", '+', "{ [i] -> [i] }",
4614 "{ [i] -> [2i] }" },
4615 { "{ [i] -> [i] }", '-', "{ [i] -> [i] }",
4617 { "{ [i] -> [i] }", '*', "{ [i] -> [2] }",
4618 "{ [i] -> [2i] }" },
4619 { "{ [i] -> [2] }", '*', "{ [i] -> [i] }",
4620 "{ [i] -> [2i] }" },
4621 { "{ [i] -> [i] }", '/', "{ [i] -> [2] }",
4622 "{ [i] -> [i/2] }" },
4623 { "{ [i] -> [2i] }", '/', "{ [i] -> [2] }",
4625 { "{ [i] -> [i] }", '+', "{ [i] -> [NaN] }",
4626 "{ [i] -> [NaN] }" },
4627 { "{ [i] -> [i] }", '-', "{ [i] -> [NaN] }",
4628 "{ [i] -> [NaN] }" },
4629 { "{ [i] -> [i] }", '*', "{ [i] -> [NaN] }",
4630 "{ [i] -> [NaN] }" },
4631 { "{ [i] -> [2] }", '*', "{ [i] -> [NaN] }",
4632 "{ [i] -> [NaN] }" },
4633 { "{ [i] -> [i] }", '/', "{ [i] -> [NaN] }",
4634 "{ [i] -> [NaN] }" },
4635 { "{ [i] -> [2] }", '/', "{ [i] -> [NaN] }",
4636 "{ [i] -> [NaN] }" },
4637 { "{ [i] -> [NaN] }", '+', "{ [i] -> [i] }",
4638 "{ [i] -> [NaN] }" },
4639 { "{ [i] -> [NaN] }", '-', "{ [i] -> [i] }",
4640 "{ [i] -> [NaN] }" },
4641 { "{ [i] -> [NaN] }", '*', "{ [i] -> [2] }",
4642 "{ [i] -> [NaN] }" },
4643 { "{ [i] -> [NaN] }", '*', "{ [i] -> [i] }",
4644 "{ [i] -> [NaN] }" },
4645 { "{ [i] -> [NaN] }", '/', "{ [i] -> [2] }",
4646 "{ [i] -> [NaN] }" },
4647 { "{ [i] -> [NaN] }", '/', "{ [i] -> [i] }",
4648 "{ [i] -> [NaN] }" },
4651 /* Perform some basic tests of binary operations on isl_aff objects.
4653 static int test_bin_aff(isl_ctx
*ctx
)
4656 isl_aff
*aff1
, *aff2
, *res
;
4657 __isl_give isl_aff
*(*fn
)(__isl_take isl_aff
*aff1
,
4658 __isl_take isl_aff
*aff2
);
4661 for (i
= 0; i
< ARRAY_SIZE(aff_bin_tests
); ++i
) {
4662 aff1
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg1
);
4663 aff2
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].arg2
);
4664 res
= isl_aff_read_from_str(ctx
, aff_bin_tests
[i
].res
);
4665 fn
= aff_bin_op
[aff_bin_tests
[i
].op
].fn
;
4666 aff1
= fn(aff1
, aff2
);
4667 if (isl_aff_is_nan(res
))
4668 ok
= isl_aff_is_nan(aff1
);
4670 ok
= isl_aff_plain_is_equal(aff1
, res
);
4676 isl_die(ctx
, isl_error_unknown
,
4677 "unexpected result", return -1);
4684 __isl_give isl_pw_aff
*(*fn
)(__isl_take isl_pw_aff
*pa1
,
4685 __isl_take isl_pw_aff
*pa2
);
4686 } pw_aff_bin_op
[] = {
4687 ['m'] = { &isl_pw_aff_min
},
4688 ['M'] = { &isl_pw_aff_max
},
4691 /* Inputs for binary isl_pw_aff operation tests.
4692 * "arg1" and "arg2" are the two arguments, "op" identifies the operation
4693 * defined by pw_aff_bin_op, and "res" is the expected result.
4700 } pw_aff_bin_tests
[] = {
4701 { "{ [i] -> [i] }", 'm', "{ [i] -> [i] }",
4703 { "{ [i] -> [i] }", 'M', "{ [i] -> [i] }",
4705 { "{ [i] -> [i] }", 'm', "{ [i] -> [0] }",
4706 "{ [i] -> [i] : i <= 0; [i] -> [0] : i > 0 }" },
4707 { "{ [i] -> [i] }", 'M', "{ [i] -> [0] }",
4708 "{ [i] -> [i] : i >= 0; [i] -> [0] : i < 0 }" },
4709 { "{ [i] -> [i] }", 'm', "{ [i] -> [NaN] }",
4710 "{ [i] -> [NaN] }" },
4711 { "{ [i] -> [NaN] }", 'm', "{ [i] -> [i] }",
4712 "{ [i] -> [NaN] }" },
4715 /* Perform some basic tests of binary operations on isl_pw_aff objects.
4717 static int test_bin_pw_aff(isl_ctx
*ctx
)
4721 isl_pw_aff
*pa1
, *pa2
, *res
;
4723 for (i
= 0; i
< ARRAY_SIZE(pw_aff_bin_tests
); ++i
) {
4724 pa1
= isl_pw_aff_read_from_str(ctx
, pw_aff_bin_tests
[i
].arg1
);
4725 pa2
= isl_pw_aff_read_from_str(ctx
, pw_aff_bin_tests
[i
].arg2
);
4726 res
= isl_pw_aff_read_from_str(ctx
, pw_aff_bin_tests
[i
].res
);
4727 pa1
= pw_aff_bin_op
[pw_aff_bin_tests
[i
].op
].fn(pa1
, pa2
);
4728 if (isl_pw_aff_involves_nan(res
))
4729 ok
= isl_pw_aff_involves_nan(pa1
);
4731 ok
= isl_pw_aff_plain_is_equal(pa1
, res
);
4732 isl_pw_aff_free(pa1
);
4733 isl_pw_aff_free(res
);
4737 isl_die(ctx
, isl_error_unknown
,
4738 "unexpected result", return -1);
4745 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4746 __isl_take isl_union_pw_multi_aff
*upma1
,
4747 __isl_take isl_union_pw_multi_aff
*upma2
);
4751 } upma_bin_tests
[] = {
4752 { &isl_union_pw_multi_aff_add
, "{ A[] -> [0]; B[0] -> [1] }",
4753 "{ B[x] -> [2] : x >= 0 }", "{ B[0] -> [3] }" },
4754 { &isl_union_pw_multi_aff_union_add
, "{ A[] -> [0]; B[0] -> [1] }",
4755 "{ B[x] -> [2] : x >= 0 }",
4756 "{ A[] -> [0]; B[0] -> [3]; B[x] -> [2] : x >= 1 }" },
4757 { &isl_union_pw_multi_aff_pullback_union_pw_multi_aff
,
4758 "{ A[] -> B[0]; C[x] -> B[1] : x < 10; C[y] -> B[2] : y >= 10 }",
4759 "{ D[i] -> A[] : i < 0; D[i] -> C[i + 5] : i >= 0 }",
4760 "{ D[i] -> B[0] : i < 0; D[i] -> B[1] : 0 <= i < 5; "
4761 "D[i] -> B[2] : i >= 5 }" },
4762 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4763 "{ B[x] -> C[2] : x > 0 }",
4764 "{ B[x] -> A[1] : x <= 0; B[x] -> C[2] : x > 0 }" },
4765 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4766 "{ B[x] -> A[2] : x >= 0 }",
4767 "{ B[x] -> A[1] : x < 0; B[x] -> A[2] : x > 0; B[0] -> A[3] }" },
4770 /* Perform some basic tests of binary operations on
4771 * isl_union_pw_multi_aff objects.
4773 static int test_bin_upma(isl_ctx
*ctx
)
4776 isl_union_pw_multi_aff
*upma1
, *upma2
, *res
;
4779 for (i
= 0; i
< ARRAY_SIZE(upma_bin_tests
); ++i
) {
4780 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4781 upma_bin_tests
[i
].arg1
);
4782 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4783 upma_bin_tests
[i
].arg2
);
4784 res
= isl_union_pw_multi_aff_read_from_str(ctx
,
4785 upma_bin_tests
[i
].res
);
4786 upma1
= upma_bin_tests
[i
].fn(upma1
, upma2
);
4787 ok
= isl_union_pw_multi_aff_plain_is_equal(upma1
, res
);
4788 isl_union_pw_multi_aff_free(upma1
);
4789 isl_union_pw_multi_aff_free(res
);
4793 isl_die(ctx
, isl_error_unknown
,
4794 "unexpected result", return -1);
4801 __isl_give isl_union_pw_multi_aff
*(*fn
)(
4802 __isl_take isl_union_pw_multi_aff
*upma1
,
4803 __isl_take isl_union_pw_multi_aff
*upma2
);
4806 } upma_bin_fail_tests
[] = {
4807 { &isl_union_pw_multi_aff_union_add
, "{ B[x] -> A[1] : x <= 0 }",
4808 "{ B[x] -> C[2] : x >= 0 }" },
4811 /* Perform some basic tests of binary operations on
4812 * isl_union_pw_multi_aff objects that are expected to fail.
4814 static int test_bin_upma_fail(isl_ctx
*ctx
)
4817 isl_union_pw_multi_aff
*upma1
, *upma2
;
4820 on_error
= isl_options_get_on_error(ctx
);
4821 isl_options_set_on_error(ctx
, ISL_ON_ERROR_CONTINUE
);
4822 n
= ARRAY_SIZE(upma_bin_fail_tests
);
4823 for (i
= 0; i
< n
; ++i
) {
4824 upma1
= isl_union_pw_multi_aff_read_from_str(ctx
,
4825 upma_bin_fail_tests
[i
].arg1
);
4826 upma2
= isl_union_pw_multi_aff_read_from_str(ctx
,
4827 upma_bin_fail_tests
[i
].arg2
);
4828 upma1
= upma_bin_fail_tests
[i
].fn(upma1
, upma2
);
4829 isl_union_pw_multi_aff_free(upma1
);
4833 isl_options_set_on_error(ctx
, on_error
);
4835 isl_die(ctx
, isl_error_unknown
,
4836 "operation not expected to succeed", return -1);
4841 int test_aff(isl_ctx
*ctx
)
4846 isl_local_space
*ls
;
4850 if (test_bin_aff(ctx
) < 0)
4852 if (test_bin_pw_aff(ctx
) < 0)
4854 if (test_bin_upma(ctx
) < 0)
4856 if (test_bin_upma_fail(ctx
) < 0)
4859 space
= isl_space_set_alloc(ctx
, 0, 1);
4860 ls
= isl_local_space_from_space(space
);
4861 aff
= isl_aff_zero_on_domain(ls
);
4863 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4864 aff
= isl_aff_scale_down_ui(aff
, 3);
4865 aff
= isl_aff_floor(aff
);
4866 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4867 aff
= isl_aff_scale_down_ui(aff
, 2);
4868 aff
= isl_aff_floor(aff
);
4869 aff
= isl_aff_add_coefficient_si(aff
, isl_dim_in
, 0, 1);
4872 set
= isl_set_read_from_str(ctx
, str
);
4873 aff
= isl_aff_gist(aff
, set
);
4875 aff
= isl_aff_add_constant_si(aff
, -16);
4876 zero
= isl_aff_plain_is_zero(aff
);
4882 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4884 aff
= isl_aff_read_from_str(ctx
, "{ [-1] }");
4885 aff
= isl_aff_scale_down_ui(aff
, 64);
4886 aff
= isl_aff_floor(aff
);
4887 equal
= aff_check_plain_equal(aff
, "{ [-1] }");
4895 /* Check that the computation below results in a single expression.
4896 * One or two expressions may result depending on which constraint
4897 * ends up being considered as redundant with respect to the other
4898 * constraints after the projection that is performed internally
4899 * by isl_set_dim_min.
4901 static int test_dim_max_1(isl_ctx
*ctx
)
4908 str
= "[n] -> { [a, b] : n >= 0 and 4a >= -4 + n and b >= 0 and "
4909 "-4a <= b <= 3 and b < n - 4a }";
4910 set
= isl_set_read_from_str(ctx
, str
);
4911 pa
= isl_set_dim_min(set
, 0);
4912 n
= isl_pw_aff_n_piece(pa
);
4913 isl_pw_aff_free(pa
);
4918 isl_die(ctx
, isl_error_unknown
, "expecting single expression",
4924 int test_dim_max(isl_ctx
*ctx
)
4928 isl_set
*set1
, *set2
;
4933 if (test_dim_max_1(ctx
) < 0)
4936 str
= "[N] -> { [i] : 0 <= i <= min(N,10) }";
4937 set
= isl_set_read_from_str(ctx
, str
);
4938 pwaff
= isl_set_dim_max(set
, 0);
4939 set1
= isl_set_from_pw_aff(pwaff
);
4940 str
= "[N] -> { [10] : N >= 10; [N] : N <= 9 and N >= 0 }";
4941 set2
= isl_set_read_from_str(ctx
, str
);
4942 equal
= isl_set_is_equal(set1
, set2
);
4948 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4950 str
= "[N] -> { [i] : 0 <= i <= max(2N,N+6) }";
4951 set
= isl_set_read_from_str(ctx
, str
);
4952 pwaff
= isl_set_dim_max(set
, 0);
4953 set1
= isl_set_from_pw_aff(pwaff
);
4954 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4955 set2
= isl_set_read_from_str(ctx
, str
);
4956 equal
= isl_set_is_equal(set1
, set2
);
4962 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4964 str
= "[N] -> { [i] : 0 <= i <= 2N or 0 <= i <= N+6 }";
4965 set
= isl_set_read_from_str(ctx
, str
);
4966 pwaff
= isl_set_dim_max(set
, 0);
4967 set1
= isl_set_from_pw_aff(pwaff
);
4968 str
= "[N] -> { [6 + N] : -6 <= N <= 5; [2N] : N >= 6 }";
4969 set2
= isl_set_read_from_str(ctx
, str
);
4970 equal
= isl_set_is_equal(set1
, set2
);
4976 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
4978 str
= "[N,M] -> { [i,j] -> [([i/16]), i%16, ([j/16]), j%16] : "
4979 "0 <= i < N and 0 <= j < M }";
4980 map
= isl_map_read_from_str(ctx
, str
);
4981 set
= isl_map_range(map
);
4983 pwaff
= isl_set_dim_max(isl_set_copy(set
), 0);
4984 set1
= isl_set_from_pw_aff(pwaff
);
4985 str
= "[N,M] -> { [([(N-1)/16])] : M,N > 0 }";
4986 set2
= isl_set_read_from_str(ctx
, str
);
4987 equal
= isl_set_is_equal(set1
, set2
);
4991 pwaff
= isl_set_dim_max(isl_set_copy(set
), 3);
4992 set1
= isl_set_from_pw_aff(pwaff
);
4993 str
= "[N,M] -> { [t] : t = min(M-1,15) and M,N > 0 }";
4994 set2
= isl_set_read_from_str(ctx
, str
);
4995 if (equal
>= 0 && equal
)
4996 equal
= isl_set_is_equal(set1
, set2
);
5005 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5007 /* Check that solutions are properly merged. */
5008 str
= "[n] -> { [a, b, c] : c >= -4a - 2b and "
5009 "c <= -1 + n - 4a - 2b and c >= -2b and "
5010 "4a >= -4 + n and c >= 0 }";
5011 set
= isl_set_read_from_str(ctx
, str
);
5012 pwaff
= isl_set_dim_min(set
, 2);
5013 set1
= isl_set_from_pw_aff(pwaff
);
5014 str
= "[n] -> { [(0)] : n >= 1 }";
5015 set2
= isl_set_read_from_str(ctx
, str
);
5016 equal
= isl_set_is_equal(set1
, set2
);
5023 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5025 /* Check that empty solution lie in the right space. */
5026 str
= "[n] -> { [t,a] : 1 = 0 }";
5027 set
= isl_set_read_from_str(ctx
, str
);
5028 pwaff
= isl_set_dim_max(set
, 0);
5029 set1
= isl_set_from_pw_aff(pwaff
);
5030 str
= "[n] -> { [t] : 1 = 0 }";
5031 set2
= isl_set_read_from_str(ctx
, str
);
5032 equal
= isl_set_is_equal(set1
, set2
);
5039 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5044 /* Is "pma" obviously equal to the isl_pw_multi_aff represented by "str"?
5046 static int pw_multi_aff_plain_is_equal(__isl_keep isl_pw_multi_aff
*pma
,
5050 isl_pw_multi_aff
*pma2
;
5056 ctx
= isl_pw_multi_aff_get_ctx(pma
);
5057 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5058 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma2
);
5059 isl_pw_multi_aff_free(pma2
);
5064 /* Check that "pma" is obviously equal to the isl_pw_multi_aff
5065 * represented by "str".
5067 static int pw_multi_aff_check_plain_equal(__isl_keep isl_pw_multi_aff
*pma
,
5072 equal
= pw_multi_aff_plain_is_equal(pma
, str
);
5076 isl_die(isl_pw_multi_aff_get_ctx(pma
), isl_error_unknown
,
5077 "result not as expected", return -1);
5081 /* Basic test for isl_pw_multi_aff_product.
5083 * Check that multiple pieces are properly handled.
5085 static int test_product_pma(isl_ctx
*ctx
)
5089 isl_pw_multi_aff
*pma1
, *pma2
;
5091 str
= "{ A[i] -> B[1] : i < 0; A[i] -> B[2] : i >= 0 }";
5092 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5093 str
= "{ C[] -> D[] }";
5094 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
5095 pma1
= isl_pw_multi_aff_product(pma1
, pma2
);
5096 str
= "{ [A[i] -> C[]] -> [B[(1)] -> D[]] : i < 0;"
5097 "[A[i] -> C[]] -> [B[(2)] -> D[]] : i >= 0 }";
5098 equal
= pw_multi_aff_check_plain_equal(pma1
, str
);
5099 isl_pw_multi_aff_free(pma1
);
5106 int test_product(isl_ctx
*ctx
)
5110 isl_union_set
*uset1
, *uset2
;
5114 set
= isl_set_read_from_str(ctx
, str
);
5115 set
= isl_set_product(set
, isl_set_copy(set
));
5116 ok
= isl_set_is_wrapping(set
);
5121 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5124 uset1
= isl_union_set_read_from_str(ctx
, str
);
5125 uset1
= isl_union_set_product(uset1
, isl_union_set_copy(uset1
));
5126 str
= "{ [[] -> []] }";
5127 uset2
= isl_union_set_read_from_str(ctx
, str
);
5128 ok
= isl_union_set_is_equal(uset1
, uset2
);
5129 isl_union_set_free(uset1
);
5130 isl_union_set_free(uset2
);
5134 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5136 if (test_product_pma(ctx
) < 0)
5142 /* Check that two sets are not considered disjoint just because
5143 * they have a different set of (named) parameters.
5145 static int test_disjoint(isl_ctx
*ctx
)
5148 isl_set
*set
, *set2
;
5151 str
= "[n] -> { [[]->[]] }";
5152 set
= isl_set_read_from_str(ctx
, str
);
5153 str
= "{ [[]->[]] }";
5154 set2
= isl_set_read_from_str(ctx
, str
);
5155 disjoint
= isl_set_is_disjoint(set
, set2
);
5161 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5166 /* Inputs for isl_pw_multi_aff_is_equal tests.
5167 * "f1" and "f2" are the two function that need to be compared.
5168 * "equal" is the expected result.
5174 } pma_equal_tests
[] = {
5175 { 1, "[N] -> { [floor(N/2)] : 0 <= N <= 1 }",
5176 "[N] -> { [0] : 0 <= N <= 1 }" },
5177 { 1, "[N] -> { [floor(N/2)] : 0 <= N <= 2 }",
5178 "[N] -> { [0] : 0 <= N <= 1; [1] : N = 2 }" },
5179 { 0, "[N] -> { [floor(N/2)] : 0 <= N <= 2 }",
5180 "[N] -> { [0] : 0 <= N <= 1 }" },
5181 { 0, "{ [NaN] }", "{ [NaN] }" },
5184 int test_equal(isl_ctx
*ctx
)
5188 isl_set
*set
, *set2
;
5192 set
= isl_set_read_from_str(ctx
, str
);
5194 set2
= isl_set_read_from_str(ctx
, str
);
5195 equal
= isl_set_is_equal(set
, set2
);
5201 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5203 for (i
= 0; i
< ARRAY_SIZE(pma_equal_tests
); ++i
) {
5204 int expected
= pma_equal_tests
[i
].equal
;
5205 isl_pw_multi_aff
*f1
, *f2
;
5207 f1
= isl_pw_multi_aff_read_from_str(ctx
, pma_equal_tests
[i
].f1
);
5208 f2
= isl_pw_multi_aff_read_from_str(ctx
, pma_equal_tests
[i
].f2
);
5209 equal
= isl_pw_multi_aff_is_equal(f1
, f2
);
5210 isl_pw_multi_aff_free(f1
);
5211 isl_pw_multi_aff_free(f2
);
5214 if (equal
!= expected
)
5215 isl_die(ctx
, isl_error_unknown
,
5216 "unexpected equality result", return -1);
5222 static int test_plain_fixed(isl_ctx
*ctx
, __isl_take isl_map
*map
,
5223 enum isl_dim_type type
, unsigned pos
, int fixed
)
5227 test
= isl_map_plain_is_fixed(map
, type
, pos
, NULL
);
5234 isl_die(ctx
, isl_error_unknown
,
5235 "map not detected as fixed", return -1);
5237 isl_die(ctx
, isl_error_unknown
,
5238 "map detected as fixed", return -1);
5241 int test_fixed(isl_ctx
*ctx
)
5246 str
= "{ [i] -> [i] }";
5247 map
= isl_map_read_from_str(ctx
, str
);
5248 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 0))
5250 str
= "{ [i] -> [1] }";
5251 map
= isl_map_read_from_str(ctx
, str
);
5252 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
5254 str
= "{ S_1[p1] -> [o0] : o0 = -2 and p1 >= 1 and p1 <= 7 }";
5255 map
= isl_map_read_from_str(ctx
, str
);
5256 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
5258 map
= isl_map_read_from_str(ctx
, str
);
5259 map
= isl_map_neg(map
);
5260 if (test_plain_fixed(ctx
, map
, isl_dim_out
, 0, 1))
5266 struct isl_vertices_test_data
{
5269 const char *vertex
[6];
5270 } vertices_tests
[] = {
5271 { "{ A[t, i] : t = 12 and i >= 4 and i <= 12 }",
5272 2, { "{ A[12, 4] }", "{ A[12, 12] }" } },
5273 { "{ A[t, i] : t = 14 and i = 1 }",
5274 1, { "{ A[14, 1] }" } },
5275 { "[n, m] -> { [a, b, c] : b <= a and a <= n and b > 0 and c >= b and "
5276 "c <= m and m <= n and m > 0 }",
5278 "[n, m] -> { [n, m, m] : 0 < m <= n }",
5279 "[n, m] -> { [n, 1, m] : 0 < m <= n }",
5280 "[n, m] -> { [n, 1, 1] : 0 < m <= n }",
5281 "[n, m] -> { [m, m, m] : 0 < m <= n }",
5282 "[n, m] -> { [1, 1, m] : 0 < m <= n }",
5283 "[n, m] -> { [1, 1, 1] : 0 < m <= n }"
5287 /* Check that "vertex" corresponds to one of the vertices in data->vertex.
5289 static isl_stat
find_vertex(__isl_take isl_vertex
*vertex
, void *user
)
5291 struct isl_vertices_test_data
*data
= user
;
5294 isl_basic_set
*bset
;
5295 isl_pw_multi_aff
*pma
;
5299 ctx
= isl_vertex_get_ctx(vertex
);
5300 bset
= isl_vertex_get_domain(vertex
);
5301 ma
= isl_vertex_get_expr(vertex
);
5302 pma
= isl_pw_multi_aff_alloc(isl_set_from_basic_set(bset
), ma
);
5304 for (i
= 0; i
< data
->n
; ++i
) {
5305 isl_pw_multi_aff
*pma_i
;
5307 pma_i
= isl_pw_multi_aff_read_from_str(ctx
, data
->vertex
[i
]);
5308 equal
= isl_pw_multi_aff_plain_is_equal(pma
, pma_i
);
5309 isl_pw_multi_aff_free(pma_i
);
5311 if (equal
< 0 || equal
)
5315 isl_pw_multi_aff_free(pma
);
5316 isl_vertex_free(vertex
);
5319 return isl_stat_error
;
5321 return equal
? isl_stat_ok
: isl_stat_error
;
5324 int test_vertices(isl_ctx
*ctx
)
5328 for (i
= 0; i
< ARRAY_SIZE(vertices_tests
); ++i
) {
5329 isl_basic_set
*bset
;
5330 isl_vertices
*vertices
;
5334 bset
= isl_basic_set_read_from_str(ctx
, vertices_tests
[i
].set
);
5335 vertices
= isl_basic_set_compute_vertices(bset
);
5336 n
= isl_vertices_get_n_vertices(vertices
);
5337 if (vertices_tests
[i
].n
!= n
)
5339 if (isl_vertices_foreach_vertex(vertices
, &find_vertex
,
5340 &vertices_tests
[i
]) < 0)
5342 isl_vertices_free(vertices
);
5343 isl_basic_set_free(bset
);
5348 isl_die(ctx
, isl_error_unknown
, "unexpected vertices",
5355 int test_union_pw(isl_ctx
*ctx
)
5359 isl_union_set
*uset
;
5360 isl_union_pw_qpolynomial
*upwqp1
, *upwqp2
;
5362 str
= "{ [x] -> x^2 }";
5363 upwqp1
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
5364 upwqp2
= isl_union_pw_qpolynomial_copy(upwqp1
);
5365 uset
= isl_union_pw_qpolynomial_domain(upwqp1
);
5366 upwqp1
= isl_union_pw_qpolynomial_copy(upwqp2
);
5367 upwqp1
= isl_union_pw_qpolynomial_intersect_domain(upwqp1
, uset
);
5368 equal
= isl_union_pw_qpolynomial_plain_is_equal(upwqp1
, upwqp2
);
5369 isl_union_pw_qpolynomial_free(upwqp1
);
5370 isl_union_pw_qpolynomial_free(upwqp2
);
5374 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5379 /* Test that isl_union_pw_qpolynomial_eval picks up the function
5380 * defined over the correct domain space.
5382 static int test_eval_1(isl_ctx
*ctx
)
5387 isl_union_pw_qpolynomial
*upwqp
;
5391 str
= "{ A[x] -> x^2; B[x] -> -x^2 }";
5392 upwqp
= isl_union_pw_qpolynomial_read_from_str(ctx
, str
);
5394 set
= isl_set_read_from_str(ctx
, str
);
5395 pnt
= isl_set_sample_point(set
);
5396 v
= isl_union_pw_qpolynomial_eval(upwqp
, pnt
);
5397 cmp
= isl_val_cmp_si(v
, 36);
5403 isl_die(ctx
, isl_error_unknown
, "unexpected value", return -1);
5408 /* Check that isl_qpolynomial_eval handles getting called on a void point.
5410 static int test_eval_2(isl_ctx
*ctx
)
5415 isl_qpolynomial
*qp
;
5419 str
= "{ A[x] -> [x] }";
5420 qp
= isl_qpolynomial_from_aff(isl_aff_read_from_str(ctx
, str
));
5421 str
= "{ A[x] : false }";
5422 set
= isl_set_read_from_str(ctx
, str
);
5423 pnt
= isl_set_sample_point(set
);
5424 v
= isl_qpolynomial_eval(qp
, pnt
);
5425 ok
= isl_val_is_nan(v
);
5431 isl_die(ctx
, isl_error_unknown
, "expecting NaN", return -1);
5436 /* Perform basic polynomial evaluation tests.
5438 static int test_eval(isl_ctx
*ctx
)
5440 if (test_eval_1(ctx
) < 0)
5442 if (test_eval_2(ctx
) < 0)
5447 /* Descriptions of sets that are tested for reparsing after printing.
5449 const char *output_tests
[] = {
5450 "{ [1, y] : 0 <= y <= 1; [x, -x] : 0 <= x <= 1 }",
5453 "{ [x] : x mod 2 = 0 }",
5454 "{ [x] : x mod 2 = 1 }",
5455 "{ [x, y] : x mod 2 = 0 and 3*floor(y/2) < x }",
5456 "{ [y, x] : x mod 2 = 0 and 3*floor(y/2) < x }",
5457 "{ [x, y] : x mod 2 = 0 and 3*floor(y/2) = x + y }",
5458 "{ [y, x] : x mod 2 = 0 and 3*floor(y/2) = x + y }",
5459 "[n] -> { [y, x] : 2*((x + 2y) mod 3) = n }",
5460 "{ [x, y] : (2*floor(x/3) + 3*floor(y/4)) mod 5 = x }",
5463 /* Check that printing a set and reparsing a set from the printed output
5464 * results in the same set.
5466 static int test_output_set(isl_ctx
*ctx
)
5470 isl_set
*set1
, *set2
;
5473 for (i
= 0; i
< ARRAY_SIZE(output_tests
); ++i
) {
5474 set1
= isl_set_read_from_str(ctx
, output_tests
[i
]);
5475 str
= isl_set_to_str(set1
);
5476 set2
= isl_set_read_from_str(ctx
, str
);
5478 equal
= isl_set_is_equal(set1
, set2
);
5484 isl_die(ctx
, isl_error_unknown
,
5485 "parsed output not the same", return -1);
5491 int test_output(isl_ctx
*ctx
)
5499 if (test_output_set(ctx
) < 0)
5502 str
= "[x] -> { [1] : x % 4 <= 2; [2] : x = 3 }";
5503 pa
= isl_pw_aff_read_from_str(ctx
, str
);
5505 p
= isl_printer_to_str(ctx
);
5506 p
= isl_printer_set_output_format(p
, ISL_FORMAT_C
);
5507 p
= isl_printer_print_pw_aff(p
, pa
);
5508 s
= isl_printer_get_str(p
);
5509 isl_printer_free(p
);
5510 isl_pw_aff_free(pa
);
5514 equal
= !strcmp(s
, "4 * floord(x, 4) + 2 >= x ? 1 : 2");
5519 isl_die(ctx
, isl_error_unknown
, "unexpected result", return -1);
5524 int test_sample(isl_ctx
*ctx
)
5527 isl_basic_set
*bset1
, *bset2
;
5530 str
= "{ [a, b, c, d, e, f, g, h, i, j, k] : "
5531 "3i >= 1073741823b - c - 1073741823e + f and c >= 0 and "
5532 "3i >= -1 + 3221225466b + c + d - 3221225466e - f and "
5533 "2e >= a - b and 3e <= 2a and 3k <= -a and f <= -1 + a and "
5534 "3i <= 4 - a + 4b + 2c - e - 2f and 3k <= -a + c - f and "
5535 "3h >= -2 + a and 3g >= -3 - a and 3k >= -2 - a and "
5536 "3i >= -2 - a - 2c + 3e + 2f and 3h <= a + c - f and "
5537 "3h >= a + 2147483646b + 2c - 2147483646e - 2f and "
5538 "3g <= -1 - a and 3i <= 1 + c + d - f and a <= 1073741823 and "
5539 "f >= 1 - a + 1073741822b + c + d - 1073741822e and "
5540 "3i >= 1 + 2b - 2c + e + 2f + 3g and "
5541 "1073741822f <= 1073741822 - a + 1073741821b + 1073741822c +"
5542 "d - 1073741821e and "
5543 "3j <= 3 - a + 3b and 3g <= -2 - 2b + c + d - e - f and "
5544 "3j >= 1 - a + b + 2e and "
5545 "3f >= -3 + a + 3221225462b + 3c + d - 3221225465e and "
5546 "3i <= 4 - a + 4b - e and "
5547 "f <= 1073741822 + 1073741822b - 1073741822e and 3h <= a and "
5548 "f >= 0 and 2e <= 4 - a + 5b - d and 2e <= a - b + d and "
5549 "c <= -1 + a and 3i >= -2 - a + 3e and "
5550 "1073741822e <= 1073741823 - a + 1073741822b + c and "
5551 "3g >= -4 + 3221225464b + 3c + d - 3221225467e - 3f and "
5552 "3i >= -1 + 3221225466b + 3c + d - 3221225466e - 3f and "
5553 "1073741823e >= 1 + 1073741823b - d and "
5554 "3i >= 1073741823b + c - 1073741823e - f and "
5555 "3i >= 1 + 2b + e + 3g }";
5556 bset1
= isl_basic_set_read_from_str(ctx
, str
);
5557 bset2
= isl_basic_set_sample(isl_basic_set_copy(bset1
));
5558 empty
= isl_basic_set_is_empty(bset2
);
5559 subset
= isl_basic_set_is_subset(bset2
, bset1
);
5560 isl_basic_set_free(bset1
);
5561 isl_basic_set_free(bset2
);
5562 if (empty
< 0 || subset
< 0)
5565 isl_die(ctx
, isl_error_unknown
, "point not found", return -1);
5567 isl_die(ctx
, isl_error_unknown
, "bad point found", return -1);
5572 int test_fixed_power(isl_ctx
*ctx
)
5580 str
= "{ [i] -> [i + 1] }";
5581 map
= isl_map_read_from_str(ctx
, str
);
5582 isl_int_set_si(exp
, 23);
5583 map
= isl_map_fixed_power(map
, exp
);
5584 equal
= map_check_equal(map
, "{ [i] -> [i + 23] }");
5593 int test_slice(isl_ctx
*ctx
)
5599 str
= "{ [i] -> [j] }";
5600 map
= isl_map_read_from_str(ctx
, str
);
5601 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5602 equal
= map_check_equal(map
, "{ [i] -> [i] }");
5607 str
= "{ [i] -> [j] }";
5608 map
= isl_map_read_from_str(ctx
, str
);
5609 map
= isl_map_equate(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5610 equal
= map_check_equal(map
, "{ [i] -> [j] }");
5615 str
= "{ [i] -> [j] }";
5616 map
= isl_map_read_from_str(ctx
, str
);
5617 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5618 equal
= map_check_equal(map
, "{ [i] -> [-i] }");
5623 str
= "{ [i] -> [j] }";
5624 map
= isl_map_read_from_str(ctx
, str
);
5625 map
= isl_map_oppose(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5626 equal
= map_check_equal(map
, "{ [0] -> [j] }");
5631 str
= "{ [i] -> [j] }";
5632 map
= isl_map_read_from_str(ctx
, str
);
5633 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_out
, 0);
5634 equal
= map_check_equal(map
, "{ [i] -> [j] : i > j }");
5639 str
= "{ [i] -> [j] }";
5640 map
= isl_map_read_from_str(ctx
, str
);
5641 map
= isl_map_order_gt(map
, isl_dim_in
, 0, isl_dim_in
, 0);
5642 equal
= map_check_equal(map
, "{ [i] -> [j] : false }");
5650 int test_eliminate(isl_ctx
*ctx
)
5656 str
= "{ [i] -> [j] : i = 2j }";
5657 map
= isl_map_read_from_str(ctx
, str
);
5658 map
= isl_map_eliminate(map
, isl_dim_out
, 0, 1);
5659 equal
= map_check_equal(map
, "{ [i] -> [j] : exists a : i = 2a }");
5667 /* Check that isl_set_dim_residue_class detects that the values of j
5668 * in the set below are all odd and that it does not detect any spurious
5671 static int test_residue_class(isl_ctx
*ctx
)
5678 str
= "{ [i,j] : j = 4 i + 1 and 0 <= i <= 100; "
5679 "[i,j] : j = 4 i + 3 and 500 <= i <= 600 }";
5680 set
= isl_set_read_from_str(ctx
, str
);
5683 res
= isl_set_dim_residue_class(set
, 1, &m
, &r
);
5685 (isl_int_cmp_si(m
, 2) != 0 || isl_int_cmp_si(r
, 1) != 0))
5686 isl_die(ctx
, isl_error_unknown
, "incorrect residue class",
5687 res
= isl_stat_error
);
5695 int test_align_parameters(isl_ctx
*ctx
)
5699 isl_multi_aff
*ma1
, *ma2
;
5702 str
= "{ A[B[] -> C[]] -> D[E[] -> F[]] }";
5703 ma1
= isl_multi_aff_read_from_str(ctx
, str
);
5705 space
= isl_space_params_alloc(ctx
, 1);
5706 space
= isl_space_set_dim_name(space
, isl_dim_param
, 0, "N");
5707 ma1
= isl_multi_aff_align_params(ma1
, space
);
5709 str
= "[N] -> { A[B[] -> C[]] -> D[E[] -> F[]] }";
5710 ma2
= isl_multi_aff_read_from_str(ctx
, str
);
5712 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
5714 isl_multi_aff_free(ma1
);
5715 isl_multi_aff_free(ma2
);
5720 isl_die(ctx
, isl_error_unknown
,
5721 "result not as expected", return -1);
5726 static int test_list(isl_ctx
*ctx
)
5728 isl_id
*a
, *b
, *c
, *d
, *id
;
5732 a
= isl_id_alloc(ctx
, "a", NULL
);
5733 b
= isl_id_alloc(ctx
, "b", NULL
);
5734 c
= isl_id_alloc(ctx
, "c", NULL
);
5735 d
= isl_id_alloc(ctx
, "d", NULL
);
5737 list
= isl_id_list_alloc(ctx
, 4);
5738 list
= isl_id_list_add(list
, b
);
5739 list
= isl_id_list_insert(list
, 0, a
);
5740 list
= isl_id_list_add(list
, c
);
5741 list
= isl_id_list_add(list
, d
);
5742 list
= isl_id_list_drop(list
, 1, 1);
5746 if (isl_id_list_n_id(list
) != 3) {
5747 isl_id_list_free(list
);
5748 isl_die(ctx
, isl_error_unknown
,
5749 "unexpected number of elements in list", return -1);
5752 id
= isl_id_list_get_id(list
, 0);
5755 id
= isl_id_list_get_id(list
, 1);
5758 id
= isl_id_list_get_id(list
, 2);
5762 isl_id_list_free(list
);
5765 isl_die(ctx
, isl_error_unknown
,
5766 "unexpected elements in list", return -1);
5771 const char *set_conversion_tests
[] = {
5772 "[N] -> { [i] : N - 1 <= 2 i <= N }",
5773 "[N] -> { [i] : exists a : i = 4 a and N - 1 <= i <= N }",
5774 "[N] -> { [i,j] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
5775 "[N] -> { [[i]->[j]] : exists a : i = 4 a and N - 1 <= i, 2j <= N }",
5776 "[N] -> { [3*floor(N/2) + 5*floor(N/3)] }",
5777 "[a, b] -> { [c, d] : (4*floor((-a + c)/4) = -a + c and "
5778 "32*floor((-b + d)/32) = -b + d and 5 <= c <= 8 and "
5779 "-3 + c <= d <= 28 + c) }",
5782 /* Check that converting from isl_set to isl_pw_multi_aff and back
5783 * to isl_set produces the original isl_set.
5785 static int test_set_conversion(isl_ctx
*ctx
)
5789 isl_set
*set1
, *set2
;
5790 isl_pw_multi_aff
*pma
;
5793 for (i
= 0; i
< ARRAY_SIZE(set_conversion_tests
); ++i
) {
5794 str
= set_conversion_tests
[i
];
5795 set1
= isl_set_read_from_str(ctx
, str
);
5796 pma
= isl_pw_multi_aff_from_set(isl_set_copy(set1
));
5797 set2
= isl_set_from_pw_multi_aff(pma
);
5798 equal
= isl_set_is_equal(set1
, set2
);
5805 isl_die(ctx
, isl_error_unknown
, "bad conversion",
5812 const char *conversion_tests
[] = {
5813 "{ [a, b, c, d] -> s0[a, b, e, f] : "
5814 "exists (e0 = [(a - 2c)/3], e1 = [(-4 + b - 5d)/9], "
5815 "e2 = [(-d + f)/9]: 3e0 = a - 2c and 9e1 = -4 + b - 5d and "
5816 "9e2 = -d + f and f >= 0 and f <= 8 and 9e >= -5 - 2a and "
5818 "{ [a, b] -> [c] : exists (e0 = floor((-a - b + c)/5): "
5819 "5e0 = -a - b + c and c >= -a and c <= 4 - a) }",
5820 "{ [a, b] -> [c] : exists d : 18 * d = -3 - a + 2c and 1 <= c <= 3 }",
5823 /* Check that converting from isl_map to isl_pw_multi_aff and back
5824 * to isl_map produces the original isl_map.
5826 static int test_map_conversion(isl_ctx
*ctx
)
5829 isl_map
*map1
, *map2
;
5830 isl_pw_multi_aff
*pma
;
5833 for (i
= 0; i
< ARRAY_SIZE(conversion_tests
); ++i
) {
5834 map1
= isl_map_read_from_str(ctx
, conversion_tests
[i
]);
5835 pma
= isl_pw_multi_aff_from_map(isl_map_copy(map1
));
5836 map2
= isl_map_from_pw_multi_aff(pma
);
5837 equal
= isl_map_is_equal(map1
, map2
);
5844 isl_die(ctx
, isl_error_unknown
, "bad conversion",
5851 static int test_conversion(isl_ctx
*ctx
)
5853 if (test_set_conversion(ctx
) < 0)
5855 if (test_map_conversion(ctx
) < 0)
5860 /* Check that isl_basic_map_curry does not modify input.
5862 static int test_curry(isl_ctx
*ctx
)
5865 isl_basic_map
*bmap1
, *bmap2
;
5868 str
= "{ [A[] -> B[]] -> C[] }";
5869 bmap1
= isl_basic_map_read_from_str(ctx
, str
);
5870 bmap2
= isl_basic_map_curry(isl_basic_map_copy(bmap1
));
5871 equal
= isl_basic_map_is_equal(bmap1
, bmap2
);
5872 isl_basic_map_free(bmap1
);
5873 isl_basic_map_free(bmap2
);
5878 isl_die(ctx
, isl_error_unknown
,
5879 "curried map should not be equal to original",
5889 } preimage_tests
[] = {
5890 { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
5891 "{ A[j,i] -> B[i,j] }",
5892 "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
5893 { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
5894 "{ A[a,b] -> B[a/2,b/6] }",
5895 "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
5896 { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
5897 "{ A[a,b] -> B[a/2,b/6] }",
5898 "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
5899 "exists i,j : a = 2 i and b = 6 j }" },
5900 { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
5901 "[n] -> { : 0 <= n <= 100 }" },
5902 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
5903 "{ A[a] -> B[2a] }",
5904 "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
5905 { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
5906 "{ A[a] -> B[([a/2])] }",
5907 "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
5908 { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
5909 "{ A[a] -> B[a,a,a/3] }",
5910 "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
5911 { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
5912 "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
5915 static int test_preimage_basic_set(isl_ctx
*ctx
)
5918 isl_basic_set
*bset1
, *bset2
;
5922 for (i
= 0; i
< ARRAY_SIZE(preimage_tests
); ++i
) {
5923 bset1
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].set
);
5924 ma
= isl_multi_aff_read_from_str(ctx
, preimage_tests
[i
].ma
);
5925 bset2
= isl_basic_set_read_from_str(ctx
, preimage_tests
[i
].res
);
5926 bset1
= isl_basic_set_preimage_multi_aff(bset1
, ma
);
5927 equal
= isl_basic_set_is_equal(bset1
, bset2
);
5928 isl_basic_set_free(bset1
);
5929 isl_basic_set_free(bset2
);
5933 isl_die(ctx
, isl_error_unknown
, "bad preimage",
5944 } preimage_domain_tests
[] = {
5945 { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
5946 "{ A[j,i] -> B[i,j] }",
5947 "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
5948 { "{ B[i] -> C[i]; D[i] -> E[i] }",
5949 "{ A[i] -> B[i + 1] }",
5950 "{ A[i] -> C[i + 1] }" },
5951 { "{ B[i] -> C[i]; B[i] -> E[i] }",
5952 "{ A[i] -> B[i + 1] }",
5953 "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
5954 { "{ B[i] -> C[([i/2])] }",
5955 "{ A[i] -> B[2i] }",
5956 "{ A[i] -> C[i] }" },
5957 { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
5958 "{ A[i] -> B[([i/5]), ([i/7])] }",
5959 "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
5960 { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
5961 "[N] -> { A[] -> B[([N/5])] }",
5962 "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
5963 { "{ B[i] -> C[i] : exists a : i = 5 a }",
5964 "{ A[i] -> B[2i] }",
5965 "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
5966 { "{ B[i] -> C[i] : exists a : i = 2 a; "
5967 "B[i] -> D[i] : exists a : i = 2 a + 1 }",
5968 "{ A[i] -> B[2i] }",
5969 "{ A[i] -> C[2i] }" },
5970 { "{ A[i] -> B[i] }", "{ C[i] -> A[(i + floor(i/3))/2] }",
5971 "{ C[i] -> B[j] : 2j = i + floor(i/3) }" },
5974 static int test_preimage_union_map(isl_ctx
*ctx
)
5977 isl_union_map
*umap1
, *umap2
;
5981 for (i
= 0; i
< ARRAY_SIZE(preimage_domain_tests
); ++i
) {
5982 umap1
= isl_union_map_read_from_str(ctx
,
5983 preimage_domain_tests
[i
].map
);
5984 ma
= isl_multi_aff_read_from_str(ctx
,
5985 preimage_domain_tests
[i
].ma
);
5986 umap2
= isl_union_map_read_from_str(ctx
,
5987 preimage_domain_tests
[i
].res
);
5988 umap1
= isl_union_map_preimage_domain_multi_aff(umap1
, ma
);
5989 equal
= isl_union_map_is_equal(umap1
, umap2
);
5990 isl_union_map_free(umap1
);
5991 isl_union_map_free(umap2
);
5995 isl_die(ctx
, isl_error_unknown
, "bad preimage",
6002 static int test_preimage(isl_ctx
*ctx
)
6004 if (test_preimage_basic_set(ctx
) < 0)
6006 if (test_preimage_union_map(ctx
) < 0)
6016 } pullback_tests
[] = {
6017 { "{ B[i,j] -> C[i + 2j] }" , "{ A[a,b] -> B[b,a] }",
6018 "{ A[a,b] -> C[b + 2a] }" },
6019 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/2] }", "{ A[a] -> C[a] }" },
6020 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[2a] }", "{ A[a] -> C[a] }" },
6021 { "{ B[i] -> C[(i)/2] }", "{ A[a] -> B[(a)/3] }",
6022 "{ A[a] -> C[(a)/6] }" },
6023 { "{ B[i] -> C[2i] }", "{ A[a] -> B[5a] }", "{ A[a] -> C[10a] }" },
6024 { "{ B[i] -> C[2i] }", "{ A[a] -> B[(a)/3] }",
6025 "{ A[a] -> C[(2a)/3] }" },
6026 { "{ B[i,j] -> C[i + j] }", "{ A[a] -> B[a,a] }", "{ A[a] -> C[2a] }"},
6027 { "{ B[a] -> C[a,a] }", "{ A[i,j] -> B[i + j] }",
6028 "{ A[i,j] -> C[i + j, i + j] }"},
6029 { "{ B[i] -> C[([i/2])] }", "{ B[5] }", "{ C[2] }" },
6030 { "[n] -> { B[i,j] -> C[([i/2]) + 2j] }",
6031 "[n] -> { B[n,[n/3]] }", "[n] -> { C[([n/2]) + 2*[n/3]] }", },
6032 { "{ [i, j] -> [floor((i)/4) + floor((2*i+j)/5)] }",
6033 "{ [i, j] -> [floor((i)/3), j] }",
6034 "{ [i, j] -> [(floor((i)/12) + floor((j + 2*floor((i)/3))/5))] }" },
6037 static int test_pullback(isl_ctx
*ctx
)
6040 isl_multi_aff
*ma1
, *ma2
;
6044 for (i
= 0; i
< ARRAY_SIZE(pullback_tests
); ++i
) {
6045 ma1
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma1
);
6046 ma
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].ma
);
6047 ma2
= isl_multi_aff_read_from_str(ctx
, pullback_tests
[i
].res
);
6048 ma1
= isl_multi_aff_pullback_multi_aff(ma1
, ma
);
6049 equal
= isl_multi_aff_plain_is_equal(ma1
, ma2
);
6050 isl_multi_aff_free(ma1
);
6051 isl_multi_aff_free(ma2
);
6055 isl_die(ctx
, isl_error_unknown
, "bad pullback",
6062 /* Check that negation is printed correctly and that equal expressions
6063 * are correctly identified.
6065 static int test_ast(isl_ctx
*ctx
)
6067 isl_ast_expr
*expr
, *expr1
, *expr2
, *expr3
;
6071 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
6072 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
6073 expr
= isl_ast_expr_add(expr1
, expr2
);
6074 expr2
= isl_ast_expr_copy(expr
);
6075 expr
= isl_ast_expr_neg(expr
);
6076 expr2
= isl_ast_expr_neg(expr2
);
6077 equal
= isl_ast_expr_is_equal(expr
, expr2
);
6078 str
= isl_ast_expr_to_C_str(expr
);
6079 ok
= str
? !strcmp(str
, "-(A + B)") : -1;
6081 isl_ast_expr_free(expr
);
6082 isl_ast_expr_free(expr2
);
6084 if (ok
< 0 || equal
< 0)
6087 isl_die(ctx
, isl_error_unknown
,
6088 "equal expressions not considered equal", return -1);
6090 isl_die(ctx
, isl_error_unknown
,
6091 "isl_ast_expr printed incorrectly", return -1);
6093 expr1
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "A", NULL
));
6094 expr2
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "B", NULL
));
6095 expr
= isl_ast_expr_add(expr1
, expr2
);
6096 expr3
= isl_ast_expr_from_id(isl_id_alloc(ctx
, "C", NULL
));
6097 expr
= isl_ast_expr_sub(expr3
, expr
);
6098 str
= isl_ast_expr_to_C_str(expr
);
6099 ok
= str
? !strcmp(str
, "C - (A + B)") : -1;
6101 isl_ast_expr_free(expr
);
6106 isl_die(ctx
, isl_error_unknown
,
6107 "isl_ast_expr printed incorrectly", return -1);
6112 /* Check that isl_ast_build_expr_from_set returns a valid expression
6113 * for an empty set. Note that isl_ast_build_expr_from_set getting
6114 * called on an empty set probably indicates a bug in the caller.
6116 static int test_ast_build(isl_ctx
*ctx
)
6119 isl_ast_build
*build
;
6122 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6123 build
= isl_ast_build_from_context(set
);
6125 set
= isl_set_empty(isl_space_params_alloc(ctx
, 0));
6126 expr
= isl_ast_build_expr_from_set(build
, set
);
6128 isl_ast_expr_free(expr
);
6129 isl_ast_build_free(build
);
6137 /* Internal data structure for before_for and after_for callbacks.
6139 * depth is the current depth
6140 * before is the number of times before_for has been called
6141 * after is the number of times after_for has been called
6143 struct isl_test_codegen_data
{
6149 /* This function is called before each for loop in the AST generated
6150 * from test_ast_gen1.
6152 * Increment the number of calls and the depth.
6153 * Check that the space returned by isl_ast_build_get_schedule_space
6154 * matches the target space of the schedule returned by
6155 * isl_ast_build_get_schedule.
6156 * Return an isl_id that is checked by the corresponding call
6159 static __isl_give isl_id
*before_for(__isl_keep isl_ast_build
*build
,
6162 struct isl_test_codegen_data
*data
= user
;
6165 isl_union_map
*schedule
;
6166 isl_union_set
*uset
;
6171 ctx
= isl_ast_build_get_ctx(build
);
6173 if (data
->before
>= 3)
6174 isl_die(ctx
, isl_error_unknown
,
6175 "unexpected number of for nodes", return NULL
);
6176 if (data
->depth
>= 2)
6177 isl_die(ctx
, isl_error_unknown
,
6178 "unexpected depth", return NULL
);
6180 snprintf(name
, sizeof(name
), "d%d", data
->depth
);
6184 schedule
= isl_ast_build_get_schedule(build
);
6185 uset
= isl_union_map_range(schedule
);
6188 if (isl_union_set_n_set(uset
) != 1) {
6189 isl_union_set_free(uset
);
6190 isl_die(ctx
, isl_error_unknown
,
6191 "expecting single range space", return NULL
);
6194 space
= isl_ast_build_get_schedule_space(build
);
6195 set
= isl_union_set_extract_set(uset
, space
);
6196 isl_union_set_free(uset
);
6197 empty
= isl_set_is_empty(set
);
6203 isl_die(ctx
, isl_error_unknown
,
6204 "spaces don't match", return NULL
);
6206 return isl_id_alloc(ctx
, name
, NULL
);
6209 /* This function is called after each for loop in the AST generated
6210 * from test_ast_gen1.
6212 * Increment the number of calls and decrement the depth.
6213 * Check that the annotation attached to the node matches
6214 * the isl_id returned by the corresponding call to before_for.
6216 static __isl_give isl_ast_node
*after_for(__isl_take isl_ast_node
*node
,
6217 __isl_keep isl_ast_build
*build
, void *user
)
6219 struct isl_test_codegen_data
*data
= user
;
6227 if (data
->after
> data
->before
)
6228 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
6229 "mismatch in number of for nodes",
6230 return isl_ast_node_free(node
));
6232 id
= isl_ast_node_get_annotation(node
);
6234 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
6235 "missing annotation", return isl_ast_node_free(node
));
6237 name
= isl_id_get_name(id
);
6238 valid
= name
&& atoi(name
+ 1) == data
->depth
;
6242 isl_die(isl_ast_node_get_ctx(node
), isl_error_unknown
,
6243 "wrong annotation", return isl_ast_node_free(node
));
6248 /* Check that the before_each_for and after_each_for callbacks
6249 * are called for each for loop in the generated code,
6250 * that they are called in the right order and that the isl_id
6251 * returned from the before_each_for callback is attached to
6252 * the isl_ast_node passed to the corresponding after_each_for call.
6254 static int test_ast_gen1(isl_ctx
*ctx
)
6258 isl_union_map
*schedule
;
6259 isl_ast_build
*build
;
6261 struct isl_test_codegen_data data
;
6263 str
= "[N] -> { : N >= 10 }";
6264 set
= isl_set_read_from_str(ctx
, str
);
6265 str
= "[N] -> { A[i,j] -> S[8,i,3,j] : 0 <= i,j <= N; "
6266 "B[i,j] -> S[8,j,9,i] : 0 <= i,j <= N }";
6267 schedule
= isl_union_map_read_from_str(ctx
, str
);
6272 build
= isl_ast_build_from_context(set
);
6273 build
= isl_ast_build_set_before_each_for(build
,
6274 &before_for
, &data
);
6275 build
= isl_ast_build_set_after_each_for(build
,
6277 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6278 isl_ast_build_free(build
);
6282 isl_ast_node_free(tree
);
6284 if (data
.before
!= 3 || data
.after
!= 3)
6285 isl_die(ctx
, isl_error_unknown
,
6286 "unexpected number of for nodes", return -1);
6291 /* Check that the AST generator handles domains that are integrally disjoint
6292 * but not rationally disjoint.
6294 static int test_ast_gen2(isl_ctx
*ctx
)
6298 isl_union_map
*schedule
;
6299 isl_union_map
*options
;
6300 isl_ast_build
*build
;
6303 str
= "{ A[i,j] -> [i,j] : 0 <= i,j <= 1 }";
6304 schedule
= isl_union_map_read_from_str(ctx
, str
);
6305 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6306 build
= isl_ast_build_from_context(set
);
6308 str
= "{ [i,j] -> atomic[1] : i + j = 1; [i,j] -> unroll[1] : i = j }";
6309 options
= isl_union_map_read_from_str(ctx
, str
);
6310 build
= isl_ast_build_set_options(build
, options
);
6311 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6312 isl_ast_build_free(build
);
6315 isl_ast_node_free(tree
);
6320 /* Increment *user on each call.
6322 static __isl_give isl_ast_node
*count_domains(__isl_take isl_ast_node
*node
,
6323 __isl_keep isl_ast_build
*build
, void *user
)
6332 /* Test that unrolling tries to minimize the number of instances.
6333 * In particular, for the schedule given below, make sure it generates
6334 * 3 nodes (rather than 101).
6336 static int test_ast_gen3(isl_ctx
*ctx
)
6340 isl_union_map
*schedule
;
6341 isl_union_map
*options
;
6342 isl_ast_build
*build
;
6346 str
= "[n] -> { A[i] -> [i] : 0 <= i <= 100 and n <= i <= n + 2 }";
6347 schedule
= isl_union_map_read_from_str(ctx
, str
);
6348 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6350 str
= "{ [i] -> unroll[0] }";
6351 options
= isl_union_map_read_from_str(ctx
, str
);
6353 build
= isl_ast_build_from_context(set
);
6354 build
= isl_ast_build_set_options(build
, options
);
6355 build
= isl_ast_build_set_at_each_domain(build
,
6356 &count_domains
, &n_domain
);
6357 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6358 isl_ast_build_free(build
);
6362 isl_ast_node_free(tree
);
6365 isl_die(ctx
, isl_error_unknown
,
6366 "unexpected number of for nodes", return -1);
6371 /* Check that if the ast_build_exploit_nested_bounds options is set,
6372 * we do not get an outer if node in the generated AST,
6373 * while we do get such an outer if node if the options is not set.
6375 static int test_ast_gen4(isl_ctx
*ctx
)
6379 isl_union_map
*schedule
;
6380 isl_ast_build
*build
;
6382 enum isl_ast_node_type type
;
6385 enb
= isl_options_get_ast_build_exploit_nested_bounds(ctx
);
6386 str
= "[N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 0 <= j <= M }";
6388 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 1);
6390 schedule
= isl_union_map_read_from_str(ctx
, str
);
6391 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6392 build
= isl_ast_build_from_context(set
);
6393 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6394 isl_ast_build_free(build
);
6398 type
= isl_ast_node_get_type(tree
);
6399 isl_ast_node_free(tree
);
6401 if (type
== isl_ast_node_if
)
6402 isl_die(ctx
, isl_error_unknown
,
6403 "not expecting if node", return -1);
6405 isl_options_set_ast_build_exploit_nested_bounds(ctx
, 0);
6407 schedule
= isl_union_map_read_from_str(ctx
, str
);
6408 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6409 build
= isl_ast_build_from_context(set
);
6410 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6411 isl_ast_build_free(build
);
6415 type
= isl_ast_node_get_type(tree
);
6416 isl_ast_node_free(tree
);
6418 if (type
!= isl_ast_node_if
)
6419 isl_die(ctx
, isl_error_unknown
,
6420 "expecting if node", return -1);
6422 isl_options_set_ast_build_exploit_nested_bounds(ctx
, enb
);
6427 /* This function is called for each leaf in the AST generated
6428 * from test_ast_gen5.
6430 * We finalize the AST generation by extending the outer schedule
6431 * with a zero-dimensional schedule. If this results in any for loops,
6432 * then this means that we did not pass along enough information
6433 * about the outer schedule to the inner AST generation.
6435 static __isl_give isl_ast_node
*create_leaf(__isl_take isl_ast_build
*build
,
6438 isl_union_map
*schedule
, *extra
;
6441 schedule
= isl_ast_build_get_schedule(build
);
6442 extra
= isl_union_map_copy(schedule
);
6443 extra
= isl_union_map_from_domain(isl_union_map_domain(extra
));
6444 schedule
= isl_union_map_range_product(schedule
, extra
);
6445 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6446 isl_ast_build_free(build
);
6451 if (isl_ast_node_get_type(tree
) == isl_ast_node_for
)
6452 isl_die(isl_ast_node_get_ctx(tree
), isl_error_unknown
,
6453 "code should not contain any for loop",
6454 return isl_ast_node_free(tree
));
6459 /* Check that we do not lose any information when going back and
6460 * forth between internal and external schedule.
6462 * In particular, we create an AST where we unroll the only
6463 * non-constant dimension in the schedule. We therefore do
6464 * not expect any for loops in the AST. However, older versions
6465 * of isl would not pass along enough information about the outer
6466 * schedule when performing an inner code generation from a create_leaf
6467 * callback, resulting in the inner code generation producing a for loop.
6469 static int test_ast_gen5(isl_ctx
*ctx
)
6473 isl_union_map
*schedule
, *options
;
6474 isl_ast_build
*build
;
6477 str
= "{ A[] -> [1, 1, 2]; B[i] -> [1, i, 0] : i >= 1 and i <= 2 }";
6478 schedule
= isl_union_map_read_from_str(ctx
, str
);
6480 str
= "{ [a, b, c] -> unroll[1] : exists (e0 = [(a)/4]: "
6481 "4e0 >= -1 + a - b and 4e0 <= -2 + a + b) }";
6482 options
= isl_union_map_read_from_str(ctx
, str
);
6484 set
= isl_set_universe(isl_space_params_alloc(ctx
, 0));
6485 build
= isl_ast_build_from_context(set
);
6486 build
= isl_ast_build_set_options(build
, options
);
6487 build
= isl_ast_build_set_create_leaf(build
, &create_leaf
, NULL
);
6488 tree
= isl_ast_build_node_from_schedule_map(build
, schedule
);
6489 isl_ast_build_free(build
);
6490 isl_ast_node_free(tree
);
6497 /* Check that the expression
6499 * [n] -> { [n/2] : n <= 0 and n % 2 = 0; [0] : n > 0 }
6501 * is not combined into
6505 * as this would result in n/2 being evaluated in parts of
6506 * the definition domain where n is not a multiple of 2.
6508 static int test_ast_expr(isl_ctx
*ctx
)
6512 isl_ast_build
*build
;
6517 min_max
= isl_options_get_ast_build_detect_min_max(ctx
);
6518 isl_options_set_ast_build_detect_min_max(ctx
, 1);
6520 str
= "[n] -> { [n/2] : n <= 0 and n % 2 = 0; [0] : n > 0 }";
6521 pa
= isl_pw_aff_read_from_str(ctx
, str
);
6522 build
= isl_ast_build_alloc(ctx
);
6523 expr
= isl_ast_build_expr_from_pw_aff(build
, pa
);
6524 is_min
= isl_ast_expr_get_type(expr
) == isl_ast_expr_op
&&
6525 isl_ast_expr_get_op_type(expr
) == isl_ast_op_min
;
6526 isl_ast_build_free(build
);
6527 isl_ast_expr_free(expr
);
6529 isl_options_set_ast_build_detect_min_max(ctx
, min_max
);
6534 isl_die(ctx
, isl_error_unknown
,
6535 "expressions should not be combined", return -1);
6540 static int test_ast_gen(isl_ctx
*ctx
)
6542 if (test_ast_gen1(ctx
) < 0)
6544 if (test_ast_gen2(ctx
) < 0)
6546 if (test_ast_gen3(ctx
) < 0)
6548 if (test_ast_gen4(ctx
) < 0)
6550 if (test_ast_gen5(ctx
) < 0)
6552 if (test_ast_expr(ctx
) < 0)
6557 /* Check if dropping output dimensions from an isl_pw_multi_aff
6560 static int test_pw_multi_aff(isl_ctx
*ctx
)
6563 isl_pw_multi_aff
*pma1
, *pma2
;
6566 str
= "{ [i,j] -> [i+j, 4i-j] }";
6567 pma1
= isl_pw_multi_aff_read_from_str(ctx
, str
);
6568 str
= "{ [i,j] -> [4i-j] }";
6569 pma2
= isl_pw_multi_aff_read_from_str(ctx
, str
);
6571 pma1
= isl_pw_multi_aff_drop_dims(pma1
, isl_dim_out
, 0, 1);
6573 equal
= isl_pw_multi_aff_plain_is_equal(pma1
, pma2
);
6575 isl_pw_multi_aff_free(pma1
);
6576 isl_pw_multi_aff_free(pma2
);
6580 isl_die(ctx
, isl_error_unknown
,
6581 "expressions not equal", return -1);
6586 /* Check that we can properly parse multi piecewise affine expressions
6587 * where the piecewise affine expressions have different domains.
6589 static int test_multi_pw_aff(isl_ctx
*ctx
)
6592 isl_set
*dom
, *dom2
;
6593 isl_multi_pw_aff
*mpa1
, *mpa2
;
6598 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [i] }");
6599 dom
= isl_set_read_from_str(ctx
, "{ [i] : i > 0 }");
6600 mpa1
= isl_multi_pw_aff_intersect_domain(mpa1
, dom
);
6601 mpa2
= isl_multi_pw_aff_read_from_str(ctx
, "{ [i] -> [2i] }");
6602 mpa2
= isl_multi_pw_aff_flat_range_product(mpa1
, mpa2
);
6603 str
= "{ [i] -> [(i : i > 0), 2i] }";
6604 mpa1
= isl_multi_pw_aff_read_from_str(ctx
, str
);
6606 equal
= isl_multi_pw_aff_plain_is_equal(mpa1
, mpa2
);
6608 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 0);
6609 dom
= isl_pw_aff_domain(pa
);
6610 pa
= isl_multi_pw_aff_get_pw_aff(mpa1
, 1);
6611 dom2
= isl_pw_aff_domain(pa
);
6612 equal_domain
= isl_set_is_equal(dom
, dom2
);
6616 isl_multi_pw_aff_free(mpa1
);
6617 isl_multi_pw_aff_free(mpa2
);
6622 isl_die(ctx
, isl_error_unknown
,
6623 "expressions not equal", return -1);
6625 if (equal_domain
< 0)
6628 isl_die(ctx
, isl_error_unknown
,
6629 "domains unexpectedly equal", return -1);
6634 /* This is a regression test for a bug where isl_basic_map_simplify
6635 * would end up in an infinite loop. In particular, we construct
6636 * an empty basic set that is not obviously empty.
6637 * isl_basic_set_is_empty marks the basic set as empty.
6638 * After projecting out i3, the variable can be dropped completely,
6639 * but isl_basic_map_simplify refrains from doing so if the basic set
6640 * is empty and would end up in an infinite loop if it didn't test
6641 * explicitly for empty basic maps in the outer loop.
6643 static int test_simplify_1(isl_ctx
*ctx
)
6646 isl_basic_set
*bset
;
6649 str
= "{ [i0, i1, i2, i3] : i0 >= -2 and 6i2 <= 4 + i0 + 5i1 and "
6650 "i2 <= 22 and 75i2 <= 111 + 13i0 + 60i1 and "
6651 "25i2 >= 38 + 6i0 + 20i1 and i0 <= -1 and i2 >= 20 and "
6653 bset
= isl_basic_set_read_from_str(ctx
, str
);
6654 empty
= isl_basic_set_is_empty(bset
);
6655 bset
= isl_basic_set_project_out(bset
, isl_dim_set
, 3, 1);
6656 isl_basic_set_free(bset
);
6660 isl_die(ctx
, isl_error_unknown
,
6661 "basic set should be empty", return -1);
6666 /* Check that the equality in the set description below
6667 * is simplified away.
6669 static int test_simplify_2(isl_ctx
*ctx
)
6672 isl_basic_set
*bset
;
6675 str
= "{ [a] : exists e0, e1: 32e1 = 31 + 31a + 31e0 }";
6676 bset
= isl_basic_set_read_from_str(ctx
, str
);
6677 universe
= isl_basic_set_plain_is_universe(bset
);
6678 isl_basic_set_free(bset
);
6683 isl_die(ctx
, isl_error_unknown
,
6684 "equality not simplified away", return -1);
6688 /* Some simplification tests.
6690 static int test_simplify(isl_ctx
*ctx
)
6692 if (test_simplify_1(ctx
) < 0)
6694 if (test_simplify_2(ctx
) < 0)
6699 /* This is a regression test for a bug where isl_tab_basic_map_partial_lexopt
6700 * with gbr context would fail to disable the use of the shifted tableau
6701 * when transferring equalities for the input to the context, resulting
6702 * in invalid sample values.
6704 static int test_partial_lexmin(isl_ctx
*ctx
)
6707 isl_basic_set
*bset
;
6708 isl_basic_map
*bmap
;
6711 str
= "{ [1, b, c, 1 - c] -> [e] : 2e <= -c and 2e >= -3 + c }";
6712 bmap
= isl_basic_map_read_from_str(ctx
, str
);
6713 str
= "{ [a, b, c, d] : c <= 1 and 2d >= 6 - 4b - c }";
6714 bset
= isl_basic_set_read_from_str(ctx
, str
);
6715 map
= isl_basic_map_partial_lexmin(bmap
, bset
, NULL
);
6724 /* Check that the variable compression performed on the existentially
6725 * quantified variables inside isl_basic_set_compute_divs is not confused
6726 * by the implicit equalities among the parameters.
6728 static int test_compute_divs(isl_ctx
*ctx
)
6731 isl_basic_set
*bset
;
6734 str
= "[a, b, c, d, e] -> { [] : exists (e0: 2d = b and a <= 124 and "
6735 "b <= 2046 and b >= 0 and b <= 60 + 64a and 2e >= b + 2c and "
6736 "2e >= b and 2e <= 1 + b and 2e <= 1 + b + 2c and "
6737 "32768e0 >= -124 + a and 2097152e0 <= 60 + 64a - b) }";
6738 bset
= isl_basic_set_read_from_str(ctx
, str
);
6739 set
= isl_basic_set_compute_divs(bset
);
6747 /* Check that the reaching domain elements and the prefix schedule
6748 * at a leaf node are the same before and after grouping.
6750 static int test_schedule_tree_group_1(isl_ctx
*ctx
)
6755 isl_union_set
*uset
;
6756 isl_multi_union_pw_aff
*mupa
;
6757 isl_union_pw_multi_aff
*upma1
, *upma2
;
6758 isl_union_set
*domain1
, *domain2
;
6759 isl_union_map
*umap1
, *umap2
;
6760 isl_schedule_node
*node
;
6762 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10 }";
6763 uset
= isl_union_set_read_from_str(ctx
, str
);
6764 node
= isl_schedule_node_from_domain(uset
);
6765 node
= isl_schedule_node_child(node
, 0);
6766 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [9 - i] }]";
6767 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6768 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6769 node
= isl_schedule_node_child(node
, 0);
6770 str
= "[{ S1[i,j] -> [j]; S2[i,j] -> [j] }]";
6771 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6772 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6773 node
= isl_schedule_node_child(node
, 0);
6774 umap1
= isl_schedule_node_get_prefix_schedule_union_map(node
);
6775 upma1
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
6776 domain1
= isl_schedule_node_get_domain(node
);
6777 id
= isl_id_alloc(ctx
, "group", NULL
);
6778 node
= isl_schedule_node_parent(node
);
6779 node
= isl_schedule_node_group(node
, id
);
6780 node
= isl_schedule_node_child(node
, 0);
6781 umap2
= isl_schedule_node_get_prefix_schedule_union_map(node
);
6782 upma2
= isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(node
);
6783 domain2
= isl_schedule_node_get_domain(node
);
6784 equal
= isl_union_pw_multi_aff_plain_is_equal(upma1
, upma2
);
6785 if (equal
>= 0 && equal
)
6786 equal
= isl_union_set_is_equal(domain1
, domain2
);
6787 if (equal
>= 0 && equal
)
6788 equal
= isl_union_map_is_equal(umap1
, umap2
);
6789 isl_union_map_free(umap1
);
6790 isl_union_map_free(umap2
);
6791 isl_union_set_free(domain1
);
6792 isl_union_set_free(domain2
);
6793 isl_union_pw_multi_aff_free(upma1
);
6794 isl_union_pw_multi_aff_free(upma2
);
6795 isl_schedule_node_free(node
);
6800 isl_die(ctx
, isl_error_unknown
,
6801 "expressions not equal", return -1);
6806 /* Check that we can have nested groupings and that the union map
6807 * schedule representation is the same before and after the grouping.
6808 * Note that after the grouping, the union map representation contains
6809 * the domain constraints from the ranges of the expansion nodes,
6810 * while they are missing from the union map representation of
6811 * the tree without expansion nodes.
6813 * Also check that the global expansion is as expected.
6815 static int test_schedule_tree_group_2(isl_ctx
*ctx
)
6817 int equal
, equal_expansion
;
6820 isl_union_set
*uset
;
6821 isl_union_map
*umap1
, *umap2
;
6822 isl_union_map
*expansion1
, *expansion2
;
6823 isl_union_set_list
*filters
;
6824 isl_multi_union_pw_aff
*mupa
;
6825 isl_schedule
*schedule
;
6826 isl_schedule_node
*node
;
6828 str
= "{ S1[i,j] : 0 <= i,j < 10; S2[i,j] : 0 <= i,j < 10; "
6829 "S3[i,j] : 0 <= i,j < 10 }";
6830 uset
= isl_union_set_read_from_str(ctx
, str
);
6831 node
= isl_schedule_node_from_domain(uset
);
6832 node
= isl_schedule_node_child(node
, 0);
6833 str
= "[{ S1[i,j] -> [i]; S2[i,j] -> [i]; S3[i,j] -> [i] }]";
6834 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
6835 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
6836 node
= isl_schedule_node_child(node
, 0);
6837 str
= "{ S1[i,j] }";
6838 uset
= isl_union_set_read_from_str(ctx
, str
);
6839 filters
= isl_union_set_list_from_union_set(uset
);
6840 str
= "{ S2[i,j]; S3[i,j] }";
6841 uset
= isl_union_set_read_from_str(ctx
, str
);
6842 filters
= isl_union_set_list_add(filters
, uset
);
6843 node
= isl_schedule_node_insert_sequence(node
, filters
);
6844 node
= isl_schedule_node_child(node
, 1);
6845 node
= isl_schedule_node_child(node
, 0);
6846 str
= "{ S2[i,j] }";
6847 uset
= isl_union_set_read_from_str(ctx
, str
);
6848 filters
= isl_union_set_list_from_union_set(uset
);
6849 str
= "{ S3[i,j] }";
6850 uset
= isl_union_set_read_from_str(ctx
, str
);
6851 filters
= isl_union_set_list_add(filters
, uset
);
6852 node
= isl_schedule_node_insert_sequence(node
, filters
);
6854 schedule
= isl_schedule_node_get_schedule(node
);
6855 umap1
= isl_schedule_get_map(schedule
);
6856 uset
= isl_schedule_get_domain(schedule
);
6857 umap1
= isl_union_map_intersect_domain(umap1
, uset
);
6858 isl_schedule_free(schedule
);
6860 node
= isl_schedule_node_parent(node
);
6861 node
= isl_schedule_node_parent(node
);
6862 id
= isl_id_alloc(ctx
, "group1", NULL
);
6863 node
= isl_schedule_node_group(node
, id
);
6864 node
= isl_schedule_node_child(node
, 1);
6865 node
= isl_schedule_node_child(node
, 0);
6866 id
= isl_id_alloc(ctx
, "group2", NULL
);
6867 node
= isl_schedule_node_group(node
, id
);
6869 schedule
= isl_schedule_node_get_schedule(node
);
6870 umap2
= isl_schedule_get_map(schedule
);
6871 isl_schedule_free(schedule
);
6873 node
= isl_schedule_node_root(node
);
6874 node
= isl_schedule_node_child(node
, 0);
6875 expansion1
= isl_schedule_node_get_subtree_expansion(node
);
6876 isl_schedule_node_free(node
);
6878 str
= "{ group1[i] -> S1[i,j] : 0 <= i,j < 10; "
6879 "group1[i] -> S2[i,j] : 0 <= i,j < 10; "
6880 "group1[i] -> S3[i,j] : 0 <= i,j < 10 }";
6882 expansion2
= isl_union_map_read_from_str(ctx
, str
);
6884 equal
= isl_union_map_is_equal(umap1
, umap2
);
6885 equal_expansion
= isl_union_map_is_equal(expansion1
, expansion2
);
6887 isl_union_map_free(umap1
);
6888 isl_union_map_free(umap2
);
6889 isl_union_map_free(expansion1
);
6890 isl_union_map_free(expansion2
);
6892 if (equal
< 0 || equal_expansion
< 0)
6895 isl_die(ctx
, isl_error_unknown
,
6896 "expressions not equal", return -1);
6897 if (!equal_expansion
)
6898 isl_die(ctx
, isl_error_unknown
,
6899 "unexpected expansion", return -1);
6904 /* Some tests for the isl_schedule_node_group function.
6906 static int test_schedule_tree_group(isl_ctx
*ctx
)
6908 if (test_schedule_tree_group_1(ctx
) < 0)
6910 if (test_schedule_tree_group_2(ctx
) < 0)
6919 { "{ rat: [i] : 0 <= i <= 10 }",
6920 "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }" },
6921 { "{ rat: [i] : FALSE }",
6922 "{ rat: coefficients[[cst] -> [a]] }" },
6924 "{ rat: coefficients[[cst] -> [0]] : cst >= 0 }" },
6931 { "{ rat: coefficients[[cst] -> [a]] : cst >= 0 and 10a + cst >= 0 }",
6932 "{ rat: [i] : 0 <= i <= 10 }" },
6933 { "{ rat: coefficients[[cst] -> [a]] : FALSE }",
6935 { "{ rat: coefficients[[cst] -> [a]] }",
6936 "{ rat: [i] : FALSE }" },
6939 /* Test the basic functionality of isl_basic_set_coefficients and
6940 * isl_basic_set_solutions.
6942 static int test_dual(isl_ctx
*ctx
)
6946 for (i
= 0; i
< ARRAY_SIZE(coef_tests
); ++i
) {
6948 isl_basic_set
*bset1
, *bset2
;
6950 bset1
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].set
);
6951 bset2
= isl_basic_set_read_from_str(ctx
, coef_tests
[i
].dual
);
6952 bset1
= isl_basic_set_coefficients(bset1
);
6953 equal
= isl_basic_set_is_equal(bset1
, bset2
);
6954 isl_basic_set_free(bset1
);
6955 isl_basic_set_free(bset2
);
6959 isl_die(ctx
, isl_error_unknown
,
6960 "incorrect dual", return -1);
6963 for (i
= 0; i
< ARRAY_SIZE(sol_tests
); ++i
) {
6965 isl_basic_set
*bset1
, *bset2
;
6967 bset1
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].set
);
6968 bset2
= isl_basic_set_read_from_str(ctx
, sol_tests
[i
].dual
);
6969 bset1
= isl_basic_set_solutions(bset1
);
6970 equal
= isl_basic_set_is_equal(bset1
, bset2
);
6971 isl_basic_set_free(bset1
);
6972 isl_basic_set_free(bset2
);
6976 isl_die(ctx
, isl_error_unknown
,
6977 "incorrect dual", return -1);
6987 const char *schedule
;
6992 { 0, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
6993 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6995 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
6996 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
6998 { 1, 0, "[n] -> { S[i,j] : 0 <= i,j < n }",
6999 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
7001 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
7002 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
7004 { 0, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
7005 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
7007 "[{ S[i,j] -> [floor(i/32)] }, { S[i,j] -> [floor(j/32)] }]",
7008 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
7010 { 1, 1, "[n] -> { S[i,j] : 0 <= i,j < n }",
7011 "[{ S[i,j] -> [i] }, { S[i,j] -> [j] }]",
7013 "[{ S[i,j] -> [32*floor(i/32)] }, { S[i,j] -> [32*floor(j/32)] }]",
7014 "[{ S[i,j] -> [i%32] }, { S[i,j] -> [j%32] }]",
7018 /* Basic tiling tests. Create a schedule tree with a domain and a band node,
7019 * tile the band and then check if the tile and point bands have the
7020 * expected partial schedule.
7022 static int test_tile(isl_ctx
*ctx
)
7028 scale
= isl_options_get_tile_scale_tile_loops(ctx
);
7029 shift
= isl_options_get_tile_shift_point_loops(ctx
);
7031 for (i
= 0; i
< ARRAY_SIZE(tile_tests
); ++i
) {
7035 isl_union_set
*domain
;
7036 isl_multi_union_pw_aff
*mupa
, *mupa2
;
7037 isl_schedule_node
*node
;
7038 isl_multi_val
*sizes
;
7040 opt
= tile_tests
[i
].scale_tile
;
7041 isl_options_set_tile_scale_tile_loops(ctx
, opt
);
7042 opt
= tile_tests
[i
].shift_point
;
7043 isl_options_set_tile_shift_point_loops(ctx
, opt
);
7045 str
= tile_tests
[i
].domain
;
7046 domain
= isl_union_set_read_from_str(ctx
, str
);
7047 node
= isl_schedule_node_from_domain(domain
);
7048 node
= isl_schedule_node_child(node
, 0);
7049 str
= tile_tests
[i
].schedule
;
7050 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
7051 node
= isl_schedule_node_insert_partial_schedule(node
, mupa
);
7052 str
= tile_tests
[i
].sizes
;
7053 sizes
= isl_multi_val_read_from_str(ctx
, str
);
7054 node
= isl_schedule_node_band_tile(node
, sizes
);
7056 str
= tile_tests
[i
].tile
;
7057 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
7058 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
7059 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
, mupa2
);
7060 isl_multi_union_pw_aff_free(mupa
);
7061 isl_multi_union_pw_aff_free(mupa2
);
7063 node
= isl_schedule_node_child(node
, 0);
7065 str
= tile_tests
[i
].point
;
7066 mupa
= isl_multi_union_pw_aff_read_from_str(ctx
, str
);
7067 mupa2
= isl_schedule_node_band_get_partial_schedule(node
);
7068 if (equal
>= 0 && equal
)
7069 equal
= isl_multi_union_pw_aff_plain_is_equal(mupa
,
7071 isl_multi_union_pw_aff_free(mupa
);
7072 isl_multi_union_pw_aff_free(mupa2
);
7074 isl_schedule_node_free(node
);
7079 isl_die(ctx
, isl_error_unknown
,
7080 "unexpected result", return -1);
7083 isl_options_set_tile_scale_tile_loops(ctx
, scale
);
7084 isl_options_set_tile_shift_point_loops(ctx
, shift
);
7089 /* Check that the domain hash of a space is equal to the hash
7090 * of the domain of the space.
7092 static int test_domain_hash(isl_ctx
*ctx
)
7096 uint32_t hash1
, hash2
;
7098 map
= isl_map_read_from_str(ctx
, "[n] -> { A[B[x] -> C[]] -> D[] }");
7099 space
= isl_map_get_space(map
);
7101 hash1
= isl_space_get_domain_hash(space
);
7102 space
= isl_space_domain(space
);
7103 hash2
= isl_space_get_hash(space
);
7104 isl_space_free(space
);
7109 isl_die(ctx
, isl_error_unknown
,
7110 "domain hash not equal to hash of domain", return -1);
7115 /* Check that a universe basic set that is not obviously equal to the universe
7116 * is still recognized as being equal to the universe.
7118 static int test_universe(isl_ctx
*ctx
)
7121 isl_basic_set
*bset
;
7124 s
= "{ [] : exists x, y : 3y <= 2x and y >= -3 + 2x and 2y >= 2 - x }";
7125 bset
= isl_basic_set_read_from_str(ctx
, s
);
7126 is_univ
= isl_basic_set_is_universe(bset
);
7127 isl_basic_set_free(bset
);
7132 isl_die(ctx
, isl_error_unknown
,
7133 "not recognized as universe set", return -1);
7138 /* Sets for which chambers are computed and checked.
7140 const char *chambers_tests
[] = {
7141 "[A, B, C] -> { [x, y, z] : x >= 0 and y >= 0 and y <= A - x and "
7142 "z >= 0 and z <= C - y and z <= B - x - y }",
7145 /* Add the domain of "cell" to "cells".
7147 static isl_stat
add_cell(__isl_take isl_cell
*cell
, void *user
)
7149 isl_basic_set_list
**cells
= user
;
7152 dom
= isl_cell_get_domain(cell
);
7153 isl_cell_free(cell
);
7154 *cells
= isl_basic_set_list_add(*cells
, dom
);
7156 return *cells
? isl_stat_ok
: isl_stat_error
;
7159 /* Check that the elements of "list" are pairwise disjoint.
7161 static isl_stat
check_pairwise_disjoint(__isl_keep isl_basic_set_list
*list
)
7166 return isl_stat_error
;
7168 n
= isl_basic_set_list_n_basic_set(list
);
7169 for (i
= 0; i
< n
; ++i
) {
7170 isl_basic_set
*bset_i
;
7172 bset_i
= isl_basic_set_list_get_basic_set(list
, i
);
7173 for (j
= i
+ 1; j
< n
; ++j
) {
7174 isl_basic_set
*bset_j
;
7177 bset_j
= isl_basic_set_list_get_basic_set(list
, j
);
7178 disjoint
= isl_basic_set_is_disjoint(bset_i
, bset_j
);
7179 isl_basic_set_free(bset_j
);
7181 isl_die(isl_basic_set_list_get_ctx(list
),
7182 isl_error_unknown
, "not disjoint",
7184 if (disjoint
< 0 || !disjoint
)
7187 isl_basic_set_free(bset_i
);
7189 return isl_stat_error
;
7195 /* Check that the chambers computed by isl_vertices_foreach_disjoint_cell
7196 * are pairwise disjoint.
7198 static int test_chambers(isl_ctx
*ctx
)
7202 for (i
= 0; i
< ARRAY_SIZE(chambers_tests
); ++i
) {
7203 isl_basic_set
*bset
;
7204 isl_vertices
*vertices
;
7205 isl_basic_set_list
*cells
;
7208 bset
= isl_basic_set_read_from_str(ctx
, chambers_tests
[i
]);
7209 vertices
= isl_basic_set_compute_vertices(bset
);
7210 cells
= isl_basic_set_list_alloc(ctx
, 0);
7211 if (isl_vertices_foreach_disjoint_cell(vertices
, &add_cell
,
7213 cells
= isl_basic_set_list_free(cells
);
7214 ok
= check_pairwise_disjoint(cells
);
7215 isl_basic_set_list_free(cells
);
7216 isl_vertices_free(vertices
);
7217 isl_basic_set_free(bset
);
7228 int (*fn
)(isl_ctx
*ctx
);
7230 { "universe", &test_universe
},
7231 { "domain hash", &test_domain_hash
},
7232 { "dual", &test_dual
},
7233 { "dependence analysis", &test_flow
},
7234 { "val", &test_val
},
7235 { "compute divs", &test_compute_divs
},
7236 { "partial lexmin", &test_partial_lexmin
},
7237 { "simplify", &test_simplify
},
7238 { "curry", &test_curry
},
7239 { "piecewise multi affine expressions", &test_pw_multi_aff
},
7240 { "multi piecewise affine expressions", &test_multi_pw_aff
},
7241 { "conversion", &test_conversion
},
7242 { "list", &test_list
},
7243 { "align parameters", &test_align_parameters
},
7244 { "preimage", &test_preimage
},
7245 { "pullback", &test_pullback
},
7246 { "AST", &test_ast
},
7247 { "AST build", &test_ast_build
},
7248 { "AST generation", &test_ast_gen
},
7249 { "eliminate", &test_eliminate
},
7250 { "residue class", &test_residue_class
},
7251 { "div", &test_div
},
7252 { "slice", &test_slice
},
7253 { "fixed power", &test_fixed_power
},
7254 { "sample", &test_sample
},
7255 { "output", &test_output
},
7256 { "vertices", &test_vertices
},
7257 { "chambers", &test_chambers
},
7258 { "fixed", &test_fixed
},
7259 { "equal", &test_equal
},
7260 { "disjoint", &test_disjoint
},
7261 { "product", &test_product
},
7262 { "dim_max", &test_dim_max
},
7263 { "affine", &test_aff
},
7264 { "injective", &test_injective
},
7265 { "schedule (whole component)", &test_schedule_whole
},
7266 { "schedule (incremental)", &test_schedule_incremental
},
7267 { "schedule tree grouping", &test_schedule_tree_group
},
7268 { "tile", &test_tile
},
7269 { "union_pw", &test_union_pw
},
7270 { "eval", &test_eval
},
7271 { "parse", &test_parse
},
7272 { "single-valued", &test_sv
},
7273 { "affine hull", &test_affine_hull
},
7274 { "simple_hull", &test_simple_hull
},
7275 { "coalesce", &test_coalesce
},
7276 { "factorize", &test_factorize
},
7277 { "subset", &test_subset
},
7278 { "subtract", &test_subtract
},
7279 { "intersect", &test_intersect
},
7280 { "lexmin", &test_lexmin
},
7281 { "min", &test_min
},
7282 { "gist", &test_gist
},
7283 { "piecewise quasi-polynomials", &test_pwqp
},
7284 { "lift", &test_lift
},
7285 { "bound", &test_bound
},
7286 { "union", &test_union
},
7287 { "split periods", &test_split_periods
},
7288 { "lexicographic order", &test_lex
},
7289 { "bijectivity", &test_bijective
},
7290 { "dataflow analysis", &test_dep
},
7291 { "reading", &test_read
},
7292 { "bounded", &test_bounded
},
7293 { "construction", &test_construction
},
7294 { "dimension manipulation", &test_dim
},
7295 { "map application", &test_application
},
7296 { "convex hull", &test_convex_hull
},
7297 { "transitive closure", &test_closure
},
7300 int main(int argc
, char **argv
)
7303 struct isl_ctx
*ctx
;
7304 struct isl_options
*options
;
7306 options
= isl_options_new_with_defaults();
7308 argc
= isl_options_parse(options
, argc
, argv
, ISL_ARG_ALL
);
7310 ctx
= isl_ctx_alloc_with_options(&isl_options_args
, options
);
7311 for (i
= 0; i
< ARRAY_SIZE(tests
); ++i
) {
7312 printf("%s\n", tests
[i
].name
);
7313 if (tests
[i
].fn(ctx
) < 0)