3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
22 The source of C<isl> can be obtained either as a tarball
23 or from the git repository. Both are available from
24 L<http://freshmeat.net/projects/isl/>.
25 The installation process depends on how you obtained
28 =head2 Installation from the git repository
32 =item 1 Clone or update the repository
34 The first time the source is obtained, you need to clone
37 git clone git://repo.or.cz/isl.git
39 To obtain updates, you need to pull in the latest changes
43 =item 2 Get submodule (optional)
45 C<isl> can optionally use the C<piplib> library and provides
46 this library as a submodule. If you want to use it, then
47 after you have cloned C<isl>, you need to grab the submodules
52 To obtain updates, you only need
56 Note that C<isl> currently does not use any C<piplib>
57 functionality by default.
59 =item 3 Generate C<configure>
65 After performing the above steps, continue
66 with the L<Common installation instructions>.
68 =head2 Common installation instructions
74 Building C<isl> requires C<GMP>, including its headers files.
75 Your distribution may not provide these header files by default
76 and you may need to install a package called C<gmp-devel> or something
77 similar. Alternatively, C<GMP> can be built from
78 source, available from L<http://gmplib.org/>.
82 C<isl> uses the standard C<autoconf> C<configure> script.
87 optionally followed by some configure options.
88 A complete list of options can be obtained by running
92 Below we discuss some of the more common options.
94 C<isl> can optionally use C<piplib>, but no
95 C<piplib> functionality is currently used by default.
96 The C<--with-piplib> option can
97 be used to specify which C<piplib>
98 library to use, either an installed version (C<system>),
99 an externally built version (C<build>), a bundled version (C<bundled>)
100 or no version (C<no>). The option C<build> is mostly useful
101 in C<configure> scripts of larger projects that bundle both C<isl>
108 Installation prefix for C<isl>
110 =item C<--with-gmp-prefix>
112 Installation prefix for C<GMP> (architecture-independent files).
114 =item C<--with-gmp-exec-prefix>
116 Installation prefix for C<GMP> (architecture-dependent files).
118 =item C<--with-piplib>
120 Which copy of C<piplib> to use, either C<no> (default), C<system>, C<build>
121 or C<bundled>. Note that C<bundled> only works if you have obtained
122 C<isl> and its submodules from the git repository.
124 =item C<--with-piplib-prefix>
126 Installation prefix for C<system> C<piplib> (architecture-independent files).
128 =item C<--with-piplib-exec-prefix>
130 Installation prefix for C<system> C<piplib> (architecture-dependent files).
132 =item C<--with-piplib-builddir>
134 Location where C<build> C<piplib> was built.
142 =item 4 Install (optional)
150 =head2 Initialization
152 All manipulations of integer sets and relations occur within
153 the context of an C<isl_ctx>.
154 A given C<isl_ctx> can only be used within a single thread.
155 All arguments of a function are required to have been allocated
156 within the same context.
157 There are currently no functions available for moving an object
158 from one C<isl_ctx> to another C<isl_ctx>. This means that
159 there is currently no way of safely moving an object from one
160 thread to another, unless the whole C<isl_ctx> is moved.
162 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
163 freed using C<isl_ctx_free>.
164 All objects allocated within an C<isl_ctx> should be freed
165 before the C<isl_ctx> itself is freed.
167 isl_ctx *isl_ctx_alloc();
168 void isl_ctx_free(isl_ctx *ctx);
172 All operations on integers, mainly the coefficients
173 of the constraints describing the sets and relations,
174 are performed in exact integer arithmetic using C<GMP>.
175 However, to allow future versions of C<isl> to optionally
176 support fixed integer arithmetic, all calls to C<GMP>
177 are wrapped inside C<isl> specific macros.
178 The basic type is C<isl_int> and the following operations
179 are available on this type.
180 The meanings of these operations are essentially the same
181 as their C<GMP> C<mpz_> counterparts.
182 As always with C<GMP> types, C<isl_int>s need to be
183 initialized with C<isl_int_init> before they can be used
184 and they need to be released with C<isl_int_clear>
189 =item isl_int_init(i)
191 =item isl_int_clear(i)
193 =item isl_int_set(r,i)
195 =item isl_int_set_si(r,i)
197 =item isl_int_abs(r,i)
199 =item isl_int_neg(r,i)
201 =item isl_int_swap(i,j)
203 =item isl_int_swap_or_set(i,j)
205 =item isl_int_add_ui(r,i,j)
207 =item isl_int_sub_ui(r,i,j)
209 =item isl_int_add(r,i,j)
211 =item isl_int_sub(r,i,j)
213 =item isl_int_mul(r,i,j)
215 =item isl_int_mul_ui(r,i,j)
217 =item isl_int_addmul(r,i,j)
219 =item isl_int_submul(r,i,j)
221 =item isl_int_gcd(r,i,j)
223 =item isl_int_lcm(r,i,j)
225 =item isl_int_divexact(r,i,j)
227 =item isl_int_cdiv_q(r,i,j)
229 =item isl_int_fdiv_q(r,i,j)
231 =item isl_int_fdiv_r(r,i,j)
233 =item isl_int_fdiv_q_ui(r,i,j)
235 =item isl_int_read(r,s)
237 =item isl_int_print(out,i,width)
241 =item isl_int_cmp(i,j)
243 =item isl_int_cmp_si(i,si)
245 =item isl_int_eq(i,j)
247 =item isl_int_ne(i,j)
249 =item isl_int_lt(i,j)
251 =item isl_int_le(i,j)
253 =item isl_int_gt(i,j)
255 =item isl_int_ge(i,j)
257 =item isl_int_abs_eq(i,j)
259 =item isl_int_abs_ne(i,j)
261 =item isl_int_abs_lt(i,j)
263 =item isl_int_abs_gt(i,j)
265 =item isl_int_abs_ge(i,j)
267 =item isl_int_is_zero(i)
269 =item isl_int_is_one(i)
271 =item isl_int_is_negone(i)
273 =item isl_int_is_pos(i)
275 =item isl_int_is_neg(i)
277 =item isl_int_is_nonpos(i)
279 =item isl_int_is_nonneg(i)
281 =item isl_int_is_divisible_by(i,j)
285 =head2 Sets and Relations
287 C<isl> uses four types of objects for representing sets and relations,
288 C<isl_basic_set>, C<isl_basic_map>, C<isl_set> and C<isl_map>.
289 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
290 can be described as a conjunction of affine constraints, while
291 C<isl_set> and C<isl_map> represent unions of
292 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
293 The difference between sets and relations (maps) is that sets have
294 one set of variables, while relations have two sets of variables,
295 input variables and output variables.
297 =head2 Memory Management
299 Since a high-level operation on sets and/or relations usually involves
300 several substeps and since the user is usually not interested in
301 the intermediate results, most functions that return a new object
302 will also release all the objects passed as arguments.
303 If the user still wants to use one or more of these arguments
304 after the function call, she should pass along a copy of the
305 object rather than the object itself.
306 The user is then responsible for make sure that the original
307 object gets used somewhere else or is explicitly freed.
309 The arguments and return values of all documents functions are
310 annotated to make clear which arguments are released and which
311 arguments are preserved. In particular, the following annotations
318 C<__isl_give> means that a new object is returned.
319 The user should make sure that the returned pointer is
320 used exactly once as a value for an C<__isl_take> argument.
321 In between, it can be used as a value for as many
322 C<__isl_keep> arguments as the user likes.
323 There is one exception, and that is the case where the
324 pointer returned is C<NULL>. Is this case, the user
325 is free to use it as an C<__isl_take> argument or not.
329 C<__isl_take> means that the object the argument points to
330 is taken over by the function and may no longer be used
331 by the user as an argument to any other function.
332 The pointer value must be one returned by a function
333 returning an C<__isl_give> pointer.
334 If the user passes in a C<NULL> value, then this will
335 be treated as an error in the sense that the function will
336 not perform its usual operation. However, it will still
337 make sure that all the the other C<__isl_take> arguments
342 C<__isl_keep> means that the function will only use the object
343 temporarily. After the function has finished, the user
344 can still use it as an argument to other functions.
345 A C<NULL> value will be treated in the same way as
346 a C<NULL> value for an C<__isl_take> argument.
350 =head2 Dimension Specifications
352 Whenever a new set or relation is created from scratch,
353 its dimension needs to be specified using an C<isl_dim>.
356 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
357 unsigned nparam, unsigned n_in, unsigned n_out);
358 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
359 unsigned nparam, unsigned dim);
360 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
361 void isl_dim_free(__isl_take isl_dim *dim);
362 unsigned isl_dim_size(__isl_keep isl_dim *dim,
363 enum isl_dim_type type);
365 The dimension specification used for creating a set
366 needs to be created using C<isl_dim_set_alloc>, while
367 that for creating a relation
368 needs to be created using C<isl_dim_alloc>.
369 C<isl_dim_size> can be used
370 to find out the number of dimensions of each type in
371 a dimension specification, where type may be
372 C<isl_dim_param>, C<isl_dim_in> (only for relations),
373 C<isl_dim_out> (only for relations), C<isl_dim_set>
374 (only for sets) or C<isl_dim_all>.
376 =head2 Input and Output
378 C<isl> supports its own input/output format, which is similar
379 to the C<Omega> format, but also supports the C<PolyLib> format
384 The C<isl> format is similar to that of C<Omega>, but has a different
385 syntax for describing the parameters and allows for the definition
386 of an existentially quantified variable as the integer division
387 of an affine expression.
388 For example, the set of integers C<i> between C<0> and C<n>
389 such that C<i % 10 <= 6> can be described as
391 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
394 A set or relation can have several disjuncts, separated
395 by the keyword C<or>. Each disjunct is either a conjunction
396 of constraints or a projection (C<exists>) of a conjunction
397 of constraints. The constraints are separated by the keyword
400 =head3 C<PolyLib> format
402 If the represented set is a union, then the first line
403 contains a single number representing the number of disjuncts.
404 Otherwise, a line containing the number C<1> is optional.
406 Each disjunct is represented by a matrix of constraints.
407 The first line contains two numbers representing
408 the number of rows and columns,
409 where the number of rows is equal to the number of constraints
410 and the number of columns is equal to two plus the number of variables.
411 The following lines contain the actual rows of the constraint matrix.
412 In each row, the first column indicates whether the constraint
413 is an equality (C<0>) or inequality (C<1>). The final column
414 corresponds to the constant term.
416 If the set is parametric, then the coefficients of the parameters
417 appear in the last columns before the constant column.
418 The coefficients of any existentially quantified variables appear
419 between those of the set variables and those of the parameters.
424 __isl_give isl_basic_set *isl_basic_set_read_from_file(
425 isl_ctx *ctx, FILE *input, int nparam);
426 __isl_give isl_basic_set *isl_basic_set_read_from_str(
427 isl_ctx *ctx, const char *str, int nparam);
428 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
429 FILE *input, int nparam);
430 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
431 const char *str, int nparam);
434 __isl_give isl_basic_map *isl_basic_map_read_from_file(
435 isl_ctx *ctx, FILE *input, int nparam);
436 __isl_give isl_basic_map *isl_basic_map_read_from_str(
437 isl_ctx *ctx, const char *str, int nparam);
438 __isl_give isl_map *isl_map_read_from_file(
439 struct isl_ctx *ctx, FILE *input, int nparam);
440 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
441 const char *str, int nparam);
443 The input format is autodetected and may be either the C<PolyLib> format
444 or the C<isl> format.
445 C<nparam> specifies how many of the final columns in
446 the C<PolyLib> format correspond to parameters.
447 If input is given in the C<isl> format, then the number
448 of parameters needs to be equal to C<nparam>.
449 If C<nparam> is negative, then any number of parameters
450 is accepted in the C<isl> format and zero parameters
451 are assumed in the C<PolyLib> format.
456 void isl_basic_set_print(__isl_keep isl_basic_set *bset,
457 FILE *out, int indent,
458 const char *prefix, const char *suffix,
459 unsigned output_format);
460 void isl_set_print(__isl_keep struct isl_set *set,
461 FILE *out, int indent, unsigned output_format);
464 void isl_basic_map_print(__isl_keep isl_basic_map *bmap,
465 FILE *out, int indent,
466 const char *prefix, const char *suffix,
467 unsigned output_format);
468 void isl_map_print(__isl_keep struct isl_map *map,
469 FILE *out, int indent, unsigned output_format);
471 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
472 or C<ISL_FORMAT_POLYLIB>.
473 Each line in the output is indented by C<indent> spaces,
474 prefixed by C<prefix> and suffixed by C<suffix>.
475 In the C<PolyLib> format output,
476 the coefficients of the existentially quantified variables
477 appear between those of the set variables and those
480 =head2 Creating New Sets and Relations
482 C<isl> has functions for creating some standard sets and relations.
486 =item * Empty sets and relations
488 __isl_give isl_basic_set *isl_basic_set_empty(
489 __isl_take isl_dim *dim);
490 __isl_give isl_basic_map *isl_basic_map_empty(
491 __isl_take isl_dim *dim);
492 __isl_give isl_set *isl_set_empty(
493 __isl_take isl_dim *dim);
494 __isl_give isl_map *isl_map_empty(
495 __isl_take isl_dim *dim);
497 =item * Universe sets and relations
499 __isl_give isl_basic_set *isl_basic_set_universe(
500 __isl_take isl_dim *dim);
501 __isl_give isl_basic_map *isl_basic_map_universe(
502 __isl_take isl_dim *dim);
503 __isl_give isl_set *isl_set_universe(
504 __isl_take isl_dim *dim);
505 __isl_give isl_map *isl_map_universe(
506 __isl_take isl_dim *dim);
508 =item * Identity relations
510 __isl_give isl_basic_map *isl_basic_map_identity(
511 __isl_take isl_dim *set_dim);
512 __isl_give isl_map *isl_map_identity(
513 __isl_take isl_dim *set_dim);
515 These functions take a dimension specification for a B<set>
516 and return an identity relation between two such sets.
518 =item * Lexicographic order
520 __isl_give isl_map *isl_map_lex_lt(
521 __isl_take isl_dim *set_dim);
522 __isl_give isl_map *isl_map_lex_le(
523 __isl_take isl_dim *set_dim);
524 __isl_give isl_map *isl_map_lex_gt(
525 __isl_take isl_dim *set_dim);
526 __isl_give isl_map *isl_map_lex_ge(
527 __isl_take isl_dim *set_dim);
529 These functions take a dimension specification for a B<set>
530 and return relations that express that the elements in the domain
531 are lexicographically less
532 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
533 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
534 than the elements in the range.
538 A basic set or relation can be converted to a set or relation
539 using the following functions.
541 __isl_give isl_set *isl_set_from_basic_set(
542 __isl_take isl_basic_set *bset);
543 __isl_give isl_map *isl_map_from_basic_map(
544 __isl_take isl_basic_map *bmap);
546 Sets and relations can be copied and freed again using the following
549 __isl_give isl_basic_set *isl_basic_set_copy(
550 __isl_keep isl_basic_set *bset);
551 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
552 __isl_give isl_basic_map *isl_basic_map_copy(
553 __isl_keep isl_basic_map *bmap);
554 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
555 void isl_basic_set_free(__isl_take isl_basic_set *bset);
556 void isl_set_free(__isl_take isl_set *set);
557 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
558 void isl_map_free(__isl_take isl_map *map);
560 Other sets and relations can be constructed by starting
561 from a universe set or relation, adding equality and/or
562 inequality constraints and then projecting out the
563 existentially quantified variables, if any.
564 Constraints can be constructed, manipulated and
565 added to basic sets and relations using the following functions.
567 #include <isl_constraint.h>
568 __isl_give isl_constraint *isl_equality_alloc(
569 __isl_take isl_dim *dim);
570 __isl_give isl_constraint *isl_inequality_alloc(
571 __isl_take isl_dim *dim);
572 void isl_constraint_set_constant(
573 __isl_keep isl_constraint *constraint, isl_int v);
574 void isl_constraint_set_coefficient(
575 __isl_keep isl_constraint *constraint,
576 enum isl_dim_type type, int pos, isl_int v);
577 __isl_give isl_basic_map *isl_basic_map_add_constraint(
578 __isl_take isl_basic_map *bmap,
579 __isl_take isl_constraint *constraint);
580 __isl_give isl_basic_set *isl_basic_set_add_constraint(
581 __isl_take isl_basic_set *bset,
582 __isl_take isl_constraint *constraint);
584 For example, to create a set containing the even integers
585 between 10 and 42, you would use the following code.
589 struct isl_constraint *c;
590 struct isl_basic_set *bset;
593 dim = isl_dim_set_alloc(ctx, 0, 2);
594 bset = isl_basic_set_universe(isl_dim_copy(dim));
596 c = isl_equality_alloc(isl_dim_copy(dim));
597 isl_int_set_si(v, -1);
598 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
599 isl_int_set_si(v, 2);
600 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
601 bset = isl_basic_set_add_constraint(bset, c);
603 c = isl_inequality_alloc(isl_dim_copy(dim));
604 isl_int_set_si(v, -10);
605 isl_constraint_set_constant(c, v);
606 isl_int_set_si(v, 1);
607 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
608 bset = isl_basic_set_add_constraint(bset, c);
610 c = isl_inequality_alloc(dim);
611 isl_int_set_si(v, 42);
612 isl_constraint_set_constant(c, v);
613 isl_int_set_si(v, -1);
614 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
615 bset = isl_basic_set_add_constraint(bset, c);
617 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
623 struct isl_basic_set *bset;
624 bset = isl_basic_set_read_from_str(ctx,
625 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
629 =head3 Unary Properties
635 The following functions test whether the given set or relation
636 contains any integer points. The ``fast'' variants do not perform
637 any computations, but simply check if the given set or relation
638 is already known to be empty.
640 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
641 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
642 int isl_set_is_empty(__isl_keep isl_set *set);
643 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
644 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
645 int isl_map_fast_is_empty(__isl_keep isl_map *map);
646 int isl_map_is_empty(__isl_keep isl_map *map);
650 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
651 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
655 =head3 Binary Properties
661 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
662 __isl_keep isl_set *set2);
663 int isl_set_is_equal(__isl_keep isl_set *set1,
664 __isl_keep isl_set *set2);
665 int isl_map_is_equal(__isl_keep isl_map *map1,
666 __isl_keep isl_map *map2);
667 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
668 __isl_keep isl_map *map2);
669 int isl_basic_map_is_equal(
670 __isl_keep isl_basic_map *bmap1,
671 __isl_keep isl_basic_map *bmap2);
675 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
676 __isl_keep isl_set *set2);
680 int isl_set_is_subset(__isl_keep isl_set *set1,
681 __isl_keep isl_set *set2);
682 int isl_set_is_strict_subset(
683 __isl_keep isl_set *set1,
684 __isl_keep isl_set *set2);
685 int isl_basic_map_is_subset(
686 __isl_keep isl_basic_map *bmap1,
687 __isl_keep isl_basic_map *bmap2);
688 int isl_basic_map_is_strict_subset(
689 __isl_keep isl_basic_map *bmap1,
690 __isl_keep isl_basic_map *bmap2);
691 int isl_map_is_subset(
692 __isl_keep isl_map *map1,
693 __isl_keep isl_map *map2);
694 int isl_map_is_strict_subset(
695 __isl_keep isl_map *map1,
696 __isl_keep isl_map *map2);
700 =head2 Unary Operations
706 __isl_give isl_basic_set *isl_basic_set_project_out(
707 __isl_take isl_basic_set *bset,
708 enum isl_dim_type type, unsigned first, unsigned n);
709 __isl_give isl_basic_map *isl_basic_map_project_out(
710 __isl_take isl_basic_map *bmap,
711 enum isl_dim_type type, unsigned first, unsigned n);
712 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
713 enum isl_dim_type type, unsigned first, unsigned n);
714 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
715 enum isl_dim_type type, unsigned first, unsigned n);
716 __isl_give isl_basic_set *isl_basic_map_domain(
717 __isl_take isl_basic_map *bmap);
718 __isl_give isl_basic_set *isl_basic_map_range(
719 __isl_take isl_basic_map *bmap);
720 __isl_give isl_set *isl_map_domain(
721 __isl_take isl_map *bmap);
722 __isl_give isl_set *isl_map_range(
723 __isl_take isl_map *map);
727 Simplify the representation of a set or relation by trying
728 to combine pairs of basic sets or relations into a single
729 basic set or relation.
731 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
732 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
736 __isl_give isl_basic_set *isl_set_convex_hull(
737 __isl_take isl_set *set);
738 __isl_give isl_basic_map *isl_map_convex_hull(
739 __isl_take isl_map *map);
741 If the input set or relation has any existentially quantified
742 variables, then the result of these operations is currently undefined.
746 __isl_give isl_basic_set *isl_basic_set_affine_hull(
747 __isl_take isl_basic_set *bset);
748 __isl_give isl_basic_set *isl_set_affine_hull(
749 __isl_take isl_set *set);
750 __isl_give isl_basic_map *isl_basic_map_affine_hull(
751 __isl_take isl_basic_map *bmap);
752 __isl_give isl_basic_map *isl_map_affine_hull(
753 __isl_take isl_map *map);
757 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
758 unsigned param, int *exact);
760 Compute a parametric representation for all positive powers I<k> of C<map>.
761 The power I<k> is equated to the parameter at position C<param>.
762 The result may be an overapproximation. If the result is exact,
763 then C<*exact> is set to C<1>.
764 The current implementation only produces exact results for particular
765 cases of piecewise translations (i.e., piecewise uniform dependences).
767 =item * Transitive closure
769 __isl_give isl_map *isl_map_transitive_closure(
770 __isl_take isl_map *map, int *exact);
772 Compute the transitive closure of C<map>.
773 The result may be an overapproximation. If the result is known to be exact,
774 then C<*exact> is set to C<1>.
775 The current implementation only produces exact results for particular
776 cases of piecewise translations (i.e., piecewise uniform dependences).
780 =head2 Binary Operations
782 The two arguments of a binary operation not only need to live
783 in the same C<isl_ctx>, they currently also need to have
784 the same (number of) parameters.
786 =head3 Basic Operations
792 __isl_give isl_basic_set *isl_basic_set_intersect(
793 __isl_take isl_basic_set *bset1,
794 __isl_take isl_basic_set *bset2);
795 __isl_give isl_set *isl_set_intersect(
796 __isl_take isl_set *set1,
797 __isl_take isl_set *set2);
798 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
799 __isl_take isl_basic_map *bmap,
800 __isl_take isl_basic_set *bset);
801 __isl_give isl_basic_map *isl_basic_map_intersect_range(
802 __isl_take isl_basic_map *bmap,
803 __isl_take isl_basic_set *bset);
804 __isl_give isl_basic_map *isl_basic_map_intersect(
805 __isl_take isl_basic_map *bmap1,
806 __isl_take isl_basic_map *bmap2);
807 __isl_give isl_map *isl_map_intersect_domain(
808 __isl_take isl_map *map,
809 __isl_take isl_set *set);
810 __isl_give isl_map *isl_map_intersect_range(
811 __isl_take isl_map *map,
812 __isl_take isl_set *set);
813 __isl_give isl_map *isl_map_intersect(
814 __isl_take isl_map *map1,
815 __isl_take isl_map *map2);
819 __isl_give isl_set *isl_basic_set_union(
820 __isl_take isl_basic_set *bset1,
821 __isl_take isl_basic_set *bset2);
822 __isl_give isl_map *isl_basic_map_union(
823 __isl_take isl_basic_map *bmap1,
824 __isl_take isl_basic_map *bmap2);
825 __isl_give isl_set *isl_set_union(
826 __isl_take isl_set *set1,
827 __isl_take isl_set *set2);
828 __isl_give isl_map *isl_map_union(
829 __isl_take isl_map *map1,
830 __isl_take isl_map *map2);
832 =item * Set difference
834 __isl_give isl_set *isl_set_subtract(
835 __isl_take isl_set *set1,
836 __isl_take isl_set *set2);
837 __isl_give isl_map *isl_map_subtract(
838 __isl_take isl_map *map1,
839 __isl_take isl_map *map2);
843 __isl_give isl_basic_set *isl_basic_set_apply(
844 __isl_take isl_basic_set *bset,
845 __isl_take isl_basic_map *bmap);
846 __isl_give isl_set *isl_set_apply(
847 __isl_take isl_set *set,
848 __isl_take isl_map *map);
849 __isl_give isl_basic_map *isl_basic_map_apply_domain(
850 __isl_take isl_basic_map *bmap1,
851 __isl_take isl_basic_map *bmap2);
852 __isl_give isl_basic_map *isl_basic_map_apply_range(
853 __isl_take isl_basic_map *bmap1,
854 __isl_take isl_basic_map *bmap2);
855 __isl_give isl_map *isl_map_apply_domain(
856 __isl_take isl_map *map1,
857 __isl_take isl_map *map2);
858 __isl_give isl_map *isl_map_apply_range(
859 __isl_take isl_map *map1,
860 __isl_take isl_map *map2);
864 =head3 Lexicographic Optimization
866 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
867 the following functions
868 compute a set that contains the lexicographic minimum or maximum
869 of the elements in C<set> (or C<bset>) for those values of the parameters
871 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
872 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
874 In other words, the union of the parameter values
875 for which the result is non-empty and of C<*empty>
878 __isl_give isl_set *isl_basic_set_partial_lexmin(
879 __isl_take isl_basic_set *bset,
880 __isl_take isl_basic_set *dom,
881 __isl_give isl_set **empty);
882 __isl_give isl_set *isl_basic_set_partial_lexmax(
883 __isl_take isl_basic_set *bset,
884 __isl_take isl_basic_set *dom,
885 __isl_give isl_set **empty);
886 __isl_give isl_set *isl_set_partial_lexmin(
887 __isl_take isl_set *set, __isl_take isl_set *dom,
888 __isl_give isl_set **empty);
889 __isl_give isl_set *isl_set_partial_lexmax(
890 __isl_take isl_set *set, __isl_take isl_set *dom,
891 __isl_give isl_set **empty);
893 Given a (basic) set C<set> (or C<bset>), the following functions simply
894 return a set containing the lexicographic minimum or maximum
895 of the elements in C<set> (or C<bset>).
897 __isl_give isl_set *isl_basic_set_lexmin(
898 __isl_take isl_basic_set *bset);
899 __isl_give isl_set *isl_basic_set_lexmax(
900 __isl_take isl_basic_set *bset);
901 __isl_give isl_set *isl_set_lexmin(
902 __isl_take isl_set *set);
903 __isl_give isl_set *isl_set_lexmax(
904 __isl_take isl_set *set);
906 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
907 the following functions
908 compute a relation that maps each element of C<dom>
909 to the single lexicographic minimum or maximum
910 of the elements that are associated to that same
911 element in C<map> (or C<bmap>).
912 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
913 that contains the elements in C<dom> that do not map
914 to any elements in C<map> (or C<bmap>).
915 In other words, the union of the domain of the result and of C<*empty>
918 __isl_give isl_map *isl_basic_map_partial_lexmax(
919 __isl_take isl_basic_map *bmap,
920 __isl_take isl_basic_set *dom,
921 __isl_give isl_set **empty);
922 __isl_give isl_map *isl_basic_map_partial_lexmin(
923 __isl_take isl_basic_map *bmap,
924 __isl_take isl_basic_set *dom,
925 __isl_give isl_set **empty);
926 __isl_give isl_map *isl_map_partial_lexmax(
927 __isl_take isl_map *map, __isl_take isl_set *dom,
928 __isl_give isl_set **empty);
929 __isl_give isl_map *isl_map_partial_lexmin(
930 __isl_take isl_map *map, __isl_take isl_set *dom,
931 __isl_give isl_set **empty);
933 Given a (basic) map C<map> (or C<bmap>), the following functions simply
934 return a map mapping each element in the domain of
935 C<map> (or C<bmap>) to the lexicographic minimum or maximum
936 of all elements associated to that element.
938 __isl_give isl_map *isl_basic_map_lexmin(
939 __isl_take isl_basic_map *bmap);
940 __isl_give isl_map *isl_basic_map_lexmax(
941 __isl_take isl_basic_map *bmap);
942 __isl_give isl_map *isl_map_lexmin(
943 __isl_take isl_map *map);
944 __isl_give isl_map *isl_map_lexmax(
945 __isl_take isl_map *map);
947 =head2 Dependence Analysis
949 C<isl> contains specialized functionality for performing
950 array dataflow analysis. That is, given a I<sink> access relation
951 and a collection of possible I<source> access relations,
952 C<isl> can compute relations that describe
953 for each iteration of the sink access, which iteration
954 of which of the source access relations was the last
955 to access the same data element before the given iteration
957 To compute standard flow dependences, the sink should be
958 a read, while the sources should be writes.
960 #include <isl_flow.h>
962 __isl_give isl_access_info *isl_access_info_alloc(
963 __isl_take isl_map *sink,
964 void *sink_user, isl_access_level_before fn,
966 __isl_give isl_access_info *isl_access_info_add_source(
967 __isl_take isl_access_info *acc,
968 __isl_take isl_map *source, void *source_user);
970 __isl_give isl_flow *isl_access_info_compute_flow(
971 __isl_take isl_access_info *acc);
973 int isl_flow_foreach(__isl_keep isl_flow *deps,
974 int (*fn)(__isl_take isl_map *dep, void *dep_user,
977 __isl_give isl_set *isl_flow_get_no_source(
978 __isl_keep isl_flow *deps);
979 void isl_flow_free(__isl_take isl_flow *deps);
981 The function C<isl_access_info_compute_flow> performs the actual
982 dependence analysis. The other functions are used to construct
983 the input for this function or to read off the output.
985 The input is collected in an C<isl_access_info>, which can
986 be created through a call to C<isl_access_info_alloc>.
987 The arguments to this functions are the sink access relation
988 C<sink>, a token C<sink_user> used to identify the sink
989 access to the user, a callback function for specifying the
990 relative order of source and sink accesses, and the number
991 of source access relations that will be added.
992 The callback function has type C<int (*)(void *first, void *second)>.
993 The function is called with two user supplied tokens identifying
994 either a source or the sink and it should return the shared nesting
995 level and the relative order of the two accesses.
996 In particular, let I<n> be the number of loops shared by
997 the two accesses. If C<first> precedes C<second> textually,
998 then the function should return I<2 * n + 1>; otherwise,
999 it should return I<2 * n>.
1000 The sources can be added to the C<isl_access_info> by performing
1001 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1002 The C<source_user> token is again used to identify
1003 the source access. The range of the source access relation
1004 C<source> should have the same dimension as the range
1005 of the sink access relation.
1007 The result of the dependence analysis is collected in an
1008 C<isl_flow>. There may be elements in the domain of
1009 the sink access for which no preceding source access could be
1010 find. The set of these elements can be obtained through
1011 a call to C<isl_flow_get_no_source>.
1012 In the case of standard flow dependence analysis,
1013 this set corresponds to the reads from uninitialized
1015 The actual flow dependences can be extracted using
1016 C<isl_flow_foreach>. This function will call the user-specified
1017 callback function C<fn> for each B<non-empty> dependence between
1018 a source and the sink. The callback function is called
1019 with three arguments, the actual flow dependence relation
1020 mapping source iterations to sink iterations, a token
1021 identifying the source and an additional C<void *> with value
1022 equal to the third argument of the C<isl_flow_foreach> call.
1024 After finishing with an C<isl_flow>, the user should call
1025 C<isl_flow_free> to free all associated memory.
1029 Although C<isl> is mainly meant to be used as a library,
1030 it also contains some basic applications that use some
1031 of the functionality of C<isl>.
1032 The input may specified either in the L<isl format>
1033 or the L<PolyLib format>.
1035 =head2 C<isl_polyhedron_sample>
1037 C<isl_polyhedron_sample> takes a polyhedron as input and prints
1038 an integer element of the polyhedron, if there is any.
1039 The first column in the output is the denominator and is always
1040 equal to 1. If the polyhedron contains no integer points,
1041 then a vector of length zero is printed.
1045 C<isl_pip> takes the same input as the C<example> program
1046 from the C<piplib> distribution, i.e., a set of constraints
1047 on the parameters, a line contains only -1 and finally a set
1048 of constraints on a parametric polyhedron.
1049 The coefficients of the parameters appear in the last columns
1050 (but before the final constant column).
1051 The output is the lexicographic minimum of the parametric polyhedron.
1052 As C<isl> currently does not have its own output format, the output
1053 is just a dump of the internal state.
1055 =head2 C<isl_polyhedron_minimize>
1057 C<isl_polyhedron_minimize> computes the minimum of some linear
1058 or affine objective function over the integer points in a polyhedron.
1059 If an affine objective function
1060 is given, then the constant should appear in the last column.
1062 =head2 C<isl_polytope_scan>
1064 Given a polytope, C<isl_polytope_scan> prints
1065 all integer points in the polytope.
1067 =head1 C<isl-polylib>
1069 The C<isl-polylib> library provides the following functions for converting
1070 between C<isl> objects and C<PolyLib> objects.
1071 The library is distributed separately for licensing reasons.
1073 #include <isl_set_polylib.h>
1074 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
1075 Polyhedron *P, __isl_take isl_dim *dim);
1076 Polyhedron *isl_basic_set_to_polylib(
1077 __isl_keep isl_basic_set *bset);
1078 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
1079 __isl_take isl_dim *dim);
1080 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
1082 #include <isl_map_polylib.h>
1083 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
1084 Polyhedron *P, __isl_take isl_dim *dim);
1085 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
1086 __isl_take isl_dim *dim);
1087 Polyhedron *isl_basic_map_to_polylib(
1088 __isl_keep isl_basic_map *bmap);
1089 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);