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.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
477 __isl_keep isl_pw_qpolynomial *pwqp);
478 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
479 __isl_keep isl_union_pw_qpolynomial *upwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
481 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
484 __isl_give isl_dim *isl_aff_get_dim(
485 __isl_keep isl_aff *aff);
487 The names of the individual dimensions may be set or read off
488 using the following functions.
491 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
492 enum isl_dim_type type, unsigned pos,
493 __isl_keep const char *name);
494 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
495 enum isl_dim_type type, unsigned pos);
497 Note that C<isl_dim_get_name> returns a pointer to some internal
498 data structure, so the result can only be used while the
499 corresponding C<isl_dim> is alive.
500 Also note that every function that operates on two sets or relations
501 requires that both arguments have the same parameters. This also
502 means that if one of the arguments has named parameters, then the
503 other needs to have named parameters too and the names need to match.
504 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
505 have different parameters (as long as they are named), in which case
506 the result will have as parameters the union of the parameters of
509 The names of entire spaces may be set or read off
510 using the following functions.
513 __isl_give isl_dim *isl_dim_set_tuple_name(
514 __isl_take isl_dim *dim,
515 enum isl_dim_type type, const char *s);
516 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
517 enum isl_dim_type type);
519 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
520 or C<isl_dim_set>. As with C<isl_dim_get_name>,
521 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
523 Binary operations require the corresponding spaces of their arguments
524 to have the same name.
526 Spaces can be nested. In particular, the domain of a set or
527 the domain or range of a relation can be a nested relation.
528 The following functions can be used to construct and deconstruct
529 such nested dimension specifications.
532 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
533 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
534 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
536 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
537 be the dimension specification of a set, while that of
538 C<isl_dim_wrap> should be the dimension specification of a relation.
539 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
540 of a relation, while that of C<isl_dim_wrap> is the dimension specification
543 Dimension specifications can be created from other dimension
544 specifications using the following functions.
546 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
547 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
548 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
549 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
550 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
551 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
552 __isl_take isl_dim *right);
553 __isl_give isl_dim *isl_dim_align_params(
554 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
555 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
556 enum isl_dim_type type, unsigned pos, unsigned n);
557 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
558 enum isl_dim_type type, unsigned n);
559 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
560 enum isl_dim_type type, unsigned first, unsigned n);
561 __isl_give isl_dim *isl_dim_map_from_set(
562 __isl_take isl_dim *dim);
563 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
565 Note that if dimensions are added or removed from a space, then
566 the name and the internal structure are lost.
570 A local space is essentially a dimension specification with
571 zero or more existentially quantified variables.
572 The local space of a basic set or relation can be obtained
573 using the following functions.
576 __isl_give isl_local_space *isl_basic_set_get_local_space(
577 __isl_keep isl_basic_set *bset);
580 __isl_give isl_local_space *isl_basic_map_get_local_space(
581 __isl_keep isl_basic_map *bmap);
583 A new local space can be created from a dimension specification using
585 #include <isl/local_space.h>
586 __isl_give isl_local_space *isl_local_space_from_dim(
587 __isl_take isl_dim *dim);
589 They can be inspected, copied and freed using the following functions.
591 #include <isl/local_space.h>
592 isl_ctx *isl_local_space_get_ctx(
593 __isl_keep isl_local_space *ls);
594 int isl_local_space_dim(__isl_keep isl_local_space *ls,
595 enum isl_dim_type type);
596 const char *isl_local_space_get_dim_name(
597 __isl_keep isl_local_space *ls,
598 enum isl_dim_type type, unsigned pos);
599 __isl_give isl_dim *isl_local_space_get_dim(
600 __isl_keep isl_local_space *ls);
601 __isl_give isl_div *isl_local_space_get_div(
602 __isl_keep isl_local_space *ls, int pos);
603 __isl_give isl_local_space *isl_local_space_copy(
604 __isl_keep isl_local_space *ls);
605 void *isl_local_space_free(__isl_take isl_local_space *ls);
607 Local spaces can be created from other local spaces
608 using the following function.
610 __isl_give isl_local_space *isl_local_space_from_domain(
611 __isl_take isl_local_space *ls);
613 =head2 Input and Output
615 C<isl> supports its own input/output format, which is similar
616 to the C<Omega> format, but also supports the C<PolyLib> format
621 The C<isl> format is similar to that of C<Omega>, but has a different
622 syntax for describing the parameters and allows for the definition
623 of an existentially quantified variable as the integer division
624 of an affine expression.
625 For example, the set of integers C<i> between C<0> and C<n>
626 such that C<i % 10 <= 6> can be described as
628 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
631 A set or relation can have several disjuncts, separated
632 by the keyword C<or>. Each disjunct is either a conjunction
633 of constraints or a projection (C<exists>) of a conjunction
634 of constraints. The constraints are separated by the keyword
637 =head3 C<PolyLib> format
639 If the represented set is a union, then the first line
640 contains a single number representing the number of disjuncts.
641 Otherwise, a line containing the number C<1> is optional.
643 Each disjunct is represented by a matrix of constraints.
644 The first line contains two numbers representing
645 the number of rows and columns,
646 where the number of rows is equal to the number of constraints
647 and the number of columns is equal to two plus the number of variables.
648 The following lines contain the actual rows of the constraint matrix.
649 In each row, the first column indicates whether the constraint
650 is an equality (C<0>) or inequality (C<1>). The final column
651 corresponds to the constant term.
653 If the set is parametric, then the coefficients of the parameters
654 appear in the last columns before the constant column.
655 The coefficients of any existentially quantified variables appear
656 between those of the set variables and those of the parameters.
658 =head3 Extended C<PolyLib> format
660 The extended C<PolyLib> format is nearly identical to the
661 C<PolyLib> format. The only difference is that the line
662 containing the number of rows and columns of a constraint matrix
663 also contains four additional numbers:
664 the number of output dimensions, the number of input dimensions,
665 the number of local dimensions (i.e., the number of existentially
666 quantified variables) and the number of parameters.
667 For sets, the number of ``output'' dimensions is equal
668 to the number of set dimensions, while the number of ``input''
674 __isl_give isl_basic_set *isl_basic_set_read_from_file(
675 isl_ctx *ctx, FILE *input, int nparam);
676 __isl_give isl_basic_set *isl_basic_set_read_from_str(
677 isl_ctx *ctx, const char *str, int nparam);
678 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
679 FILE *input, int nparam);
680 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
681 const char *str, int nparam);
684 __isl_give isl_basic_map *isl_basic_map_read_from_file(
685 isl_ctx *ctx, FILE *input, int nparam);
686 __isl_give isl_basic_map *isl_basic_map_read_from_str(
687 isl_ctx *ctx, const char *str, int nparam);
688 __isl_give isl_map *isl_map_read_from_file(
689 struct isl_ctx *ctx, FILE *input, int nparam);
690 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
691 const char *str, int nparam);
693 #include <isl/union_set.h>
694 __isl_give isl_union_set *isl_union_set_read_from_file(
695 isl_ctx *ctx, FILE *input);
696 __isl_give isl_union_set *isl_union_set_read_from_str(
697 struct isl_ctx *ctx, const char *str);
699 #include <isl/union_map.h>
700 __isl_give isl_union_map *isl_union_map_read_from_file(
701 isl_ctx *ctx, FILE *input);
702 __isl_give isl_union_map *isl_union_map_read_from_str(
703 struct isl_ctx *ctx, const char *str);
705 The input format is autodetected and may be either the C<PolyLib> format
706 or the C<isl> format.
707 C<nparam> specifies how many of the final columns in
708 the C<PolyLib> format correspond to parameters.
709 If input is given in the C<isl> format, then the number
710 of parameters needs to be equal to C<nparam>.
711 If C<nparam> is negative, then any number of parameters
712 is accepted in the C<isl> format and zero parameters
713 are assumed in the C<PolyLib> format.
717 Before anything can be printed, an C<isl_printer> needs to
720 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
722 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
723 void isl_printer_free(__isl_take isl_printer *printer);
724 __isl_give char *isl_printer_get_str(
725 __isl_keep isl_printer *printer);
727 The behavior of the printer can be modified in various ways
729 __isl_give isl_printer *isl_printer_set_output_format(
730 __isl_take isl_printer *p, int output_format);
731 __isl_give isl_printer *isl_printer_set_indent(
732 __isl_take isl_printer *p, int indent);
733 __isl_give isl_printer *isl_printer_indent(
734 __isl_take isl_printer *p, int indent);
735 __isl_give isl_printer *isl_printer_set_prefix(
736 __isl_take isl_printer *p, const char *prefix);
737 __isl_give isl_printer *isl_printer_set_suffix(
738 __isl_take isl_printer *p, const char *suffix);
740 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
741 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
742 and defaults to C<ISL_FORMAT_ISL>.
743 Each line in the output is indented by C<indent> (set by
744 C<isl_printer_set_indent>) spaces
745 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
746 In the C<PolyLib> format output,
747 the coefficients of the existentially quantified variables
748 appear between those of the set variables and those
750 The function C<isl_printer_indent> increases the indentation
751 by the specified amount (which may be negative).
753 To actually print something, use
756 __isl_give isl_printer *isl_printer_print_basic_set(
757 __isl_take isl_printer *printer,
758 __isl_keep isl_basic_set *bset);
759 __isl_give isl_printer *isl_printer_print_set(
760 __isl_take isl_printer *printer,
761 __isl_keep isl_set *set);
764 __isl_give isl_printer *isl_printer_print_basic_map(
765 __isl_take isl_printer *printer,
766 __isl_keep isl_basic_map *bmap);
767 __isl_give isl_printer *isl_printer_print_map(
768 __isl_take isl_printer *printer,
769 __isl_keep isl_map *map);
771 #include <isl/union_set.h>
772 __isl_give isl_printer *isl_printer_print_union_set(
773 __isl_take isl_printer *p,
774 __isl_keep isl_union_set *uset);
776 #include <isl/union_map.h>
777 __isl_give isl_printer *isl_printer_print_union_map(
778 __isl_take isl_printer *p,
779 __isl_keep isl_union_map *umap);
781 When called on a file printer, the following function flushes
782 the file. When called on a string printer, the buffer is cleared.
784 __isl_give isl_printer *isl_printer_flush(
785 __isl_take isl_printer *p);
787 =head2 Creating New Sets and Relations
789 C<isl> has functions for creating some standard sets and relations.
793 =item * Empty sets and relations
795 __isl_give isl_basic_set *isl_basic_set_empty(
796 __isl_take isl_dim *dim);
797 __isl_give isl_basic_map *isl_basic_map_empty(
798 __isl_take isl_dim *dim);
799 __isl_give isl_set *isl_set_empty(
800 __isl_take isl_dim *dim);
801 __isl_give isl_map *isl_map_empty(
802 __isl_take isl_dim *dim);
803 __isl_give isl_union_set *isl_union_set_empty(
804 __isl_take isl_dim *dim);
805 __isl_give isl_union_map *isl_union_map_empty(
806 __isl_take isl_dim *dim);
808 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
809 is only used to specify the parameters.
811 =item * Universe sets and relations
813 __isl_give isl_basic_set *isl_basic_set_universe(
814 __isl_take isl_dim *dim);
815 __isl_give isl_basic_map *isl_basic_map_universe(
816 __isl_take isl_dim *dim);
817 __isl_give isl_set *isl_set_universe(
818 __isl_take isl_dim *dim);
819 __isl_give isl_map *isl_map_universe(
820 __isl_take isl_dim *dim);
821 __isl_give isl_union_set *isl_union_set_universe(
822 __isl_take isl_union_set *uset);
823 __isl_give isl_union_map *isl_union_map_universe(
824 __isl_take isl_union_map *umap);
826 The sets and relations constructed by the functions above
827 contain all integer values, while those constructed by the
828 functions below only contain non-negative values.
830 __isl_give isl_basic_set *isl_basic_set_nat_universe(
831 __isl_take isl_dim *dim);
832 __isl_give isl_basic_map *isl_basic_map_nat_universe(
833 __isl_take isl_dim *dim);
834 __isl_give isl_set *isl_set_nat_universe(
835 __isl_take isl_dim *dim);
836 __isl_give isl_map *isl_map_nat_universe(
837 __isl_take isl_dim *dim);
839 =item * Identity relations
841 __isl_give isl_basic_map *isl_basic_map_identity(
842 __isl_take isl_dim *dim);
843 __isl_give isl_map *isl_map_identity(
844 __isl_take isl_dim *dim);
846 The number of input and output dimensions in C<dim> needs
849 =item * Lexicographic order
851 __isl_give isl_map *isl_map_lex_lt(
852 __isl_take isl_dim *set_dim);
853 __isl_give isl_map *isl_map_lex_le(
854 __isl_take isl_dim *set_dim);
855 __isl_give isl_map *isl_map_lex_gt(
856 __isl_take isl_dim *set_dim);
857 __isl_give isl_map *isl_map_lex_ge(
858 __isl_take isl_dim *set_dim);
859 __isl_give isl_map *isl_map_lex_lt_first(
860 __isl_take isl_dim *dim, unsigned n);
861 __isl_give isl_map *isl_map_lex_le_first(
862 __isl_take isl_dim *dim, unsigned n);
863 __isl_give isl_map *isl_map_lex_gt_first(
864 __isl_take isl_dim *dim, unsigned n);
865 __isl_give isl_map *isl_map_lex_ge_first(
866 __isl_take isl_dim *dim, unsigned n);
868 The first four functions take a dimension specification for a B<set>
869 and return relations that express that the elements in the domain
870 are lexicographically less
871 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
872 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
873 than the elements in the range.
874 The last four functions take a dimension specification for a map
875 and return relations that express that the first C<n> dimensions
876 in the domain are lexicographically less
877 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
878 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
879 than the first C<n> dimensions in the range.
883 A basic set or relation can be converted to a set or relation
884 using the following functions.
886 __isl_give isl_set *isl_set_from_basic_set(
887 __isl_take isl_basic_set *bset);
888 __isl_give isl_map *isl_map_from_basic_map(
889 __isl_take isl_basic_map *bmap);
891 Sets and relations can be converted to union sets and relations
892 using the following functions.
894 __isl_give isl_union_map *isl_union_map_from_map(
895 __isl_take isl_map *map);
896 __isl_give isl_union_set *isl_union_set_from_set(
897 __isl_take isl_set *set);
899 Sets and relations can be copied and freed again using the following
902 __isl_give isl_basic_set *isl_basic_set_copy(
903 __isl_keep isl_basic_set *bset);
904 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
905 __isl_give isl_union_set *isl_union_set_copy(
906 __isl_keep isl_union_set *uset);
907 __isl_give isl_basic_map *isl_basic_map_copy(
908 __isl_keep isl_basic_map *bmap);
909 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
910 __isl_give isl_union_map *isl_union_map_copy(
911 __isl_keep isl_union_map *umap);
912 void isl_basic_set_free(__isl_take isl_basic_set *bset);
913 void isl_set_free(__isl_take isl_set *set);
914 void isl_union_set_free(__isl_take isl_union_set *uset);
915 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
916 void isl_map_free(__isl_take isl_map *map);
917 void isl_union_map_free(__isl_take isl_union_map *umap);
919 Other sets and relations can be constructed by starting
920 from a universe set or relation, adding equality and/or
921 inequality constraints and then projecting out the
922 existentially quantified variables, if any.
923 Constraints can be constructed, manipulated and
924 added to (basic) sets and relations using the following functions.
926 #include <isl/constraint.h>
927 __isl_give isl_constraint *isl_equality_alloc(
928 __isl_take isl_dim *dim);
929 __isl_give isl_constraint *isl_inequality_alloc(
930 __isl_take isl_dim *dim);
931 void isl_constraint_set_constant(
932 __isl_keep isl_constraint *constraint, isl_int v);
933 void isl_constraint_set_coefficient(
934 __isl_keep isl_constraint *constraint,
935 enum isl_dim_type type, int pos, isl_int v);
936 __isl_give isl_basic_map *isl_basic_map_add_constraint(
937 __isl_take isl_basic_map *bmap,
938 __isl_take isl_constraint *constraint);
939 __isl_give isl_basic_set *isl_basic_set_add_constraint(
940 __isl_take isl_basic_set *bset,
941 __isl_take isl_constraint *constraint);
942 __isl_give isl_map *isl_map_add_constraint(
943 __isl_take isl_map *map,
944 __isl_take isl_constraint *constraint);
945 __isl_give isl_set *isl_set_add_constraint(
946 __isl_take isl_set *set,
947 __isl_take isl_constraint *constraint);
949 For example, to create a set containing the even integers
950 between 10 and 42, you would use the following code.
954 struct isl_constraint *c;
955 struct isl_basic_set *bset;
958 dim = isl_dim_set_alloc(ctx, 0, 2);
959 bset = isl_basic_set_universe(isl_dim_copy(dim));
961 c = isl_equality_alloc(isl_dim_copy(dim));
962 isl_int_set_si(v, -1);
963 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
964 isl_int_set_si(v, 2);
965 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
966 bset = isl_basic_set_add_constraint(bset, c);
968 c = isl_inequality_alloc(isl_dim_copy(dim));
969 isl_int_set_si(v, -10);
970 isl_constraint_set_constant(c, v);
971 isl_int_set_si(v, 1);
972 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
973 bset = isl_basic_set_add_constraint(bset, c);
975 c = isl_inequality_alloc(dim);
976 isl_int_set_si(v, 42);
977 isl_constraint_set_constant(c, v);
978 isl_int_set_si(v, -1);
979 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
980 bset = isl_basic_set_add_constraint(bset, c);
982 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
988 struct isl_basic_set *bset;
989 bset = isl_basic_set_read_from_str(ctx,
990 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
992 A basic set or relation can also be constructed from two matrices
993 describing the equalities and the inequalities.
995 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
996 __isl_take isl_dim *dim,
997 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
998 enum isl_dim_type c1,
999 enum isl_dim_type c2, enum isl_dim_type c3,
1000 enum isl_dim_type c4);
1001 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1002 __isl_take isl_dim *dim,
1003 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1004 enum isl_dim_type c1,
1005 enum isl_dim_type c2, enum isl_dim_type c3,
1006 enum isl_dim_type c4, enum isl_dim_type c5);
1008 The C<isl_dim_type> arguments indicate the order in which
1009 different kinds of variables appear in the input matrices
1010 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1011 C<isl_dim_set> and C<isl_dim_div> for sets and
1012 of C<isl_dim_cst>, C<isl_dim_param>,
1013 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1015 =head2 Inspecting Sets and Relations
1017 Usually, the user should not have to care about the actual constraints
1018 of the sets and maps, but should instead apply the abstract operations
1019 explained in the following sections.
1020 Occasionally, however, it may be required to inspect the individual
1021 coefficients of the constraints. This section explains how to do so.
1022 In these cases, it may also be useful to have C<isl> compute
1023 an explicit representation of the existentially quantified variables.
1025 __isl_give isl_set *isl_set_compute_divs(
1026 __isl_take isl_set *set);
1027 __isl_give isl_map *isl_map_compute_divs(
1028 __isl_take isl_map *map);
1029 __isl_give isl_union_set *isl_union_set_compute_divs(
1030 __isl_take isl_union_set *uset);
1031 __isl_give isl_union_map *isl_union_map_compute_divs(
1032 __isl_take isl_union_map *umap);
1034 This explicit representation defines the existentially quantified
1035 variables as integer divisions of the other variables, possibly
1036 including earlier existentially quantified variables.
1037 An explicitly represented existentially quantified variable therefore
1038 has a unique value when the values of the other variables are known.
1039 If, furthermore, the same existentials, i.e., existentials
1040 with the same explicit representations, should appear in the
1041 same order in each of the disjuncts of a set or map, then the user should call
1042 either of the following functions.
1044 __isl_give isl_set *isl_set_align_divs(
1045 __isl_take isl_set *set);
1046 __isl_give isl_map *isl_map_align_divs(
1047 __isl_take isl_map *map);
1049 Alternatively, the existentially quantified variables can be removed
1050 using the following functions, which compute an overapproximation.
1052 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1053 __isl_take isl_basic_set *bset);
1054 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1055 __isl_take isl_basic_map *bmap);
1056 __isl_give isl_set *isl_set_remove_divs(
1057 __isl_take isl_set *set);
1058 __isl_give isl_map *isl_map_remove_divs(
1059 __isl_take isl_map *map);
1061 To iterate over all the sets or maps in a union set or map, use
1063 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1064 int (*fn)(__isl_take isl_set *set, void *user),
1066 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1067 int (*fn)(__isl_take isl_map *map, void *user),
1070 The number of sets or maps in a union set or map can be obtained
1073 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1074 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1076 To extract the set or map from a union with a given dimension
1079 __isl_give isl_set *isl_union_set_extract_set(
1080 __isl_keep isl_union_set *uset,
1081 __isl_take isl_dim *dim);
1082 __isl_give isl_map *isl_union_map_extract_map(
1083 __isl_keep isl_union_map *umap,
1084 __isl_take isl_dim *dim);
1086 To iterate over all the basic sets or maps in a set or map, use
1088 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1089 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1091 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1092 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1095 The callback function C<fn> should return 0 if successful and
1096 -1 if an error occurs. In the latter case, or if any other error
1097 occurs, the above functions will return -1.
1099 It should be noted that C<isl> does not guarantee that
1100 the basic sets or maps passed to C<fn> are disjoint.
1101 If this is required, then the user should call one of
1102 the following functions first.
1104 __isl_give isl_set *isl_set_make_disjoint(
1105 __isl_take isl_set *set);
1106 __isl_give isl_map *isl_map_make_disjoint(
1107 __isl_take isl_map *map);
1109 The number of basic sets in a set can be obtained
1112 int isl_set_n_basic_set(__isl_keep isl_set *set);
1114 To iterate over the constraints of a basic set or map, use
1116 #include <isl/constraint.h>
1118 int isl_basic_map_foreach_constraint(
1119 __isl_keep isl_basic_map *bmap,
1120 int (*fn)(__isl_take isl_constraint *c, void *user),
1122 void isl_constraint_free(struct isl_constraint *c);
1124 Again, the callback function C<fn> should return 0 if successful and
1125 -1 if an error occurs. In the latter case, or if any other error
1126 occurs, the above functions will return -1.
1127 The constraint C<c> represents either an equality or an inequality.
1128 Use the following function to find out whether a constraint
1129 represents an equality. If not, it represents an inequality.
1131 int isl_constraint_is_equality(
1132 __isl_keep isl_constraint *constraint);
1134 The coefficients of the constraints can be inspected using
1135 the following functions.
1137 void isl_constraint_get_constant(
1138 __isl_keep isl_constraint *constraint, isl_int *v);
1139 void isl_constraint_get_coefficient(
1140 __isl_keep isl_constraint *constraint,
1141 enum isl_dim_type type, int pos, isl_int *v);
1142 int isl_constraint_involves_dims(
1143 __isl_keep isl_constraint *constraint,
1144 enum isl_dim_type type, unsigned first, unsigned n);
1146 The explicit representations of the existentially quantified
1147 variables can be inspected using the following functions.
1148 Note that the user is only allowed to use these functions
1149 if the inspected set or map is the result of a call
1150 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1152 __isl_give isl_div *isl_constraint_div(
1153 __isl_keep isl_constraint *constraint, int pos);
1154 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1155 void isl_div_get_constant(__isl_keep isl_div *div,
1157 void isl_div_get_denominator(__isl_keep isl_div *div,
1159 void isl_div_get_coefficient(__isl_keep isl_div *div,
1160 enum isl_dim_type type, int pos, isl_int *v);
1162 To obtain the constraints of a basic set or map in matrix
1163 form, use the following functions.
1165 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1166 __isl_keep isl_basic_set *bset,
1167 enum isl_dim_type c1, enum isl_dim_type c2,
1168 enum isl_dim_type c3, enum isl_dim_type c4);
1169 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1170 __isl_keep isl_basic_set *bset,
1171 enum isl_dim_type c1, enum isl_dim_type c2,
1172 enum isl_dim_type c3, enum isl_dim_type c4);
1173 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1174 __isl_keep isl_basic_map *bmap,
1175 enum isl_dim_type c1,
1176 enum isl_dim_type c2, enum isl_dim_type c3,
1177 enum isl_dim_type c4, enum isl_dim_type c5);
1178 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1179 __isl_keep isl_basic_map *bmap,
1180 enum isl_dim_type c1,
1181 enum isl_dim_type c2, enum isl_dim_type c3,
1182 enum isl_dim_type c4, enum isl_dim_type c5);
1184 The C<isl_dim_type> arguments dictate the order in which
1185 different kinds of variables appear in the resulting matrix
1186 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1187 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1189 The names of the domain and range spaces of a set or relation can be
1190 read off using the following functions.
1192 const char *isl_basic_set_get_tuple_name(
1193 __isl_keep isl_basic_set *bset);
1194 const char *isl_set_get_tuple_name(
1195 __isl_keep isl_set *set);
1196 const char *isl_basic_map_get_tuple_name(
1197 __isl_keep isl_basic_map *bmap,
1198 enum isl_dim_type type);
1199 const char *isl_map_get_tuple_name(
1200 __isl_keep isl_map *map,
1201 enum isl_dim_type type);
1203 As with C<isl_dim_get_tuple_name>, the value returned points to
1204 an internal data structure.
1205 The names of individual dimensions can be read off using
1206 the following functions.
1208 const char *isl_constraint_get_dim_name(
1209 __isl_keep isl_constraint *constraint,
1210 enum isl_dim_type type, unsigned pos);
1211 const char *isl_basic_set_get_dim_name(
1212 __isl_keep isl_basic_set *bset,
1213 enum isl_dim_type type, unsigned pos);
1214 const char *isl_set_get_dim_name(
1215 __isl_keep isl_set *set,
1216 enum isl_dim_type type, unsigned pos);
1217 const char *isl_basic_map_get_dim_name(
1218 __isl_keep isl_basic_map *bmap,
1219 enum isl_dim_type type, unsigned pos);
1220 const char *isl_map_get_dim_name(
1221 __isl_keep isl_map *map,
1222 enum isl_dim_type type, unsigned pos);
1224 These functions are mostly useful to obtain the names
1229 =head3 Unary Properties
1235 The following functions test whether the given set or relation
1236 contains any integer points. The ``plain'' variants do not perform
1237 any computations, but simply check if the given set or relation
1238 is already known to be empty.
1240 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1241 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1242 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1243 int isl_set_is_empty(__isl_keep isl_set *set);
1244 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1245 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1246 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1247 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1248 int isl_map_is_empty(__isl_keep isl_map *map);
1249 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1251 =item * Universality
1253 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1254 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1255 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1257 =item * Single-valuedness
1259 int isl_map_is_single_valued(__isl_keep isl_map *map);
1260 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1264 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1265 int isl_map_is_injective(__isl_keep isl_map *map);
1266 int isl_union_map_plain_is_injective(
1267 __isl_keep isl_union_map *umap);
1268 int isl_union_map_is_injective(
1269 __isl_keep isl_union_map *umap);
1273 int isl_map_is_bijective(__isl_keep isl_map *map);
1274 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1278 The following functions check whether the domain of the given
1279 (basic) set is a wrapped relation.
1281 int isl_basic_set_is_wrapping(
1282 __isl_keep isl_basic_set *bset);
1283 int isl_set_is_wrapping(__isl_keep isl_set *set);
1285 =item * Internal Product
1287 int isl_basic_map_can_zip(
1288 __isl_keep isl_basic_map *bmap);
1289 int isl_map_can_zip(__isl_keep isl_map *map);
1291 Check whether the product of domain and range of the given relation
1293 i.e., whether both domain and range are nested relations.
1297 =head3 Binary Properties
1303 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1304 __isl_keep isl_set *set2);
1305 int isl_set_is_equal(__isl_keep isl_set *set1,
1306 __isl_keep isl_set *set2);
1307 int isl_union_set_is_equal(
1308 __isl_keep isl_union_set *uset1,
1309 __isl_keep isl_union_set *uset2);
1310 int isl_basic_map_is_equal(
1311 __isl_keep isl_basic_map *bmap1,
1312 __isl_keep isl_basic_map *bmap2);
1313 int isl_map_is_equal(__isl_keep isl_map *map1,
1314 __isl_keep isl_map *map2);
1315 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1316 __isl_keep isl_map *map2);
1317 int isl_union_map_is_equal(
1318 __isl_keep isl_union_map *umap1,
1319 __isl_keep isl_union_map *umap2);
1321 =item * Disjointness
1323 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1324 __isl_keep isl_set *set2);
1328 int isl_set_is_subset(__isl_keep isl_set *set1,
1329 __isl_keep isl_set *set2);
1330 int isl_set_is_strict_subset(
1331 __isl_keep isl_set *set1,
1332 __isl_keep isl_set *set2);
1333 int isl_union_set_is_subset(
1334 __isl_keep isl_union_set *uset1,
1335 __isl_keep isl_union_set *uset2);
1336 int isl_union_set_is_strict_subset(
1337 __isl_keep isl_union_set *uset1,
1338 __isl_keep isl_union_set *uset2);
1339 int isl_basic_map_is_subset(
1340 __isl_keep isl_basic_map *bmap1,
1341 __isl_keep isl_basic_map *bmap2);
1342 int isl_basic_map_is_strict_subset(
1343 __isl_keep isl_basic_map *bmap1,
1344 __isl_keep isl_basic_map *bmap2);
1345 int isl_map_is_subset(
1346 __isl_keep isl_map *map1,
1347 __isl_keep isl_map *map2);
1348 int isl_map_is_strict_subset(
1349 __isl_keep isl_map *map1,
1350 __isl_keep isl_map *map2);
1351 int isl_union_map_is_subset(
1352 __isl_keep isl_union_map *umap1,
1353 __isl_keep isl_union_map *umap2);
1354 int isl_union_map_is_strict_subset(
1355 __isl_keep isl_union_map *umap1,
1356 __isl_keep isl_union_map *umap2);
1360 =head2 Unary Operations
1366 __isl_give isl_set *isl_set_complement(
1367 __isl_take isl_set *set);
1371 __isl_give isl_basic_map *isl_basic_map_reverse(
1372 __isl_take isl_basic_map *bmap);
1373 __isl_give isl_map *isl_map_reverse(
1374 __isl_take isl_map *map);
1375 __isl_give isl_union_map *isl_union_map_reverse(
1376 __isl_take isl_union_map *umap);
1380 __isl_give isl_basic_set *isl_basic_set_project_out(
1381 __isl_take isl_basic_set *bset,
1382 enum isl_dim_type type, unsigned first, unsigned n);
1383 __isl_give isl_basic_map *isl_basic_map_project_out(
1384 __isl_take isl_basic_map *bmap,
1385 enum isl_dim_type type, unsigned first, unsigned n);
1386 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1387 enum isl_dim_type type, unsigned first, unsigned n);
1388 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1389 enum isl_dim_type type, unsigned first, unsigned n);
1390 __isl_give isl_basic_set *isl_basic_map_domain(
1391 __isl_take isl_basic_map *bmap);
1392 __isl_give isl_basic_set *isl_basic_map_range(
1393 __isl_take isl_basic_map *bmap);
1394 __isl_give isl_set *isl_map_domain(
1395 __isl_take isl_map *bmap);
1396 __isl_give isl_set *isl_map_range(
1397 __isl_take isl_map *map);
1398 __isl_give isl_union_set *isl_union_map_domain(
1399 __isl_take isl_union_map *umap);
1400 __isl_give isl_union_set *isl_union_map_range(
1401 __isl_take isl_union_map *umap);
1403 __isl_give isl_basic_map *isl_basic_map_domain_map(
1404 __isl_take isl_basic_map *bmap);
1405 __isl_give isl_basic_map *isl_basic_map_range_map(
1406 __isl_take isl_basic_map *bmap);
1407 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1408 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1409 __isl_give isl_union_map *isl_union_map_domain_map(
1410 __isl_take isl_union_map *umap);
1411 __isl_give isl_union_map *isl_union_map_range_map(
1412 __isl_take isl_union_map *umap);
1414 The functions above construct a (basic, regular or union) relation
1415 that maps (a wrapped version of) the input relation to its domain or range.
1419 __isl_give isl_set *isl_set_eliminate(
1420 __isl_take isl_set *set, enum isl_dim_type type,
1421 unsigned first, unsigned n);
1423 Eliminate the coefficients for the given dimensions from the constraints,
1424 without removing the dimensions.
1428 __isl_give isl_basic_set *isl_basic_set_fix(
1429 __isl_take isl_basic_set *bset,
1430 enum isl_dim_type type, unsigned pos,
1432 __isl_give isl_basic_set *isl_basic_set_fix_si(
1433 __isl_take isl_basic_set *bset,
1434 enum isl_dim_type type, unsigned pos, int value);
1435 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1436 enum isl_dim_type type, unsigned pos,
1438 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1439 enum isl_dim_type type, unsigned pos, int value);
1440 __isl_give isl_basic_map *isl_basic_map_fix_si(
1441 __isl_take isl_basic_map *bmap,
1442 enum isl_dim_type type, unsigned pos, int value);
1443 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1444 enum isl_dim_type type, unsigned pos, int value);
1446 Intersect the set or relation with the hyperplane where the given
1447 dimension has the fixed given value.
1451 __isl_give isl_map *isl_set_identity(
1452 __isl_take isl_set *set);
1453 __isl_give isl_union_map *isl_union_set_identity(
1454 __isl_take isl_union_set *uset);
1456 Construct an identity relation on the given (union) set.
1460 __isl_give isl_basic_set *isl_basic_map_deltas(
1461 __isl_take isl_basic_map *bmap);
1462 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1463 __isl_give isl_union_set *isl_union_map_deltas(
1464 __isl_take isl_union_map *umap);
1466 These functions return a (basic) set containing the differences
1467 between image elements and corresponding domain elements in the input.
1469 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1470 __isl_take isl_basic_map *bmap);
1471 __isl_give isl_map *isl_map_deltas_map(
1472 __isl_take isl_map *map);
1473 __isl_give isl_union_map *isl_union_map_deltas_map(
1474 __isl_take isl_union_map *umap);
1476 The functions above construct a (basic, regular or union) relation
1477 that maps (a wrapped version of) the input relation to its delta set.
1481 Simplify the representation of a set or relation by trying
1482 to combine pairs of basic sets or relations into a single
1483 basic set or relation.
1485 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1486 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1487 __isl_give isl_union_set *isl_union_set_coalesce(
1488 __isl_take isl_union_set *uset);
1489 __isl_give isl_union_map *isl_union_map_coalesce(
1490 __isl_take isl_union_map *umap);
1492 =item * Detecting equalities
1494 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1495 __isl_take isl_basic_set *bset);
1496 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1497 __isl_take isl_basic_map *bmap);
1498 __isl_give isl_set *isl_set_detect_equalities(
1499 __isl_take isl_set *set);
1500 __isl_give isl_map *isl_map_detect_equalities(
1501 __isl_take isl_map *map);
1502 __isl_give isl_union_set *isl_union_set_detect_equalities(
1503 __isl_take isl_union_set *uset);
1504 __isl_give isl_union_map *isl_union_map_detect_equalities(
1505 __isl_take isl_union_map *umap);
1507 Simplify the representation of a set or relation by detecting implicit
1510 =item * Removing redundant constraints
1512 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1513 __isl_take isl_basic_set *bset);
1514 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1515 __isl_take isl_basic_map *bmap);
1519 __isl_give isl_basic_set *isl_set_convex_hull(
1520 __isl_take isl_set *set);
1521 __isl_give isl_basic_map *isl_map_convex_hull(
1522 __isl_take isl_map *map);
1524 If the input set or relation has any existentially quantified
1525 variables, then the result of these operations is currently undefined.
1529 __isl_give isl_basic_set *isl_set_simple_hull(
1530 __isl_take isl_set *set);
1531 __isl_give isl_basic_map *isl_map_simple_hull(
1532 __isl_take isl_map *map);
1533 __isl_give isl_union_map *isl_union_map_simple_hull(
1534 __isl_take isl_union_map *umap);
1536 These functions compute a single basic set or relation
1537 that contains the whole input set or relation.
1538 In particular, the output is described by translates
1539 of the constraints describing the basic sets or relations in the input.
1543 (See \autoref{s:simple hull}.)
1549 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1550 __isl_take isl_basic_set *bset);
1551 __isl_give isl_basic_set *isl_set_affine_hull(
1552 __isl_take isl_set *set);
1553 __isl_give isl_union_set *isl_union_set_affine_hull(
1554 __isl_take isl_union_set *uset);
1555 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1556 __isl_take isl_basic_map *bmap);
1557 __isl_give isl_basic_map *isl_map_affine_hull(
1558 __isl_take isl_map *map);
1559 __isl_give isl_union_map *isl_union_map_affine_hull(
1560 __isl_take isl_union_map *umap);
1562 In case of union sets and relations, the affine hull is computed
1565 =item * Polyhedral hull
1567 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1568 __isl_take isl_set *set);
1569 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1570 __isl_take isl_map *map);
1571 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1572 __isl_take isl_union_set *uset);
1573 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1574 __isl_take isl_union_map *umap);
1576 These functions compute a single basic set or relation
1577 not involving any existentially quantified variables
1578 that contains the whole input set or relation.
1579 In case of union sets and relations, the polyhedral hull is computed
1582 =item * Optimization
1584 #include <isl/ilp.h>
1585 enum isl_lp_result isl_basic_set_max(
1586 __isl_keep isl_basic_set *bset,
1587 __isl_keep isl_aff *obj, isl_int *opt)
1588 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1589 __isl_keep isl_aff *obj, isl_int *opt);
1591 Compute the maximum of the integer affine expression C<obj>
1592 over the points in C<set>, returning the result in C<opt>.
1593 The return value may be one of C<isl_lp_error>,
1594 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1598 The following functions compute either the set of (rational) coefficient
1599 values of valid constraints for the given set or the set of (rational)
1600 values satisfying the constraints with coefficients from the given set.
1601 Internally, these two sets of functions perform essentially the
1602 same operations, except that the set of coefficients is assumed to
1603 be a cone, while the set of values may be any polyhedron.
1604 The current implementation is based on the Farkas lemma and
1605 Fourier-Motzkin elimination, but this may change or be made optional
1606 in future. In particular, future implementations may use different
1607 dualization algorithms or skip the elimination step.
1609 __isl_give isl_basic_set *isl_basic_set_coefficients(
1610 __isl_take isl_basic_set *bset);
1611 __isl_give isl_basic_set *isl_set_coefficients(
1612 __isl_take isl_set *set);
1613 __isl_give isl_union_set *isl_union_set_coefficients(
1614 __isl_take isl_union_set *bset);
1615 __isl_give isl_basic_set *isl_basic_set_solutions(
1616 __isl_take isl_basic_set *bset);
1617 __isl_give isl_basic_set *isl_set_solutions(
1618 __isl_take isl_set *set);
1619 __isl_give isl_union_set *isl_union_set_solutions(
1620 __isl_take isl_union_set *bset);
1624 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1626 __isl_give isl_union_map *isl_union_map_power(
1627 __isl_take isl_union_map *umap, int *exact);
1629 Compute a parametric representation for all positive powers I<k> of C<map>.
1630 The result maps I<k> to a nested relation corresponding to the
1631 I<k>th power of C<map>.
1632 The result may be an overapproximation. If the result is known to be exact,
1633 then C<*exact> is set to C<1>.
1635 =item * Transitive closure
1637 __isl_give isl_map *isl_map_transitive_closure(
1638 __isl_take isl_map *map, int *exact);
1639 __isl_give isl_union_map *isl_union_map_transitive_closure(
1640 __isl_take isl_union_map *umap, int *exact);
1642 Compute the transitive closure of C<map>.
1643 The result may be an overapproximation. If the result is known to be exact,
1644 then C<*exact> is set to C<1>.
1646 =item * Reaching path lengths
1648 __isl_give isl_map *isl_map_reaching_path_lengths(
1649 __isl_take isl_map *map, int *exact);
1651 Compute a relation that maps each element in the range of C<map>
1652 to the lengths of all paths composed of edges in C<map> that
1653 end up in the given element.
1654 The result may be an overapproximation. If the result is known to be exact,
1655 then C<*exact> is set to C<1>.
1656 To compute the I<maximal> path length, the resulting relation
1657 should be postprocessed by C<isl_map_lexmax>.
1658 In particular, if the input relation is a dependence relation
1659 (mapping sources to sinks), then the maximal path length corresponds
1660 to the free schedule.
1661 Note, however, that C<isl_map_lexmax> expects the maximum to be
1662 finite, so if the path lengths are unbounded (possibly due to
1663 the overapproximation), then you will get an error message.
1667 __isl_give isl_basic_set *isl_basic_map_wrap(
1668 __isl_take isl_basic_map *bmap);
1669 __isl_give isl_set *isl_map_wrap(
1670 __isl_take isl_map *map);
1671 __isl_give isl_union_set *isl_union_map_wrap(
1672 __isl_take isl_union_map *umap);
1673 __isl_give isl_basic_map *isl_basic_set_unwrap(
1674 __isl_take isl_basic_set *bset);
1675 __isl_give isl_map *isl_set_unwrap(
1676 __isl_take isl_set *set);
1677 __isl_give isl_union_map *isl_union_set_unwrap(
1678 __isl_take isl_union_set *uset);
1682 Remove any internal structure of domain (and range) of the given
1683 set or relation. If there is any such internal structure in the input,
1684 then the name of the space is also removed.
1686 __isl_give isl_basic_set *isl_basic_set_flatten(
1687 __isl_take isl_basic_set *bset);
1688 __isl_give isl_set *isl_set_flatten(
1689 __isl_take isl_set *set);
1690 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1691 __isl_take isl_basic_map *bmap);
1692 __isl_give isl_map *isl_map_flatten_range(
1693 __isl_take isl_map *map);
1694 __isl_give isl_basic_map *isl_basic_map_flatten(
1695 __isl_take isl_basic_map *bmap);
1696 __isl_give isl_map *isl_map_flatten(
1697 __isl_take isl_map *map);
1699 __isl_give isl_map *isl_set_flatten_map(
1700 __isl_take isl_set *set);
1702 The function above constructs a relation
1703 that maps the input set to a flattened version of the set.
1707 Lift the input set to a space with extra dimensions corresponding
1708 to the existentially quantified variables in the input.
1709 In particular, the result lives in a wrapped map where the domain
1710 is the original space and the range corresponds to the original
1711 existentially quantified variables.
1713 __isl_give isl_basic_set *isl_basic_set_lift(
1714 __isl_take isl_basic_set *bset);
1715 __isl_give isl_set *isl_set_lift(
1716 __isl_take isl_set *set);
1717 __isl_give isl_union_set *isl_union_set_lift(
1718 __isl_take isl_union_set *uset);
1720 =item * Internal Product
1722 __isl_give isl_basic_map *isl_basic_map_zip(
1723 __isl_take isl_basic_map *bmap);
1724 __isl_give isl_map *isl_map_zip(
1725 __isl_take isl_map *map);
1726 __isl_give isl_union_map *isl_union_map_zip(
1727 __isl_take isl_union_map *umap);
1729 Given a relation with nested relations for domain and range,
1730 interchange the range of the domain with the domain of the range.
1732 =item * Aligning parameters
1734 __isl_give isl_set *isl_set_align_params(
1735 __isl_take isl_set *set,
1736 __isl_take isl_dim *model);
1737 __isl_give isl_map *isl_map_align_params(
1738 __isl_take isl_map *map,
1739 __isl_take isl_dim *model);
1741 Change the order of the parameters of the given set or relation
1742 such that the first parameters match those of C<model>.
1743 This may involve the introduction of extra parameters.
1744 All parameters need to be named.
1746 =item * Dimension manipulation
1748 __isl_give isl_set *isl_set_add_dims(
1749 __isl_take isl_set *set,
1750 enum isl_dim_type type, unsigned n);
1751 __isl_give isl_map *isl_map_add_dims(
1752 __isl_take isl_map *map,
1753 enum isl_dim_type type, unsigned n);
1755 It is usually not advisable to directly change the (input or output)
1756 space of a set or a relation as this removes the name and the internal
1757 structure of the space. However, the above functions can be useful
1758 to add new parameters, assuming
1759 C<isl_set_align_params> and C<isl_map_align_params>
1764 =head2 Binary Operations
1766 The two arguments of a binary operation not only need to live
1767 in the same C<isl_ctx>, they currently also need to have
1768 the same (number of) parameters.
1770 =head3 Basic Operations
1774 =item * Intersection
1776 __isl_give isl_basic_set *isl_basic_set_intersect(
1777 __isl_take isl_basic_set *bset1,
1778 __isl_take isl_basic_set *bset2);
1779 __isl_give isl_set *isl_set_intersect(
1780 __isl_take isl_set *set1,
1781 __isl_take isl_set *set2);
1782 __isl_give isl_union_set *isl_union_set_intersect(
1783 __isl_take isl_union_set *uset1,
1784 __isl_take isl_union_set *uset2);
1785 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1786 __isl_take isl_basic_map *bmap,
1787 __isl_take isl_basic_set *bset);
1788 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1789 __isl_take isl_basic_map *bmap,
1790 __isl_take isl_basic_set *bset);
1791 __isl_give isl_basic_map *isl_basic_map_intersect(
1792 __isl_take isl_basic_map *bmap1,
1793 __isl_take isl_basic_map *bmap2);
1794 __isl_give isl_map *isl_map_intersect_domain(
1795 __isl_take isl_map *map,
1796 __isl_take isl_set *set);
1797 __isl_give isl_map *isl_map_intersect_range(
1798 __isl_take isl_map *map,
1799 __isl_take isl_set *set);
1800 __isl_give isl_map *isl_map_intersect(
1801 __isl_take isl_map *map1,
1802 __isl_take isl_map *map2);
1803 __isl_give isl_union_map *isl_union_map_intersect_domain(
1804 __isl_take isl_union_map *umap,
1805 __isl_take isl_union_set *uset);
1806 __isl_give isl_union_map *isl_union_map_intersect_range(
1807 __isl_take isl_union_map *umap,
1808 __isl_take isl_union_set *uset);
1809 __isl_give isl_union_map *isl_union_map_intersect(
1810 __isl_take isl_union_map *umap1,
1811 __isl_take isl_union_map *umap2);
1815 __isl_give isl_set *isl_basic_set_union(
1816 __isl_take isl_basic_set *bset1,
1817 __isl_take isl_basic_set *bset2);
1818 __isl_give isl_map *isl_basic_map_union(
1819 __isl_take isl_basic_map *bmap1,
1820 __isl_take isl_basic_map *bmap2);
1821 __isl_give isl_set *isl_set_union(
1822 __isl_take isl_set *set1,
1823 __isl_take isl_set *set2);
1824 __isl_give isl_map *isl_map_union(
1825 __isl_take isl_map *map1,
1826 __isl_take isl_map *map2);
1827 __isl_give isl_union_set *isl_union_set_union(
1828 __isl_take isl_union_set *uset1,
1829 __isl_take isl_union_set *uset2);
1830 __isl_give isl_union_map *isl_union_map_union(
1831 __isl_take isl_union_map *umap1,
1832 __isl_take isl_union_map *umap2);
1834 =item * Set difference
1836 __isl_give isl_set *isl_set_subtract(
1837 __isl_take isl_set *set1,
1838 __isl_take isl_set *set2);
1839 __isl_give isl_map *isl_map_subtract(
1840 __isl_take isl_map *map1,
1841 __isl_take isl_map *map2);
1842 __isl_give isl_union_set *isl_union_set_subtract(
1843 __isl_take isl_union_set *uset1,
1844 __isl_take isl_union_set *uset2);
1845 __isl_give isl_union_map *isl_union_map_subtract(
1846 __isl_take isl_union_map *umap1,
1847 __isl_take isl_union_map *umap2);
1851 __isl_give isl_basic_set *isl_basic_set_apply(
1852 __isl_take isl_basic_set *bset,
1853 __isl_take isl_basic_map *bmap);
1854 __isl_give isl_set *isl_set_apply(
1855 __isl_take isl_set *set,
1856 __isl_take isl_map *map);
1857 __isl_give isl_union_set *isl_union_set_apply(
1858 __isl_take isl_union_set *uset,
1859 __isl_take isl_union_map *umap);
1860 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1861 __isl_take isl_basic_map *bmap1,
1862 __isl_take isl_basic_map *bmap2);
1863 __isl_give isl_basic_map *isl_basic_map_apply_range(
1864 __isl_take isl_basic_map *bmap1,
1865 __isl_take isl_basic_map *bmap2);
1866 __isl_give isl_map *isl_map_apply_domain(
1867 __isl_take isl_map *map1,
1868 __isl_take isl_map *map2);
1869 __isl_give isl_union_map *isl_union_map_apply_domain(
1870 __isl_take isl_union_map *umap1,
1871 __isl_take isl_union_map *umap2);
1872 __isl_give isl_map *isl_map_apply_range(
1873 __isl_take isl_map *map1,
1874 __isl_take isl_map *map2);
1875 __isl_give isl_union_map *isl_union_map_apply_range(
1876 __isl_take isl_union_map *umap1,
1877 __isl_take isl_union_map *umap2);
1879 =item * Cartesian Product
1881 __isl_give isl_set *isl_set_product(
1882 __isl_take isl_set *set1,
1883 __isl_take isl_set *set2);
1884 __isl_give isl_union_set *isl_union_set_product(
1885 __isl_take isl_union_set *uset1,
1886 __isl_take isl_union_set *uset2);
1887 __isl_give isl_basic_map *isl_basic_map_range_product(
1888 __isl_take isl_basic_map *bmap1,
1889 __isl_take isl_basic_map *bmap2);
1890 __isl_give isl_map *isl_map_range_product(
1891 __isl_take isl_map *map1,
1892 __isl_take isl_map *map2);
1893 __isl_give isl_union_map *isl_union_map_range_product(
1894 __isl_take isl_union_map *umap1,
1895 __isl_take isl_union_map *umap2);
1896 __isl_give isl_map *isl_map_product(
1897 __isl_take isl_map *map1,
1898 __isl_take isl_map *map2);
1899 __isl_give isl_union_map *isl_union_map_product(
1900 __isl_take isl_union_map *umap1,
1901 __isl_take isl_union_map *umap2);
1903 The above functions compute the cross product of the given
1904 sets or relations. The domains and ranges of the results
1905 are wrapped maps between domains and ranges of the inputs.
1906 To obtain a ``flat'' product, use the following functions
1909 __isl_give isl_basic_set *isl_basic_set_flat_product(
1910 __isl_take isl_basic_set *bset1,
1911 __isl_take isl_basic_set *bset2);
1912 __isl_give isl_set *isl_set_flat_product(
1913 __isl_take isl_set *set1,
1914 __isl_take isl_set *set2);
1915 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1916 __isl_take isl_basic_map *bmap1,
1917 __isl_take isl_basic_map *bmap2);
1918 __isl_give isl_map *isl_map_flat_range_product(
1919 __isl_take isl_map *map1,
1920 __isl_take isl_map *map2);
1921 __isl_give isl_union_map *isl_union_map_flat_range_product(
1922 __isl_take isl_union_map *umap1,
1923 __isl_take isl_union_map *umap2);
1924 __isl_give isl_basic_map *isl_basic_map_flat_product(
1925 __isl_take isl_basic_map *bmap1,
1926 __isl_take isl_basic_map *bmap2);
1927 __isl_give isl_map *isl_map_flat_product(
1928 __isl_take isl_map *map1,
1929 __isl_take isl_map *map2);
1931 =item * Simplification
1933 __isl_give isl_basic_set *isl_basic_set_gist(
1934 __isl_take isl_basic_set *bset,
1935 __isl_take isl_basic_set *context);
1936 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1937 __isl_take isl_set *context);
1938 __isl_give isl_union_set *isl_union_set_gist(
1939 __isl_take isl_union_set *uset,
1940 __isl_take isl_union_set *context);
1941 __isl_give isl_basic_map *isl_basic_map_gist(
1942 __isl_take isl_basic_map *bmap,
1943 __isl_take isl_basic_map *context);
1944 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1945 __isl_take isl_map *context);
1946 __isl_give isl_union_map *isl_union_map_gist(
1947 __isl_take isl_union_map *umap,
1948 __isl_take isl_union_map *context);
1950 The gist operation returns a set or relation that has the
1951 same intersection with the context as the input set or relation.
1952 Any implicit equality in the intersection is made explicit in the result,
1953 while all inequalities that are redundant with respect to the intersection
1955 In case of union sets and relations, the gist operation is performed
1960 =head3 Lexicographic Optimization
1962 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1963 the following functions
1964 compute a set that contains the lexicographic minimum or maximum
1965 of the elements in C<set> (or C<bset>) for those values of the parameters
1966 that satisfy C<dom>.
1967 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1968 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1970 In other words, the union of the parameter values
1971 for which the result is non-empty and of C<*empty>
1974 __isl_give isl_set *isl_basic_set_partial_lexmin(
1975 __isl_take isl_basic_set *bset,
1976 __isl_take isl_basic_set *dom,
1977 __isl_give isl_set **empty);
1978 __isl_give isl_set *isl_basic_set_partial_lexmax(
1979 __isl_take isl_basic_set *bset,
1980 __isl_take isl_basic_set *dom,
1981 __isl_give isl_set **empty);
1982 __isl_give isl_set *isl_set_partial_lexmin(
1983 __isl_take isl_set *set, __isl_take isl_set *dom,
1984 __isl_give isl_set **empty);
1985 __isl_give isl_set *isl_set_partial_lexmax(
1986 __isl_take isl_set *set, __isl_take isl_set *dom,
1987 __isl_give isl_set **empty);
1989 Given a (basic) set C<set> (or C<bset>), the following functions simply
1990 return a set containing the lexicographic minimum or maximum
1991 of the elements in C<set> (or C<bset>).
1992 In case of union sets, the optimum is computed per space.
1994 __isl_give isl_set *isl_basic_set_lexmin(
1995 __isl_take isl_basic_set *bset);
1996 __isl_give isl_set *isl_basic_set_lexmax(
1997 __isl_take isl_basic_set *bset);
1998 __isl_give isl_set *isl_set_lexmin(
1999 __isl_take isl_set *set);
2000 __isl_give isl_set *isl_set_lexmax(
2001 __isl_take isl_set *set);
2002 __isl_give isl_union_set *isl_union_set_lexmin(
2003 __isl_take isl_union_set *uset);
2004 __isl_give isl_union_set *isl_union_set_lexmax(
2005 __isl_take isl_union_set *uset);
2007 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2008 the following functions
2009 compute a relation that maps each element of C<dom>
2010 to the single lexicographic minimum or maximum
2011 of the elements that are associated to that same
2012 element in C<map> (or C<bmap>).
2013 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2014 that contains the elements in C<dom> that do not map
2015 to any elements in C<map> (or C<bmap>).
2016 In other words, the union of the domain of the result and of C<*empty>
2019 __isl_give isl_map *isl_basic_map_partial_lexmax(
2020 __isl_take isl_basic_map *bmap,
2021 __isl_take isl_basic_set *dom,
2022 __isl_give isl_set **empty);
2023 __isl_give isl_map *isl_basic_map_partial_lexmin(
2024 __isl_take isl_basic_map *bmap,
2025 __isl_take isl_basic_set *dom,
2026 __isl_give isl_set **empty);
2027 __isl_give isl_map *isl_map_partial_lexmax(
2028 __isl_take isl_map *map, __isl_take isl_set *dom,
2029 __isl_give isl_set **empty);
2030 __isl_give isl_map *isl_map_partial_lexmin(
2031 __isl_take isl_map *map, __isl_take isl_set *dom,
2032 __isl_give isl_set **empty);
2034 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2035 return a map mapping each element in the domain of
2036 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2037 of all elements associated to that element.
2038 In case of union relations, the optimum is computed per space.
2040 __isl_give isl_map *isl_basic_map_lexmin(
2041 __isl_take isl_basic_map *bmap);
2042 __isl_give isl_map *isl_basic_map_lexmax(
2043 __isl_take isl_basic_map *bmap);
2044 __isl_give isl_map *isl_map_lexmin(
2045 __isl_take isl_map *map);
2046 __isl_give isl_map *isl_map_lexmax(
2047 __isl_take isl_map *map);
2048 __isl_give isl_union_map *isl_union_map_lexmin(
2049 __isl_take isl_union_map *umap);
2050 __isl_give isl_union_map *isl_union_map_lexmax(
2051 __isl_take isl_union_map *umap);
2055 Lists are defined over several element types, including
2056 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2057 Here we take lists of C<isl_set>s as an example.
2058 Lists can be created, copied and freed using the following functions.
2060 #include <isl/list.h>
2061 __isl_give isl_set_list *isl_set_list_alloc(
2062 isl_ctx *ctx, int n);
2063 __isl_give isl_set_list *isl_set_list_copy(
2064 __isl_keep isl_set_list *list);
2065 __isl_give isl_set_list *isl_set_list_add(
2066 __isl_take isl_set_list *list,
2067 __isl_take isl_set *el);
2068 void isl_set_list_free(__isl_take isl_set_list *list);
2070 C<isl_set_list_alloc> creates an empty list with a capacity for
2073 Lists can be inspected using the following functions.
2075 #include <isl/list.h>
2076 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2077 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2078 __isl_give struct isl_set *isl_set_list_get_set(
2079 __isl_keep isl_set_list *list, int index);
2080 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2081 int (*fn)(__isl_take struct isl_set *el, void *user),
2084 Lists can be printed using
2086 #include <isl/list.h>
2087 __isl_give isl_printer *isl_printer_print_set_list(
2088 __isl_take isl_printer *p,
2089 __isl_keep isl_set_list *list);
2093 Matrices can be created, copied and freed using the following functions.
2095 #include <isl/mat.h>
2096 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2097 unsigned n_row, unsigned n_col);
2098 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2099 void isl_mat_free(__isl_take isl_mat *mat);
2101 Note that the elements of a newly created matrix may have arbitrary values.
2102 The elements can be changed and inspected using the following functions.
2104 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2105 int isl_mat_rows(__isl_keep isl_mat *mat);
2106 int isl_mat_cols(__isl_keep isl_mat *mat);
2107 int isl_mat_get_element(__isl_keep isl_mat *mat,
2108 int row, int col, isl_int *v);
2109 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2110 int row, int col, isl_int v);
2111 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2112 int row, int col, int v);
2114 C<isl_mat_get_element> will return a negative value if anything went wrong.
2115 In that case, the value of C<*v> is undefined.
2117 The following function can be used to compute the (right) inverse
2118 of a matrix, i.e., a matrix such that the product of the original
2119 and the inverse (in that order) is a multiple of the identity matrix.
2120 The input matrix is assumed to be of full row-rank.
2122 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2124 The following function can be used to compute the (right) kernel
2125 (or null space) of a matrix, i.e., a matrix such that the product of
2126 the original and the kernel (in that order) is the zero matrix.
2128 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2130 =head2 Quasi Affine Expressions
2132 The zero quasi affine expression can be created using
2134 __isl_give isl_aff *isl_aff_zero(
2135 __isl_take isl_local_space *ls);
2137 Quasi affine expressions can be copied and free using
2139 #include <isl/aff.h>
2140 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2141 void *isl_aff_free(__isl_take isl_aff *aff);
2143 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2144 using the following function. The constraint is required to have
2145 a non-zero coefficient for the specified dimension.
2147 #include <isl/constraint.h>
2148 __isl_give isl_aff *isl_constraint_get_bound(
2149 __isl_keep isl_constraint *constraint,
2150 enum isl_dim_type type, int pos);
2152 Conversely, an equality constraint equating
2153 the affine expression to zero or an inequality constraint enforcing
2154 the affine expression to be non-negative, can be constructed using
2156 __isl_give isl_constraint *isl_equality_from_aff(
2157 __isl_take isl_aff *aff);
2158 __isl_give isl_constraint *isl_inequality_from_aff(
2159 __isl_take isl_aff *aff);
2161 The expression can be inspected using
2163 #include <isl/aff.h>
2164 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2165 int isl_aff_dim(__isl_keep isl_aff *aff,
2166 enum isl_dim_type type);
2167 __isl_give isl_local_space *isl_aff_get_local_space(
2168 __isl_keep isl_aff *aff);
2169 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2170 enum isl_dim_type type, unsigned pos);
2171 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2173 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2174 enum isl_dim_type type, int pos, isl_int *v);
2175 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2177 __isl_give isl_div *isl_aff_get_div(
2178 __isl_keep isl_aff *aff, int pos);
2180 It can be modified using
2182 #include <isl/aff.h>
2183 __isl_give isl_aff *isl_aff_set_constant(
2184 __isl_take isl_aff *aff, isl_int v);
2185 __isl_give isl_aff *isl_aff_set_constant_si(
2186 __isl_take isl_aff *aff, int v);
2187 __isl_give isl_aff *isl_aff_set_coefficient(
2188 __isl_take isl_aff *aff,
2189 enum isl_dim_type type, int pos, isl_int v);
2190 __isl_give isl_aff *isl_aff_set_coefficient_si(
2191 __isl_take isl_aff *aff,
2192 enum isl_dim_type type, int pos, int v);
2193 __isl_give isl_aff *isl_aff_set_denominator(
2194 __isl_take isl_aff *aff, isl_int v);
2196 __isl_give isl_aff *isl_aff_add_constant(
2197 __isl_take isl_aff *aff, isl_int v);
2198 __isl_give isl_aff *isl_aff_add_coefficient_si(
2199 __isl_take isl_aff *aff,
2200 enum isl_dim_type type, int pos, int v);
2202 Note that the C<set_constant> and C<set_coefficient> functions
2203 set the I<numerator> of the constant or coefficient, while
2204 C<add_constant> and C<add_coefficient> add an integer value to
2205 the possibly rational constant or coefficient.
2209 #include <isl/aff.h>
2210 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2211 __isl_take isl_aff *aff2);
2212 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2213 __isl_take isl_aff *aff2);
2214 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2215 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2216 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2218 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2221 An expression can be printed using
2223 #include <isl/aff.h>
2224 __isl_give isl_printer *isl_printer_print_aff(
2225 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2229 Points are elements of a set. They can be used to construct
2230 simple sets (boxes) or they can be used to represent the
2231 individual elements of a set.
2232 The zero point (the origin) can be created using
2234 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2236 The coordinates of a point can be inspected, set and changed
2239 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2240 enum isl_dim_type type, int pos, isl_int *v);
2241 __isl_give isl_point *isl_point_set_coordinate(
2242 __isl_take isl_point *pnt,
2243 enum isl_dim_type type, int pos, isl_int v);
2245 __isl_give isl_point *isl_point_add_ui(
2246 __isl_take isl_point *pnt,
2247 enum isl_dim_type type, int pos, unsigned val);
2248 __isl_give isl_point *isl_point_sub_ui(
2249 __isl_take isl_point *pnt,
2250 enum isl_dim_type type, int pos, unsigned val);
2252 Points can be copied or freed using
2254 __isl_give isl_point *isl_point_copy(
2255 __isl_keep isl_point *pnt);
2256 void isl_point_free(__isl_take isl_point *pnt);
2258 A singleton set can be created from a point using
2260 __isl_give isl_basic_set *isl_basic_set_from_point(
2261 __isl_take isl_point *pnt);
2262 __isl_give isl_set *isl_set_from_point(
2263 __isl_take isl_point *pnt);
2265 and a box can be created from two opposite extremal points using
2267 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2268 __isl_take isl_point *pnt1,
2269 __isl_take isl_point *pnt2);
2270 __isl_give isl_set *isl_set_box_from_points(
2271 __isl_take isl_point *pnt1,
2272 __isl_take isl_point *pnt2);
2274 All elements of a B<bounded> (union) set can be enumerated using
2275 the following functions.
2277 int isl_set_foreach_point(__isl_keep isl_set *set,
2278 int (*fn)(__isl_take isl_point *pnt, void *user),
2280 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2281 int (*fn)(__isl_take isl_point *pnt, void *user),
2284 The function C<fn> is called for each integer point in
2285 C<set> with as second argument the last argument of
2286 the C<isl_set_foreach_point> call. The function C<fn>
2287 should return C<0> on success and C<-1> on failure.
2288 In the latter case, C<isl_set_foreach_point> will stop
2289 enumerating and return C<-1> as well.
2290 If the enumeration is performed successfully and to completion,
2291 then C<isl_set_foreach_point> returns C<0>.
2293 To obtain a single point of a (basic) set, use
2295 __isl_give isl_point *isl_basic_set_sample_point(
2296 __isl_take isl_basic_set *bset);
2297 __isl_give isl_point *isl_set_sample_point(
2298 __isl_take isl_set *set);
2300 If C<set> does not contain any (integer) points, then the
2301 resulting point will be ``void'', a property that can be
2304 int isl_point_is_void(__isl_keep isl_point *pnt);
2306 =head2 Piecewise Quasipolynomials
2308 A piecewise quasipolynomial is a particular kind of function that maps
2309 a parametric point to a rational value.
2310 More specifically, a quasipolynomial is a polynomial expression in greatest
2311 integer parts of affine expressions of parameters and variables.
2312 A piecewise quasipolynomial is a subdivision of a given parametric
2313 domain into disjoint cells with a quasipolynomial associated to
2314 each cell. The value of the piecewise quasipolynomial at a given
2315 point is the value of the quasipolynomial associated to the cell
2316 that contains the point. Outside of the union of cells,
2317 the value is assumed to be zero.
2318 For example, the piecewise quasipolynomial
2320 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2322 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2323 A given piecewise quasipolynomial has a fixed domain dimension.
2324 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2325 defined over different domains.
2326 Piecewise quasipolynomials are mainly used by the C<barvinok>
2327 library for representing the number of elements in a parametric set or map.
2328 For example, the piecewise quasipolynomial above represents
2329 the number of points in the map
2331 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2333 =head3 Printing (Piecewise) Quasipolynomials
2335 Quasipolynomials and piecewise quasipolynomials can be printed
2336 using the following functions.
2338 __isl_give isl_printer *isl_printer_print_qpolynomial(
2339 __isl_take isl_printer *p,
2340 __isl_keep isl_qpolynomial *qp);
2342 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2343 __isl_take isl_printer *p,
2344 __isl_keep isl_pw_qpolynomial *pwqp);
2346 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2347 __isl_take isl_printer *p,
2348 __isl_keep isl_union_pw_qpolynomial *upwqp);
2350 The output format of the printer
2351 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2352 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2354 In case of printing in C<ISL_FORMAT_C>, the user may want
2355 to set the names of all dimensions
2357 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2358 __isl_take isl_qpolynomial *qp,
2359 enum isl_dim_type type, unsigned pos,
2361 __isl_give isl_pw_qpolynomial *
2362 isl_pw_qpolynomial_set_dim_name(
2363 __isl_take isl_pw_qpolynomial *pwqp,
2364 enum isl_dim_type type, unsigned pos,
2367 =head3 Creating New (Piecewise) Quasipolynomials
2369 Some simple quasipolynomials can be created using the following functions.
2370 More complicated quasipolynomials can be created by applying
2371 operations such as addition and multiplication
2372 on the resulting quasipolynomials
2374 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2375 __isl_take isl_dim *dim);
2376 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2377 __isl_take isl_dim *dim);
2378 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2379 __isl_take isl_dim *dim);
2380 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2381 __isl_take isl_dim *dim);
2382 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2383 __isl_take isl_dim *dim);
2384 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2385 __isl_take isl_dim *dim,
2386 const isl_int n, const isl_int d);
2387 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2388 __isl_take isl_div *div);
2389 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2390 __isl_take isl_dim *dim,
2391 enum isl_dim_type type, unsigned pos);
2392 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2393 __isl_take isl_aff *aff);
2395 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2396 with a single cell can be created using the following functions.
2397 Multiple of these single cell piecewise quasipolynomials can
2398 be combined to create more complicated piecewise quasipolynomials.
2400 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2401 __isl_take isl_dim *dim);
2402 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2403 __isl_take isl_set *set,
2404 __isl_take isl_qpolynomial *qp);
2406 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2407 __isl_take isl_dim *dim);
2408 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2409 __isl_take isl_pw_qpolynomial *pwqp);
2410 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2411 __isl_take isl_union_pw_qpolynomial *upwqp,
2412 __isl_take isl_pw_qpolynomial *pwqp);
2414 Quasipolynomials can be copied and freed again using the following
2417 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2418 __isl_keep isl_qpolynomial *qp);
2419 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2421 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2422 __isl_keep isl_pw_qpolynomial *pwqp);
2423 void isl_pw_qpolynomial_free(
2424 __isl_take isl_pw_qpolynomial *pwqp);
2426 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2427 __isl_keep isl_union_pw_qpolynomial *upwqp);
2428 void isl_union_pw_qpolynomial_free(
2429 __isl_take isl_union_pw_qpolynomial *upwqp);
2431 =head3 Inspecting (Piecewise) Quasipolynomials
2433 To iterate over all piecewise quasipolynomials in a union
2434 piecewise quasipolynomial, use the following function
2436 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2437 __isl_keep isl_union_pw_qpolynomial *upwqp,
2438 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2441 To extract the piecewise quasipolynomial from a union with a given dimension
2444 __isl_give isl_pw_qpolynomial *
2445 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2446 __isl_keep isl_union_pw_qpolynomial *upwqp,
2447 __isl_take isl_dim *dim);
2449 To iterate over the cells in a piecewise quasipolynomial,
2450 use either of the following two functions
2452 int isl_pw_qpolynomial_foreach_piece(
2453 __isl_keep isl_pw_qpolynomial *pwqp,
2454 int (*fn)(__isl_take isl_set *set,
2455 __isl_take isl_qpolynomial *qp,
2456 void *user), void *user);
2457 int isl_pw_qpolynomial_foreach_lifted_piece(
2458 __isl_keep isl_pw_qpolynomial *pwqp,
2459 int (*fn)(__isl_take isl_set *set,
2460 __isl_take isl_qpolynomial *qp,
2461 void *user), void *user);
2463 As usual, the function C<fn> should return C<0> on success
2464 and C<-1> on failure. The difference between
2465 C<isl_pw_qpolynomial_foreach_piece> and
2466 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2467 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2468 compute unique representations for all existentially quantified
2469 variables and then turn these existentially quantified variables
2470 into extra set variables, adapting the associated quasipolynomial
2471 accordingly. This means that the C<set> passed to C<fn>
2472 will not have any existentially quantified variables, but that
2473 the dimensions of the sets may be different for different
2474 invocations of C<fn>.
2476 To iterate over all terms in a quasipolynomial,
2479 int isl_qpolynomial_foreach_term(
2480 __isl_keep isl_qpolynomial *qp,
2481 int (*fn)(__isl_take isl_term *term,
2482 void *user), void *user);
2484 The terms themselves can be inspected and freed using
2487 unsigned isl_term_dim(__isl_keep isl_term *term,
2488 enum isl_dim_type type);
2489 void isl_term_get_num(__isl_keep isl_term *term,
2491 void isl_term_get_den(__isl_keep isl_term *term,
2493 int isl_term_get_exp(__isl_keep isl_term *term,
2494 enum isl_dim_type type, unsigned pos);
2495 __isl_give isl_div *isl_term_get_div(
2496 __isl_keep isl_term *term, unsigned pos);
2497 void isl_term_free(__isl_take isl_term *term);
2499 Each term is a product of parameters, set variables and
2500 integer divisions. The function C<isl_term_get_exp>
2501 returns the exponent of a given dimensions in the given term.
2502 The C<isl_int>s in the arguments of C<isl_term_get_num>
2503 and C<isl_term_get_den> need to have been initialized
2504 using C<isl_int_init> before calling these functions.
2506 =head3 Properties of (Piecewise) Quasipolynomials
2508 To check whether a quasipolynomial is actually a constant,
2509 use the following function.
2511 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2512 isl_int *n, isl_int *d);
2514 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2515 then the numerator and denominator of the constant
2516 are returned in C<*n> and C<*d>, respectively.
2518 =head3 Operations on (Piecewise) Quasipolynomials
2520 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2521 __isl_take isl_qpolynomial *qp);
2522 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2523 __isl_take isl_qpolynomial *qp1,
2524 __isl_take isl_qpolynomial *qp2);
2525 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2526 __isl_take isl_qpolynomial *qp1,
2527 __isl_take isl_qpolynomial *qp2);
2528 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2529 __isl_take isl_qpolynomial *qp1,
2530 __isl_take isl_qpolynomial *qp2);
2531 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2532 __isl_take isl_qpolynomial *qp, unsigned exponent);
2534 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2535 __isl_take isl_pw_qpolynomial *pwqp1,
2536 __isl_take isl_pw_qpolynomial *pwqp2);
2537 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2538 __isl_take isl_pw_qpolynomial *pwqp1,
2539 __isl_take isl_pw_qpolynomial *pwqp2);
2540 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2541 __isl_take isl_pw_qpolynomial *pwqp1,
2542 __isl_take isl_pw_qpolynomial *pwqp2);
2543 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2544 __isl_take isl_pw_qpolynomial *pwqp);
2545 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2546 __isl_take isl_pw_qpolynomial *pwqp1,
2547 __isl_take isl_pw_qpolynomial *pwqp2);
2549 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2550 __isl_take isl_union_pw_qpolynomial *upwqp1,
2551 __isl_take isl_union_pw_qpolynomial *upwqp2);
2552 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2553 __isl_take isl_union_pw_qpolynomial *upwqp1,
2554 __isl_take isl_union_pw_qpolynomial *upwqp2);
2555 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2556 __isl_take isl_union_pw_qpolynomial *upwqp1,
2557 __isl_take isl_union_pw_qpolynomial *upwqp2);
2559 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2560 __isl_take isl_pw_qpolynomial *pwqp,
2561 __isl_take isl_point *pnt);
2563 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2564 __isl_take isl_union_pw_qpolynomial *upwqp,
2565 __isl_take isl_point *pnt);
2567 __isl_give isl_set *isl_pw_qpolynomial_domain(
2568 __isl_take isl_pw_qpolynomial *pwqp);
2569 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2570 __isl_take isl_pw_qpolynomial *pwpq,
2571 __isl_take isl_set *set);
2573 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2574 __isl_take isl_union_pw_qpolynomial *upwqp);
2575 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2576 __isl_take isl_union_pw_qpolynomial *upwpq,
2577 __isl_take isl_union_set *uset);
2579 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2580 __isl_take isl_qpolynomial *qp,
2581 __isl_take isl_dim *model);
2583 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2584 __isl_take isl_union_pw_qpolynomial *upwqp);
2586 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2587 __isl_take isl_qpolynomial *qp,
2588 __isl_take isl_set *context);
2590 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2591 __isl_take isl_pw_qpolynomial *pwqp,
2592 __isl_take isl_set *context);
2594 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2595 __isl_take isl_union_pw_qpolynomial *upwqp,
2596 __isl_take isl_union_set *context);
2598 The gist operation applies the gist operation to each of
2599 the cells in the domain of the input piecewise quasipolynomial.
2600 The context is also exploited
2601 to simplify the quasipolynomials associated to each cell.
2603 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2604 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2605 __isl_give isl_union_pw_qpolynomial *
2606 isl_union_pw_qpolynomial_to_polynomial(
2607 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2609 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2610 the polynomial will be an overapproximation. If C<sign> is negative,
2611 it will be an underapproximation. If C<sign> is zero, the approximation
2612 will lie somewhere in between.
2614 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2616 A piecewise quasipolynomial reduction is a piecewise
2617 reduction (or fold) of quasipolynomials.
2618 In particular, the reduction can be maximum or a minimum.
2619 The objects are mainly used to represent the result of
2620 an upper or lower bound on a quasipolynomial over its domain,
2621 i.e., as the result of the following function.
2623 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2624 __isl_take isl_pw_qpolynomial *pwqp,
2625 enum isl_fold type, int *tight);
2627 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2628 __isl_take isl_union_pw_qpolynomial *upwqp,
2629 enum isl_fold type, int *tight);
2631 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2632 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2633 is the returned bound is known be tight, i.e., for each value
2634 of the parameters there is at least
2635 one element in the domain that reaches the bound.
2636 If the domain of C<pwqp> is not wrapping, then the bound is computed
2637 over all elements in that domain and the result has a purely parametric
2638 domain. If the domain of C<pwqp> is wrapping, then the bound is
2639 computed over the range of the wrapped relation. The domain of the
2640 wrapped relation becomes the domain of the result.
2642 A (piecewise) quasipolynomial reduction can be copied or freed using the
2643 following functions.
2645 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2646 __isl_keep isl_qpolynomial_fold *fold);
2647 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2648 __isl_keep isl_pw_qpolynomial_fold *pwf);
2649 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2650 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2651 void isl_qpolynomial_fold_free(
2652 __isl_take isl_qpolynomial_fold *fold);
2653 void isl_pw_qpolynomial_fold_free(
2654 __isl_take isl_pw_qpolynomial_fold *pwf);
2655 void isl_union_pw_qpolynomial_fold_free(
2656 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2658 =head3 Printing Piecewise Quasipolynomial Reductions
2660 Piecewise quasipolynomial reductions can be printed
2661 using the following function.
2663 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2664 __isl_take isl_printer *p,
2665 __isl_keep isl_pw_qpolynomial_fold *pwf);
2666 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2667 __isl_take isl_printer *p,
2668 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2670 For C<isl_printer_print_pw_qpolynomial_fold>,
2671 output format of the printer
2672 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2673 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2674 output format of the printer
2675 needs to be set to C<ISL_FORMAT_ISL>.
2676 In case of printing in C<ISL_FORMAT_C>, the user may want
2677 to set the names of all dimensions
2679 __isl_give isl_pw_qpolynomial_fold *
2680 isl_pw_qpolynomial_fold_set_dim_name(
2681 __isl_take isl_pw_qpolynomial_fold *pwf,
2682 enum isl_dim_type type, unsigned pos,
2685 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2687 To iterate over all piecewise quasipolynomial reductions in a union
2688 piecewise quasipolynomial reduction, use the following function
2690 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2691 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2692 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2693 void *user), void *user);
2695 To iterate over the cells in a piecewise quasipolynomial reduction,
2696 use either of the following two functions
2698 int isl_pw_qpolynomial_fold_foreach_piece(
2699 __isl_keep isl_pw_qpolynomial_fold *pwf,
2700 int (*fn)(__isl_take isl_set *set,
2701 __isl_take isl_qpolynomial_fold *fold,
2702 void *user), void *user);
2703 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2704 __isl_keep isl_pw_qpolynomial_fold *pwf,
2705 int (*fn)(__isl_take isl_set *set,
2706 __isl_take isl_qpolynomial_fold *fold,
2707 void *user), void *user);
2709 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2710 of the difference between these two functions.
2712 To iterate over all quasipolynomials in a reduction, use
2714 int isl_qpolynomial_fold_foreach_qpolynomial(
2715 __isl_keep isl_qpolynomial_fold *fold,
2716 int (*fn)(__isl_take isl_qpolynomial *qp,
2717 void *user), void *user);
2719 =head3 Operations on Piecewise Quasipolynomial Reductions
2721 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2722 __isl_take isl_pw_qpolynomial_fold *pwf1,
2723 __isl_take isl_pw_qpolynomial_fold *pwf2);
2725 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2726 __isl_take isl_pw_qpolynomial_fold *pwf1,
2727 __isl_take isl_pw_qpolynomial_fold *pwf2);
2729 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2730 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2731 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2733 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2734 __isl_take isl_pw_qpolynomial_fold *pwf,
2735 __isl_take isl_point *pnt);
2737 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2738 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2739 __isl_take isl_point *pnt);
2741 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2742 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2743 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2744 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2745 __isl_take isl_union_set *uset);
2747 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2748 __isl_take isl_pw_qpolynomial_fold *pwf);
2750 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2751 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2753 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2754 __isl_take isl_pw_qpolynomial_fold *pwf,
2755 __isl_take isl_set *context);
2757 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2758 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2759 __isl_take isl_union_set *context);
2761 The gist operation applies the gist operation to each of
2762 the cells in the domain of the input piecewise quasipolynomial reduction.
2763 In future, the operation will also exploit the context
2764 to simplify the quasipolynomial reductions associated to each cell.
2766 __isl_give isl_pw_qpolynomial_fold *
2767 isl_set_apply_pw_qpolynomial_fold(
2768 __isl_take isl_set *set,
2769 __isl_take isl_pw_qpolynomial_fold *pwf,
2771 __isl_give isl_pw_qpolynomial_fold *
2772 isl_map_apply_pw_qpolynomial_fold(
2773 __isl_take isl_map *map,
2774 __isl_take isl_pw_qpolynomial_fold *pwf,
2776 __isl_give isl_union_pw_qpolynomial_fold *
2777 isl_union_set_apply_union_pw_qpolynomial_fold(
2778 __isl_take isl_union_set *uset,
2779 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2781 __isl_give isl_union_pw_qpolynomial_fold *
2782 isl_union_map_apply_union_pw_qpolynomial_fold(
2783 __isl_take isl_union_map *umap,
2784 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2787 The functions taking a map
2788 compose the given map with the given piecewise quasipolynomial reduction.
2789 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2790 over all elements in the intersection of the range of the map
2791 and the domain of the piecewise quasipolynomial reduction
2792 as a function of an element in the domain of the map.
2793 The functions taking a set compute a bound over all elements in the
2794 intersection of the set and the domain of the
2795 piecewise quasipolynomial reduction.
2797 =head2 Dependence Analysis
2799 C<isl> contains specialized functionality for performing
2800 array dataflow analysis. That is, given a I<sink> access relation
2801 and a collection of possible I<source> access relations,
2802 C<isl> can compute relations that describe
2803 for each iteration of the sink access, which iteration
2804 of which of the source access relations was the last
2805 to access the same data element before the given iteration
2807 To compute standard flow dependences, the sink should be
2808 a read, while the sources should be writes.
2809 If any of the source accesses are marked as being I<may>
2810 accesses, then there will be a dependence to the last
2811 I<must> access B<and> to any I<may> access that follows
2812 this last I<must> access.
2813 In particular, if I<all> sources are I<may> accesses,
2814 then memory based dependence analysis is performed.
2815 If, on the other hand, all sources are I<must> accesses,
2816 then value based dependence analysis is performed.
2818 #include <isl/flow.h>
2820 typedef int (*isl_access_level_before)(void *first, void *second);
2822 __isl_give isl_access_info *isl_access_info_alloc(
2823 __isl_take isl_map *sink,
2824 void *sink_user, isl_access_level_before fn,
2826 __isl_give isl_access_info *isl_access_info_add_source(
2827 __isl_take isl_access_info *acc,
2828 __isl_take isl_map *source, int must,
2830 void isl_access_info_free(__isl_take isl_access_info *acc);
2832 __isl_give isl_flow *isl_access_info_compute_flow(
2833 __isl_take isl_access_info *acc);
2835 int isl_flow_foreach(__isl_keep isl_flow *deps,
2836 int (*fn)(__isl_take isl_map *dep, int must,
2837 void *dep_user, void *user),
2839 __isl_give isl_map *isl_flow_get_no_source(
2840 __isl_keep isl_flow *deps, int must);
2841 void isl_flow_free(__isl_take isl_flow *deps);
2843 The function C<isl_access_info_compute_flow> performs the actual
2844 dependence analysis. The other functions are used to construct
2845 the input for this function or to read off the output.
2847 The input is collected in an C<isl_access_info>, which can
2848 be created through a call to C<isl_access_info_alloc>.
2849 The arguments to this functions are the sink access relation
2850 C<sink>, a token C<sink_user> used to identify the sink
2851 access to the user, a callback function for specifying the
2852 relative order of source and sink accesses, and the number
2853 of source access relations that will be added.
2854 The callback function has type C<int (*)(void *first, void *second)>.
2855 The function is called with two user supplied tokens identifying
2856 either a source or the sink and it should return the shared nesting
2857 level and the relative order of the two accesses.
2858 In particular, let I<n> be the number of loops shared by
2859 the two accesses. If C<first> precedes C<second> textually,
2860 then the function should return I<2 * n + 1>; otherwise,
2861 it should return I<2 * n>.
2862 The sources can be added to the C<isl_access_info> by performing
2863 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2864 C<must> indicates whether the source is a I<must> access
2865 or a I<may> access. Note that a multi-valued access relation
2866 should only be marked I<must> if every iteration in the domain
2867 of the relation accesses I<all> elements in its image.
2868 The C<source_user> token is again used to identify
2869 the source access. The range of the source access relation
2870 C<source> should have the same dimension as the range
2871 of the sink access relation.
2872 The C<isl_access_info_free> function should usually not be
2873 called explicitly, because it is called implicitly by
2874 C<isl_access_info_compute_flow>.
2876 The result of the dependence analysis is collected in an
2877 C<isl_flow>. There may be elements of
2878 the sink access for which no preceding source access could be
2879 found or for which all preceding sources are I<may> accesses.
2880 The relations containing these elements can be obtained through
2881 calls to C<isl_flow_get_no_source>, the first with C<must> set
2882 and the second with C<must> unset.
2883 In the case of standard flow dependence analysis,
2884 with the sink a read and the sources I<must> writes,
2885 the first relation corresponds to the reads from uninitialized
2886 array elements and the second relation is empty.
2887 The actual flow dependences can be extracted using
2888 C<isl_flow_foreach>. This function will call the user-specified
2889 callback function C<fn> for each B<non-empty> dependence between
2890 a source and the sink. The callback function is called
2891 with four arguments, the actual flow dependence relation
2892 mapping source iterations to sink iterations, a boolean that
2893 indicates whether it is a I<must> or I<may> dependence, a token
2894 identifying the source and an additional C<void *> with value
2895 equal to the third argument of the C<isl_flow_foreach> call.
2896 A dependence is marked I<must> if it originates from a I<must>
2897 source and if it is not followed by any I<may> sources.
2899 After finishing with an C<isl_flow>, the user should call
2900 C<isl_flow_free> to free all associated memory.
2902 A higher-level interface to dependence analysis is provided
2903 by the following function.
2905 #include <isl/flow.h>
2907 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2908 __isl_take isl_union_map *must_source,
2909 __isl_take isl_union_map *may_source,
2910 __isl_take isl_union_map *schedule,
2911 __isl_give isl_union_map **must_dep,
2912 __isl_give isl_union_map **may_dep,
2913 __isl_give isl_union_map **must_no_source,
2914 __isl_give isl_union_map **may_no_source);
2916 The arrays are identified by the tuple names of the ranges
2917 of the accesses. The iteration domains by the tuple names
2918 of the domains of the accesses and of the schedule.
2919 The relative order of the iteration domains is given by the
2920 schedule. The relations returned through C<must_no_source>
2921 and C<may_no_source> are subsets of C<sink>.
2922 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2923 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2924 any of the other arguments is treated as an error.
2928 B<The functionality described in this section is fairly new
2929 and may be subject to change.>
2931 The following function can be used to compute a schedule
2932 for a union of domains. The generated schedule respects
2933 all C<validity> dependences. That is, all dependence distances
2934 over these dependences in the scheduled space are lexicographically
2935 positive. The generated schedule schedule also tries to minimize
2936 the dependence distances over C<proximity> dependences.
2937 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2938 for groups of domains where the dependence distances have only
2939 non-negative values.
2940 The algorithm used to construct the schedule is similar to that
2943 #include <isl/schedule.h>
2944 __isl_give isl_schedule *isl_union_set_compute_schedule(
2945 __isl_take isl_union_set *domain,
2946 __isl_take isl_union_map *validity,
2947 __isl_take isl_union_map *proximity);
2948 void *isl_schedule_free(__isl_take isl_schedule *sched);
2950 A mapping from the domains to the scheduled space can be obtained
2951 from an C<isl_schedule> using the following function.
2953 __isl_give isl_union_map *isl_schedule_get_map(
2954 __isl_keep isl_schedule *sched);
2956 A representation of the schedule can be printed using
2958 __isl_give isl_printer *isl_printer_print_schedule(
2959 __isl_take isl_printer *p,
2960 __isl_keep isl_schedule *schedule);
2962 A representation of the schedule as a forest of bands can be obtained
2963 using the following function.
2965 __isl_give isl_band_list *isl_schedule_get_band_forest(
2966 __isl_keep isl_schedule *schedule);
2968 The list can be manipulated as explained in L<"Lists">.
2969 The bands inside the list can be copied and freed using the following
2972 #include <isl/band.h>
2973 __isl_give isl_band *isl_band_copy(
2974 __isl_keep isl_band *band);
2975 void *isl_band_free(__isl_take isl_band *band);
2977 Each band contains zero or more scheduling dimensions.
2978 These are referred to as the members of the band.
2979 The section of the schedule that corresponds to the band is
2980 referred to as the partial schedule of the band.
2981 For those nodes that participate in a band, the outer scheduling
2982 dimensions form the prefix schedule, while the inner scheduling
2983 dimensions form the suffix schedule.
2984 That is, if we take a cut of the band forest, then the union of
2985 the concatenations of the prefix, partial and suffix schedules of
2986 each band in the cut is equal to the entire schedule (modulo
2987 some possible padding at the end with zero scheduling dimensions).
2988 The properties of a band can be inspected using the following functions.
2990 #include <isl/band.h>
2991 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
2993 int isl_band_has_children(__isl_keep isl_band *band);
2994 __isl_give isl_band_list *isl_band_get_children(
2995 __isl_keep isl_band *band);
2997 __isl_give isl_union_map *isl_band_get_prefix_schedule(
2998 __isl_keep isl_band *band);
2999 __isl_give isl_union_map *isl_band_get_partial_schedule(
3000 __isl_keep isl_band *band);
3001 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3002 __isl_keep isl_band *band);
3004 int isl_band_n_member(__isl_keep isl_band *band);
3005 int isl_band_member_is_parallel(__isl_keep isl_band *band,
3008 Note that a scheduling dimension is considered parallel if it
3009 does not carry any proximity dependences.
3011 A representation of the band can be printed using
3013 #include <isl/band.h>
3014 __isl_give isl_printer *isl_printer_print_band(
3015 __isl_take isl_printer *p,
3016 __isl_keep isl_band *band);
3018 Alternatively, the schedule mapping
3019 can also be obtained in pieces using the following functions.
3021 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3022 __isl_give isl_union_map *isl_schedule_get_band(
3023 __isl_keep isl_schedule *sched, unsigned band);
3025 C<isl_schedule_n_band> returns the maximal number of bands.
3026 C<isl_schedule_get_band> returns a union of mappings from a domain to
3027 the band of consecutive schedule dimensions with the given sequence
3028 number for that domain. Bands with the same sequence number but for
3029 different domains may be completely unrelated.
3030 Within a band, the corresponding coordinates of the distance vectors
3031 are all non-negative, assuming that the coordinates for all previous
3034 =head2 Parametric Vertex Enumeration
3036 The parametric vertex enumeration described in this section
3037 is mainly intended to be used internally and by the C<barvinok>
3040 #include <isl/vertices.h>
3041 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3042 __isl_keep isl_basic_set *bset);
3044 The function C<isl_basic_set_compute_vertices> performs the
3045 actual computation of the parametric vertices and the chamber
3046 decomposition and store the result in an C<isl_vertices> object.
3047 This information can be queried by either iterating over all
3048 the vertices or iterating over all the chambers or cells
3049 and then iterating over all vertices that are active on the chamber.
3051 int isl_vertices_foreach_vertex(
3052 __isl_keep isl_vertices *vertices,
3053 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3056 int isl_vertices_foreach_cell(
3057 __isl_keep isl_vertices *vertices,
3058 int (*fn)(__isl_take isl_cell *cell, void *user),
3060 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3061 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3064 Other operations that can be performed on an C<isl_vertices> object are
3067 isl_ctx *isl_vertices_get_ctx(
3068 __isl_keep isl_vertices *vertices);
3069 int isl_vertices_get_n_vertices(
3070 __isl_keep isl_vertices *vertices);
3071 void isl_vertices_free(__isl_take isl_vertices *vertices);
3073 Vertices can be inspected and destroyed using the following functions.
3075 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3076 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3077 __isl_give isl_basic_set *isl_vertex_get_domain(
3078 __isl_keep isl_vertex *vertex);
3079 __isl_give isl_basic_set *isl_vertex_get_expr(
3080 __isl_keep isl_vertex *vertex);
3081 void isl_vertex_free(__isl_take isl_vertex *vertex);
3083 C<isl_vertex_get_expr> returns a singleton parametric set describing
3084 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3086 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3087 B<rational> basic sets, so they should mainly be used for inspection
3088 and should not be mixed with integer sets.
3090 Chambers can be inspected and destroyed using the following functions.
3092 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3093 __isl_give isl_basic_set *isl_cell_get_domain(
3094 __isl_keep isl_cell *cell);
3095 void isl_cell_free(__isl_take isl_cell *cell);
3099 Although C<isl> is mainly meant to be used as a library,
3100 it also contains some basic applications that use some
3101 of the functionality of C<isl>.
3102 The input may be specified in either the L<isl format>
3103 or the L<PolyLib format>.
3105 =head2 C<isl_polyhedron_sample>
3107 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3108 an integer element of the polyhedron, if there is any.
3109 The first column in the output is the denominator and is always
3110 equal to 1. If the polyhedron contains no integer points,
3111 then a vector of length zero is printed.
3115 C<isl_pip> takes the same input as the C<example> program
3116 from the C<piplib> distribution, i.e., a set of constraints
3117 on the parameters, a line containing only -1 and finally a set
3118 of constraints on a parametric polyhedron.
3119 The coefficients of the parameters appear in the last columns
3120 (but before the final constant column).
3121 The output is the lexicographic minimum of the parametric polyhedron.
3122 As C<isl> currently does not have its own output format, the output
3123 is just a dump of the internal state.
3125 =head2 C<isl_polyhedron_minimize>
3127 C<isl_polyhedron_minimize> computes the minimum of some linear
3128 or affine objective function over the integer points in a polyhedron.
3129 If an affine objective function
3130 is given, then the constant should appear in the last column.
3132 =head2 C<isl_polytope_scan>
3134 Given a polytope, C<isl_polytope_scan> prints
3135 all integer points in the polytope.