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_qpolynomial_fold_get_dim(
477 __isl_keep isl_qpolynomial_fold *fold);
478 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
479 __isl_keep isl_pw_qpolynomial *pwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
481 __isl_keep isl_union_pw_qpolynomial *upwqp);
482 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
483 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
486 __isl_give isl_dim *isl_aff_get_dim(
487 __isl_keep isl_aff *aff);
489 #include <isl/point.h>
490 __isl_give isl_dim *isl_point_get_dim(
491 __isl_keep isl_point *pnt);
493 The names of the individual dimensions may be set or read off
494 using the following functions.
497 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
498 enum isl_dim_type type, unsigned pos,
499 __isl_keep const char *name);
500 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
501 enum isl_dim_type type, unsigned pos);
503 Note that C<isl_dim_get_name> returns a pointer to some internal
504 data structure, so the result can only be used while the
505 corresponding C<isl_dim> is alive.
506 Also note that every function that operates on two sets or relations
507 requires that both arguments have the same parameters. This also
508 means that if one of the arguments has named parameters, then the
509 other needs to have named parameters too and the names need to match.
510 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
511 have different parameters (as long as they are named), in which case
512 the result will have as parameters the union of the parameters of
515 The names of entire spaces may be set or read off
516 using the following functions.
519 __isl_give isl_dim *isl_dim_set_tuple_name(
520 __isl_take isl_dim *dim,
521 enum isl_dim_type type, const char *s);
522 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
523 enum isl_dim_type type);
525 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
526 or C<isl_dim_set>. As with C<isl_dim_get_name>,
527 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
529 Binary operations require the corresponding spaces of their arguments
530 to have the same name.
532 Spaces can be nested. In particular, the domain of a set or
533 the domain or range of a relation can be a nested relation.
534 The following functions can be used to construct and deconstruct
535 such nested dimension specifications.
538 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
539 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
540 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
542 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
543 be the dimension specification of a set, while that of
544 C<isl_dim_wrap> should be the dimension specification of a relation.
545 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
546 of a relation, while that of C<isl_dim_wrap> is the dimension specification
549 Dimension specifications can be created from other dimension
550 specifications using the following functions.
552 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
553 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
554 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
555 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
556 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
557 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
558 __isl_take isl_dim *right);
559 __isl_give isl_dim *isl_dim_align_params(
560 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
561 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
562 enum isl_dim_type type, unsigned pos, unsigned n);
563 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
564 enum isl_dim_type type, unsigned n);
565 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
566 enum isl_dim_type type, unsigned first, unsigned n);
567 __isl_give isl_dim *isl_dim_map_from_set(
568 __isl_take isl_dim *dim);
569 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
571 Note that if dimensions are added or removed from a space, then
572 the name and the internal structure are lost.
576 A local space is essentially a dimension specification with
577 zero or more existentially quantified variables.
578 The local space of a basic set or relation can be obtained
579 using the following functions.
582 __isl_give isl_local_space *isl_basic_set_get_local_space(
583 __isl_keep isl_basic_set *bset);
586 __isl_give isl_local_space *isl_basic_map_get_local_space(
587 __isl_keep isl_basic_map *bmap);
589 A new local space can be created from a dimension specification using
591 #include <isl/local_space.h>
592 __isl_give isl_local_space *isl_local_space_from_dim(
593 __isl_take isl_dim *dim);
595 They can be inspected, copied and freed using the following functions.
597 #include <isl/local_space.h>
598 isl_ctx *isl_local_space_get_ctx(
599 __isl_keep isl_local_space *ls);
600 int isl_local_space_dim(__isl_keep isl_local_space *ls,
601 enum isl_dim_type type);
602 const char *isl_local_space_get_dim_name(
603 __isl_keep isl_local_space *ls,
604 enum isl_dim_type type, unsigned pos);
605 __isl_give isl_dim *isl_local_space_get_dim(
606 __isl_keep isl_local_space *ls);
607 __isl_give isl_div *isl_local_space_get_div(
608 __isl_keep isl_local_space *ls, int pos);
609 __isl_give isl_local_space *isl_local_space_copy(
610 __isl_keep isl_local_space *ls);
611 void *isl_local_space_free(__isl_take isl_local_space *ls);
613 Two local spaces can be compared using
615 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
616 __isl_keep isl_local_space *ls2);
618 Local spaces can be created from other local spaces
619 using the following functions.
621 __isl_give isl_local_space *isl_local_space_from_domain(
622 __isl_take isl_local_space *ls);
623 __isl_give isl_local_space *isl_local_space_add_dim(
624 __isl_take isl_local_space *ls,
625 enum isl_dim_type type, unsigned n);
627 =head2 Input and Output
629 C<isl> supports its own input/output format, which is similar
630 to the C<Omega> format, but also supports the C<PolyLib> format
635 The C<isl> format is similar to that of C<Omega>, but has a different
636 syntax for describing the parameters and allows for the definition
637 of an existentially quantified variable as the integer division
638 of an affine expression.
639 For example, the set of integers C<i> between C<0> and C<n>
640 such that C<i % 10 <= 6> can be described as
642 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
645 A set or relation can have several disjuncts, separated
646 by the keyword C<or>. Each disjunct is either a conjunction
647 of constraints or a projection (C<exists>) of a conjunction
648 of constraints. The constraints are separated by the keyword
651 =head3 C<PolyLib> format
653 If the represented set is a union, then the first line
654 contains a single number representing the number of disjuncts.
655 Otherwise, a line containing the number C<1> is optional.
657 Each disjunct is represented by a matrix of constraints.
658 The first line contains two numbers representing
659 the number of rows and columns,
660 where the number of rows is equal to the number of constraints
661 and the number of columns is equal to two plus the number of variables.
662 The following lines contain the actual rows of the constraint matrix.
663 In each row, the first column indicates whether the constraint
664 is an equality (C<0>) or inequality (C<1>). The final column
665 corresponds to the constant term.
667 If the set is parametric, then the coefficients of the parameters
668 appear in the last columns before the constant column.
669 The coefficients of any existentially quantified variables appear
670 between those of the set variables and those of the parameters.
672 =head3 Extended C<PolyLib> format
674 The extended C<PolyLib> format is nearly identical to the
675 C<PolyLib> format. The only difference is that the line
676 containing the number of rows and columns of a constraint matrix
677 also contains four additional numbers:
678 the number of output dimensions, the number of input dimensions,
679 the number of local dimensions (i.e., the number of existentially
680 quantified variables) and the number of parameters.
681 For sets, the number of ``output'' dimensions is equal
682 to the number of set dimensions, while the number of ``input''
688 __isl_give isl_basic_set *isl_basic_set_read_from_file(
689 isl_ctx *ctx, FILE *input, int nparam);
690 __isl_give isl_basic_set *isl_basic_set_read_from_str(
691 isl_ctx *ctx, const char *str, int nparam);
692 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
693 FILE *input, int nparam);
694 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
695 const char *str, int nparam);
698 __isl_give isl_basic_map *isl_basic_map_read_from_file(
699 isl_ctx *ctx, FILE *input, int nparam);
700 __isl_give isl_basic_map *isl_basic_map_read_from_str(
701 isl_ctx *ctx, const char *str, int nparam);
702 __isl_give isl_map *isl_map_read_from_file(
703 struct isl_ctx *ctx, FILE *input, int nparam);
704 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
705 const char *str, int nparam);
707 #include <isl/union_set.h>
708 __isl_give isl_union_set *isl_union_set_read_from_file(
709 isl_ctx *ctx, FILE *input);
710 __isl_give isl_union_set *isl_union_set_read_from_str(
711 struct isl_ctx *ctx, const char *str);
713 #include <isl/union_map.h>
714 __isl_give isl_union_map *isl_union_map_read_from_file(
715 isl_ctx *ctx, FILE *input);
716 __isl_give isl_union_map *isl_union_map_read_from_str(
717 struct isl_ctx *ctx, const char *str);
719 The input format is autodetected and may be either the C<PolyLib> format
720 or the C<isl> format.
721 C<nparam> specifies how many of the final columns in
722 the C<PolyLib> format correspond to parameters.
723 If input is given in the C<isl> format, then the number
724 of parameters needs to be equal to C<nparam>.
725 If C<nparam> is negative, then any number of parameters
726 is accepted in the C<isl> format and zero parameters
727 are assumed in the C<PolyLib> format.
731 Before anything can be printed, an C<isl_printer> needs to
734 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
736 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
737 void isl_printer_free(__isl_take isl_printer *printer);
738 __isl_give char *isl_printer_get_str(
739 __isl_keep isl_printer *printer);
741 The behavior of the printer can be modified in various ways
743 __isl_give isl_printer *isl_printer_set_output_format(
744 __isl_take isl_printer *p, int output_format);
745 __isl_give isl_printer *isl_printer_set_indent(
746 __isl_take isl_printer *p, int indent);
747 __isl_give isl_printer *isl_printer_indent(
748 __isl_take isl_printer *p, int indent);
749 __isl_give isl_printer *isl_printer_set_prefix(
750 __isl_take isl_printer *p, const char *prefix);
751 __isl_give isl_printer *isl_printer_set_suffix(
752 __isl_take isl_printer *p, const char *suffix);
754 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
755 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
756 and defaults to C<ISL_FORMAT_ISL>.
757 Each line in the output is indented by C<indent> (set by
758 C<isl_printer_set_indent>) spaces
759 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
760 In the C<PolyLib> format output,
761 the coefficients of the existentially quantified variables
762 appear between those of the set variables and those
764 The function C<isl_printer_indent> increases the indentation
765 by the specified amount (which may be negative).
767 To actually print something, use
770 __isl_give isl_printer *isl_printer_print_basic_set(
771 __isl_take isl_printer *printer,
772 __isl_keep isl_basic_set *bset);
773 __isl_give isl_printer *isl_printer_print_set(
774 __isl_take isl_printer *printer,
775 __isl_keep isl_set *set);
778 __isl_give isl_printer *isl_printer_print_basic_map(
779 __isl_take isl_printer *printer,
780 __isl_keep isl_basic_map *bmap);
781 __isl_give isl_printer *isl_printer_print_map(
782 __isl_take isl_printer *printer,
783 __isl_keep isl_map *map);
785 #include <isl/union_set.h>
786 __isl_give isl_printer *isl_printer_print_union_set(
787 __isl_take isl_printer *p,
788 __isl_keep isl_union_set *uset);
790 #include <isl/union_map.h>
791 __isl_give isl_printer *isl_printer_print_union_map(
792 __isl_take isl_printer *p,
793 __isl_keep isl_union_map *umap);
795 When called on a file printer, the following function flushes
796 the file. When called on a string printer, the buffer is cleared.
798 __isl_give isl_printer *isl_printer_flush(
799 __isl_take isl_printer *p);
801 =head2 Creating New Sets and Relations
803 C<isl> has functions for creating some standard sets and relations.
807 =item * Empty sets and relations
809 __isl_give isl_basic_set *isl_basic_set_empty(
810 __isl_take isl_dim *dim);
811 __isl_give isl_basic_map *isl_basic_map_empty(
812 __isl_take isl_dim *dim);
813 __isl_give isl_set *isl_set_empty(
814 __isl_take isl_dim *dim);
815 __isl_give isl_map *isl_map_empty(
816 __isl_take isl_dim *dim);
817 __isl_give isl_union_set *isl_union_set_empty(
818 __isl_take isl_dim *dim);
819 __isl_give isl_union_map *isl_union_map_empty(
820 __isl_take isl_dim *dim);
822 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
823 is only used to specify the parameters.
825 =item * Universe sets and relations
827 __isl_give isl_basic_set *isl_basic_set_universe(
828 __isl_take isl_dim *dim);
829 __isl_give isl_basic_map *isl_basic_map_universe(
830 __isl_take isl_dim *dim);
831 __isl_give isl_set *isl_set_universe(
832 __isl_take isl_dim *dim);
833 __isl_give isl_map *isl_map_universe(
834 __isl_take isl_dim *dim);
835 __isl_give isl_union_set *isl_union_set_universe(
836 __isl_take isl_union_set *uset);
837 __isl_give isl_union_map *isl_union_map_universe(
838 __isl_take isl_union_map *umap);
840 The sets and relations constructed by the functions above
841 contain all integer values, while those constructed by the
842 functions below only contain non-negative values.
844 __isl_give isl_basic_set *isl_basic_set_nat_universe(
845 __isl_take isl_dim *dim);
846 __isl_give isl_basic_map *isl_basic_map_nat_universe(
847 __isl_take isl_dim *dim);
848 __isl_give isl_set *isl_set_nat_universe(
849 __isl_take isl_dim *dim);
850 __isl_give isl_map *isl_map_nat_universe(
851 __isl_take isl_dim *dim);
853 =item * Identity relations
855 __isl_give isl_basic_map *isl_basic_map_identity(
856 __isl_take isl_dim *dim);
857 __isl_give isl_map *isl_map_identity(
858 __isl_take isl_dim *dim);
860 The number of input and output dimensions in C<dim> needs
863 =item * Lexicographic order
865 __isl_give isl_map *isl_map_lex_lt(
866 __isl_take isl_dim *set_dim);
867 __isl_give isl_map *isl_map_lex_le(
868 __isl_take isl_dim *set_dim);
869 __isl_give isl_map *isl_map_lex_gt(
870 __isl_take isl_dim *set_dim);
871 __isl_give isl_map *isl_map_lex_ge(
872 __isl_take isl_dim *set_dim);
873 __isl_give isl_map *isl_map_lex_lt_first(
874 __isl_take isl_dim *dim, unsigned n);
875 __isl_give isl_map *isl_map_lex_le_first(
876 __isl_take isl_dim *dim, unsigned n);
877 __isl_give isl_map *isl_map_lex_gt_first(
878 __isl_take isl_dim *dim, unsigned n);
879 __isl_give isl_map *isl_map_lex_ge_first(
880 __isl_take isl_dim *dim, unsigned n);
882 The first four functions take a dimension specification for a B<set>
883 and return relations that express that the elements in the domain
884 are lexicographically less
885 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
886 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
887 than the elements in the range.
888 The last four functions take a dimension specification for a map
889 and return relations that express that the first C<n> dimensions
890 in the domain are lexicographically less
891 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
892 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
893 than the first C<n> dimensions in the range.
897 A basic set or relation can be converted to a set or relation
898 using the following functions.
900 __isl_give isl_set *isl_set_from_basic_set(
901 __isl_take isl_basic_set *bset);
902 __isl_give isl_map *isl_map_from_basic_map(
903 __isl_take isl_basic_map *bmap);
905 Sets and relations can be converted to union sets and relations
906 using the following functions.
908 __isl_give isl_union_map *isl_union_map_from_map(
909 __isl_take isl_map *map);
910 __isl_give isl_union_set *isl_union_set_from_set(
911 __isl_take isl_set *set);
913 Sets and relations can be copied and freed again using the following
916 __isl_give isl_basic_set *isl_basic_set_copy(
917 __isl_keep isl_basic_set *bset);
918 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
919 __isl_give isl_union_set *isl_union_set_copy(
920 __isl_keep isl_union_set *uset);
921 __isl_give isl_basic_map *isl_basic_map_copy(
922 __isl_keep isl_basic_map *bmap);
923 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
924 __isl_give isl_union_map *isl_union_map_copy(
925 __isl_keep isl_union_map *umap);
926 void isl_basic_set_free(__isl_take isl_basic_set *bset);
927 void isl_set_free(__isl_take isl_set *set);
928 void isl_union_set_free(__isl_take isl_union_set *uset);
929 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
930 void isl_map_free(__isl_take isl_map *map);
931 void isl_union_map_free(__isl_take isl_union_map *umap);
933 Other sets and relations can be constructed by starting
934 from a universe set or relation, adding equality and/or
935 inequality constraints and then projecting out the
936 existentially quantified variables, if any.
937 Constraints can be constructed, manipulated and
938 added to (basic) sets and relations using the following functions.
940 #include <isl/constraint.h>
941 __isl_give isl_constraint *isl_equality_alloc(
942 __isl_take isl_dim *dim);
943 __isl_give isl_constraint *isl_inequality_alloc(
944 __isl_take isl_dim *dim);
945 void isl_constraint_set_constant(
946 __isl_keep isl_constraint *constraint, isl_int v);
947 void isl_constraint_set_coefficient(
948 __isl_keep isl_constraint *constraint,
949 enum isl_dim_type type, int pos, isl_int v);
950 __isl_give isl_basic_map *isl_basic_map_add_constraint(
951 __isl_take isl_basic_map *bmap,
952 __isl_take isl_constraint *constraint);
953 __isl_give isl_basic_set *isl_basic_set_add_constraint(
954 __isl_take isl_basic_set *bset,
955 __isl_take isl_constraint *constraint);
956 __isl_give isl_map *isl_map_add_constraint(
957 __isl_take isl_map *map,
958 __isl_take isl_constraint *constraint);
959 __isl_give isl_set *isl_set_add_constraint(
960 __isl_take isl_set *set,
961 __isl_take isl_constraint *constraint);
963 For example, to create a set containing the even integers
964 between 10 and 42, you would use the following code.
968 struct isl_constraint *c;
969 struct isl_basic_set *bset;
972 dim = isl_dim_set_alloc(ctx, 0, 2);
973 bset = isl_basic_set_universe(isl_dim_copy(dim));
975 c = isl_equality_alloc(isl_dim_copy(dim));
976 isl_int_set_si(v, -1);
977 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
978 isl_int_set_si(v, 2);
979 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
980 bset = isl_basic_set_add_constraint(bset, c);
982 c = isl_inequality_alloc(isl_dim_copy(dim));
983 isl_int_set_si(v, -10);
984 isl_constraint_set_constant(c, v);
985 isl_int_set_si(v, 1);
986 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
987 bset = isl_basic_set_add_constraint(bset, c);
989 c = isl_inequality_alloc(dim);
990 isl_int_set_si(v, 42);
991 isl_constraint_set_constant(c, v);
992 isl_int_set_si(v, -1);
993 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
994 bset = isl_basic_set_add_constraint(bset, c);
996 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1002 struct isl_basic_set *bset;
1003 bset = isl_basic_set_read_from_str(ctx,
1004 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1006 A basic set or relation can also be constructed from two matrices
1007 describing the equalities and the inequalities.
1009 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1010 __isl_take isl_dim *dim,
1011 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1012 enum isl_dim_type c1,
1013 enum isl_dim_type c2, enum isl_dim_type c3,
1014 enum isl_dim_type c4);
1015 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1016 __isl_take isl_dim *dim,
1017 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1018 enum isl_dim_type c1,
1019 enum isl_dim_type c2, enum isl_dim_type c3,
1020 enum isl_dim_type c4, enum isl_dim_type c5);
1022 The C<isl_dim_type> arguments indicate the order in which
1023 different kinds of variables appear in the input matrices
1024 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1025 C<isl_dim_set> and C<isl_dim_div> for sets and
1026 of C<isl_dim_cst>, C<isl_dim_param>,
1027 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1029 A basic relation can also be constructed from an affine expression
1030 or a list of affine expressions (See L<"Quasi Affine Expressions">).
1032 __isl_give isl_basic_map *isl_basic_map_from_aff(
1033 __isl_take isl_aff *aff);
1034 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1035 __isl_take isl_dim *domain_dim,
1036 __isl_take isl_aff_list *list);
1038 The C<domain_dim> argument describes the domain of the resulting
1039 basic relation. It is required because the C<list> may consist
1040 of zero affine expressions.
1042 =head2 Inspecting Sets and Relations
1044 Usually, the user should not have to care about the actual constraints
1045 of the sets and maps, but should instead apply the abstract operations
1046 explained in the following sections.
1047 Occasionally, however, it may be required to inspect the individual
1048 coefficients of the constraints. This section explains how to do so.
1049 In these cases, it may also be useful to have C<isl> compute
1050 an explicit representation of the existentially quantified variables.
1052 __isl_give isl_set *isl_set_compute_divs(
1053 __isl_take isl_set *set);
1054 __isl_give isl_map *isl_map_compute_divs(
1055 __isl_take isl_map *map);
1056 __isl_give isl_union_set *isl_union_set_compute_divs(
1057 __isl_take isl_union_set *uset);
1058 __isl_give isl_union_map *isl_union_map_compute_divs(
1059 __isl_take isl_union_map *umap);
1061 This explicit representation defines the existentially quantified
1062 variables as integer divisions of the other variables, possibly
1063 including earlier existentially quantified variables.
1064 An explicitly represented existentially quantified variable therefore
1065 has a unique value when the values of the other variables are known.
1066 If, furthermore, the same existentials, i.e., existentials
1067 with the same explicit representations, should appear in the
1068 same order in each of the disjuncts of a set or map, then the user should call
1069 either of the following functions.
1071 __isl_give isl_set *isl_set_align_divs(
1072 __isl_take isl_set *set);
1073 __isl_give isl_map *isl_map_align_divs(
1074 __isl_take isl_map *map);
1076 Alternatively, the existentially quantified variables can be removed
1077 using the following functions, which compute an overapproximation.
1079 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1080 __isl_take isl_basic_set *bset);
1081 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1082 __isl_take isl_basic_map *bmap);
1083 __isl_give isl_set *isl_set_remove_divs(
1084 __isl_take isl_set *set);
1085 __isl_give isl_map *isl_map_remove_divs(
1086 __isl_take isl_map *map);
1088 To iterate over all the sets or maps in a union set or map, use
1090 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1091 int (*fn)(__isl_take isl_set *set, void *user),
1093 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1094 int (*fn)(__isl_take isl_map *map, void *user),
1097 The number of sets or maps in a union set or map can be obtained
1100 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1101 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1103 To extract the set or map from a union with a given dimension
1106 __isl_give isl_set *isl_union_set_extract_set(
1107 __isl_keep isl_union_set *uset,
1108 __isl_take isl_dim *dim);
1109 __isl_give isl_map *isl_union_map_extract_map(
1110 __isl_keep isl_union_map *umap,
1111 __isl_take isl_dim *dim);
1113 To iterate over all the basic sets or maps in a set or map, use
1115 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1116 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1118 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1119 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1122 The callback function C<fn> should return 0 if successful and
1123 -1 if an error occurs. In the latter case, or if any other error
1124 occurs, the above functions will return -1.
1126 It should be noted that C<isl> does not guarantee that
1127 the basic sets or maps passed to C<fn> are disjoint.
1128 If this is required, then the user should call one of
1129 the following functions first.
1131 __isl_give isl_set *isl_set_make_disjoint(
1132 __isl_take isl_set *set);
1133 __isl_give isl_map *isl_map_make_disjoint(
1134 __isl_take isl_map *map);
1136 The number of basic sets in a set can be obtained
1139 int isl_set_n_basic_set(__isl_keep isl_set *set);
1141 To iterate over the constraints of a basic set or map, use
1143 #include <isl/constraint.h>
1145 int isl_basic_map_foreach_constraint(
1146 __isl_keep isl_basic_map *bmap,
1147 int (*fn)(__isl_take isl_constraint *c, void *user),
1149 void isl_constraint_free(struct isl_constraint *c);
1151 Again, the callback function C<fn> should return 0 if successful and
1152 -1 if an error occurs. In the latter case, or if any other error
1153 occurs, the above functions will return -1.
1154 The constraint C<c> represents either an equality or an inequality.
1155 Use the following function to find out whether a constraint
1156 represents an equality. If not, it represents an inequality.
1158 int isl_constraint_is_equality(
1159 __isl_keep isl_constraint *constraint);
1161 The coefficients of the constraints can be inspected using
1162 the following functions.
1164 void isl_constraint_get_constant(
1165 __isl_keep isl_constraint *constraint, isl_int *v);
1166 void isl_constraint_get_coefficient(
1167 __isl_keep isl_constraint *constraint,
1168 enum isl_dim_type type, int pos, isl_int *v);
1169 int isl_constraint_involves_dims(
1170 __isl_keep isl_constraint *constraint,
1171 enum isl_dim_type type, unsigned first, unsigned n);
1173 The explicit representations of the existentially quantified
1174 variables can be inspected using the following functions.
1175 Note that the user is only allowed to use these functions
1176 if the inspected set or map is the result of a call
1177 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1179 __isl_give isl_div *isl_constraint_div(
1180 __isl_keep isl_constraint *constraint, int pos);
1181 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1182 void isl_div_get_constant(__isl_keep isl_div *div,
1184 void isl_div_get_denominator(__isl_keep isl_div *div,
1186 void isl_div_get_coefficient(__isl_keep isl_div *div,
1187 enum isl_dim_type type, int pos, isl_int *v);
1189 To obtain the constraints of a basic set or map in matrix
1190 form, use the following functions.
1192 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1193 __isl_keep isl_basic_set *bset,
1194 enum isl_dim_type c1, enum isl_dim_type c2,
1195 enum isl_dim_type c3, enum isl_dim_type c4);
1196 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1197 __isl_keep isl_basic_set *bset,
1198 enum isl_dim_type c1, enum isl_dim_type c2,
1199 enum isl_dim_type c3, enum isl_dim_type c4);
1200 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1201 __isl_keep isl_basic_map *bmap,
1202 enum isl_dim_type c1,
1203 enum isl_dim_type c2, enum isl_dim_type c3,
1204 enum isl_dim_type c4, enum isl_dim_type c5);
1205 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1206 __isl_keep isl_basic_map *bmap,
1207 enum isl_dim_type c1,
1208 enum isl_dim_type c2, enum isl_dim_type c3,
1209 enum isl_dim_type c4, enum isl_dim_type c5);
1211 The C<isl_dim_type> arguments dictate the order in which
1212 different kinds of variables appear in the resulting matrix
1213 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1214 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1216 The names of the domain and range spaces of a set or relation can be
1217 read off using the following functions.
1219 const char *isl_basic_set_get_tuple_name(
1220 __isl_keep isl_basic_set *bset);
1221 const char *isl_set_get_tuple_name(
1222 __isl_keep isl_set *set);
1223 const char *isl_basic_map_get_tuple_name(
1224 __isl_keep isl_basic_map *bmap,
1225 enum isl_dim_type type);
1226 const char *isl_map_get_tuple_name(
1227 __isl_keep isl_map *map,
1228 enum isl_dim_type type);
1230 As with C<isl_dim_get_tuple_name>, the value returned points to
1231 an internal data structure.
1232 The names of individual dimensions can be read off using
1233 the following functions.
1235 const char *isl_constraint_get_dim_name(
1236 __isl_keep isl_constraint *constraint,
1237 enum isl_dim_type type, unsigned pos);
1238 const char *isl_basic_set_get_dim_name(
1239 __isl_keep isl_basic_set *bset,
1240 enum isl_dim_type type, unsigned pos);
1241 const char *isl_set_get_dim_name(
1242 __isl_keep isl_set *set,
1243 enum isl_dim_type type, unsigned pos);
1244 const char *isl_basic_map_get_dim_name(
1245 __isl_keep isl_basic_map *bmap,
1246 enum isl_dim_type type, unsigned pos);
1247 const char *isl_map_get_dim_name(
1248 __isl_keep isl_map *map,
1249 enum isl_dim_type type, unsigned pos);
1251 These functions are mostly useful to obtain the names
1256 =head3 Unary Properties
1262 The following functions test whether the given set or relation
1263 contains any integer points. The ``plain'' variants do not perform
1264 any computations, but simply check if the given set or relation
1265 is already known to be empty.
1267 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1268 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1269 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1270 int isl_set_is_empty(__isl_keep isl_set *set);
1271 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1272 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1273 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1274 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1275 int isl_map_is_empty(__isl_keep isl_map *map);
1276 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1278 =item * Universality
1280 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1281 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1282 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1284 =item * Single-valuedness
1286 int isl_map_is_single_valued(__isl_keep isl_map *map);
1287 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1291 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1292 int isl_map_is_injective(__isl_keep isl_map *map);
1293 int isl_union_map_plain_is_injective(
1294 __isl_keep isl_union_map *umap);
1295 int isl_union_map_is_injective(
1296 __isl_keep isl_union_map *umap);
1300 int isl_map_is_bijective(__isl_keep isl_map *map);
1301 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1305 The following functions check whether the domain of the given
1306 (basic) set is a wrapped relation.
1308 int isl_basic_set_is_wrapping(
1309 __isl_keep isl_basic_set *bset);
1310 int isl_set_is_wrapping(__isl_keep isl_set *set);
1312 =item * Internal Product
1314 int isl_basic_map_can_zip(
1315 __isl_keep isl_basic_map *bmap);
1316 int isl_map_can_zip(__isl_keep isl_map *map);
1318 Check whether the product of domain and range of the given relation
1320 i.e., whether both domain and range are nested relations.
1324 =head3 Binary Properties
1330 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1331 __isl_keep isl_set *set2);
1332 int isl_set_is_equal(__isl_keep isl_set *set1,
1333 __isl_keep isl_set *set2);
1334 int isl_union_set_is_equal(
1335 __isl_keep isl_union_set *uset1,
1336 __isl_keep isl_union_set *uset2);
1337 int isl_basic_map_is_equal(
1338 __isl_keep isl_basic_map *bmap1,
1339 __isl_keep isl_basic_map *bmap2);
1340 int isl_map_is_equal(__isl_keep isl_map *map1,
1341 __isl_keep isl_map *map2);
1342 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1343 __isl_keep isl_map *map2);
1344 int isl_union_map_is_equal(
1345 __isl_keep isl_union_map *umap1,
1346 __isl_keep isl_union_map *umap2);
1348 =item * Disjointness
1350 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1351 __isl_keep isl_set *set2);
1355 int isl_set_is_subset(__isl_keep isl_set *set1,
1356 __isl_keep isl_set *set2);
1357 int isl_set_is_strict_subset(
1358 __isl_keep isl_set *set1,
1359 __isl_keep isl_set *set2);
1360 int isl_union_set_is_subset(
1361 __isl_keep isl_union_set *uset1,
1362 __isl_keep isl_union_set *uset2);
1363 int isl_union_set_is_strict_subset(
1364 __isl_keep isl_union_set *uset1,
1365 __isl_keep isl_union_set *uset2);
1366 int isl_basic_map_is_subset(
1367 __isl_keep isl_basic_map *bmap1,
1368 __isl_keep isl_basic_map *bmap2);
1369 int isl_basic_map_is_strict_subset(
1370 __isl_keep isl_basic_map *bmap1,
1371 __isl_keep isl_basic_map *bmap2);
1372 int isl_map_is_subset(
1373 __isl_keep isl_map *map1,
1374 __isl_keep isl_map *map2);
1375 int isl_map_is_strict_subset(
1376 __isl_keep isl_map *map1,
1377 __isl_keep isl_map *map2);
1378 int isl_union_map_is_subset(
1379 __isl_keep isl_union_map *umap1,
1380 __isl_keep isl_union_map *umap2);
1381 int isl_union_map_is_strict_subset(
1382 __isl_keep isl_union_map *umap1,
1383 __isl_keep isl_union_map *umap2);
1387 =head2 Unary Operations
1393 __isl_give isl_set *isl_set_complement(
1394 __isl_take isl_set *set);
1398 __isl_give isl_basic_map *isl_basic_map_reverse(
1399 __isl_take isl_basic_map *bmap);
1400 __isl_give isl_map *isl_map_reverse(
1401 __isl_take isl_map *map);
1402 __isl_give isl_union_map *isl_union_map_reverse(
1403 __isl_take isl_union_map *umap);
1407 __isl_give isl_basic_set *isl_basic_set_project_out(
1408 __isl_take isl_basic_set *bset,
1409 enum isl_dim_type type, unsigned first, unsigned n);
1410 __isl_give isl_basic_map *isl_basic_map_project_out(
1411 __isl_take isl_basic_map *bmap,
1412 enum isl_dim_type type, unsigned first, unsigned n);
1413 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1414 enum isl_dim_type type, unsigned first, unsigned n);
1415 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1416 enum isl_dim_type type, unsigned first, unsigned n);
1417 __isl_give isl_basic_set *isl_basic_map_domain(
1418 __isl_take isl_basic_map *bmap);
1419 __isl_give isl_basic_set *isl_basic_map_range(
1420 __isl_take isl_basic_map *bmap);
1421 __isl_give isl_set *isl_map_domain(
1422 __isl_take isl_map *bmap);
1423 __isl_give isl_set *isl_map_range(
1424 __isl_take isl_map *map);
1425 __isl_give isl_union_set *isl_union_map_domain(
1426 __isl_take isl_union_map *umap);
1427 __isl_give isl_union_set *isl_union_map_range(
1428 __isl_take isl_union_map *umap);
1430 __isl_give isl_basic_map *isl_basic_map_domain_map(
1431 __isl_take isl_basic_map *bmap);
1432 __isl_give isl_basic_map *isl_basic_map_range_map(
1433 __isl_take isl_basic_map *bmap);
1434 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1435 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1436 __isl_give isl_union_map *isl_union_map_domain_map(
1437 __isl_take isl_union_map *umap);
1438 __isl_give isl_union_map *isl_union_map_range_map(
1439 __isl_take isl_union_map *umap);
1441 The functions above construct a (basic, regular or union) relation
1442 that maps (a wrapped version of) the input relation to its domain or range.
1446 __isl_give isl_set *isl_set_eliminate(
1447 __isl_take isl_set *set, enum isl_dim_type type,
1448 unsigned first, unsigned n);
1450 Eliminate the coefficients for the given dimensions from the constraints,
1451 without removing the dimensions.
1455 __isl_give isl_basic_set *isl_basic_set_fix(
1456 __isl_take isl_basic_set *bset,
1457 enum isl_dim_type type, unsigned pos,
1459 __isl_give isl_basic_set *isl_basic_set_fix_si(
1460 __isl_take isl_basic_set *bset,
1461 enum isl_dim_type type, unsigned pos, int value);
1462 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1463 enum isl_dim_type type, unsigned pos,
1465 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1466 enum isl_dim_type type, unsigned pos, int value);
1467 __isl_give isl_basic_map *isl_basic_map_fix_si(
1468 __isl_take isl_basic_map *bmap,
1469 enum isl_dim_type type, unsigned pos, int value);
1470 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1471 enum isl_dim_type type, unsigned pos, int value);
1473 Intersect the set or relation with the hyperplane where the given
1474 dimension has the fixed given value.
1478 __isl_give isl_map *isl_set_identity(
1479 __isl_take isl_set *set);
1480 __isl_give isl_union_map *isl_union_set_identity(
1481 __isl_take isl_union_set *uset);
1483 Construct an identity relation on the given (union) set.
1487 __isl_give isl_basic_set *isl_basic_map_deltas(
1488 __isl_take isl_basic_map *bmap);
1489 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1490 __isl_give isl_union_set *isl_union_map_deltas(
1491 __isl_take isl_union_map *umap);
1493 These functions return a (basic) set containing the differences
1494 between image elements and corresponding domain elements in the input.
1496 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1497 __isl_take isl_basic_map *bmap);
1498 __isl_give isl_map *isl_map_deltas_map(
1499 __isl_take isl_map *map);
1500 __isl_give isl_union_map *isl_union_map_deltas_map(
1501 __isl_take isl_union_map *umap);
1503 The functions above construct a (basic, regular or union) relation
1504 that maps (a wrapped version of) the input relation to its delta set.
1508 Simplify the representation of a set or relation by trying
1509 to combine pairs of basic sets or relations into a single
1510 basic set or relation.
1512 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1513 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1514 __isl_give isl_union_set *isl_union_set_coalesce(
1515 __isl_take isl_union_set *uset);
1516 __isl_give isl_union_map *isl_union_map_coalesce(
1517 __isl_take isl_union_map *umap);
1519 =item * Detecting equalities
1521 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1522 __isl_take isl_basic_set *bset);
1523 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1524 __isl_take isl_basic_map *bmap);
1525 __isl_give isl_set *isl_set_detect_equalities(
1526 __isl_take isl_set *set);
1527 __isl_give isl_map *isl_map_detect_equalities(
1528 __isl_take isl_map *map);
1529 __isl_give isl_union_set *isl_union_set_detect_equalities(
1530 __isl_take isl_union_set *uset);
1531 __isl_give isl_union_map *isl_union_map_detect_equalities(
1532 __isl_take isl_union_map *umap);
1534 Simplify the representation of a set or relation by detecting implicit
1537 =item * Removing redundant constraints
1539 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1540 __isl_take isl_basic_set *bset);
1541 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1542 __isl_take isl_basic_map *bmap);
1546 __isl_give isl_basic_set *isl_set_convex_hull(
1547 __isl_take isl_set *set);
1548 __isl_give isl_basic_map *isl_map_convex_hull(
1549 __isl_take isl_map *map);
1551 If the input set or relation has any existentially quantified
1552 variables, then the result of these operations is currently undefined.
1556 __isl_give isl_basic_set *isl_set_simple_hull(
1557 __isl_take isl_set *set);
1558 __isl_give isl_basic_map *isl_map_simple_hull(
1559 __isl_take isl_map *map);
1560 __isl_give isl_union_map *isl_union_map_simple_hull(
1561 __isl_take isl_union_map *umap);
1563 These functions compute a single basic set or relation
1564 that contains the whole input set or relation.
1565 In particular, the output is described by translates
1566 of the constraints describing the basic sets or relations in the input.
1570 (See \autoref{s:simple hull}.)
1576 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1577 __isl_take isl_basic_set *bset);
1578 __isl_give isl_basic_set *isl_set_affine_hull(
1579 __isl_take isl_set *set);
1580 __isl_give isl_union_set *isl_union_set_affine_hull(
1581 __isl_take isl_union_set *uset);
1582 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1583 __isl_take isl_basic_map *bmap);
1584 __isl_give isl_basic_map *isl_map_affine_hull(
1585 __isl_take isl_map *map);
1586 __isl_give isl_union_map *isl_union_map_affine_hull(
1587 __isl_take isl_union_map *umap);
1589 In case of union sets and relations, the affine hull is computed
1592 =item * Polyhedral hull
1594 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1595 __isl_take isl_set *set);
1596 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1597 __isl_take isl_map *map);
1598 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1599 __isl_take isl_union_set *uset);
1600 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1601 __isl_take isl_union_map *umap);
1603 These functions compute a single basic set or relation
1604 not involving any existentially quantified variables
1605 that contains the whole input set or relation.
1606 In case of union sets and relations, the polyhedral hull is computed
1609 =item * Optimization
1611 #include <isl/ilp.h>
1612 enum isl_lp_result isl_basic_set_max(
1613 __isl_keep isl_basic_set *bset,
1614 __isl_keep isl_aff *obj, isl_int *opt)
1615 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1616 __isl_keep isl_aff *obj, isl_int *opt);
1618 Compute the maximum of the integer affine expression C<obj>
1619 over the points in C<set>, returning the result in C<opt>.
1620 The return value may be one of C<isl_lp_error>,
1621 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1625 The following functions compute either the set of (rational) coefficient
1626 values of valid constraints for the given set or the set of (rational)
1627 values satisfying the constraints with coefficients from the given set.
1628 Internally, these two sets of functions perform essentially the
1629 same operations, except that the set of coefficients is assumed to
1630 be a cone, while the set of values may be any polyhedron.
1631 The current implementation is based on the Farkas lemma and
1632 Fourier-Motzkin elimination, but this may change or be made optional
1633 in future. In particular, future implementations may use different
1634 dualization algorithms or skip the elimination step.
1636 __isl_give isl_basic_set *isl_basic_set_coefficients(
1637 __isl_take isl_basic_set *bset);
1638 __isl_give isl_basic_set *isl_set_coefficients(
1639 __isl_take isl_set *set);
1640 __isl_give isl_union_set *isl_union_set_coefficients(
1641 __isl_take isl_union_set *bset);
1642 __isl_give isl_basic_set *isl_basic_set_solutions(
1643 __isl_take isl_basic_set *bset);
1644 __isl_give isl_basic_set *isl_set_solutions(
1645 __isl_take isl_set *set);
1646 __isl_give isl_union_set *isl_union_set_solutions(
1647 __isl_take isl_union_set *bset);
1651 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1653 __isl_give isl_union_map *isl_union_map_power(
1654 __isl_take isl_union_map *umap, int *exact);
1656 Compute a parametric representation for all positive powers I<k> of C<map>.
1657 The result maps I<k> to a nested relation corresponding to the
1658 I<k>th power of C<map>.
1659 The result may be an overapproximation. If the result is known to be exact,
1660 then C<*exact> is set to C<1>.
1662 =item * Transitive closure
1664 __isl_give isl_map *isl_map_transitive_closure(
1665 __isl_take isl_map *map, int *exact);
1666 __isl_give isl_union_map *isl_union_map_transitive_closure(
1667 __isl_take isl_union_map *umap, int *exact);
1669 Compute the transitive closure of C<map>.
1670 The result may be an overapproximation. If the result is known to be exact,
1671 then C<*exact> is set to C<1>.
1673 =item * Reaching path lengths
1675 __isl_give isl_map *isl_map_reaching_path_lengths(
1676 __isl_take isl_map *map, int *exact);
1678 Compute a relation that maps each element in the range of C<map>
1679 to the lengths of all paths composed of edges in C<map> that
1680 end up in the given element.
1681 The result may be an overapproximation. If the result is known to be exact,
1682 then C<*exact> is set to C<1>.
1683 To compute the I<maximal> path length, the resulting relation
1684 should be postprocessed by C<isl_map_lexmax>.
1685 In particular, if the input relation is a dependence relation
1686 (mapping sources to sinks), then the maximal path length corresponds
1687 to the free schedule.
1688 Note, however, that C<isl_map_lexmax> expects the maximum to be
1689 finite, so if the path lengths are unbounded (possibly due to
1690 the overapproximation), then you will get an error message.
1694 __isl_give isl_basic_set *isl_basic_map_wrap(
1695 __isl_take isl_basic_map *bmap);
1696 __isl_give isl_set *isl_map_wrap(
1697 __isl_take isl_map *map);
1698 __isl_give isl_union_set *isl_union_map_wrap(
1699 __isl_take isl_union_map *umap);
1700 __isl_give isl_basic_map *isl_basic_set_unwrap(
1701 __isl_take isl_basic_set *bset);
1702 __isl_give isl_map *isl_set_unwrap(
1703 __isl_take isl_set *set);
1704 __isl_give isl_union_map *isl_union_set_unwrap(
1705 __isl_take isl_union_set *uset);
1709 Remove any internal structure of domain (and range) of the given
1710 set or relation. If there is any such internal structure in the input,
1711 then the name of the space is also removed.
1713 __isl_give isl_basic_set *isl_basic_set_flatten(
1714 __isl_take isl_basic_set *bset);
1715 __isl_give isl_set *isl_set_flatten(
1716 __isl_take isl_set *set);
1717 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1718 __isl_take isl_basic_map *bmap);
1719 __isl_give isl_map *isl_map_flatten_range(
1720 __isl_take isl_map *map);
1721 __isl_give isl_basic_map *isl_basic_map_flatten(
1722 __isl_take isl_basic_map *bmap);
1723 __isl_give isl_map *isl_map_flatten(
1724 __isl_take isl_map *map);
1726 __isl_give isl_map *isl_set_flatten_map(
1727 __isl_take isl_set *set);
1729 The function above constructs a relation
1730 that maps the input set to a flattened version of the set.
1734 Lift the input set to a space with extra dimensions corresponding
1735 to the existentially quantified variables in the input.
1736 In particular, the result lives in a wrapped map where the domain
1737 is the original space and the range corresponds to the original
1738 existentially quantified variables.
1740 __isl_give isl_basic_set *isl_basic_set_lift(
1741 __isl_take isl_basic_set *bset);
1742 __isl_give isl_set *isl_set_lift(
1743 __isl_take isl_set *set);
1744 __isl_give isl_union_set *isl_union_set_lift(
1745 __isl_take isl_union_set *uset);
1747 =item * Internal Product
1749 __isl_give isl_basic_map *isl_basic_map_zip(
1750 __isl_take isl_basic_map *bmap);
1751 __isl_give isl_map *isl_map_zip(
1752 __isl_take isl_map *map);
1753 __isl_give isl_union_map *isl_union_map_zip(
1754 __isl_take isl_union_map *umap);
1756 Given a relation with nested relations for domain and range,
1757 interchange the range of the domain with the domain of the range.
1759 =item * Aligning parameters
1761 __isl_give isl_set *isl_set_align_params(
1762 __isl_take isl_set *set,
1763 __isl_take isl_dim *model);
1764 __isl_give isl_map *isl_map_align_params(
1765 __isl_take isl_map *map,
1766 __isl_take isl_dim *model);
1768 Change the order of the parameters of the given set or relation
1769 such that the first parameters match those of C<model>.
1770 This may involve the introduction of extra parameters.
1771 All parameters need to be named.
1773 =item * Dimension manipulation
1775 __isl_give isl_set *isl_set_add_dims(
1776 __isl_take isl_set *set,
1777 enum isl_dim_type type, unsigned n);
1778 __isl_give isl_map *isl_map_add_dims(
1779 __isl_take isl_map *map,
1780 enum isl_dim_type type, unsigned n);
1782 It is usually not advisable to directly change the (input or output)
1783 space of a set or a relation as this removes the name and the internal
1784 structure of the space. However, the above functions can be useful
1785 to add new parameters, assuming
1786 C<isl_set_align_params> and C<isl_map_align_params>
1791 =head2 Binary Operations
1793 The two arguments of a binary operation not only need to live
1794 in the same C<isl_ctx>, they currently also need to have
1795 the same (number of) parameters.
1797 =head3 Basic Operations
1801 =item * Intersection
1803 __isl_give isl_basic_set *isl_basic_set_intersect(
1804 __isl_take isl_basic_set *bset1,
1805 __isl_take isl_basic_set *bset2);
1806 __isl_give isl_set *isl_set_intersect(
1807 __isl_take isl_set *set1,
1808 __isl_take isl_set *set2);
1809 __isl_give isl_union_set *isl_union_set_intersect(
1810 __isl_take isl_union_set *uset1,
1811 __isl_take isl_union_set *uset2);
1812 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1813 __isl_take isl_basic_map *bmap,
1814 __isl_take isl_basic_set *bset);
1815 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1816 __isl_take isl_basic_map *bmap,
1817 __isl_take isl_basic_set *bset);
1818 __isl_give isl_basic_map *isl_basic_map_intersect(
1819 __isl_take isl_basic_map *bmap1,
1820 __isl_take isl_basic_map *bmap2);
1821 __isl_give isl_map *isl_map_intersect_domain(
1822 __isl_take isl_map *map,
1823 __isl_take isl_set *set);
1824 __isl_give isl_map *isl_map_intersect_range(
1825 __isl_take isl_map *map,
1826 __isl_take isl_set *set);
1827 __isl_give isl_map *isl_map_intersect(
1828 __isl_take isl_map *map1,
1829 __isl_take isl_map *map2);
1830 __isl_give isl_union_map *isl_union_map_intersect_domain(
1831 __isl_take isl_union_map *umap,
1832 __isl_take isl_union_set *uset);
1833 __isl_give isl_union_map *isl_union_map_intersect_range(
1834 __isl_take isl_union_map *umap,
1835 __isl_take isl_union_set *uset);
1836 __isl_give isl_union_map *isl_union_map_intersect(
1837 __isl_take isl_union_map *umap1,
1838 __isl_take isl_union_map *umap2);
1842 __isl_give isl_set *isl_basic_set_union(
1843 __isl_take isl_basic_set *bset1,
1844 __isl_take isl_basic_set *bset2);
1845 __isl_give isl_map *isl_basic_map_union(
1846 __isl_take isl_basic_map *bmap1,
1847 __isl_take isl_basic_map *bmap2);
1848 __isl_give isl_set *isl_set_union(
1849 __isl_take isl_set *set1,
1850 __isl_take isl_set *set2);
1851 __isl_give isl_map *isl_map_union(
1852 __isl_take isl_map *map1,
1853 __isl_take isl_map *map2);
1854 __isl_give isl_union_set *isl_union_set_union(
1855 __isl_take isl_union_set *uset1,
1856 __isl_take isl_union_set *uset2);
1857 __isl_give isl_union_map *isl_union_map_union(
1858 __isl_take isl_union_map *umap1,
1859 __isl_take isl_union_map *umap2);
1861 =item * Set difference
1863 __isl_give isl_set *isl_set_subtract(
1864 __isl_take isl_set *set1,
1865 __isl_take isl_set *set2);
1866 __isl_give isl_map *isl_map_subtract(
1867 __isl_take isl_map *map1,
1868 __isl_take isl_map *map2);
1869 __isl_give isl_union_set *isl_union_set_subtract(
1870 __isl_take isl_union_set *uset1,
1871 __isl_take isl_union_set *uset2);
1872 __isl_give isl_union_map *isl_union_map_subtract(
1873 __isl_take isl_union_map *umap1,
1874 __isl_take isl_union_map *umap2);
1878 __isl_give isl_basic_set *isl_basic_set_apply(
1879 __isl_take isl_basic_set *bset,
1880 __isl_take isl_basic_map *bmap);
1881 __isl_give isl_set *isl_set_apply(
1882 __isl_take isl_set *set,
1883 __isl_take isl_map *map);
1884 __isl_give isl_union_set *isl_union_set_apply(
1885 __isl_take isl_union_set *uset,
1886 __isl_take isl_union_map *umap);
1887 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1888 __isl_take isl_basic_map *bmap1,
1889 __isl_take isl_basic_map *bmap2);
1890 __isl_give isl_basic_map *isl_basic_map_apply_range(
1891 __isl_take isl_basic_map *bmap1,
1892 __isl_take isl_basic_map *bmap2);
1893 __isl_give isl_map *isl_map_apply_domain(
1894 __isl_take isl_map *map1,
1895 __isl_take isl_map *map2);
1896 __isl_give isl_union_map *isl_union_map_apply_domain(
1897 __isl_take isl_union_map *umap1,
1898 __isl_take isl_union_map *umap2);
1899 __isl_give isl_map *isl_map_apply_range(
1900 __isl_take isl_map *map1,
1901 __isl_take isl_map *map2);
1902 __isl_give isl_union_map *isl_union_map_apply_range(
1903 __isl_take isl_union_map *umap1,
1904 __isl_take isl_union_map *umap2);
1906 =item * Cartesian Product
1908 __isl_give isl_set *isl_set_product(
1909 __isl_take isl_set *set1,
1910 __isl_take isl_set *set2);
1911 __isl_give isl_union_set *isl_union_set_product(
1912 __isl_take isl_union_set *uset1,
1913 __isl_take isl_union_set *uset2);
1914 __isl_give isl_basic_map *isl_basic_map_range_product(
1915 __isl_take isl_basic_map *bmap1,
1916 __isl_take isl_basic_map *bmap2);
1917 __isl_give isl_map *isl_map_range_product(
1918 __isl_take isl_map *map1,
1919 __isl_take isl_map *map2);
1920 __isl_give isl_union_map *isl_union_map_range_product(
1921 __isl_take isl_union_map *umap1,
1922 __isl_take isl_union_map *umap2);
1923 __isl_give isl_map *isl_map_product(
1924 __isl_take isl_map *map1,
1925 __isl_take isl_map *map2);
1926 __isl_give isl_union_map *isl_union_map_product(
1927 __isl_take isl_union_map *umap1,
1928 __isl_take isl_union_map *umap2);
1930 The above functions compute the cross product of the given
1931 sets or relations. The domains and ranges of the results
1932 are wrapped maps between domains and ranges of the inputs.
1933 To obtain a ``flat'' product, use the following functions
1936 __isl_give isl_basic_set *isl_basic_set_flat_product(
1937 __isl_take isl_basic_set *bset1,
1938 __isl_take isl_basic_set *bset2);
1939 __isl_give isl_set *isl_set_flat_product(
1940 __isl_take isl_set *set1,
1941 __isl_take isl_set *set2);
1942 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1943 __isl_take isl_basic_map *bmap1,
1944 __isl_take isl_basic_map *bmap2);
1945 __isl_give isl_map *isl_map_flat_range_product(
1946 __isl_take isl_map *map1,
1947 __isl_take isl_map *map2);
1948 __isl_give isl_union_map *isl_union_map_flat_range_product(
1949 __isl_take isl_union_map *umap1,
1950 __isl_take isl_union_map *umap2);
1951 __isl_give isl_basic_map *isl_basic_map_flat_product(
1952 __isl_take isl_basic_map *bmap1,
1953 __isl_take isl_basic_map *bmap2);
1954 __isl_give isl_map *isl_map_flat_product(
1955 __isl_take isl_map *map1,
1956 __isl_take isl_map *map2);
1958 =item * Simplification
1960 __isl_give isl_basic_set *isl_basic_set_gist(
1961 __isl_take isl_basic_set *bset,
1962 __isl_take isl_basic_set *context);
1963 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1964 __isl_take isl_set *context);
1965 __isl_give isl_union_set *isl_union_set_gist(
1966 __isl_take isl_union_set *uset,
1967 __isl_take isl_union_set *context);
1968 __isl_give isl_basic_map *isl_basic_map_gist(
1969 __isl_take isl_basic_map *bmap,
1970 __isl_take isl_basic_map *context);
1971 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1972 __isl_take isl_map *context);
1973 __isl_give isl_union_map *isl_union_map_gist(
1974 __isl_take isl_union_map *umap,
1975 __isl_take isl_union_map *context);
1977 The gist operation returns a set or relation that has the
1978 same intersection with the context as the input set or relation.
1979 Any implicit equality in the intersection is made explicit in the result,
1980 while all inequalities that are redundant with respect to the intersection
1982 In case of union sets and relations, the gist operation is performed
1987 =head3 Lexicographic Optimization
1989 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1990 the following functions
1991 compute a set that contains the lexicographic minimum or maximum
1992 of the elements in C<set> (or C<bset>) for those values of the parameters
1993 that satisfy C<dom>.
1994 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1995 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1997 In other words, the union of the parameter values
1998 for which the result is non-empty and of C<*empty>
2001 __isl_give isl_set *isl_basic_set_partial_lexmin(
2002 __isl_take isl_basic_set *bset,
2003 __isl_take isl_basic_set *dom,
2004 __isl_give isl_set **empty);
2005 __isl_give isl_set *isl_basic_set_partial_lexmax(
2006 __isl_take isl_basic_set *bset,
2007 __isl_take isl_basic_set *dom,
2008 __isl_give isl_set **empty);
2009 __isl_give isl_set *isl_set_partial_lexmin(
2010 __isl_take isl_set *set, __isl_take isl_set *dom,
2011 __isl_give isl_set **empty);
2012 __isl_give isl_set *isl_set_partial_lexmax(
2013 __isl_take isl_set *set, __isl_take isl_set *dom,
2014 __isl_give isl_set **empty);
2016 Given a (basic) set C<set> (or C<bset>), the following functions simply
2017 return a set containing the lexicographic minimum or maximum
2018 of the elements in C<set> (or C<bset>).
2019 In case of union sets, the optimum is computed per space.
2021 __isl_give isl_set *isl_basic_set_lexmin(
2022 __isl_take isl_basic_set *bset);
2023 __isl_give isl_set *isl_basic_set_lexmax(
2024 __isl_take isl_basic_set *bset);
2025 __isl_give isl_set *isl_set_lexmin(
2026 __isl_take isl_set *set);
2027 __isl_give isl_set *isl_set_lexmax(
2028 __isl_take isl_set *set);
2029 __isl_give isl_union_set *isl_union_set_lexmin(
2030 __isl_take isl_union_set *uset);
2031 __isl_give isl_union_set *isl_union_set_lexmax(
2032 __isl_take isl_union_set *uset);
2034 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2035 the following functions
2036 compute a relation that maps each element of C<dom>
2037 to the single lexicographic minimum or maximum
2038 of the elements that are associated to that same
2039 element in C<map> (or C<bmap>).
2040 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2041 that contains the elements in C<dom> that do not map
2042 to any elements in C<map> (or C<bmap>).
2043 In other words, the union of the domain of the result and of C<*empty>
2046 __isl_give isl_map *isl_basic_map_partial_lexmax(
2047 __isl_take isl_basic_map *bmap,
2048 __isl_take isl_basic_set *dom,
2049 __isl_give isl_set **empty);
2050 __isl_give isl_map *isl_basic_map_partial_lexmin(
2051 __isl_take isl_basic_map *bmap,
2052 __isl_take isl_basic_set *dom,
2053 __isl_give isl_set **empty);
2054 __isl_give isl_map *isl_map_partial_lexmax(
2055 __isl_take isl_map *map, __isl_take isl_set *dom,
2056 __isl_give isl_set **empty);
2057 __isl_give isl_map *isl_map_partial_lexmin(
2058 __isl_take isl_map *map, __isl_take isl_set *dom,
2059 __isl_give isl_set **empty);
2061 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2062 return a map mapping each element in the domain of
2063 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2064 of all elements associated to that element.
2065 In case of union relations, the optimum is computed per space.
2067 __isl_give isl_map *isl_basic_map_lexmin(
2068 __isl_take isl_basic_map *bmap);
2069 __isl_give isl_map *isl_basic_map_lexmax(
2070 __isl_take isl_basic_map *bmap);
2071 __isl_give isl_map *isl_map_lexmin(
2072 __isl_take isl_map *map);
2073 __isl_give isl_map *isl_map_lexmax(
2074 __isl_take isl_map *map);
2075 __isl_give isl_union_map *isl_union_map_lexmin(
2076 __isl_take isl_union_map *umap);
2077 __isl_give isl_union_map *isl_union_map_lexmax(
2078 __isl_take isl_union_map *umap);
2082 Lists are defined over several element types, including
2083 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2084 Here we take lists of C<isl_set>s as an example.
2085 Lists can be created, copied and freed using the following functions.
2087 #include <isl/list.h>
2088 __isl_give isl_set_list *isl_set_list_alloc(
2089 isl_ctx *ctx, int n);
2090 __isl_give isl_set_list *isl_set_list_copy(
2091 __isl_keep isl_set_list *list);
2092 __isl_give isl_set_list *isl_set_list_add(
2093 __isl_take isl_set_list *list,
2094 __isl_take isl_set *el);
2095 void isl_set_list_free(__isl_take isl_set_list *list);
2097 C<isl_set_list_alloc> creates an empty list with a capacity for
2100 Lists can be inspected using the following functions.
2102 #include <isl/list.h>
2103 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2104 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2105 __isl_give struct isl_set *isl_set_list_get_set(
2106 __isl_keep isl_set_list *list, int index);
2107 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2108 int (*fn)(__isl_take struct isl_set *el, void *user),
2111 Lists can be printed using
2113 #include <isl/list.h>
2114 __isl_give isl_printer *isl_printer_print_set_list(
2115 __isl_take isl_printer *p,
2116 __isl_keep isl_set_list *list);
2120 Matrices can be created, copied and freed using the following functions.
2122 #include <isl/mat.h>
2123 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2124 unsigned n_row, unsigned n_col);
2125 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2126 void isl_mat_free(__isl_take isl_mat *mat);
2128 Note that the elements of a newly created matrix may have arbitrary values.
2129 The elements can be changed and inspected using the following functions.
2131 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2132 int isl_mat_rows(__isl_keep isl_mat *mat);
2133 int isl_mat_cols(__isl_keep isl_mat *mat);
2134 int isl_mat_get_element(__isl_keep isl_mat *mat,
2135 int row, int col, isl_int *v);
2136 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2137 int row, int col, isl_int v);
2138 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2139 int row, int col, int v);
2141 C<isl_mat_get_element> will return a negative value if anything went wrong.
2142 In that case, the value of C<*v> is undefined.
2144 The following function can be used to compute the (right) inverse
2145 of a matrix, i.e., a matrix such that the product of the original
2146 and the inverse (in that order) is a multiple of the identity matrix.
2147 The input matrix is assumed to be of full row-rank.
2149 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2151 The following function can be used to compute the (right) kernel
2152 (or null space) of a matrix, i.e., a matrix such that the product of
2153 the original and the kernel (in that order) is the zero matrix.
2155 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2157 =head2 Quasi Affine Expressions
2159 The zero quasi affine expression can be created using
2161 __isl_give isl_aff *isl_aff_zero(
2162 __isl_take isl_local_space *ls);
2164 Quasi affine expressions can be copied and free using
2166 #include <isl/aff.h>
2167 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2168 void *isl_aff_free(__isl_take isl_aff *aff);
2170 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2171 using the following function. The constraint is required to have
2172 a non-zero coefficient for the specified dimension.
2174 #include <isl/constraint.h>
2175 __isl_give isl_aff *isl_constraint_get_bound(
2176 __isl_keep isl_constraint *constraint,
2177 enum isl_dim_type type, int pos);
2179 Conversely, an equality constraint equating
2180 the affine expression to zero or an inequality constraint enforcing
2181 the affine expression to be non-negative, can be constructed using
2183 __isl_give isl_constraint *isl_equality_from_aff(
2184 __isl_take isl_aff *aff);
2185 __isl_give isl_constraint *isl_inequality_from_aff(
2186 __isl_take isl_aff *aff);
2188 The expression can be inspected using
2190 #include <isl/aff.h>
2191 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2192 int isl_aff_dim(__isl_keep isl_aff *aff,
2193 enum isl_dim_type type);
2194 __isl_give isl_local_space *isl_aff_get_local_space(
2195 __isl_keep isl_aff *aff);
2196 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2197 enum isl_dim_type type, unsigned pos);
2198 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2200 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2201 enum isl_dim_type type, int pos, isl_int *v);
2202 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2204 __isl_give isl_div *isl_aff_get_div(
2205 __isl_keep isl_aff *aff, int pos);
2207 It can be modified using
2209 #include <isl/aff.h>
2210 __isl_give isl_aff *isl_aff_set_constant(
2211 __isl_take isl_aff *aff, isl_int v);
2212 __isl_give isl_aff *isl_aff_set_constant_si(
2213 __isl_take isl_aff *aff, int v);
2214 __isl_give isl_aff *isl_aff_set_coefficient(
2215 __isl_take isl_aff *aff,
2216 enum isl_dim_type type, int pos, isl_int v);
2217 __isl_give isl_aff *isl_aff_set_coefficient_si(
2218 __isl_take isl_aff *aff,
2219 enum isl_dim_type type, int pos, int v);
2220 __isl_give isl_aff *isl_aff_set_denominator(
2221 __isl_take isl_aff *aff, isl_int v);
2223 __isl_give isl_aff *isl_aff_add_constant(
2224 __isl_take isl_aff *aff, isl_int v);
2225 __isl_give isl_aff *isl_aff_add_coefficient_si(
2226 __isl_take isl_aff *aff,
2227 enum isl_dim_type type, int pos, int v);
2229 Note that the C<set_constant> and C<set_coefficient> functions
2230 set the I<numerator> of the constant or coefficient, while
2231 C<add_constant> and C<add_coefficient> add an integer value to
2232 the possibly rational constant or coefficient.
2236 #include <isl/aff.h>
2237 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2238 __isl_take isl_aff *aff2);
2239 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2240 __isl_take isl_aff *aff2);
2241 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2242 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2243 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2245 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2248 An expression can be printed using
2250 #include <isl/aff.h>
2251 __isl_give isl_printer *isl_printer_print_aff(
2252 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2256 Points are elements of a set. They can be used to construct
2257 simple sets (boxes) or they can be used to represent the
2258 individual elements of a set.
2259 The zero point (the origin) can be created using
2261 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2263 The coordinates of a point can be inspected, set and changed
2266 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2267 enum isl_dim_type type, int pos, isl_int *v);
2268 __isl_give isl_point *isl_point_set_coordinate(
2269 __isl_take isl_point *pnt,
2270 enum isl_dim_type type, int pos, isl_int v);
2272 __isl_give isl_point *isl_point_add_ui(
2273 __isl_take isl_point *pnt,
2274 enum isl_dim_type type, int pos, unsigned val);
2275 __isl_give isl_point *isl_point_sub_ui(
2276 __isl_take isl_point *pnt,
2277 enum isl_dim_type type, int pos, unsigned val);
2279 Other properties can be obtained using
2281 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2283 Points can be copied or freed using
2285 __isl_give isl_point *isl_point_copy(
2286 __isl_keep isl_point *pnt);
2287 void isl_point_free(__isl_take isl_point *pnt);
2289 A singleton set can be created from a point using
2291 __isl_give isl_basic_set *isl_basic_set_from_point(
2292 __isl_take isl_point *pnt);
2293 __isl_give isl_set *isl_set_from_point(
2294 __isl_take isl_point *pnt);
2296 and a box can be created from two opposite extremal points using
2298 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2299 __isl_take isl_point *pnt1,
2300 __isl_take isl_point *pnt2);
2301 __isl_give isl_set *isl_set_box_from_points(
2302 __isl_take isl_point *pnt1,
2303 __isl_take isl_point *pnt2);
2305 All elements of a B<bounded> (union) set can be enumerated using
2306 the following functions.
2308 int isl_set_foreach_point(__isl_keep isl_set *set,
2309 int (*fn)(__isl_take isl_point *pnt, void *user),
2311 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2312 int (*fn)(__isl_take isl_point *pnt, void *user),
2315 The function C<fn> is called for each integer point in
2316 C<set> with as second argument the last argument of
2317 the C<isl_set_foreach_point> call. The function C<fn>
2318 should return C<0> on success and C<-1> on failure.
2319 In the latter case, C<isl_set_foreach_point> will stop
2320 enumerating and return C<-1> as well.
2321 If the enumeration is performed successfully and to completion,
2322 then C<isl_set_foreach_point> returns C<0>.
2324 To obtain a single point of a (basic) set, use
2326 __isl_give isl_point *isl_basic_set_sample_point(
2327 __isl_take isl_basic_set *bset);
2328 __isl_give isl_point *isl_set_sample_point(
2329 __isl_take isl_set *set);
2331 If C<set> does not contain any (integer) points, then the
2332 resulting point will be ``void'', a property that can be
2335 int isl_point_is_void(__isl_keep isl_point *pnt);
2337 =head2 Piecewise Quasipolynomials
2339 A piecewise quasipolynomial is a particular kind of function that maps
2340 a parametric point to a rational value.
2341 More specifically, a quasipolynomial is a polynomial expression in greatest
2342 integer parts of affine expressions of parameters and variables.
2343 A piecewise quasipolynomial is a subdivision of a given parametric
2344 domain into disjoint cells with a quasipolynomial associated to
2345 each cell. The value of the piecewise quasipolynomial at a given
2346 point is the value of the quasipolynomial associated to the cell
2347 that contains the point. Outside of the union of cells,
2348 the value is assumed to be zero.
2349 For example, the piecewise quasipolynomial
2351 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2353 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2354 A given piecewise quasipolynomial has a fixed domain dimension.
2355 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2356 defined over different domains.
2357 Piecewise quasipolynomials are mainly used by the C<barvinok>
2358 library for representing the number of elements in a parametric set or map.
2359 For example, the piecewise quasipolynomial above represents
2360 the number of points in the map
2362 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2364 =head3 Printing (Piecewise) Quasipolynomials
2366 Quasipolynomials and piecewise quasipolynomials can be printed
2367 using the following functions.
2369 __isl_give isl_printer *isl_printer_print_qpolynomial(
2370 __isl_take isl_printer *p,
2371 __isl_keep isl_qpolynomial *qp);
2373 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2374 __isl_take isl_printer *p,
2375 __isl_keep isl_pw_qpolynomial *pwqp);
2377 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2378 __isl_take isl_printer *p,
2379 __isl_keep isl_union_pw_qpolynomial *upwqp);
2381 The output format of the printer
2382 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2383 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2385 In case of printing in C<ISL_FORMAT_C>, the user may want
2386 to set the names of all dimensions
2388 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2389 __isl_take isl_qpolynomial *qp,
2390 enum isl_dim_type type, unsigned pos,
2392 __isl_give isl_pw_qpolynomial *
2393 isl_pw_qpolynomial_set_dim_name(
2394 __isl_take isl_pw_qpolynomial *pwqp,
2395 enum isl_dim_type type, unsigned pos,
2398 =head3 Creating New (Piecewise) Quasipolynomials
2400 Some simple quasipolynomials can be created using the following functions.
2401 More complicated quasipolynomials can be created by applying
2402 operations such as addition and multiplication
2403 on the resulting quasipolynomials
2405 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2406 __isl_take isl_dim *dim);
2407 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2408 __isl_take isl_dim *dim);
2409 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2410 __isl_take isl_dim *dim);
2411 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2412 __isl_take isl_dim *dim);
2413 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2414 __isl_take isl_dim *dim);
2415 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2416 __isl_take isl_dim *dim,
2417 const isl_int n, const isl_int d);
2418 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2419 __isl_take isl_div *div);
2420 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2421 __isl_take isl_dim *dim,
2422 enum isl_dim_type type, unsigned pos);
2423 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2424 __isl_take isl_aff *aff);
2426 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2427 with a single cell can be created using the following functions.
2428 Multiple of these single cell piecewise quasipolynomials can
2429 be combined to create more complicated piecewise quasipolynomials.
2431 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2432 __isl_take isl_dim *dim);
2433 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2434 __isl_take isl_set *set,
2435 __isl_take isl_qpolynomial *qp);
2437 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2438 __isl_take isl_dim *dim);
2439 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2440 __isl_take isl_pw_qpolynomial *pwqp);
2441 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2442 __isl_take isl_union_pw_qpolynomial *upwqp,
2443 __isl_take isl_pw_qpolynomial *pwqp);
2445 Quasipolynomials can be copied and freed again using the following
2448 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2449 __isl_keep isl_qpolynomial *qp);
2450 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2452 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2453 __isl_keep isl_pw_qpolynomial *pwqp);
2454 void isl_pw_qpolynomial_free(
2455 __isl_take isl_pw_qpolynomial *pwqp);
2457 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2458 __isl_keep isl_union_pw_qpolynomial *upwqp);
2459 void isl_union_pw_qpolynomial_free(
2460 __isl_take isl_union_pw_qpolynomial *upwqp);
2462 =head3 Inspecting (Piecewise) Quasipolynomials
2464 To iterate over all piecewise quasipolynomials in a union
2465 piecewise quasipolynomial, use the following function
2467 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2468 __isl_keep isl_union_pw_qpolynomial *upwqp,
2469 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2472 To extract the piecewise quasipolynomial from a union with a given dimension
2475 __isl_give isl_pw_qpolynomial *
2476 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2477 __isl_keep isl_union_pw_qpolynomial *upwqp,
2478 __isl_take isl_dim *dim);
2480 To iterate over the cells in a piecewise quasipolynomial,
2481 use either of the following two functions
2483 int isl_pw_qpolynomial_foreach_piece(
2484 __isl_keep isl_pw_qpolynomial *pwqp,
2485 int (*fn)(__isl_take isl_set *set,
2486 __isl_take isl_qpolynomial *qp,
2487 void *user), void *user);
2488 int isl_pw_qpolynomial_foreach_lifted_piece(
2489 __isl_keep isl_pw_qpolynomial *pwqp,
2490 int (*fn)(__isl_take isl_set *set,
2491 __isl_take isl_qpolynomial *qp,
2492 void *user), void *user);
2494 As usual, the function C<fn> should return C<0> on success
2495 and C<-1> on failure. The difference between
2496 C<isl_pw_qpolynomial_foreach_piece> and
2497 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2498 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2499 compute unique representations for all existentially quantified
2500 variables and then turn these existentially quantified variables
2501 into extra set variables, adapting the associated quasipolynomial
2502 accordingly. This means that the C<set> passed to C<fn>
2503 will not have any existentially quantified variables, but that
2504 the dimensions of the sets may be different for different
2505 invocations of C<fn>.
2507 To iterate over all terms in a quasipolynomial,
2510 int isl_qpolynomial_foreach_term(
2511 __isl_keep isl_qpolynomial *qp,
2512 int (*fn)(__isl_take isl_term *term,
2513 void *user), void *user);
2515 The terms themselves can be inspected and freed using
2518 unsigned isl_term_dim(__isl_keep isl_term *term,
2519 enum isl_dim_type type);
2520 void isl_term_get_num(__isl_keep isl_term *term,
2522 void isl_term_get_den(__isl_keep isl_term *term,
2524 int isl_term_get_exp(__isl_keep isl_term *term,
2525 enum isl_dim_type type, unsigned pos);
2526 __isl_give isl_div *isl_term_get_div(
2527 __isl_keep isl_term *term, unsigned pos);
2528 void isl_term_free(__isl_take isl_term *term);
2530 Each term is a product of parameters, set variables and
2531 integer divisions. The function C<isl_term_get_exp>
2532 returns the exponent of a given dimensions in the given term.
2533 The C<isl_int>s in the arguments of C<isl_term_get_num>
2534 and C<isl_term_get_den> need to have been initialized
2535 using C<isl_int_init> before calling these functions.
2537 =head3 Properties of (Piecewise) Quasipolynomials
2539 To check whether a quasipolynomial is actually a constant,
2540 use the following function.
2542 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2543 isl_int *n, isl_int *d);
2545 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2546 then the numerator and denominator of the constant
2547 are returned in C<*n> and C<*d>, respectively.
2549 =head3 Operations on (Piecewise) Quasipolynomials
2551 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2552 __isl_take isl_qpolynomial *qp);
2553 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2554 __isl_take isl_qpolynomial *qp1,
2555 __isl_take isl_qpolynomial *qp2);
2556 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2557 __isl_take isl_qpolynomial *qp1,
2558 __isl_take isl_qpolynomial *qp2);
2559 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2560 __isl_take isl_qpolynomial *qp1,
2561 __isl_take isl_qpolynomial *qp2);
2562 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2563 __isl_take isl_qpolynomial *qp, unsigned exponent);
2565 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2566 __isl_take isl_pw_qpolynomial *pwqp1,
2567 __isl_take isl_pw_qpolynomial *pwqp2);
2568 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2569 __isl_take isl_pw_qpolynomial *pwqp1,
2570 __isl_take isl_pw_qpolynomial *pwqp2);
2571 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2572 __isl_take isl_pw_qpolynomial *pwqp1,
2573 __isl_take isl_pw_qpolynomial *pwqp2);
2574 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2575 __isl_take isl_pw_qpolynomial *pwqp);
2576 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2577 __isl_take isl_pw_qpolynomial *pwqp1,
2578 __isl_take isl_pw_qpolynomial *pwqp2);
2580 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2581 __isl_take isl_union_pw_qpolynomial *upwqp1,
2582 __isl_take isl_union_pw_qpolynomial *upwqp2);
2583 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2584 __isl_take isl_union_pw_qpolynomial *upwqp1,
2585 __isl_take isl_union_pw_qpolynomial *upwqp2);
2586 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2587 __isl_take isl_union_pw_qpolynomial *upwqp1,
2588 __isl_take isl_union_pw_qpolynomial *upwqp2);
2590 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2591 __isl_take isl_pw_qpolynomial *pwqp,
2592 __isl_take isl_point *pnt);
2594 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2595 __isl_take isl_union_pw_qpolynomial *upwqp,
2596 __isl_take isl_point *pnt);
2598 __isl_give isl_set *isl_pw_qpolynomial_domain(
2599 __isl_take isl_pw_qpolynomial *pwqp);
2600 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2601 __isl_take isl_pw_qpolynomial *pwpq,
2602 __isl_take isl_set *set);
2604 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2605 __isl_take isl_union_pw_qpolynomial *upwqp);
2606 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2607 __isl_take isl_union_pw_qpolynomial *upwpq,
2608 __isl_take isl_union_set *uset);
2610 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2611 __isl_take isl_qpolynomial *qp,
2612 __isl_take isl_dim *model);
2614 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2615 __isl_take isl_union_pw_qpolynomial *upwqp);
2617 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2618 __isl_take isl_qpolynomial *qp,
2619 __isl_take isl_set *context);
2621 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2622 __isl_take isl_pw_qpolynomial *pwqp,
2623 __isl_take isl_set *context);
2625 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2626 __isl_take isl_union_pw_qpolynomial *upwqp,
2627 __isl_take isl_union_set *context);
2629 The gist operation applies the gist operation to each of
2630 the cells in the domain of the input piecewise quasipolynomial.
2631 The context is also exploited
2632 to simplify the quasipolynomials associated to each cell.
2634 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2635 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2636 __isl_give isl_union_pw_qpolynomial *
2637 isl_union_pw_qpolynomial_to_polynomial(
2638 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2640 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2641 the polynomial will be an overapproximation. If C<sign> is negative,
2642 it will be an underapproximation. If C<sign> is zero, the approximation
2643 will lie somewhere in between.
2645 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2647 A piecewise quasipolynomial reduction is a piecewise
2648 reduction (or fold) of quasipolynomials.
2649 In particular, the reduction can be maximum or a minimum.
2650 The objects are mainly used to represent the result of
2651 an upper or lower bound on a quasipolynomial over its domain,
2652 i.e., as the result of the following function.
2654 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2655 __isl_take isl_pw_qpolynomial *pwqp,
2656 enum isl_fold type, int *tight);
2658 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2659 __isl_take isl_union_pw_qpolynomial *upwqp,
2660 enum isl_fold type, int *tight);
2662 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2663 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2664 is the returned bound is known be tight, i.e., for each value
2665 of the parameters there is at least
2666 one element in the domain that reaches the bound.
2667 If the domain of C<pwqp> is not wrapping, then the bound is computed
2668 over all elements in that domain and the result has a purely parametric
2669 domain. If the domain of C<pwqp> is wrapping, then the bound is
2670 computed over the range of the wrapped relation. The domain of the
2671 wrapped relation becomes the domain of the result.
2673 A (piecewise) quasipolynomial reduction can be copied or freed using the
2674 following functions.
2676 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2677 __isl_keep isl_qpolynomial_fold *fold);
2678 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2679 __isl_keep isl_pw_qpolynomial_fold *pwf);
2680 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2681 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2682 void isl_qpolynomial_fold_free(
2683 __isl_take isl_qpolynomial_fold *fold);
2684 void isl_pw_qpolynomial_fold_free(
2685 __isl_take isl_pw_qpolynomial_fold *pwf);
2686 void isl_union_pw_qpolynomial_fold_free(
2687 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2689 =head3 Printing Piecewise Quasipolynomial Reductions
2691 Piecewise quasipolynomial reductions can be printed
2692 using the following function.
2694 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2695 __isl_take isl_printer *p,
2696 __isl_keep isl_pw_qpolynomial_fold *pwf);
2697 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2698 __isl_take isl_printer *p,
2699 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2701 For C<isl_printer_print_pw_qpolynomial_fold>,
2702 output format of the printer
2703 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2704 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2705 output format of the printer
2706 needs to be set to C<ISL_FORMAT_ISL>.
2707 In case of printing in C<ISL_FORMAT_C>, the user may want
2708 to set the names of all dimensions
2710 __isl_give isl_pw_qpolynomial_fold *
2711 isl_pw_qpolynomial_fold_set_dim_name(
2712 __isl_take isl_pw_qpolynomial_fold *pwf,
2713 enum isl_dim_type type, unsigned pos,
2716 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2718 To iterate over all piecewise quasipolynomial reductions in a union
2719 piecewise quasipolynomial reduction, use the following function
2721 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2722 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2723 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2724 void *user), void *user);
2726 To iterate over the cells in a piecewise quasipolynomial reduction,
2727 use either of the following two functions
2729 int isl_pw_qpolynomial_fold_foreach_piece(
2730 __isl_keep isl_pw_qpolynomial_fold *pwf,
2731 int (*fn)(__isl_take isl_set *set,
2732 __isl_take isl_qpolynomial_fold *fold,
2733 void *user), void *user);
2734 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2735 __isl_keep isl_pw_qpolynomial_fold *pwf,
2736 int (*fn)(__isl_take isl_set *set,
2737 __isl_take isl_qpolynomial_fold *fold,
2738 void *user), void *user);
2740 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2741 of the difference between these two functions.
2743 To iterate over all quasipolynomials in a reduction, use
2745 int isl_qpolynomial_fold_foreach_qpolynomial(
2746 __isl_keep isl_qpolynomial_fold *fold,
2747 int (*fn)(__isl_take isl_qpolynomial *qp,
2748 void *user), void *user);
2750 =head3 Operations on Piecewise Quasipolynomial Reductions
2752 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2753 __isl_take isl_pw_qpolynomial_fold *pwf1,
2754 __isl_take isl_pw_qpolynomial_fold *pwf2);
2756 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2757 __isl_take isl_pw_qpolynomial_fold *pwf1,
2758 __isl_take isl_pw_qpolynomial_fold *pwf2);
2760 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2761 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2762 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2764 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2765 __isl_take isl_pw_qpolynomial_fold *pwf,
2766 __isl_take isl_point *pnt);
2768 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2769 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2770 __isl_take isl_point *pnt);
2772 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2773 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2774 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2775 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2776 __isl_take isl_union_set *uset);
2778 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2779 __isl_take isl_pw_qpolynomial_fold *pwf);
2781 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2782 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2784 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2785 __isl_take isl_pw_qpolynomial_fold *pwf,
2786 __isl_take isl_set *context);
2788 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2789 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2790 __isl_take isl_union_set *context);
2792 The gist operation applies the gist operation to each of
2793 the cells in the domain of the input piecewise quasipolynomial reduction.
2794 In future, the operation will also exploit the context
2795 to simplify the quasipolynomial reductions associated to each cell.
2797 __isl_give isl_pw_qpolynomial_fold *
2798 isl_set_apply_pw_qpolynomial_fold(
2799 __isl_take isl_set *set,
2800 __isl_take isl_pw_qpolynomial_fold *pwf,
2802 __isl_give isl_pw_qpolynomial_fold *
2803 isl_map_apply_pw_qpolynomial_fold(
2804 __isl_take isl_map *map,
2805 __isl_take isl_pw_qpolynomial_fold *pwf,
2807 __isl_give isl_union_pw_qpolynomial_fold *
2808 isl_union_set_apply_union_pw_qpolynomial_fold(
2809 __isl_take isl_union_set *uset,
2810 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2812 __isl_give isl_union_pw_qpolynomial_fold *
2813 isl_union_map_apply_union_pw_qpolynomial_fold(
2814 __isl_take isl_union_map *umap,
2815 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2818 The functions taking a map
2819 compose the given map with the given piecewise quasipolynomial reduction.
2820 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2821 over all elements in the intersection of the range of the map
2822 and the domain of the piecewise quasipolynomial reduction
2823 as a function of an element in the domain of the map.
2824 The functions taking a set compute a bound over all elements in the
2825 intersection of the set and the domain of the
2826 piecewise quasipolynomial reduction.
2828 =head2 Dependence Analysis
2830 C<isl> contains specialized functionality for performing
2831 array dataflow analysis. That is, given a I<sink> access relation
2832 and a collection of possible I<source> access relations,
2833 C<isl> can compute relations that describe
2834 for each iteration of the sink access, which iteration
2835 of which of the source access relations was the last
2836 to access the same data element before the given iteration
2838 To compute standard flow dependences, the sink should be
2839 a read, while the sources should be writes.
2840 If any of the source accesses are marked as being I<may>
2841 accesses, then there will be a dependence to the last
2842 I<must> access B<and> to any I<may> access that follows
2843 this last I<must> access.
2844 In particular, if I<all> sources are I<may> accesses,
2845 then memory based dependence analysis is performed.
2846 If, on the other hand, all sources are I<must> accesses,
2847 then value based dependence analysis is performed.
2849 #include <isl/flow.h>
2851 typedef int (*isl_access_level_before)(void *first, void *second);
2853 __isl_give isl_access_info *isl_access_info_alloc(
2854 __isl_take isl_map *sink,
2855 void *sink_user, isl_access_level_before fn,
2857 __isl_give isl_access_info *isl_access_info_add_source(
2858 __isl_take isl_access_info *acc,
2859 __isl_take isl_map *source, int must,
2861 void isl_access_info_free(__isl_take isl_access_info *acc);
2863 __isl_give isl_flow *isl_access_info_compute_flow(
2864 __isl_take isl_access_info *acc);
2866 int isl_flow_foreach(__isl_keep isl_flow *deps,
2867 int (*fn)(__isl_take isl_map *dep, int must,
2868 void *dep_user, void *user),
2870 __isl_give isl_map *isl_flow_get_no_source(
2871 __isl_keep isl_flow *deps, int must);
2872 void isl_flow_free(__isl_take isl_flow *deps);
2874 The function C<isl_access_info_compute_flow> performs the actual
2875 dependence analysis. The other functions are used to construct
2876 the input for this function or to read off the output.
2878 The input is collected in an C<isl_access_info>, which can
2879 be created through a call to C<isl_access_info_alloc>.
2880 The arguments to this functions are the sink access relation
2881 C<sink>, a token C<sink_user> used to identify the sink
2882 access to the user, a callback function for specifying the
2883 relative order of source and sink accesses, and the number
2884 of source access relations that will be added.
2885 The callback function has type C<int (*)(void *first, void *second)>.
2886 The function is called with two user supplied tokens identifying
2887 either a source or the sink and it should return the shared nesting
2888 level and the relative order of the two accesses.
2889 In particular, let I<n> be the number of loops shared by
2890 the two accesses. If C<first> precedes C<second> textually,
2891 then the function should return I<2 * n + 1>; otherwise,
2892 it should return I<2 * n>.
2893 The sources can be added to the C<isl_access_info> by performing
2894 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2895 C<must> indicates whether the source is a I<must> access
2896 or a I<may> access. Note that a multi-valued access relation
2897 should only be marked I<must> if every iteration in the domain
2898 of the relation accesses I<all> elements in its image.
2899 The C<source_user> token is again used to identify
2900 the source access. The range of the source access relation
2901 C<source> should have the same dimension as the range
2902 of the sink access relation.
2903 The C<isl_access_info_free> function should usually not be
2904 called explicitly, because it is called implicitly by
2905 C<isl_access_info_compute_flow>.
2907 The result of the dependence analysis is collected in an
2908 C<isl_flow>. There may be elements of
2909 the sink access for which no preceding source access could be
2910 found or for which all preceding sources are I<may> accesses.
2911 The relations containing these elements can be obtained through
2912 calls to C<isl_flow_get_no_source>, the first with C<must> set
2913 and the second with C<must> unset.
2914 In the case of standard flow dependence analysis,
2915 with the sink a read and the sources I<must> writes,
2916 the first relation corresponds to the reads from uninitialized
2917 array elements and the second relation is empty.
2918 The actual flow dependences can be extracted using
2919 C<isl_flow_foreach>. This function will call the user-specified
2920 callback function C<fn> for each B<non-empty> dependence between
2921 a source and the sink. The callback function is called
2922 with four arguments, the actual flow dependence relation
2923 mapping source iterations to sink iterations, a boolean that
2924 indicates whether it is a I<must> or I<may> dependence, a token
2925 identifying the source and an additional C<void *> with value
2926 equal to the third argument of the C<isl_flow_foreach> call.
2927 A dependence is marked I<must> if it originates from a I<must>
2928 source and if it is not followed by any I<may> sources.
2930 After finishing with an C<isl_flow>, the user should call
2931 C<isl_flow_free> to free all associated memory.
2933 A higher-level interface to dependence analysis is provided
2934 by the following function.
2936 #include <isl/flow.h>
2938 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2939 __isl_take isl_union_map *must_source,
2940 __isl_take isl_union_map *may_source,
2941 __isl_take isl_union_map *schedule,
2942 __isl_give isl_union_map **must_dep,
2943 __isl_give isl_union_map **may_dep,
2944 __isl_give isl_union_map **must_no_source,
2945 __isl_give isl_union_map **may_no_source);
2947 The arrays are identified by the tuple names of the ranges
2948 of the accesses. The iteration domains by the tuple names
2949 of the domains of the accesses and of the schedule.
2950 The relative order of the iteration domains is given by the
2951 schedule. The relations returned through C<must_no_source>
2952 and C<may_no_source> are subsets of C<sink>.
2953 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2954 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2955 any of the other arguments is treated as an error.
2959 B<The functionality described in this section is fairly new
2960 and may be subject to change.>
2962 The following function can be used to compute a schedule
2963 for a union of domains. The generated schedule respects
2964 all C<validity> dependences. That is, all dependence distances
2965 over these dependences in the scheduled space are lexicographically
2966 positive. The generated schedule schedule also tries to minimize
2967 the dependence distances over C<proximity> dependences.
2968 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2969 for groups of domains where the dependence distances have only
2970 non-negative values.
2971 The algorithm used to construct the schedule is similar to that
2974 #include <isl/schedule.h>
2975 __isl_give isl_schedule *isl_union_set_compute_schedule(
2976 __isl_take isl_union_set *domain,
2977 __isl_take isl_union_map *validity,
2978 __isl_take isl_union_map *proximity);
2979 void *isl_schedule_free(__isl_take isl_schedule *sched);
2981 A mapping from the domains to the scheduled space can be obtained
2982 from an C<isl_schedule> using the following function.
2984 __isl_give isl_union_map *isl_schedule_get_map(
2985 __isl_keep isl_schedule *sched);
2987 A representation of the schedule can be printed using
2989 __isl_give isl_printer *isl_printer_print_schedule(
2990 __isl_take isl_printer *p,
2991 __isl_keep isl_schedule *schedule);
2993 A representation of the schedule as a forest of bands can be obtained
2994 using the following function.
2996 __isl_give isl_band_list *isl_schedule_get_band_forest(
2997 __isl_keep isl_schedule *schedule);
2999 The list can be manipulated as explained in L<"Lists">.
3000 The bands inside the list can be copied and freed using the following
3003 #include <isl/band.h>
3004 __isl_give isl_band *isl_band_copy(
3005 __isl_keep isl_band *band);
3006 void *isl_band_free(__isl_take isl_band *band);
3008 Each band contains zero or more scheduling dimensions.
3009 These are referred to as the members of the band.
3010 The section of the schedule that corresponds to the band is
3011 referred to as the partial schedule of the band.
3012 For those nodes that participate in a band, the outer scheduling
3013 dimensions form the prefix schedule, while the inner scheduling
3014 dimensions form the suffix schedule.
3015 That is, if we take a cut of the band forest, then the union of
3016 the concatenations of the prefix, partial and suffix schedules of
3017 each band in the cut is equal to the entire schedule (modulo
3018 some possible padding at the end with zero scheduling dimensions).
3019 The properties of a band can be inspected using the following functions.
3021 #include <isl/band.h>
3022 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3024 int isl_band_has_children(__isl_keep isl_band *band);
3025 __isl_give isl_band_list *isl_band_get_children(
3026 __isl_keep isl_band *band);
3028 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3029 __isl_keep isl_band *band);
3030 __isl_give isl_union_map *isl_band_get_partial_schedule(
3031 __isl_keep isl_band *band);
3032 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3033 __isl_keep isl_band *band);
3035 int isl_band_n_member(__isl_keep isl_band *band);
3036 int isl_band_member_is_zero_distance(
3037 __isl_keep isl_band *band, int pos);
3039 Note that a scheduling dimension is considered to be ``zero
3040 distance'' if it does not carry any proximity dependences
3042 That is, if the dependence distances of the proximity
3043 dependences are all zero in that direction (for fixed
3044 iterations of outer bands).
3046 A representation of the band can be printed using
3048 #include <isl/band.h>
3049 __isl_give isl_printer *isl_printer_print_band(
3050 __isl_take isl_printer *p,
3051 __isl_keep isl_band *band);
3053 Alternatively, the schedule mapping
3054 can also be obtained in pieces using the following functions.
3056 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3057 __isl_give isl_union_map *isl_schedule_get_band(
3058 __isl_keep isl_schedule *sched, unsigned band);
3060 C<isl_schedule_n_band> returns the maximal number of bands.
3061 C<isl_schedule_get_band> returns a union of mappings from a domain to
3062 the band of consecutive schedule dimensions with the given sequence
3063 number for that domain. Bands with the same sequence number but for
3064 different domains may be completely unrelated.
3065 Within a band, the corresponding coordinates of the distance vectors
3066 are all non-negative, assuming that the coordinates for all previous
3069 =head2 Parametric Vertex Enumeration
3071 The parametric vertex enumeration described in this section
3072 is mainly intended to be used internally and by the C<barvinok>
3075 #include <isl/vertices.h>
3076 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3077 __isl_keep isl_basic_set *bset);
3079 The function C<isl_basic_set_compute_vertices> performs the
3080 actual computation of the parametric vertices and the chamber
3081 decomposition and store the result in an C<isl_vertices> object.
3082 This information can be queried by either iterating over all
3083 the vertices or iterating over all the chambers or cells
3084 and then iterating over all vertices that are active on the chamber.
3086 int isl_vertices_foreach_vertex(
3087 __isl_keep isl_vertices *vertices,
3088 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3091 int isl_vertices_foreach_cell(
3092 __isl_keep isl_vertices *vertices,
3093 int (*fn)(__isl_take isl_cell *cell, void *user),
3095 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3096 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3099 Other operations that can be performed on an C<isl_vertices> object are
3102 isl_ctx *isl_vertices_get_ctx(
3103 __isl_keep isl_vertices *vertices);
3104 int isl_vertices_get_n_vertices(
3105 __isl_keep isl_vertices *vertices);
3106 void isl_vertices_free(__isl_take isl_vertices *vertices);
3108 Vertices can be inspected and destroyed using the following functions.
3110 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3111 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3112 __isl_give isl_basic_set *isl_vertex_get_domain(
3113 __isl_keep isl_vertex *vertex);
3114 __isl_give isl_basic_set *isl_vertex_get_expr(
3115 __isl_keep isl_vertex *vertex);
3116 void isl_vertex_free(__isl_take isl_vertex *vertex);
3118 C<isl_vertex_get_expr> returns a singleton parametric set describing
3119 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3121 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3122 B<rational> basic sets, so they should mainly be used for inspection
3123 and should not be mixed with integer sets.
3125 Chambers can be inspected and destroyed using the following functions.
3127 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3128 __isl_give isl_basic_set *isl_cell_get_domain(
3129 __isl_keep isl_cell *cell);
3130 void isl_cell_free(__isl_take isl_cell *cell);
3134 Although C<isl> is mainly meant to be used as a library,
3135 it also contains some basic applications that use some
3136 of the functionality of C<isl>.
3137 The input may be specified in either the L<isl format>
3138 or the L<PolyLib format>.
3140 =head2 C<isl_polyhedron_sample>
3142 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3143 an integer element of the polyhedron, if there is any.
3144 The first column in the output is the denominator and is always
3145 equal to 1. If the polyhedron contains no integer points,
3146 then a vector of length zero is printed.
3150 C<isl_pip> takes the same input as the C<example> program
3151 from the C<piplib> distribution, i.e., a set of constraints
3152 on the parameters, a line containing only -1 and finally a set
3153 of constraints on a parametric polyhedron.
3154 The coefficients of the parameters appear in the last columns
3155 (but before the final constant column).
3156 The output is the lexicographic minimum of the parametric polyhedron.
3157 As C<isl> currently does not have its own output format, the output
3158 is just a dump of the internal state.
3160 =head2 C<isl_polyhedron_minimize>
3162 C<isl_polyhedron_minimize> computes the minimum of some linear
3163 or affine objective function over the integer points in a polyhedron.
3164 If an affine objective function
3165 is given, then the constant should appear in the last column.
3167 =head2 C<isl_polytope_scan>
3169 Given a polytope, C<isl_polytope_scan> prints
3170 all integer points in the polytope.