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_local_space *isl_local_space_set_dim_name(
606 __isl_take isl_local_space *ls,
607 enum isl_dim_type type, unsigned pos, const char *s);
608 __isl_give isl_dim *isl_local_space_get_dim(
609 __isl_keep isl_local_space *ls);
610 __isl_give isl_div *isl_local_space_get_div(
611 __isl_keep isl_local_space *ls, int pos);
612 __isl_give isl_local_space *isl_local_space_copy(
613 __isl_keep isl_local_space *ls);
614 void *isl_local_space_free(__isl_take isl_local_space *ls);
616 Two local spaces can be compared using
618 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
619 __isl_keep isl_local_space *ls2);
621 Local spaces can be created from other local spaces
622 using the following functions.
624 __isl_give isl_local_space *isl_local_space_from_domain(
625 __isl_take isl_local_space *ls);
626 __isl_give isl_local_space *isl_local_space_add_dim(
627 __isl_take isl_local_space *ls,
628 enum isl_dim_type type, unsigned n);
630 =head2 Input and Output
632 C<isl> supports its own input/output format, which is similar
633 to the C<Omega> format, but also supports the C<PolyLib> format
638 The C<isl> format is similar to that of C<Omega>, but has a different
639 syntax for describing the parameters and allows for the definition
640 of an existentially quantified variable as the integer division
641 of an affine expression.
642 For example, the set of integers C<i> between C<0> and C<n>
643 such that C<i % 10 <= 6> can be described as
645 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
648 A set or relation can have several disjuncts, separated
649 by the keyword C<or>. Each disjunct is either a conjunction
650 of constraints or a projection (C<exists>) of a conjunction
651 of constraints. The constraints are separated by the keyword
654 =head3 C<PolyLib> format
656 If the represented set is a union, then the first line
657 contains a single number representing the number of disjuncts.
658 Otherwise, a line containing the number C<1> is optional.
660 Each disjunct is represented by a matrix of constraints.
661 The first line contains two numbers representing
662 the number of rows and columns,
663 where the number of rows is equal to the number of constraints
664 and the number of columns is equal to two plus the number of variables.
665 The following lines contain the actual rows of the constraint matrix.
666 In each row, the first column indicates whether the constraint
667 is an equality (C<0>) or inequality (C<1>). The final column
668 corresponds to the constant term.
670 If the set is parametric, then the coefficients of the parameters
671 appear in the last columns before the constant column.
672 The coefficients of any existentially quantified variables appear
673 between those of the set variables and those of the parameters.
675 =head3 Extended C<PolyLib> format
677 The extended C<PolyLib> format is nearly identical to the
678 C<PolyLib> format. The only difference is that the line
679 containing the number of rows and columns of a constraint matrix
680 also contains four additional numbers:
681 the number of output dimensions, the number of input dimensions,
682 the number of local dimensions (i.e., the number of existentially
683 quantified variables) and the number of parameters.
684 For sets, the number of ``output'' dimensions is equal
685 to the number of set dimensions, while the number of ``input''
691 __isl_give isl_basic_set *isl_basic_set_read_from_file(
692 isl_ctx *ctx, FILE *input, int nparam);
693 __isl_give isl_basic_set *isl_basic_set_read_from_str(
694 isl_ctx *ctx, const char *str, int nparam);
695 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
696 FILE *input, int nparam);
697 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
698 const char *str, int nparam);
701 __isl_give isl_basic_map *isl_basic_map_read_from_file(
702 isl_ctx *ctx, FILE *input, int nparam);
703 __isl_give isl_basic_map *isl_basic_map_read_from_str(
704 isl_ctx *ctx, const char *str, int nparam);
705 __isl_give isl_map *isl_map_read_from_file(
706 struct isl_ctx *ctx, FILE *input, int nparam);
707 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
708 const char *str, int nparam);
710 #include <isl/union_set.h>
711 __isl_give isl_union_set *isl_union_set_read_from_file(
712 isl_ctx *ctx, FILE *input);
713 __isl_give isl_union_set *isl_union_set_read_from_str(
714 struct isl_ctx *ctx, const char *str);
716 #include <isl/union_map.h>
717 __isl_give isl_union_map *isl_union_map_read_from_file(
718 isl_ctx *ctx, FILE *input);
719 __isl_give isl_union_map *isl_union_map_read_from_str(
720 struct isl_ctx *ctx, const char *str);
722 The input format is autodetected and may be either the C<PolyLib> format
723 or the C<isl> format.
724 C<nparam> specifies how many of the final columns in
725 the C<PolyLib> format correspond to parameters.
726 If input is given in the C<isl> format, then the number
727 of parameters needs to be equal to C<nparam>.
728 If C<nparam> is negative, then any number of parameters
729 is accepted in the C<isl> format and zero parameters
730 are assumed in the C<PolyLib> format.
734 Before anything can be printed, an C<isl_printer> needs to
737 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
739 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
740 void isl_printer_free(__isl_take isl_printer *printer);
741 __isl_give char *isl_printer_get_str(
742 __isl_keep isl_printer *printer);
744 The behavior of the printer can be modified in various ways
746 __isl_give isl_printer *isl_printer_set_output_format(
747 __isl_take isl_printer *p, int output_format);
748 __isl_give isl_printer *isl_printer_set_indent(
749 __isl_take isl_printer *p, int indent);
750 __isl_give isl_printer *isl_printer_indent(
751 __isl_take isl_printer *p, int indent);
752 __isl_give isl_printer *isl_printer_set_prefix(
753 __isl_take isl_printer *p, const char *prefix);
754 __isl_give isl_printer *isl_printer_set_suffix(
755 __isl_take isl_printer *p, const char *suffix);
757 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
758 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
759 and defaults to C<ISL_FORMAT_ISL>.
760 Each line in the output is indented by C<indent> (set by
761 C<isl_printer_set_indent>) spaces
762 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
763 In the C<PolyLib> format output,
764 the coefficients of the existentially quantified variables
765 appear between those of the set variables and those
767 The function C<isl_printer_indent> increases the indentation
768 by the specified amount (which may be negative).
770 To actually print something, use
773 __isl_give isl_printer *isl_printer_print_basic_set(
774 __isl_take isl_printer *printer,
775 __isl_keep isl_basic_set *bset);
776 __isl_give isl_printer *isl_printer_print_set(
777 __isl_take isl_printer *printer,
778 __isl_keep isl_set *set);
781 __isl_give isl_printer *isl_printer_print_basic_map(
782 __isl_take isl_printer *printer,
783 __isl_keep isl_basic_map *bmap);
784 __isl_give isl_printer *isl_printer_print_map(
785 __isl_take isl_printer *printer,
786 __isl_keep isl_map *map);
788 #include <isl/union_set.h>
789 __isl_give isl_printer *isl_printer_print_union_set(
790 __isl_take isl_printer *p,
791 __isl_keep isl_union_set *uset);
793 #include <isl/union_map.h>
794 __isl_give isl_printer *isl_printer_print_union_map(
795 __isl_take isl_printer *p,
796 __isl_keep isl_union_map *umap);
798 When called on a file printer, the following function flushes
799 the file. When called on a string printer, the buffer is cleared.
801 __isl_give isl_printer *isl_printer_flush(
802 __isl_take isl_printer *p);
804 =head2 Creating New Sets and Relations
806 C<isl> has functions for creating some standard sets and relations.
810 =item * Empty sets and relations
812 __isl_give isl_basic_set *isl_basic_set_empty(
813 __isl_take isl_dim *dim);
814 __isl_give isl_basic_map *isl_basic_map_empty(
815 __isl_take isl_dim *dim);
816 __isl_give isl_set *isl_set_empty(
817 __isl_take isl_dim *dim);
818 __isl_give isl_map *isl_map_empty(
819 __isl_take isl_dim *dim);
820 __isl_give isl_union_set *isl_union_set_empty(
821 __isl_take isl_dim *dim);
822 __isl_give isl_union_map *isl_union_map_empty(
823 __isl_take isl_dim *dim);
825 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
826 is only used to specify the parameters.
828 =item * Universe sets and relations
830 __isl_give isl_basic_set *isl_basic_set_universe(
831 __isl_take isl_dim *dim);
832 __isl_give isl_basic_map *isl_basic_map_universe(
833 __isl_take isl_dim *dim);
834 __isl_give isl_set *isl_set_universe(
835 __isl_take isl_dim *dim);
836 __isl_give isl_map *isl_map_universe(
837 __isl_take isl_dim *dim);
838 __isl_give isl_union_set *isl_union_set_universe(
839 __isl_take isl_union_set *uset);
840 __isl_give isl_union_map *isl_union_map_universe(
841 __isl_take isl_union_map *umap);
843 The sets and relations constructed by the functions above
844 contain all integer values, while those constructed by the
845 functions below only contain non-negative values.
847 __isl_give isl_basic_set *isl_basic_set_nat_universe(
848 __isl_take isl_dim *dim);
849 __isl_give isl_basic_map *isl_basic_map_nat_universe(
850 __isl_take isl_dim *dim);
851 __isl_give isl_set *isl_set_nat_universe(
852 __isl_take isl_dim *dim);
853 __isl_give isl_map *isl_map_nat_universe(
854 __isl_take isl_dim *dim);
856 =item * Identity relations
858 __isl_give isl_basic_map *isl_basic_map_identity(
859 __isl_take isl_dim *dim);
860 __isl_give isl_map *isl_map_identity(
861 __isl_take isl_dim *dim);
863 The number of input and output dimensions in C<dim> needs
866 =item * Lexicographic order
868 __isl_give isl_map *isl_map_lex_lt(
869 __isl_take isl_dim *set_dim);
870 __isl_give isl_map *isl_map_lex_le(
871 __isl_take isl_dim *set_dim);
872 __isl_give isl_map *isl_map_lex_gt(
873 __isl_take isl_dim *set_dim);
874 __isl_give isl_map *isl_map_lex_ge(
875 __isl_take isl_dim *set_dim);
876 __isl_give isl_map *isl_map_lex_lt_first(
877 __isl_take isl_dim *dim, unsigned n);
878 __isl_give isl_map *isl_map_lex_le_first(
879 __isl_take isl_dim *dim, unsigned n);
880 __isl_give isl_map *isl_map_lex_gt_first(
881 __isl_take isl_dim *dim, unsigned n);
882 __isl_give isl_map *isl_map_lex_ge_first(
883 __isl_take isl_dim *dim, unsigned n);
885 The first four functions take a dimension specification for a B<set>
886 and return relations that express that the elements in the domain
887 are lexicographically less
888 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
889 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
890 than the elements in the range.
891 The last four functions take a dimension specification for a map
892 and return relations that express that the first C<n> dimensions
893 in the domain are lexicographically less
894 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
895 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
896 than the first C<n> dimensions in the range.
900 A basic set or relation can be converted to a set or relation
901 using the following functions.
903 __isl_give isl_set *isl_set_from_basic_set(
904 __isl_take isl_basic_set *bset);
905 __isl_give isl_map *isl_map_from_basic_map(
906 __isl_take isl_basic_map *bmap);
908 Sets and relations can be converted to union sets and relations
909 using the following functions.
911 __isl_give isl_union_map *isl_union_map_from_map(
912 __isl_take isl_map *map);
913 __isl_give isl_union_set *isl_union_set_from_set(
914 __isl_take isl_set *set);
916 Sets and relations can be copied and freed again using the following
919 __isl_give isl_basic_set *isl_basic_set_copy(
920 __isl_keep isl_basic_set *bset);
921 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
922 __isl_give isl_union_set *isl_union_set_copy(
923 __isl_keep isl_union_set *uset);
924 __isl_give isl_basic_map *isl_basic_map_copy(
925 __isl_keep isl_basic_map *bmap);
926 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
927 __isl_give isl_union_map *isl_union_map_copy(
928 __isl_keep isl_union_map *umap);
929 void isl_basic_set_free(__isl_take isl_basic_set *bset);
930 void isl_set_free(__isl_take isl_set *set);
931 void isl_union_set_free(__isl_take isl_union_set *uset);
932 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
933 void isl_map_free(__isl_take isl_map *map);
934 void isl_union_map_free(__isl_take isl_union_map *umap);
936 Other sets and relations can be constructed by starting
937 from a universe set or relation, adding equality and/or
938 inequality constraints and then projecting out the
939 existentially quantified variables, if any.
940 Constraints can be constructed, manipulated and
941 added to (basic) sets and relations using the following functions.
943 #include <isl/constraint.h>
944 __isl_give isl_constraint *isl_equality_alloc(
945 __isl_take isl_dim *dim);
946 __isl_give isl_constraint *isl_inequality_alloc(
947 __isl_take isl_dim *dim);
948 void isl_constraint_set_constant(
949 __isl_keep isl_constraint *constraint, isl_int v);
950 void isl_constraint_set_coefficient(
951 __isl_keep isl_constraint *constraint,
952 enum isl_dim_type type, int pos, isl_int v);
953 __isl_give isl_basic_map *isl_basic_map_add_constraint(
954 __isl_take isl_basic_map *bmap,
955 __isl_take isl_constraint *constraint);
956 __isl_give isl_basic_set *isl_basic_set_add_constraint(
957 __isl_take isl_basic_set *bset,
958 __isl_take isl_constraint *constraint);
959 __isl_give isl_map *isl_map_add_constraint(
960 __isl_take isl_map *map,
961 __isl_take isl_constraint *constraint);
962 __isl_give isl_set *isl_set_add_constraint(
963 __isl_take isl_set *set,
964 __isl_take isl_constraint *constraint);
966 For example, to create a set containing the even integers
967 between 10 and 42, you would use the following code.
971 struct isl_constraint *c;
972 struct isl_basic_set *bset;
975 dim = isl_dim_set_alloc(ctx, 0, 2);
976 bset = isl_basic_set_universe(isl_dim_copy(dim));
978 c = isl_equality_alloc(isl_dim_copy(dim));
979 isl_int_set_si(v, -1);
980 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
981 isl_int_set_si(v, 2);
982 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
983 bset = isl_basic_set_add_constraint(bset, c);
985 c = isl_inequality_alloc(isl_dim_copy(dim));
986 isl_int_set_si(v, -10);
987 isl_constraint_set_constant(c, v);
988 isl_int_set_si(v, 1);
989 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
990 bset = isl_basic_set_add_constraint(bset, c);
992 c = isl_inequality_alloc(dim);
993 isl_int_set_si(v, 42);
994 isl_constraint_set_constant(c, v);
995 isl_int_set_si(v, -1);
996 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
997 bset = isl_basic_set_add_constraint(bset, c);
999 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1005 struct isl_basic_set *bset;
1006 bset = isl_basic_set_read_from_str(ctx,
1007 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1009 A basic set or relation can also be constructed from two matrices
1010 describing the equalities and the inequalities.
1012 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1013 __isl_take isl_dim *dim,
1014 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1015 enum isl_dim_type c1,
1016 enum isl_dim_type c2, enum isl_dim_type c3,
1017 enum isl_dim_type c4);
1018 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1019 __isl_take isl_dim *dim,
1020 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1021 enum isl_dim_type c1,
1022 enum isl_dim_type c2, enum isl_dim_type c3,
1023 enum isl_dim_type c4, enum isl_dim_type c5);
1025 The C<isl_dim_type> arguments indicate the order in which
1026 different kinds of variables appear in the input matrices
1027 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1028 C<isl_dim_set> and C<isl_dim_div> for sets and
1029 of C<isl_dim_cst>, C<isl_dim_param>,
1030 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1032 A basic relation can also be constructed from an affine expression
1033 or a list of affine expressions (See L<"Quasi Affine Expressions">).
1035 __isl_give isl_basic_map *isl_basic_map_from_aff(
1036 __isl_take isl_aff *aff);
1037 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1038 __isl_take isl_dim *domain_dim,
1039 __isl_take isl_aff_list *list);
1041 The C<domain_dim> argument describes the domain of the resulting
1042 basic relation. It is required because the C<list> may consist
1043 of zero affine expressions.
1045 =head2 Inspecting Sets and Relations
1047 Usually, the user should not have to care about the actual constraints
1048 of the sets and maps, but should instead apply the abstract operations
1049 explained in the following sections.
1050 Occasionally, however, it may be required to inspect the individual
1051 coefficients of the constraints. This section explains how to do so.
1052 In these cases, it may also be useful to have C<isl> compute
1053 an explicit representation of the existentially quantified variables.
1055 __isl_give isl_set *isl_set_compute_divs(
1056 __isl_take isl_set *set);
1057 __isl_give isl_map *isl_map_compute_divs(
1058 __isl_take isl_map *map);
1059 __isl_give isl_union_set *isl_union_set_compute_divs(
1060 __isl_take isl_union_set *uset);
1061 __isl_give isl_union_map *isl_union_map_compute_divs(
1062 __isl_take isl_union_map *umap);
1064 This explicit representation defines the existentially quantified
1065 variables as integer divisions of the other variables, possibly
1066 including earlier existentially quantified variables.
1067 An explicitly represented existentially quantified variable therefore
1068 has a unique value when the values of the other variables are known.
1069 If, furthermore, the same existentials, i.e., existentials
1070 with the same explicit representations, should appear in the
1071 same order in each of the disjuncts of a set or map, then the user should call
1072 either of the following functions.
1074 __isl_give isl_set *isl_set_align_divs(
1075 __isl_take isl_set *set);
1076 __isl_give isl_map *isl_map_align_divs(
1077 __isl_take isl_map *map);
1079 Alternatively, the existentially quantified variables can be removed
1080 using the following functions, which compute an overapproximation.
1082 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1083 __isl_take isl_basic_set *bset);
1084 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1085 __isl_take isl_basic_map *bmap);
1086 __isl_give isl_set *isl_set_remove_divs(
1087 __isl_take isl_set *set);
1088 __isl_give isl_map *isl_map_remove_divs(
1089 __isl_take isl_map *map);
1091 To iterate over all the sets or maps in a union set or map, use
1093 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1094 int (*fn)(__isl_take isl_set *set, void *user),
1096 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1097 int (*fn)(__isl_take isl_map *map, void *user),
1100 The number of sets or maps in a union set or map can be obtained
1103 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1104 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1106 To extract the set or map from a union with a given dimension
1109 __isl_give isl_set *isl_union_set_extract_set(
1110 __isl_keep isl_union_set *uset,
1111 __isl_take isl_dim *dim);
1112 __isl_give isl_map *isl_union_map_extract_map(
1113 __isl_keep isl_union_map *umap,
1114 __isl_take isl_dim *dim);
1116 To iterate over all the basic sets or maps in a set or map, use
1118 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1119 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1121 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1122 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1125 The callback function C<fn> should return 0 if successful and
1126 -1 if an error occurs. In the latter case, or if any other error
1127 occurs, the above functions will return -1.
1129 It should be noted that C<isl> does not guarantee that
1130 the basic sets or maps passed to C<fn> are disjoint.
1131 If this is required, then the user should call one of
1132 the following functions first.
1134 __isl_give isl_set *isl_set_make_disjoint(
1135 __isl_take isl_set *set);
1136 __isl_give isl_map *isl_map_make_disjoint(
1137 __isl_take isl_map *map);
1139 The number of basic sets in a set can be obtained
1142 int isl_set_n_basic_set(__isl_keep isl_set *set);
1144 To iterate over the constraints of a basic set or map, use
1146 #include <isl/constraint.h>
1148 int isl_basic_map_foreach_constraint(
1149 __isl_keep isl_basic_map *bmap,
1150 int (*fn)(__isl_take isl_constraint *c, void *user),
1152 void isl_constraint_free(struct isl_constraint *c);
1154 Again, the callback function C<fn> should return 0 if successful and
1155 -1 if an error occurs. In the latter case, or if any other error
1156 occurs, the above functions will return -1.
1157 The constraint C<c> represents either an equality or an inequality.
1158 Use the following function to find out whether a constraint
1159 represents an equality. If not, it represents an inequality.
1161 int isl_constraint_is_equality(
1162 __isl_keep isl_constraint *constraint);
1164 The coefficients of the constraints can be inspected using
1165 the following functions.
1167 void isl_constraint_get_constant(
1168 __isl_keep isl_constraint *constraint, isl_int *v);
1169 void isl_constraint_get_coefficient(
1170 __isl_keep isl_constraint *constraint,
1171 enum isl_dim_type type, int pos, isl_int *v);
1172 int isl_constraint_involves_dims(
1173 __isl_keep isl_constraint *constraint,
1174 enum isl_dim_type type, unsigned first, unsigned n);
1176 The explicit representations of the existentially quantified
1177 variables can be inspected using the following functions.
1178 Note that the user is only allowed to use these functions
1179 if the inspected set or map is the result of a call
1180 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1182 __isl_give isl_div *isl_constraint_div(
1183 __isl_keep isl_constraint *constraint, int pos);
1184 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1185 void isl_div_get_constant(__isl_keep isl_div *div,
1187 void isl_div_get_denominator(__isl_keep isl_div *div,
1189 void isl_div_get_coefficient(__isl_keep isl_div *div,
1190 enum isl_dim_type type, int pos, isl_int *v);
1192 To obtain the constraints of a basic set or map in matrix
1193 form, use the following functions.
1195 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1196 __isl_keep isl_basic_set *bset,
1197 enum isl_dim_type c1, enum isl_dim_type c2,
1198 enum isl_dim_type c3, enum isl_dim_type c4);
1199 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1200 __isl_keep isl_basic_set *bset,
1201 enum isl_dim_type c1, enum isl_dim_type c2,
1202 enum isl_dim_type c3, enum isl_dim_type c4);
1203 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1204 __isl_keep isl_basic_map *bmap,
1205 enum isl_dim_type c1,
1206 enum isl_dim_type c2, enum isl_dim_type c3,
1207 enum isl_dim_type c4, enum isl_dim_type c5);
1208 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1209 __isl_keep isl_basic_map *bmap,
1210 enum isl_dim_type c1,
1211 enum isl_dim_type c2, enum isl_dim_type c3,
1212 enum isl_dim_type c4, enum isl_dim_type c5);
1214 The C<isl_dim_type> arguments dictate the order in which
1215 different kinds of variables appear in the resulting matrix
1216 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1217 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1219 The names of the domain and range spaces of a set or relation can be
1220 read off using the following functions.
1222 const char *isl_basic_set_get_tuple_name(
1223 __isl_keep isl_basic_set *bset);
1224 const char *isl_set_get_tuple_name(
1225 __isl_keep isl_set *set);
1226 const char *isl_basic_map_get_tuple_name(
1227 __isl_keep isl_basic_map *bmap,
1228 enum isl_dim_type type);
1229 const char *isl_map_get_tuple_name(
1230 __isl_keep isl_map *map,
1231 enum isl_dim_type type);
1233 As with C<isl_dim_get_tuple_name>, the value returned points to
1234 an internal data structure.
1235 The names of individual dimensions can be read off using
1236 the following functions.
1238 const char *isl_constraint_get_dim_name(
1239 __isl_keep isl_constraint *constraint,
1240 enum isl_dim_type type, unsigned pos);
1241 const char *isl_basic_set_get_dim_name(
1242 __isl_keep isl_basic_set *bset,
1243 enum isl_dim_type type, unsigned pos);
1244 const char *isl_set_get_dim_name(
1245 __isl_keep isl_set *set,
1246 enum isl_dim_type type, unsigned pos);
1247 const char *isl_basic_map_get_dim_name(
1248 __isl_keep isl_basic_map *bmap,
1249 enum isl_dim_type type, unsigned pos);
1250 const char *isl_map_get_dim_name(
1251 __isl_keep isl_map *map,
1252 enum isl_dim_type type, unsigned pos);
1254 These functions are mostly useful to obtain the names
1259 =head3 Unary Properties
1265 The following functions test whether the given set or relation
1266 contains any integer points. The ``plain'' variants do not perform
1267 any computations, but simply check if the given set or relation
1268 is already known to be empty.
1270 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1271 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1272 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1273 int isl_set_is_empty(__isl_keep isl_set *set);
1274 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1275 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1276 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1277 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1278 int isl_map_is_empty(__isl_keep isl_map *map);
1279 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1281 =item * Universality
1283 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1284 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1285 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1287 =item * Single-valuedness
1289 int isl_map_is_single_valued(__isl_keep isl_map *map);
1290 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1294 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1295 int isl_map_is_injective(__isl_keep isl_map *map);
1296 int isl_union_map_plain_is_injective(
1297 __isl_keep isl_union_map *umap);
1298 int isl_union_map_is_injective(
1299 __isl_keep isl_union_map *umap);
1303 int isl_map_is_bijective(__isl_keep isl_map *map);
1304 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1308 The following functions check whether the domain of the given
1309 (basic) set is a wrapped relation.
1311 int isl_basic_set_is_wrapping(
1312 __isl_keep isl_basic_set *bset);
1313 int isl_set_is_wrapping(__isl_keep isl_set *set);
1315 =item * Internal Product
1317 int isl_basic_map_can_zip(
1318 __isl_keep isl_basic_map *bmap);
1319 int isl_map_can_zip(__isl_keep isl_map *map);
1321 Check whether the product of domain and range of the given relation
1323 i.e., whether both domain and range are nested relations.
1327 =head3 Binary Properties
1333 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1334 __isl_keep isl_set *set2);
1335 int isl_set_is_equal(__isl_keep isl_set *set1,
1336 __isl_keep isl_set *set2);
1337 int isl_union_set_is_equal(
1338 __isl_keep isl_union_set *uset1,
1339 __isl_keep isl_union_set *uset2);
1340 int isl_basic_map_is_equal(
1341 __isl_keep isl_basic_map *bmap1,
1342 __isl_keep isl_basic_map *bmap2);
1343 int isl_map_is_equal(__isl_keep isl_map *map1,
1344 __isl_keep isl_map *map2);
1345 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1346 __isl_keep isl_map *map2);
1347 int isl_union_map_is_equal(
1348 __isl_keep isl_union_map *umap1,
1349 __isl_keep isl_union_map *umap2);
1351 =item * Disjointness
1353 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1354 __isl_keep isl_set *set2);
1358 int isl_set_is_subset(__isl_keep isl_set *set1,
1359 __isl_keep isl_set *set2);
1360 int isl_set_is_strict_subset(
1361 __isl_keep isl_set *set1,
1362 __isl_keep isl_set *set2);
1363 int isl_union_set_is_subset(
1364 __isl_keep isl_union_set *uset1,
1365 __isl_keep isl_union_set *uset2);
1366 int isl_union_set_is_strict_subset(
1367 __isl_keep isl_union_set *uset1,
1368 __isl_keep isl_union_set *uset2);
1369 int isl_basic_map_is_subset(
1370 __isl_keep isl_basic_map *bmap1,
1371 __isl_keep isl_basic_map *bmap2);
1372 int isl_basic_map_is_strict_subset(
1373 __isl_keep isl_basic_map *bmap1,
1374 __isl_keep isl_basic_map *bmap2);
1375 int isl_map_is_subset(
1376 __isl_keep isl_map *map1,
1377 __isl_keep isl_map *map2);
1378 int isl_map_is_strict_subset(
1379 __isl_keep isl_map *map1,
1380 __isl_keep isl_map *map2);
1381 int isl_union_map_is_subset(
1382 __isl_keep isl_union_map *umap1,
1383 __isl_keep isl_union_map *umap2);
1384 int isl_union_map_is_strict_subset(
1385 __isl_keep isl_union_map *umap1,
1386 __isl_keep isl_union_map *umap2);
1390 =head2 Unary Operations
1396 __isl_give isl_set *isl_set_complement(
1397 __isl_take isl_set *set);
1401 __isl_give isl_basic_map *isl_basic_map_reverse(
1402 __isl_take isl_basic_map *bmap);
1403 __isl_give isl_map *isl_map_reverse(
1404 __isl_take isl_map *map);
1405 __isl_give isl_union_map *isl_union_map_reverse(
1406 __isl_take isl_union_map *umap);
1410 __isl_give isl_basic_set *isl_basic_set_project_out(
1411 __isl_take isl_basic_set *bset,
1412 enum isl_dim_type type, unsigned first, unsigned n);
1413 __isl_give isl_basic_map *isl_basic_map_project_out(
1414 __isl_take isl_basic_map *bmap,
1415 enum isl_dim_type type, unsigned first, unsigned n);
1416 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1417 enum isl_dim_type type, unsigned first, unsigned n);
1418 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1419 enum isl_dim_type type, unsigned first, unsigned n);
1420 __isl_give isl_basic_set *isl_basic_map_domain(
1421 __isl_take isl_basic_map *bmap);
1422 __isl_give isl_basic_set *isl_basic_map_range(
1423 __isl_take isl_basic_map *bmap);
1424 __isl_give isl_set *isl_map_domain(
1425 __isl_take isl_map *bmap);
1426 __isl_give isl_set *isl_map_range(
1427 __isl_take isl_map *map);
1428 __isl_give isl_union_set *isl_union_map_domain(
1429 __isl_take isl_union_map *umap);
1430 __isl_give isl_union_set *isl_union_map_range(
1431 __isl_take isl_union_map *umap);
1433 __isl_give isl_basic_map *isl_basic_map_domain_map(
1434 __isl_take isl_basic_map *bmap);
1435 __isl_give isl_basic_map *isl_basic_map_range_map(
1436 __isl_take isl_basic_map *bmap);
1437 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1438 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1439 __isl_give isl_union_map *isl_union_map_domain_map(
1440 __isl_take isl_union_map *umap);
1441 __isl_give isl_union_map *isl_union_map_range_map(
1442 __isl_take isl_union_map *umap);
1444 The functions above construct a (basic, regular or union) relation
1445 that maps (a wrapped version of) the input relation to its domain or range.
1449 __isl_give isl_set *isl_set_eliminate(
1450 __isl_take isl_set *set, enum isl_dim_type type,
1451 unsigned first, unsigned n);
1453 Eliminate the coefficients for the given dimensions from the constraints,
1454 without removing the dimensions.
1458 __isl_give isl_basic_set *isl_basic_set_fix(
1459 __isl_take isl_basic_set *bset,
1460 enum isl_dim_type type, unsigned pos,
1462 __isl_give isl_basic_set *isl_basic_set_fix_si(
1463 __isl_take isl_basic_set *bset,
1464 enum isl_dim_type type, unsigned pos, int value);
1465 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1466 enum isl_dim_type type, unsigned pos,
1468 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1469 enum isl_dim_type type, unsigned pos, int value);
1470 __isl_give isl_basic_map *isl_basic_map_fix_si(
1471 __isl_take isl_basic_map *bmap,
1472 enum isl_dim_type type, unsigned pos, int value);
1473 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1474 enum isl_dim_type type, unsigned pos, int value);
1476 Intersect the set or relation with the hyperplane where the given
1477 dimension has the fixed given value.
1481 __isl_give isl_map *isl_set_identity(
1482 __isl_take isl_set *set);
1483 __isl_give isl_union_map *isl_union_set_identity(
1484 __isl_take isl_union_set *uset);
1486 Construct an identity relation on the given (union) set.
1490 __isl_give isl_basic_set *isl_basic_map_deltas(
1491 __isl_take isl_basic_map *bmap);
1492 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1493 __isl_give isl_union_set *isl_union_map_deltas(
1494 __isl_take isl_union_map *umap);
1496 These functions return a (basic) set containing the differences
1497 between image elements and corresponding domain elements in the input.
1499 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1500 __isl_take isl_basic_map *bmap);
1501 __isl_give isl_map *isl_map_deltas_map(
1502 __isl_take isl_map *map);
1503 __isl_give isl_union_map *isl_union_map_deltas_map(
1504 __isl_take isl_union_map *umap);
1506 The functions above construct a (basic, regular or union) relation
1507 that maps (a wrapped version of) the input relation to its delta set.
1511 Simplify the representation of a set or relation by trying
1512 to combine pairs of basic sets or relations into a single
1513 basic set or relation.
1515 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1516 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1517 __isl_give isl_union_set *isl_union_set_coalesce(
1518 __isl_take isl_union_set *uset);
1519 __isl_give isl_union_map *isl_union_map_coalesce(
1520 __isl_take isl_union_map *umap);
1522 =item * Detecting equalities
1524 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1525 __isl_take isl_basic_set *bset);
1526 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1527 __isl_take isl_basic_map *bmap);
1528 __isl_give isl_set *isl_set_detect_equalities(
1529 __isl_take isl_set *set);
1530 __isl_give isl_map *isl_map_detect_equalities(
1531 __isl_take isl_map *map);
1532 __isl_give isl_union_set *isl_union_set_detect_equalities(
1533 __isl_take isl_union_set *uset);
1534 __isl_give isl_union_map *isl_union_map_detect_equalities(
1535 __isl_take isl_union_map *umap);
1537 Simplify the representation of a set or relation by detecting implicit
1540 =item * Removing redundant constraints
1542 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1543 __isl_take isl_basic_set *bset);
1544 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1545 __isl_take isl_basic_map *bmap);
1549 __isl_give isl_basic_set *isl_set_convex_hull(
1550 __isl_take isl_set *set);
1551 __isl_give isl_basic_map *isl_map_convex_hull(
1552 __isl_take isl_map *map);
1554 If the input set or relation has any existentially quantified
1555 variables, then the result of these operations is currently undefined.
1559 __isl_give isl_basic_set *isl_set_simple_hull(
1560 __isl_take isl_set *set);
1561 __isl_give isl_basic_map *isl_map_simple_hull(
1562 __isl_take isl_map *map);
1563 __isl_give isl_union_map *isl_union_map_simple_hull(
1564 __isl_take isl_union_map *umap);
1566 These functions compute a single basic set or relation
1567 that contains the whole input set or relation.
1568 In particular, the output is described by translates
1569 of the constraints describing the basic sets or relations in the input.
1573 (See \autoref{s:simple hull}.)
1579 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1580 __isl_take isl_basic_set *bset);
1581 __isl_give isl_basic_set *isl_set_affine_hull(
1582 __isl_take isl_set *set);
1583 __isl_give isl_union_set *isl_union_set_affine_hull(
1584 __isl_take isl_union_set *uset);
1585 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1586 __isl_take isl_basic_map *bmap);
1587 __isl_give isl_basic_map *isl_map_affine_hull(
1588 __isl_take isl_map *map);
1589 __isl_give isl_union_map *isl_union_map_affine_hull(
1590 __isl_take isl_union_map *umap);
1592 In case of union sets and relations, the affine hull is computed
1595 =item * Polyhedral hull
1597 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1598 __isl_take isl_set *set);
1599 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1600 __isl_take isl_map *map);
1601 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1602 __isl_take isl_union_set *uset);
1603 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1604 __isl_take isl_union_map *umap);
1606 These functions compute a single basic set or relation
1607 not involving any existentially quantified variables
1608 that contains the whole input set or relation.
1609 In case of union sets and relations, the polyhedral hull is computed
1612 =item * Optimization
1614 #include <isl/ilp.h>
1615 enum isl_lp_result isl_basic_set_max(
1616 __isl_keep isl_basic_set *bset,
1617 __isl_keep isl_aff *obj, isl_int *opt)
1618 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1619 __isl_keep isl_aff *obj, isl_int *opt);
1621 Compute the maximum of the integer affine expression C<obj>
1622 over the points in C<set>, returning the result in C<opt>.
1623 The return value may be one of C<isl_lp_error>,
1624 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1628 The following functions compute either the set of (rational) coefficient
1629 values of valid constraints for the given set or the set of (rational)
1630 values satisfying the constraints with coefficients from the given set.
1631 Internally, these two sets of functions perform essentially the
1632 same operations, except that the set of coefficients is assumed to
1633 be a cone, while the set of values may be any polyhedron.
1634 The current implementation is based on the Farkas lemma and
1635 Fourier-Motzkin elimination, but this may change or be made optional
1636 in future. In particular, future implementations may use different
1637 dualization algorithms or skip the elimination step.
1639 __isl_give isl_basic_set *isl_basic_set_coefficients(
1640 __isl_take isl_basic_set *bset);
1641 __isl_give isl_basic_set *isl_set_coefficients(
1642 __isl_take isl_set *set);
1643 __isl_give isl_union_set *isl_union_set_coefficients(
1644 __isl_take isl_union_set *bset);
1645 __isl_give isl_basic_set *isl_basic_set_solutions(
1646 __isl_take isl_basic_set *bset);
1647 __isl_give isl_basic_set *isl_set_solutions(
1648 __isl_take isl_set *set);
1649 __isl_give isl_union_set *isl_union_set_solutions(
1650 __isl_take isl_union_set *bset);
1654 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1656 __isl_give isl_union_map *isl_union_map_power(
1657 __isl_take isl_union_map *umap, int *exact);
1659 Compute a parametric representation for all positive powers I<k> of C<map>.
1660 The result maps I<k> to a nested relation corresponding to the
1661 I<k>th power of C<map>.
1662 The result may be an overapproximation. If the result is known to be exact,
1663 then C<*exact> is set to C<1>.
1665 =item * Transitive closure
1667 __isl_give isl_map *isl_map_transitive_closure(
1668 __isl_take isl_map *map, int *exact);
1669 __isl_give isl_union_map *isl_union_map_transitive_closure(
1670 __isl_take isl_union_map *umap, int *exact);
1672 Compute the transitive closure of C<map>.
1673 The result may be an overapproximation. If the result is known to be exact,
1674 then C<*exact> is set to C<1>.
1676 =item * Reaching path lengths
1678 __isl_give isl_map *isl_map_reaching_path_lengths(
1679 __isl_take isl_map *map, int *exact);
1681 Compute a relation that maps each element in the range of C<map>
1682 to the lengths of all paths composed of edges in C<map> that
1683 end up in the given element.
1684 The result may be an overapproximation. If the result is known to be exact,
1685 then C<*exact> is set to C<1>.
1686 To compute the I<maximal> path length, the resulting relation
1687 should be postprocessed by C<isl_map_lexmax>.
1688 In particular, if the input relation is a dependence relation
1689 (mapping sources to sinks), then the maximal path length corresponds
1690 to the free schedule.
1691 Note, however, that C<isl_map_lexmax> expects the maximum to be
1692 finite, so if the path lengths are unbounded (possibly due to
1693 the overapproximation), then you will get an error message.
1697 __isl_give isl_basic_set *isl_basic_map_wrap(
1698 __isl_take isl_basic_map *bmap);
1699 __isl_give isl_set *isl_map_wrap(
1700 __isl_take isl_map *map);
1701 __isl_give isl_union_set *isl_union_map_wrap(
1702 __isl_take isl_union_map *umap);
1703 __isl_give isl_basic_map *isl_basic_set_unwrap(
1704 __isl_take isl_basic_set *bset);
1705 __isl_give isl_map *isl_set_unwrap(
1706 __isl_take isl_set *set);
1707 __isl_give isl_union_map *isl_union_set_unwrap(
1708 __isl_take isl_union_set *uset);
1712 Remove any internal structure of domain (and range) of the given
1713 set or relation. If there is any such internal structure in the input,
1714 then the name of the space is also removed.
1716 __isl_give isl_basic_set *isl_basic_set_flatten(
1717 __isl_take isl_basic_set *bset);
1718 __isl_give isl_set *isl_set_flatten(
1719 __isl_take isl_set *set);
1720 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1721 __isl_take isl_basic_map *bmap);
1722 __isl_give isl_map *isl_map_flatten_range(
1723 __isl_take isl_map *map);
1724 __isl_give isl_basic_map *isl_basic_map_flatten(
1725 __isl_take isl_basic_map *bmap);
1726 __isl_give isl_map *isl_map_flatten(
1727 __isl_take isl_map *map);
1729 __isl_give isl_map *isl_set_flatten_map(
1730 __isl_take isl_set *set);
1732 The function above constructs a relation
1733 that maps the input set to a flattened version of the set.
1737 Lift the input set to a space with extra dimensions corresponding
1738 to the existentially quantified variables in the input.
1739 In particular, the result lives in a wrapped map where the domain
1740 is the original space and the range corresponds to the original
1741 existentially quantified variables.
1743 __isl_give isl_basic_set *isl_basic_set_lift(
1744 __isl_take isl_basic_set *bset);
1745 __isl_give isl_set *isl_set_lift(
1746 __isl_take isl_set *set);
1747 __isl_give isl_union_set *isl_union_set_lift(
1748 __isl_take isl_union_set *uset);
1750 =item * Internal Product
1752 __isl_give isl_basic_map *isl_basic_map_zip(
1753 __isl_take isl_basic_map *bmap);
1754 __isl_give isl_map *isl_map_zip(
1755 __isl_take isl_map *map);
1756 __isl_give isl_union_map *isl_union_map_zip(
1757 __isl_take isl_union_map *umap);
1759 Given a relation with nested relations for domain and range,
1760 interchange the range of the domain with the domain of the range.
1762 =item * Aligning parameters
1764 __isl_give isl_set *isl_set_align_params(
1765 __isl_take isl_set *set,
1766 __isl_take isl_dim *model);
1767 __isl_give isl_map *isl_map_align_params(
1768 __isl_take isl_map *map,
1769 __isl_take isl_dim *model);
1771 Change the order of the parameters of the given set or relation
1772 such that the first parameters match those of C<model>.
1773 This may involve the introduction of extra parameters.
1774 All parameters need to be named.
1776 =item * Dimension manipulation
1778 __isl_give isl_set *isl_set_add_dims(
1779 __isl_take isl_set *set,
1780 enum isl_dim_type type, unsigned n);
1781 __isl_give isl_map *isl_map_add_dims(
1782 __isl_take isl_map *map,
1783 enum isl_dim_type type, unsigned n);
1785 It is usually not advisable to directly change the (input or output)
1786 space of a set or a relation as this removes the name and the internal
1787 structure of the space. However, the above functions can be useful
1788 to add new parameters, assuming
1789 C<isl_set_align_params> and C<isl_map_align_params>
1794 =head2 Binary Operations
1796 The two arguments of a binary operation not only need to live
1797 in the same C<isl_ctx>, they currently also need to have
1798 the same (number of) parameters.
1800 =head3 Basic Operations
1804 =item * Intersection
1806 __isl_give isl_basic_set *isl_basic_set_intersect(
1807 __isl_take isl_basic_set *bset1,
1808 __isl_take isl_basic_set *bset2);
1809 __isl_give isl_set *isl_set_intersect(
1810 __isl_take isl_set *set1,
1811 __isl_take isl_set *set2);
1812 __isl_give isl_union_set *isl_union_set_intersect(
1813 __isl_take isl_union_set *uset1,
1814 __isl_take isl_union_set *uset2);
1815 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1816 __isl_take isl_basic_map *bmap,
1817 __isl_take isl_basic_set *bset);
1818 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1819 __isl_take isl_basic_map *bmap,
1820 __isl_take isl_basic_set *bset);
1821 __isl_give isl_basic_map *isl_basic_map_intersect(
1822 __isl_take isl_basic_map *bmap1,
1823 __isl_take isl_basic_map *bmap2);
1824 __isl_give isl_map *isl_map_intersect_domain(
1825 __isl_take isl_map *map,
1826 __isl_take isl_set *set);
1827 __isl_give isl_map *isl_map_intersect_range(
1828 __isl_take isl_map *map,
1829 __isl_take isl_set *set);
1830 __isl_give isl_map *isl_map_intersect(
1831 __isl_take isl_map *map1,
1832 __isl_take isl_map *map2);
1833 __isl_give isl_union_map *isl_union_map_intersect_domain(
1834 __isl_take isl_union_map *umap,
1835 __isl_take isl_union_set *uset);
1836 __isl_give isl_union_map *isl_union_map_intersect_range(
1837 __isl_take isl_union_map *umap,
1838 __isl_take isl_union_set *uset);
1839 __isl_give isl_union_map *isl_union_map_intersect(
1840 __isl_take isl_union_map *umap1,
1841 __isl_take isl_union_map *umap2);
1845 __isl_give isl_set *isl_basic_set_union(
1846 __isl_take isl_basic_set *bset1,
1847 __isl_take isl_basic_set *bset2);
1848 __isl_give isl_map *isl_basic_map_union(
1849 __isl_take isl_basic_map *bmap1,
1850 __isl_take isl_basic_map *bmap2);
1851 __isl_give isl_set *isl_set_union(
1852 __isl_take isl_set *set1,
1853 __isl_take isl_set *set2);
1854 __isl_give isl_map *isl_map_union(
1855 __isl_take isl_map *map1,
1856 __isl_take isl_map *map2);
1857 __isl_give isl_union_set *isl_union_set_union(
1858 __isl_take isl_union_set *uset1,
1859 __isl_take isl_union_set *uset2);
1860 __isl_give isl_union_map *isl_union_map_union(
1861 __isl_take isl_union_map *umap1,
1862 __isl_take isl_union_map *umap2);
1864 =item * Set difference
1866 __isl_give isl_set *isl_set_subtract(
1867 __isl_take isl_set *set1,
1868 __isl_take isl_set *set2);
1869 __isl_give isl_map *isl_map_subtract(
1870 __isl_take isl_map *map1,
1871 __isl_take isl_map *map2);
1872 __isl_give isl_union_set *isl_union_set_subtract(
1873 __isl_take isl_union_set *uset1,
1874 __isl_take isl_union_set *uset2);
1875 __isl_give isl_union_map *isl_union_map_subtract(
1876 __isl_take isl_union_map *umap1,
1877 __isl_take isl_union_map *umap2);
1881 __isl_give isl_basic_set *isl_basic_set_apply(
1882 __isl_take isl_basic_set *bset,
1883 __isl_take isl_basic_map *bmap);
1884 __isl_give isl_set *isl_set_apply(
1885 __isl_take isl_set *set,
1886 __isl_take isl_map *map);
1887 __isl_give isl_union_set *isl_union_set_apply(
1888 __isl_take isl_union_set *uset,
1889 __isl_take isl_union_map *umap);
1890 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1891 __isl_take isl_basic_map *bmap1,
1892 __isl_take isl_basic_map *bmap2);
1893 __isl_give isl_basic_map *isl_basic_map_apply_range(
1894 __isl_take isl_basic_map *bmap1,
1895 __isl_take isl_basic_map *bmap2);
1896 __isl_give isl_map *isl_map_apply_domain(
1897 __isl_take isl_map *map1,
1898 __isl_take isl_map *map2);
1899 __isl_give isl_union_map *isl_union_map_apply_domain(
1900 __isl_take isl_union_map *umap1,
1901 __isl_take isl_union_map *umap2);
1902 __isl_give isl_map *isl_map_apply_range(
1903 __isl_take isl_map *map1,
1904 __isl_take isl_map *map2);
1905 __isl_give isl_union_map *isl_union_map_apply_range(
1906 __isl_take isl_union_map *umap1,
1907 __isl_take isl_union_map *umap2);
1909 =item * Cartesian Product
1911 __isl_give isl_set *isl_set_product(
1912 __isl_take isl_set *set1,
1913 __isl_take isl_set *set2);
1914 __isl_give isl_union_set *isl_union_set_product(
1915 __isl_take isl_union_set *uset1,
1916 __isl_take isl_union_set *uset2);
1917 __isl_give isl_basic_map *isl_basic_map_range_product(
1918 __isl_take isl_basic_map *bmap1,
1919 __isl_take isl_basic_map *bmap2);
1920 __isl_give isl_map *isl_map_range_product(
1921 __isl_take isl_map *map1,
1922 __isl_take isl_map *map2);
1923 __isl_give isl_union_map *isl_union_map_range_product(
1924 __isl_take isl_union_map *umap1,
1925 __isl_take isl_union_map *umap2);
1926 __isl_give isl_map *isl_map_product(
1927 __isl_take isl_map *map1,
1928 __isl_take isl_map *map2);
1929 __isl_give isl_union_map *isl_union_map_product(
1930 __isl_take isl_union_map *umap1,
1931 __isl_take isl_union_map *umap2);
1933 The above functions compute the cross product of the given
1934 sets or relations. The domains and ranges of the results
1935 are wrapped maps between domains and ranges of the inputs.
1936 To obtain a ``flat'' product, use the following functions
1939 __isl_give isl_basic_set *isl_basic_set_flat_product(
1940 __isl_take isl_basic_set *bset1,
1941 __isl_take isl_basic_set *bset2);
1942 __isl_give isl_set *isl_set_flat_product(
1943 __isl_take isl_set *set1,
1944 __isl_take isl_set *set2);
1945 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1946 __isl_take isl_basic_map *bmap1,
1947 __isl_take isl_basic_map *bmap2);
1948 __isl_give isl_map *isl_map_flat_range_product(
1949 __isl_take isl_map *map1,
1950 __isl_take isl_map *map2);
1951 __isl_give isl_union_map *isl_union_map_flat_range_product(
1952 __isl_take isl_union_map *umap1,
1953 __isl_take isl_union_map *umap2);
1954 __isl_give isl_basic_map *isl_basic_map_flat_product(
1955 __isl_take isl_basic_map *bmap1,
1956 __isl_take isl_basic_map *bmap2);
1957 __isl_give isl_map *isl_map_flat_product(
1958 __isl_take isl_map *map1,
1959 __isl_take isl_map *map2);
1961 =item * Simplification
1963 __isl_give isl_basic_set *isl_basic_set_gist(
1964 __isl_take isl_basic_set *bset,
1965 __isl_take isl_basic_set *context);
1966 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1967 __isl_take isl_set *context);
1968 __isl_give isl_union_set *isl_union_set_gist(
1969 __isl_take isl_union_set *uset,
1970 __isl_take isl_union_set *context);
1971 __isl_give isl_basic_map *isl_basic_map_gist(
1972 __isl_take isl_basic_map *bmap,
1973 __isl_take isl_basic_map *context);
1974 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1975 __isl_take isl_map *context);
1976 __isl_give isl_union_map *isl_union_map_gist(
1977 __isl_take isl_union_map *umap,
1978 __isl_take isl_union_map *context);
1980 The gist operation returns a set or relation that has the
1981 same intersection with the context as the input set or relation.
1982 Any implicit equality in the intersection is made explicit in the result,
1983 while all inequalities that are redundant with respect to the intersection
1985 In case of union sets and relations, the gist operation is performed
1990 =head3 Lexicographic Optimization
1992 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1993 the following functions
1994 compute a set that contains the lexicographic minimum or maximum
1995 of the elements in C<set> (or C<bset>) for those values of the parameters
1996 that satisfy C<dom>.
1997 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1998 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2000 In other words, the union of the parameter values
2001 for which the result is non-empty and of C<*empty>
2004 __isl_give isl_set *isl_basic_set_partial_lexmin(
2005 __isl_take isl_basic_set *bset,
2006 __isl_take isl_basic_set *dom,
2007 __isl_give isl_set **empty);
2008 __isl_give isl_set *isl_basic_set_partial_lexmax(
2009 __isl_take isl_basic_set *bset,
2010 __isl_take isl_basic_set *dom,
2011 __isl_give isl_set **empty);
2012 __isl_give isl_set *isl_set_partial_lexmin(
2013 __isl_take isl_set *set, __isl_take isl_set *dom,
2014 __isl_give isl_set **empty);
2015 __isl_give isl_set *isl_set_partial_lexmax(
2016 __isl_take isl_set *set, __isl_take isl_set *dom,
2017 __isl_give isl_set **empty);
2019 Given a (basic) set C<set> (or C<bset>), the following functions simply
2020 return a set containing the lexicographic minimum or maximum
2021 of the elements in C<set> (or C<bset>).
2022 In case of union sets, the optimum is computed per space.
2024 __isl_give isl_set *isl_basic_set_lexmin(
2025 __isl_take isl_basic_set *bset);
2026 __isl_give isl_set *isl_basic_set_lexmax(
2027 __isl_take isl_basic_set *bset);
2028 __isl_give isl_set *isl_set_lexmin(
2029 __isl_take isl_set *set);
2030 __isl_give isl_set *isl_set_lexmax(
2031 __isl_take isl_set *set);
2032 __isl_give isl_union_set *isl_union_set_lexmin(
2033 __isl_take isl_union_set *uset);
2034 __isl_give isl_union_set *isl_union_set_lexmax(
2035 __isl_take isl_union_set *uset);
2037 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2038 the following functions
2039 compute a relation that maps each element of C<dom>
2040 to the single lexicographic minimum or maximum
2041 of the elements that are associated to that same
2042 element in C<map> (or C<bmap>).
2043 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2044 that contains the elements in C<dom> that do not map
2045 to any elements in C<map> (or C<bmap>).
2046 In other words, the union of the domain of the result and of C<*empty>
2049 __isl_give isl_map *isl_basic_map_partial_lexmax(
2050 __isl_take isl_basic_map *bmap,
2051 __isl_take isl_basic_set *dom,
2052 __isl_give isl_set **empty);
2053 __isl_give isl_map *isl_basic_map_partial_lexmin(
2054 __isl_take isl_basic_map *bmap,
2055 __isl_take isl_basic_set *dom,
2056 __isl_give isl_set **empty);
2057 __isl_give isl_map *isl_map_partial_lexmax(
2058 __isl_take isl_map *map, __isl_take isl_set *dom,
2059 __isl_give isl_set **empty);
2060 __isl_give isl_map *isl_map_partial_lexmin(
2061 __isl_take isl_map *map, __isl_take isl_set *dom,
2062 __isl_give isl_set **empty);
2064 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2065 return a map mapping each element in the domain of
2066 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2067 of all elements associated to that element.
2068 In case of union relations, the optimum is computed per space.
2070 __isl_give isl_map *isl_basic_map_lexmin(
2071 __isl_take isl_basic_map *bmap);
2072 __isl_give isl_map *isl_basic_map_lexmax(
2073 __isl_take isl_basic_map *bmap);
2074 __isl_give isl_map *isl_map_lexmin(
2075 __isl_take isl_map *map);
2076 __isl_give isl_map *isl_map_lexmax(
2077 __isl_take isl_map *map);
2078 __isl_give isl_union_map *isl_union_map_lexmin(
2079 __isl_take isl_union_map *umap);
2080 __isl_give isl_union_map *isl_union_map_lexmax(
2081 __isl_take isl_union_map *umap);
2085 Lists are defined over several element types, including
2086 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2087 Here we take lists of C<isl_set>s as an example.
2088 Lists can be created, copied and freed using the following functions.
2090 #include <isl/list.h>
2091 __isl_give isl_set_list *isl_set_list_alloc(
2092 isl_ctx *ctx, int n);
2093 __isl_give isl_set_list *isl_set_list_copy(
2094 __isl_keep isl_set_list *list);
2095 __isl_give isl_set_list *isl_set_list_add(
2096 __isl_take isl_set_list *list,
2097 __isl_take isl_set *el);
2098 void isl_set_list_free(__isl_take isl_set_list *list);
2100 C<isl_set_list_alloc> creates an empty list with a capacity for
2103 Lists can be inspected using the following functions.
2105 #include <isl/list.h>
2106 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2107 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2108 __isl_give struct isl_set *isl_set_list_get_set(
2109 __isl_keep isl_set_list *list, int index);
2110 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2111 int (*fn)(__isl_take struct isl_set *el, void *user),
2114 Lists can be printed using
2116 #include <isl/list.h>
2117 __isl_give isl_printer *isl_printer_print_set_list(
2118 __isl_take isl_printer *p,
2119 __isl_keep isl_set_list *list);
2123 Matrices can be created, copied and freed using the following functions.
2125 #include <isl/mat.h>
2126 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2127 unsigned n_row, unsigned n_col);
2128 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2129 void isl_mat_free(__isl_take isl_mat *mat);
2131 Note that the elements of a newly created matrix may have arbitrary values.
2132 The elements can be changed and inspected using the following functions.
2134 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2135 int isl_mat_rows(__isl_keep isl_mat *mat);
2136 int isl_mat_cols(__isl_keep isl_mat *mat);
2137 int isl_mat_get_element(__isl_keep isl_mat *mat,
2138 int row, int col, isl_int *v);
2139 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2140 int row, int col, isl_int v);
2141 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2142 int row, int col, int v);
2144 C<isl_mat_get_element> will return a negative value if anything went wrong.
2145 In that case, the value of C<*v> is undefined.
2147 The following function can be used to compute the (right) inverse
2148 of a matrix, i.e., a matrix such that the product of the original
2149 and the inverse (in that order) is a multiple of the identity matrix.
2150 The input matrix is assumed to be of full row-rank.
2152 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2154 The following function can be used to compute the (right) kernel
2155 (or null space) of a matrix, i.e., a matrix such that the product of
2156 the original and the kernel (in that order) is the zero matrix.
2158 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2160 =head2 Quasi Affine Expressions
2162 The zero quasi affine expression can be created using
2164 __isl_give isl_aff *isl_aff_zero(
2165 __isl_take isl_local_space *ls);
2167 Quasi affine expressions can be copied and free using
2169 #include <isl/aff.h>
2170 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2171 void *isl_aff_free(__isl_take isl_aff *aff);
2173 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2174 using the following function. The constraint is required to have
2175 a non-zero coefficient for the specified dimension.
2177 #include <isl/constraint.h>
2178 __isl_give isl_aff *isl_constraint_get_bound(
2179 __isl_keep isl_constraint *constraint,
2180 enum isl_dim_type type, int pos);
2182 Conversely, an equality constraint equating
2183 the affine expression to zero or an inequality constraint enforcing
2184 the affine expression to be non-negative, can be constructed using
2186 __isl_give isl_constraint *isl_equality_from_aff(
2187 __isl_take isl_aff *aff);
2188 __isl_give isl_constraint *isl_inequality_from_aff(
2189 __isl_take isl_aff *aff);
2191 The expression can be inspected using
2193 #include <isl/aff.h>
2194 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2195 int isl_aff_dim(__isl_keep isl_aff *aff,
2196 enum isl_dim_type type);
2197 __isl_give isl_local_space *isl_aff_get_local_space(
2198 __isl_keep isl_aff *aff);
2199 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2200 enum isl_dim_type type, unsigned pos);
2201 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2203 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2204 enum isl_dim_type type, int pos, isl_int *v);
2205 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2207 __isl_give isl_div *isl_aff_get_div(
2208 __isl_keep isl_aff *aff, int pos);
2210 It can be modified using
2212 #include <isl/aff.h>
2213 __isl_give isl_aff *isl_aff_set_constant(
2214 __isl_take isl_aff *aff, isl_int v);
2215 __isl_give isl_aff *isl_aff_set_constant_si(
2216 __isl_take isl_aff *aff, int v);
2217 __isl_give isl_aff *isl_aff_set_coefficient(
2218 __isl_take isl_aff *aff,
2219 enum isl_dim_type type, int pos, isl_int v);
2220 __isl_give isl_aff *isl_aff_set_coefficient_si(
2221 __isl_take isl_aff *aff,
2222 enum isl_dim_type type, int pos, int v);
2223 __isl_give isl_aff *isl_aff_set_denominator(
2224 __isl_take isl_aff *aff, isl_int v);
2226 __isl_give isl_aff *isl_aff_add_constant(
2227 __isl_take isl_aff *aff, isl_int v);
2228 __isl_give isl_aff *isl_aff_add_coefficient_si(
2229 __isl_take isl_aff *aff,
2230 enum isl_dim_type type, int pos, int v);
2232 Note that the C<set_constant> and C<set_coefficient> functions
2233 set the I<numerator> of the constant or coefficient, while
2234 C<add_constant> and C<add_coefficient> add an integer value to
2235 the possibly rational constant or coefficient.
2239 #include <isl/aff.h>
2240 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2241 __isl_take isl_aff *aff2);
2242 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2243 __isl_take isl_aff *aff2);
2244 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2245 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2246 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2248 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2251 An expression can be printed using
2253 #include <isl/aff.h>
2254 __isl_give isl_printer *isl_printer_print_aff(
2255 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2259 Points are elements of a set. They can be used to construct
2260 simple sets (boxes) or they can be used to represent the
2261 individual elements of a set.
2262 The zero point (the origin) can be created using
2264 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2266 The coordinates of a point can be inspected, set and changed
2269 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2270 enum isl_dim_type type, int pos, isl_int *v);
2271 __isl_give isl_point *isl_point_set_coordinate(
2272 __isl_take isl_point *pnt,
2273 enum isl_dim_type type, int pos, isl_int v);
2275 __isl_give isl_point *isl_point_add_ui(
2276 __isl_take isl_point *pnt,
2277 enum isl_dim_type type, int pos, unsigned val);
2278 __isl_give isl_point *isl_point_sub_ui(
2279 __isl_take isl_point *pnt,
2280 enum isl_dim_type type, int pos, unsigned val);
2282 Other properties can be obtained using
2284 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2286 Points can be copied or freed using
2288 __isl_give isl_point *isl_point_copy(
2289 __isl_keep isl_point *pnt);
2290 void isl_point_free(__isl_take isl_point *pnt);
2292 A singleton set can be created from a point using
2294 __isl_give isl_basic_set *isl_basic_set_from_point(
2295 __isl_take isl_point *pnt);
2296 __isl_give isl_set *isl_set_from_point(
2297 __isl_take isl_point *pnt);
2299 and a box can be created from two opposite extremal points using
2301 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2302 __isl_take isl_point *pnt1,
2303 __isl_take isl_point *pnt2);
2304 __isl_give isl_set *isl_set_box_from_points(
2305 __isl_take isl_point *pnt1,
2306 __isl_take isl_point *pnt2);
2308 All elements of a B<bounded> (union) set can be enumerated using
2309 the following functions.
2311 int isl_set_foreach_point(__isl_keep isl_set *set,
2312 int (*fn)(__isl_take isl_point *pnt, void *user),
2314 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2315 int (*fn)(__isl_take isl_point *pnt, void *user),
2318 The function C<fn> is called for each integer point in
2319 C<set> with as second argument the last argument of
2320 the C<isl_set_foreach_point> call. The function C<fn>
2321 should return C<0> on success and C<-1> on failure.
2322 In the latter case, C<isl_set_foreach_point> will stop
2323 enumerating and return C<-1> as well.
2324 If the enumeration is performed successfully and to completion,
2325 then C<isl_set_foreach_point> returns C<0>.
2327 To obtain a single point of a (basic) set, use
2329 __isl_give isl_point *isl_basic_set_sample_point(
2330 __isl_take isl_basic_set *bset);
2331 __isl_give isl_point *isl_set_sample_point(
2332 __isl_take isl_set *set);
2334 If C<set> does not contain any (integer) points, then the
2335 resulting point will be ``void'', a property that can be
2338 int isl_point_is_void(__isl_keep isl_point *pnt);
2340 =head2 Piecewise Quasipolynomials
2342 A piecewise quasipolynomial is a particular kind of function that maps
2343 a parametric point to a rational value.
2344 More specifically, a quasipolynomial is a polynomial expression in greatest
2345 integer parts of affine expressions of parameters and variables.
2346 A piecewise quasipolynomial is a subdivision of a given parametric
2347 domain into disjoint cells with a quasipolynomial associated to
2348 each cell. The value of the piecewise quasipolynomial at a given
2349 point is the value of the quasipolynomial associated to the cell
2350 that contains the point. Outside of the union of cells,
2351 the value is assumed to be zero.
2352 For example, the piecewise quasipolynomial
2354 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2356 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2357 A given piecewise quasipolynomial has a fixed domain dimension.
2358 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2359 defined over different domains.
2360 Piecewise quasipolynomials are mainly used by the C<barvinok>
2361 library for representing the number of elements in a parametric set or map.
2362 For example, the piecewise quasipolynomial above represents
2363 the number of points in the map
2365 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2367 =head3 Printing (Piecewise) Quasipolynomials
2369 Quasipolynomials and piecewise quasipolynomials can be printed
2370 using the following functions.
2372 __isl_give isl_printer *isl_printer_print_qpolynomial(
2373 __isl_take isl_printer *p,
2374 __isl_keep isl_qpolynomial *qp);
2376 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2377 __isl_take isl_printer *p,
2378 __isl_keep isl_pw_qpolynomial *pwqp);
2380 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2381 __isl_take isl_printer *p,
2382 __isl_keep isl_union_pw_qpolynomial *upwqp);
2384 The output format of the printer
2385 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2386 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2388 In case of printing in C<ISL_FORMAT_C>, the user may want
2389 to set the names of all dimensions
2391 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2392 __isl_take isl_qpolynomial *qp,
2393 enum isl_dim_type type, unsigned pos,
2395 __isl_give isl_pw_qpolynomial *
2396 isl_pw_qpolynomial_set_dim_name(
2397 __isl_take isl_pw_qpolynomial *pwqp,
2398 enum isl_dim_type type, unsigned pos,
2401 =head3 Creating New (Piecewise) Quasipolynomials
2403 Some simple quasipolynomials can be created using the following functions.
2404 More complicated quasipolynomials can be created by applying
2405 operations such as addition and multiplication
2406 on the resulting quasipolynomials
2408 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2409 __isl_take isl_dim *dim);
2410 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2411 __isl_take isl_dim *dim);
2412 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2413 __isl_take isl_dim *dim);
2414 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2415 __isl_take isl_dim *dim);
2416 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2417 __isl_take isl_dim *dim);
2418 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2419 __isl_take isl_dim *dim,
2420 const isl_int n, const isl_int d);
2421 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2422 __isl_take isl_div *div);
2423 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2424 __isl_take isl_dim *dim,
2425 enum isl_dim_type type, unsigned pos);
2426 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2427 __isl_take isl_aff *aff);
2429 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2430 with a single cell can be created using the following functions.
2431 Multiple of these single cell piecewise quasipolynomials can
2432 be combined to create more complicated piecewise quasipolynomials.
2434 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2435 __isl_take isl_dim *dim);
2436 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2437 __isl_take isl_set *set,
2438 __isl_take isl_qpolynomial *qp);
2440 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2441 __isl_take isl_dim *dim);
2442 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2443 __isl_take isl_pw_qpolynomial *pwqp);
2444 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2445 __isl_take isl_union_pw_qpolynomial *upwqp,
2446 __isl_take isl_pw_qpolynomial *pwqp);
2448 Quasipolynomials can be copied and freed again using the following
2451 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2452 __isl_keep isl_qpolynomial *qp);
2453 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2455 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2456 __isl_keep isl_pw_qpolynomial *pwqp);
2457 void isl_pw_qpolynomial_free(
2458 __isl_take isl_pw_qpolynomial *pwqp);
2460 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2461 __isl_keep isl_union_pw_qpolynomial *upwqp);
2462 void isl_union_pw_qpolynomial_free(
2463 __isl_take isl_union_pw_qpolynomial *upwqp);
2465 =head3 Inspecting (Piecewise) Quasipolynomials
2467 To iterate over all piecewise quasipolynomials in a union
2468 piecewise quasipolynomial, use the following function
2470 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2471 __isl_keep isl_union_pw_qpolynomial *upwqp,
2472 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2475 To extract the piecewise quasipolynomial from a union with a given dimension
2478 __isl_give isl_pw_qpolynomial *
2479 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2480 __isl_keep isl_union_pw_qpolynomial *upwqp,
2481 __isl_take isl_dim *dim);
2483 To iterate over the cells in a piecewise quasipolynomial,
2484 use either of the following two functions
2486 int isl_pw_qpolynomial_foreach_piece(
2487 __isl_keep isl_pw_qpolynomial *pwqp,
2488 int (*fn)(__isl_take isl_set *set,
2489 __isl_take isl_qpolynomial *qp,
2490 void *user), void *user);
2491 int isl_pw_qpolynomial_foreach_lifted_piece(
2492 __isl_keep isl_pw_qpolynomial *pwqp,
2493 int (*fn)(__isl_take isl_set *set,
2494 __isl_take isl_qpolynomial *qp,
2495 void *user), void *user);
2497 As usual, the function C<fn> should return C<0> on success
2498 and C<-1> on failure. The difference between
2499 C<isl_pw_qpolynomial_foreach_piece> and
2500 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2501 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2502 compute unique representations for all existentially quantified
2503 variables and then turn these existentially quantified variables
2504 into extra set variables, adapting the associated quasipolynomial
2505 accordingly. This means that the C<set> passed to C<fn>
2506 will not have any existentially quantified variables, but that
2507 the dimensions of the sets may be different for different
2508 invocations of C<fn>.
2510 To iterate over all terms in a quasipolynomial,
2513 int isl_qpolynomial_foreach_term(
2514 __isl_keep isl_qpolynomial *qp,
2515 int (*fn)(__isl_take isl_term *term,
2516 void *user), void *user);
2518 The terms themselves can be inspected and freed using
2521 unsigned isl_term_dim(__isl_keep isl_term *term,
2522 enum isl_dim_type type);
2523 void isl_term_get_num(__isl_keep isl_term *term,
2525 void isl_term_get_den(__isl_keep isl_term *term,
2527 int isl_term_get_exp(__isl_keep isl_term *term,
2528 enum isl_dim_type type, unsigned pos);
2529 __isl_give isl_div *isl_term_get_div(
2530 __isl_keep isl_term *term, unsigned pos);
2531 void isl_term_free(__isl_take isl_term *term);
2533 Each term is a product of parameters, set variables and
2534 integer divisions. The function C<isl_term_get_exp>
2535 returns the exponent of a given dimensions in the given term.
2536 The C<isl_int>s in the arguments of C<isl_term_get_num>
2537 and C<isl_term_get_den> need to have been initialized
2538 using C<isl_int_init> before calling these functions.
2540 =head3 Properties of (Piecewise) Quasipolynomials
2542 To check whether a quasipolynomial is actually a constant,
2543 use the following function.
2545 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2546 isl_int *n, isl_int *d);
2548 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2549 then the numerator and denominator of the constant
2550 are returned in C<*n> and C<*d>, respectively.
2552 =head3 Operations on (Piecewise) Quasipolynomials
2554 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2555 __isl_take isl_qpolynomial *qp);
2556 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2557 __isl_take isl_qpolynomial *qp1,
2558 __isl_take isl_qpolynomial *qp2);
2559 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2560 __isl_take isl_qpolynomial *qp1,
2561 __isl_take isl_qpolynomial *qp2);
2562 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2563 __isl_take isl_qpolynomial *qp1,
2564 __isl_take isl_qpolynomial *qp2);
2565 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2566 __isl_take isl_qpolynomial *qp, unsigned exponent);
2568 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2569 __isl_take isl_pw_qpolynomial *pwqp1,
2570 __isl_take isl_pw_qpolynomial *pwqp2);
2571 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2572 __isl_take isl_pw_qpolynomial *pwqp1,
2573 __isl_take isl_pw_qpolynomial *pwqp2);
2574 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2575 __isl_take isl_pw_qpolynomial *pwqp1,
2576 __isl_take isl_pw_qpolynomial *pwqp2);
2577 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2578 __isl_take isl_pw_qpolynomial *pwqp);
2579 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2580 __isl_take isl_pw_qpolynomial *pwqp1,
2581 __isl_take isl_pw_qpolynomial *pwqp2);
2583 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
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_sub(
2587 __isl_take isl_union_pw_qpolynomial *upwqp1,
2588 __isl_take isl_union_pw_qpolynomial *upwqp2);
2589 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2590 __isl_take isl_union_pw_qpolynomial *upwqp1,
2591 __isl_take isl_union_pw_qpolynomial *upwqp2);
2593 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2594 __isl_take isl_pw_qpolynomial *pwqp,
2595 __isl_take isl_point *pnt);
2597 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2598 __isl_take isl_union_pw_qpolynomial *upwqp,
2599 __isl_take isl_point *pnt);
2601 __isl_give isl_set *isl_pw_qpolynomial_domain(
2602 __isl_take isl_pw_qpolynomial *pwqp);
2603 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2604 __isl_take isl_pw_qpolynomial *pwpq,
2605 __isl_take isl_set *set);
2607 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2608 __isl_take isl_union_pw_qpolynomial *upwqp);
2609 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2610 __isl_take isl_union_pw_qpolynomial *upwpq,
2611 __isl_take isl_union_set *uset);
2613 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2614 __isl_take isl_qpolynomial *qp,
2615 __isl_take isl_dim *model);
2617 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2618 __isl_take isl_union_pw_qpolynomial *upwqp);
2620 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2621 __isl_take isl_qpolynomial *qp,
2622 __isl_take isl_set *context);
2624 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2625 __isl_take isl_pw_qpolynomial *pwqp,
2626 __isl_take isl_set *context);
2628 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2629 __isl_take isl_union_pw_qpolynomial *upwqp,
2630 __isl_take isl_union_set *context);
2632 The gist operation applies the gist operation to each of
2633 the cells in the domain of the input piecewise quasipolynomial.
2634 The context is also exploited
2635 to simplify the quasipolynomials associated to each cell.
2637 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2638 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2639 __isl_give isl_union_pw_qpolynomial *
2640 isl_union_pw_qpolynomial_to_polynomial(
2641 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2643 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2644 the polynomial will be an overapproximation. If C<sign> is negative,
2645 it will be an underapproximation. If C<sign> is zero, the approximation
2646 will lie somewhere in between.
2648 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2650 A piecewise quasipolynomial reduction is a piecewise
2651 reduction (or fold) of quasipolynomials.
2652 In particular, the reduction can be maximum or a minimum.
2653 The objects are mainly used to represent the result of
2654 an upper or lower bound on a quasipolynomial over its domain,
2655 i.e., as the result of the following function.
2657 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2658 __isl_take isl_pw_qpolynomial *pwqp,
2659 enum isl_fold type, int *tight);
2661 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2662 __isl_take isl_union_pw_qpolynomial *upwqp,
2663 enum isl_fold type, int *tight);
2665 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2666 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2667 is the returned bound is known be tight, i.e., for each value
2668 of the parameters there is at least
2669 one element in the domain that reaches the bound.
2670 If the domain of C<pwqp> is not wrapping, then the bound is computed
2671 over all elements in that domain and the result has a purely parametric
2672 domain. If the domain of C<pwqp> is wrapping, then the bound is
2673 computed over the range of the wrapped relation. The domain of the
2674 wrapped relation becomes the domain of the result.
2676 A (piecewise) quasipolynomial reduction can be copied or freed using the
2677 following functions.
2679 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2680 __isl_keep isl_qpolynomial_fold *fold);
2681 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2682 __isl_keep isl_pw_qpolynomial_fold *pwf);
2683 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2684 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2685 void isl_qpolynomial_fold_free(
2686 __isl_take isl_qpolynomial_fold *fold);
2687 void isl_pw_qpolynomial_fold_free(
2688 __isl_take isl_pw_qpolynomial_fold *pwf);
2689 void isl_union_pw_qpolynomial_fold_free(
2690 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2692 =head3 Printing Piecewise Quasipolynomial Reductions
2694 Piecewise quasipolynomial reductions can be printed
2695 using the following function.
2697 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2698 __isl_take isl_printer *p,
2699 __isl_keep isl_pw_qpolynomial_fold *pwf);
2700 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2701 __isl_take isl_printer *p,
2702 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2704 For C<isl_printer_print_pw_qpolynomial_fold>,
2705 output format of the printer
2706 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2707 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2708 output format of the printer
2709 needs to be set to C<ISL_FORMAT_ISL>.
2710 In case of printing in C<ISL_FORMAT_C>, the user may want
2711 to set the names of all dimensions
2713 __isl_give isl_pw_qpolynomial_fold *
2714 isl_pw_qpolynomial_fold_set_dim_name(
2715 __isl_take isl_pw_qpolynomial_fold *pwf,
2716 enum isl_dim_type type, unsigned pos,
2719 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2721 To iterate over all piecewise quasipolynomial reductions in a union
2722 piecewise quasipolynomial reduction, use the following function
2724 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2725 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2726 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2727 void *user), void *user);
2729 To iterate over the cells in a piecewise quasipolynomial reduction,
2730 use either of the following two functions
2732 int isl_pw_qpolynomial_fold_foreach_piece(
2733 __isl_keep isl_pw_qpolynomial_fold *pwf,
2734 int (*fn)(__isl_take isl_set *set,
2735 __isl_take isl_qpolynomial_fold *fold,
2736 void *user), void *user);
2737 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2738 __isl_keep isl_pw_qpolynomial_fold *pwf,
2739 int (*fn)(__isl_take isl_set *set,
2740 __isl_take isl_qpolynomial_fold *fold,
2741 void *user), void *user);
2743 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2744 of the difference between these two functions.
2746 To iterate over all quasipolynomials in a reduction, use
2748 int isl_qpolynomial_fold_foreach_qpolynomial(
2749 __isl_keep isl_qpolynomial_fold *fold,
2750 int (*fn)(__isl_take isl_qpolynomial *qp,
2751 void *user), void *user);
2753 =head3 Operations on Piecewise Quasipolynomial Reductions
2755 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2756 __isl_take isl_pw_qpolynomial_fold *pwf1,
2757 __isl_take isl_pw_qpolynomial_fold *pwf2);
2759 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2760 __isl_take isl_pw_qpolynomial_fold *pwf1,
2761 __isl_take isl_pw_qpolynomial_fold *pwf2);
2763 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2764 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2765 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2767 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2768 __isl_take isl_pw_qpolynomial_fold *pwf,
2769 __isl_take isl_point *pnt);
2771 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2772 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2773 __isl_take isl_point *pnt);
2775 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2776 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2777 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2778 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2779 __isl_take isl_union_set *uset);
2781 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2782 __isl_take isl_pw_qpolynomial_fold *pwf);
2784 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2785 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2787 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2788 __isl_take isl_pw_qpolynomial_fold *pwf,
2789 __isl_take isl_set *context);
2791 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2792 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2793 __isl_take isl_union_set *context);
2795 The gist operation applies the gist operation to each of
2796 the cells in the domain of the input piecewise quasipolynomial reduction.
2797 In future, the operation will also exploit the context
2798 to simplify the quasipolynomial reductions associated to each cell.
2800 __isl_give isl_pw_qpolynomial_fold *
2801 isl_set_apply_pw_qpolynomial_fold(
2802 __isl_take isl_set *set,
2803 __isl_take isl_pw_qpolynomial_fold *pwf,
2805 __isl_give isl_pw_qpolynomial_fold *
2806 isl_map_apply_pw_qpolynomial_fold(
2807 __isl_take isl_map *map,
2808 __isl_take isl_pw_qpolynomial_fold *pwf,
2810 __isl_give isl_union_pw_qpolynomial_fold *
2811 isl_union_set_apply_union_pw_qpolynomial_fold(
2812 __isl_take isl_union_set *uset,
2813 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2815 __isl_give isl_union_pw_qpolynomial_fold *
2816 isl_union_map_apply_union_pw_qpolynomial_fold(
2817 __isl_take isl_union_map *umap,
2818 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2821 The functions taking a map
2822 compose the given map with the given piecewise quasipolynomial reduction.
2823 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2824 over all elements in the intersection of the range of the map
2825 and the domain of the piecewise quasipolynomial reduction
2826 as a function of an element in the domain of the map.
2827 The functions taking a set compute a bound over all elements in the
2828 intersection of the set and the domain of the
2829 piecewise quasipolynomial reduction.
2831 =head2 Dependence Analysis
2833 C<isl> contains specialized functionality for performing
2834 array dataflow analysis. That is, given a I<sink> access relation
2835 and a collection of possible I<source> access relations,
2836 C<isl> can compute relations that describe
2837 for each iteration of the sink access, which iteration
2838 of which of the source access relations was the last
2839 to access the same data element before the given iteration
2841 To compute standard flow dependences, the sink should be
2842 a read, while the sources should be writes.
2843 If any of the source accesses are marked as being I<may>
2844 accesses, then there will be a dependence to the last
2845 I<must> access B<and> to any I<may> access that follows
2846 this last I<must> access.
2847 In particular, if I<all> sources are I<may> accesses,
2848 then memory based dependence analysis is performed.
2849 If, on the other hand, all sources are I<must> accesses,
2850 then value based dependence analysis is performed.
2852 #include <isl/flow.h>
2854 typedef int (*isl_access_level_before)(void *first, void *second);
2856 __isl_give isl_access_info *isl_access_info_alloc(
2857 __isl_take isl_map *sink,
2858 void *sink_user, isl_access_level_before fn,
2860 __isl_give isl_access_info *isl_access_info_add_source(
2861 __isl_take isl_access_info *acc,
2862 __isl_take isl_map *source, int must,
2864 void isl_access_info_free(__isl_take isl_access_info *acc);
2866 __isl_give isl_flow *isl_access_info_compute_flow(
2867 __isl_take isl_access_info *acc);
2869 int isl_flow_foreach(__isl_keep isl_flow *deps,
2870 int (*fn)(__isl_take isl_map *dep, int must,
2871 void *dep_user, void *user),
2873 __isl_give isl_map *isl_flow_get_no_source(
2874 __isl_keep isl_flow *deps, int must);
2875 void isl_flow_free(__isl_take isl_flow *deps);
2877 The function C<isl_access_info_compute_flow> performs the actual
2878 dependence analysis. The other functions are used to construct
2879 the input for this function or to read off the output.
2881 The input is collected in an C<isl_access_info>, which can
2882 be created through a call to C<isl_access_info_alloc>.
2883 The arguments to this functions are the sink access relation
2884 C<sink>, a token C<sink_user> used to identify the sink
2885 access to the user, a callback function for specifying the
2886 relative order of source and sink accesses, and the number
2887 of source access relations that will be added.
2888 The callback function has type C<int (*)(void *first, void *second)>.
2889 The function is called with two user supplied tokens identifying
2890 either a source or the sink and it should return the shared nesting
2891 level and the relative order of the two accesses.
2892 In particular, let I<n> be the number of loops shared by
2893 the two accesses. If C<first> precedes C<second> textually,
2894 then the function should return I<2 * n + 1>; otherwise,
2895 it should return I<2 * n>.
2896 The sources can be added to the C<isl_access_info> by performing
2897 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2898 C<must> indicates whether the source is a I<must> access
2899 or a I<may> access. Note that a multi-valued access relation
2900 should only be marked I<must> if every iteration in the domain
2901 of the relation accesses I<all> elements in its image.
2902 The C<source_user> token is again used to identify
2903 the source access. The range of the source access relation
2904 C<source> should have the same dimension as the range
2905 of the sink access relation.
2906 The C<isl_access_info_free> function should usually not be
2907 called explicitly, because it is called implicitly by
2908 C<isl_access_info_compute_flow>.
2910 The result of the dependence analysis is collected in an
2911 C<isl_flow>. There may be elements of
2912 the sink access for which no preceding source access could be
2913 found or for which all preceding sources are I<may> accesses.
2914 The relations containing these elements can be obtained through
2915 calls to C<isl_flow_get_no_source>, the first with C<must> set
2916 and the second with C<must> unset.
2917 In the case of standard flow dependence analysis,
2918 with the sink a read and the sources I<must> writes,
2919 the first relation corresponds to the reads from uninitialized
2920 array elements and the second relation is empty.
2921 The actual flow dependences can be extracted using
2922 C<isl_flow_foreach>. This function will call the user-specified
2923 callback function C<fn> for each B<non-empty> dependence between
2924 a source and the sink. The callback function is called
2925 with four arguments, the actual flow dependence relation
2926 mapping source iterations to sink iterations, a boolean that
2927 indicates whether it is a I<must> or I<may> dependence, a token
2928 identifying the source and an additional C<void *> with value
2929 equal to the third argument of the C<isl_flow_foreach> call.
2930 A dependence is marked I<must> if it originates from a I<must>
2931 source and if it is not followed by any I<may> sources.
2933 After finishing with an C<isl_flow>, the user should call
2934 C<isl_flow_free> to free all associated memory.
2936 A higher-level interface to dependence analysis is provided
2937 by the following function.
2939 #include <isl/flow.h>
2941 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2942 __isl_take isl_union_map *must_source,
2943 __isl_take isl_union_map *may_source,
2944 __isl_take isl_union_map *schedule,
2945 __isl_give isl_union_map **must_dep,
2946 __isl_give isl_union_map **may_dep,
2947 __isl_give isl_union_map **must_no_source,
2948 __isl_give isl_union_map **may_no_source);
2950 The arrays are identified by the tuple names of the ranges
2951 of the accesses. The iteration domains by the tuple names
2952 of the domains of the accesses and of the schedule.
2953 The relative order of the iteration domains is given by the
2954 schedule. The relations returned through C<must_no_source>
2955 and C<may_no_source> are subsets of C<sink>.
2956 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2957 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2958 any of the other arguments is treated as an error.
2962 B<The functionality described in this section is fairly new
2963 and may be subject to change.>
2965 The following function can be used to compute a schedule
2966 for a union of domains. The generated schedule respects
2967 all C<validity> dependences. That is, all dependence distances
2968 over these dependences in the scheduled space are lexicographically
2969 positive. The generated schedule schedule also tries to minimize
2970 the dependence distances over C<proximity> dependences.
2971 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2972 for groups of domains where the dependence distances have only
2973 non-negative values.
2974 The algorithm used to construct the schedule is similar to that
2977 #include <isl/schedule.h>
2978 __isl_give isl_schedule *isl_union_set_compute_schedule(
2979 __isl_take isl_union_set *domain,
2980 __isl_take isl_union_map *validity,
2981 __isl_take isl_union_map *proximity);
2982 void *isl_schedule_free(__isl_take isl_schedule *sched);
2984 A mapping from the domains to the scheduled space can be obtained
2985 from an C<isl_schedule> using the following function.
2987 __isl_give isl_union_map *isl_schedule_get_map(
2988 __isl_keep isl_schedule *sched);
2990 A representation of the schedule can be printed using
2992 __isl_give isl_printer *isl_printer_print_schedule(
2993 __isl_take isl_printer *p,
2994 __isl_keep isl_schedule *schedule);
2996 A representation of the schedule as a forest of bands can be obtained
2997 using the following function.
2999 __isl_give isl_band_list *isl_schedule_get_band_forest(
3000 __isl_keep isl_schedule *schedule);
3002 The list can be manipulated as explained in L<"Lists">.
3003 The bands inside the list can be copied and freed using the following
3006 #include <isl/band.h>
3007 __isl_give isl_band *isl_band_copy(
3008 __isl_keep isl_band *band);
3009 void *isl_band_free(__isl_take isl_band *band);
3011 Each band contains zero or more scheduling dimensions.
3012 These are referred to as the members of the band.
3013 The section of the schedule that corresponds to the band is
3014 referred to as the partial schedule of the band.
3015 For those nodes that participate in a band, the outer scheduling
3016 dimensions form the prefix schedule, while the inner scheduling
3017 dimensions form the suffix schedule.
3018 That is, if we take a cut of the band forest, then the union of
3019 the concatenations of the prefix, partial and suffix schedules of
3020 each band in the cut is equal to the entire schedule (modulo
3021 some possible padding at the end with zero scheduling dimensions).
3022 The properties of a band can be inspected using the following functions.
3024 #include <isl/band.h>
3025 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3027 int isl_band_has_children(__isl_keep isl_band *band);
3028 __isl_give isl_band_list *isl_band_get_children(
3029 __isl_keep isl_band *band);
3031 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3032 __isl_keep isl_band *band);
3033 __isl_give isl_union_map *isl_band_get_partial_schedule(
3034 __isl_keep isl_band *band);
3035 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3036 __isl_keep isl_band *band);
3038 int isl_band_n_member(__isl_keep isl_band *band);
3039 int isl_band_member_is_zero_distance(
3040 __isl_keep isl_band *band, int pos);
3042 Note that a scheduling dimension is considered to be ``zero
3043 distance'' if it does not carry any proximity dependences
3045 That is, if the dependence distances of the proximity
3046 dependences are all zero in that direction (for fixed
3047 iterations of outer bands).
3049 A representation of the band can be printed using
3051 #include <isl/band.h>
3052 __isl_give isl_printer *isl_printer_print_band(
3053 __isl_take isl_printer *p,
3054 __isl_keep isl_band *band);
3056 Alternatively, the schedule mapping
3057 can also be obtained in pieces using the following functions.
3059 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3060 __isl_give isl_union_map *isl_schedule_get_band(
3061 __isl_keep isl_schedule *sched, unsigned band);
3063 C<isl_schedule_n_band> returns the maximal number of bands.
3064 C<isl_schedule_get_band> returns a union of mappings from a domain to
3065 the band of consecutive schedule dimensions with the given sequence
3066 number for that domain. Bands with the same sequence number but for
3067 different domains may be completely unrelated.
3068 Within a band, the corresponding coordinates of the distance vectors
3069 are all non-negative, assuming that the coordinates for all previous
3072 =head2 Parametric Vertex Enumeration
3074 The parametric vertex enumeration described in this section
3075 is mainly intended to be used internally and by the C<barvinok>
3078 #include <isl/vertices.h>
3079 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3080 __isl_keep isl_basic_set *bset);
3082 The function C<isl_basic_set_compute_vertices> performs the
3083 actual computation of the parametric vertices and the chamber
3084 decomposition and store the result in an C<isl_vertices> object.
3085 This information can be queried by either iterating over all
3086 the vertices or iterating over all the chambers or cells
3087 and then iterating over all vertices that are active on the chamber.
3089 int isl_vertices_foreach_vertex(
3090 __isl_keep isl_vertices *vertices,
3091 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3094 int isl_vertices_foreach_cell(
3095 __isl_keep isl_vertices *vertices,
3096 int (*fn)(__isl_take isl_cell *cell, void *user),
3098 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3099 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3102 Other operations that can be performed on an C<isl_vertices> object are
3105 isl_ctx *isl_vertices_get_ctx(
3106 __isl_keep isl_vertices *vertices);
3107 int isl_vertices_get_n_vertices(
3108 __isl_keep isl_vertices *vertices);
3109 void isl_vertices_free(__isl_take isl_vertices *vertices);
3111 Vertices can be inspected and destroyed using the following functions.
3113 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3114 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3115 __isl_give isl_basic_set *isl_vertex_get_domain(
3116 __isl_keep isl_vertex *vertex);
3117 __isl_give isl_basic_set *isl_vertex_get_expr(
3118 __isl_keep isl_vertex *vertex);
3119 void isl_vertex_free(__isl_take isl_vertex *vertex);
3121 C<isl_vertex_get_expr> returns a singleton parametric set describing
3122 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3124 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3125 B<rational> basic sets, so they should mainly be used for inspection
3126 and should not be mixed with integer sets.
3128 Chambers can be inspected and destroyed using the following functions.
3130 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3131 __isl_give isl_basic_set *isl_cell_get_domain(
3132 __isl_keep isl_cell *cell);
3133 void isl_cell_free(__isl_take isl_cell *cell);
3137 Although C<isl> is mainly meant to be used as a library,
3138 it also contains some basic applications that use some
3139 of the functionality of C<isl>.
3140 The input may be specified in either the L<isl format>
3141 or the L<PolyLib format>.
3143 =head2 C<isl_polyhedron_sample>
3145 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3146 an integer element of the polyhedron, if there is any.
3147 The first column in the output is the denominator and is always
3148 equal to 1. If the polyhedron contains no integer points,
3149 then a vector of length zero is printed.
3153 C<isl_pip> takes the same input as the C<example> program
3154 from the C<piplib> distribution, i.e., a set of constraints
3155 on the parameters, a line containing only -1 and finally a set
3156 of constraints on a parametric polyhedron.
3157 The coefficients of the parameters appear in the last columns
3158 (but before the final constant column).
3159 The output is the lexicographic minimum of the parametric polyhedron.
3160 As C<isl> currently does not have its own output format, the output
3161 is just a dump of the internal state.
3163 =head2 C<isl_polyhedron_minimize>
3165 C<isl_polyhedron_minimize> computes the minimum of some linear
3166 or affine objective function over the integer points in a polyhedron.
3167 If an affine objective function
3168 is given, then the constant should appear in the last column.
3170 =head2 C<isl_polytope_scan>
3172 Given a polytope, C<isl_polytope_scan> prints
3173 all integer points in the polytope.