3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
477 __isl_keep isl_pw_qpolynomial *pwqp);
478 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
479 __isl_keep isl_union_pw_qpolynomial *upwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
481 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
484 __isl_give isl_dim *isl_aff_get_dim(
485 __isl_keep isl_aff *aff);
487 The names of the individual dimensions may be set or read off
488 using the following functions.
491 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
492 enum isl_dim_type type, unsigned pos,
493 __isl_keep const char *name);
494 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
495 enum isl_dim_type type, unsigned pos);
497 Note that C<isl_dim_get_name> returns a pointer to some internal
498 data structure, so the result can only be used while the
499 corresponding C<isl_dim> is alive.
500 Also note that every function that operates on two sets or relations
501 requires that both arguments have the same parameters. This also
502 means that if one of the arguments has named parameters, then the
503 other needs to have named parameters too and the names need to match.
504 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
505 have different parameters (as long as they are named), in which case
506 the result will have as parameters the union of the parameters of
509 The names of entire spaces may be set or read off
510 using the following functions.
513 __isl_give isl_dim *isl_dim_set_tuple_name(
514 __isl_take isl_dim *dim,
515 enum isl_dim_type type, const char *s);
516 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
517 enum isl_dim_type type);
519 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
520 or C<isl_dim_set>. As with C<isl_dim_get_name>,
521 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
523 Binary operations require the corresponding spaces of their arguments
524 to have the same name.
526 Spaces can be nested. In particular, the domain of a set or
527 the domain or range of a relation can be a nested relation.
528 The following functions can be used to construct and deconstruct
529 such nested dimension specifications.
532 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
533 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
534 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
536 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
537 be the dimension specification of a set, while that of
538 C<isl_dim_wrap> should be the dimension specification of a relation.
539 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
540 of a relation, while that of C<isl_dim_wrap> is the dimension specification
543 Dimension specifications can be created from other dimension
544 specifications using the following functions.
546 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
547 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
548 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
549 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
550 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
551 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
552 __isl_take isl_dim *right);
553 __isl_give isl_dim *isl_dim_align_params(
554 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
555 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
556 enum isl_dim_type type, unsigned pos, unsigned n);
557 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
558 enum isl_dim_type type, unsigned n);
559 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
560 enum isl_dim_type type, unsigned first, unsigned n);
561 __isl_give isl_dim *isl_dim_map_from_set(
562 __isl_take isl_dim *dim);
563 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
565 Note that if dimensions are added or removed from a space, then
566 the name and the internal structure are lost.
570 A local space is essentially a dimension specification with
571 zero or more existentially quantified variables.
572 The local space of a basic set or relation can be obtained
573 using the following functions.
576 __isl_give isl_local_space *isl_basic_set_get_local_space(
577 __isl_keep isl_basic_set *bset);
580 __isl_give isl_local_space *isl_basic_map_get_local_space(
581 __isl_keep isl_basic_map *bmap);
583 A new local space can be created from a dimension specification using
585 #include <isl/local_space.h>
586 __isl_give isl_local_space *isl_local_space_from_dim(
587 __isl_take isl_dim *dim);
589 They can be inspected, copied and freed using the following functions.
591 #include <isl/local_space.h>
592 isl_ctx *isl_local_space_get_ctx(
593 __isl_keep isl_local_space *ls);
594 int isl_local_space_dim(__isl_keep isl_local_space *ls,
595 enum isl_dim_type type);
596 const char *isl_local_space_get_dim_name(
597 __isl_keep isl_local_space *ls,
598 enum isl_dim_type type, unsigned pos);
599 __isl_give isl_dim *isl_local_space_get_dim(
600 __isl_keep isl_local_space *ls);
601 __isl_give isl_div *isl_local_space_get_div(
602 __isl_keep isl_local_space *ls, int pos);
603 __isl_give isl_local_space *isl_local_space_copy(
604 __isl_keep isl_local_space *ls);
605 void *isl_local_space_free(__isl_take isl_local_space *ls);
607 =head2 Input and Output
609 C<isl> supports its own input/output format, which is similar
610 to the C<Omega> format, but also supports the C<PolyLib> format
615 The C<isl> format is similar to that of C<Omega>, but has a different
616 syntax for describing the parameters and allows for the definition
617 of an existentially quantified variable as the integer division
618 of an affine expression.
619 For example, the set of integers C<i> between C<0> and C<n>
620 such that C<i % 10 <= 6> can be described as
622 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
625 A set or relation can have several disjuncts, separated
626 by the keyword C<or>. Each disjunct is either a conjunction
627 of constraints or a projection (C<exists>) of a conjunction
628 of constraints. The constraints are separated by the keyword
631 =head3 C<PolyLib> format
633 If the represented set is a union, then the first line
634 contains a single number representing the number of disjuncts.
635 Otherwise, a line containing the number C<1> is optional.
637 Each disjunct is represented by a matrix of constraints.
638 The first line contains two numbers representing
639 the number of rows and columns,
640 where the number of rows is equal to the number of constraints
641 and the number of columns is equal to two plus the number of variables.
642 The following lines contain the actual rows of the constraint matrix.
643 In each row, the first column indicates whether the constraint
644 is an equality (C<0>) or inequality (C<1>). The final column
645 corresponds to the constant term.
647 If the set is parametric, then the coefficients of the parameters
648 appear in the last columns before the constant column.
649 The coefficients of any existentially quantified variables appear
650 between those of the set variables and those of the parameters.
652 =head3 Extended C<PolyLib> format
654 The extended C<PolyLib> format is nearly identical to the
655 C<PolyLib> format. The only difference is that the line
656 containing the number of rows and columns of a constraint matrix
657 also contains four additional numbers:
658 the number of output dimensions, the number of input dimensions,
659 the number of local dimensions (i.e., the number of existentially
660 quantified variables) and the number of parameters.
661 For sets, the number of ``output'' dimensions is equal
662 to the number of set dimensions, while the number of ``input''
668 __isl_give isl_basic_set *isl_basic_set_read_from_file(
669 isl_ctx *ctx, FILE *input, int nparam);
670 __isl_give isl_basic_set *isl_basic_set_read_from_str(
671 isl_ctx *ctx, const char *str, int nparam);
672 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
673 FILE *input, int nparam);
674 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
675 const char *str, int nparam);
678 __isl_give isl_basic_map *isl_basic_map_read_from_file(
679 isl_ctx *ctx, FILE *input, int nparam);
680 __isl_give isl_basic_map *isl_basic_map_read_from_str(
681 isl_ctx *ctx, const char *str, int nparam);
682 __isl_give isl_map *isl_map_read_from_file(
683 struct isl_ctx *ctx, FILE *input, int nparam);
684 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
685 const char *str, int nparam);
687 #include <isl/union_set.h>
688 __isl_give isl_union_set *isl_union_set_read_from_file(
689 isl_ctx *ctx, FILE *input);
690 __isl_give isl_union_set *isl_union_set_read_from_str(
691 struct isl_ctx *ctx, const char *str);
693 #include <isl/union_map.h>
694 __isl_give isl_union_map *isl_union_map_read_from_file(
695 isl_ctx *ctx, FILE *input);
696 __isl_give isl_union_map *isl_union_map_read_from_str(
697 struct isl_ctx *ctx, const char *str);
699 The input format is autodetected and may be either the C<PolyLib> format
700 or the C<isl> format.
701 C<nparam> specifies how many of the final columns in
702 the C<PolyLib> format correspond to parameters.
703 If input is given in the C<isl> format, then the number
704 of parameters needs to be equal to C<nparam>.
705 If C<nparam> is negative, then any number of parameters
706 is accepted in the C<isl> format and zero parameters
707 are assumed in the C<PolyLib> format.
711 Before anything can be printed, an C<isl_printer> needs to
714 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
716 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
717 void isl_printer_free(__isl_take isl_printer *printer);
718 __isl_give char *isl_printer_get_str(
719 __isl_keep isl_printer *printer);
721 The behavior of the printer can be modified in various ways
723 __isl_give isl_printer *isl_printer_set_output_format(
724 __isl_take isl_printer *p, int output_format);
725 __isl_give isl_printer *isl_printer_set_indent(
726 __isl_take isl_printer *p, int indent);
727 __isl_give isl_printer *isl_printer_indent(
728 __isl_take isl_printer *p, int indent);
729 __isl_give isl_printer *isl_printer_set_prefix(
730 __isl_take isl_printer *p, const char *prefix);
731 __isl_give isl_printer *isl_printer_set_suffix(
732 __isl_take isl_printer *p, const char *suffix);
734 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
735 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
736 and defaults to C<ISL_FORMAT_ISL>.
737 Each line in the output is indented by C<indent> (set by
738 C<isl_printer_set_indent>) spaces
739 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
740 In the C<PolyLib> format output,
741 the coefficients of the existentially quantified variables
742 appear between those of the set variables and those
744 The function C<isl_printer_indent> increases the indentation
745 by the specified amount (which may be negative).
747 To actually print something, use
750 __isl_give isl_printer *isl_printer_print_basic_set(
751 __isl_take isl_printer *printer,
752 __isl_keep isl_basic_set *bset);
753 __isl_give isl_printer *isl_printer_print_set(
754 __isl_take isl_printer *printer,
755 __isl_keep isl_set *set);
758 __isl_give isl_printer *isl_printer_print_basic_map(
759 __isl_take isl_printer *printer,
760 __isl_keep isl_basic_map *bmap);
761 __isl_give isl_printer *isl_printer_print_map(
762 __isl_take isl_printer *printer,
763 __isl_keep isl_map *map);
765 #include <isl/union_set.h>
766 __isl_give isl_printer *isl_printer_print_union_set(
767 __isl_take isl_printer *p,
768 __isl_keep isl_union_set *uset);
770 #include <isl/union_map.h>
771 __isl_give isl_printer *isl_printer_print_union_map(
772 __isl_take isl_printer *p,
773 __isl_keep isl_union_map *umap);
775 When called on a file printer, the following function flushes
776 the file. When called on a string printer, the buffer is cleared.
778 __isl_give isl_printer *isl_printer_flush(
779 __isl_take isl_printer *p);
781 =head2 Creating New Sets and Relations
783 C<isl> has functions for creating some standard sets and relations.
787 =item * Empty sets and relations
789 __isl_give isl_basic_set *isl_basic_set_empty(
790 __isl_take isl_dim *dim);
791 __isl_give isl_basic_map *isl_basic_map_empty(
792 __isl_take isl_dim *dim);
793 __isl_give isl_set *isl_set_empty(
794 __isl_take isl_dim *dim);
795 __isl_give isl_map *isl_map_empty(
796 __isl_take isl_dim *dim);
797 __isl_give isl_union_set *isl_union_set_empty(
798 __isl_take isl_dim *dim);
799 __isl_give isl_union_map *isl_union_map_empty(
800 __isl_take isl_dim *dim);
802 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
803 is only used to specify the parameters.
805 =item * Universe sets and relations
807 __isl_give isl_basic_set *isl_basic_set_universe(
808 __isl_take isl_dim *dim);
809 __isl_give isl_basic_map *isl_basic_map_universe(
810 __isl_take isl_dim *dim);
811 __isl_give isl_set *isl_set_universe(
812 __isl_take isl_dim *dim);
813 __isl_give isl_map *isl_map_universe(
814 __isl_take isl_dim *dim);
815 __isl_give isl_union_set *isl_union_set_universe(
816 __isl_take isl_union_set *uset);
817 __isl_give isl_union_map *isl_union_map_universe(
818 __isl_take isl_union_map *umap);
820 The sets and relations constructed by the functions above
821 contain all integer values, while those constructed by the
822 functions below only contain non-negative values.
824 __isl_give isl_basic_set *isl_basic_set_nat_universe(
825 __isl_take isl_dim *dim);
826 __isl_give isl_basic_map *isl_basic_map_nat_universe(
827 __isl_take isl_dim *dim);
828 __isl_give isl_set *isl_set_nat_universe(
829 __isl_take isl_dim *dim);
830 __isl_give isl_map *isl_map_nat_universe(
831 __isl_take isl_dim *dim);
833 =item * Identity relations
835 __isl_give isl_basic_map *isl_basic_map_identity(
836 __isl_take isl_dim *dim);
837 __isl_give isl_map *isl_map_identity(
838 __isl_take isl_dim *dim);
840 The number of input and output dimensions in C<dim> needs
843 =item * Lexicographic order
845 __isl_give isl_map *isl_map_lex_lt(
846 __isl_take isl_dim *set_dim);
847 __isl_give isl_map *isl_map_lex_le(
848 __isl_take isl_dim *set_dim);
849 __isl_give isl_map *isl_map_lex_gt(
850 __isl_take isl_dim *set_dim);
851 __isl_give isl_map *isl_map_lex_ge(
852 __isl_take isl_dim *set_dim);
853 __isl_give isl_map *isl_map_lex_lt_first(
854 __isl_take isl_dim *dim, unsigned n);
855 __isl_give isl_map *isl_map_lex_le_first(
856 __isl_take isl_dim *dim, unsigned n);
857 __isl_give isl_map *isl_map_lex_gt_first(
858 __isl_take isl_dim *dim, unsigned n);
859 __isl_give isl_map *isl_map_lex_ge_first(
860 __isl_take isl_dim *dim, unsigned n);
862 The first four functions take a dimension specification for a B<set>
863 and return relations that express that the elements in the domain
864 are lexicographically less
865 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
866 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
867 than the elements in the range.
868 The last four functions take a dimension specification for a map
869 and return relations that express that the first C<n> dimensions
870 in the domain are lexicographically less
871 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
872 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
873 than the first C<n> dimensions in the range.
877 A basic set or relation can be converted to a set or relation
878 using the following functions.
880 __isl_give isl_set *isl_set_from_basic_set(
881 __isl_take isl_basic_set *bset);
882 __isl_give isl_map *isl_map_from_basic_map(
883 __isl_take isl_basic_map *bmap);
885 Sets and relations can be converted to union sets and relations
886 using the following functions.
888 __isl_give isl_union_map *isl_union_map_from_map(
889 __isl_take isl_map *map);
890 __isl_give isl_union_set *isl_union_set_from_set(
891 __isl_take isl_set *set);
893 Sets and relations can be copied and freed again using the following
896 __isl_give isl_basic_set *isl_basic_set_copy(
897 __isl_keep isl_basic_set *bset);
898 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
899 __isl_give isl_union_set *isl_union_set_copy(
900 __isl_keep isl_union_set *uset);
901 __isl_give isl_basic_map *isl_basic_map_copy(
902 __isl_keep isl_basic_map *bmap);
903 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
904 __isl_give isl_union_map *isl_union_map_copy(
905 __isl_keep isl_union_map *umap);
906 void isl_basic_set_free(__isl_take isl_basic_set *bset);
907 void isl_set_free(__isl_take isl_set *set);
908 void isl_union_set_free(__isl_take isl_union_set *uset);
909 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
910 void isl_map_free(__isl_take isl_map *map);
911 void isl_union_map_free(__isl_take isl_union_map *umap);
913 Other sets and relations can be constructed by starting
914 from a universe set or relation, adding equality and/or
915 inequality constraints and then projecting out the
916 existentially quantified variables, if any.
917 Constraints can be constructed, manipulated and
918 added to (basic) sets and relations using the following functions.
920 #include <isl/constraint.h>
921 __isl_give isl_constraint *isl_equality_alloc(
922 __isl_take isl_dim *dim);
923 __isl_give isl_constraint *isl_inequality_alloc(
924 __isl_take isl_dim *dim);
925 void isl_constraint_set_constant(
926 __isl_keep isl_constraint *constraint, isl_int v);
927 void isl_constraint_set_coefficient(
928 __isl_keep isl_constraint *constraint,
929 enum isl_dim_type type, int pos, isl_int v);
930 __isl_give isl_basic_map *isl_basic_map_add_constraint(
931 __isl_take isl_basic_map *bmap,
932 __isl_take isl_constraint *constraint);
933 __isl_give isl_basic_set *isl_basic_set_add_constraint(
934 __isl_take isl_basic_set *bset,
935 __isl_take isl_constraint *constraint);
936 __isl_give isl_map *isl_map_add_constraint(
937 __isl_take isl_map *map,
938 __isl_take isl_constraint *constraint);
939 __isl_give isl_set *isl_set_add_constraint(
940 __isl_take isl_set *set,
941 __isl_take isl_constraint *constraint);
943 For example, to create a set containing the even integers
944 between 10 and 42, you would use the following code.
948 struct isl_constraint *c;
949 struct isl_basic_set *bset;
952 dim = isl_dim_set_alloc(ctx, 0, 2);
953 bset = isl_basic_set_universe(isl_dim_copy(dim));
955 c = isl_equality_alloc(isl_dim_copy(dim));
956 isl_int_set_si(v, -1);
957 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
958 isl_int_set_si(v, 2);
959 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
960 bset = isl_basic_set_add_constraint(bset, c);
962 c = isl_inequality_alloc(isl_dim_copy(dim));
963 isl_int_set_si(v, -10);
964 isl_constraint_set_constant(c, v);
965 isl_int_set_si(v, 1);
966 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
967 bset = isl_basic_set_add_constraint(bset, c);
969 c = isl_inequality_alloc(dim);
970 isl_int_set_si(v, 42);
971 isl_constraint_set_constant(c, v);
972 isl_int_set_si(v, -1);
973 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
974 bset = isl_basic_set_add_constraint(bset, c);
976 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
982 struct isl_basic_set *bset;
983 bset = isl_basic_set_read_from_str(ctx,
984 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
986 A basic set or relation can also be constructed from two matrices
987 describing the equalities and the inequalities.
989 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
990 __isl_take isl_dim *dim,
991 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
992 enum isl_dim_type c1,
993 enum isl_dim_type c2, enum isl_dim_type c3,
994 enum isl_dim_type c4);
995 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
996 __isl_take isl_dim *dim,
997 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
998 enum isl_dim_type c1,
999 enum isl_dim_type c2, enum isl_dim_type c3,
1000 enum isl_dim_type c4, enum isl_dim_type c5);
1002 The C<isl_dim_type> arguments indicate the order in which
1003 different kinds of variables appear in the input matrices
1004 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1005 C<isl_dim_set> and C<isl_dim_div> for sets and
1006 of C<isl_dim_cst>, C<isl_dim_param>,
1007 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1009 =head2 Inspecting Sets and Relations
1011 Usually, the user should not have to care about the actual constraints
1012 of the sets and maps, but should instead apply the abstract operations
1013 explained in the following sections.
1014 Occasionally, however, it may be required to inspect the individual
1015 coefficients of the constraints. This section explains how to do so.
1016 In these cases, it may also be useful to have C<isl> compute
1017 an explicit representation of the existentially quantified variables.
1019 __isl_give isl_set *isl_set_compute_divs(
1020 __isl_take isl_set *set);
1021 __isl_give isl_map *isl_map_compute_divs(
1022 __isl_take isl_map *map);
1023 __isl_give isl_union_set *isl_union_set_compute_divs(
1024 __isl_take isl_union_set *uset);
1025 __isl_give isl_union_map *isl_union_map_compute_divs(
1026 __isl_take isl_union_map *umap);
1028 This explicit representation defines the existentially quantified
1029 variables as integer divisions of the other variables, possibly
1030 including earlier existentially quantified variables.
1031 An explicitly represented existentially quantified variable therefore
1032 has a unique value when the values of the other variables are known.
1033 If, furthermore, the same existentials, i.e., existentials
1034 with the same explicit representations, should appear in the
1035 same order in each of the disjuncts of a set or map, then the user should call
1036 either of the following functions.
1038 __isl_give isl_set *isl_set_align_divs(
1039 __isl_take isl_set *set);
1040 __isl_give isl_map *isl_map_align_divs(
1041 __isl_take isl_map *map);
1043 Alternatively, the existentially quantified variables can be removed
1044 using the following functions, which compute an overapproximation.
1046 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1047 __isl_take isl_basic_set *bset);
1048 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1049 __isl_take isl_basic_map *bmap);
1050 __isl_give isl_set *isl_set_remove_divs(
1051 __isl_take isl_set *set);
1052 __isl_give isl_map *isl_map_remove_divs(
1053 __isl_take isl_map *map);
1055 To iterate over all the sets or maps in a union set or map, use
1057 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1058 int (*fn)(__isl_take isl_set *set, void *user),
1060 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1061 int (*fn)(__isl_take isl_map *map, void *user),
1064 The number of sets or maps in a union set or map can be obtained
1067 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1068 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1070 To extract the set or map from a union with a given dimension
1073 __isl_give isl_set *isl_union_set_extract_set(
1074 __isl_keep isl_union_set *uset,
1075 __isl_take isl_dim *dim);
1076 __isl_give isl_map *isl_union_map_extract_map(
1077 __isl_keep isl_union_map *umap,
1078 __isl_take isl_dim *dim);
1080 To iterate over all the basic sets or maps in a set or map, use
1082 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1083 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1085 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1086 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1089 The callback function C<fn> should return 0 if successful and
1090 -1 if an error occurs. In the latter case, or if any other error
1091 occurs, the above functions will return -1.
1093 It should be noted that C<isl> does not guarantee that
1094 the basic sets or maps passed to C<fn> are disjoint.
1095 If this is required, then the user should call one of
1096 the following functions first.
1098 __isl_give isl_set *isl_set_make_disjoint(
1099 __isl_take isl_set *set);
1100 __isl_give isl_map *isl_map_make_disjoint(
1101 __isl_take isl_map *map);
1103 The number of basic sets in a set can be obtained
1106 int isl_set_n_basic_set(__isl_keep isl_set *set);
1108 To iterate over the constraints of a basic set or map, use
1110 #include <isl/constraint.h>
1112 int isl_basic_map_foreach_constraint(
1113 __isl_keep isl_basic_map *bmap,
1114 int (*fn)(__isl_take isl_constraint *c, void *user),
1116 void isl_constraint_free(struct isl_constraint *c);
1118 Again, the callback function C<fn> should return 0 if successful and
1119 -1 if an error occurs. In the latter case, or if any other error
1120 occurs, the above functions will return -1.
1121 The constraint C<c> represents either an equality or an inequality.
1122 Use the following function to find out whether a constraint
1123 represents an equality. If not, it represents an inequality.
1125 int isl_constraint_is_equality(
1126 __isl_keep isl_constraint *constraint);
1128 The coefficients of the constraints can be inspected using
1129 the following functions.
1131 void isl_constraint_get_constant(
1132 __isl_keep isl_constraint *constraint, isl_int *v);
1133 void isl_constraint_get_coefficient(
1134 __isl_keep isl_constraint *constraint,
1135 enum isl_dim_type type, int pos, isl_int *v);
1136 int isl_constraint_involves_dims(
1137 __isl_keep isl_constraint *constraint,
1138 enum isl_dim_type type, unsigned first, unsigned n);
1140 The explicit representations of the existentially quantified
1141 variables can be inspected using the following functions.
1142 Note that the user is only allowed to use these functions
1143 if the inspected set or map is the result of a call
1144 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1146 __isl_give isl_div *isl_constraint_div(
1147 __isl_keep isl_constraint *constraint, int pos);
1148 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1149 void isl_div_get_constant(__isl_keep isl_div *div,
1151 void isl_div_get_denominator(__isl_keep isl_div *div,
1153 void isl_div_get_coefficient(__isl_keep isl_div *div,
1154 enum isl_dim_type type, int pos, isl_int *v);
1156 To obtain the constraints of a basic set or map in matrix
1157 form, use the following functions.
1159 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1160 __isl_keep isl_basic_set *bset,
1161 enum isl_dim_type c1, enum isl_dim_type c2,
1162 enum isl_dim_type c3, enum isl_dim_type c4);
1163 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1164 __isl_keep isl_basic_set *bset,
1165 enum isl_dim_type c1, enum isl_dim_type c2,
1166 enum isl_dim_type c3, enum isl_dim_type c4);
1167 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1168 __isl_keep isl_basic_map *bmap,
1169 enum isl_dim_type c1,
1170 enum isl_dim_type c2, enum isl_dim_type c3,
1171 enum isl_dim_type c4, enum isl_dim_type c5);
1172 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1173 __isl_keep isl_basic_map *bmap,
1174 enum isl_dim_type c1,
1175 enum isl_dim_type c2, enum isl_dim_type c3,
1176 enum isl_dim_type c4, enum isl_dim_type c5);
1178 The C<isl_dim_type> arguments dictate the order in which
1179 different kinds of variables appear in the resulting matrix
1180 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1181 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1183 The names of the domain and range spaces of a set or relation can be
1184 read off using the following functions.
1186 const char *isl_basic_set_get_tuple_name(
1187 __isl_keep isl_basic_set *bset);
1188 const char *isl_set_get_tuple_name(
1189 __isl_keep isl_set *set);
1190 const char *isl_basic_map_get_tuple_name(
1191 __isl_keep isl_basic_map *bmap,
1192 enum isl_dim_type type);
1193 const char *isl_map_get_tuple_name(
1194 __isl_keep isl_map *map,
1195 enum isl_dim_type type);
1197 As with C<isl_dim_get_tuple_name>, the value returned points to
1198 an internal data structure.
1199 The names of individual dimensions can be read off using
1200 the following functions.
1202 const char *isl_constraint_get_dim_name(
1203 __isl_keep isl_constraint *constraint,
1204 enum isl_dim_type type, unsigned pos);
1205 const char *isl_basic_set_get_dim_name(
1206 __isl_keep isl_basic_set *bset,
1207 enum isl_dim_type type, unsigned pos);
1208 const char *isl_set_get_dim_name(
1209 __isl_keep isl_set *set,
1210 enum isl_dim_type type, unsigned pos);
1211 const char *isl_basic_map_get_dim_name(
1212 __isl_keep isl_basic_map *bmap,
1213 enum isl_dim_type type, unsigned pos);
1214 const char *isl_map_get_dim_name(
1215 __isl_keep isl_map *map,
1216 enum isl_dim_type type, unsigned pos);
1218 These functions are mostly useful to obtain the names
1223 =head3 Unary Properties
1229 The following functions test whether the given set or relation
1230 contains any integer points. The ``plain'' variants do not perform
1231 any computations, but simply check if the given set or relation
1232 is already known to be empty.
1234 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1235 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1236 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1237 int isl_set_is_empty(__isl_keep isl_set *set);
1238 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1239 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1240 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1241 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1242 int isl_map_is_empty(__isl_keep isl_map *map);
1243 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1245 =item * Universality
1247 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1248 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1249 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1251 =item * Single-valuedness
1253 int isl_map_is_single_valued(__isl_keep isl_map *map);
1254 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1258 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1259 int isl_map_is_injective(__isl_keep isl_map *map);
1260 int isl_union_map_plain_is_injective(
1261 __isl_keep isl_union_map *umap);
1262 int isl_union_map_is_injective(
1263 __isl_keep isl_union_map *umap);
1267 int isl_map_is_bijective(__isl_keep isl_map *map);
1268 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1272 The following functions check whether the domain of the given
1273 (basic) set is a wrapped relation.
1275 int isl_basic_set_is_wrapping(
1276 __isl_keep isl_basic_set *bset);
1277 int isl_set_is_wrapping(__isl_keep isl_set *set);
1279 =item * Internal Product
1281 int isl_basic_map_can_zip(
1282 __isl_keep isl_basic_map *bmap);
1283 int isl_map_can_zip(__isl_keep isl_map *map);
1285 Check whether the product of domain and range of the given relation
1287 i.e., whether both domain and range are nested relations.
1291 =head3 Binary Properties
1297 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1298 __isl_keep isl_set *set2);
1299 int isl_set_is_equal(__isl_keep isl_set *set1,
1300 __isl_keep isl_set *set2);
1301 int isl_union_set_is_equal(
1302 __isl_keep isl_union_set *uset1,
1303 __isl_keep isl_union_set *uset2);
1304 int isl_basic_map_is_equal(
1305 __isl_keep isl_basic_map *bmap1,
1306 __isl_keep isl_basic_map *bmap2);
1307 int isl_map_is_equal(__isl_keep isl_map *map1,
1308 __isl_keep isl_map *map2);
1309 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1310 __isl_keep isl_map *map2);
1311 int isl_union_map_is_equal(
1312 __isl_keep isl_union_map *umap1,
1313 __isl_keep isl_union_map *umap2);
1315 =item * Disjointness
1317 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1318 __isl_keep isl_set *set2);
1322 int isl_set_is_subset(__isl_keep isl_set *set1,
1323 __isl_keep isl_set *set2);
1324 int isl_set_is_strict_subset(
1325 __isl_keep isl_set *set1,
1326 __isl_keep isl_set *set2);
1327 int isl_union_set_is_subset(
1328 __isl_keep isl_union_set *uset1,
1329 __isl_keep isl_union_set *uset2);
1330 int isl_union_set_is_strict_subset(
1331 __isl_keep isl_union_set *uset1,
1332 __isl_keep isl_union_set *uset2);
1333 int isl_basic_map_is_subset(
1334 __isl_keep isl_basic_map *bmap1,
1335 __isl_keep isl_basic_map *bmap2);
1336 int isl_basic_map_is_strict_subset(
1337 __isl_keep isl_basic_map *bmap1,
1338 __isl_keep isl_basic_map *bmap2);
1339 int isl_map_is_subset(
1340 __isl_keep isl_map *map1,
1341 __isl_keep isl_map *map2);
1342 int isl_map_is_strict_subset(
1343 __isl_keep isl_map *map1,
1344 __isl_keep isl_map *map2);
1345 int isl_union_map_is_subset(
1346 __isl_keep isl_union_map *umap1,
1347 __isl_keep isl_union_map *umap2);
1348 int isl_union_map_is_strict_subset(
1349 __isl_keep isl_union_map *umap1,
1350 __isl_keep isl_union_map *umap2);
1354 =head2 Unary Operations
1360 __isl_give isl_set *isl_set_complement(
1361 __isl_take isl_set *set);
1365 __isl_give isl_basic_map *isl_basic_map_reverse(
1366 __isl_take isl_basic_map *bmap);
1367 __isl_give isl_map *isl_map_reverse(
1368 __isl_take isl_map *map);
1369 __isl_give isl_union_map *isl_union_map_reverse(
1370 __isl_take isl_union_map *umap);
1374 __isl_give isl_basic_set *isl_basic_set_project_out(
1375 __isl_take isl_basic_set *bset,
1376 enum isl_dim_type type, unsigned first, unsigned n);
1377 __isl_give isl_basic_map *isl_basic_map_project_out(
1378 __isl_take isl_basic_map *bmap,
1379 enum isl_dim_type type, unsigned first, unsigned n);
1380 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1381 enum isl_dim_type type, unsigned first, unsigned n);
1382 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1383 enum isl_dim_type type, unsigned first, unsigned n);
1384 __isl_give isl_basic_set *isl_basic_map_domain(
1385 __isl_take isl_basic_map *bmap);
1386 __isl_give isl_basic_set *isl_basic_map_range(
1387 __isl_take isl_basic_map *bmap);
1388 __isl_give isl_set *isl_map_domain(
1389 __isl_take isl_map *bmap);
1390 __isl_give isl_set *isl_map_range(
1391 __isl_take isl_map *map);
1392 __isl_give isl_union_set *isl_union_map_domain(
1393 __isl_take isl_union_map *umap);
1394 __isl_give isl_union_set *isl_union_map_range(
1395 __isl_take isl_union_map *umap);
1397 __isl_give isl_basic_map *isl_basic_map_domain_map(
1398 __isl_take isl_basic_map *bmap);
1399 __isl_give isl_basic_map *isl_basic_map_range_map(
1400 __isl_take isl_basic_map *bmap);
1401 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1402 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1403 __isl_give isl_union_map *isl_union_map_domain_map(
1404 __isl_take isl_union_map *umap);
1405 __isl_give isl_union_map *isl_union_map_range_map(
1406 __isl_take isl_union_map *umap);
1408 The functions above construct a (basic, regular or union) relation
1409 that maps (a wrapped version of) the input relation to its domain or range.
1413 __isl_give isl_set *isl_set_eliminate(
1414 __isl_take isl_set *set, enum isl_dim_type type,
1415 unsigned first, unsigned n);
1417 Eliminate the coefficients for the given dimensions from the constraints,
1418 without removing the dimensions.
1422 __isl_give isl_basic_set *isl_basic_set_fix(
1423 __isl_take isl_basic_set *bset,
1424 enum isl_dim_type type, unsigned pos,
1426 __isl_give isl_basic_set *isl_basic_set_fix_si(
1427 __isl_take isl_basic_set *bset,
1428 enum isl_dim_type type, unsigned pos, int value);
1429 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1430 enum isl_dim_type type, unsigned pos,
1432 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1433 enum isl_dim_type type, unsigned pos, int value);
1434 __isl_give isl_basic_map *isl_basic_map_fix_si(
1435 __isl_take isl_basic_map *bmap,
1436 enum isl_dim_type type, unsigned pos, int value);
1437 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1438 enum isl_dim_type type, unsigned pos, int value);
1440 Intersect the set or relation with the hyperplane where the given
1441 dimension has the fixed given value.
1445 __isl_give isl_map *isl_set_identity(
1446 __isl_take isl_set *set);
1447 __isl_give isl_union_map *isl_union_set_identity(
1448 __isl_take isl_union_set *uset);
1450 Construct an identity relation on the given (union) set.
1454 __isl_give isl_basic_set *isl_basic_map_deltas(
1455 __isl_take isl_basic_map *bmap);
1456 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1457 __isl_give isl_union_set *isl_union_map_deltas(
1458 __isl_take isl_union_map *umap);
1460 These functions return a (basic) set containing the differences
1461 between image elements and corresponding domain elements in the input.
1463 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1464 __isl_take isl_basic_map *bmap);
1465 __isl_give isl_map *isl_map_deltas_map(
1466 __isl_take isl_map *map);
1467 __isl_give isl_union_map *isl_union_map_deltas_map(
1468 __isl_take isl_union_map *umap);
1470 The functions above construct a (basic, regular or union) relation
1471 that maps (a wrapped version of) the input relation to its delta set.
1475 Simplify the representation of a set or relation by trying
1476 to combine pairs of basic sets or relations into a single
1477 basic set or relation.
1479 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1480 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1481 __isl_give isl_union_set *isl_union_set_coalesce(
1482 __isl_take isl_union_set *uset);
1483 __isl_give isl_union_map *isl_union_map_coalesce(
1484 __isl_take isl_union_map *umap);
1486 =item * Detecting equalities
1488 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1489 __isl_take isl_basic_set *bset);
1490 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1491 __isl_take isl_basic_map *bmap);
1492 __isl_give isl_set *isl_set_detect_equalities(
1493 __isl_take isl_set *set);
1494 __isl_give isl_map *isl_map_detect_equalities(
1495 __isl_take isl_map *map);
1496 __isl_give isl_union_set *isl_union_set_detect_equalities(
1497 __isl_take isl_union_set *uset);
1498 __isl_give isl_union_map *isl_union_map_detect_equalities(
1499 __isl_take isl_union_map *umap);
1501 Simplify the representation of a set or relation by detecting implicit
1504 =item * Removing redundant constraints
1506 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1507 __isl_take isl_basic_set *bset);
1508 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1509 __isl_take isl_basic_map *bmap);
1513 __isl_give isl_basic_set *isl_set_convex_hull(
1514 __isl_take isl_set *set);
1515 __isl_give isl_basic_map *isl_map_convex_hull(
1516 __isl_take isl_map *map);
1518 If the input set or relation has any existentially quantified
1519 variables, then the result of these operations is currently undefined.
1523 __isl_give isl_basic_set *isl_set_simple_hull(
1524 __isl_take isl_set *set);
1525 __isl_give isl_basic_map *isl_map_simple_hull(
1526 __isl_take isl_map *map);
1527 __isl_give isl_union_map *isl_union_map_simple_hull(
1528 __isl_take isl_union_map *umap);
1530 These functions compute a single basic set or relation
1531 that contains the whole input set or relation.
1532 In particular, the output is described by translates
1533 of the constraints describing the basic sets or relations in the input.
1537 (See \autoref{s:simple hull}.)
1543 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1544 __isl_take isl_basic_set *bset);
1545 __isl_give isl_basic_set *isl_set_affine_hull(
1546 __isl_take isl_set *set);
1547 __isl_give isl_union_set *isl_union_set_affine_hull(
1548 __isl_take isl_union_set *uset);
1549 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1550 __isl_take isl_basic_map *bmap);
1551 __isl_give isl_basic_map *isl_map_affine_hull(
1552 __isl_take isl_map *map);
1553 __isl_give isl_union_map *isl_union_map_affine_hull(
1554 __isl_take isl_union_map *umap);
1556 In case of union sets and relations, the affine hull is computed
1559 =item * Polyhedral hull
1561 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1562 __isl_take isl_set *set);
1563 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1564 __isl_take isl_map *map);
1565 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1566 __isl_take isl_union_set *uset);
1567 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1568 __isl_take isl_union_map *umap);
1570 These functions compute a single basic set or relation
1571 not involving any existentially quantified variables
1572 that contains the whole input set or relation.
1573 In case of union sets and relations, the polyhedral hull is computed
1576 =item * Optimization
1578 #include <isl/ilp.h>
1579 enum isl_lp_result isl_basic_set_max(
1580 __isl_keep isl_basic_set *bset,
1581 __isl_keep isl_aff *obj, isl_int *opt)
1582 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1583 __isl_keep isl_aff *obj, isl_int *opt);
1585 Compute the maximum of the integer affine expression C<obj>
1586 over the points in C<set>, returning the result in C<opt>.
1587 The return value may be one of C<isl_lp_error>,
1588 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1592 The following functions compute either the set of (rational) coefficient
1593 values of valid constraints for the given set or the set of (rational)
1594 values satisfying the constraints with coefficients from the given set.
1595 Internally, these two sets of functions perform essentially the
1596 same operations, except that the set of coefficients is assumed to
1597 be a cone, while the set of values may be any polyhedron.
1598 The current implementation is based on the Farkas lemma and
1599 Fourier-Motzkin elimination, but this may change or be made optional
1600 in future. In particular, future implementations may use different
1601 dualization algorithms or skip the elimination step.
1603 __isl_give isl_basic_set *isl_basic_set_coefficients(
1604 __isl_take isl_basic_set *bset);
1605 __isl_give isl_basic_set *isl_set_coefficients(
1606 __isl_take isl_set *set);
1607 __isl_give isl_union_set *isl_union_set_coefficients(
1608 __isl_take isl_union_set *bset);
1609 __isl_give isl_basic_set *isl_basic_set_solutions(
1610 __isl_take isl_basic_set *bset);
1611 __isl_give isl_basic_set *isl_set_solutions(
1612 __isl_take isl_set *set);
1613 __isl_give isl_union_set *isl_union_set_solutions(
1614 __isl_take isl_union_set *bset);
1618 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1620 __isl_give isl_union_map *isl_union_map_power(
1621 __isl_take isl_union_map *umap, int *exact);
1623 Compute a parametric representation for all positive powers I<k> of C<map>.
1624 The result maps I<k> to a nested relation corresponding to the
1625 I<k>th power of C<map>.
1626 The result may be an overapproximation. If the result is known to be exact,
1627 then C<*exact> is set to C<1>.
1629 =item * Transitive closure
1631 __isl_give isl_map *isl_map_transitive_closure(
1632 __isl_take isl_map *map, int *exact);
1633 __isl_give isl_union_map *isl_union_map_transitive_closure(
1634 __isl_take isl_union_map *umap, int *exact);
1636 Compute the transitive closure of C<map>.
1637 The result may be an overapproximation. If the result is known to be exact,
1638 then C<*exact> is set to C<1>.
1640 =item * Reaching path lengths
1642 __isl_give isl_map *isl_map_reaching_path_lengths(
1643 __isl_take isl_map *map, int *exact);
1645 Compute a relation that maps each element in the range of C<map>
1646 to the lengths of all paths composed of edges in C<map> that
1647 end up in the given element.
1648 The result may be an overapproximation. If the result is known to be exact,
1649 then C<*exact> is set to C<1>.
1650 To compute the I<maximal> path length, the resulting relation
1651 should be postprocessed by C<isl_map_lexmax>.
1652 In particular, if the input relation is a dependence relation
1653 (mapping sources to sinks), then the maximal path length corresponds
1654 to the free schedule.
1655 Note, however, that C<isl_map_lexmax> expects the maximum to be
1656 finite, so if the path lengths are unbounded (possibly due to
1657 the overapproximation), then you will get an error message.
1661 __isl_give isl_basic_set *isl_basic_map_wrap(
1662 __isl_take isl_basic_map *bmap);
1663 __isl_give isl_set *isl_map_wrap(
1664 __isl_take isl_map *map);
1665 __isl_give isl_union_set *isl_union_map_wrap(
1666 __isl_take isl_union_map *umap);
1667 __isl_give isl_basic_map *isl_basic_set_unwrap(
1668 __isl_take isl_basic_set *bset);
1669 __isl_give isl_map *isl_set_unwrap(
1670 __isl_take isl_set *set);
1671 __isl_give isl_union_map *isl_union_set_unwrap(
1672 __isl_take isl_union_set *uset);
1676 Remove any internal structure of domain (and range) of the given
1677 set or relation. If there is any such internal structure in the input,
1678 then the name of the space is also removed.
1680 __isl_give isl_basic_set *isl_basic_set_flatten(
1681 __isl_take isl_basic_set *bset);
1682 __isl_give isl_set *isl_set_flatten(
1683 __isl_take isl_set *set);
1684 __isl_give isl_map *isl_map_flatten_range(
1685 __isl_take isl_map *map);
1686 __isl_give isl_basic_map *isl_basic_map_flatten(
1687 __isl_take isl_basic_map *bmap);
1688 __isl_give isl_map *isl_map_flatten(
1689 __isl_take isl_map *map);
1691 __isl_give isl_map *isl_set_flatten_map(
1692 __isl_take isl_set *set);
1694 The function above constructs a relation
1695 that maps the input set to a flattened version of the set.
1699 Lift the input set to a space with extra dimensions corresponding
1700 to the existentially quantified variables in the input.
1701 In particular, the result lives in a wrapped map where the domain
1702 is the original space and the range corresponds to the original
1703 existentially quantified variables.
1705 __isl_give isl_basic_set *isl_basic_set_lift(
1706 __isl_take isl_basic_set *bset);
1707 __isl_give isl_set *isl_set_lift(
1708 __isl_take isl_set *set);
1709 __isl_give isl_union_set *isl_union_set_lift(
1710 __isl_take isl_union_set *uset);
1712 =item * Internal Product
1714 __isl_give isl_basic_map *isl_basic_map_zip(
1715 __isl_take isl_basic_map *bmap);
1716 __isl_give isl_map *isl_map_zip(
1717 __isl_take isl_map *map);
1718 __isl_give isl_union_map *isl_union_map_zip(
1719 __isl_take isl_union_map *umap);
1721 Given a relation with nested relations for domain and range,
1722 interchange the range of the domain with the domain of the range.
1724 =item * Aligning parameters
1726 __isl_give isl_set *isl_set_align_params(
1727 __isl_take isl_set *set,
1728 __isl_take isl_dim *model);
1729 __isl_give isl_map *isl_map_align_params(
1730 __isl_take isl_map *map,
1731 __isl_take isl_dim *model);
1733 Change the order of the parameters of the given set or relation
1734 such that the first parameters match those of C<model>.
1735 This may involve the introduction of extra parameters.
1736 All parameters need to be named.
1738 =item * Dimension manipulation
1740 __isl_give isl_set *isl_set_add_dims(
1741 __isl_take isl_set *set,
1742 enum isl_dim_type type, unsigned n);
1743 __isl_give isl_map *isl_map_add_dims(
1744 __isl_take isl_map *map,
1745 enum isl_dim_type type, unsigned n);
1747 It is usually not advisable to directly change the (input or output)
1748 space of a set or a relation as this removes the name and the internal
1749 structure of the space. However, the above functions can be useful
1750 to add new parameters, assuming
1751 C<isl_set_align_params> and C<isl_map_align_params>
1756 =head2 Binary Operations
1758 The two arguments of a binary operation not only need to live
1759 in the same C<isl_ctx>, they currently also need to have
1760 the same (number of) parameters.
1762 =head3 Basic Operations
1766 =item * Intersection
1768 __isl_give isl_basic_set *isl_basic_set_intersect(
1769 __isl_take isl_basic_set *bset1,
1770 __isl_take isl_basic_set *bset2);
1771 __isl_give isl_set *isl_set_intersect(
1772 __isl_take isl_set *set1,
1773 __isl_take isl_set *set2);
1774 __isl_give isl_union_set *isl_union_set_intersect(
1775 __isl_take isl_union_set *uset1,
1776 __isl_take isl_union_set *uset2);
1777 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1778 __isl_take isl_basic_map *bmap,
1779 __isl_take isl_basic_set *bset);
1780 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1781 __isl_take isl_basic_map *bmap,
1782 __isl_take isl_basic_set *bset);
1783 __isl_give isl_basic_map *isl_basic_map_intersect(
1784 __isl_take isl_basic_map *bmap1,
1785 __isl_take isl_basic_map *bmap2);
1786 __isl_give isl_map *isl_map_intersect_domain(
1787 __isl_take isl_map *map,
1788 __isl_take isl_set *set);
1789 __isl_give isl_map *isl_map_intersect_range(
1790 __isl_take isl_map *map,
1791 __isl_take isl_set *set);
1792 __isl_give isl_map *isl_map_intersect(
1793 __isl_take isl_map *map1,
1794 __isl_take isl_map *map2);
1795 __isl_give isl_union_map *isl_union_map_intersect_domain(
1796 __isl_take isl_union_map *umap,
1797 __isl_take isl_union_set *uset);
1798 __isl_give isl_union_map *isl_union_map_intersect_range(
1799 __isl_take isl_union_map *umap,
1800 __isl_take isl_union_set *uset);
1801 __isl_give isl_union_map *isl_union_map_intersect(
1802 __isl_take isl_union_map *umap1,
1803 __isl_take isl_union_map *umap2);
1807 __isl_give isl_set *isl_basic_set_union(
1808 __isl_take isl_basic_set *bset1,
1809 __isl_take isl_basic_set *bset2);
1810 __isl_give isl_map *isl_basic_map_union(
1811 __isl_take isl_basic_map *bmap1,
1812 __isl_take isl_basic_map *bmap2);
1813 __isl_give isl_set *isl_set_union(
1814 __isl_take isl_set *set1,
1815 __isl_take isl_set *set2);
1816 __isl_give isl_map *isl_map_union(
1817 __isl_take isl_map *map1,
1818 __isl_take isl_map *map2);
1819 __isl_give isl_union_set *isl_union_set_union(
1820 __isl_take isl_union_set *uset1,
1821 __isl_take isl_union_set *uset2);
1822 __isl_give isl_union_map *isl_union_map_union(
1823 __isl_take isl_union_map *umap1,
1824 __isl_take isl_union_map *umap2);
1826 =item * Set difference
1828 __isl_give isl_set *isl_set_subtract(
1829 __isl_take isl_set *set1,
1830 __isl_take isl_set *set2);
1831 __isl_give isl_map *isl_map_subtract(
1832 __isl_take isl_map *map1,
1833 __isl_take isl_map *map2);
1834 __isl_give isl_union_set *isl_union_set_subtract(
1835 __isl_take isl_union_set *uset1,
1836 __isl_take isl_union_set *uset2);
1837 __isl_give isl_union_map *isl_union_map_subtract(
1838 __isl_take isl_union_map *umap1,
1839 __isl_take isl_union_map *umap2);
1843 __isl_give isl_basic_set *isl_basic_set_apply(
1844 __isl_take isl_basic_set *bset,
1845 __isl_take isl_basic_map *bmap);
1846 __isl_give isl_set *isl_set_apply(
1847 __isl_take isl_set *set,
1848 __isl_take isl_map *map);
1849 __isl_give isl_union_set *isl_union_set_apply(
1850 __isl_take isl_union_set *uset,
1851 __isl_take isl_union_map *umap);
1852 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1853 __isl_take isl_basic_map *bmap1,
1854 __isl_take isl_basic_map *bmap2);
1855 __isl_give isl_basic_map *isl_basic_map_apply_range(
1856 __isl_take isl_basic_map *bmap1,
1857 __isl_take isl_basic_map *bmap2);
1858 __isl_give isl_map *isl_map_apply_domain(
1859 __isl_take isl_map *map1,
1860 __isl_take isl_map *map2);
1861 __isl_give isl_union_map *isl_union_map_apply_domain(
1862 __isl_take isl_union_map *umap1,
1863 __isl_take isl_union_map *umap2);
1864 __isl_give isl_map *isl_map_apply_range(
1865 __isl_take isl_map *map1,
1866 __isl_take isl_map *map2);
1867 __isl_give isl_union_map *isl_union_map_apply_range(
1868 __isl_take isl_union_map *umap1,
1869 __isl_take isl_union_map *umap2);
1871 =item * Cartesian Product
1873 __isl_give isl_set *isl_set_product(
1874 __isl_take isl_set *set1,
1875 __isl_take isl_set *set2);
1876 __isl_give isl_union_set *isl_union_set_product(
1877 __isl_take isl_union_set *uset1,
1878 __isl_take isl_union_set *uset2);
1879 __isl_give isl_basic_map *isl_basic_map_range_product(
1880 __isl_take isl_basic_map *bmap1,
1881 __isl_take isl_basic_map *bmap2);
1882 __isl_give isl_map *isl_map_range_product(
1883 __isl_take isl_map *map1,
1884 __isl_take isl_map *map2);
1885 __isl_give isl_union_map *isl_union_map_range_product(
1886 __isl_take isl_union_map *umap1,
1887 __isl_take isl_union_map *umap2);
1888 __isl_give isl_map *isl_map_product(
1889 __isl_take isl_map *map1,
1890 __isl_take isl_map *map2);
1891 __isl_give isl_union_map *isl_union_map_product(
1892 __isl_take isl_union_map *umap1,
1893 __isl_take isl_union_map *umap2);
1895 The above functions compute the cross product of the given
1896 sets or relations. The domains and ranges of the results
1897 are wrapped maps between domains and ranges of the inputs.
1898 To obtain a ``flat'' product, use the following functions
1901 __isl_give isl_basic_set *isl_basic_set_flat_product(
1902 __isl_take isl_basic_set *bset1,
1903 __isl_take isl_basic_set *bset2);
1904 __isl_give isl_set *isl_set_flat_product(
1905 __isl_take isl_set *set1,
1906 __isl_take isl_set *set2);
1907 __isl_give isl_map *isl_map_flat_range_product(
1908 __isl_take isl_map *map1,
1909 __isl_take isl_map *map2);
1910 __isl_give isl_union_map *isl_union_map_flat_range_product(
1911 __isl_take isl_union_map *umap1,
1912 __isl_take isl_union_map *umap2);
1913 __isl_give isl_basic_map *isl_basic_map_flat_product(
1914 __isl_take isl_basic_map *bmap1,
1915 __isl_take isl_basic_map *bmap2);
1916 __isl_give isl_map *isl_map_flat_product(
1917 __isl_take isl_map *map1,
1918 __isl_take isl_map *map2);
1920 =item * Simplification
1922 __isl_give isl_basic_set *isl_basic_set_gist(
1923 __isl_take isl_basic_set *bset,
1924 __isl_take isl_basic_set *context);
1925 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1926 __isl_take isl_set *context);
1927 __isl_give isl_union_set *isl_union_set_gist(
1928 __isl_take isl_union_set *uset,
1929 __isl_take isl_union_set *context);
1930 __isl_give isl_basic_map *isl_basic_map_gist(
1931 __isl_take isl_basic_map *bmap,
1932 __isl_take isl_basic_map *context);
1933 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1934 __isl_take isl_map *context);
1935 __isl_give isl_union_map *isl_union_map_gist(
1936 __isl_take isl_union_map *umap,
1937 __isl_take isl_union_map *context);
1939 The gist operation returns a set or relation that has the
1940 same intersection with the context as the input set or relation.
1941 Any implicit equality in the intersection is made explicit in the result,
1942 while all inequalities that are redundant with respect to the intersection
1944 In case of union sets and relations, the gist operation is performed
1949 =head3 Lexicographic Optimization
1951 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1952 the following functions
1953 compute a set that contains the lexicographic minimum or maximum
1954 of the elements in C<set> (or C<bset>) for those values of the parameters
1955 that satisfy C<dom>.
1956 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1957 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1959 In other words, the union of the parameter values
1960 for which the result is non-empty and of C<*empty>
1963 __isl_give isl_set *isl_basic_set_partial_lexmin(
1964 __isl_take isl_basic_set *bset,
1965 __isl_take isl_basic_set *dom,
1966 __isl_give isl_set **empty);
1967 __isl_give isl_set *isl_basic_set_partial_lexmax(
1968 __isl_take isl_basic_set *bset,
1969 __isl_take isl_basic_set *dom,
1970 __isl_give isl_set **empty);
1971 __isl_give isl_set *isl_set_partial_lexmin(
1972 __isl_take isl_set *set, __isl_take isl_set *dom,
1973 __isl_give isl_set **empty);
1974 __isl_give isl_set *isl_set_partial_lexmax(
1975 __isl_take isl_set *set, __isl_take isl_set *dom,
1976 __isl_give isl_set **empty);
1978 Given a (basic) set C<set> (or C<bset>), the following functions simply
1979 return a set containing the lexicographic minimum or maximum
1980 of the elements in C<set> (or C<bset>).
1981 In case of union sets, the optimum is computed per space.
1983 __isl_give isl_set *isl_basic_set_lexmin(
1984 __isl_take isl_basic_set *bset);
1985 __isl_give isl_set *isl_basic_set_lexmax(
1986 __isl_take isl_basic_set *bset);
1987 __isl_give isl_set *isl_set_lexmin(
1988 __isl_take isl_set *set);
1989 __isl_give isl_set *isl_set_lexmax(
1990 __isl_take isl_set *set);
1991 __isl_give isl_union_set *isl_union_set_lexmin(
1992 __isl_take isl_union_set *uset);
1993 __isl_give isl_union_set *isl_union_set_lexmax(
1994 __isl_take isl_union_set *uset);
1996 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1997 the following functions
1998 compute a relation that maps each element of C<dom>
1999 to the single lexicographic minimum or maximum
2000 of the elements that are associated to that same
2001 element in C<map> (or C<bmap>).
2002 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2003 that contains the elements in C<dom> that do not map
2004 to any elements in C<map> (or C<bmap>).
2005 In other words, the union of the domain of the result and of C<*empty>
2008 __isl_give isl_map *isl_basic_map_partial_lexmax(
2009 __isl_take isl_basic_map *bmap,
2010 __isl_take isl_basic_set *dom,
2011 __isl_give isl_set **empty);
2012 __isl_give isl_map *isl_basic_map_partial_lexmin(
2013 __isl_take isl_basic_map *bmap,
2014 __isl_take isl_basic_set *dom,
2015 __isl_give isl_set **empty);
2016 __isl_give isl_map *isl_map_partial_lexmax(
2017 __isl_take isl_map *map, __isl_take isl_set *dom,
2018 __isl_give isl_set **empty);
2019 __isl_give isl_map *isl_map_partial_lexmin(
2020 __isl_take isl_map *map, __isl_take isl_set *dom,
2021 __isl_give isl_set **empty);
2023 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2024 return a map mapping each element in the domain of
2025 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2026 of all elements associated to that element.
2027 In case of union relations, the optimum is computed per space.
2029 __isl_give isl_map *isl_basic_map_lexmin(
2030 __isl_take isl_basic_map *bmap);
2031 __isl_give isl_map *isl_basic_map_lexmax(
2032 __isl_take isl_basic_map *bmap);
2033 __isl_give isl_map *isl_map_lexmin(
2034 __isl_take isl_map *map);
2035 __isl_give isl_map *isl_map_lexmax(
2036 __isl_take isl_map *map);
2037 __isl_give isl_union_map *isl_union_map_lexmin(
2038 __isl_take isl_union_map *umap);
2039 __isl_give isl_union_map *isl_union_map_lexmax(
2040 __isl_take isl_union_map *umap);
2044 Lists are defined over several element types, including
2045 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2046 Here we take lists of C<isl_set>s as an example.
2047 Lists can be created, copied and freed using the following functions.
2049 #include <isl/list.h>
2050 __isl_give isl_set_list *isl_set_list_alloc(
2051 isl_ctx *ctx, int n);
2052 __isl_give isl_set_list *isl_set_list_copy(
2053 __isl_keep isl_set_list *list);
2054 __isl_give isl_set_list *isl_set_list_add(
2055 __isl_take isl_set_list *list,
2056 __isl_take isl_set *el);
2057 void isl_set_list_free(__isl_take isl_set_list *list);
2059 C<isl_set_list_alloc> creates an empty list with a capacity for
2062 Lists can be inspected using the following functions.
2064 #include <isl/list.h>
2065 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2066 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2067 __isl_give struct isl_set *isl_set_list_get_set(
2068 __isl_keep isl_set_list *list, int index);
2069 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2070 int (*fn)(__isl_take struct isl_set *el, void *user),
2073 Lists can be printed using
2075 #include <isl/list.h>
2076 __isl_give isl_printer *isl_printer_print_set_list(
2077 __isl_take isl_printer *p,
2078 __isl_keep isl_set_list *list);
2082 Matrices can be created, copied and freed using the following functions.
2084 #include <isl/mat.h>
2085 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2086 unsigned n_row, unsigned n_col);
2087 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2088 void isl_mat_free(__isl_take isl_mat *mat);
2090 Note that the elements of a newly created matrix may have arbitrary values.
2091 The elements can be changed and inspected using the following functions.
2093 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2094 int isl_mat_rows(__isl_keep isl_mat *mat);
2095 int isl_mat_cols(__isl_keep isl_mat *mat);
2096 int isl_mat_get_element(__isl_keep isl_mat *mat,
2097 int row, int col, isl_int *v);
2098 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2099 int row, int col, isl_int v);
2100 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2101 int row, int col, int v);
2103 C<isl_mat_get_element> will return a negative value if anything went wrong.
2104 In that case, the value of C<*v> is undefined.
2106 The following function can be used to compute the (right) inverse
2107 of a matrix, i.e., a matrix such that the product of the original
2108 and the inverse (in that order) is a multiple of the identity matrix.
2109 The input matrix is assumed to be of full row-rank.
2111 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2113 The following function can be used to compute the (right) kernel
2114 (or null space) of a matrix, i.e., a matrix such that the product of
2115 the original and the kernel (in that order) is the zero matrix.
2117 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2119 =head2 Quasi Affine Expressions
2121 The zero quasi affine expression can be created using
2123 __isl_give isl_aff *isl_aff_zero(
2124 __isl_take isl_local_space *ls);
2126 Quasi affine expressions can be copied and free using
2128 #include <isl/aff.h>
2129 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2130 void *isl_aff_free(__isl_take isl_aff *aff);
2132 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2133 using the following function. The constraint is required to have
2134 a non-zero coefficient for the specified dimension.
2136 #include <isl/constraint.h>
2137 __isl_give isl_aff *isl_constraint_get_bound(
2138 __isl_keep isl_constraint *constraint,
2139 enum isl_dim_type type, int pos);
2141 Conversely, an equality constraint equating
2142 the affine expression to zero or an inequality constraint enforcing
2143 the affine expression to be non-negative, can be constructed using
2145 __isl_give isl_constraint *isl_equality_from_aff(
2146 __isl_take isl_aff *aff);
2147 __isl_give isl_constraint *isl_inequality_from_aff(
2148 __isl_take isl_aff *aff);
2150 The expression can be inspected using
2152 #include <isl/aff.h>
2153 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2154 int isl_aff_dim(__isl_keep isl_aff *aff,
2155 enum isl_dim_type type);
2156 __isl_give isl_local_space *isl_aff_get_local_space(
2157 __isl_keep isl_aff *aff);
2158 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2159 enum isl_dim_type type, unsigned pos);
2160 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2162 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2163 enum isl_dim_type type, int pos, isl_int *v);
2164 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2166 __isl_give isl_div *isl_aff_get_div(
2167 __isl_keep isl_aff *aff, int pos);
2169 It can be modified using
2171 #include <isl/aff.h>
2172 __isl_give isl_aff *isl_aff_set_constant(
2173 __isl_take isl_aff *aff, isl_int v);
2174 __isl_give isl_aff *isl_aff_set_constant_si(
2175 __isl_take isl_aff *aff, int v);
2176 __isl_give isl_aff *isl_aff_set_coefficient(
2177 __isl_take isl_aff *aff,
2178 enum isl_dim_type type, int pos, isl_int v);
2179 __isl_give isl_aff *isl_aff_set_coefficient_si(
2180 __isl_take isl_aff *aff,
2181 enum isl_dim_type type, int pos, int v);
2182 __isl_give isl_aff *isl_aff_set_denominator(
2183 __isl_take isl_aff *aff, isl_int v);
2185 __isl_give isl_aff *isl_aff_add_constant(
2186 __isl_take isl_aff *aff, isl_int v);
2187 __isl_give isl_aff *isl_aff_add_coefficient_si(
2188 __isl_take isl_aff *aff,
2189 enum isl_dim_type type, int pos, int v);
2191 Note that the C<set_constant> and C<set_coefficient> functions
2192 set the I<numerator> of the constant or coefficient, while
2193 C<add_constant> and C<add_coefficient> add an integer value to
2194 the possibly rational constant or coefficient.
2198 #include <isl/aff.h>
2199 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2200 __isl_take isl_aff *aff2);
2201 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2202 __isl_take isl_aff *aff2);
2203 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2204 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2205 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2207 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2210 An expression can be printed using
2212 #include <isl/aff.h>
2213 __isl_give isl_printer *isl_printer_print_aff(
2214 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2218 Points are elements of a set. They can be used to construct
2219 simple sets (boxes) or they can be used to represent the
2220 individual elements of a set.
2221 The zero point (the origin) can be created using
2223 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2225 The coordinates of a point can be inspected, set and changed
2228 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2229 enum isl_dim_type type, int pos, isl_int *v);
2230 __isl_give isl_point *isl_point_set_coordinate(
2231 __isl_take isl_point *pnt,
2232 enum isl_dim_type type, int pos, isl_int v);
2234 __isl_give isl_point *isl_point_add_ui(
2235 __isl_take isl_point *pnt,
2236 enum isl_dim_type type, int pos, unsigned val);
2237 __isl_give isl_point *isl_point_sub_ui(
2238 __isl_take isl_point *pnt,
2239 enum isl_dim_type type, int pos, unsigned val);
2241 Points can be copied or freed using
2243 __isl_give isl_point *isl_point_copy(
2244 __isl_keep isl_point *pnt);
2245 void isl_point_free(__isl_take isl_point *pnt);
2247 A singleton set can be created from a point using
2249 __isl_give isl_basic_set *isl_basic_set_from_point(
2250 __isl_take isl_point *pnt);
2251 __isl_give isl_set *isl_set_from_point(
2252 __isl_take isl_point *pnt);
2254 and a box can be created from two opposite extremal points using
2256 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2257 __isl_take isl_point *pnt1,
2258 __isl_take isl_point *pnt2);
2259 __isl_give isl_set *isl_set_box_from_points(
2260 __isl_take isl_point *pnt1,
2261 __isl_take isl_point *pnt2);
2263 All elements of a B<bounded> (union) set can be enumerated using
2264 the following functions.
2266 int isl_set_foreach_point(__isl_keep isl_set *set,
2267 int (*fn)(__isl_take isl_point *pnt, void *user),
2269 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2270 int (*fn)(__isl_take isl_point *pnt, void *user),
2273 The function C<fn> is called for each integer point in
2274 C<set> with as second argument the last argument of
2275 the C<isl_set_foreach_point> call. The function C<fn>
2276 should return C<0> on success and C<-1> on failure.
2277 In the latter case, C<isl_set_foreach_point> will stop
2278 enumerating and return C<-1> as well.
2279 If the enumeration is performed successfully and to completion,
2280 then C<isl_set_foreach_point> returns C<0>.
2282 To obtain a single point of a (basic) set, use
2284 __isl_give isl_point *isl_basic_set_sample_point(
2285 __isl_take isl_basic_set *bset);
2286 __isl_give isl_point *isl_set_sample_point(
2287 __isl_take isl_set *set);
2289 If C<set> does not contain any (integer) points, then the
2290 resulting point will be ``void'', a property that can be
2293 int isl_point_is_void(__isl_keep isl_point *pnt);
2295 =head2 Piecewise Quasipolynomials
2297 A piecewise quasipolynomial is a particular kind of function that maps
2298 a parametric point to a rational value.
2299 More specifically, a quasipolynomial is a polynomial expression in greatest
2300 integer parts of affine expressions of parameters and variables.
2301 A piecewise quasipolynomial is a subdivision of a given parametric
2302 domain into disjoint cells with a quasipolynomial associated to
2303 each cell. The value of the piecewise quasipolynomial at a given
2304 point is the value of the quasipolynomial associated to the cell
2305 that contains the point. Outside of the union of cells,
2306 the value is assumed to be zero.
2307 For example, the piecewise quasipolynomial
2309 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2311 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2312 A given piecewise quasipolynomial has a fixed domain dimension.
2313 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2314 defined over different domains.
2315 Piecewise quasipolynomials are mainly used by the C<barvinok>
2316 library for representing the number of elements in a parametric set or map.
2317 For example, the piecewise quasipolynomial above represents
2318 the number of points in the map
2320 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2322 =head3 Printing (Piecewise) Quasipolynomials
2324 Quasipolynomials and piecewise quasipolynomials can be printed
2325 using the following functions.
2327 __isl_give isl_printer *isl_printer_print_qpolynomial(
2328 __isl_take isl_printer *p,
2329 __isl_keep isl_qpolynomial *qp);
2331 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2332 __isl_take isl_printer *p,
2333 __isl_keep isl_pw_qpolynomial *pwqp);
2335 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2336 __isl_take isl_printer *p,
2337 __isl_keep isl_union_pw_qpolynomial *upwqp);
2339 The output format of the printer
2340 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2341 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2343 In case of printing in C<ISL_FORMAT_C>, the user may want
2344 to set the names of all dimensions
2346 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2347 __isl_take isl_qpolynomial *qp,
2348 enum isl_dim_type type, unsigned pos,
2350 __isl_give isl_pw_qpolynomial *
2351 isl_pw_qpolynomial_set_dim_name(
2352 __isl_take isl_pw_qpolynomial *pwqp,
2353 enum isl_dim_type type, unsigned pos,
2356 =head3 Creating New (Piecewise) Quasipolynomials
2358 Some simple quasipolynomials can be created using the following functions.
2359 More complicated quasipolynomials can be created by applying
2360 operations such as addition and multiplication
2361 on the resulting quasipolynomials
2363 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2364 __isl_take isl_dim *dim);
2365 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2366 __isl_take isl_dim *dim);
2367 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2368 __isl_take isl_dim *dim);
2369 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2370 __isl_take isl_dim *dim);
2371 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2372 __isl_take isl_dim *dim);
2373 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2374 __isl_take isl_dim *dim,
2375 const isl_int n, const isl_int d);
2376 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2377 __isl_take isl_div *div);
2378 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2379 __isl_take isl_dim *dim,
2380 enum isl_dim_type type, unsigned pos);
2381 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2382 __isl_take isl_aff *aff);
2384 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2385 with a single cell can be created using the following functions.
2386 Multiple of these single cell piecewise quasipolynomials can
2387 be combined to create more complicated piecewise quasipolynomials.
2389 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2390 __isl_take isl_dim *dim);
2391 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2392 __isl_take isl_set *set,
2393 __isl_take isl_qpolynomial *qp);
2395 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2396 __isl_take isl_dim *dim);
2397 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2398 __isl_take isl_pw_qpolynomial *pwqp);
2399 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2400 __isl_take isl_union_pw_qpolynomial *upwqp,
2401 __isl_take isl_pw_qpolynomial *pwqp);
2403 Quasipolynomials can be copied and freed again using the following
2406 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2407 __isl_keep isl_qpolynomial *qp);
2408 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2410 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2411 __isl_keep isl_pw_qpolynomial *pwqp);
2412 void isl_pw_qpolynomial_free(
2413 __isl_take isl_pw_qpolynomial *pwqp);
2415 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2416 __isl_keep isl_union_pw_qpolynomial *upwqp);
2417 void isl_union_pw_qpolynomial_free(
2418 __isl_take isl_union_pw_qpolynomial *upwqp);
2420 =head3 Inspecting (Piecewise) Quasipolynomials
2422 To iterate over all piecewise quasipolynomials in a union
2423 piecewise quasipolynomial, use the following function
2425 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2426 __isl_keep isl_union_pw_qpolynomial *upwqp,
2427 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2430 To extract the piecewise quasipolynomial from a union with a given dimension
2433 __isl_give isl_pw_qpolynomial *
2434 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2435 __isl_keep isl_union_pw_qpolynomial *upwqp,
2436 __isl_take isl_dim *dim);
2438 To iterate over the cells in a piecewise quasipolynomial,
2439 use either of the following two functions
2441 int isl_pw_qpolynomial_foreach_piece(
2442 __isl_keep isl_pw_qpolynomial *pwqp,
2443 int (*fn)(__isl_take isl_set *set,
2444 __isl_take isl_qpolynomial *qp,
2445 void *user), void *user);
2446 int isl_pw_qpolynomial_foreach_lifted_piece(
2447 __isl_keep isl_pw_qpolynomial *pwqp,
2448 int (*fn)(__isl_take isl_set *set,
2449 __isl_take isl_qpolynomial *qp,
2450 void *user), void *user);
2452 As usual, the function C<fn> should return C<0> on success
2453 and C<-1> on failure. The difference between
2454 C<isl_pw_qpolynomial_foreach_piece> and
2455 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2456 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2457 compute unique representations for all existentially quantified
2458 variables and then turn these existentially quantified variables
2459 into extra set variables, adapting the associated quasipolynomial
2460 accordingly. This means that the C<set> passed to C<fn>
2461 will not have any existentially quantified variables, but that
2462 the dimensions of the sets may be different for different
2463 invocations of C<fn>.
2465 To iterate over all terms in a quasipolynomial,
2468 int isl_qpolynomial_foreach_term(
2469 __isl_keep isl_qpolynomial *qp,
2470 int (*fn)(__isl_take isl_term *term,
2471 void *user), void *user);
2473 The terms themselves can be inspected and freed using
2476 unsigned isl_term_dim(__isl_keep isl_term *term,
2477 enum isl_dim_type type);
2478 void isl_term_get_num(__isl_keep isl_term *term,
2480 void isl_term_get_den(__isl_keep isl_term *term,
2482 int isl_term_get_exp(__isl_keep isl_term *term,
2483 enum isl_dim_type type, unsigned pos);
2484 __isl_give isl_div *isl_term_get_div(
2485 __isl_keep isl_term *term, unsigned pos);
2486 void isl_term_free(__isl_take isl_term *term);
2488 Each term is a product of parameters, set variables and
2489 integer divisions. The function C<isl_term_get_exp>
2490 returns the exponent of a given dimensions in the given term.
2491 The C<isl_int>s in the arguments of C<isl_term_get_num>
2492 and C<isl_term_get_den> need to have been initialized
2493 using C<isl_int_init> before calling these functions.
2495 =head3 Properties of (Piecewise) Quasipolynomials
2497 To check whether a quasipolynomial is actually a constant,
2498 use the following function.
2500 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2501 isl_int *n, isl_int *d);
2503 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2504 then the numerator and denominator of the constant
2505 are returned in C<*n> and C<*d>, respectively.
2507 =head3 Operations on (Piecewise) Quasipolynomials
2509 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2510 __isl_take isl_qpolynomial *qp);
2511 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2512 __isl_take isl_qpolynomial *qp1,
2513 __isl_take isl_qpolynomial *qp2);
2514 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2515 __isl_take isl_qpolynomial *qp1,
2516 __isl_take isl_qpolynomial *qp2);
2517 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2518 __isl_take isl_qpolynomial *qp1,
2519 __isl_take isl_qpolynomial *qp2);
2520 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2521 __isl_take isl_qpolynomial *qp, unsigned exponent);
2523 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2524 __isl_take isl_pw_qpolynomial *pwqp1,
2525 __isl_take isl_pw_qpolynomial *pwqp2);
2526 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2527 __isl_take isl_pw_qpolynomial *pwqp1,
2528 __isl_take isl_pw_qpolynomial *pwqp2);
2529 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2530 __isl_take isl_pw_qpolynomial *pwqp1,
2531 __isl_take isl_pw_qpolynomial *pwqp2);
2532 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2533 __isl_take isl_pw_qpolynomial *pwqp);
2534 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2535 __isl_take isl_pw_qpolynomial *pwqp1,
2536 __isl_take isl_pw_qpolynomial *pwqp2);
2538 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2539 __isl_take isl_union_pw_qpolynomial *upwqp1,
2540 __isl_take isl_union_pw_qpolynomial *upwqp2);
2541 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2542 __isl_take isl_union_pw_qpolynomial *upwqp1,
2543 __isl_take isl_union_pw_qpolynomial *upwqp2);
2544 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2545 __isl_take isl_union_pw_qpolynomial *upwqp1,
2546 __isl_take isl_union_pw_qpolynomial *upwqp2);
2548 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2549 __isl_take isl_pw_qpolynomial *pwqp,
2550 __isl_take isl_point *pnt);
2552 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2553 __isl_take isl_union_pw_qpolynomial *upwqp,
2554 __isl_take isl_point *pnt);
2556 __isl_give isl_set *isl_pw_qpolynomial_domain(
2557 __isl_take isl_pw_qpolynomial *pwqp);
2558 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2559 __isl_take isl_pw_qpolynomial *pwpq,
2560 __isl_take isl_set *set);
2562 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2563 __isl_take isl_union_pw_qpolynomial *upwqp);
2564 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2565 __isl_take isl_union_pw_qpolynomial *upwpq,
2566 __isl_take isl_union_set *uset);
2568 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2569 __isl_take isl_qpolynomial *qp,
2570 __isl_take isl_dim *model);
2572 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2573 __isl_take isl_union_pw_qpolynomial *upwqp);
2575 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2576 __isl_take isl_qpolynomial *qp,
2577 __isl_take isl_set *context);
2579 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2580 __isl_take isl_pw_qpolynomial *pwqp,
2581 __isl_take isl_set *context);
2583 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2584 __isl_take isl_union_pw_qpolynomial *upwqp,
2585 __isl_take isl_union_set *context);
2587 The gist operation applies the gist operation to each of
2588 the cells in the domain of the input piecewise quasipolynomial.
2589 The context is also exploited
2590 to simplify the quasipolynomials associated to each cell.
2592 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2593 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2594 __isl_give isl_union_pw_qpolynomial *
2595 isl_union_pw_qpolynomial_to_polynomial(
2596 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2598 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2599 the polynomial will be an overapproximation. If C<sign> is negative,
2600 it will be an underapproximation. If C<sign> is zero, the approximation
2601 will lie somewhere in between.
2603 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2605 A piecewise quasipolynomial reduction is a piecewise
2606 reduction (or fold) of quasipolynomials.
2607 In particular, the reduction can be maximum or a minimum.
2608 The objects are mainly used to represent the result of
2609 an upper or lower bound on a quasipolynomial over its domain,
2610 i.e., as the result of the following function.
2612 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2613 __isl_take isl_pw_qpolynomial *pwqp,
2614 enum isl_fold type, int *tight);
2616 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2617 __isl_take isl_union_pw_qpolynomial *upwqp,
2618 enum isl_fold type, int *tight);
2620 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2621 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2622 is the returned bound is known be tight, i.e., for each value
2623 of the parameters there is at least
2624 one element in the domain that reaches the bound.
2625 If the domain of C<pwqp> is not wrapping, then the bound is computed
2626 over all elements in that domain and the result has a purely parametric
2627 domain. If the domain of C<pwqp> is wrapping, then the bound is
2628 computed over the range of the wrapped relation. The domain of the
2629 wrapped relation becomes the domain of the result.
2631 A (piecewise) quasipolynomial reduction can be copied or freed using the
2632 following functions.
2634 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2635 __isl_keep isl_qpolynomial_fold *fold);
2636 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2637 __isl_keep isl_pw_qpolynomial_fold *pwf);
2638 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2639 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2640 void isl_qpolynomial_fold_free(
2641 __isl_take isl_qpolynomial_fold *fold);
2642 void isl_pw_qpolynomial_fold_free(
2643 __isl_take isl_pw_qpolynomial_fold *pwf);
2644 void isl_union_pw_qpolynomial_fold_free(
2645 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2647 =head3 Printing Piecewise Quasipolynomial Reductions
2649 Piecewise quasipolynomial reductions can be printed
2650 using the following function.
2652 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2653 __isl_take isl_printer *p,
2654 __isl_keep isl_pw_qpolynomial_fold *pwf);
2655 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2656 __isl_take isl_printer *p,
2657 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2659 For C<isl_printer_print_pw_qpolynomial_fold>,
2660 output format of the printer
2661 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2662 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2663 output format of the printer
2664 needs to be set to C<ISL_FORMAT_ISL>.
2665 In case of printing in C<ISL_FORMAT_C>, the user may want
2666 to set the names of all dimensions
2668 __isl_give isl_pw_qpolynomial_fold *
2669 isl_pw_qpolynomial_fold_set_dim_name(
2670 __isl_take isl_pw_qpolynomial_fold *pwf,
2671 enum isl_dim_type type, unsigned pos,
2674 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2676 To iterate over all piecewise quasipolynomial reductions in a union
2677 piecewise quasipolynomial reduction, use the following function
2679 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2680 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2681 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2682 void *user), void *user);
2684 To iterate over the cells in a piecewise quasipolynomial reduction,
2685 use either of the following two functions
2687 int isl_pw_qpolynomial_fold_foreach_piece(
2688 __isl_keep isl_pw_qpolynomial_fold *pwf,
2689 int (*fn)(__isl_take isl_set *set,
2690 __isl_take isl_qpolynomial_fold *fold,
2691 void *user), void *user);
2692 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2693 __isl_keep isl_pw_qpolynomial_fold *pwf,
2694 int (*fn)(__isl_take isl_set *set,
2695 __isl_take isl_qpolynomial_fold *fold,
2696 void *user), void *user);
2698 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2699 of the difference between these two functions.
2701 To iterate over all quasipolynomials in a reduction, use
2703 int isl_qpolynomial_fold_foreach_qpolynomial(
2704 __isl_keep isl_qpolynomial_fold *fold,
2705 int (*fn)(__isl_take isl_qpolynomial *qp,
2706 void *user), void *user);
2708 =head3 Operations on Piecewise Quasipolynomial Reductions
2710 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2711 __isl_take isl_pw_qpolynomial_fold *pwf1,
2712 __isl_take isl_pw_qpolynomial_fold *pwf2);
2714 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2715 __isl_take isl_pw_qpolynomial_fold *pwf1,
2716 __isl_take isl_pw_qpolynomial_fold *pwf2);
2718 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2719 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2720 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2722 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2723 __isl_take isl_pw_qpolynomial_fold *pwf,
2724 __isl_take isl_point *pnt);
2726 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2727 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2728 __isl_take isl_point *pnt);
2730 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2731 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2732 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2733 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2734 __isl_take isl_union_set *uset);
2736 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2737 __isl_take isl_pw_qpolynomial_fold *pwf);
2739 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2740 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2742 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2743 __isl_take isl_pw_qpolynomial_fold *pwf,
2744 __isl_take isl_set *context);
2746 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2747 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2748 __isl_take isl_union_set *context);
2750 The gist operation applies the gist operation to each of
2751 the cells in the domain of the input piecewise quasipolynomial reduction.
2752 In future, the operation will also exploit the context
2753 to simplify the quasipolynomial reductions associated to each cell.
2755 __isl_give isl_pw_qpolynomial_fold *
2756 isl_set_apply_pw_qpolynomial_fold(
2757 __isl_take isl_set *set,
2758 __isl_take isl_pw_qpolynomial_fold *pwf,
2760 __isl_give isl_pw_qpolynomial_fold *
2761 isl_map_apply_pw_qpolynomial_fold(
2762 __isl_take isl_map *map,
2763 __isl_take isl_pw_qpolynomial_fold *pwf,
2765 __isl_give isl_union_pw_qpolynomial_fold *
2766 isl_union_set_apply_union_pw_qpolynomial_fold(
2767 __isl_take isl_union_set *uset,
2768 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2770 __isl_give isl_union_pw_qpolynomial_fold *
2771 isl_union_map_apply_union_pw_qpolynomial_fold(
2772 __isl_take isl_union_map *umap,
2773 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2776 The functions taking a map
2777 compose the given map with the given piecewise quasipolynomial reduction.
2778 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2779 over all elements in the intersection of the range of the map
2780 and the domain of the piecewise quasipolynomial reduction
2781 as a function of an element in the domain of the map.
2782 The functions taking a set compute a bound over all elements in the
2783 intersection of the set and the domain of the
2784 piecewise quasipolynomial reduction.
2786 =head2 Dependence Analysis
2788 C<isl> contains specialized functionality for performing
2789 array dataflow analysis. That is, given a I<sink> access relation
2790 and a collection of possible I<source> access relations,
2791 C<isl> can compute relations that describe
2792 for each iteration of the sink access, which iteration
2793 of which of the source access relations was the last
2794 to access the same data element before the given iteration
2796 To compute standard flow dependences, the sink should be
2797 a read, while the sources should be writes.
2798 If any of the source accesses are marked as being I<may>
2799 accesses, then there will be a dependence to the last
2800 I<must> access B<and> to any I<may> access that follows
2801 this last I<must> access.
2802 In particular, if I<all> sources are I<may> accesses,
2803 then memory based dependence analysis is performed.
2804 If, on the other hand, all sources are I<must> accesses,
2805 then value based dependence analysis is performed.
2807 #include <isl/flow.h>
2809 typedef int (*isl_access_level_before)(void *first, void *second);
2811 __isl_give isl_access_info *isl_access_info_alloc(
2812 __isl_take isl_map *sink,
2813 void *sink_user, isl_access_level_before fn,
2815 __isl_give isl_access_info *isl_access_info_add_source(
2816 __isl_take isl_access_info *acc,
2817 __isl_take isl_map *source, int must,
2819 void isl_access_info_free(__isl_take isl_access_info *acc);
2821 __isl_give isl_flow *isl_access_info_compute_flow(
2822 __isl_take isl_access_info *acc);
2824 int isl_flow_foreach(__isl_keep isl_flow *deps,
2825 int (*fn)(__isl_take isl_map *dep, int must,
2826 void *dep_user, void *user),
2828 __isl_give isl_map *isl_flow_get_no_source(
2829 __isl_keep isl_flow *deps, int must);
2830 void isl_flow_free(__isl_take isl_flow *deps);
2832 The function C<isl_access_info_compute_flow> performs the actual
2833 dependence analysis. The other functions are used to construct
2834 the input for this function or to read off the output.
2836 The input is collected in an C<isl_access_info>, which can
2837 be created through a call to C<isl_access_info_alloc>.
2838 The arguments to this functions are the sink access relation
2839 C<sink>, a token C<sink_user> used to identify the sink
2840 access to the user, a callback function for specifying the
2841 relative order of source and sink accesses, and the number
2842 of source access relations that will be added.
2843 The callback function has type C<int (*)(void *first, void *second)>.
2844 The function is called with two user supplied tokens identifying
2845 either a source or the sink and it should return the shared nesting
2846 level and the relative order of the two accesses.
2847 In particular, let I<n> be the number of loops shared by
2848 the two accesses. If C<first> precedes C<second> textually,
2849 then the function should return I<2 * n + 1>; otherwise,
2850 it should return I<2 * n>.
2851 The sources can be added to the C<isl_access_info> by performing
2852 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2853 C<must> indicates whether the source is a I<must> access
2854 or a I<may> access. Note that a multi-valued access relation
2855 should only be marked I<must> if every iteration in the domain
2856 of the relation accesses I<all> elements in its image.
2857 The C<source_user> token is again used to identify
2858 the source access. The range of the source access relation
2859 C<source> should have the same dimension as the range
2860 of the sink access relation.
2861 The C<isl_access_info_free> function should usually not be
2862 called explicitly, because it is called implicitly by
2863 C<isl_access_info_compute_flow>.
2865 The result of the dependence analysis is collected in an
2866 C<isl_flow>. There may be elements of
2867 the sink access for which no preceding source access could be
2868 found or for which all preceding sources are I<may> accesses.
2869 The relations containing these elements can be obtained through
2870 calls to C<isl_flow_get_no_source>, the first with C<must> set
2871 and the second with C<must> unset.
2872 In the case of standard flow dependence analysis,
2873 with the sink a read and the sources I<must> writes,
2874 the first relation corresponds to the reads from uninitialized
2875 array elements and the second relation is empty.
2876 The actual flow dependences can be extracted using
2877 C<isl_flow_foreach>. This function will call the user-specified
2878 callback function C<fn> for each B<non-empty> dependence between
2879 a source and the sink. The callback function is called
2880 with four arguments, the actual flow dependence relation
2881 mapping source iterations to sink iterations, a boolean that
2882 indicates whether it is a I<must> or I<may> dependence, a token
2883 identifying the source and an additional C<void *> with value
2884 equal to the third argument of the C<isl_flow_foreach> call.
2885 A dependence is marked I<must> if it originates from a I<must>
2886 source and if it is not followed by any I<may> sources.
2888 After finishing with an C<isl_flow>, the user should call
2889 C<isl_flow_free> to free all associated memory.
2891 A higher-level interface to dependence analysis is provided
2892 by the following function.
2894 #include <isl/flow.h>
2896 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2897 __isl_take isl_union_map *must_source,
2898 __isl_take isl_union_map *may_source,
2899 __isl_take isl_union_map *schedule,
2900 __isl_give isl_union_map **must_dep,
2901 __isl_give isl_union_map **may_dep,
2902 __isl_give isl_union_map **must_no_source,
2903 __isl_give isl_union_map **may_no_source);
2905 The arrays are identified by the tuple names of the ranges
2906 of the accesses. The iteration domains by the tuple names
2907 of the domains of the accesses and of the schedule.
2908 The relative order of the iteration domains is given by the
2909 schedule. The relations returned through C<must_no_source>
2910 and C<may_no_source> are subsets of C<sink>.
2911 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2912 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2913 any of the other arguments is treated as an error.
2917 B<The functionality described in this section is fairly new
2918 and may be subject to change.>
2920 The following function can be used to compute a schedule
2921 for a union of domains. The generated schedule respects
2922 all C<validity> dependences. That is, all dependence distances
2923 over these dependences in the scheduled space are lexicographically
2924 positive. The generated schedule schedule also tries to minimize
2925 the dependence distances over C<proximity> dependences.
2926 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2927 for groups of domains where the dependence distances have only
2928 non-negative values.
2929 The algorithm used to construct the schedule is similar to that
2932 #include <isl/schedule.h>
2933 __isl_give isl_schedule *isl_union_set_compute_schedule(
2934 __isl_take isl_union_set *domain,
2935 __isl_take isl_union_map *validity,
2936 __isl_take isl_union_map *proximity);
2937 void *isl_schedule_free(__isl_take isl_schedule *sched);
2939 A mapping from the domains to the scheduled space can be obtained
2940 from an C<isl_schedule> using the following function.
2942 __isl_give isl_union_map *isl_schedule_get_map(
2943 __isl_keep isl_schedule *sched);
2945 A representation of the schedule can be printed using
2947 __isl_give isl_printer *isl_printer_print_schedule(
2948 __isl_take isl_printer *p,
2949 __isl_keep isl_schedule *schedule);
2951 A representation of the schedule as a forest of bands can be obtained
2952 using the following function.
2954 __isl_give isl_band_list *isl_schedule_get_band_forest(
2955 __isl_keep isl_schedule *schedule);
2957 The list can be manipulated as explained in L<"Lists">.
2958 The bands inside the list can be copied and freed using the following
2961 #include <isl/band.h>
2962 __isl_give isl_band *isl_band_copy(
2963 __isl_keep isl_band *band);
2964 void *isl_band_free(__isl_take isl_band *band);
2966 Each band contains zero or more scheduling dimensions.
2967 These are referred to as the members of the band.
2968 The section of the schedule that corresponds to the band is
2969 referred to as the partial schedule of the band.
2970 For those nodes that participate in a band, the outer scheduling
2971 dimensions form the prefix schedule, while the inner scheduling
2972 dimensions form the suffix schedule.
2973 That is, if we take a cut of the band forest, then the union of
2974 the concatenations of the prefix, partial and suffix schedules of
2975 each band in the cut is equal to the entire schedule (modulo
2976 some possible padding at the end with zero scheduling dimensions).
2977 The properties of a band can be inspected using the following functions.
2979 #include <isl/band.h>
2980 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
2982 int isl_band_has_children(__isl_keep isl_band *band);
2983 __isl_give isl_band_list *isl_band_get_children(
2984 __isl_keep isl_band *band);
2986 __isl_give isl_union_map *isl_band_get_prefix_schedule(
2987 __isl_keep isl_band *band);
2988 __isl_give isl_union_map *isl_band_get_partial_schedule(
2989 __isl_keep isl_band *band);
2990 __isl_give isl_union_map *isl_band_get_suffix_schedule(
2991 __isl_keep isl_band *band);
2993 int isl_band_n_member(__isl_keep isl_band *band);
2994 int isl_band_member_is_parallel(__isl_keep isl_band *band,
2997 Note that a scheduling dimension is considered parallel if it
2998 does not carry any proximity dependences.
3000 A representation of the band can be printed using
3002 #include <isl/band.h>
3003 __isl_give isl_printer *isl_printer_print_band(
3004 __isl_take isl_printer *p,
3005 __isl_keep isl_band *band);
3007 Alternatively, the schedule mapping
3008 can also be obtained in pieces using the following functions.
3010 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3011 __isl_give isl_union_map *isl_schedule_get_band(
3012 __isl_keep isl_schedule *sched, unsigned band);
3014 C<isl_schedule_n_band> returns the maximal number of bands.
3015 C<isl_schedule_get_band> returns a union of mappings from a domain to
3016 the band of consecutive schedule dimensions with the given sequence
3017 number for that domain. Bands with the same sequence number but for
3018 different domains may be completely unrelated.
3019 Within a band, the corresponding coordinates of the distance vectors
3020 are all non-negative, assuming that the coordinates for all previous
3023 =head2 Parametric Vertex Enumeration
3025 The parametric vertex enumeration described in this section
3026 is mainly intended to be used internally and by the C<barvinok>
3029 #include <isl/vertices.h>
3030 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3031 __isl_keep isl_basic_set *bset);
3033 The function C<isl_basic_set_compute_vertices> performs the
3034 actual computation of the parametric vertices and the chamber
3035 decomposition and store the result in an C<isl_vertices> object.
3036 This information can be queried by either iterating over all
3037 the vertices or iterating over all the chambers or cells
3038 and then iterating over all vertices that are active on the chamber.
3040 int isl_vertices_foreach_vertex(
3041 __isl_keep isl_vertices *vertices,
3042 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3045 int isl_vertices_foreach_cell(
3046 __isl_keep isl_vertices *vertices,
3047 int (*fn)(__isl_take isl_cell *cell, void *user),
3049 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3050 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3053 Other operations that can be performed on an C<isl_vertices> object are
3056 isl_ctx *isl_vertices_get_ctx(
3057 __isl_keep isl_vertices *vertices);
3058 int isl_vertices_get_n_vertices(
3059 __isl_keep isl_vertices *vertices);
3060 void isl_vertices_free(__isl_take isl_vertices *vertices);
3062 Vertices can be inspected and destroyed using the following functions.
3064 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3065 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3066 __isl_give isl_basic_set *isl_vertex_get_domain(
3067 __isl_keep isl_vertex *vertex);
3068 __isl_give isl_basic_set *isl_vertex_get_expr(
3069 __isl_keep isl_vertex *vertex);
3070 void isl_vertex_free(__isl_take isl_vertex *vertex);
3072 C<isl_vertex_get_expr> returns a singleton parametric set describing
3073 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3075 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3076 B<rational> basic sets, so they should mainly be used for inspection
3077 and should not be mixed with integer sets.
3079 Chambers can be inspected and destroyed using the following functions.
3081 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3082 __isl_give isl_basic_set *isl_cell_get_domain(
3083 __isl_keep isl_cell *cell);
3084 void isl_cell_free(__isl_take isl_cell *cell);
3088 Although C<isl> is mainly meant to be used as a library,
3089 it also contains some basic applications that use some
3090 of the functionality of C<isl>.
3091 The input may be specified in either the L<isl format>
3092 or the L<PolyLib format>.
3094 =head2 C<isl_polyhedron_sample>
3096 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3097 an integer element of the polyhedron, if there is any.
3098 The first column in the output is the denominator and is always
3099 equal to 1. If the polyhedron contains no integer points,
3100 then a vector of length zero is printed.
3104 C<isl_pip> takes the same input as the C<example> program
3105 from the C<piplib> distribution, i.e., a set of constraints
3106 on the parameters, a line containing only -1 and finally a set
3107 of constraints on a parametric polyhedron.
3108 The coefficients of the parameters appear in the last columns
3109 (but before the final constant column).
3110 The output is the lexicographic minimum of the parametric polyhedron.
3111 As C<isl> currently does not have its own output format, the output
3112 is just a dump of the internal state.
3114 =head2 C<isl_polyhedron_minimize>
3116 C<isl_polyhedron_minimize> computes the minimum of some linear
3117 or affine objective function over the integer points in a polyhedron.
3118 If an affine objective function
3119 is given, then the constant should appear in the last column.
3121 =head2 C<isl_polytope_scan>
3123 Given a polytope, C<isl_polytope_scan> prints
3124 all integer points in the polytope.