3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
477 __isl_keep isl_pw_qpolynomial *pwqp);
478 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
479 __isl_keep isl_union_pw_qpolynomial *upwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
481 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
484 __isl_give isl_dim *isl_aff_get_dim(
485 __isl_keep isl_aff *aff);
487 The names of the individual dimensions may be set or read off
488 using the following functions.
491 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
492 enum isl_dim_type type, unsigned pos,
493 __isl_keep const char *name);
494 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
495 enum isl_dim_type type, unsigned pos);
497 Note that C<isl_dim_get_name> returns a pointer to some internal
498 data structure, so the result can only be used while the
499 corresponding C<isl_dim> is alive.
500 Also note that every function that operates on two sets or relations
501 requires that both arguments have the same parameters. This also
502 means that if one of the arguments has named parameters, then the
503 other needs to have named parameters too and the names need to match.
504 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
505 have different parameters (as long as they are named), in which case
506 the result will have as parameters the union of the parameters of
509 The names of entire spaces may be set or read off
510 using the following functions.
513 __isl_give isl_dim *isl_dim_set_tuple_name(
514 __isl_take isl_dim *dim,
515 enum isl_dim_type type, const char *s);
516 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
517 enum isl_dim_type type);
519 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
520 or C<isl_dim_set>. As with C<isl_dim_get_name>,
521 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
523 Binary operations require the corresponding spaces of their arguments
524 to have the same name.
526 Spaces can be nested. In particular, the domain of a set or
527 the domain or range of a relation can be a nested relation.
528 The following functions can be used to construct and deconstruct
529 such nested dimension specifications.
532 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
533 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
534 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
536 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
537 be the dimension specification of a set, while that of
538 C<isl_dim_wrap> should be the dimension specification of a relation.
539 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
540 of a relation, while that of C<isl_dim_wrap> is the dimension specification
543 Dimension specifications can be created from other dimension
544 specifications using the following functions.
546 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
547 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
548 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
549 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
550 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
551 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
552 __isl_take isl_dim *right);
553 __isl_give isl_dim *isl_dim_align_params(
554 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
555 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
556 enum isl_dim_type type, unsigned pos, unsigned n);
557 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
558 enum isl_dim_type type, unsigned n);
559 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
560 enum isl_dim_type type, unsigned first, unsigned n);
561 __isl_give isl_dim *isl_dim_map_from_set(
562 __isl_take isl_dim *dim);
563 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
565 Note that if dimensions are added or removed from a space, then
566 the name and the internal structure are lost.
570 A local space is essentially a dimension specification with
571 zero or more existentially quantified variables.
572 The local space of a basic set or relation can be obtained
573 using the following functions.
576 __isl_give isl_local_space *isl_basic_set_get_local_space(
577 __isl_keep isl_basic_set *bset);
580 __isl_give isl_local_space *isl_basic_map_get_local_space(
581 __isl_keep isl_basic_map *bmap);
583 A new local space can be created from a dimension specification using
585 #include <isl/local_space.h>
586 __isl_give isl_local_space *isl_local_space_from_dim(
587 __isl_take isl_dim *dim);
589 They can be inspected, copied and freed using the following functions.
591 #include <isl/local_space.h>
592 isl_ctx *isl_local_space_get_ctx(
593 __isl_keep isl_local_space *ls);
594 int isl_local_space_dim(__isl_keep isl_local_space *ls,
595 enum isl_dim_type type);
596 const char *isl_local_space_get_dim_name(
597 __isl_keep isl_local_space *ls,
598 enum isl_dim_type type, unsigned pos);
599 __isl_give isl_dim *isl_local_space_get_dim(
600 __isl_keep isl_local_space *ls);
601 __isl_give isl_div *isl_local_space_get_div(
602 __isl_keep isl_local_space *ls, int pos);
603 __isl_give isl_local_space *isl_local_space_copy(
604 __isl_keep isl_local_space *ls);
605 void *isl_local_space_free(__isl_take isl_local_space *ls);
607 Local spaces can be created from other local spaces
608 using the following functions.
610 __isl_give isl_local_space *isl_local_space_from_domain(
611 __isl_take isl_local_space *ls);
612 __isl_give isl_local_space *isl_local_space_add_dim(
613 __isl_take isl_local_space *ls,
614 enum isl_dim_type type, unsigned n);
616 =head2 Input and Output
618 C<isl> supports its own input/output format, which is similar
619 to the C<Omega> format, but also supports the C<PolyLib> format
624 The C<isl> format is similar to that of C<Omega>, but has a different
625 syntax for describing the parameters and allows for the definition
626 of an existentially quantified variable as the integer division
627 of an affine expression.
628 For example, the set of integers C<i> between C<0> and C<n>
629 such that C<i % 10 <= 6> can be described as
631 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
634 A set or relation can have several disjuncts, separated
635 by the keyword C<or>. Each disjunct is either a conjunction
636 of constraints or a projection (C<exists>) of a conjunction
637 of constraints. The constraints are separated by the keyword
640 =head3 C<PolyLib> format
642 If the represented set is a union, then the first line
643 contains a single number representing the number of disjuncts.
644 Otherwise, a line containing the number C<1> is optional.
646 Each disjunct is represented by a matrix of constraints.
647 The first line contains two numbers representing
648 the number of rows and columns,
649 where the number of rows is equal to the number of constraints
650 and the number of columns is equal to two plus the number of variables.
651 The following lines contain the actual rows of the constraint matrix.
652 In each row, the first column indicates whether the constraint
653 is an equality (C<0>) or inequality (C<1>). The final column
654 corresponds to the constant term.
656 If the set is parametric, then the coefficients of the parameters
657 appear in the last columns before the constant column.
658 The coefficients of any existentially quantified variables appear
659 between those of the set variables and those of the parameters.
661 =head3 Extended C<PolyLib> format
663 The extended C<PolyLib> format is nearly identical to the
664 C<PolyLib> format. The only difference is that the line
665 containing the number of rows and columns of a constraint matrix
666 also contains four additional numbers:
667 the number of output dimensions, the number of input dimensions,
668 the number of local dimensions (i.e., the number of existentially
669 quantified variables) and the number of parameters.
670 For sets, the number of ``output'' dimensions is equal
671 to the number of set dimensions, while the number of ``input''
677 __isl_give isl_basic_set *isl_basic_set_read_from_file(
678 isl_ctx *ctx, FILE *input, int nparam);
679 __isl_give isl_basic_set *isl_basic_set_read_from_str(
680 isl_ctx *ctx, const char *str, int nparam);
681 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
682 FILE *input, int nparam);
683 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
684 const char *str, int nparam);
687 __isl_give isl_basic_map *isl_basic_map_read_from_file(
688 isl_ctx *ctx, FILE *input, int nparam);
689 __isl_give isl_basic_map *isl_basic_map_read_from_str(
690 isl_ctx *ctx, const char *str, int nparam);
691 __isl_give isl_map *isl_map_read_from_file(
692 struct isl_ctx *ctx, FILE *input, int nparam);
693 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
694 const char *str, int nparam);
696 #include <isl/union_set.h>
697 __isl_give isl_union_set *isl_union_set_read_from_file(
698 isl_ctx *ctx, FILE *input);
699 __isl_give isl_union_set *isl_union_set_read_from_str(
700 struct isl_ctx *ctx, const char *str);
702 #include <isl/union_map.h>
703 __isl_give isl_union_map *isl_union_map_read_from_file(
704 isl_ctx *ctx, FILE *input);
705 __isl_give isl_union_map *isl_union_map_read_from_str(
706 struct isl_ctx *ctx, const char *str);
708 The input format is autodetected and may be either the C<PolyLib> format
709 or the C<isl> format.
710 C<nparam> specifies how many of the final columns in
711 the C<PolyLib> format correspond to parameters.
712 If input is given in the C<isl> format, then the number
713 of parameters needs to be equal to C<nparam>.
714 If C<nparam> is negative, then any number of parameters
715 is accepted in the C<isl> format and zero parameters
716 are assumed in the C<PolyLib> format.
720 Before anything can be printed, an C<isl_printer> needs to
723 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
725 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
726 void isl_printer_free(__isl_take isl_printer *printer);
727 __isl_give char *isl_printer_get_str(
728 __isl_keep isl_printer *printer);
730 The behavior of the printer can be modified in various ways
732 __isl_give isl_printer *isl_printer_set_output_format(
733 __isl_take isl_printer *p, int output_format);
734 __isl_give isl_printer *isl_printer_set_indent(
735 __isl_take isl_printer *p, int indent);
736 __isl_give isl_printer *isl_printer_indent(
737 __isl_take isl_printer *p, int indent);
738 __isl_give isl_printer *isl_printer_set_prefix(
739 __isl_take isl_printer *p, const char *prefix);
740 __isl_give isl_printer *isl_printer_set_suffix(
741 __isl_take isl_printer *p, const char *suffix);
743 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
744 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
745 and defaults to C<ISL_FORMAT_ISL>.
746 Each line in the output is indented by C<indent> (set by
747 C<isl_printer_set_indent>) spaces
748 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
749 In the C<PolyLib> format output,
750 the coefficients of the existentially quantified variables
751 appear between those of the set variables and those
753 The function C<isl_printer_indent> increases the indentation
754 by the specified amount (which may be negative).
756 To actually print something, use
759 __isl_give isl_printer *isl_printer_print_basic_set(
760 __isl_take isl_printer *printer,
761 __isl_keep isl_basic_set *bset);
762 __isl_give isl_printer *isl_printer_print_set(
763 __isl_take isl_printer *printer,
764 __isl_keep isl_set *set);
767 __isl_give isl_printer *isl_printer_print_basic_map(
768 __isl_take isl_printer *printer,
769 __isl_keep isl_basic_map *bmap);
770 __isl_give isl_printer *isl_printer_print_map(
771 __isl_take isl_printer *printer,
772 __isl_keep isl_map *map);
774 #include <isl/union_set.h>
775 __isl_give isl_printer *isl_printer_print_union_set(
776 __isl_take isl_printer *p,
777 __isl_keep isl_union_set *uset);
779 #include <isl/union_map.h>
780 __isl_give isl_printer *isl_printer_print_union_map(
781 __isl_take isl_printer *p,
782 __isl_keep isl_union_map *umap);
784 When called on a file printer, the following function flushes
785 the file. When called on a string printer, the buffer is cleared.
787 __isl_give isl_printer *isl_printer_flush(
788 __isl_take isl_printer *p);
790 =head2 Creating New Sets and Relations
792 C<isl> has functions for creating some standard sets and relations.
796 =item * Empty sets and relations
798 __isl_give isl_basic_set *isl_basic_set_empty(
799 __isl_take isl_dim *dim);
800 __isl_give isl_basic_map *isl_basic_map_empty(
801 __isl_take isl_dim *dim);
802 __isl_give isl_set *isl_set_empty(
803 __isl_take isl_dim *dim);
804 __isl_give isl_map *isl_map_empty(
805 __isl_take isl_dim *dim);
806 __isl_give isl_union_set *isl_union_set_empty(
807 __isl_take isl_dim *dim);
808 __isl_give isl_union_map *isl_union_map_empty(
809 __isl_take isl_dim *dim);
811 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
812 is only used to specify the parameters.
814 =item * Universe sets and relations
816 __isl_give isl_basic_set *isl_basic_set_universe(
817 __isl_take isl_dim *dim);
818 __isl_give isl_basic_map *isl_basic_map_universe(
819 __isl_take isl_dim *dim);
820 __isl_give isl_set *isl_set_universe(
821 __isl_take isl_dim *dim);
822 __isl_give isl_map *isl_map_universe(
823 __isl_take isl_dim *dim);
824 __isl_give isl_union_set *isl_union_set_universe(
825 __isl_take isl_union_set *uset);
826 __isl_give isl_union_map *isl_union_map_universe(
827 __isl_take isl_union_map *umap);
829 The sets and relations constructed by the functions above
830 contain all integer values, while those constructed by the
831 functions below only contain non-negative values.
833 __isl_give isl_basic_set *isl_basic_set_nat_universe(
834 __isl_take isl_dim *dim);
835 __isl_give isl_basic_map *isl_basic_map_nat_universe(
836 __isl_take isl_dim *dim);
837 __isl_give isl_set *isl_set_nat_universe(
838 __isl_take isl_dim *dim);
839 __isl_give isl_map *isl_map_nat_universe(
840 __isl_take isl_dim *dim);
842 =item * Identity relations
844 __isl_give isl_basic_map *isl_basic_map_identity(
845 __isl_take isl_dim *dim);
846 __isl_give isl_map *isl_map_identity(
847 __isl_take isl_dim *dim);
849 The number of input and output dimensions in C<dim> needs
852 =item * Lexicographic order
854 __isl_give isl_map *isl_map_lex_lt(
855 __isl_take isl_dim *set_dim);
856 __isl_give isl_map *isl_map_lex_le(
857 __isl_take isl_dim *set_dim);
858 __isl_give isl_map *isl_map_lex_gt(
859 __isl_take isl_dim *set_dim);
860 __isl_give isl_map *isl_map_lex_ge(
861 __isl_take isl_dim *set_dim);
862 __isl_give isl_map *isl_map_lex_lt_first(
863 __isl_take isl_dim *dim, unsigned n);
864 __isl_give isl_map *isl_map_lex_le_first(
865 __isl_take isl_dim *dim, unsigned n);
866 __isl_give isl_map *isl_map_lex_gt_first(
867 __isl_take isl_dim *dim, unsigned n);
868 __isl_give isl_map *isl_map_lex_ge_first(
869 __isl_take isl_dim *dim, unsigned n);
871 The first four functions take a dimension specification for a B<set>
872 and return relations that express that the elements in the domain
873 are lexicographically less
874 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
875 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
876 than the elements in the range.
877 The last four functions take a dimension specification for a map
878 and return relations that express that the first C<n> dimensions
879 in the domain are lexicographically less
880 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
881 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
882 than the first C<n> dimensions in the range.
886 A basic set or relation can be converted to a set or relation
887 using the following functions.
889 __isl_give isl_set *isl_set_from_basic_set(
890 __isl_take isl_basic_set *bset);
891 __isl_give isl_map *isl_map_from_basic_map(
892 __isl_take isl_basic_map *bmap);
894 Sets and relations can be converted to union sets and relations
895 using the following functions.
897 __isl_give isl_union_map *isl_union_map_from_map(
898 __isl_take isl_map *map);
899 __isl_give isl_union_set *isl_union_set_from_set(
900 __isl_take isl_set *set);
902 Sets and relations can be copied and freed again using the following
905 __isl_give isl_basic_set *isl_basic_set_copy(
906 __isl_keep isl_basic_set *bset);
907 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
908 __isl_give isl_union_set *isl_union_set_copy(
909 __isl_keep isl_union_set *uset);
910 __isl_give isl_basic_map *isl_basic_map_copy(
911 __isl_keep isl_basic_map *bmap);
912 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
913 __isl_give isl_union_map *isl_union_map_copy(
914 __isl_keep isl_union_map *umap);
915 void isl_basic_set_free(__isl_take isl_basic_set *bset);
916 void isl_set_free(__isl_take isl_set *set);
917 void isl_union_set_free(__isl_take isl_union_set *uset);
918 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
919 void isl_map_free(__isl_take isl_map *map);
920 void isl_union_map_free(__isl_take isl_union_map *umap);
922 Other sets and relations can be constructed by starting
923 from a universe set or relation, adding equality and/or
924 inequality constraints and then projecting out the
925 existentially quantified variables, if any.
926 Constraints can be constructed, manipulated and
927 added to (basic) sets and relations using the following functions.
929 #include <isl/constraint.h>
930 __isl_give isl_constraint *isl_equality_alloc(
931 __isl_take isl_dim *dim);
932 __isl_give isl_constraint *isl_inequality_alloc(
933 __isl_take isl_dim *dim);
934 void isl_constraint_set_constant(
935 __isl_keep isl_constraint *constraint, isl_int v);
936 void isl_constraint_set_coefficient(
937 __isl_keep isl_constraint *constraint,
938 enum isl_dim_type type, int pos, isl_int v);
939 __isl_give isl_basic_map *isl_basic_map_add_constraint(
940 __isl_take isl_basic_map *bmap,
941 __isl_take isl_constraint *constraint);
942 __isl_give isl_basic_set *isl_basic_set_add_constraint(
943 __isl_take isl_basic_set *bset,
944 __isl_take isl_constraint *constraint);
945 __isl_give isl_map *isl_map_add_constraint(
946 __isl_take isl_map *map,
947 __isl_take isl_constraint *constraint);
948 __isl_give isl_set *isl_set_add_constraint(
949 __isl_take isl_set *set,
950 __isl_take isl_constraint *constraint);
952 For example, to create a set containing the even integers
953 between 10 and 42, you would use the following code.
957 struct isl_constraint *c;
958 struct isl_basic_set *bset;
961 dim = isl_dim_set_alloc(ctx, 0, 2);
962 bset = isl_basic_set_universe(isl_dim_copy(dim));
964 c = isl_equality_alloc(isl_dim_copy(dim));
965 isl_int_set_si(v, -1);
966 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
967 isl_int_set_si(v, 2);
968 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
969 bset = isl_basic_set_add_constraint(bset, c);
971 c = isl_inequality_alloc(isl_dim_copy(dim));
972 isl_int_set_si(v, -10);
973 isl_constraint_set_constant(c, v);
974 isl_int_set_si(v, 1);
975 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
976 bset = isl_basic_set_add_constraint(bset, c);
978 c = isl_inequality_alloc(dim);
979 isl_int_set_si(v, 42);
980 isl_constraint_set_constant(c, v);
981 isl_int_set_si(v, -1);
982 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
983 bset = isl_basic_set_add_constraint(bset, c);
985 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
991 struct isl_basic_set *bset;
992 bset = isl_basic_set_read_from_str(ctx,
993 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
995 A basic set or relation can also be constructed from two matrices
996 describing the equalities and the inequalities.
998 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
999 __isl_take isl_dim *dim,
1000 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1001 enum isl_dim_type c1,
1002 enum isl_dim_type c2, enum isl_dim_type c3,
1003 enum isl_dim_type c4);
1004 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1005 __isl_take isl_dim *dim,
1006 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1007 enum isl_dim_type c1,
1008 enum isl_dim_type c2, enum isl_dim_type c3,
1009 enum isl_dim_type c4, enum isl_dim_type c5);
1011 The C<isl_dim_type> arguments indicate the order in which
1012 different kinds of variables appear in the input matrices
1013 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1014 C<isl_dim_set> and C<isl_dim_div> for sets and
1015 of C<isl_dim_cst>, C<isl_dim_param>,
1016 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1018 A basic relation can also be constructed from an affine expression
1019 or a list of affine expressions (See L<"Quasi Affine Expressions">).
1021 __isl_give isl_basic_map *isl_basic_map_from_aff(
1022 __isl_take isl_aff *aff);
1023 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1024 __isl_take isl_dim *domain_dim,
1025 __isl_take isl_aff_list *list);
1027 The C<domain_dim> argument describes the domain of the resulting
1028 basic relation. It is required because the C<list> may consist
1029 of zero affine expressions.
1031 =head2 Inspecting Sets and Relations
1033 Usually, the user should not have to care about the actual constraints
1034 of the sets and maps, but should instead apply the abstract operations
1035 explained in the following sections.
1036 Occasionally, however, it may be required to inspect the individual
1037 coefficients of the constraints. This section explains how to do so.
1038 In these cases, it may also be useful to have C<isl> compute
1039 an explicit representation of the existentially quantified variables.
1041 __isl_give isl_set *isl_set_compute_divs(
1042 __isl_take isl_set *set);
1043 __isl_give isl_map *isl_map_compute_divs(
1044 __isl_take isl_map *map);
1045 __isl_give isl_union_set *isl_union_set_compute_divs(
1046 __isl_take isl_union_set *uset);
1047 __isl_give isl_union_map *isl_union_map_compute_divs(
1048 __isl_take isl_union_map *umap);
1050 This explicit representation defines the existentially quantified
1051 variables as integer divisions of the other variables, possibly
1052 including earlier existentially quantified variables.
1053 An explicitly represented existentially quantified variable therefore
1054 has a unique value when the values of the other variables are known.
1055 If, furthermore, the same existentials, i.e., existentials
1056 with the same explicit representations, should appear in the
1057 same order in each of the disjuncts of a set or map, then the user should call
1058 either of the following functions.
1060 __isl_give isl_set *isl_set_align_divs(
1061 __isl_take isl_set *set);
1062 __isl_give isl_map *isl_map_align_divs(
1063 __isl_take isl_map *map);
1065 Alternatively, the existentially quantified variables can be removed
1066 using the following functions, which compute an overapproximation.
1068 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1069 __isl_take isl_basic_set *bset);
1070 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1071 __isl_take isl_basic_map *bmap);
1072 __isl_give isl_set *isl_set_remove_divs(
1073 __isl_take isl_set *set);
1074 __isl_give isl_map *isl_map_remove_divs(
1075 __isl_take isl_map *map);
1077 To iterate over all the sets or maps in a union set or map, use
1079 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1080 int (*fn)(__isl_take isl_set *set, void *user),
1082 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1083 int (*fn)(__isl_take isl_map *map, void *user),
1086 The number of sets or maps in a union set or map can be obtained
1089 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1090 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1092 To extract the set or map from a union with a given dimension
1095 __isl_give isl_set *isl_union_set_extract_set(
1096 __isl_keep isl_union_set *uset,
1097 __isl_take isl_dim *dim);
1098 __isl_give isl_map *isl_union_map_extract_map(
1099 __isl_keep isl_union_map *umap,
1100 __isl_take isl_dim *dim);
1102 To iterate over all the basic sets or maps in a set or map, use
1104 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1105 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1107 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1108 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1111 The callback function C<fn> should return 0 if successful and
1112 -1 if an error occurs. In the latter case, or if any other error
1113 occurs, the above functions will return -1.
1115 It should be noted that C<isl> does not guarantee that
1116 the basic sets or maps passed to C<fn> are disjoint.
1117 If this is required, then the user should call one of
1118 the following functions first.
1120 __isl_give isl_set *isl_set_make_disjoint(
1121 __isl_take isl_set *set);
1122 __isl_give isl_map *isl_map_make_disjoint(
1123 __isl_take isl_map *map);
1125 The number of basic sets in a set can be obtained
1128 int isl_set_n_basic_set(__isl_keep isl_set *set);
1130 To iterate over the constraints of a basic set or map, use
1132 #include <isl/constraint.h>
1134 int isl_basic_map_foreach_constraint(
1135 __isl_keep isl_basic_map *bmap,
1136 int (*fn)(__isl_take isl_constraint *c, void *user),
1138 void isl_constraint_free(struct isl_constraint *c);
1140 Again, the callback function C<fn> should return 0 if successful and
1141 -1 if an error occurs. In the latter case, or if any other error
1142 occurs, the above functions will return -1.
1143 The constraint C<c> represents either an equality or an inequality.
1144 Use the following function to find out whether a constraint
1145 represents an equality. If not, it represents an inequality.
1147 int isl_constraint_is_equality(
1148 __isl_keep isl_constraint *constraint);
1150 The coefficients of the constraints can be inspected using
1151 the following functions.
1153 void isl_constraint_get_constant(
1154 __isl_keep isl_constraint *constraint, isl_int *v);
1155 void isl_constraint_get_coefficient(
1156 __isl_keep isl_constraint *constraint,
1157 enum isl_dim_type type, int pos, isl_int *v);
1158 int isl_constraint_involves_dims(
1159 __isl_keep isl_constraint *constraint,
1160 enum isl_dim_type type, unsigned first, unsigned n);
1162 The explicit representations of the existentially quantified
1163 variables can be inspected using the following functions.
1164 Note that the user is only allowed to use these functions
1165 if the inspected set or map is the result of a call
1166 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1168 __isl_give isl_div *isl_constraint_div(
1169 __isl_keep isl_constraint *constraint, int pos);
1170 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1171 void isl_div_get_constant(__isl_keep isl_div *div,
1173 void isl_div_get_denominator(__isl_keep isl_div *div,
1175 void isl_div_get_coefficient(__isl_keep isl_div *div,
1176 enum isl_dim_type type, int pos, isl_int *v);
1178 To obtain the constraints of a basic set or map in matrix
1179 form, use the following functions.
1181 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1182 __isl_keep isl_basic_set *bset,
1183 enum isl_dim_type c1, enum isl_dim_type c2,
1184 enum isl_dim_type c3, enum isl_dim_type c4);
1185 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1186 __isl_keep isl_basic_set *bset,
1187 enum isl_dim_type c1, enum isl_dim_type c2,
1188 enum isl_dim_type c3, enum isl_dim_type c4);
1189 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1190 __isl_keep isl_basic_map *bmap,
1191 enum isl_dim_type c1,
1192 enum isl_dim_type c2, enum isl_dim_type c3,
1193 enum isl_dim_type c4, enum isl_dim_type c5);
1194 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1195 __isl_keep isl_basic_map *bmap,
1196 enum isl_dim_type c1,
1197 enum isl_dim_type c2, enum isl_dim_type c3,
1198 enum isl_dim_type c4, enum isl_dim_type c5);
1200 The C<isl_dim_type> arguments dictate the order in which
1201 different kinds of variables appear in the resulting matrix
1202 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1203 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1205 The names of the domain and range spaces of a set or relation can be
1206 read off using the following functions.
1208 const char *isl_basic_set_get_tuple_name(
1209 __isl_keep isl_basic_set *bset);
1210 const char *isl_set_get_tuple_name(
1211 __isl_keep isl_set *set);
1212 const char *isl_basic_map_get_tuple_name(
1213 __isl_keep isl_basic_map *bmap,
1214 enum isl_dim_type type);
1215 const char *isl_map_get_tuple_name(
1216 __isl_keep isl_map *map,
1217 enum isl_dim_type type);
1219 As with C<isl_dim_get_tuple_name>, the value returned points to
1220 an internal data structure.
1221 The names of individual dimensions can be read off using
1222 the following functions.
1224 const char *isl_constraint_get_dim_name(
1225 __isl_keep isl_constraint *constraint,
1226 enum isl_dim_type type, unsigned pos);
1227 const char *isl_basic_set_get_dim_name(
1228 __isl_keep isl_basic_set *bset,
1229 enum isl_dim_type type, unsigned pos);
1230 const char *isl_set_get_dim_name(
1231 __isl_keep isl_set *set,
1232 enum isl_dim_type type, unsigned pos);
1233 const char *isl_basic_map_get_dim_name(
1234 __isl_keep isl_basic_map *bmap,
1235 enum isl_dim_type type, unsigned pos);
1236 const char *isl_map_get_dim_name(
1237 __isl_keep isl_map *map,
1238 enum isl_dim_type type, unsigned pos);
1240 These functions are mostly useful to obtain the names
1245 =head3 Unary Properties
1251 The following functions test whether the given set or relation
1252 contains any integer points. The ``plain'' variants do not perform
1253 any computations, but simply check if the given set or relation
1254 is already known to be empty.
1256 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1257 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1258 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1259 int isl_set_is_empty(__isl_keep isl_set *set);
1260 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1261 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1262 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1263 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1264 int isl_map_is_empty(__isl_keep isl_map *map);
1265 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1267 =item * Universality
1269 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1270 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1271 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1273 =item * Single-valuedness
1275 int isl_map_is_single_valued(__isl_keep isl_map *map);
1276 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1280 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1281 int isl_map_is_injective(__isl_keep isl_map *map);
1282 int isl_union_map_plain_is_injective(
1283 __isl_keep isl_union_map *umap);
1284 int isl_union_map_is_injective(
1285 __isl_keep isl_union_map *umap);
1289 int isl_map_is_bijective(__isl_keep isl_map *map);
1290 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1294 The following functions check whether the domain of the given
1295 (basic) set is a wrapped relation.
1297 int isl_basic_set_is_wrapping(
1298 __isl_keep isl_basic_set *bset);
1299 int isl_set_is_wrapping(__isl_keep isl_set *set);
1301 =item * Internal Product
1303 int isl_basic_map_can_zip(
1304 __isl_keep isl_basic_map *bmap);
1305 int isl_map_can_zip(__isl_keep isl_map *map);
1307 Check whether the product of domain and range of the given relation
1309 i.e., whether both domain and range are nested relations.
1313 =head3 Binary Properties
1319 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1320 __isl_keep isl_set *set2);
1321 int isl_set_is_equal(__isl_keep isl_set *set1,
1322 __isl_keep isl_set *set2);
1323 int isl_union_set_is_equal(
1324 __isl_keep isl_union_set *uset1,
1325 __isl_keep isl_union_set *uset2);
1326 int isl_basic_map_is_equal(
1327 __isl_keep isl_basic_map *bmap1,
1328 __isl_keep isl_basic_map *bmap2);
1329 int isl_map_is_equal(__isl_keep isl_map *map1,
1330 __isl_keep isl_map *map2);
1331 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1332 __isl_keep isl_map *map2);
1333 int isl_union_map_is_equal(
1334 __isl_keep isl_union_map *umap1,
1335 __isl_keep isl_union_map *umap2);
1337 =item * Disjointness
1339 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1340 __isl_keep isl_set *set2);
1344 int isl_set_is_subset(__isl_keep isl_set *set1,
1345 __isl_keep isl_set *set2);
1346 int isl_set_is_strict_subset(
1347 __isl_keep isl_set *set1,
1348 __isl_keep isl_set *set2);
1349 int isl_union_set_is_subset(
1350 __isl_keep isl_union_set *uset1,
1351 __isl_keep isl_union_set *uset2);
1352 int isl_union_set_is_strict_subset(
1353 __isl_keep isl_union_set *uset1,
1354 __isl_keep isl_union_set *uset2);
1355 int isl_basic_map_is_subset(
1356 __isl_keep isl_basic_map *bmap1,
1357 __isl_keep isl_basic_map *bmap2);
1358 int isl_basic_map_is_strict_subset(
1359 __isl_keep isl_basic_map *bmap1,
1360 __isl_keep isl_basic_map *bmap2);
1361 int isl_map_is_subset(
1362 __isl_keep isl_map *map1,
1363 __isl_keep isl_map *map2);
1364 int isl_map_is_strict_subset(
1365 __isl_keep isl_map *map1,
1366 __isl_keep isl_map *map2);
1367 int isl_union_map_is_subset(
1368 __isl_keep isl_union_map *umap1,
1369 __isl_keep isl_union_map *umap2);
1370 int isl_union_map_is_strict_subset(
1371 __isl_keep isl_union_map *umap1,
1372 __isl_keep isl_union_map *umap2);
1376 =head2 Unary Operations
1382 __isl_give isl_set *isl_set_complement(
1383 __isl_take isl_set *set);
1387 __isl_give isl_basic_map *isl_basic_map_reverse(
1388 __isl_take isl_basic_map *bmap);
1389 __isl_give isl_map *isl_map_reverse(
1390 __isl_take isl_map *map);
1391 __isl_give isl_union_map *isl_union_map_reverse(
1392 __isl_take isl_union_map *umap);
1396 __isl_give isl_basic_set *isl_basic_set_project_out(
1397 __isl_take isl_basic_set *bset,
1398 enum isl_dim_type type, unsigned first, unsigned n);
1399 __isl_give isl_basic_map *isl_basic_map_project_out(
1400 __isl_take isl_basic_map *bmap,
1401 enum isl_dim_type type, unsigned first, unsigned n);
1402 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1403 enum isl_dim_type type, unsigned first, unsigned n);
1404 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1405 enum isl_dim_type type, unsigned first, unsigned n);
1406 __isl_give isl_basic_set *isl_basic_map_domain(
1407 __isl_take isl_basic_map *bmap);
1408 __isl_give isl_basic_set *isl_basic_map_range(
1409 __isl_take isl_basic_map *bmap);
1410 __isl_give isl_set *isl_map_domain(
1411 __isl_take isl_map *bmap);
1412 __isl_give isl_set *isl_map_range(
1413 __isl_take isl_map *map);
1414 __isl_give isl_union_set *isl_union_map_domain(
1415 __isl_take isl_union_map *umap);
1416 __isl_give isl_union_set *isl_union_map_range(
1417 __isl_take isl_union_map *umap);
1419 __isl_give isl_basic_map *isl_basic_map_domain_map(
1420 __isl_take isl_basic_map *bmap);
1421 __isl_give isl_basic_map *isl_basic_map_range_map(
1422 __isl_take isl_basic_map *bmap);
1423 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1424 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1425 __isl_give isl_union_map *isl_union_map_domain_map(
1426 __isl_take isl_union_map *umap);
1427 __isl_give isl_union_map *isl_union_map_range_map(
1428 __isl_take isl_union_map *umap);
1430 The functions above construct a (basic, regular or union) relation
1431 that maps (a wrapped version of) the input relation to its domain or range.
1435 __isl_give isl_set *isl_set_eliminate(
1436 __isl_take isl_set *set, enum isl_dim_type type,
1437 unsigned first, unsigned n);
1439 Eliminate the coefficients for the given dimensions from the constraints,
1440 without removing the dimensions.
1444 __isl_give isl_basic_set *isl_basic_set_fix(
1445 __isl_take isl_basic_set *bset,
1446 enum isl_dim_type type, unsigned pos,
1448 __isl_give isl_basic_set *isl_basic_set_fix_si(
1449 __isl_take isl_basic_set *bset,
1450 enum isl_dim_type type, unsigned pos, int value);
1451 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1452 enum isl_dim_type type, unsigned pos,
1454 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1455 enum isl_dim_type type, unsigned pos, int value);
1456 __isl_give isl_basic_map *isl_basic_map_fix_si(
1457 __isl_take isl_basic_map *bmap,
1458 enum isl_dim_type type, unsigned pos, int value);
1459 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1460 enum isl_dim_type type, unsigned pos, int value);
1462 Intersect the set or relation with the hyperplane where the given
1463 dimension has the fixed given value.
1467 __isl_give isl_map *isl_set_identity(
1468 __isl_take isl_set *set);
1469 __isl_give isl_union_map *isl_union_set_identity(
1470 __isl_take isl_union_set *uset);
1472 Construct an identity relation on the given (union) set.
1476 __isl_give isl_basic_set *isl_basic_map_deltas(
1477 __isl_take isl_basic_map *bmap);
1478 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1479 __isl_give isl_union_set *isl_union_map_deltas(
1480 __isl_take isl_union_map *umap);
1482 These functions return a (basic) set containing the differences
1483 between image elements and corresponding domain elements in the input.
1485 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1486 __isl_take isl_basic_map *bmap);
1487 __isl_give isl_map *isl_map_deltas_map(
1488 __isl_take isl_map *map);
1489 __isl_give isl_union_map *isl_union_map_deltas_map(
1490 __isl_take isl_union_map *umap);
1492 The functions above construct a (basic, regular or union) relation
1493 that maps (a wrapped version of) the input relation to its delta set.
1497 Simplify the representation of a set or relation by trying
1498 to combine pairs of basic sets or relations into a single
1499 basic set or relation.
1501 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1502 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1503 __isl_give isl_union_set *isl_union_set_coalesce(
1504 __isl_take isl_union_set *uset);
1505 __isl_give isl_union_map *isl_union_map_coalesce(
1506 __isl_take isl_union_map *umap);
1508 =item * Detecting equalities
1510 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1511 __isl_take isl_basic_set *bset);
1512 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1513 __isl_take isl_basic_map *bmap);
1514 __isl_give isl_set *isl_set_detect_equalities(
1515 __isl_take isl_set *set);
1516 __isl_give isl_map *isl_map_detect_equalities(
1517 __isl_take isl_map *map);
1518 __isl_give isl_union_set *isl_union_set_detect_equalities(
1519 __isl_take isl_union_set *uset);
1520 __isl_give isl_union_map *isl_union_map_detect_equalities(
1521 __isl_take isl_union_map *umap);
1523 Simplify the representation of a set or relation by detecting implicit
1526 =item * Removing redundant constraints
1528 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1529 __isl_take isl_basic_set *bset);
1530 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1531 __isl_take isl_basic_map *bmap);
1535 __isl_give isl_basic_set *isl_set_convex_hull(
1536 __isl_take isl_set *set);
1537 __isl_give isl_basic_map *isl_map_convex_hull(
1538 __isl_take isl_map *map);
1540 If the input set or relation has any existentially quantified
1541 variables, then the result of these operations is currently undefined.
1545 __isl_give isl_basic_set *isl_set_simple_hull(
1546 __isl_take isl_set *set);
1547 __isl_give isl_basic_map *isl_map_simple_hull(
1548 __isl_take isl_map *map);
1549 __isl_give isl_union_map *isl_union_map_simple_hull(
1550 __isl_take isl_union_map *umap);
1552 These functions compute a single basic set or relation
1553 that contains the whole input set or relation.
1554 In particular, the output is described by translates
1555 of the constraints describing the basic sets or relations in the input.
1559 (See \autoref{s:simple hull}.)
1565 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1566 __isl_take isl_basic_set *bset);
1567 __isl_give isl_basic_set *isl_set_affine_hull(
1568 __isl_take isl_set *set);
1569 __isl_give isl_union_set *isl_union_set_affine_hull(
1570 __isl_take isl_union_set *uset);
1571 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1572 __isl_take isl_basic_map *bmap);
1573 __isl_give isl_basic_map *isl_map_affine_hull(
1574 __isl_take isl_map *map);
1575 __isl_give isl_union_map *isl_union_map_affine_hull(
1576 __isl_take isl_union_map *umap);
1578 In case of union sets and relations, the affine hull is computed
1581 =item * Polyhedral hull
1583 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1584 __isl_take isl_set *set);
1585 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1586 __isl_take isl_map *map);
1587 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1588 __isl_take isl_union_set *uset);
1589 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1590 __isl_take isl_union_map *umap);
1592 These functions compute a single basic set or relation
1593 not involving any existentially quantified variables
1594 that contains the whole input set or relation.
1595 In case of union sets and relations, the polyhedral hull is computed
1598 =item * Optimization
1600 #include <isl/ilp.h>
1601 enum isl_lp_result isl_basic_set_max(
1602 __isl_keep isl_basic_set *bset,
1603 __isl_keep isl_aff *obj, isl_int *opt)
1604 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1605 __isl_keep isl_aff *obj, isl_int *opt);
1607 Compute the maximum of the integer affine expression C<obj>
1608 over the points in C<set>, returning the result in C<opt>.
1609 The return value may be one of C<isl_lp_error>,
1610 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1614 The following functions compute either the set of (rational) coefficient
1615 values of valid constraints for the given set or the set of (rational)
1616 values satisfying the constraints with coefficients from the given set.
1617 Internally, these two sets of functions perform essentially the
1618 same operations, except that the set of coefficients is assumed to
1619 be a cone, while the set of values may be any polyhedron.
1620 The current implementation is based on the Farkas lemma and
1621 Fourier-Motzkin elimination, but this may change or be made optional
1622 in future. In particular, future implementations may use different
1623 dualization algorithms or skip the elimination step.
1625 __isl_give isl_basic_set *isl_basic_set_coefficients(
1626 __isl_take isl_basic_set *bset);
1627 __isl_give isl_basic_set *isl_set_coefficients(
1628 __isl_take isl_set *set);
1629 __isl_give isl_union_set *isl_union_set_coefficients(
1630 __isl_take isl_union_set *bset);
1631 __isl_give isl_basic_set *isl_basic_set_solutions(
1632 __isl_take isl_basic_set *bset);
1633 __isl_give isl_basic_set *isl_set_solutions(
1634 __isl_take isl_set *set);
1635 __isl_give isl_union_set *isl_union_set_solutions(
1636 __isl_take isl_union_set *bset);
1640 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1642 __isl_give isl_union_map *isl_union_map_power(
1643 __isl_take isl_union_map *umap, int *exact);
1645 Compute a parametric representation for all positive powers I<k> of C<map>.
1646 The result maps I<k> to a nested relation corresponding to the
1647 I<k>th power of C<map>.
1648 The result may be an overapproximation. If the result is known to be exact,
1649 then C<*exact> is set to C<1>.
1651 =item * Transitive closure
1653 __isl_give isl_map *isl_map_transitive_closure(
1654 __isl_take isl_map *map, int *exact);
1655 __isl_give isl_union_map *isl_union_map_transitive_closure(
1656 __isl_take isl_union_map *umap, int *exact);
1658 Compute the transitive closure of C<map>.
1659 The result may be an overapproximation. If the result is known to be exact,
1660 then C<*exact> is set to C<1>.
1662 =item * Reaching path lengths
1664 __isl_give isl_map *isl_map_reaching_path_lengths(
1665 __isl_take isl_map *map, int *exact);
1667 Compute a relation that maps each element in the range of C<map>
1668 to the lengths of all paths composed of edges in C<map> that
1669 end up in the given element.
1670 The result may be an overapproximation. If the result is known to be exact,
1671 then C<*exact> is set to C<1>.
1672 To compute the I<maximal> path length, the resulting relation
1673 should be postprocessed by C<isl_map_lexmax>.
1674 In particular, if the input relation is a dependence relation
1675 (mapping sources to sinks), then the maximal path length corresponds
1676 to the free schedule.
1677 Note, however, that C<isl_map_lexmax> expects the maximum to be
1678 finite, so if the path lengths are unbounded (possibly due to
1679 the overapproximation), then you will get an error message.
1683 __isl_give isl_basic_set *isl_basic_map_wrap(
1684 __isl_take isl_basic_map *bmap);
1685 __isl_give isl_set *isl_map_wrap(
1686 __isl_take isl_map *map);
1687 __isl_give isl_union_set *isl_union_map_wrap(
1688 __isl_take isl_union_map *umap);
1689 __isl_give isl_basic_map *isl_basic_set_unwrap(
1690 __isl_take isl_basic_set *bset);
1691 __isl_give isl_map *isl_set_unwrap(
1692 __isl_take isl_set *set);
1693 __isl_give isl_union_map *isl_union_set_unwrap(
1694 __isl_take isl_union_set *uset);
1698 Remove any internal structure of domain (and range) of the given
1699 set or relation. If there is any such internal structure in the input,
1700 then the name of the space is also removed.
1702 __isl_give isl_basic_set *isl_basic_set_flatten(
1703 __isl_take isl_basic_set *bset);
1704 __isl_give isl_set *isl_set_flatten(
1705 __isl_take isl_set *set);
1706 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1707 __isl_take isl_basic_map *bmap);
1708 __isl_give isl_map *isl_map_flatten_range(
1709 __isl_take isl_map *map);
1710 __isl_give isl_basic_map *isl_basic_map_flatten(
1711 __isl_take isl_basic_map *bmap);
1712 __isl_give isl_map *isl_map_flatten(
1713 __isl_take isl_map *map);
1715 __isl_give isl_map *isl_set_flatten_map(
1716 __isl_take isl_set *set);
1718 The function above constructs a relation
1719 that maps the input set to a flattened version of the set.
1723 Lift the input set to a space with extra dimensions corresponding
1724 to the existentially quantified variables in the input.
1725 In particular, the result lives in a wrapped map where the domain
1726 is the original space and the range corresponds to the original
1727 existentially quantified variables.
1729 __isl_give isl_basic_set *isl_basic_set_lift(
1730 __isl_take isl_basic_set *bset);
1731 __isl_give isl_set *isl_set_lift(
1732 __isl_take isl_set *set);
1733 __isl_give isl_union_set *isl_union_set_lift(
1734 __isl_take isl_union_set *uset);
1736 =item * Internal Product
1738 __isl_give isl_basic_map *isl_basic_map_zip(
1739 __isl_take isl_basic_map *bmap);
1740 __isl_give isl_map *isl_map_zip(
1741 __isl_take isl_map *map);
1742 __isl_give isl_union_map *isl_union_map_zip(
1743 __isl_take isl_union_map *umap);
1745 Given a relation with nested relations for domain and range,
1746 interchange the range of the domain with the domain of the range.
1748 =item * Aligning parameters
1750 __isl_give isl_set *isl_set_align_params(
1751 __isl_take isl_set *set,
1752 __isl_take isl_dim *model);
1753 __isl_give isl_map *isl_map_align_params(
1754 __isl_take isl_map *map,
1755 __isl_take isl_dim *model);
1757 Change the order of the parameters of the given set or relation
1758 such that the first parameters match those of C<model>.
1759 This may involve the introduction of extra parameters.
1760 All parameters need to be named.
1762 =item * Dimension manipulation
1764 __isl_give isl_set *isl_set_add_dims(
1765 __isl_take isl_set *set,
1766 enum isl_dim_type type, unsigned n);
1767 __isl_give isl_map *isl_map_add_dims(
1768 __isl_take isl_map *map,
1769 enum isl_dim_type type, unsigned n);
1771 It is usually not advisable to directly change the (input or output)
1772 space of a set or a relation as this removes the name and the internal
1773 structure of the space. However, the above functions can be useful
1774 to add new parameters, assuming
1775 C<isl_set_align_params> and C<isl_map_align_params>
1780 =head2 Binary Operations
1782 The two arguments of a binary operation not only need to live
1783 in the same C<isl_ctx>, they currently also need to have
1784 the same (number of) parameters.
1786 =head3 Basic Operations
1790 =item * Intersection
1792 __isl_give isl_basic_set *isl_basic_set_intersect(
1793 __isl_take isl_basic_set *bset1,
1794 __isl_take isl_basic_set *bset2);
1795 __isl_give isl_set *isl_set_intersect(
1796 __isl_take isl_set *set1,
1797 __isl_take isl_set *set2);
1798 __isl_give isl_union_set *isl_union_set_intersect(
1799 __isl_take isl_union_set *uset1,
1800 __isl_take isl_union_set *uset2);
1801 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1802 __isl_take isl_basic_map *bmap,
1803 __isl_take isl_basic_set *bset);
1804 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1805 __isl_take isl_basic_map *bmap,
1806 __isl_take isl_basic_set *bset);
1807 __isl_give isl_basic_map *isl_basic_map_intersect(
1808 __isl_take isl_basic_map *bmap1,
1809 __isl_take isl_basic_map *bmap2);
1810 __isl_give isl_map *isl_map_intersect_domain(
1811 __isl_take isl_map *map,
1812 __isl_take isl_set *set);
1813 __isl_give isl_map *isl_map_intersect_range(
1814 __isl_take isl_map *map,
1815 __isl_take isl_set *set);
1816 __isl_give isl_map *isl_map_intersect(
1817 __isl_take isl_map *map1,
1818 __isl_take isl_map *map2);
1819 __isl_give isl_union_map *isl_union_map_intersect_domain(
1820 __isl_take isl_union_map *umap,
1821 __isl_take isl_union_set *uset);
1822 __isl_give isl_union_map *isl_union_map_intersect_range(
1823 __isl_take isl_union_map *umap,
1824 __isl_take isl_union_set *uset);
1825 __isl_give isl_union_map *isl_union_map_intersect(
1826 __isl_take isl_union_map *umap1,
1827 __isl_take isl_union_map *umap2);
1831 __isl_give isl_set *isl_basic_set_union(
1832 __isl_take isl_basic_set *bset1,
1833 __isl_take isl_basic_set *bset2);
1834 __isl_give isl_map *isl_basic_map_union(
1835 __isl_take isl_basic_map *bmap1,
1836 __isl_take isl_basic_map *bmap2);
1837 __isl_give isl_set *isl_set_union(
1838 __isl_take isl_set *set1,
1839 __isl_take isl_set *set2);
1840 __isl_give isl_map *isl_map_union(
1841 __isl_take isl_map *map1,
1842 __isl_take isl_map *map2);
1843 __isl_give isl_union_set *isl_union_set_union(
1844 __isl_take isl_union_set *uset1,
1845 __isl_take isl_union_set *uset2);
1846 __isl_give isl_union_map *isl_union_map_union(
1847 __isl_take isl_union_map *umap1,
1848 __isl_take isl_union_map *umap2);
1850 =item * Set difference
1852 __isl_give isl_set *isl_set_subtract(
1853 __isl_take isl_set *set1,
1854 __isl_take isl_set *set2);
1855 __isl_give isl_map *isl_map_subtract(
1856 __isl_take isl_map *map1,
1857 __isl_take isl_map *map2);
1858 __isl_give isl_union_set *isl_union_set_subtract(
1859 __isl_take isl_union_set *uset1,
1860 __isl_take isl_union_set *uset2);
1861 __isl_give isl_union_map *isl_union_map_subtract(
1862 __isl_take isl_union_map *umap1,
1863 __isl_take isl_union_map *umap2);
1867 __isl_give isl_basic_set *isl_basic_set_apply(
1868 __isl_take isl_basic_set *bset,
1869 __isl_take isl_basic_map *bmap);
1870 __isl_give isl_set *isl_set_apply(
1871 __isl_take isl_set *set,
1872 __isl_take isl_map *map);
1873 __isl_give isl_union_set *isl_union_set_apply(
1874 __isl_take isl_union_set *uset,
1875 __isl_take isl_union_map *umap);
1876 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1877 __isl_take isl_basic_map *bmap1,
1878 __isl_take isl_basic_map *bmap2);
1879 __isl_give isl_basic_map *isl_basic_map_apply_range(
1880 __isl_take isl_basic_map *bmap1,
1881 __isl_take isl_basic_map *bmap2);
1882 __isl_give isl_map *isl_map_apply_domain(
1883 __isl_take isl_map *map1,
1884 __isl_take isl_map *map2);
1885 __isl_give isl_union_map *isl_union_map_apply_domain(
1886 __isl_take isl_union_map *umap1,
1887 __isl_take isl_union_map *umap2);
1888 __isl_give isl_map *isl_map_apply_range(
1889 __isl_take isl_map *map1,
1890 __isl_take isl_map *map2);
1891 __isl_give isl_union_map *isl_union_map_apply_range(
1892 __isl_take isl_union_map *umap1,
1893 __isl_take isl_union_map *umap2);
1895 =item * Cartesian Product
1897 __isl_give isl_set *isl_set_product(
1898 __isl_take isl_set *set1,
1899 __isl_take isl_set *set2);
1900 __isl_give isl_union_set *isl_union_set_product(
1901 __isl_take isl_union_set *uset1,
1902 __isl_take isl_union_set *uset2);
1903 __isl_give isl_basic_map *isl_basic_map_range_product(
1904 __isl_take isl_basic_map *bmap1,
1905 __isl_take isl_basic_map *bmap2);
1906 __isl_give isl_map *isl_map_range_product(
1907 __isl_take isl_map *map1,
1908 __isl_take isl_map *map2);
1909 __isl_give isl_union_map *isl_union_map_range_product(
1910 __isl_take isl_union_map *umap1,
1911 __isl_take isl_union_map *umap2);
1912 __isl_give isl_map *isl_map_product(
1913 __isl_take isl_map *map1,
1914 __isl_take isl_map *map2);
1915 __isl_give isl_union_map *isl_union_map_product(
1916 __isl_take isl_union_map *umap1,
1917 __isl_take isl_union_map *umap2);
1919 The above functions compute the cross product of the given
1920 sets or relations. The domains and ranges of the results
1921 are wrapped maps between domains and ranges of the inputs.
1922 To obtain a ``flat'' product, use the following functions
1925 __isl_give isl_basic_set *isl_basic_set_flat_product(
1926 __isl_take isl_basic_set *bset1,
1927 __isl_take isl_basic_set *bset2);
1928 __isl_give isl_set *isl_set_flat_product(
1929 __isl_take isl_set *set1,
1930 __isl_take isl_set *set2);
1931 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1932 __isl_take isl_basic_map *bmap1,
1933 __isl_take isl_basic_map *bmap2);
1934 __isl_give isl_map *isl_map_flat_range_product(
1935 __isl_take isl_map *map1,
1936 __isl_take isl_map *map2);
1937 __isl_give isl_union_map *isl_union_map_flat_range_product(
1938 __isl_take isl_union_map *umap1,
1939 __isl_take isl_union_map *umap2);
1940 __isl_give isl_basic_map *isl_basic_map_flat_product(
1941 __isl_take isl_basic_map *bmap1,
1942 __isl_take isl_basic_map *bmap2);
1943 __isl_give isl_map *isl_map_flat_product(
1944 __isl_take isl_map *map1,
1945 __isl_take isl_map *map2);
1947 =item * Simplification
1949 __isl_give isl_basic_set *isl_basic_set_gist(
1950 __isl_take isl_basic_set *bset,
1951 __isl_take isl_basic_set *context);
1952 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1953 __isl_take isl_set *context);
1954 __isl_give isl_union_set *isl_union_set_gist(
1955 __isl_take isl_union_set *uset,
1956 __isl_take isl_union_set *context);
1957 __isl_give isl_basic_map *isl_basic_map_gist(
1958 __isl_take isl_basic_map *bmap,
1959 __isl_take isl_basic_map *context);
1960 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1961 __isl_take isl_map *context);
1962 __isl_give isl_union_map *isl_union_map_gist(
1963 __isl_take isl_union_map *umap,
1964 __isl_take isl_union_map *context);
1966 The gist operation returns a set or relation that has the
1967 same intersection with the context as the input set or relation.
1968 Any implicit equality in the intersection is made explicit in the result,
1969 while all inequalities that are redundant with respect to the intersection
1971 In case of union sets and relations, the gist operation is performed
1976 =head3 Lexicographic Optimization
1978 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1979 the following functions
1980 compute a set that contains the lexicographic minimum or maximum
1981 of the elements in C<set> (or C<bset>) for those values of the parameters
1982 that satisfy C<dom>.
1983 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1984 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1986 In other words, the union of the parameter values
1987 for which the result is non-empty and of C<*empty>
1990 __isl_give isl_set *isl_basic_set_partial_lexmin(
1991 __isl_take isl_basic_set *bset,
1992 __isl_take isl_basic_set *dom,
1993 __isl_give isl_set **empty);
1994 __isl_give isl_set *isl_basic_set_partial_lexmax(
1995 __isl_take isl_basic_set *bset,
1996 __isl_take isl_basic_set *dom,
1997 __isl_give isl_set **empty);
1998 __isl_give isl_set *isl_set_partial_lexmin(
1999 __isl_take isl_set *set, __isl_take isl_set *dom,
2000 __isl_give isl_set **empty);
2001 __isl_give isl_set *isl_set_partial_lexmax(
2002 __isl_take isl_set *set, __isl_take isl_set *dom,
2003 __isl_give isl_set **empty);
2005 Given a (basic) set C<set> (or C<bset>), the following functions simply
2006 return a set containing the lexicographic minimum or maximum
2007 of the elements in C<set> (or C<bset>).
2008 In case of union sets, the optimum is computed per space.
2010 __isl_give isl_set *isl_basic_set_lexmin(
2011 __isl_take isl_basic_set *bset);
2012 __isl_give isl_set *isl_basic_set_lexmax(
2013 __isl_take isl_basic_set *bset);
2014 __isl_give isl_set *isl_set_lexmin(
2015 __isl_take isl_set *set);
2016 __isl_give isl_set *isl_set_lexmax(
2017 __isl_take isl_set *set);
2018 __isl_give isl_union_set *isl_union_set_lexmin(
2019 __isl_take isl_union_set *uset);
2020 __isl_give isl_union_set *isl_union_set_lexmax(
2021 __isl_take isl_union_set *uset);
2023 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2024 the following functions
2025 compute a relation that maps each element of C<dom>
2026 to the single lexicographic minimum or maximum
2027 of the elements that are associated to that same
2028 element in C<map> (or C<bmap>).
2029 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2030 that contains the elements in C<dom> that do not map
2031 to any elements in C<map> (or C<bmap>).
2032 In other words, the union of the domain of the result and of C<*empty>
2035 __isl_give isl_map *isl_basic_map_partial_lexmax(
2036 __isl_take isl_basic_map *bmap,
2037 __isl_take isl_basic_set *dom,
2038 __isl_give isl_set **empty);
2039 __isl_give isl_map *isl_basic_map_partial_lexmin(
2040 __isl_take isl_basic_map *bmap,
2041 __isl_take isl_basic_set *dom,
2042 __isl_give isl_set **empty);
2043 __isl_give isl_map *isl_map_partial_lexmax(
2044 __isl_take isl_map *map, __isl_take isl_set *dom,
2045 __isl_give isl_set **empty);
2046 __isl_give isl_map *isl_map_partial_lexmin(
2047 __isl_take isl_map *map, __isl_take isl_set *dom,
2048 __isl_give isl_set **empty);
2050 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2051 return a map mapping each element in the domain of
2052 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2053 of all elements associated to that element.
2054 In case of union relations, the optimum is computed per space.
2056 __isl_give isl_map *isl_basic_map_lexmin(
2057 __isl_take isl_basic_map *bmap);
2058 __isl_give isl_map *isl_basic_map_lexmax(
2059 __isl_take isl_basic_map *bmap);
2060 __isl_give isl_map *isl_map_lexmin(
2061 __isl_take isl_map *map);
2062 __isl_give isl_map *isl_map_lexmax(
2063 __isl_take isl_map *map);
2064 __isl_give isl_union_map *isl_union_map_lexmin(
2065 __isl_take isl_union_map *umap);
2066 __isl_give isl_union_map *isl_union_map_lexmax(
2067 __isl_take isl_union_map *umap);
2071 Lists are defined over several element types, including
2072 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2073 Here we take lists of C<isl_set>s as an example.
2074 Lists can be created, copied and freed using the following functions.
2076 #include <isl/list.h>
2077 __isl_give isl_set_list *isl_set_list_alloc(
2078 isl_ctx *ctx, int n);
2079 __isl_give isl_set_list *isl_set_list_copy(
2080 __isl_keep isl_set_list *list);
2081 __isl_give isl_set_list *isl_set_list_add(
2082 __isl_take isl_set_list *list,
2083 __isl_take isl_set *el);
2084 void isl_set_list_free(__isl_take isl_set_list *list);
2086 C<isl_set_list_alloc> creates an empty list with a capacity for
2089 Lists can be inspected using the following functions.
2091 #include <isl/list.h>
2092 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2093 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2094 __isl_give struct isl_set *isl_set_list_get_set(
2095 __isl_keep isl_set_list *list, int index);
2096 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2097 int (*fn)(__isl_take struct isl_set *el, void *user),
2100 Lists can be printed using
2102 #include <isl/list.h>
2103 __isl_give isl_printer *isl_printer_print_set_list(
2104 __isl_take isl_printer *p,
2105 __isl_keep isl_set_list *list);
2109 Matrices can be created, copied and freed using the following functions.
2111 #include <isl/mat.h>
2112 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2113 unsigned n_row, unsigned n_col);
2114 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2115 void isl_mat_free(__isl_take isl_mat *mat);
2117 Note that the elements of a newly created matrix may have arbitrary values.
2118 The elements can be changed and inspected using the following functions.
2120 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2121 int isl_mat_rows(__isl_keep isl_mat *mat);
2122 int isl_mat_cols(__isl_keep isl_mat *mat);
2123 int isl_mat_get_element(__isl_keep isl_mat *mat,
2124 int row, int col, isl_int *v);
2125 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2126 int row, int col, isl_int v);
2127 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2128 int row, int col, int v);
2130 C<isl_mat_get_element> will return a negative value if anything went wrong.
2131 In that case, the value of C<*v> is undefined.
2133 The following function can be used to compute the (right) inverse
2134 of a matrix, i.e., a matrix such that the product of the original
2135 and the inverse (in that order) is a multiple of the identity matrix.
2136 The input matrix is assumed to be of full row-rank.
2138 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2140 The following function can be used to compute the (right) kernel
2141 (or null space) of a matrix, i.e., a matrix such that the product of
2142 the original and the kernel (in that order) is the zero matrix.
2144 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2146 =head2 Quasi Affine Expressions
2148 The zero quasi affine expression can be created using
2150 __isl_give isl_aff *isl_aff_zero(
2151 __isl_take isl_local_space *ls);
2153 Quasi affine expressions can be copied and free using
2155 #include <isl/aff.h>
2156 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2157 void *isl_aff_free(__isl_take isl_aff *aff);
2159 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2160 using the following function. The constraint is required to have
2161 a non-zero coefficient for the specified dimension.
2163 #include <isl/constraint.h>
2164 __isl_give isl_aff *isl_constraint_get_bound(
2165 __isl_keep isl_constraint *constraint,
2166 enum isl_dim_type type, int pos);
2168 Conversely, an equality constraint equating
2169 the affine expression to zero or an inequality constraint enforcing
2170 the affine expression to be non-negative, can be constructed using
2172 __isl_give isl_constraint *isl_equality_from_aff(
2173 __isl_take isl_aff *aff);
2174 __isl_give isl_constraint *isl_inequality_from_aff(
2175 __isl_take isl_aff *aff);
2177 The expression can be inspected using
2179 #include <isl/aff.h>
2180 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2181 int isl_aff_dim(__isl_keep isl_aff *aff,
2182 enum isl_dim_type type);
2183 __isl_give isl_local_space *isl_aff_get_local_space(
2184 __isl_keep isl_aff *aff);
2185 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2186 enum isl_dim_type type, unsigned pos);
2187 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2189 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2190 enum isl_dim_type type, int pos, isl_int *v);
2191 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2193 __isl_give isl_div *isl_aff_get_div(
2194 __isl_keep isl_aff *aff, int pos);
2196 It can be modified using
2198 #include <isl/aff.h>
2199 __isl_give isl_aff *isl_aff_set_constant(
2200 __isl_take isl_aff *aff, isl_int v);
2201 __isl_give isl_aff *isl_aff_set_constant_si(
2202 __isl_take isl_aff *aff, int v);
2203 __isl_give isl_aff *isl_aff_set_coefficient(
2204 __isl_take isl_aff *aff,
2205 enum isl_dim_type type, int pos, isl_int v);
2206 __isl_give isl_aff *isl_aff_set_coefficient_si(
2207 __isl_take isl_aff *aff,
2208 enum isl_dim_type type, int pos, int v);
2209 __isl_give isl_aff *isl_aff_set_denominator(
2210 __isl_take isl_aff *aff, isl_int v);
2212 __isl_give isl_aff *isl_aff_add_constant(
2213 __isl_take isl_aff *aff, isl_int v);
2214 __isl_give isl_aff *isl_aff_add_coefficient_si(
2215 __isl_take isl_aff *aff,
2216 enum isl_dim_type type, int pos, int v);
2218 Note that the C<set_constant> and C<set_coefficient> functions
2219 set the I<numerator> of the constant or coefficient, while
2220 C<add_constant> and C<add_coefficient> add an integer value to
2221 the possibly rational constant or coefficient.
2225 #include <isl/aff.h>
2226 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2227 __isl_take isl_aff *aff2);
2228 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2229 __isl_take isl_aff *aff2);
2230 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2231 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2232 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2234 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2237 An expression can be printed using
2239 #include <isl/aff.h>
2240 __isl_give isl_printer *isl_printer_print_aff(
2241 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2245 Points are elements of a set. They can be used to construct
2246 simple sets (boxes) or they can be used to represent the
2247 individual elements of a set.
2248 The zero point (the origin) can be created using
2250 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2252 The coordinates of a point can be inspected, set and changed
2255 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2256 enum isl_dim_type type, int pos, isl_int *v);
2257 __isl_give isl_point *isl_point_set_coordinate(
2258 __isl_take isl_point *pnt,
2259 enum isl_dim_type type, int pos, isl_int v);
2261 __isl_give isl_point *isl_point_add_ui(
2262 __isl_take isl_point *pnt,
2263 enum isl_dim_type type, int pos, unsigned val);
2264 __isl_give isl_point *isl_point_sub_ui(
2265 __isl_take isl_point *pnt,
2266 enum isl_dim_type type, int pos, unsigned val);
2268 Points can be copied or freed using
2270 __isl_give isl_point *isl_point_copy(
2271 __isl_keep isl_point *pnt);
2272 void isl_point_free(__isl_take isl_point *pnt);
2274 A singleton set can be created from a point using
2276 __isl_give isl_basic_set *isl_basic_set_from_point(
2277 __isl_take isl_point *pnt);
2278 __isl_give isl_set *isl_set_from_point(
2279 __isl_take isl_point *pnt);
2281 and a box can be created from two opposite extremal points using
2283 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2284 __isl_take isl_point *pnt1,
2285 __isl_take isl_point *pnt2);
2286 __isl_give isl_set *isl_set_box_from_points(
2287 __isl_take isl_point *pnt1,
2288 __isl_take isl_point *pnt2);
2290 All elements of a B<bounded> (union) set can be enumerated using
2291 the following functions.
2293 int isl_set_foreach_point(__isl_keep isl_set *set,
2294 int (*fn)(__isl_take isl_point *pnt, void *user),
2296 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2297 int (*fn)(__isl_take isl_point *pnt, void *user),
2300 The function C<fn> is called for each integer point in
2301 C<set> with as second argument the last argument of
2302 the C<isl_set_foreach_point> call. The function C<fn>
2303 should return C<0> on success and C<-1> on failure.
2304 In the latter case, C<isl_set_foreach_point> will stop
2305 enumerating and return C<-1> as well.
2306 If the enumeration is performed successfully and to completion,
2307 then C<isl_set_foreach_point> returns C<0>.
2309 To obtain a single point of a (basic) set, use
2311 __isl_give isl_point *isl_basic_set_sample_point(
2312 __isl_take isl_basic_set *bset);
2313 __isl_give isl_point *isl_set_sample_point(
2314 __isl_take isl_set *set);
2316 If C<set> does not contain any (integer) points, then the
2317 resulting point will be ``void'', a property that can be
2320 int isl_point_is_void(__isl_keep isl_point *pnt);
2322 =head2 Piecewise Quasipolynomials
2324 A piecewise quasipolynomial is a particular kind of function that maps
2325 a parametric point to a rational value.
2326 More specifically, a quasipolynomial is a polynomial expression in greatest
2327 integer parts of affine expressions of parameters and variables.
2328 A piecewise quasipolynomial is a subdivision of a given parametric
2329 domain into disjoint cells with a quasipolynomial associated to
2330 each cell. The value of the piecewise quasipolynomial at a given
2331 point is the value of the quasipolynomial associated to the cell
2332 that contains the point. Outside of the union of cells,
2333 the value is assumed to be zero.
2334 For example, the piecewise quasipolynomial
2336 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2338 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2339 A given piecewise quasipolynomial has a fixed domain dimension.
2340 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2341 defined over different domains.
2342 Piecewise quasipolynomials are mainly used by the C<barvinok>
2343 library for representing the number of elements in a parametric set or map.
2344 For example, the piecewise quasipolynomial above represents
2345 the number of points in the map
2347 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2349 =head3 Printing (Piecewise) Quasipolynomials
2351 Quasipolynomials and piecewise quasipolynomials can be printed
2352 using the following functions.
2354 __isl_give isl_printer *isl_printer_print_qpolynomial(
2355 __isl_take isl_printer *p,
2356 __isl_keep isl_qpolynomial *qp);
2358 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2359 __isl_take isl_printer *p,
2360 __isl_keep isl_pw_qpolynomial *pwqp);
2362 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2363 __isl_take isl_printer *p,
2364 __isl_keep isl_union_pw_qpolynomial *upwqp);
2366 The output format of the printer
2367 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2368 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2370 In case of printing in C<ISL_FORMAT_C>, the user may want
2371 to set the names of all dimensions
2373 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2374 __isl_take isl_qpolynomial *qp,
2375 enum isl_dim_type type, unsigned pos,
2377 __isl_give isl_pw_qpolynomial *
2378 isl_pw_qpolynomial_set_dim_name(
2379 __isl_take isl_pw_qpolynomial *pwqp,
2380 enum isl_dim_type type, unsigned pos,
2383 =head3 Creating New (Piecewise) Quasipolynomials
2385 Some simple quasipolynomials can be created using the following functions.
2386 More complicated quasipolynomials can be created by applying
2387 operations such as addition and multiplication
2388 on the resulting quasipolynomials
2390 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2391 __isl_take isl_dim *dim);
2392 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2393 __isl_take isl_dim *dim);
2394 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2395 __isl_take isl_dim *dim);
2396 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2397 __isl_take isl_dim *dim);
2398 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2399 __isl_take isl_dim *dim);
2400 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2401 __isl_take isl_dim *dim,
2402 const isl_int n, const isl_int d);
2403 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2404 __isl_take isl_div *div);
2405 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2406 __isl_take isl_dim *dim,
2407 enum isl_dim_type type, unsigned pos);
2408 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2409 __isl_take isl_aff *aff);
2411 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2412 with a single cell can be created using the following functions.
2413 Multiple of these single cell piecewise quasipolynomials can
2414 be combined to create more complicated piecewise quasipolynomials.
2416 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2417 __isl_take isl_dim *dim);
2418 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2419 __isl_take isl_set *set,
2420 __isl_take isl_qpolynomial *qp);
2422 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2423 __isl_take isl_dim *dim);
2424 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2425 __isl_take isl_pw_qpolynomial *pwqp);
2426 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2427 __isl_take isl_union_pw_qpolynomial *upwqp,
2428 __isl_take isl_pw_qpolynomial *pwqp);
2430 Quasipolynomials can be copied and freed again using the following
2433 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2434 __isl_keep isl_qpolynomial *qp);
2435 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2437 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2438 __isl_keep isl_pw_qpolynomial *pwqp);
2439 void isl_pw_qpolynomial_free(
2440 __isl_take isl_pw_qpolynomial *pwqp);
2442 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2443 __isl_keep isl_union_pw_qpolynomial *upwqp);
2444 void isl_union_pw_qpolynomial_free(
2445 __isl_take isl_union_pw_qpolynomial *upwqp);
2447 =head3 Inspecting (Piecewise) Quasipolynomials
2449 To iterate over all piecewise quasipolynomials in a union
2450 piecewise quasipolynomial, use the following function
2452 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2453 __isl_keep isl_union_pw_qpolynomial *upwqp,
2454 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2457 To extract the piecewise quasipolynomial from a union with a given dimension
2460 __isl_give isl_pw_qpolynomial *
2461 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2462 __isl_keep isl_union_pw_qpolynomial *upwqp,
2463 __isl_take isl_dim *dim);
2465 To iterate over the cells in a piecewise quasipolynomial,
2466 use either of the following two functions
2468 int isl_pw_qpolynomial_foreach_piece(
2469 __isl_keep isl_pw_qpolynomial *pwqp,
2470 int (*fn)(__isl_take isl_set *set,
2471 __isl_take isl_qpolynomial *qp,
2472 void *user), void *user);
2473 int isl_pw_qpolynomial_foreach_lifted_piece(
2474 __isl_keep isl_pw_qpolynomial *pwqp,
2475 int (*fn)(__isl_take isl_set *set,
2476 __isl_take isl_qpolynomial *qp,
2477 void *user), void *user);
2479 As usual, the function C<fn> should return C<0> on success
2480 and C<-1> on failure. The difference between
2481 C<isl_pw_qpolynomial_foreach_piece> and
2482 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2483 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2484 compute unique representations for all existentially quantified
2485 variables and then turn these existentially quantified variables
2486 into extra set variables, adapting the associated quasipolynomial
2487 accordingly. This means that the C<set> passed to C<fn>
2488 will not have any existentially quantified variables, but that
2489 the dimensions of the sets may be different for different
2490 invocations of C<fn>.
2492 To iterate over all terms in a quasipolynomial,
2495 int isl_qpolynomial_foreach_term(
2496 __isl_keep isl_qpolynomial *qp,
2497 int (*fn)(__isl_take isl_term *term,
2498 void *user), void *user);
2500 The terms themselves can be inspected and freed using
2503 unsigned isl_term_dim(__isl_keep isl_term *term,
2504 enum isl_dim_type type);
2505 void isl_term_get_num(__isl_keep isl_term *term,
2507 void isl_term_get_den(__isl_keep isl_term *term,
2509 int isl_term_get_exp(__isl_keep isl_term *term,
2510 enum isl_dim_type type, unsigned pos);
2511 __isl_give isl_div *isl_term_get_div(
2512 __isl_keep isl_term *term, unsigned pos);
2513 void isl_term_free(__isl_take isl_term *term);
2515 Each term is a product of parameters, set variables and
2516 integer divisions. The function C<isl_term_get_exp>
2517 returns the exponent of a given dimensions in the given term.
2518 The C<isl_int>s in the arguments of C<isl_term_get_num>
2519 and C<isl_term_get_den> need to have been initialized
2520 using C<isl_int_init> before calling these functions.
2522 =head3 Properties of (Piecewise) Quasipolynomials
2524 To check whether a quasipolynomial is actually a constant,
2525 use the following function.
2527 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2528 isl_int *n, isl_int *d);
2530 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2531 then the numerator and denominator of the constant
2532 are returned in C<*n> and C<*d>, respectively.
2534 =head3 Operations on (Piecewise) Quasipolynomials
2536 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2537 __isl_take isl_qpolynomial *qp);
2538 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2539 __isl_take isl_qpolynomial *qp1,
2540 __isl_take isl_qpolynomial *qp2);
2541 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2542 __isl_take isl_qpolynomial *qp1,
2543 __isl_take isl_qpolynomial *qp2);
2544 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2545 __isl_take isl_qpolynomial *qp1,
2546 __isl_take isl_qpolynomial *qp2);
2547 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2548 __isl_take isl_qpolynomial *qp, unsigned exponent);
2550 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2551 __isl_take isl_pw_qpolynomial *pwqp1,
2552 __isl_take isl_pw_qpolynomial *pwqp2);
2553 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2554 __isl_take isl_pw_qpolynomial *pwqp1,
2555 __isl_take isl_pw_qpolynomial *pwqp2);
2556 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2557 __isl_take isl_pw_qpolynomial *pwqp1,
2558 __isl_take isl_pw_qpolynomial *pwqp2);
2559 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2560 __isl_take isl_pw_qpolynomial *pwqp);
2561 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2562 __isl_take isl_pw_qpolynomial *pwqp1,
2563 __isl_take isl_pw_qpolynomial *pwqp2);
2565 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2566 __isl_take isl_union_pw_qpolynomial *upwqp1,
2567 __isl_take isl_union_pw_qpolynomial *upwqp2);
2568 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2569 __isl_take isl_union_pw_qpolynomial *upwqp1,
2570 __isl_take isl_union_pw_qpolynomial *upwqp2);
2571 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2572 __isl_take isl_union_pw_qpolynomial *upwqp1,
2573 __isl_take isl_union_pw_qpolynomial *upwqp2);
2575 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2576 __isl_take isl_pw_qpolynomial *pwqp,
2577 __isl_take isl_point *pnt);
2579 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2580 __isl_take isl_union_pw_qpolynomial *upwqp,
2581 __isl_take isl_point *pnt);
2583 __isl_give isl_set *isl_pw_qpolynomial_domain(
2584 __isl_take isl_pw_qpolynomial *pwqp);
2585 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2586 __isl_take isl_pw_qpolynomial *pwpq,
2587 __isl_take isl_set *set);
2589 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2590 __isl_take isl_union_pw_qpolynomial *upwqp);
2591 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2592 __isl_take isl_union_pw_qpolynomial *upwpq,
2593 __isl_take isl_union_set *uset);
2595 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2596 __isl_take isl_qpolynomial *qp,
2597 __isl_take isl_dim *model);
2599 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2600 __isl_take isl_union_pw_qpolynomial *upwqp);
2602 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2603 __isl_take isl_qpolynomial *qp,
2604 __isl_take isl_set *context);
2606 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2607 __isl_take isl_pw_qpolynomial *pwqp,
2608 __isl_take isl_set *context);
2610 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2611 __isl_take isl_union_pw_qpolynomial *upwqp,
2612 __isl_take isl_union_set *context);
2614 The gist operation applies the gist operation to each of
2615 the cells in the domain of the input piecewise quasipolynomial.
2616 The context is also exploited
2617 to simplify the quasipolynomials associated to each cell.
2619 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2620 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2621 __isl_give isl_union_pw_qpolynomial *
2622 isl_union_pw_qpolynomial_to_polynomial(
2623 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2625 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2626 the polynomial will be an overapproximation. If C<sign> is negative,
2627 it will be an underapproximation. If C<sign> is zero, the approximation
2628 will lie somewhere in between.
2630 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2632 A piecewise quasipolynomial reduction is a piecewise
2633 reduction (or fold) of quasipolynomials.
2634 In particular, the reduction can be maximum or a minimum.
2635 The objects are mainly used to represent the result of
2636 an upper or lower bound on a quasipolynomial over its domain,
2637 i.e., as the result of the following function.
2639 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2640 __isl_take isl_pw_qpolynomial *pwqp,
2641 enum isl_fold type, int *tight);
2643 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2644 __isl_take isl_union_pw_qpolynomial *upwqp,
2645 enum isl_fold type, int *tight);
2647 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2648 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2649 is the returned bound is known be tight, i.e., for each value
2650 of the parameters there is at least
2651 one element in the domain that reaches the bound.
2652 If the domain of C<pwqp> is not wrapping, then the bound is computed
2653 over all elements in that domain and the result has a purely parametric
2654 domain. If the domain of C<pwqp> is wrapping, then the bound is
2655 computed over the range of the wrapped relation. The domain of the
2656 wrapped relation becomes the domain of the result.
2658 A (piecewise) quasipolynomial reduction can be copied or freed using the
2659 following functions.
2661 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2662 __isl_keep isl_qpolynomial_fold *fold);
2663 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2664 __isl_keep isl_pw_qpolynomial_fold *pwf);
2665 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2666 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2667 void isl_qpolynomial_fold_free(
2668 __isl_take isl_qpolynomial_fold *fold);
2669 void isl_pw_qpolynomial_fold_free(
2670 __isl_take isl_pw_qpolynomial_fold *pwf);
2671 void isl_union_pw_qpolynomial_fold_free(
2672 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2674 =head3 Printing Piecewise Quasipolynomial Reductions
2676 Piecewise quasipolynomial reductions can be printed
2677 using the following function.
2679 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2680 __isl_take isl_printer *p,
2681 __isl_keep isl_pw_qpolynomial_fold *pwf);
2682 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2683 __isl_take isl_printer *p,
2684 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2686 For C<isl_printer_print_pw_qpolynomial_fold>,
2687 output format of the printer
2688 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2689 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2690 output format of the printer
2691 needs to be set to C<ISL_FORMAT_ISL>.
2692 In case of printing in C<ISL_FORMAT_C>, the user may want
2693 to set the names of all dimensions
2695 __isl_give isl_pw_qpolynomial_fold *
2696 isl_pw_qpolynomial_fold_set_dim_name(
2697 __isl_take isl_pw_qpolynomial_fold *pwf,
2698 enum isl_dim_type type, unsigned pos,
2701 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2703 To iterate over all piecewise quasipolynomial reductions in a union
2704 piecewise quasipolynomial reduction, use the following function
2706 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2707 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2708 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2709 void *user), void *user);
2711 To iterate over the cells in a piecewise quasipolynomial reduction,
2712 use either of the following two functions
2714 int isl_pw_qpolynomial_fold_foreach_piece(
2715 __isl_keep isl_pw_qpolynomial_fold *pwf,
2716 int (*fn)(__isl_take isl_set *set,
2717 __isl_take isl_qpolynomial_fold *fold,
2718 void *user), void *user);
2719 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2720 __isl_keep isl_pw_qpolynomial_fold *pwf,
2721 int (*fn)(__isl_take isl_set *set,
2722 __isl_take isl_qpolynomial_fold *fold,
2723 void *user), void *user);
2725 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2726 of the difference between these two functions.
2728 To iterate over all quasipolynomials in a reduction, use
2730 int isl_qpolynomial_fold_foreach_qpolynomial(
2731 __isl_keep isl_qpolynomial_fold *fold,
2732 int (*fn)(__isl_take isl_qpolynomial *qp,
2733 void *user), void *user);
2735 =head3 Operations on Piecewise Quasipolynomial Reductions
2737 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2738 __isl_take isl_pw_qpolynomial_fold *pwf1,
2739 __isl_take isl_pw_qpolynomial_fold *pwf2);
2741 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2742 __isl_take isl_pw_qpolynomial_fold *pwf1,
2743 __isl_take isl_pw_qpolynomial_fold *pwf2);
2745 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2746 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2747 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2749 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2750 __isl_take isl_pw_qpolynomial_fold *pwf,
2751 __isl_take isl_point *pnt);
2753 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2754 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2755 __isl_take isl_point *pnt);
2757 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2758 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2759 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2760 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2761 __isl_take isl_union_set *uset);
2763 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2764 __isl_take isl_pw_qpolynomial_fold *pwf);
2766 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2767 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2769 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2770 __isl_take isl_pw_qpolynomial_fold *pwf,
2771 __isl_take isl_set *context);
2773 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2774 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2775 __isl_take isl_union_set *context);
2777 The gist operation applies the gist operation to each of
2778 the cells in the domain of the input piecewise quasipolynomial reduction.
2779 In future, the operation will also exploit the context
2780 to simplify the quasipolynomial reductions associated to each cell.
2782 __isl_give isl_pw_qpolynomial_fold *
2783 isl_set_apply_pw_qpolynomial_fold(
2784 __isl_take isl_set *set,
2785 __isl_take isl_pw_qpolynomial_fold *pwf,
2787 __isl_give isl_pw_qpolynomial_fold *
2788 isl_map_apply_pw_qpolynomial_fold(
2789 __isl_take isl_map *map,
2790 __isl_take isl_pw_qpolynomial_fold *pwf,
2792 __isl_give isl_union_pw_qpolynomial_fold *
2793 isl_union_set_apply_union_pw_qpolynomial_fold(
2794 __isl_take isl_union_set *uset,
2795 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2797 __isl_give isl_union_pw_qpolynomial_fold *
2798 isl_union_map_apply_union_pw_qpolynomial_fold(
2799 __isl_take isl_union_map *umap,
2800 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2803 The functions taking a map
2804 compose the given map with the given piecewise quasipolynomial reduction.
2805 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2806 over all elements in the intersection of the range of the map
2807 and the domain of the piecewise quasipolynomial reduction
2808 as a function of an element in the domain of the map.
2809 The functions taking a set compute a bound over all elements in the
2810 intersection of the set and the domain of the
2811 piecewise quasipolynomial reduction.
2813 =head2 Dependence Analysis
2815 C<isl> contains specialized functionality for performing
2816 array dataflow analysis. That is, given a I<sink> access relation
2817 and a collection of possible I<source> access relations,
2818 C<isl> can compute relations that describe
2819 for each iteration of the sink access, which iteration
2820 of which of the source access relations was the last
2821 to access the same data element before the given iteration
2823 To compute standard flow dependences, the sink should be
2824 a read, while the sources should be writes.
2825 If any of the source accesses are marked as being I<may>
2826 accesses, then there will be a dependence to the last
2827 I<must> access B<and> to any I<may> access that follows
2828 this last I<must> access.
2829 In particular, if I<all> sources are I<may> accesses,
2830 then memory based dependence analysis is performed.
2831 If, on the other hand, all sources are I<must> accesses,
2832 then value based dependence analysis is performed.
2834 #include <isl/flow.h>
2836 typedef int (*isl_access_level_before)(void *first, void *second);
2838 __isl_give isl_access_info *isl_access_info_alloc(
2839 __isl_take isl_map *sink,
2840 void *sink_user, isl_access_level_before fn,
2842 __isl_give isl_access_info *isl_access_info_add_source(
2843 __isl_take isl_access_info *acc,
2844 __isl_take isl_map *source, int must,
2846 void isl_access_info_free(__isl_take isl_access_info *acc);
2848 __isl_give isl_flow *isl_access_info_compute_flow(
2849 __isl_take isl_access_info *acc);
2851 int isl_flow_foreach(__isl_keep isl_flow *deps,
2852 int (*fn)(__isl_take isl_map *dep, int must,
2853 void *dep_user, void *user),
2855 __isl_give isl_map *isl_flow_get_no_source(
2856 __isl_keep isl_flow *deps, int must);
2857 void isl_flow_free(__isl_take isl_flow *deps);
2859 The function C<isl_access_info_compute_flow> performs the actual
2860 dependence analysis. The other functions are used to construct
2861 the input for this function or to read off the output.
2863 The input is collected in an C<isl_access_info>, which can
2864 be created through a call to C<isl_access_info_alloc>.
2865 The arguments to this functions are the sink access relation
2866 C<sink>, a token C<sink_user> used to identify the sink
2867 access to the user, a callback function for specifying the
2868 relative order of source and sink accesses, and the number
2869 of source access relations that will be added.
2870 The callback function has type C<int (*)(void *first, void *second)>.
2871 The function is called with two user supplied tokens identifying
2872 either a source or the sink and it should return the shared nesting
2873 level and the relative order of the two accesses.
2874 In particular, let I<n> be the number of loops shared by
2875 the two accesses. If C<first> precedes C<second> textually,
2876 then the function should return I<2 * n + 1>; otherwise,
2877 it should return I<2 * n>.
2878 The sources can be added to the C<isl_access_info> by performing
2879 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2880 C<must> indicates whether the source is a I<must> access
2881 or a I<may> access. Note that a multi-valued access relation
2882 should only be marked I<must> if every iteration in the domain
2883 of the relation accesses I<all> elements in its image.
2884 The C<source_user> token is again used to identify
2885 the source access. The range of the source access relation
2886 C<source> should have the same dimension as the range
2887 of the sink access relation.
2888 The C<isl_access_info_free> function should usually not be
2889 called explicitly, because it is called implicitly by
2890 C<isl_access_info_compute_flow>.
2892 The result of the dependence analysis is collected in an
2893 C<isl_flow>. There may be elements of
2894 the sink access for which no preceding source access could be
2895 found or for which all preceding sources are I<may> accesses.
2896 The relations containing these elements can be obtained through
2897 calls to C<isl_flow_get_no_source>, the first with C<must> set
2898 and the second with C<must> unset.
2899 In the case of standard flow dependence analysis,
2900 with the sink a read and the sources I<must> writes,
2901 the first relation corresponds to the reads from uninitialized
2902 array elements and the second relation is empty.
2903 The actual flow dependences can be extracted using
2904 C<isl_flow_foreach>. This function will call the user-specified
2905 callback function C<fn> for each B<non-empty> dependence between
2906 a source and the sink. The callback function is called
2907 with four arguments, the actual flow dependence relation
2908 mapping source iterations to sink iterations, a boolean that
2909 indicates whether it is a I<must> or I<may> dependence, a token
2910 identifying the source and an additional C<void *> with value
2911 equal to the third argument of the C<isl_flow_foreach> call.
2912 A dependence is marked I<must> if it originates from a I<must>
2913 source and if it is not followed by any I<may> sources.
2915 After finishing with an C<isl_flow>, the user should call
2916 C<isl_flow_free> to free all associated memory.
2918 A higher-level interface to dependence analysis is provided
2919 by the following function.
2921 #include <isl/flow.h>
2923 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2924 __isl_take isl_union_map *must_source,
2925 __isl_take isl_union_map *may_source,
2926 __isl_take isl_union_map *schedule,
2927 __isl_give isl_union_map **must_dep,
2928 __isl_give isl_union_map **may_dep,
2929 __isl_give isl_union_map **must_no_source,
2930 __isl_give isl_union_map **may_no_source);
2932 The arrays are identified by the tuple names of the ranges
2933 of the accesses. The iteration domains by the tuple names
2934 of the domains of the accesses and of the schedule.
2935 The relative order of the iteration domains is given by the
2936 schedule. The relations returned through C<must_no_source>
2937 and C<may_no_source> are subsets of C<sink>.
2938 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2939 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2940 any of the other arguments is treated as an error.
2944 B<The functionality described in this section is fairly new
2945 and may be subject to change.>
2947 The following function can be used to compute a schedule
2948 for a union of domains. The generated schedule respects
2949 all C<validity> dependences. That is, all dependence distances
2950 over these dependences in the scheduled space are lexicographically
2951 positive. The generated schedule schedule also tries to minimize
2952 the dependence distances over C<proximity> dependences.
2953 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2954 for groups of domains where the dependence distances have only
2955 non-negative values.
2956 The algorithm used to construct the schedule is similar to that
2959 #include <isl/schedule.h>
2960 __isl_give isl_schedule *isl_union_set_compute_schedule(
2961 __isl_take isl_union_set *domain,
2962 __isl_take isl_union_map *validity,
2963 __isl_take isl_union_map *proximity);
2964 void *isl_schedule_free(__isl_take isl_schedule *sched);
2966 A mapping from the domains to the scheduled space can be obtained
2967 from an C<isl_schedule> using the following function.
2969 __isl_give isl_union_map *isl_schedule_get_map(
2970 __isl_keep isl_schedule *sched);
2972 A representation of the schedule can be printed using
2974 __isl_give isl_printer *isl_printer_print_schedule(
2975 __isl_take isl_printer *p,
2976 __isl_keep isl_schedule *schedule);
2978 A representation of the schedule as a forest of bands can be obtained
2979 using the following function.
2981 __isl_give isl_band_list *isl_schedule_get_band_forest(
2982 __isl_keep isl_schedule *schedule);
2984 The list can be manipulated as explained in L<"Lists">.
2985 The bands inside the list can be copied and freed using the following
2988 #include <isl/band.h>
2989 __isl_give isl_band *isl_band_copy(
2990 __isl_keep isl_band *band);
2991 void *isl_band_free(__isl_take isl_band *band);
2993 Each band contains zero or more scheduling dimensions.
2994 These are referred to as the members of the band.
2995 The section of the schedule that corresponds to the band is
2996 referred to as the partial schedule of the band.
2997 For those nodes that participate in a band, the outer scheduling
2998 dimensions form the prefix schedule, while the inner scheduling
2999 dimensions form the suffix schedule.
3000 That is, if we take a cut of the band forest, then the union of
3001 the concatenations of the prefix, partial and suffix schedules of
3002 each band in the cut is equal to the entire schedule (modulo
3003 some possible padding at the end with zero scheduling dimensions).
3004 The properties of a band can be inspected using the following functions.
3006 #include <isl/band.h>
3007 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3009 int isl_band_has_children(__isl_keep isl_band *band);
3010 __isl_give isl_band_list *isl_band_get_children(
3011 __isl_keep isl_band *band);
3013 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3014 __isl_keep isl_band *band);
3015 __isl_give isl_union_map *isl_band_get_partial_schedule(
3016 __isl_keep isl_band *band);
3017 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3018 __isl_keep isl_band *band);
3020 int isl_band_n_member(__isl_keep isl_band *band);
3021 int isl_band_member_is_zero_distance(
3022 __isl_keep isl_band *band, int pos);
3024 Note that a scheduling dimension is considered to be ``zero
3025 distance'' if it does not carry any proximity dependences
3027 That is, if the dependence distances of the proximity
3028 dependences are all zero in that direction (for fixed
3029 iterations of outer bands).
3031 A representation of the band can be printed using
3033 #include <isl/band.h>
3034 __isl_give isl_printer *isl_printer_print_band(
3035 __isl_take isl_printer *p,
3036 __isl_keep isl_band *band);
3038 Alternatively, the schedule mapping
3039 can also be obtained in pieces using the following functions.
3041 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3042 __isl_give isl_union_map *isl_schedule_get_band(
3043 __isl_keep isl_schedule *sched, unsigned band);
3045 C<isl_schedule_n_band> returns the maximal number of bands.
3046 C<isl_schedule_get_band> returns a union of mappings from a domain to
3047 the band of consecutive schedule dimensions with the given sequence
3048 number for that domain. Bands with the same sequence number but for
3049 different domains may be completely unrelated.
3050 Within a band, the corresponding coordinates of the distance vectors
3051 are all non-negative, assuming that the coordinates for all previous
3054 =head2 Parametric Vertex Enumeration
3056 The parametric vertex enumeration described in this section
3057 is mainly intended to be used internally and by the C<barvinok>
3060 #include <isl/vertices.h>
3061 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3062 __isl_keep isl_basic_set *bset);
3064 The function C<isl_basic_set_compute_vertices> performs the
3065 actual computation of the parametric vertices and the chamber
3066 decomposition and store the result in an C<isl_vertices> object.
3067 This information can be queried by either iterating over all
3068 the vertices or iterating over all the chambers or cells
3069 and then iterating over all vertices that are active on the chamber.
3071 int isl_vertices_foreach_vertex(
3072 __isl_keep isl_vertices *vertices,
3073 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3076 int isl_vertices_foreach_cell(
3077 __isl_keep isl_vertices *vertices,
3078 int (*fn)(__isl_take isl_cell *cell, void *user),
3080 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3081 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3084 Other operations that can be performed on an C<isl_vertices> object are
3087 isl_ctx *isl_vertices_get_ctx(
3088 __isl_keep isl_vertices *vertices);
3089 int isl_vertices_get_n_vertices(
3090 __isl_keep isl_vertices *vertices);
3091 void isl_vertices_free(__isl_take isl_vertices *vertices);
3093 Vertices can be inspected and destroyed using the following functions.
3095 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3096 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3097 __isl_give isl_basic_set *isl_vertex_get_domain(
3098 __isl_keep isl_vertex *vertex);
3099 __isl_give isl_basic_set *isl_vertex_get_expr(
3100 __isl_keep isl_vertex *vertex);
3101 void isl_vertex_free(__isl_take isl_vertex *vertex);
3103 C<isl_vertex_get_expr> returns a singleton parametric set describing
3104 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3106 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3107 B<rational> basic sets, so they should mainly be used for inspection
3108 and should not be mixed with integer sets.
3110 Chambers can be inspected and destroyed using the following functions.
3112 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3113 __isl_give isl_basic_set *isl_cell_get_domain(
3114 __isl_keep isl_cell *cell);
3115 void isl_cell_free(__isl_take isl_cell *cell);
3119 Although C<isl> is mainly meant to be used as a library,
3120 it also contains some basic applications that use some
3121 of the functionality of C<isl>.
3122 The input may be specified in either the L<isl format>
3123 or the L<PolyLib format>.
3125 =head2 C<isl_polyhedron_sample>
3127 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3128 an integer element of the polyhedron, if there is any.
3129 The first column in the output is the denominator and is always
3130 equal to 1. If the polyhedron contains no integer points,
3131 then a vector of length zero is printed.
3135 C<isl_pip> takes the same input as the C<example> program
3136 from the C<piplib> distribution, i.e., a set of constraints
3137 on the parameters, a line containing only -1 and finally a set
3138 of constraints on a parametric polyhedron.
3139 The coefficients of the parameters appear in the last columns
3140 (but before the final constant column).
3141 The output is the lexicographic minimum of the parametric polyhedron.
3142 As C<isl> currently does not have its own output format, the output
3143 is just a dump of the internal state.
3145 =head2 C<isl_polyhedron_minimize>
3147 C<isl_polyhedron_minimize> computes the minimum of some linear
3148 or affine objective function over the integer points in a polyhedron.
3149 If an affine objective function
3150 is given, then the constant should appear in the last column.
3152 =head2 C<isl_polytope_scan>
3154 Given a polytope, C<isl_polytope_scan> prints
3155 all integer points in the polytope.