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 =head2 Inspecting Sets and Relations
1020 Usually, the user should not have to care about the actual constraints
1021 of the sets and maps, but should instead apply the abstract operations
1022 explained in the following sections.
1023 Occasionally, however, it may be required to inspect the individual
1024 coefficients of the constraints. This section explains how to do so.
1025 In these cases, it may also be useful to have C<isl> compute
1026 an explicit representation of the existentially quantified variables.
1028 __isl_give isl_set *isl_set_compute_divs(
1029 __isl_take isl_set *set);
1030 __isl_give isl_map *isl_map_compute_divs(
1031 __isl_take isl_map *map);
1032 __isl_give isl_union_set *isl_union_set_compute_divs(
1033 __isl_take isl_union_set *uset);
1034 __isl_give isl_union_map *isl_union_map_compute_divs(
1035 __isl_take isl_union_map *umap);
1037 This explicit representation defines the existentially quantified
1038 variables as integer divisions of the other variables, possibly
1039 including earlier existentially quantified variables.
1040 An explicitly represented existentially quantified variable therefore
1041 has a unique value when the values of the other variables are known.
1042 If, furthermore, the same existentials, i.e., existentials
1043 with the same explicit representations, should appear in the
1044 same order in each of the disjuncts of a set or map, then the user should call
1045 either of the following functions.
1047 __isl_give isl_set *isl_set_align_divs(
1048 __isl_take isl_set *set);
1049 __isl_give isl_map *isl_map_align_divs(
1050 __isl_take isl_map *map);
1052 Alternatively, the existentially quantified variables can be removed
1053 using the following functions, which compute an overapproximation.
1055 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1056 __isl_take isl_basic_set *bset);
1057 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1058 __isl_take isl_basic_map *bmap);
1059 __isl_give isl_set *isl_set_remove_divs(
1060 __isl_take isl_set *set);
1061 __isl_give isl_map *isl_map_remove_divs(
1062 __isl_take isl_map *map);
1064 To iterate over all the sets or maps in a union set or map, use
1066 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1067 int (*fn)(__isl_take isl_set *set, void *user),
1069 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1070 int (*fn)(__isl_take isl_map *map, void *user),
1073 The number of sets or maps in a union set or map can be obtained
1076 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1077 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1079 To extract the set or map from a union with a given dimension
1082 __isl_give isl_set *isl_union_set_extract_set(
1083 __isl_keep isl_union_set *uset,
1084 __isl_take isl_dim *dim);
1085 __isl_give isl_map *isl_union_map_extract_map(
1086 __isl_keep isl_union_map *umap,
1087 __isl_take isl_dim *dim);
1089 To iterate over all the basic sets or maps in a set or map, use
1091 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1092 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1094 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1095 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1098 The callback function C<fn> should return 0 if successful and
1099 -1 if an error occurs. In the latter case, or if any other error
1100 occurs, the above functions will return -1.
1102 It should be noted that C<isl> does not guarantee that
1103 the basic sets or maps passed to C<fn> are disjoint.
1104 If this is required, then the user should call one of
1105 the following functions first.
1107 __isl_give isl_set *isl_set_make_disjoint(
1108 __isl_take isl_set *set);
1109 __isl_give isl_map *isl_map_make_disjoint(
1110 __isl_take isl_map *map);
1112 The number of basic sets in a set can be obtained
1115 int isl_set_n_basic_set(__isl_keep isl_set *set);
1117 To iterate over the constraints of a basic set or map, use
1119 #include <isl/constraint.h>
1121 int isl_basic_map_foreach_constraint(
1122 __isl_keep isl_basic_map *bmap,
1123 int (*fn)(__isl_take isl_constraint *c, void *user),
1125 void isl_constraint_free(struct isl_constraint *c);
1127 Again, the callback function C<fn> should return 0 if successful and
1128 -1 if an error occurs. In the latter case, or if any other error
1129 occurs, the above functions will return -1.
1130 The constraint C<c> represents either an equality or an inequality.
1131 Use the following function to find out whether a constraint
1132 represents an equality. If not, it represents an inequality.
1134 int isl_constraint_is_equality(
1135 __isl_keep isl_constraint *constraint);
1137 The coefficients of the constraints can be inspected using
1138 the following functions.
1140 void isl_constraint_get_constant(
1141 __isl_keep isl_constraint *constraint, isl_int *v);
1142 void isl_constraint_get_coefficient(
1143 __isl_keep isl_constraint *constraint,
1144 enum isl_dim_type type, int pos, isl_int *v);
1145 int isl_constraint_involves_dims(
1146 __isl_keep isl_constraint *constraint,
1147 enum isl_dim_type type, unsigned first, unsigned n);
1149 The explicit representations of the existentially quantified
1150 variables can be inspected using the following functions.
1151 Note that the user is only allowed to use these functions
1152 if the inspected set or map is the result of a call
1153 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1155 __isl_give isl_div *isl_constraint_div(
1156 __isl_keep isl_constraint *constraint, int pos);
1157 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1158 void isl_div_get_constant(__isl_keep isl_div *div,
1160 void isl_div_get_denominator(__isl_keep isl_div *div,
1162 void isl_div_get_coefficient(__isl_keep isl_div *div,
1163 enum isl_dim_type type, int pos, isl_int *v);
1165 To obtain the constraints of a basic set or map in matrix
1166 form, use the following functions.
1168 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1169 __isl_keep isl_basic_set *bset,
1170 enum isl_dim_type c1, enum isl_dim_type c2,
1171 enum isl_dim_type c3, enum isl_dim_type c4);
1172 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1173 __isl_keep isl_basic_set *bset,
1174 enum isl_dim_type c1, enum isl_dim_type c2,
1175 enum isl_dim_type c3, enum isl_dim_type c4);
1176 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1177 __isl_keep isl_basic_map *bmap,
1178 enum isl_dim_type c1,
1179 enum isl_dim_type c2, enum isl_dim_type c3,
1180 enum isl_dim_type c4, enum isl_dim_type c5);
1181 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1182 __isl_keep isl_basic_map *bmap,
1183 enum isl_dim_type c1,
1184 enum isl_dim_type c2, enum isl_dim_type c3,
1185 enum isl_dim_type c4, enum isl_dim_type c5);
1187 The C<isl_dim_type> arguments dictate the order in which
1188 different kinds of variables appear in the resulting matrix
1189 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1190 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1192 The names of the domain and range spaces of a set or relation can be
1193 read off using the following functions.
1195 const char *isl_basic_set_get_tuple_name(
1196 __isl_keep isl_basic_set *bset);
1197 const char *isl_set_get_tuple_name(
1198 __isl_keep isl_set *set);
1199 const char *isl_basic_map_get_tuple_name(
1200 __isl_keep isl_basic_map *bmap,
1201 enum isl_dim_type type);
1202 const char *isl_map_get_tuple_name(
1203 __isl_keep isl_map *map,
1204 enum isl_dim_type type);
1206 As with C<isl_dim_get_tuple_name>, the value returned points to
1207 an internal data structure.
1208 The names of individual dimensions can be read off using
1209 the following functions.
1211 const char *isl_constraint_get_dim_name(
1212 __isl_keep isl_constraint *constraint,
1213 enum isl_dim_type type, unsigned pos);
1214 const char *isl_basic_set_get_dim_name(
1215 __isl_keep isl_basic_set *bset,
1216 enum isl_dim_type type, unsigned pos);
1217 const char *isl_set_get_dim_name(
1218 __isl_keep isl_set *set,
1219 enum isl_dim_type type, unsigned pos);
1220 const char *isl_basic_map_get_dim_name(
1221 __isl_keep isl_basic_map *bmap,
1222 enum isl_dim_type type, unsigned pos);
1223 const char *isl_map_get_dim_name(
1224 __isl_keep isl_map *map,
1225 enum isl_dim_type type, unsigned pos);
1227 These functions are mostly useful to obtain the names
1232 =head3 Unary Properties
1238 The following functions test whether the given set or relation
1239 contains any integer points. The ``plain'' variants do not perform
1240 any computations, but simply check if the given set or relation
1241 is already known to be empty.
1243 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1244 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1245 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1246 int isl_set_is_empty(__isl_keep isl_set *set);
1247 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1248 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1249 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1250 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1251 int isl_map_is_empty(__isl_keep isl_map *map);
1252 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1254 =item * Universality
1256 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1257 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1258 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1260 =item * Single-valuedness
1262 int isl_map_is_single_valued(__isl_keep isl_map *map);
1263 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1267 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1268 int isl_map_is_injective(__isl_keep isl_map *map);
1269 int isl_union_map_plain_is_injective(
1270 __isl_keep isl_union_map *umap);
1271 int isl_union_map_is_injective(
1272 __isl_keep isl_union_map *umap);
1276 int isl_map_is_bijective(__isl_keep isl_map *map);
1277 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1281 The following functions check whether the domain of the given
1282 (basic) set is a wrapped relation.
1284 int isl_basic_set_is_wrapping(
1285 __isl_keep isl_basic_set *bset);
1286 int isl_set_is_wrapping(__isl_keep isl_set *set);
1288 =item * Internal Product
1290 int isl_basic_map_can_zip(
1291 __isl_keep isl_basic_map *bmap);
1292 int isl_map_can_zip(__isl_keep isl_map *map);
1294 Check whether the product of domain and range of the given relation
1296 i.e., whether both domain and range are nested relations.
1300 =head3 Binary Properties
1306 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1307 __isl_keep isl_set *set2);
1308 int isl_set_is_equal(__isl_keep isl_set *set1,
1309 __isl_keep isl_set *set2);
1310 int isl_union_set_is_equal(
1311 __isl_keep isl_union_set *uset1,
1312 __isl_keep isl_union_set *uset2);
1313 int isl_basic_map_is_equal(
1314 __isl_keep isl_basic_map *bmap1,
1315 __isl_keep isl_basic_map *bmap2);
1316 int isl_map_is_equal(__isl_keep isl_map *map1,
1317 __isl_keep isl_map *map2);
1318 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1319 __isl_keep isl_map *map2);
1320 int isl_union_map_is_equal(
1321 __isl_keep isl_union_map *umap1,
1322 __isl_keep isl_union_map *umap2);
1324 =item * Disjointness
1326 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1327 __isl_keep isl_set *set2);
1331 int isl_set_is_subset(__isl_keep isl_set *set1,
1332 __isl_keep isl_set *set2);
1333 int isl_set_is_strict_subset(
1334 __isl_keep isl_set *set1,
1335 __isl_keep isl_set *set2);
1336 int isl_union_set_is_subset(
1337 __isl_keep isl_union_set *uset1,
1338 __isl_keep isl_union_set *uset2);
1339 int isl_union_set_is_strict_subset(
1340 __isl_keep isl_union_set *uset1,
1341 __isl_keep isl_union_set *uset2);
1342 int isl_basic_map_is_subset(
1343 __isl_keep isl_basic_map *bmap1,
1344 __isl_keep isl_basic_map *bmap2);
1345 int isl_basic_map_is_strict_subset(
1346 __isl_keep isl_basic_map *bmap1,
1347 __isl_keep isl_basic_map *bmap2);
1348 int isl_map_is_subset(
1349 __isl_keep isl_map *map1,
1350 __isl_keep isl_map *map2);
1351 int isl_map_is_strict_subset(
1352 __isl_keep isl_map *map1,
1353 __isl_keep isl_map *map2);
1354 int isl_union_map_is_subset(
1355 __isl_keep isl_union_map *umap1,
1356 __isl_keep isl_union_map *umap2);
1357 int isl_union_map_is_strict_subset(
1358 __isl_keep isl_union_map *umap1,
1359 __isl_keep isl_union_map *umap2);
1363 =head2 Unary Operations
1369 __isl_give isl_set *isl_set_complement(
1370 __isl_take isl_set *set);
1374 __isl_give isl_basic_map *isl_basic_map_reverse(
1375 __isl_take isl_basic_map *bmap);
1376 __isl_give isl_map *isl_map_reverse(
1377 __isl_take isl_map *map);
1378 __isl_give isl_union_map *isl_union_map_reverse(
1379 __isl_take isl_union_map *umap);
1383 __isl_give isl_basic_set *isl_basic_set_project_out(
1384 __isl_take isl_basic_set *bset,
1385 enum isl_dim_type type, unsigned first, unsigned n);
1386 __isl_give isl_basic_map *isl_basic_map_project_out(
1387 __isl_take isl_basic_map *bmap,
1388 enum isl_dim_type type, unsigned first, unsigned n);
1389 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1390 enum isl_dim_type type, unsigned first, unsigned n);
1391 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1392 enum isl_dim_type type, unsigned first, unsigned n);
1393 __isl_give isl_basic_set *isl_basic_map_domain(
1394 __isl_take isl_basic_map *bmap);
1395 __isl_give isl_basic_set *isl_basic_map_range(
1396 __isl_take isl_basic_map *bmap);
1397 __isl_give isl_set *isl_map_domain(
1398 __isl_take isl_map *bmap);
1399 __isl_give isl_set *isl_map_range(
1400 __isl_take isl_map *map);
1401 __isl_give isl_union_set *isl_union_map_domain(
1402 __isl_take isl_union_map *umap);
1403 __isl_give isl_union_set *isl_union_map_range(
1404 __isl_take isl_union_map *umap);
1406 __isl_give isl_basic_map *isl_basic_map_domain_map(
1407 __isl_take isl_basic_map *bmap);
1408 __isl_give isl_basic_map *isl_basic_map_range_map(
1409 __isl_take isl_basic_map *bmap);
1410 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1411 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1412 __isl_give isl_union_map *isl_union_map_domain_map(
1413 __isl_take isl_union_map *umap);
1414 __isl_give isl_union_map *isl_union_map_range_map(
1415 __isl_take isl_union_map *umap);
1417 The functions above construct a (basic, regular or union) relation
1418 that maps (a wrapped version of) the input relation to its domain or range.
1422 __isl_give isl_set *isl_set_eliminate(
1423 __isl_take isl_set *set, enum isl_dim_type type,
1424 unsigned first, unsigned n);
1426 Eliminate the coefficients for the given dimensions from the constraints,
1427 without removing the dimensions.
1431 __isl_give isl_basic_set *isl_basic_set_fix(
1432 __isl_take isl_basic_set *bset,
1433 enum isl_dim_type type, unsigned pos,
1435 __isl_give isl_basic_set *isl_basic_set_fix_si(
1436 __isl_take isl_basic_set *bset,
1437 enum isl_dim_type type, unsigned pos, int value);
1438 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1439 enum isl_dim_type type, unsigned pos,
1441 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1442 enum isl_dim_type type, unsigned pos, int value);
1443 __isl_give isl_basic_map *isl_basic_map_fix_si(
1444 __isl_take isl_basic_map *bmap,
1445 enum isl_dim_type type, unsigned pos, int value);
1446 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1447 enum isl_dim_type type, unsigned pos, int value);
1449 Intersect the set or relation with the hyperplane where the given
1450 dimension has the fixed given value.
1454 __isl_give isl_map *isl_set_identity(
1455 __isl_take isl_set *set);
1456 __isl_give isl_union_map *isl_union_set_identity(
1457 __isl_take isl_union_set *uset);
1459 Construct an identity relation on the given (union) set.
1463 __isl_give isl_basic_set *isl_basic_map_deltas(
1464 __isl_take isl_basic_map *bmap);
1465 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1466 __isl_give isl_union_set *isl_union_map_deltas(
1467 __isl_take isl_union_map *umap);
1469 These functions return a (basic) set containing the differences
1470 between image elements and corresponding domain elements in the input.
1472 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1473 __isl_take isl_basic_map *bmap);
1474 __isl_give isl_map *isl_map_deltas_map(
1475 __isl_take isl_map *map);
1476 __isl_give isl_union_map *isl_union_map_deltas_map(
1477 __isl_take isl_union_map *umap);
1479 The functions above construct a (basic, regular or union) relation
1480 that maps (a wrapped version of) the input relation to its delta set.
1484 Simplify the representation of a set or relation by trying
1485 to combine pairs of basic sets or relations into a single
1486 basic set or relation.
1488 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1489 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1490 __isl_give isl_union_set *isl_union_set_coalesce(
1491 __isl_take isl_union_set *uset);
1492 __isl_give isl_union_map *isl_union_map_coalesce(
1493 __isl_take isl_union_map *umap);
1495 =item * Detecting equalities
1497 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1498 __isl_take isl_basic_set *bset);
1499 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1500 __isl_take isl_basic_map *bmap);
1501 __isl_give isl_set *isl_set_detect_equalities(
1502 __isl_take isl_set *set);
1503 __isl_give isl_map *isl_map_detect_equalities(
1504 __isl_take isl_map *map);
1505 __isl_give isl_union_set *isl_union_set_detect_equalities(
1506 __isl_take isl_union_set *uset);
1507 __isl_give isl_union_map *isl_union_map_detect_equalities(
1508 __isl_take isl_union_map *umap);
1510 Simplify the representation of a set or relation by detecting implicit
1513 =item * Removing redundant constraints
1515 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1516 __isl_take isl_basic_set *bset);
1517 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1518 __isl_take isl_basic_map *bmap);
1522 __isl_give isl_basic_set *isl_set_convex_hull(
1523 __isl_take isl_set *set);
1524 __isl_give isl_basic_map *isl_map_convex_hull(
1525 __isl_take isl_map *map);
1527 If the input set or relation has any existentially quantified
1528 variables, then the result of these operations is currently undefined.
1532 __isl_give isl_basic_set *isl_set_simple_hull(
1533 __isl_take isl_set *set);
1534 __isl_give isl_basic_map *isl_map_simple_hull(
1535 __isl_take isl_map *map);
1536 __isl_give isl_union_map *isl_union_map_simple_hull(
1537 __isl_take isl_union_map *umap);
1539 These functions compute a single basic set or relation
1540 that contains the whole input set or relation.
1541 In particular, the output is described by translates
1542 of the constraints describing the basic sets or relations in the input.
1546 (See \autoref{s:simple hull}.)
1552 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1553 __isl_take isl_basic_set *bset);
1554 __isl_give isl_basic_set *isl_set_affine_hull(
1555 __isl_take isl_set *set);
1556 __isl_give isl_union_set *isl_union_set_affine_hull(
1557 __isl_take isl_union_set *uset);
1558 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1559 __isl_take isl_basic_map *bmap);
1560 __isl_give isl_basic_map *isl_map_affine_hull(
1561 __isl_take isl_map *map);
1562 __isl_give isl_union_map *isl_union_map_affine_hull(
1563 __isl_take isl_union_map *umap);
1565 In case of union sets and relations, the affine hull is computed
1568 =item * Polyhedral hull
1570 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1571 __isl_take isl_set *set);
1572 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1573 __isl_take isl_map *map);
1574 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1575 __isl_take isl_union_set *uset);
1576 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1577 __isl_take isl_union_map *umap);
1579 These functions compute a single basic set or relation
1580 not involving any existentially quantified variables
1581 that contains the whole input set or relation.
1582 In case of union sets and relations, the polyhedral hull is computed
1585 =item * Optimization
1587 #include <isl/ilp.h>
1588 enum isl_lp_result isl_basic_set_max(
1589 __isl_keep isl_basic_set *bset,
1590 __isl_keep isl_aff *obj, isl_int *opt)
1591 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1592 __isl_keep isl_aff *obj, isl_int *opt);
1594 Compute the maximum of the integer affine expression C<obj>
1595 over the points in C<set>, returning the result in C<opt>.
1596 The return value may be one of C<isl_lp_error>,
1597 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1601 The following functions compute either the set of (rational) coefficient
1602 values of valid constraints for the given set or the set of (rational)
1603 values satisfying the constraints with coefficients from the given set.
1604 Internally, these two sets of functions perform essentially the
1605 same operations, except that the set of coefficients is assumed to
1606 be a cone, while the set of values may be any polyhedron.
1607 The current implementation is based on the Farkas lemma and
1608 Fourier-Motzkin elimination, but this may change or be made optional
1609 in future. In particular, future implementations may use different
1610 dualization algorithms or skip the elimination step.
1612 __isl_give isl_basic_set *isl_basic_set_coefficients(
1613 __isl_take isl_basic_set *bset);
1614 __isl_give isl_basic_set *isl_set_coefficients(
1615 __isl_take isl_set *set);
1616 __isl_give isl_union_set *isl_union_set_coefficients(
1617 __isl_take isl_union_set *bset);
1618 __isl_give isl_basic_set *isl_basic_set_solutions(
1619 __isl_take isl_basic_set *bset);
1620 __isl_give isl_basic_set *isl_set_solutions(
1621 __isl_take isl_set *set);
1622 __isl_give isl_union_set *isl_union_set_solutions(
1623 __isl_take isl_union_set *bset);
1627 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1629 __isl_give isl_union_map *isl_union_map_power(
1630 __isl_take isl_union_map *umap, int *exact);
1632 Compute a parametric representation for all positive powers I<k> of C<map>.
1633 The result maps I<k> to a nested relation corresponding to the
1634 I<k>th power of C<map>.
1635 The result may be an overapproximation. If the result is known to be exact,
1636 then C<*exact> is set to C<1>.
1638 =item * Transitive closure
1640 __isl_give isl_map *isl_map_transitive_closure(
1641 __isl_take isl_map *map, int *exact);
1642 __isl_give isl_union_map *isl_union_map_transitive_closure(
1643 __isl_take isl_union_map *umap, int *exact);
1645 Compute the transitive closure of C<map>.
1646 The result may be an overapproximation. If the result is known to be exact,
1647 then C<*exact> is set to C<1>.
1649 =item * Reaching path lengths
1651 __isl_give isl_map *isl_map_reaching_path_lengths(
1652 __isl_take isl_map *map, int *exact);
1654 Compute a relation that maps each element in the range of C<map>
1655 to the lengths of all paths composed of edges in C<map> that
1656 end up in the given element.
1657 The result may be an overapproximation. If the result is known to be exact,
1658 then C<*exact> is set to C<1>.
1659 To compute the I<maximal> path length, the resulting relation
1660 should be postprocessed by C<isl_map_lexmax>.
1661 In particular, if the input relation is a dependence relation
1662 (mapping sources to sinks), then the maximal path length corresponds
1663 to the free schedule.
1664 Note, however, that C<isl_map_lexmax> expects the maximum to be
1665 finite, so if the path lengths are unbounded (possibly due to
1666 the overapproximation), then you will get an error message.
1670 __isl_give isl_basic_set *isl_basic_map_wrap(
1671 __isl_take isl_basic_map *bmap);
1672 __isl_give isl_set *isl_map_wrap(
1673 __isl_take isl_map *map);
1674 __isl_give isl_union_set *isl_union_map_wrap(
1675 __isl_take isl_union_map *umap);
1676 __isl_give isl_basic_map *isl_basic_set_unwrap(
1677 __isl_take isl_basic_set *bset);
1678 __isl_give isl_map *isl_set_unwrap(
1679 __isl_take isl_set *set);
1680 __isl_give isl_union_map *isl_union_set_unwrap(
1681 __isl_take isl_union_set *uset);
1685 Remove any internal structure of domain (and range) of the given
1686 set or relation. If there is any such internal structure in the input,
1687 then the name of the space is also removed.
1689 __isl_give isl_basic_set *isl_basic_set_flatten(
1690 __isl_take isl_basic_set *bset);
1691 __isl_give isl_set *isl_set_flatten(
1692 __isl_take isl_set *set);
1693 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1694 __isl_take isl_basic_map *bmap);
1695 __isl_give isl_map *isl_map_flatten_range(
1696 __isl_take isl_map *map);
1697 __isl_give isl_basic_map *isl_basic_map_flatten(
1698 __isl_take isl_basic_map *bmap);
1699 __isl_give isl_map *isl_map_flatten(
1700 __isl_take isl_map *map);
1702 __isl_give isl_map *isl_set_flatten_map(
1703 __isl_take isl_set *set);
1705 The function above constructs a relation
1706 that maps the input set to a flattened version of the set.
1710 Lift the input set to a space with extra dimensions corresponding
1711 to the existentially quantified variables in the input.
1712 In particular, the result lives in a wrapped map where the domain
1713 is the original space and the range corresponds to the original
1714 existentially quantified variables.
1716 __isl_give isl_basic_set *isl_basic_set_lift(
1717 __isl_take isl_basic_set *bset);
1718 __isl_give isl_set *isl_set_lift(
1719 __isl_take isl_set *set);
1720 __isl_give isl_union_set *isl_union_set_lift(
1721 __isl_take isl_union_set *uset);
1723 =item * Internal Product
1725 __isl_give isl_basic_map *isl_basic_map_zip(
1726 __isl_take isl_basic_map *bmap);
1727 __isl_give isl_map *isl_map_zip(
1728 __isl_take isl_map *map);
1729 __isl_give isl_union_map *isl_union_map_zip(
1730 __isl_take isl_union_map *umap);
1732 Given a relation with nested relations for domain and range,
1733 interchange the range of the domain with the domain of the range.
1735 =item * Aligning parameters
1737 __isl_give isl_set *isl_set_align_params(
1738 __isl_take isl_set *set,
1739 __isl_take isl_dim *model);
1740 __isl_give isl_map *isl_map_align_params(
1741 __isl_take isl_map *map,
1742 __isl_take isl_dim *model);
1744 Change the order of the parameters of the given set or relation
1745 such that the first parameters match those of C<model>.
1746 This may involve the introduction of extra parameters.
1747 All parameters need to be named.
1749 =item * Dimension manipulation
1751 __isl_give isl_set *isl_set_add_dims(
1752 __isl_take isl_set *set,
1753 enum isl_dim_type type, unsigned n);
1754 __isl_give isl_map *isl_map_add_dims(
1755 __isl_take isl_map *map,
1756 enum isl_dim_type type, unsigned n);
1758 It is usually not advisable to directly change the (input or output)
1759 space of a set or a relation as this removes the name and the internal
1760 structure of the space. However, the above functions can be useful
1761 to add new parameters, assuming
1762 C<isl_set_align_params> and C<isl_map_align_params>
1767 =head2 Binary Operations
1769 The two arguments of a binary operation not only need to live
1770 in the same C<isl_ctx>, they currently also need to have
1771 the same (number of) parameters.
1773 =head3 Basic Operations
1777 =item * Intersection
1779 __isl_give isl_basic_set *isl_basic_set_intersect(
1780 __isl_take isl_basic_set *bset1,
1781 __isl_take isl_basic_set *bset2);
1782 __isl_give isl_set *isl_set_intersect(
1783 __isl_take isl_set *set1,
1784 __isl_take isl_set *set2);
1785 __isl_give isl_union_set *isl_union_set_intersect(
1786 __isl_take isl_union_set *uset1,
1787 __isl_take isl_union_set *uset2);
1788 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1789 __isl_take isl_basic_map *bmap,
1790 __isl_take isl_basic_set *bset);
1791 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1792 __isl_take isl_basic_map *bmap,
1793 __isl_take isl_basic_set *bset);
1794 __isl_give isl_basic_map *isl_basic_map_intersect(
1795 __isl_take isl_basic_map *bmap1,
1796 __isl_take isl_basic_map *bmap2);
1797 __isl_give isl_map *isl_map_intersect_domain(
1798 __isl_take isl_map *map,
1799 __isl_take isl_set *set);
1800 __isl_give isl_map *isl_map_intersect_range(
1801 __isl_take isl_map *map,
1802 __isl_take isl_set *set);
1803 __isl_give isl_map *isl_map_intersect(
1804 __isl_take isl_map *map1,
1805 __isl_take isl_map *map2);
1806 __isl_give isl_union_map *isl_union_map_intersect_domain(
1807 __isl_take isl_union_map *umap,
1808 __isl_take isl_union_set *uset);
1809 __isl_give isl_union_map *isl_union_map_intersect_range(
1810 __isl_take isl_union_map *umap,
1811 __isl_take isl_union_set *uset);
1812 __isl_give isl_union_map *isl_union_map_intersect(
1813 __isl_take isl_union_map *umap1,
1814 __isl_take isl_union_map *umap2);
1818 __isl_give isl_set *isl_basic_set_union(
1819 __isl_take isl_basic_set *bset1,
1820 __isl_take isl_basic_set *bset2);
1821 __isl_give isl_map *isl_basic_map_union(
1822 __isl_take isl_basic_map *bmap1,
1823 __isl_take isl_basic_map *bmap2);
1824 __isl_give isl_set *isl_set_union(
1825 __isl_take isl_set *set1,
1826 __isl_take isl_set *set2);
1827 __isl_give isl_map *isl_map_union(
1828 __isl_take isl_map *map1,
1829 __isl_take isl_map *map2);
1830 __isl_give isl_union_set *isl_union_set_union(
1831 __isl_take isl_union_set *uset1,
1832 __isl_take isl_union_set *uset2);
1833 __isl_give isl_union_map *isl_union_map_union(
1834 __isl_take isl_union_map *umap1,
1835 __isl_take isl_union_map *umap2);
1837 =item * Set difference
1839 __isl_give isl_set *isl_set_subtract(
1840 __isl_take isl_set *set1,
1841 __isl_take isl_set *set2);
1842 __isl_give isl_map *isl_map_subtract(
1843 __isl_take isl_map *map1,
1844 __isl_take isl_map *map2);
1845 __isl_give isl_union_set *isl_union_set_subtract(
1846 __isl_take isl_union_set *uset1,
1847 __isl_take isl_union_set *uset2);
1848 __isl_give isl_union_map *isl_union_map_subtract(
1849 __isl_take isl_union_map *umap1,
1850 __isl_take isl_union_map *umap2);
1854 __isl_give isl_basic_set *isl_basic_set_apply(
1855 __isl_take isl_basic_set *bset,
1856 __isl_take isl_basic_map *bmap);
1857 __isl_give isl_set *isl_set_apply(
1858 __isl_take isl_set *set,
1859 __isl_take isl_map *map);
1860 __isl_give isl_union_set *isl_union_set_apply(
1861 __isl_take isl_union_set *uset,
1862 __isl_take isl_union_map *umap);
1863 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1864 __isl_take isl_basic_map *bmap1,
1865 __isl_take isl_basic_map *bmap2);
1866 __isl_give isl_basic_map *isl_basic_map_apply_range(
1867 __isl_take isl_basic_map *bmap1,
1868 __isl_take isl_basic_map *bmap2);
1869 __isl_give isl_map *isl_map_apply_domain(
1870 __isl_take isl_map *map1,
1871 __isl_take isl_map *map2);
1872 __isl_give isl_union_map *isl_union_map_apply_domain(
1873 __isl_take isl_union_map *umap1,
1874 __isl_take isl_union_map *umap2);
1875 __isl_give isl_map *isl_map_apply_range(
1876 __isl_take isl_map *map1,
1877 __isl_take isl_map *map2);
1878 __isl_give isl_union_map *isl_union_map_apply_range(
1879 __isl_take isl_union_map *umap1,
1880 __isl_take isl_union_map *umap2);
1882 =item * Cartesian Product
1884 __isl_give isl_set *isl_set_product(
1885 __isl_take isl_set *set1,
1886 __isl_take isl_set *set2);
1887 __isl_give isl_union_set *isl_union_set_product(
1888 __isl_take isl_union_set *uset1,
1889 __isl_take isl_union_set *uset2);
1890 __isl_give isl_basic_map *isl_basic_map_range_product(
1891 __isl_take isl_basic_map *bmap1,
1892 __isl_take isl_basic_map *bmap2);
1893 __isl_give isl_map *isl_map_range_product(
1894 __isl_take isl_map *map1,
1895 __isl_take isl_map *map2);
1896 __isl_give isl_union_map *isl_union_map_range_product(
1897 __isl_take isl_union_map *umap1,
1898 __isl_take isl_union_map *umap2);
1899 __isl_give isl_map *isl_map_product(
1900 __isl_take isl_map *map1,
1901 __isl_take isl_map *map2);
1902 __isl_give isl_union_map *isl_union_map_product(
1903 __isl_take isl_union_map *umap1,
1904 __isl_take isl_union_map *umap2);
1906 The above functions compute the cross product of the given
1907 sets or relations. The domains and ranges of the results
1908 are wrapped maps between domains and ranges of the inputs.
1909 To obtain a ``flat'' product, use the following functions
1912 __isl_give isl_basic_set *isl_basic_set_flat_product(
1913 __isl_take isl_basic_set *bset1,
1914 __isl_take isl_basic_set *bset2);
1915 __isl_give isl_set *isl_set_flat_product(
1916 __isl_take isl_set *set1,
1917 __isl_take isl_set *set2);
1918 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1919 __isl_take isl_basic_map *bmap1,
1920 __isl_take isl_basic_map *bmap2);
1921 __isl_give isl_map *isl_map_flat_range_product(
1922 __isl_take isl_map *map1,
1923 __isl_take isl_map *map2);
1924 __isl_give isl_union_map *isl_union_map_flat_range_product(
1925 __isl_take isl_union_map *umap1,
1926 __isl_take isl_union_map *umap2);
1927 __isl_give isl_basic_map *isl_basic_map_flat_product(
1928 __isl_take isl_basic_map *bmap1,
1929 __isl_take isl_basic_map *bmap2);
1930 __isl_give isl_map *isl_map_flat_product(
1931 __isl_take isl_map *map1,
1932 __isl_take isl_map *map2);
1934 =item * Simplification
1936 __isl_give isl_basic_set *isl_basic_set_gist(
1937 __isl_take isl_basic_set *bset,
1938 __isl_take isl_basic_set *context);
1939 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1940 __isl_take isl_set *context);
1941 __isl_give isl_union_set *isl_union_set_gist(
1942 __isl_take isl_union_set *uset,
1943 __isl_take isl_union_set *context);
1944 __isl_give isl_basic_map *isl_basic_map_gist(
1945 __isl_take isl_basic_map *bmap,
1946 __isl_take isl_basic_map *context);
1947 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1948 __isl_take isl_map *context);
1949 __isl_give isl_union_map *isl_union_map_gist(
1950 __isl_take isl_union_map *umap,
1951 __isl_take isl_union_map *context);
1953 The gist operation returns a set or relation that has the
1954 same intersection with the context as the input set or relation.
1955 Any implicit equality in the intersection is made explicit in the result,
1956 while all inequalities that are redundant with respect to the intersection
1958 In case of union sets and relations, the gist operation is performed
1963 =head3 Lexicographic Optimization
1965 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1966 the following functions
1967 compute a set that contains the lexicographic minimum or maximum
1968 of the elements in C<set> (or C<bset>) for those values of the parameters
1969 that satisfy C<dom>.
1970 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1971 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1973 In other words, the union of the parameter values
1974 for which the result is non-empty and of C<*empty>
1977 __isl_give isl_set *isl_basic_set_partial_lexmin(
1978 __isl_take isl_basic_set *bset,
1979 __isl_take isl_basic_set *dom,
1980 __isl_give isl_set **empty);
1981 __isl_give isl_set *isl_basic_set_partial_lexmax(
1982 __isl_take isl_basic_set *bset,
1983 __isl_take isl_basic_set *dom,
1984 __isl_give isl_set **empty);
1985 __isl_give isl_set *isl_set_partial_lexmin(
1986 __isl_take isl_set *set, __isl_take isl_set *dom,
1987 __isl_give isl_set **empty);
1988 __isl_give isl_set *isl_set_partial_lexmax(
1989 __isl_take isl_set *set, __isl_take isl_set *dom,
1990 __isl_give isl_set **empty);
1992 Given a (basic) set C<set> (or C<bset>), the following functions simply
1993 return a set containing the lexicographic minimum or maximum
1994 of the elements in C<set> (or C<bset>).
1995 In case of union sets, the optimum is computed per space.
1997 __isl_give isl_set *isl_basic_set_lexmin(
1998 __isl_take isl_basic_set *bset);
1999 __isl_give isl_set *isl_basic_set_lexmax(
2000 __isl_take isl_basic_set *bset);
2001 __isl_give isl_set *isl_set_lexmin(
2002 __isl_take isl_set *set);
2003 __isl_give isl_set *isl_set_lexmax(
2004 __isl_take isl_set *set);
2005 __isl_give isl_union_set *isl_union_set_lexmin(
2006 __isl_take isl_union_set *uset);
2007 __isl_give isl_union_set *isl_union_set_lexmax(
2008 __isl_take isl_union_set *uset);
2010 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2011 the following functions
2012 compute a relation that maps each element of C<dom>
2013 to the single lexicographic minimum or maximum
2014 of the elements that are associated to that same
2015 element in C<map> (or C<bmap>).
2016 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2017 that contains the elements in C<dom> that do not map
2018 to any elements in C<map> (or C<bmap>).
2019 In other words, the union of the domain of the result and of C<*empty>
2022 __isl_give isl_map *isl_basic_map_partial_lexmax(
2023 __isl_take isl_basic_map *bmap,
2024 __isl_take isl_basic_set *dom,
2025 __isl_give isl_set **empty);
2026 __isl_give isl_map *isl_basic_map_partial_lexmin(
2027 __isl_take isl_basic_map *bmap,
2028 __isl_take isl_basic_set *dom,
2029 __isl_give isl_set **empty);
2030 __isl_give isl_map *isl_map_partial_lexmax(
2031 __isl_take isl_map *map, __isl_take isl_set *dom,
2032 __isl_give isl_set **empty);
2033 __isl_give isl_map *isl_map_partial_lexmin(
2034 __isl_take isl_map *map, __isl_take isl_set *dom,
2035 __isl_give isl_set **empty);
2037 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2038 return a map mapping each element in the domain of
2039 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2040 of all elements associated to that element.
2041 In case of union relations, the optimum is computed per space.
2043 __isl_give isl_map *isl_basic_map_lexmin(
2044 __isl_take isl_basic_map *bmap);
2045 __isl_give isl_map *isl_basic_map_lexmax(
2046 __isl_take isl_basic_map *bmap);
2047 __isl_give isl_map *isl_map_lexmin(
2048 __isl_take isl_map *map);
2049 __isl_give isl_map *isl_map_lexmax(
2050 __isl_take isl_map *map);
2051 __isl_give isl_union_map *isl_union_map_lexmin(
2052 __isl_take isl_union_map *umap);
2053 __isl_give isl_union_map *isl_union_map_lexmax(
2054 __isl_take isl_union_map *umap);
2058 Lists are defined over several element types, including
2059 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2060 Here we take lists of C<isl_set>s as an example.
2061 Lists can be created, copied and freed using the following functions.
2063 #include <isl/list.h>
2064 __isl_give isl_set_list *isl_set_list_alloc(
2065 isl_ctx *ctx, int n);
2066 __isl_give isl_set_list *isl_set_list_copy(
2067 __isl_keep isl_set_list *list);
2068 __isl_give isl_set_list *isl_set_list_add(
2069 __isl_take isl_set_list *list,
2070 __isl_take isl_set *el);
2071 void isl_set_list_free(__isl_take isl_set_list *list);
2073 C<isl_set_list_alloc> creates an empty list with a capacity for
2076 Lists can be inspected using the following functions.
2078 #include <isl/list.h>
2079 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2080 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2081 __isl_give struct isl_set *isl_set_list_get_set(
2082 __isl_keep isl_set_list *list, int index);
2083 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2084 int (*fn)(__isl_take struct isl_set *el, void *user),
2087 Lists can be printed using
2089 #include <isl/list.h>
2090 __isl_give isl_printer *isl_printer_print_set_list(
2091 __isl_take isl_printer *p,
2092 __isl_keep isl_set_list *list);
2096 Matrices can be created, copied and freed using the following functions.
2098 #include <isl/mat.h>
2099 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2100 unsigned n_row, unsigned n_col);
2101 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2102 void isl_mat_free(__isl_take isl_mat *mat);
2104 Note that the elements of a newly created matrix may have arbitrary values.
2105 The elements can be changed and inspected using the following functions.
2107 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2108 int isl_mat_rows(__isl_keep isl_mat *mat);
2109 int isl_mat_cols(__isl_keep isl_mat *mat);
2110 int isl_mat_get_element(__isl_keep isl_mat *mat,
2111 int row, int col, isl_int *v);
2112 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2113 int row, int col, isl_int v);
2114 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2115 int row, int col, int v);
2117 C<isl_mat_get_element> will return a negative value if anything went wrong.
2118 In that case, the value of C<*v> is undefined.
2120 The following function can be used to compute the (right) inverse
2121 of a matrix, i.e., a matrix such that the product of the original
2122 and the inverse (in that order) is a multiple of the identity matrix.
2123 The input matrix is assumed to be of full row-rank.
2125 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2127 The following function can be used to compute the (right) kernel
2128 (or null space) of a matrix, i.e., a matrix such that the product of
2129 the original and the kernel (in that order) is the zero matrix.
2131 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2133 =head2 Quasi Affine Expressions
2135 The zero quasi affine expression can be created using
2137 __isl_give isl_aff *isl_aff_zero(
2138 __isl_take isl_local_space *ls);
2140 Quasi affine expressions can be copied and free using
2142 #include <isl/aff.h>
2143 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2144 void *isl_aff_free(__isl_take isl_aff *aff);
2146 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2147 using the following function. The constraint is required to have
2148 a non-zero coefficient for the specified dimension.
2150 #include <isl/constraint.h>
2151 __isl_give isl_aff *isl_constraint_get_bound(
2152 __isl_keep isl_constraint *constraint,
2153 enum isl_dim_type type, int pos);
2155 Conversely, an equality constraint equating
2156 the affine expression to zero or an inequality constraint enforcing
2157 the affine expression to be non-negative, can be constructed using
2159 __isl_give isl_constraint *isl_equality_from_aff(
2160 __isl_take isl_aff *aff);
2161 __isl_give isl_constraint *isl_inequality_from_aff(
2162 __isl_take isl_aff *aff);
2164 The expression can be inspected using
2166 #include <isl/aff.h>
2167 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2168 int isl_aff_dim(__isl_keep isl_aff *aff,
2169 enum isl_dim_type type);
2170 __isl_give isl_local_space *isl_aff_get_local_space(
2171 __isl_keep isl_aff *aff);
2172 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2173 enum isl_dim_type type, unsigned pos);
2174 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2176 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2177 enum isl_dim_type type, int pos, isl_int *v);
2178 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2180 __isl_give isl_div *isl_aff_get_div(
2181 __isl_keep isl_aff *aff, int pos);
2183 It can be modified using
2185 #include <isl/aff.h>
2186 __isl_give isl_aff *isl_aff_set_constant(
2187 __isl_take isl_aff *aff, isl_int v);
2188 __isl_give isl_aff *isl_aff_set_constant_si(
2189 __isl_take isl_aff *aff, int v);
2190 __isl_give isl_aff *isl_aff_set_coefficient(
2191 __isl_take isl_aff *aff,
2192 enum isl_dim_type type, int pos, isl_int v);
2193 __isl_give isl_aff *isl_aff_set_coefficient_si(
2194 __isl_take isl_aff *aff,
2195 enum isl_dim_type type, int pos, int v);
2196 __isl_give isl_aff *isl_aff_set_denominator(
2197 __isl_take isl_aff *aff, isl_int v);
2199 __isl_give isl_aff *isl_aff_add_constant(
2200 __isl_take isl_aff *aff, isl_int v);
2201 __isl_give isl_aff *isl_aff_add_coefficient_si(
2202 __isl_take isl_aff *aff,
2203 enum isl_dim_type type, int pos, int v);
2205 Note that the C<set_constant> and C<set_coefficient> functions
2206 set the I<numerator> of the constant or coefficient, while
2207 C<add_constant> and C<add_coefficient> add an integer value to
2208 the possibly rational constant or coefficient.
2212 #include <isl/aff.h>
2213 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2214 __isl_take isl_aff *aff2);
2215 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2216 __isl_take isl_aff *aff2);
2217 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2218 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2219 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2221 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2224 An expression can be printed using
2226 #include <isl/aff.h>
2227 __isl_give isl_printer *isl_printer_print_aff(
2228 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2232 Points are elements of a set. They can be used to construct
2233 simple sets (boxes) or they can be used to represent the
2234 individual elements of a set.
2235 The zero point (the origin) can be created using
2237 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2239 The coordinates of a point can be inspected, set and changed
2242 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2243 enum isl_dim_type type, int pos, isl_int *v);
2244 __isl_give isl_point *isl_point_set_coordinate(
2245 __isl_take isl_point *pnt,
2246 enum isl_dim_type type, int pos, isl_int v);
2248 __isl_give isl_point *isl_point_add_ui(
2249 __isl_take isl_point *pnt,
2250 enum isl_dim_type type, int pos, unsigned val);
2251 __isl_give isl_point *isl_point_sub_ui(
2252 __isl_take isl_point *pnt,
2253 enum isl_dim_type type, int pos, unsigned val);
2255 Points can be copied or freed using
2257 __isl_give isl_point *isl_point_copy(
2258 __isl_keep isl_point *pnt);
2259 void isl_point_free(__isl_take isl_point *pnt);
2261 A singleton set can be created from a point using
2263 __isl_give isl_basic_set *isl_basic_set_from_point(
2264 __isl_take isl_point *pnt);
2265 __isl_give isl_set *isl_set_from_point(
2266 __isl_take isl_point *pnt);
2268 and a box can be created from two opposite extremal points using
2270 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2271 __isl_take isl_point *pnt1,
2272 __isl_take isl_point *pnt2);
2273 __isl_give isl_set *isl_set_box_from_points(
2274 __isl_take isl_point *pnt1,
2275 __isl_take isl_point *pnt2);
2277 All elements of a B<bounded> (union) set can be enumerated using
2278 the following functions.
2280 int isl_set_foreach_point(__isl_keep isl_set *set,
2281 int (*fn)(__isl_take isl_point *pnt, void *user),
2283 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2284 int (*fn)(__isl_take isl_point *pnt, void *user),
2287 The function C<fn> is called for each integer point in
2288 C<set> with as second argument the last argument of
2289 the C<isl_set_foreach_point> call. The function C<fn>
2290 should return C<0> on success and C<-1> on failure.
2291 In the latter case, C<isl_set_foreach_point> will stop
2292 enumerating and return C<-1> as well.
2293 If the enumeration is performed successfully and to completion,
2294 then C<isl_set_foreach_point> returns C<0>.
2296 To obtain a single point of a (basic) set, use
2298 __isl_give isl_point *isl_basic_set_sample_point(
2299 __isl_take isl_basic_set *bset);
2300 __isl_give isl_point *isl_set_sample_point(
2301 __isl_take isl_set *set);
2303 If C<set> does not contain any (integer) points, then the
2304 resulting point will be ``void'', a property that can be
2307 int isl_point_is_void(__isl_keep isl_point *pnt);
2309 =head2 Piecewise Quasipolynomials
2311 A piecewise quasipolynomial is a particular kind of function that maps
2312 a parametric point to a rational value.
2313 More specifically, a quasipolynomial is a polynomial expression in greatest
2314 integer parts of affine expressions of parameters and variables.
2315 A piecewise quasipolynomial is a subdivision of a given parametric
2316 domain into disjoint cells with a quasipolynomial associated to
2317 each cell. The value of the piecewise quasipolynomial at a given
2318 point is the value of the quasipolynomial associated to the cell
2319 that contains the point. Outside of the union of cells,
2320 the value is assumed to be zero.
2321 For example, the piecewise quasipolynomial
2323 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2325 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2326 A given piecewise quasipolynomial has a fixed domain dimension.
2327 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2328 defined over different domains.
2329 Piecewise quasipolynomials are mainly used by the C<barvinok>
2330 library for representing the number of elements in a parametric set or map.
2331 For example, the piecewise quasipolynomial above represents
2332 the number of points in the map
2334 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2336 =head3 Printing (Piecewise) Quasipolynomials
2338 Quasipolynomials and piecewise quasipolynomials can be printed
2339 using the following functions.
2341 __isl_give isl_printer *isl_printer_print_qpolynomial(
2342 __isl_take isl_printer *p,
2343 __isl_keep isl_qpolynomial *qp);
2345 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2346 __isl_take isl_printer *p,
2347 __isl_keep isl_pw_qpolynomial *pwqp);
2349 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2350 __isl_take isl_printer *p,
2351 __isl_keep isl_union_pw_qpolynomial *upwqp);
2353 The output format of the printer
2354 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2355 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2357 In case of printing in C<ISL_FORMAT_C>, the user may want
2358 to set the names of all dimensions
2360 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2361 __isl_take isl_qpolynomial *qp,
2362 enum isl_dim_type type, unsigned pos,
2364 __isl_give isl_pw_qpolynomial *
2365 isl_pw_qpolynomial_set_dim_name(
2366 __isl_take isl_pw_qpolynomial *pwqp,
2367 enum isl_dim_type type, unsigned pos,
2370 =head3 Creating New (Piecewise) Quasipolynomials
2372 Some simple quasipolynomials can be created using the following functions.
2373 More complicated quasipolynomials can be created by applying
2374 operations such as addition and multiplication
2375 on the resulting quasipolynomials
2377 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2378 __isl_take isl_dim *dim);
2379 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2380 __isl_take isl_dim *dim);
2381 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2382 __isl_take isl_dim *dim);
2383 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2384 __isl_take isl_dim *dim);
2385 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2386 __isl_take isl_dim *dim);
2387 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2388 __isl_take isl_dim *dim,
2389 const isl_int n, const isl_int d);
2390 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2391 __isl_take isl_div *div);
2392 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2393 __isl_take isl_dim *dim,
2394 enum isl_dim_type type, unsigned pos);
2395 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2396 __isl_take isl_aff *aff);
2398 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2399 with a single cell can be created using the following functions.
2400 Multiple of these single cell piecewise quasipolynomials can
2401 be combined to create more complicated piecewise quasipolynomials.
2403 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2404 __isl_take isl_dim *dim);
2405 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2406 __isl_take isl_set *set,
2407 __isl_take isl_qpolynomial *qp);
2409 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2410 __isl_take isl_dim *dim);
2411 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2412 __isl_take isl_pw_qpolynomial *pwqp);
2413 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2414 __isl_take isl_union_pw_qpolynomial *upwqp,
2415 __isl_take isl_pw_qpolynomial *pwqp);
2417 Quasipolynomials can be copied and freed again using the following
2420 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2421 __isl_keep isl_qpolynomial *qp);
2422 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2424 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2425 __isl_keep isl_pw_qpolynomial *pwqp);
2426 void isl_pw_qpolynomial_free(
2427 __isl_take isl_pw_qpolynomial *pwqp);
2429 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2430 __isl_keep isl_union_pw_qpolynomial *upwqp);
2431 void isl_union_pw_qpolynomial_free(
2432 __isl_take isl_union_pw_qpolynomial *upwqp);
2434 =head3 Inspecting (Piecewise) Quasipolynomials
2436 To iterate over all piecewise quasipolynomials in a union
2437 piecewise quasipolynomial, use the following function
2439 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2440 __isl_keep isl_union_pw_qpolynomial *upwqp,
2441 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2444 To extract the piecewise quasipolynomial from a union with a given dimension
2447 __isl_give isl_pw_qpolynomial *
2448 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2449 __isl_keep isl_union_pw_qpolynomial *upwqp,
2450 __isl_take isl_dim *dim);
2452 To iterate over the cells in a piecewise quasipolynomial,
2453 use either of the following two functions
2455 int isl_pw_qpolynomial_foreach_piece(
2456 __isl_keep isl_pw_qpolynomial *pwqp,
2457 int (*fn)(__isl_take isl_set *set,
2458 __isl_take isl_qpolynomial *qp,
2459 void *user), void *user);
2460 int isl_pw_qpolynomial_foreach_lifted_piece(
2461 __isl_keep isl_pw_qpolynomial *pwqp,
2462 int (*fn)(__isl_take isl_set *set,
2463 __isl_take isl_qpolynomial *qp,
2464 void *user), void *user);
2466 As usual, the function C<fn> should return C<0> on success
2467 and C<-1> on failure. The difference between
2468 C<isl_pw_qpolynomial_foreach_piece> and
2469 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2470 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2471 compute unique representations for all existentially quantified
2472 variables and then turn these existentially quantified variables
2473 into extra set variables, adapting the associated quasipolynomial
2474 accordingly. This means that the C<set> passed to C<fn>
2475 will not have any existentially quantified variables, but that
2476 the dimensions of the sets may be different for different
2477 invocations of C<fn>.
2479 To iterate over all terms in a quasipolynomial,
2482 int isl_qpolynomial_foreach_term(
2483 __isl_keep isl_qpolynomial *qp,
2484 int (*fn)(__isl_take isl_term *term,
2485 void *user), void *user);
2487 The terms themselves can be inspected and freed using
2490 unsigned isl_term_dim(__isl_keep isl_term *term,
2491 enum isl_dim_type type);
2492 void isl_term_get_num(__isl_keep isl_term *term,
2494 void isl_term_get_den(__isl_keep isl_term *term,
2496 int isl_term_get_exp(__isl_keep isl_term *term,
2497 enum isl_dim_type type, unsigned pos);
2498 __isl_give isl_div *isl_term_get_div(
2499 __isl_keep isl_term *term, unsigned pos);
2500 void isl_term_free(__isl_take isl_term *term);
2502 Each term is a product of parameters, set variables and
2503 integer divisions. The function C<isl_term_get_exp>
2504 returns the exponent of a given dimensions in the given term.
2505 The C<isl_int>s in the arguments of C<isl_term_get_num>
2506 and C<isl_term_get_den> need to have been initialized
2507 using C<isl_int_init> before calling these functions.
2509 =head3 Properties of (Piecewise) Quasipolynomials
2511 To check whether a quasipolynomial is actually a constant,
2512 use the following function.
2514 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2515 isl_int *n, isl_int *d);
2517 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2518 then the numerator and denominator of the constant
2519 are returned in C<*n> and C<*d>, respectively.
2521 =head3 Operations on (Piecewise) Quasipolynomials
2523 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2524 __isl_take isl_qpolynomial *qp);
2525 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2526 __isl_take isl_qpolynomial *qp1,
2527 __isl_take isl_qpolynomial *qp2);
2528 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2529 __isl_take isl_qpolynomial *qp1,
2530 __isl_take isl_qpolynomial *qp2);
2531 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2532 __isl_take isl_qpolynomial *qp1,
2533 __isl_take isl_qpolynomial *qp2);
2534 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2535 __isl_take isl_qpolynomial *qp, unsigned exponent);
2537 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2538 __isl_take isl_pw_qpolynomial *pwqp1,
2539 __isl_take isl_pw_qpolynomial *pwqp2);
2540 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2541 __isl_take isl_pw_qpolynomial *pwqp1,
2542 __isl_take isl_pw_qpolynomial *pwqp2);
2543 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2544 __isl_take isl_pw_qpolynomial *pwqp1,
2545 __isl_take isl_pw_qpolynomial *pwqp2);
2546 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2547 __isl_take isl_pw_qpolynomial *pwqp);
2548 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2549 __isl_take isl_pw_qpolynomial *pwqp1,
2550 __isl_take isl_pw_qpolynomial *pwqp2);
2552 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2553 __isl_take isl_union_pw_qpolynomial *upwqp1,
2554 __isl_take isl_union_pw_qpolynomial *upwqp2);
2555 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2556 __isl_take isl_union_pw_qpolynomial *upwqp1,
2557 __isl_take isl_union_pw_qpolynomial *upwqp2);
2558 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2559 __isl_take isl_union_pw_qpolynomial *upwqp1,
2560 __isl_take isl_union_pw_qpolynomial *upwqp2);
2562 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2563 __isl_take isl_pw_qpolynomial *pwqp,
2564 __isl_take isl_point *pnt);
2566 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2567 __isl_take isl_union_pw_qpolynomial *upwqp,
2568 __isl_take isl_point *pnt);
2570 __isl_give isl_set *isl_pw_qpolynomial_domain(
2571 __isl_take isl_pw_qpolynomial *pwqp);
2572 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2573 __isl_take isl_pw_qpolynomial *pwpq,
2574 __isl_take isl_set *set);
2576 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2577 __isl_take isl_union_pw_qpolynomial *upwqp);
2578 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2579 __isl_take isl_union_pw_qpolynomial *upwpq,
2580 __isl_take isl_union_set *uset);
2582 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2583 __isl_take isl_qpolynomial *qp,
2584 __isl_take isl_dim *model);
2586 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2587 __isl_take isl_union_pw_qpolynomial *upwqp);
2589 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2590 __isl_take isl_qpolynomial *qp,
2591 __isl_take isl_set *context);
2593 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2594 __isl_take isl_pw_qpolynomial *pwqp,
2595 __isl_take isl_set *context);
2597 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2598 __isl_take isl_union_pw_qpolynomial *upwqp,
2599 __isl_take isl_union_set *context);
2601 The gist operation applies the gist operation to each of
2602 the cells in the domain of the input piecewise quasipolynomial.
2603 The context is also exploited
2604 to simplify the quasipolynomials associated to each cell.
2606 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2607 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2608 __isl_give isl_union_pw_qpolynomial *
2609 isl_union_pw_qpolynomial_to_polynomial(
2610 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2612 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2613 the polynomial will be an overapproximation. If C<sign> is negative,
2614 it will be an underapproximation. If C<sign> is zero, the approximation
2615 will lie somewhere in between.
2617 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2619 A piecewise quasipolynomial reduction is a piecewise
2620 reduction (or fold) of quasipolynomials.
2621 In particular, the reduction can be maximum or a minimum.
2622 The objects are mainly used to represent the result of
2623 an upper or lower bound on a quasipolynomial over its domain,
2624 i.e., as the result of the following function.
2626 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2627 __isl_take isl_pw_qpolynomial *pwqp,
2628 enum isl_fold type, int *tight);
2630 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2631 __isl_take isl_union_pw_qpolynomial *upwqp,
2632 enum isl_fold type, int *tight);
2634 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2635 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2636 is the returned bound is known be tight, i.e., for each value
2637 of the parameters there is at least
2638 one element in the domain that reaches the bound.
2639 If the domain of C<pwqp> is not wrapping, then the bound is computed
2640 over all elements in that domain and the result has a purely parametric
2641 domain. If the domain of C<pwqp> is wrapping, then the bound is
2642 computed over the range of the wrapped relation. The domain of the
2643 wrapped relation becomes the domain of the result.
2645 A (piecewise) quasipolynomial reduction can be copied or freed using the
2646 following functions.
2648 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2649 __isl_keep isl_qpolynomial_fold *fold);
2650 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2651 __isl_keep isl_pw_qpolynomial_fold *pwf);
2652 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2653 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2654 void isl_qpolynomial_fold_free(
2655 __isl_take isl_qpolynomial_fold *fold);
2656 void isl_pw_qpolynomial_fold_free(
2657 __isl_take isl_pw_qpolynomial_fold *pwf);
2658 void isl_union_pw_qpolynomial_fold_free(
2659 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2661 =head3 Printing Piecewise Quasipolynomial Reductions
2663 Piecewise quasipolynomial reductions can be printed
2664 using the following function.
2666 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2667 __isl_take isl_printer *p,
2668 __isl_keep isl_pw_qpolynomial_fold *pwf);
2669 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2670 __isl_take isl_printer *p,
2671 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2673 For C<isl_printer_print_pw_qpolynomial_fold>,
2674 output format of the printer
2675 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2676 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2677 output format of the printer
2678 needs to be set to C<ISL_FORMAT_ISL>.
2679 In case of printing in C<ISL_FORMAT_C>, the user may want
2680 to set the names of all dimensions
2682 __isl_give isl_pw_qpolynomial_fold *
2683 isl_pw_qpolynomial_fold_set_dim_name(
2684 __isl_take isl_pw_qpolynomial_fold *pwf,
2685 enum isl_dim_type type, unsigned pos,
2688 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2690 To iterate over all piecewise quasipolynomial reductions in a union
2691 piecewise quasipolynomial reduction, use the following function
2693 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2694 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2695 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2696 void *user), void *user);
2698 To iterate over the cells in a piecewise quasipolynomial reduction,
2699 use either of the following two functions
2701 int isl_pw_qpolynomial_fold_foreach_piece(
2702 __isl_keep isl_pw_qpolynomial_fold *pwf,
2703 int (*fn)(__isl_take isl_set *set,
2704 __isl_take isl_qpolynomial_fold *fold,
2705 void *user), void *user);
2706 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2707 __isl_keep isl_pw_qpolynomial_fold *pwf,
2708 int (*fn)(__isl_take isl_set *set,
2709 __isl_take isl_qpolynomial_fold *fold,
2710 void *user), void *user);
2712 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2713 of the difference between these two functions.
2715 To iterate over all quasipolynomials in a reduction, use
2717 int isl_qpolynomial_fold_foreach_qpolynomial(
2718 __isl_keep isl_qpolynomial_fold *fold,
2719 int (*fn)(__isl_take isl_qpolynomial *qp,
2720 void *user), void *user);
2722 =head3 Operations on Piecewise Quasipolynomial Reductions
2724 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2725 __isl_take isl_pw_qpolynomial_fold *pwf1,
2726 __isl_take isl_pw_qpolynomial_fold *pwf2);
2728 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2729 __isl_take isl_pw_qpolynomial_fold *pwf1,
2730 __isl_take isl_pw_qpolynomial_fold *pwf2);
2732 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2733 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2734 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2736 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2737 __isl_take isl_pw_qpolynomial_fold *pwf,
2738 __isl_take isl_point *pnt);
2740 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2741 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2742 __isl_take isl_point *pnt);
2744 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2745 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2746 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2747 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2748 __isl_take isl_union_set *uset);
2750 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2751 __isl_take isl_pw_qpolynomial_fold *pwf);
2753 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2754 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2756 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2757 __isl_take isl_pw_qpolynomial_fold *pwf,
2758 __isl_take isl_set *context);
2760 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2761 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2762 __isl_take isl_union_set *context);
2764 The gist operation applies the gist operation to each of
2765 the cells in the domain of the input piecewise quasipolynomial reduction.
2766 In future, the operation will also exploit the context
2767 to simplify the quasipolynomial reductions associated to each cell.
2769 __isl_give isl_pw_qpolynomial_fold *
2770 isl_set_apply_pw_qpolynomial_fold(
2771 __isl_take isl_set *set,
2772 __isl_take isl_pw_qpolynomial_fold *pwf,
2774 __isl_give isl_pw_qpolynomial_fold *
2775 isl_map_apply_pw_qpolynomial_fold(
2776 __isl_take isl_map *map,
2777 __isl_take isl_pw_qpolynomial_fold *pwf,
2779 __isl_give isl_union_pw_qpolynomial_fold *
2780 isl_union_set_apply_union_pw_qpolynomial_fold(
2781 __isl_take isl_union_set *uset,
2782 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2784 __isl_give isl_union_pw_qpolynomial_fold *
2785 isl_union_map_apply_union_pw_qpolynomial_fold(
2786 __isl_take isl_union_map *umap,
2787 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2790 The functions taking a map
2791 compose the given map with the given piecewise quasipolynomial reduction.
2792 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2793 over all elements in the intersection of the range of the map
2794 and the domain of the piecewise quasipolynomial reduction
2795 as a function of an element in the domain of the map.
2796 The functions taking a set compute a bound over all elements in the
2797 intersection of the set and the domain of the
2798 piecewise quasipolynomial reduction.
2800 =head2 Dependence Analysis
2802 C<isl> contains specialized functionality for performing
2803 array dataflow analysis. That is, given a I<sink> access relation
2804 and a collection of possible I<source> access relations,
2805 C<isl> can compute relations that describe
2806 for each iteration of the sink access, which iteration
2807 of which of the source access relations was the last
2808 to access the same data element before the given iteration
2810 To compute standard flow dependences, the sink should be
2811 a read, while the sources should be writes.
2812 If any of the source accesses are marked as being I<may>
2813 accesses, then there will be a dependence to the last
2814 I<must> access B<and> to any I<may> access that follows
2815 this last I<must> access.
2816 In particular, if I<all> sources are I<may> accesses,
2817 then memory based dependence analysis is performed.
2818 If, on the other hand, all sources are I<must> accesses,
2819 then value based dependence analysis is performed.
2821 #include <isl/flow.h>
2823 typedef int (*isl_access_level_before)(void *first, void *second);
2825 __isl_give isl_access_info *isl_access_info_alloc(
2826 __isl_take isl_map *sink,
2827 void *sink_user, isl_access_level_before fn,
2829 __isl_give isl_access_info *isl_access_info_add_source(
2830 __isl_take isl_access_info *acc,
2831 __isl_take isl_map *source, int must,
2833 void isl_access_info_free(__isl_take isl_access_info *acc);
2835 __isl_give isl_flow *isl_access_info_compute_flow(
2836 __isl_take isl_access_info *acc);
2838 int isl_flow_foreach(__isl_keep isl_flow *deps,
2839 int (*fn)(__isl_take isl_map *dep, int must,
2840 void *dep_user, void *user),
2842 __isl_give isl_map *isl_flow_get_no_source(
2843 __isl_keep isl_flow *deps, int must);
2844 void isl_flow_free(__isl_take isl_flow *deps);
2846 The function C<isl_access_info_compute_flow> performs the actual
2847 dependence analysis. The other functions are used to construct
2848 the input for this function or to read off the output.
2850 The input is collected in an C<isl_access_info>, which can
2851 be created through a call to C<isl_access_info_alloc>.
2852 The arguments to this functions are the sink access relation
2853 C<sink>, a token C<sink_user> used to identify the sink
2854 access to the user, a callback function for specifying the
2855 relative order of source and sink accesses, and the number
2856 of source access relations that will be added.
2857 The callback function has type C<int (*)(void *first, void *second)>.
2858 The function is called with two user supplied tokens identifying
2859 either a source or the sink and it should return the shared nesting
2860 level and the relative order of the two accesses.
2861 In particular, let I<n> be the number of loops shared by
2862 the two accesses. If C<first> precedes C<second> textually,
2863 then the function should return I<2 * n + 1>; otherwise,
2864 it should return I<2 * n>.
2865 The sources can be added to the C<isl_access_info> by performing
2866 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2867 C<must> indicates whether the source is a I<must> access
2868 or a I<may> access. Note that a multi-valued access relation
2869 should only be marked I<must> if every iteration in the domain
2870 of the relation accesses I<all> elements in its image.
2871 The C<source_user> token is again used to identify
2872 the source access. The range of the source access relation
2873 C<source> should have the same dimension as the range
2874 of the sink access relation.
2875 The C<isl_access_info_free> function should usually not be
2876 called explicitly, because it is called implicitly by
2877 C<isl_access_info_compute_flow>.
2879 The result of the dependence analysis is collected in an
2880 C<isl_flow>. There may be elements of
2881 the sink access for which no preceding source access could be
2882 found or for which all preceding sources are I<may> accesses.
2883 The relations containing these elements can be obtained through
2884 calls to C<isl_flow_get_no_source>, the first with C<must> set
2885 and the second with C<must> unset.
2886 In the case of standard flow dependence analysis,
2887 with the sink a read and the sources I<must> writes,
2888 the first relation corresponds to the reads from uninitialized
2889 array elements and the second relation is empty.
2890 The actual flow dependences can be extracted using
2891 C<isl_flow_foreach>. This function will call the user-specified
2892 callback function C<fn> for each B<non-empty> dependence between
2893 a source and the sink. The callback function is called
2894 with four arguments, the actual flow dependence relation
2895 mapping source iterations to sink iterations, a boolean that
2896 indicates whether it is a I<must> or I<may> dependence, a token
2897 identifying the source and an additional C<void *> with value
2898 equal to the third argument of the C<isl_flow_foreach> call.
2899 A dependence is marked I<must> if it originates from a I<must>
2900 source and if it is not followed by any I<may> sources.
2902 After finishing with an C<isl_flow>, the user should call
2903 C<isl_flow_free> to free all associated memory.
2905 A higher-level interface to dependence analysis is provided
2906 by the following function.
2908 #include <isl/flow.h>
2910 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2911 __isl_take isl_union_map *must_source,
2912 __isl_take isl_union_map *may_source,
2913 __isl_take isl_union_map *schedule,
2914 __isl_give isl_union_map **must_dep,
2915 __isl_give isl_union_map **may_dep,
2916 __isl_give isl_union_map **must_no_source,
2917 __isl_give isl_union_map **may_no_source);
2919 The arrays are identified by the tuple names of the ranges
2920 of the accesses. The iteration domains by the tuple names
2921 of the domains of the accesses and of the schedule.
2922 The relative order of the iteration domains is given by the
2923 schedule. The relations returned through C<must_no_source>
2924 and C<may_no_source> are subsets of C<sink>.
2925 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2926 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2927 any of the other arguments is treated as an error.
2931 B<The functionality described in this section is fairly new
2932 and may be subject to change.>
2934 The following function can be used to compute a schedule
2935 for a union of domains. The generated schedule respects
2936 all C<validity> dependences. That is, all dependence distances
2937 over these dependences in the scheduled space are lexicographically
2938 positive. The generated schedule schedule also tries to minimize
2939 the dependence distances over C<proximity> dependences.
2940 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2941 for groups of domains where the dependence distances have only
2942 non-negative values.
2943 The algorithm used to construct the schedule is similar to that
2946 #include <isl/schedule.h>
2947 __isl_give isl_schedule *isl_union_set_compute_schedule(
2948 __isl_take isl_union_set *domain,
2949 __isl_take isl_union_map *validity,
2950 __isl_take isl_union_map *proximity);
2951 void *isl_schedule_free(__isl_take isl_schedule *sched);
2953 A mapping from the domains to the scheduled space can be obtained
2954 from an C<isl_schedule> using the following function.
2956 __isl_give isl_union_map *isl_schedule_get_map(
2957 __isl_keep isl_schedule *sched);
2959 A representation of the schedule can be printed using
2961 __isl_give isl_printer *isl_printer_print_schedule(
2962 __isl_take isl_printer *p,
2963 __isl_keep isl_schedule *schedule);
2965 A representation of the schedule as a forest of bands can be obtained
2966 using the following function.
2968 __isl_give isl_band_list *isl_schedule_get_band_forest(
2969 __isl_keep isl_schedule *schedule);
2971 The list can be manipulated as explained in L<"Lists">.
2972 The bands inside the list can be copied and freed using the following
2975 #include <isl/band.h>
2976 __isl_give isl_band *isl_band_copy(
2977 __isl_keep isl_band *band);
2978 void *isl_band_free(__isl_take isl_band *band);
2980 Each band contains zero or more scheduling dimensions.
2981 These are referred to as the members of the band.
2982 The section of the schedule that corresponds to the band is
2983 referred to as the partial schedule of the band.
2984 For those nodes that participate in a band, the outer scheduling
2985 dimensions form the prefix schedule, while the inner scheduling
2986 dimensions form the suffix schedule.
2987 That is, if we take a cut of the band forest, then the union of
2988 the concatenations of the prefix, partial and suffix schedules of
2989 each band in the cut is equal to the entire schedule (modulo
2990 some possible padding at the end with zero scheduling dimensions).
2991 The properties of a band can be inspected using the following functions.
2993 #include <isl/band.h>
2994 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
2996 int isl_band_has_children(__isl_keep isl_band *band);
2997 __isl_give isl_band_list *isl_band_get_children(
2998 __isl_keep isl_band *band);
3000 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3001 __isl_keep isl_band *band);
3002 __isl_give isl_union_map *isl_band_get_partial_schedule(
3003 __isl_keep isl_band *band);
3004 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3005 __isl_keep isl_band *band);
3007 int isl_band_n_member(__isl_keep isl_band *band);
3008 int isl_band_member_is_parallel(__isl_keep isl_band *band,
3011 Note that a scheduling dimension is considered parallel if it
3012 does not carry any proximity dependences.
3014 A representation of the band can be printed using
3016 #include <isl/band.h>
3017 __isl_give isl_printer *isl_printer_print_band(
3018 __isl_take isl_printer *p,
3019 __isl_keep isl_band *band);
3021 Alternatively, the schedule mapping
3022 can also be obtained in pieces using the following functions.
3024 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3025 __isl_give isl_union_map *isl_schedule_get_band(
3026 __isl_keep isl_schedule *sched, unsigned band);
3028 C<isl_schedule_n_band> returns the maximal number of bands.
3029 C<isl_schedule_get_band> returns a union of mappings from a domain to
3030 the band of consecutive schedule dimensions with the given sequence
3031 number for that domain. Bands with the same sequence number but for
3032 different domains may be completely unrelated.
3033 Within a band, the corresponding coordinates of the distance vectors
3034 are all non-negative, assuming that the coordinates for all previous
3037 =head2 Parametric Vertex Enumeration
3039 The parametric vertex enumeration described in this section
3040 is mainly intended to be used internally and by the C<barvinok>
3043 #include <isl/vertices.h>
3044 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3045 __isl_keep isl_basic_set *bset);
3047 The function C<isl_basic_set_compute_vertices> performs the
3048 actual computation of the parametric vertices and the chamber
3049 decomposition and store the result in an C<isl_vertices> object.
3050 This information can be queried by either iterating over all
3051 the vertices or iterating over all the chambers or cells
3052 and then iterating over all vertices that are active on the chamber.
3054 int isl_vertices_foreach_vertex(
3055 __isl_keep isl_vertices *vertices,
3056 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3059 int isl_vertices_foreach_cell(
3060 __isl_keep isl_vertices *vertices,
3061 int (*fn)(__isl_take isl_cell *cell, void *user),
3063 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3064 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3067 Other operations that can be performed on an C<isl_vertices> object are
3070 isl_ctx *isl_vertices_get_ctx(
3071 __isl_keep isl_vertices *vertices);
3072 int isl_vertices_get_n_vertices(
3073 __isl_keep isl_vertices *vertices);
3074 void isl_vertices_free(__isl_take isl_vertices *vertices);
3076 Vertices can be inspected and destroyed using the following functions.
3078 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3079 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3080 __isl_give isl_basic_set *isl_vertex_get_domain(
3081 __isl_keep isl_vertex *vertex);
3082 __isl_give isl_basic_set *isl_vertex_get_expr(
3083 __isl_keep isl_vertex *vertex);
3084 void isl_vertex_free(__isl_take isl_vertex *vertex);
3086 C<isl_vertex_get_expr> returns a singleton parametric set describing
3087 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3089 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3090 B<rational> basic sets, so they should mainly be used for inspection
3091 and should not be mixed with integer sets.
3093 Chambers can be inspected and destroyed using the following functions.
3095 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3096 __isl_give isl_basic_set *isl_cell_get_domain(
3097 __isl_keep isl_cell *cell);
3098 void isl_cell_free(__isl_take isl_cell *cell);
3102 Although C<isl> is mainly meant to be used as a library,
3103 it also contains some basic applications that use some
3104 of the functionality of C<isl>.
3105 The input may be specified in either the L<isl format>
3106 or the L<PolyLib format>.
3108 =head2 C<isl_polyhedron_sample>
3110 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3111 an integer element of the polyhedron, if there is any.
3112 The first column in the output is the denominator and is always
3113 equal to 1. If the polyhedron contains no integer points,
3114 then a vector of length zero is printed.
3118 C<isl_pip> takes the same input as the C<example> program
3119 from the C<piplib> distribution, i.e., a set of constraints
3120 on the parameters, a line containing only -1 and finally a set
3121 of constraints on a parametric polyhedron.
3122 The coefficients of the parameters appear in the last columns
3123 (but before the final constant column).
3124 The output is the lexicographic minimum of the parametric polyhedron.
3125 As C<isl> currently does not have its own output format, the output
3126 is just a dump of the internal state.
3128 =head2 C<isl_polyhedron_minimize>
3130 C<isl_polyhedron_minimize> computes the minimum of some linear
3131 or affine objective function over the integer points in a polyhedron.
3132 If an affine objective function
3133 is given, then the constant should appear in the last column.
3135 =head2 C<isl_polytope_scan>
3137 Given a polytope, C<isl_polytope_scan> prints
3138 all integer points in the polytope.