3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
477 __isl_keep isl_qpolynomial_fold *fold);
478 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
479 __isl_keep isl_pw_qpolynomial *pwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
481 __isl_keep isl_union_pw_qpolynomial *upwqp);
482 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
483 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
486 __isl_give isl_dim *isl_aff_get_dim(
487 __isl_keep isl_aff *aff);
489 The names of the individual dimensions may be set or read off
490 using the following functions.
493 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
494 enum isl_dim_type type, unsigned pos,
495 __isl_keep const char *name);
496 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
497 enum isl_dim_type type, unsigned pos);
499 Note that C<isl_dim_get_name> returns a pointer to some internal
500 data structure, so the result can only be used while the
501 corresponding C<isl_dim> is alive.
502 Also note that every function that operates on two sets or relations
503 requires that both arguments have the same parameters. This also
504 means that if one of the arguments has named parameters, then the
505 other needs to have named parameters too and the names need to match.
506 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
507 have different parameters (as long as they are named), in which case
508 the result will have as parameters the union of the parameters of
511 The names of entire spaces may be set or read off
512 using the following functions.
515 __isl_give isl_dim *isl_dim_set_tuple_name(
516 __isl_take isl_dim *dim,
517 enum isl_dim_type type, const char *s);
518 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
519 enum isl_dim_type type);
521 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
522 or C<isl_dim_set>. As with C<isl_dim_get_name>,
523 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
525 Binary operations require the corresponding spaces of their arguments
526 to have the same name.
528 Spaces can be nested. In particular, the domain of a set or
529 the domain or range of a relation can be a nested relation.
530 The following functions can be used to construct and deconstruct
531 such nested dimension specifications.
534 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
535 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
536 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
538 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
539 be the dimension specification of a set, while that of
540 C<isl_dim_wrap> should be the dimension specification of a relation.
541 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
542 of a relation, while that of C<isl_dim_wrap> is the dimension specification
545 Dimension specifications can be created from other dimension
546 specifications using the following functions.
548 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
549 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
550 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
551 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
552 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
553 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
554 __isl_take isl_dim *right);
555 __isl_give isl_dim *isl_dim_align_params(
556 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
557 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
558 enum isl_dim_type type, unsigned pos, unsigned n);
559 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
560 enum isl_dim_type type, unsigned n);
561 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
562 enum isl_dim_type type, unsigned first, unsigned n);
563 __isl_give isl_dim *isl_dim_map_from_set(
564 __isl_take isl_dim *dim);
565 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
567 Note that if dimensions are added or removed from a space, then
568 the name and the internal structure are lost.
572 A local space is essentially a dimension specification with
573 zero or more existentially quantified variables.
574 The local space of a basic set or relation can be obtained
575 using the following functions.
578 __isl_give isl_local_space *isl_basic_set_get_local_space(
579 __isl_keep isl_basic_set *bset);
582 __isl_give isl_local_space *isl_basic_map_get_local_space(
583 __isl_keep isl_basic_map *bmap);
585 A new local space can be created from a dimension specification using
587 #include <isl/local_space.h>
588 __isl_give isl_local_space *isl_local_space_from_dim(
589 __isl_take isl_dim *dim);
591 They can be inspected, copied and freed using the following functions.
593 #include <isl/local_space.h>
594 isl_ctx *isl_local_space_get_ctx(
595 __isl_keep isl_local_space *ls);
596 int isl_local_space_dim(__isl_keep isl_local_space *ls,
597 enum isl_dim_type type);
598 const char *isl_local_space_get_dim_name(
599 __isl_keep isl_local_space *ls,
600 enum isl_dim_type type, unsigned pos);
601 __isl_give isl_dim *isl_local_space_get_dim(
602 __isl_keep isl_local_space *ls);
603 __isl_give isl_div *isl_local_space_get_div(
604 __isl_keep isl_local_space *ls, int pos);
605 __isl_give isl_local_space *isl_local_space_copy(
606 __isl_keep isl_local_space *ls);
607 void *isl_local_space_free(__isl_take isl_local_space *ls);
609 Local spaces can be created from other local spaces
610 using the following functions.
612 __isl_give isl_local_space *isl_local_space_from_domain(
613 __isl_take isl_local_space *ls);
614 __isl_give isl_local_space *isl_local_space_add_dim(
615 __isl_take isl_local_space *ls,
616 enum isl_dim_type type, unsigned n);
618 =head2 Input and Output
620 C<isl> supports its own input/output format, which is similar
621 to the C<Omega> format, but also supports the C<PolyLib> format
626 The C<isl> format is similar to that of C<Omega>, but has a different
627 syntax for describing the parameters and allows for the definition
628 of an existentially quantified variable as the integer division
629 of an affine expression.
630 For example, the set of integers C<i> between C<0> and C<n>
631 such that C<i % 10 <= 6> can be described as
633 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
636 A set or relation can have several disjuncts, separated
637 by the keyword C<or>. Each disjunct is either a conjunction
638 of constraints or a projection (C<exists>) of a conjunction
639 of constraints. The constraints are separated by the keyword
642 =head3 C<PolyLib> format
644 If the represented set is a union, then the first line
645 contains a single number representing the number of disjuncts.
646 Otherwise, a line containing the number C<1> is optional.
648 Each disjunct is represented by a matrix of constraints.
649 The first line contains two numbers representing
650 the number of rows and columns,
651 where the number of rows is equal to the number of constraints
652 and the number of columns is equal to two plus the number of variables.
653 The following lines contain the actual rows of the constraint matrix.
654 In each row, the first column indicates whether the constraint
655 is an equality (C<0>) or inequality (C<1>). The final column
656 corresponds to the constant term.
658 If the set is parametric, then the coefficients of the parameters
659 appear in the last columns before the constant column.
660 The coefficients of any existentially quantified variables appear
661 between those of the set variables and those of the parameters.
663 =head3 Extended C<PolyLib> format
665 The extended C<PolyLib> format is nearly identical to the
666 C<PolyLib> format. The only difference is that the line
667 containing the number of rows and columns of a constraint matrix
668 also contains four additional numbers:
669 the number of output dimensions, the number of input dimensions,
670 the number of local dimensions (i.e., the number of existentially
671 quantified variables) and the number of parameters.
672 For sets, the number of ``output'' dimensions is equal
673 to the number of set dimensions, while the number of ``input''
679 __isl_give isl_basic_set *isl_basic_set_read_from_file(
680 isl_ctx *ctx, FILE *input, int nparam);
681 __isl_give isl_basic_set *isl_basic_set_read_from_str(
682 isl_ctx *ctx, const char *str, int nparam);
683 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
684 FILE *input, int nparam);
685 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
686 const char *str, int nparam);
689 __isl_give isl_basic_map *isl_basic_map_read_from_file(
690 isl_ctx *ctx, FILE *input, int nparam);
691 __isl_give isl_basic_map *isl_basic_map_read_from_str(
692 isl_ctx *ctx, const char *str, int nparam);
693 __isl_give isl_map *isl_map_read_from_file(
694 struct isl_ctx *ctx, FILE *input, int nparam);
695 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
696 const char *str, int nparam);
698 #include <isl/union_set.h>
699 __isl_give isl_union_set *isl_union_set_read_from_file(
700 isl_ctx *ctx, FILE *input);
701 __isl_give isl_union_set *isl_union_set_read_from_str(
702 struct isl_ctx *ctx, const char *str);
704 #include <isl/union_map.h>
705 __isl_give isl_union_map *isl_union_map_read_from_file(
706 isl_ctx *ctx, FILE *input);
707 __isl_give isl_union_map *isl_union_map_read_from_str(
708 struct isl_ctx *ctx, const char *str);
710 The input format is autodetected and may be either the C<PolyLib> format
711 or the C<isl> format.
712 C<nparam> specifies how many of the final columns in
713 the C<PolyLib> format correspond to parameters.
714 If input is given in the C<isl> format, then the number
715 of parameters needs to be equal to C<nparam>.
716 If C<nparam> is negative, then any number of parameters
717 is accepted in the C<isl> format and zero parameters
718 are assumed in the C<PolyLib> format.
722 Before anything can be printed, an C<isl_printer> needs to
725 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
727 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
728 void isl_printer_free(__isl_take isl_printer *printer);
729 __isl_give char *isl_printer_get_str(
730 __isl_keep isl_printer *printer);
732 The behavior of the printer can be modified in various ways
734 __isl_give isl_printer *isl_printer_set_output_format(
735 __isl_take isl_printer *p, int output_format);
736 __isl_give isl_printer *isl_printer_set_indent(
737 __isl_take isl_printer *p, int indent);
738 __isl_give isl_printer *isl_printer_indent(
739 __isl_take isl_printer *p, int indent);
740 __isl_give isl_printer *isl_printer_set_prefix(
741 __isl_take isl_printer *p, const char *prefix);
742 __isl_give isl_printer *isl_printer_set_suffix(
743 __isl_take isl_printer *p, const char *suffix);
745 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
746 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
747 and defaults to C<ISL_FORMAT_ISL>.
748 Each line in the output is indented by C<indent> (set by
749 C<isl_printer_set_indent>) spaces
750 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
751 In the C<PolyLib> format output,
752 the coefficients of the existentially quantified variables
753 appear between those of the set variables and those
755 The function C<isl_printer_indent> increases the indentation
756 by the specified amount (which may be negative).
758 To actually print something, use
761 __isl_give isl_printer *isl_printer_print_basic_set(
762 __isl_take isl_printer *printer,
763 __isl_keep isl_basic_set *bset);
764 __isl_give isl_printer *isl_printer_print_set(
765 __isl_take isl_printer *printer,
766 __isl_keep isl_set *set);
769 __isl_give isl_printer *isl_printer_print_basic_map(
770 __isl_take isl_printer *printer,
771 __isl_keep isl_basic_map *bmap);
772 __isl_give isl_printer *isl_printer_print_map(
773 __isl_take isl_printer *printer,
774 __isl_keep isl_map *map);
776 #include <isl/union_set.h>
777 __isl_give isl_printer *isl_printer_print_union_set(
778 __isl_take isl_printer *p,
779 __isl_keep isl_union_set *uset);
781 #include <isl/union_map.h>
782 __isl_give isl_printer *isl_printer_print_union_map(
783 __isl_take isl_printer *p,
784 __isl_keep isl_union_map *umap);
786 When called on a file printer, the following function flushes
787 the file. When called on a string printer, the buffer is cleared.
789 __isl_give isl_printer *isl_printer_flush(
790 __isl_take isl_printer *p);
792 =head2 Creating New Sets and Relations
794 C<isl> has functions for creating some standard sets and relations.
798 =item * Empty sets and relations
800 __isl_give isl_basic_set *isl_basic_set_empty(
801 __isl_take isl_dim *dim);
802 __isl_give isl_basic_map *isl_basic_map_empty(
803 __isl_take isl_dim *dim);
804 __isl_give isl_set *isl_set_empty(
805 __isl_take isl_dim *dim);
806 __isl_give isl_map *isl_map_empty(
807 __isl_take isl_dim *dim);
808 __isl_give isl_union_set *isl_union_set_empty(
809 __isl_take isl_dim *dim);
810 __isl_give isl_union_map *isl_union_map_empty(
811 __isl_take isl_dim *dim);
813 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
814 is only used to specify the parameters.
816 =item * Universe sets and relations
818 __isl_give isl_basic_set *isl_basic_set_universe(
819 __isl_take isl_dim *dim);
820 __isl_give isl_basic_map *isl_basic_map_universe(
821 __isl_take isl_dim *dim);
822 __isl_give isl_set *isl_set_universe(
823 __isl_take isl_dim *dim);
824 __isl_give isl_map *isl_map_universe(
825 __isl_take isl_dim *dim);
826 __isl_give isl_union_set *isl_union_set_universe(
827 __isl_take isl_union_set *uset);
828 __isl_give isl_union_map *isl_union_map_universe(
829 __isl_take isl_union_map *umap);
831 The sets and relations constructed by the functions above
832 contain all integer values, while those constructed by the
833 functions below only contain non-negative values.
835 __isl_give isl_basic_set *isl_basic_set_nat_universe(
836 __isl_take isl_dim *dim);
837 __isl_give isl_basic_map *isl_basic_map_nat_universe(
838 __isl_take isl_dim *dim);
839 __isl_give isl_set *isl_set_nat_universe(
840 __isl_take isl_dim *dim);
841 __isl_give isl_map *isl_map_nat_universe(
842 __isl_take isl_dim *dim);
844 =item * Identity relations
846 __isl_give isl_basic_map *isl_basic_map_identity(
847 __isl_take isl_dim *dim);
848 __isl_give isl_map *isl_map_identity(
849 __isl_take isl_dim *dim);
851 The number of input and output dimensions in C<dim> needs
854 =item * Lexicographic order
856 __isl_give isl_map *isl_map_lex_lt(
857 __isl_take isl_dim *set_dim);
858 __isl_give isl_map *isl_map_lex_le(
859 __isl_take isl_dim *set_dim);
860 __isl_give isl_map *isl_map_lex_gt(
861 __isl_take isl_dim *set_dim);
862 __isl_give isl_map *isl_map_lex_ge(
863 __isl_take isl_dim *set_dim);
864 __isl_give isl_map *isl_map_lex_lt_first(
865 __isl_take isl_dim *dim, unsigned n);
866 __isl_give isl_map *isl_map_lex_le_first(
867 __isl_take isl_dim *dim, unsigned n);
868 __isl_give isl_map *isl_map_lex_gt_first(
869 __isl_take isl_dim *dim, unsigned n);
870 __isl_give isl_map *isl_map_lex_ge_first(
871 __isl_take isl_dim *dim, unsigned n);
873 The first four functions take a dimension specification for a B<set>
874 and return relations that express that the elements in the domain
875 are lexicographically less
876 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
877 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
878 than the elements in the range.
879 The last four functions take a dimension specification for a map
880 and return relations that express that the first C<n> dimensions
881 in the domain are lexicographically less
882 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
883 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
884 than the first C<n> dimensions in the range.
888 A basic set or relation can be converted to a set or relation
889 using the following functions.
891 __isl_give isl_set *isl_set_from_basic_set(
892 __isl_take isl_basic_set *bset);
893 __isl_give isl_map *isl_map_from_basic_map(
894 __isl_take isl_basic_map *bmap);
896 Sets and relations can be converted to union sets and relations
897 using the following functions.
899 __isl_give isl_union_map *isl_union_map_from_map(
900 __isl_take isl_map *map);
901 __isl_give isl_union_set *isl_union_set_from_set(
902 __isl_take isl_set *set);
904 Sets and relations can be copied and freed again using the following
907 __isl_give isl_basic_set *isl_basic_set_copy(
908 __isl_keep isl_basic_set *bset);
909 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
910 __isl_give isl_union_set *isl_union_set_copy(
911 __isl_keep isl_union_set *uset);
912 __isl_give isl_basic_map *isl_basic_map_copy(
913 __isl_keep isl_basic_map *bmap);
914 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
915 __isl_give isl_union_map *isl_union_map_copy(
916 __isl_keep isl_union_map *umap);
917 void isl_basic_set_free(__isl_take isl_basic_set *bset);
918 void isl_set_free(__isl_take isl_set *set);
919 void isl_union_set_free(__isl_take isl_union_set *uset);
920 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
921 void isl_map_free(__isl_take isl_map *map);
922 void isl_union_map_free(__isl_take isl_union_map *umap);
924 Other sets and relations can be constructed by starting
925 from a universe set or relation, adding equality and/or
926 inequality constraints and then projecting out the
927 existentially quantified variables, if any.
928 Constraints can be constructed, manipulated and
929 added to (basic) sets and relations using the following functions.
931 #include <isl/constraint.h>
932 __isl_give isl_constraint *isl_equality_alloc(
933 __isl_take isl_dim *dim);
934 __isl_give isl_constraint *isl_inequality_alloc(
935 __isl_take isl_dim *dim);
936 void isl_constraint_set_constant(
937 __isl_keep isl_constraint *constraint, isl_int v);
938 void isl_constraint_set_coefficient(
939 __isl_keep isl_constraint *constraint,
940 enum isl_dim_type type, int pos, isl_int v);
941 __isl_give isl_basic_map *isl_basic_map_add_constraint(
942 __isl_take isl_basic_map *bmap,
943 __isl_take isl_constraint *constraint);
944 __isl_give isl_basic_set *isl_basic_set_add_constraint(
945 __isl_take isl_basic_set *bset,
946 __isl_take isl_constraint *constraint);
947 __isl_give isl_map *isl_map_add_constraint(
948 __isl_take isl_map *map,
949 __isl_take isl_constraint *constraint);
950 __isl_give isl_set *isl_set_add_constraint(
951 __isl_take isl_set *set,
952 __isl_take isl_constraint *constraint);
954 For example, to create a set containing the even integers
955 between 10 and 42, you would use the following code.
959 struct isl_constraint *c;
960 struct isl_basic_set *bset;
963 dim = isl_dim_set_alloc(ctx, 0, 2);
964 bset = isl_basic_set_universe(isl_dim_copy(dim));
966 c = isl_equality_alloc(isl_dim_copy(dim));
967 isl_int_set_si(v, -1);
968 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
969 isl_int_set_si(v, 2);
970 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
971 bset = isl_basic_set_add_constraint(bset, c);
973 c = isl_inequality_alloc(isl_dim_copy(dim));
974 isl_int_set_si(v, -10);
975 isl_constraint_set_constant(c, v);
976 isl_int_set_si(v, 1);
977 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
978 bset = isl_basic_set_add_constraint(bset, c);
980 c = isl_inequality_alloc(dim);
981 isl_int_set_si(v, 42);
982 isl_constraint_set_constant(c, v);
983 isl_int_set_si(v, -1);
984 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
985 bset = isl_basic_set_add_constraint(bset, c);
987 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
993 struct isl_basic_set *bset;
994 bset = isl_basic_set_read_from_str(ctx,
995 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
997 A basic set or relation can also be constructed from two matrices
998 describing the equalities and the inequalities.
1000 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1001 __isl_take isl_dim *dim,
1002 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1003 enum isl_dim_type c1,
1004 enum isl_dim_type c2, enum isl_dim_type c3,
1005 enum isl_dim_type c4);
1006 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1007 __isl_take isl_dim *dim,
1008 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1009 enum isl_dim_type c1,
1010 enum isl_dim_type c2, enum isl_dim_type c3,
1011 enum isl_dim_type c4, enum isl_dim_type c5);
1013 The C<isl_dim_type> arguments indicate the order in which
1014 different kinds of variables appear in the input matrices
1015 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1016 C<isl_dim_set> and C<isl_dim_div> for sets and
1017 of C<isl_dim_cst>, C<isl_dim_param>,
1018 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1020 A basic relation can also be constructed from an affine expression
1021 or a list of affine expressions (See L<"Quasi Affine Expressions">).
1023 __isl_give isl_basic_map *isl_basic_map_from_aff(
1024 __isl_take isl_aff *aff);
1025 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1026 __isl_take isl_dim *domain_dim,
1027 __isl_take isl_aff_list *list);
1029 The C<domain_dim> argument describes the domain of the resulting
1030 basic relation. It is required because the C<list> may consist
1031 of zero affine expressions.
1033 =head2 Inspecting Sets and Relations
1035 Usually, the user should not have to care about the actual constraints
1036 of the sets and maps, but should instead apply the abstract operations
1037 explained in the following sections.
1038 Occasionally, however, it may be required to inspect the individual
1039 coefficients of the constraints. This section explains how to do so.
1040 In these cases, it may also be useful to have C<isl> compute
1041 an explicit representation of the existentially quantified variables.
1043 __isl_give isl_set *isl_set_compute_divs(
1044 __isl_take isl_set *set);
1045 __isl_give isl_map *isl_map_compute_divs(
1046 __isl_take isl_map *map);
1047 __isl_give isl_union_set *isl_union_set_compute_divs(
1048 __isl_take isl_union_set *uset);
1049 __isl_give isl_union_map *isl_union_map_compute_divs(
1050 __isl_take isl_union_map *umap);
1052 This explicit representation defines the existentially quantified
1053 variables as integer divisions of the other variables, possibly
1054 including earlier existentially quantified variables.
1055 An explicitly represented existentially quantified variable therefore
1056 has a unique value when the values of the other variables are known.
1057 If, furthermore, the same existentials, i.e., existentials
1058 with the same explicit representations, should appear in the
1059 same order in each of the disjuncts of a set or map, then the user should call
1060 either of the following functions.
1062 __isl_give isl_set *isl_set_align_divs(
1063 __isl_take isl_set *set);
1064 __isl_give isl_map *isl_map_align_divs(
1065 __isl_take isl_map *map);
1067 Alternatively, the existentially quantified variables can be removed
1068 using the following functions, which compute an overapproximation.
1070 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1071 __isl_take isl_basic_set *bset);
1072 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1073 __isl_take isl_basic_map *bmap);
1074 __isl_give isl_set *isl_set_remove_divs(
1075 __isl_take isl_set *set);
1076 __isl_give isl_map *isl_map_remove_divs(
1077 __isl_take isl_map *map);
1079 To iterate over all the sets or maps in a union set or map, use
1081 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1082 int (*fn)(__isl_take isl_set *set, void *user),
1084 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1085 int (*fn)(__isl_take isl_map *map, void *user),
1088 The number of sets or maps in a union set or map can be obtained
1091 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1092 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1094 To extract the set or map from a union with a given dimension
1097 __isl_give isl_set *isl_union_set_extract_set(
1098 __isl_keep isl_union_set *uset,
1099 __isl_take isl_dim *dim);
1100 __isl_give isl_map *isl_union_map_extract_map(
1101 __isl_keep isl_union_map *umap,
1102 __isl_take isl_dim *dim);
1104 To iterate over all the basic sets or maps in a set or map, use
1106 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1107 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1109 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1110 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1113 The callback function C<fn> should return 0 if successful and
1114 -1 if an error occurs. In the latter case, or if any other error
1115 occurs, the above functions will return -1.
1117 It should be noted that C<isl> does not guarantee that
1118 the basic sets or maps passed to C<fn> are disjoint.
1119 If this is required, then the user should call one of
1120 the following functions first.
1122 __isl_give isl_set *isl_set_make_disjoint(
1123 __isl_take isl_set *set);
1124 __isl_give isl_map *isl_map_make_disjoint(
1125 __isl_take isl_map *map);
1127 The number of basic sets in a set can be obtained
1130 int isl_set_n_basic_set(__isl_keep isl_set *set);
1132 To iterate over the constraints of a basic set or map, use
1134 #include <isl/constraint.h>
1136 int isl_basic_map_foreach_constraint(
1137 __isl_keep isl_basic_map *bmap,
1138 int (*fn)(__isl_take isl_constraint *c, void *user),
1140 void isl_constraint_free(struct isl_constraint *c);
1142 Again, the callback function C<fn> should return 0 if successful and
1143 -1 if an error occurs. In the latter case, or if any other error
1144 occurs, the above functions will return -1.
1145 The constraint C<c> represents either an equality or an inequality.
1146 Use the following function to find out whether a constraint
1147 represents an equality. If not, it represents an inequality.
1149 int isl_constraint_is_equality(
1150 __isl_keep isl_constraint *constraint);
1152 The coefficients of the constraints can be inspected using
1153 the following functions.
1155 void isl_constraint_get_constant(
1156 __isl_keep isl_constraint *constraint, isl_int *v);
1157 void isl_constraint_get_coefficient(
1158 __isl_keep isl_constraint *constraint,
1159 enum isl_dim_type type, int pos, isl_int *v);
1160 int isl_constraint_involves_dims(
1161 __isl_keep isl_constraint *constraint,
1162 enum isl_dim_type type, unsigned first, unsigned n);
1164 The explicit representations of the existentially quantified
1165 variables can be inspected using the following functions.
1166 Note that the user is only allowed to use these functions
1167 if the inspected set or map is the result of a call
1168 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1170 __isl_give isl_div *isl_constraint_div(
1171 __isl_keep isl_constraint *constraint, int pos);
1172 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1173 void isl_div_get_constant(__isl_keep isl_div *div,
1175 void isl_div_get_denominator(__isl_keep isl_div *div,
1177 void isl_div_get_coefficient(__isl_keep isl_div *div,
1178 enum isl_dim_type type, int pos, isl_int *v);
1180 To obtain the constraints of a basic set or map in matrix
1181 form, use the following functions.
1183 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1184 __isl_keep isl_basic_set *bset,
1185 enum isl_dim_type c1, enum isl_dim_type c2,
1186 enum isl_dim_type c3, enum isl_dim_type c4);
1187 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1188 __isl_keep isl_basic_set *bset,
1189 enum isl_dim_type c1, enum isl_dim_type c2,
1190 enum isl_dim_type c3, enum isl_dim_type c4);
1191 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1192 __isl_keep isl_basic_map *bmap,
1193 enum isl_dim_type c1,
1194 enum isl_dim_type c2, enum isl_dim_type c3,
1195 enum isl_dim_type c4, enum isl_dim_type c5);
1196 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1197 __isl_keep isl_basic_map *bmap,
1198 enum isl_dim_type c1,
1199 enum isl_dim_type c2, enum isl_dim_type c3,
1200 enum isl_dim_type c4, enum isl_dim_type c5);
1202 The C<isl_dim_type> arguments dictate the order in which
1203 different kinds of variables appear in the resulting matrix
1204 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1205 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1207 The names of the domain and range spaces of a set or relation can be
1208 read off using the following functions.
1210 const char *isl_basic_set_get_tuple_name(
1211 __isl_keep isl_basic_set *bset);
1212 const char *isl_set_get_tuple_name(
1213 __isl_keep isl_set *set);
1214 const char *isl_basic_map_get_tuple_name(
1215 __isl_keep isl_basic_map *bmap,
1216 enum isl_dim_type type);
1217 const char *isl_map_get_tuple_name(
1218 __isl_keep isl_map *map,
1219 enum isl_dim_type type);
1221 As with C<isl_dim_get_tuple_name>, the value returned points to
1222 an internal data structure.
1223 The names of individual dimensions can be read off using
1224 the following functions.
1226 const char *isl_constraint_get_dim_name(
1227 __isl_keep isl_constraint *constraint,
1228 enum isl_dim_type type, unsigned pos);
1229 const char *isl_basic_set_get_dim_name(
1230 __isl_keep isl_basic_set *bset,
1231 enum isl_dim_type type, unsigned pos);
1232 const char *isl_set_get_dim_name(
1233 __isl_keep isl_set *set,
1234 enum isl_dim_type type, unsigned pos);
1235 const char *isl_basic_map_get_dim_name(
1236 __isl_keep isl_basic_map *bmap,
1237 enum isl_dim_type type, unsigned pos);
1238 const char *isl_map_get_dim_name(
1239 __isl_keep isl_map *map,
1240 enum isl_dim_type type, unsigned pos);
1242 These functions are mostly useful to obtain the names
1247 =head3 Unary Properties
1253 The following functions test whether the given set or relation
1254 contains any integer points. The ``plain'' variants do not perform
1255 any computations, but simply check if the given set or relation
1256 is already known to be empty.
1258 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1259 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1260 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1261 int isl_set_is_empty(__isl_keep isl_set *set);
1262 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1263 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1264 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1265 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1266 int isl_map_is_empty(__isl_keep isl_map *map);
1267 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1269 =item * Universality
1271 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1272 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1273 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1275 =item * Single-valuedness
1277 int isl_map_is_single_valued(__isl_keep isl_map *map);
1278 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1282 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1283 int isl_map_is_injective(__isl_keep isl_map *map);
1284 int isl_union_map_plain_is_injective(
1285 __isl_keep isl_union_map *umap);
1286 int isl_union_map_is_injective(
1287 __isl_keep isl_union_map *umap);
1291 int isl_map_is_bijective(__isl_keep isl_map *map);
1292 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1296 The following functions check whether the domain of the given
1297 (basic) set is a wrapped relation.
1299 int isl_basic_set_is_wrapping(
1300 __isl_keep isl_basic_set *bset);
1301 int isl_set_is_wrapping(__isl_keep isl_set *set);
1303 =item * Internal Product
1305 int isl_basic_map_can_zip(
1306 __isl_keep isl_basic_map *bmap);
1307 int isl_map_can_zip(__isl_keep isl_map *map);
1309 Check whether the product of domain and range of the given relation
1311 i.e., whether both domain and range are nested relations.
1315 =head3 Binary Properties
1321 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1322 __isl_keep isl_set *set2);
1323 int isl_set_is_equal(__isl_keep isl_set *set1,
1324 __isl_keep isl_set *set2);
1325 int isl_union_set_is_equal(
1326 __isl_keep isl_union_set *uset1,
1327 __isl_keep isl_union_set *uset2);
1328 int isl_basic_map_is_equal(
1329 __isl_keep isl_basic_map *bmap1,
1330 __isl_keep isl_basic_map *bmap2);
1331 int isl_map_is_equal(__isl_keep isl_map *map1,
1332 __isl_keep isl_map *map2);
1333 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1334 __isl_keep isl_map *map2);
1335 int isl_union_map_is_equal(
1336 __isl_keep isl_union_map *umap1,
1337 __isl_keep isl_union_map *umap2);
1339 =item * Disjointness
1341 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1342 __isl_keep isl_set *set2);
1346 int isl_set_is_subset(__isl_keep isl_set *set1,
1347 __isl_keep isl_set *set2);
1348 int isl_set_is_strict_subset(
1349 __isl_keep isl_set *set1,
1350 __isl_keep isl_set *set2);
1351 int isl_union_set_is_subset(
1352 __isl_keep isl_union_set *uset1,
1353 __isl_keep isl_union_set *uset2);
1354 int isl_union_set_is_strict_subset(
1355 __isl_keep isl_union_set *uset1,
1356 __isl_keep isl_union_set *uset2);
1357 int isl_basic_map_is_subset(
1358 __isl_keep isl_basic_map *bmap1,
1359 __isl_keep isl_basic_map *bmap2);
1360 int isl_basic_map_is_strict_subset(
1361 __isl_keep isl_basic_map *bmap1,
1362 __isl_keep isl_basic_map *bmap2);
1363 int isl_map_is_subset(
1364 __isl_keep isl_map *map1,
1365 __isl_keep isl_map *map2);
1366 int isl_map_is_strict_subset(
1367 __isl_keep isl_map *map1,
1368 __isl_keep isl_map *map2);
1369 int isl_union_map_is_subset(
1370 __isl_keep isl_union_map *umap1,
1371 __isl_keep isl_union_map *umap2);
1372 int isl_union_map_is_strict_subset(
1373 __isl_keep isl_union_map *umap1,
1374 __isl_keep isl_union_map *umap2);
1378 =head2 Unary Operations
1384 __isl_give isl_set *isl_set_complement(
1385 __isl_take isl_set *set);
1389 __isl_give isl_basic_map *isl_basic_map_reverse(
1390 __isl_take isl_basic_map *bmap);
1391 __isl_give isl_map *isl_map_reverse(
1392 __isl_take isl_map *map);
1393 __isl_give isl_union_map *isl_union_map_reverse(
1394 __isl_take isl_union_map *umap);
1398 __isl_give isl_basic_set *isl_basic_set_project_out(
1399 __isl_take isl_basic_set *bset,
1400 enum isl_dim_type type, unsigned first, unsigned n);
1401 __isl_give isl_basic_map *isl_basic_map_project_out(
1402 __isl_take isl_basic_map *bmap,
1403 enum isl_dim_type type, unsigned first, unsigned n);
1404 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1405 enum isl_dim_type type, unsigned first, unsigned n);
1406 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1407 enum isl_dim_type type, unsigned first, unsigned n);
1408 __isl_give isl_basic_set *isl_basic_map_domain(
1409 __isl_take isl_basic_map *bmap);
1410 __isl_give isl_basic_set *isl_basic_map_range(
1411 __isl_take isl_basic_map *bmap);
1412 __isl_give isl_set *isl_map_domain(
1413 __isl_take isl_map *bmap);
1414 __isl_give isl_set *isl_map_range(
1415 __isl_take isl_map *map);
1416 __isl_give isl_union_set *isl_union_map_domain(
1417 __isl_take isl_union_map *umap);
1418 __isl_give isl_union_set *isl_union_map_range(
1419 __isl_take isl_union_map *umap);
1421 __isl_give isl_basic_map *isl_basic_map_domain_map(
1422 __isl_take isl_basic_map *bmap);
1423 __isl_give isl_basic_map *isl_basic_map_range_map(
1424 __isl_take isl_basic_map *bmap);
1425 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1426 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1427 __isl_give isl_union_map *isl_union_map_domain_map(
1428 __isl_take isl_union_map *umap);
1429 __isl_give isl_union_map *isl_union_map_range_map(
1430 __isl_take isl_union_map *umap);
1432 The functions above construct a (basic, regular or union) relation
1433 that maps (a wrapped version of) the input relation to its domain or range.
1437 __isl_give isl_set *isl_set_eliminate(
1438 __isl_take isl_set *set, enum isl_dim_type type,
1439 unsigned first, unsigned n);
1441 Eliminate the coefficients for the given dimensions from the constraints,
1442 without removing the dimensions.
1446 __isl_give isl_basic_set *isl_basic_set_fix(
1447 __isl_take isl_basic_set *bset,
1448 enum isl_dim_type type, unsigned pos,
1450 __isl_give isl_basic_set *isl_basic_set_fix_si(
1451 __isl_take isl_basic_set *bset,
1452 enum isl_dim_type type, unsigned pos, int value);
1453 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1454 enum isl_dim_type type, unsigned pos,
1456 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1457 enum isl_dim_type type, unsigned pos, int value);
1458 __isl_give isl_basic_map *isl_basic_map_fix_si(
1459 __isl_take isl_basic_map *bmap,
1460 enum isl_dim_type type, unsigned pos, int value);
1461 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1462 enum isl_dim_type type, unsigned pos, int value);
1464 Intersect the set or relation with the hyperplane where the given
1465 dimension has the fixed given value.
1469 __isl_give isl_map *isl_set_identity(
1470 __isl_take isl_set *set);
1471 __isl_give isl_union_map *isl_union_set_identity(
1472 __isl_take isl_union_set *uset);
1474 Construct an identity relation on the given (union) set.
1478 __isl_give isl_basic_set *isl_basic_map_deltas(
1479 __isl_take isl_basic_map *bmap);
1480 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1481 __isl_give isl_union_set *isl_union_map_deltas(
1482 __isl_take isl_union_map *umap);
1484 These functions return a (basic) set containing the differences
1485 between image elements and corresponding domain elements in the input.
1487 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1488 __isl_take isl_basic_map *bmap);
1489 __isl_give isl_map *isl_map_deltas_map(
1490 __isl_take isl_map *map);
1491 __isl_give isl_union_map *isl_union_map_deltas_map(
1492 __isl_take isl_union_map *umap);
1494 The functions above construct a (basic, regular or union) relation
1495 that maps (a wrapped version of) the input relation to its delta set.
1499 Simplify the representation of a set or relation by trying
1500 to combine pairs of basic sets or relations into a single
1501 basic set or relation.
1503 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1504 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1505 __isl_give isl_union_set *isl_union_set_coalesce(
1506 __isl_take isl_union_set *uset);
1507 __isl_give isl_union_map *isl_union_map_coalesce(
1508 __isl_take isl_union_map *umap);
1510 =item * Detecting equalities
1512 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1513 __isl_take isl_basic_set *bset);
1514 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1515 __isl_take isl_basic_map *bmap);
1516 __isl_give isl_set *isl_set_detect_equalities(
1517 __isl_take isl_set *set);
1518 __isl_give isl_map *isl_map_detect_equalities(
1519 __isl_take isl_map *map);
1520 __isl_give isl_union_set *isl_union_set_detect_equalities(
1521 __isl_take isl_union_set *uset);
1522 __isl_give isl_union_map *isl_union_map_detect_equalities(
1523 __isl_take isl_union_map *umap);
1525 Simplify the representation of a set or relation by detecting implicit
1528 =item * Removing redundant constraints
1530 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1531 __isl_take isl_basic_set *bset);
1532 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1533 __isl_take isl_basic_map *bmap);
1537 __isl_give isl_basic_set *isl_set_convex_hull(
1538 __isl_take isl_set *set);
1539 __isl_give isl_basic_map *isl_map_convex_hull(
1540 __isl_take isl_map *map);
1542 If the input set or relation has any existentially quantified
1543 variables, then the result of these operations is currently undefined.
1547 __isl_give isl_basic_set *isl_set_simple_hull(
1548 __isl_take isl_set *set);
1549 __isl_give isl_basic_map *isl_map_simple_hull(
1550 __isl_take isl_map *map);
1551 __isl_give isl_union_map *isl_union_map_simple_hull(
1552 __isl_take isl_union_map *umap);
1554 These functions compute a single basic set or relation
1555 that contains the whole input set or relation.
1556 In particular, the output is described by translates
1557 of the constraints describing the basic sets or relations in the input.
1561 (See \autoref{s:simple hull}.)
1567 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1568 __isl_take isl_basic_set *bset);
1569 __isl_give isl_basic_set *isl_set_affine_hull(
1570 __isl_take isl_set *set);
1571 __isl_give isl_union_set *isl_union_set_affine_hull(
1572 __isl_take isl_union_set *uset);
1573 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1574 __isl_take isl_basic_map *bmap);
1575 __isl_give isl_basic_map *isl_map_affine_hull(
1576 __isl_take isl_map *map);
1577 __isl_give isl_union_map *isl_union_map_affine_hull(
1578 __isl_take isl_union_map *umap);
1580 In case of union sets and relations, the affine hull is computed
1583 =item * Polyhedral hull
1585 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1586 __isl_take isl_set *set);
1587 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1588 __isl_take isl_map *map);
1589 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1590 __isl_take isl_union_set *uset);
1591 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1592 __isl_take isl_union_map *umap);
1594 These functions compute a single basic set or relation
1595 not involving any existentially quantified variables
1596 that contains the whole input set or relation.
1597 In case of union sets and relations, the polyhedral hull is computed
1600 =item * Optimization
1602 #include <isl/ilp.h>
1603 enum isl_lp_result isl_basic_set_max(
1604 __isl_keep isl_basic_set *bset,
1605 __isl_keep isl_aff *obj, isl_int *opt)
1606 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1607 __isl_keep isl_aff *obj, isl_int *opt);
1609 Compute the maximum of the integer affine expression C<obj>
1610 over the points in C<set>, returning the result in C<opt>.
1611 The return value may be one of C<isl_lp_error>,
1612 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1616 The following functions compute either the set of (rational) coefficient
1617 values of valid constraints for the given set or the set of (rational)
1618 values satisfying the constraints with coefficients from the given set.
1619 Internally, these two sets of functions perform essentially the
1620 same operations, except that the set of coefficients is assumed to
1621 be a cone, while the set of values may be any polyhedron.
1622 The current implementation is based on the Farkas lemma and
1623 Fourier-Motzkin elimination, but this may change or be made optional
1624 in future. In particular, future implementations may use different
1625 dualization algorithms or skip the elimination step.
1627 __isl_give isl_basic_set *isl_basic_set_coefficients(
1628 __isl_take isl_basic_set *bset);
1629 __isl_give isl_basic_set *isl_set_coefficients(
1630 __isl_take isl_set *set);
1631 __isl_give isl_union_set *isl_union_set_coefficients(
1632 __isl_take isl_union_set *bset);
1633 __isl_give isl_basic_set *isl_basic_set_solutions(
1634 __isl_take isl_basic_set *bset);
1635 __isl_give isl_basic_set *isl_set_solutions(
1636 __isl_take isl_set *set);
1637 __isl_give isl_union_set *isl_union_set_solutions(
1638 __isl_take isl_union_set *bset);
1642 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1644 __isl_give isl_union_map *isl_union_map_power(
1645 __isl_take isl_union_map *umap, int *exact);
1647 Compute a parametric representation for all positive powers I<k> of C<map>.
1648 The result maps I<k> to a nested relation corresponding to the
1649 I<k>th power of C<map>.
1650 The result may be an overapproximation. If the result is known to be exact,
1651 then C<*exact> is set to C<1>.
1653 =item * Transitive closure
1655 __isl_give isl_map *isl_map_transitive_closure(
1656 __isl_take isl_map *map, int *exact);
1657 __isl_give isl_union_map *isl_union_map_transitive_closure(
1658 __isl_take isl_union_map *umap, int *exact);
1660 Compute the transitive closure of C<map>.
1661 The result may be an overapproximation. If the result is known to be exact,
1662 then C<*exact> is set to C<1>.
1664 =item * Reaching path lengths
1666 __isl_give isl_map *isl_map_reaching_path_lengths(
1667 __isl_take isl_map *map, int *exact);
1669 Compute a relation that maps each element in the range of C<map>
1670 to the lengths of all paths composed of edges in C<map> that
1671 end up in the given element.
1672 The result may be an overapproximation. If the result is known to be exact,
1673 then C<*exact> is set to C<1>.
1674 To compute the I<maximal> path length, the resulting relation
1675 should be postprocessed by C<isl_map_lexmax>.
1676 In particular, if the input relation is a dependence relation
1677 (mapping sources to sinks), then the maximal path length corresponds
1678 to the free schedule.
1679 Note, however, that C<isl_map_lexmax> expects the maximum to be
1680 finite, so if the path lengths are unbounded (possibly due to
1681 the overapproximation), then you will get an error message.
1685 __isl_give isl_basic_set *isl_basic_map_wrap(
1686 __isl_take isl_basic_map *bmap);
1687 __isl_give isl_set *isl_map_wrap(
1688 __isl_take isl_map *map);
1689 __isl_give isl_union_set *isl_union_map_wrap(
1690 __isl_take isl_union_map *umap);
1691 __isl_give isl_basic_map *isl_basic_set_unwrap(
1692 __isl_take isl_basic_set *bset);
1693 __isl_give isl_map *isl_set_unwrap(
1694 __isl_take isl_set *set);
1695 __isl_give isl_union_map *isl_union_set_unwrap(
1696 __isl_take isl_union_set *uset);
1700 Remove any internal structure of domain (and range) of the given
1701 set or relation. If there is any such internal structure in the input,
1702 then the name of the space is also removed.
1704 __isl_give isl_basic_set *isl_basic_set_flatten(
1705 __isl_take isl_basic_set *bset);
1706 __isl_give isl_set *isl_set_flatten(
1707 __isl_take isl_set *set);
1708 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1709 __isl_take isl_basic_map *bmap);
1710 __isl_give isl_map *isl_map_flatten_range(
1711 __isl_take isl_map *map);
1712 __isl_give isl_basic_map *isl_basic_map_flatten(
1713 __isl_take isl_basic_map *bmap);
1714 __isl_give isl_map *isl_map_flatten(
1715 __isl_take isl_map *map);
1717 __isl_give isl_map *isl_set_flatten_map(
1718 __isl_take isl_set *set);
1720 The function above constructs a relation
1721 that maps the input set to a flattened version of the set.
1725 Lift the input set to a space with extra dimensions corresponding
1726 to the existentially quantified variables in the input.
1727 In particular, the result lives in a wrapped map where the domain
1728 is the original space and the range corresponds to the original
1729 existentially quantified variables.
1731 __isl_give isl_basic_set *isl_basic_set_lift(
1732 __isl_take isl_basic_set *bset);
1733 __isl_give isl_set *isl_set_lift(
1734 __isl_take isl_set *set);
1735 __isl_give isl_union_set *isl_union_set_lift(
1736 __isl_take isl_union_set *uset);
1738 =item * Internal Product
1740 __isl_give isl_basic_map *isl_basic_map_zip(
1741 __isl_take isl_basic_map *bmap);
1742 __isl_give isl_map *isl_map_zip(
1743 __isl_take isl_map *map);
1744 __isl_give isl_union_map *isl_union_map_zip(
1745 __isl_take isl_union_map *umap);
1747 Given a relation with nested relations for domain and range,
1748 interchange the range of the domain with the domain of the range.
1750 =item * Aligning parameters
1752 __isl_give isl_set *isl_set_align_params(
1753 __isl_take isl_set *set,
1754 __isl_take isl_dim *model);
1755 __isl_give isl_map *isl_map_align_params(
1756 __isl_take isl_map *map,
1757 __isl_take isl_dim *model);
1759 Change the order of the parameters of the given set or relation
1760 such that the first parameters match those of C<model>.
1761 This may involve the introduction of extra parameters.
1762 All parameters need to be named.
1764 =item * Dimension manipulation
1766 __isl_give isl_set *isl_set_add_dims(
1767 __isl_take isl_set *set,
1768 enum isl_dim_type type, unsigned n);
1769 __isl_give isl_map *isl_map_add_dims(
1770 __isl_take isl_map *map,
1771 enum isl_dim_type type, unsigned n);
1773 It is usually not advisable to directly change the (input or output)
1774 space of a set or a relation as this removes the name and the internal
1775 structure of the space. However, the above functions can be useful
1776 to add new parameters, assuming
1777 C<isl_set_align_params> and C<isl_map_align_params>
1782 =head2 Binary Operations
1784 The two arguments of a binary operation not only need to live
1785 in the same C<isl_ctx>, they currently also need to have
1786 the same (number of) parameters.
1788 =head3 Basic Operations
1792 =item * Intersection
1794 __isl_give isl_basic_set *isl_basic_set_intersect(
1795 __isl_take isl_basic_set *bset1,
1796 __isl_take isl_basic_set *bset2);
1797 __isl_give isl_set *isl_set_intersect(
1798 __isl_take isl_set *set1,
1799 __isl_take isl_set *set2);
1800 __isl_give isl_union_set *isl_union_set_intersect(
1801 __isl_take isl_union_set *uset1,
1802 __isl_take isl_union_set *uset2);
1803 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1804 __isl_take isl_basic_map *bmap,
1805 __isl_take isl_basic_set *bset);
1806 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1807 __isl_take isl_basic_map *bmap,
1808 __isl_take isl_basic_set *bset);
1809 __isl_give isl_basic_map *isl_basic_map_intersect(
1810 __isl_take isl_basic_map *bmap1,
1811 __isl_take isl_basic_map *bmap2);
1812 __isl_give isl_map *isl_map_intersect_domain(
1813 __isl_take isl_map *map,
1814 __isl_take isl_set *set);
1815 __isl_give isl_map *isl_map_intersect_range(
1816 __isl_take isl_map *map,
1817 __isl_take isl_set *set);
1818 __isl_give isl_map *isl_map_intersect(
1819 __isl_take isl_map *map1,
1820 __isl_take isl_map *map2);
1821 __isl_give isl_union_map *isl_union_map_intersect_domain(
1822 __isl_take isl_union_map *umap,
1823 __isl_take isl_union_set *uset);
1824 __isl_give isl_union_map *isl_union_map_intersect_range(
1825 __isl_take isl_union_map *umap,
1826 __isl_take isl_union_set *uset);
1827 __isl_give isl_union_map *isl_union_map_intersect(
1828 __isl_take isl_union_map *umap1,
1829 __isl_take isl_union_map *umap2);
1833 __isl_give isl_set *isl_basic_set_union(
1834 __isl_take isl_basic_set *bset1,
1835 __isl_take isl_basic_set *bset2);
1836 __isl_give isl_map *isl_basic_map_union(
1837 __isl_take isl_basic_map *bmap1,
1838 __isl_take isl_basic_map *bmap2);
1839 __isl_give isl_set *isl_set_union(
1840 __isl_take isl_set *set1,
1841 __isl_take isl_set *set2);
1842 __isl_give isl_map *isl_map_union(
1843 __isl_take isl_map *map1,
1844 __isl_take isl_map *map2);
1845 __isl_give isl_union_set *isl_union_set_union(
1846 __isl_take isl_union_set *uset1,
1847 __isl_take isl_union_set *uset2);
1848 __isl_give isl_union_map *isl_union_map_union(
1849 __isl_take isl_union_map *umap1,
1850 __isl_take isl_union_map *umap2);
1852 =item * Set difference
1854 __isl_give isl_set *isl_set_subtract(
1855 __isl_take isl_set *set1,
1856 __isl_take isl_set *set2);
1857 __isl_give isl_map *isl_map_subtract(
1858 __isl_take isl_map *map1,
1859 __isl_take isl_map *map2);
1860 __isl_give isl_union_set *isl_union_set_subtract(
1861 __isl_take isl_union_set *uset1,
1862 __isl_take isl_union_set *uset2);
1863 __isl_give isl_union_map *isl_union_map_subtract(
1864 __isl_take isl_union_map *umap1,
1865 __isl_take isl_union_map *umap2);
1869 __isl_give isl_basic_set *isl_basic_set_apply(
1870 __isl_take isl_basic_set *bset,
1871 __isl_take isl_basic_map *bmap);
1872 __isl_give isl_set *isl_set_apply(
1873 __isl_take isl_set *set,
1874 __isl_take isl_map *map);
1875 __isl_give isl_union_set *isl_union_set_apply(
1876 __isl_take isl_union_set *uset,
1877 __isl_take isl_union_map *umap);
1878 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1879 __isl_take isl_basic_map *bmap1,
1880 __isl_take isl_basic_map *bmap2);
1881 __isl_give isl_basic_map *isl_basic_map_apply_range(
1882 __isl_take isl_basic_map *bmap1,
1883 __isl_take isl_basic_map *bmap2);
1884 __isl_give isl_map *isl_map_apply_domain(
1885 __isl_take isl_map *map1,
1886 __isl_take isl_map *map2);
1887 __isl_give isl_union_map *isl_union_map_apply_domain(
1888 __isl_take isl_union_map *umap1,
1889 __isl_take isl_union_map *umap2);
1890 __isl_give isl_map *isl_map_apply_range(
1891 __isl_take isl_map *map1,
1892 __isl_take isl_map *map2);
1893 __isl_give isl_union_map *isl_union_map_apply_range(
1894 __isl_take isl_union_map *umap1,
1895 __isl_take isl_union_map *umap2);
1897 =item * Cartesian Product
1899 __isl_give isl_set *isl_set_product(
1900 __isl_take isl_set *set1,
1901 __isl_take isl_set *set2);
1902 __isl_give isl_union_set *isl_union_set_product(
1903 __isl_take isl_union_set *uset1,
1904 __isl_take isl_union_set *uset2);
1905 __isl_give isl_basic_map *isl_basic_map_range_product(
1906 __isl_take isl_basic_map *bmap1,
1907 __isl_take isl_basic_map *bmap2);
1908 __isl_give isl_map *isl_map_range_product(
1909 __isl_take isl_map *map1,
1910 __isl_take isl_map *map2);
1911 __isl_give isl_union_map *isl_union_map_range_product(
1912 __isl_take isl_union_map *umap1,
1913 __isl_take isl_union_map *umap2);
1914 __isl_give isl_map *isl_map_product(
1915 __isl_take isl_map *map1,
1916 __isl_take isl_map *map2);
1917 __isl_give isl_union_map *isl_union_map_product(
1918 __isl_take isl_union_map *umap1,
1919 __isl_take isl_union_map *umap2);
1921 The above functions compute the cross product of the given
1922 sets or relations. The domains and ranges of the results
1923 are wrapped maps between domains and ranges of the inputs.
1924 To obtain a ``flat'' product, use the following functions
1927 __isl_give isl_basic_set *isl_basic_set_flat_product(
1928 __isl_take isl_basic_set *bset1,
1929 __isl_take isl_basic_set *bset2);
1930 __isl_give isl_set *isl_set_flat_product(
1931 __isl_take isl_set *set1,
1932 __isl_take isl_set *set2);
1933 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1934 __isl_take isl_basic_map *bmap1,
1935 __isl_take isl_basic_map *bmap2);
1936 __isl_give isl_map *isl_map_flat_range_product(
1937 __isl_take isl_map *map1,
1938 __isl_take isl_map *map2);
1939 __isl_give isl_union_map *isl_union_map_flat_range_product(
1940 __isl_take isl_union_map *umap1,
1941 __isl_take isl_union_map *umap2);
1942 __isl_give isl_basic_map *isl_basic_map_flat_product(
1943 __isl_take isl_basic_map *bmap1,
1944 __isl_take isl_basic_map *bmap2);
1945 __isl_give isl_map *isl_map_flat_product(
1946 __isl_take isl_map *map1,
1947 __isl_take isl_map *map2);
1949 =item * Simplification
1951 __isl_give isl_basic_set *isl_basic_set_gist(
1952 __isl_take isl_basic_set *bset,
1953 __isl_take isl_basic_set *context);
1954 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1955 __isl_take isl_set *context);
1956 __isl_give isl_union_set *isl_union_set_gist(
1957 __isl_take isl_union_set *uset,
1958 __isl_take isl_union_set *context);
1959 __isl_give isl_basic_map *isl_basic_map_gist(
1960 __isl_take isl_basic_map *bmap,
1961 __isl_take isl_basic_map *context);
1962 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1963 __isl_take isl_map *context);
1964 __isl_give isl_union_map *isl_union_map_gist(
1965 __isl_take isl_union_map *umap,
1966 __isl_take isl_union_map *context);
1968 The gist operation returns a set or relation that has the
1969 same intersection with the context as the input set or relation.
1970 Any implicit equality in the intersection is made explicit in the result,
1971 while all inequalities that are redundant with respect to the intersection
1973 In case of union sets and relations, the gist operation is performed
1978 =head3 Lexicographic Optimization
1980 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1981 the following functions
1982 compute a set that contains the lexicographic minimum or maximum
1983 of the elements in C<set> (or C<bset>) for those values of the parameters
1984 that satisfy C<dom>.
1985 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1986 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1988 In other words, the union of the parameter values
1989 for which the result is non-empty and of C<*empty>
1992 __isl_give isl_set *isl_basic_set_partial_lexmin(
1993 __isl_take isl_basic_set *bset,
1994 __isl_take isl_basic_set *dom,
1995 __isl_give isl_set **empty);
1996 __isl_give isl_set *isl_basic_set_partial_lexmax(
1997 __isl_take isl_basic_set *bset,
1998 __isl_take isl_basic_set *dom,
1999 __isl_give isl_set **empty);
2000 __isl_give isl_set *isl_set_partial_lexmin(
2001 __isl_take isl_set *set, __isl_take isl_set *dom,
2002 __isl_give isl_set **empty);
2003 __isl_give isl_set *isl_set_partial_lexmax(
2004 __isl_take isl_set *set, __isl_take isl_set *dom,
2005 __isl_give isl_set **empty);
2007 Given a (basic) set C<set> (or C<bset>), the following functions simply
2008 return a set containing the lexicographic minimum or maximum
2009 of the elements in C<set> (or C<bset>).
2010 In case of union sets, the optimum is computed per space.
2012 __isl_give isl_set *isl_basic_set_lexmin(
2013 __isl_take isl_basic_set *bset);
2014 __isl_give isl_set *isl_basic_set_lexmax(
2015 __isl_take isl_basic_set *bset);
2016 __isl_give isl_set *isl_set_lexmin(
2017 __isl_take isl_set *set);
2018 __isl_give isl_set *isl_set_lexmax(
2019 __isl_take isl_set *set);
2020 __isl_give isl_union_set *isl_union_set_lexmin(
2021 __isl_take isl_union_set *uset);
2022 __isl_give isl_union_set *isl_union_set_lexmax(
2023 __isl_take isl_union_set *uset);
2025 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2026 the following functions
2027 compute a relation that maps each element of C<dom>
2028 to the single lexicographic minimum or maximum
2029 of the elements that are associated to that same
2030 element in C<map> (or C<bmap>).
2031 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2032 that contains the elements in C<dom> that do not map
2033 to any elements in C<map> (or C<bmap>).
2034 In other words, the union of the domain of the result and of C<*empty>
2037 __isl_give isl_map *isl_basic_map_partial_lexmax(
2038 __isl_take isl_basic_map *bmap,
2039 __isl_take isl_basic_set *dom,
2040 __isl_give isl_set **empty);
2041 __isl_give isl_map *isl_basic_map_partial_lexmin(
2042 __isl_take isl_basic_map *bmap,
2043 __isl_take isl_basic_set *dom,
2044 __isl_give isl_set **empty);
2045 __isl_give isl_map *isl_map_partial_lexmax(
2046 __isl_take isl_map *map, __isl_take isl_set *dom,
2047 __isl_give isl_set **empty);
2048 __isl_give isl_map *isl_map_partial_lexmin(
2049 __isl_take isl_map *map, __isl_take isl_set *dom,
2050 __isl_give isl_set **empty);
2052 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2053 return a map mapping each element in the domain of
2054 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2055 of all elements associated to that element.
2056 In case of union relations, the optimum is computed per space.
2058 __isl_give isl_map *isl_basic_map_lexmin(
2059 __isl_take isl_basic_map *bmap);
2060 __isl_give isl_map *isl_basic_map_lexmax(
2061 __isl_take isl_basic_map *bmap);
2062 __isl_give isl_map *isl_map_lexmin(
2063 __isl_take isl_map *map);
2064 __isl_give isl_map *isl_map_lexmax(
2065 __isl_take isl_map *map);
2066 __isl_give isl_union_map *isl_union_map_lexmin(
2067 __isl_take isl_union_map *umap);
2068 __isl_give isl_union_map *isl_union_map_lexmax(
2069 __isl_take isl_union_map *umap);
2073 Lists are defined over several element types, including
2074 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2075 Here we take lists of C<isl_set>s as an example.
2076 Lists can be created, copied and freed using the following functions.
2078 #include <isl/list.h>
2079 __isl_give isl_set_list *isl_set_list_alloc(
2080 isl_ctx *ctx, int n);
2081 __isl_give isl_set_list *isl_set_list_copy(
2082 __isl_keep isl_set_list *list);
2083 __isl_give isl_set_list *isl_set_list_add(
2084 __isl_take isl_set_list *list,
2085 __isl_take isl_set *el);
2086 void isl_set_list_free(__isl_take isl_set_list *list);
2088 C<isl_set_list_alloc> creates an empty list with a capacity for
2091 Lists can be inspected using the following functions.
2093 #include <isl/list.h>
2094 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2095 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2096 __isl_give struct isl_set *isl_set_list_get_set(
2097 __isl_keep isl_set_list *list, int index);
2098 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2099 int (*fn)(__isl_take struct isl_set *el, void *user),
2102 Lists can be printed using
2104 #include <isl/list.h>
2105 __isl_give isl_printer *isl_printer_print_set_list(
2106 __isl_take isl_printer *p,
2107 __isl_keep isl_set_list *list);
2111 Matrices can be created, copied and freed using the following functions.
2113 #include <isl/mat.h>
2114 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2115 unsigned n_row, unsigned n_col);
2116 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2117 void isl_mat_free(__isl_take isl_mat *mat);
2119 Note that the elements of a newly created matrix may have arbitrary values.
2120 The elements can be changed and inspected using the following functions.
2122 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2123 int isl_mat_rows(__isl_keep isl_mat *mat);
2124 int isl_mat_cols(__isl_keep isl_mat *mat);
2125 int isl_mat_get_element(__isl_keep isl_mat *mat,
2126 int row, int col, isl_int *v);
2127 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2128 int row, int col, isl_int v);
2129 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2130 int row, int col, int v);
2132 C<isl_mat_get_element> will return a negative value if anything went wrong.
2133 In that case, the value of C<*v> is undefined.
2135 The following function can be used to compute the (right) inverse
2136 of a matrix, i.e., a matrix such that the product of the original
2137 and the inverse (in that order) is a multiple of the identity matrix.
2138 The input matrix is assumed to be of full row-rank.
2140 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2142 The following function can be used to compute the (right) kernel
2143 (or null space) of a matrix, i.e., a matrix such that the product of
2144 the original and the kernel (in that order) is the zero matrix.
2146 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2148 =head2 Quasi Affine Expressions
2150 The zero quasi affine expression can be created using
2152 __isl_give isl_aff *isl_aff_zero(
2153 __isl_take isl_local_space *ls);
2155 Quasi affine expressions can be copied and free using
2157 #include <isl/aff.h>
2158 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2159 void *isl_aff_free(__isl_take isl_aff *aff);
2161 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2162 using the following function. The constraint is required to have
2163 a non-zero coefficient for the specified dimension.
2165 #include <isl/constraint.h>
2166 __isl_give isl_aff *isl_constraint_get_bound(
2167 __isl_keep isl_constraint *constraint,
2168 enum isl_dim_type type, int pos);
2170 Conversely, an equality constraint equating
2171 the affine expression to zero or an inequality constraint enforcing
2172 the affine expression to be non-negative, can be constructed using
2174 __isl_give isl_constraint *isl_equality_from_aff(
2175 __isl_take isl_aff *aff);
2176 __isl_give isl_constraint *isl_inequality_from_aff(
2177 __isl_take isl_aff *aff);
2179 The expression can be inspected using
2181 #include <isl/aff.h>
2182 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2183 int isl_aff_dim(__isl_keep isl_aff *aff,
2184 enum isl_dim_type type);
2185 __isl_give isl_local_space *isl_aff_get_local_space(
2186 __isl_keep isl_aff *aff);
2187 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2188 enum isl_dim_type type, unsigned pos);
2189 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2191 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2192 enum isl_dim_type type, int pos, isl_int *v);
2193 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2195 __isl_give isl_div *isl_aff_get_div(
2196 __isl_keep isl_aff *aff, int pos);
2198 It can be modified using
2200 #include <isl/aff.h>
2201 __isl_give isl_aff *isl_aff_set_constant(
2202 __isl_take isl_aff *aff, isl_int v);
2203 __isl_give isl_aff *isl_aff_set_constant_si(
2204 __isl_take isl_aff *aff, int v);
2205 __isl_give isl_aff *isl_aff_set_coefficient(
2206 __isl_take isl_aff *aff,
2207 enum isl_dim_type type, int pos, isl_int v);
2208 __isl_give isl_aff *isl_aff_set_coefficient_si(
2209 __isl_take isl_aff *aff,
2210 enum isl_dim_type type, int pos, int v);
2211 __isl_give isl_aff *isl_aff_set_denominator(
2212 __isl_take isl_aff *aff, isl_int v);
2214 __isl_give isl_aff *isl_aff_add_constant(
2215 __isl_take isl_aff *aff, isl_int v);
2216 __isl_give isl_aff *isl_aff_add_coefficient_si(
2217 __isl_take isl_aff *aff,
2218 enum isl_dim_type type, int pos, int v);
2220 Note that the C<set_constant> and C<set_coefficient> functions
2221 set the I<numerator> of the constant or coefficient, while
2222 C<add_constant> and C<add_coefficient> add an integer value to
2223 the possibly rational constant or coefficient.
2227 #include <isl/aff.h>
2228 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2229 __isl_take isl_aff *aff2);
2230 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2231 __isl_take isl_aff *aff2);
2232 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2233 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2234 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2236 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2239 An expression can be printed using
2241 #include <isl/aff.h>
2242 __isl_give isl_printer *isl_printer_print_aff(
2243 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2247 Points are elements of a set. They can be used to construct
2248 simple sets (boxes) or they can be used to represent the
2249 individual elements of a set.
2250 The zero point (the origin) can be created using
2252 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2254 The coordinates of a point can be inspected, set and changed
2257 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2258 enum isl_dim_type type, int pos, isl_int *v);
2259 __isl_give isl_point *isl_point_set_coordinate(
2260 __isl_take isl_point *pnt,
2261 enum isl_dim_type type, int pos, isl_int v);
2263 __isl_give isl_point *isl_point_add_ui(
2264 __isl_take isl_point *pnt,
2265 enum isl_dim_type type, int pos, unsigned val);
2266 __isl_give isl_point *isl_point_sub_ui(
2267 __isl_take isl_point *pnt,
2268 enum isl_dim_type type, int pos, unsigned val);
2270 Other properties can be obtained using
2272 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2274 Points can be copied or freed using
2276 __isl_give isl_point *isl_point_copy(
2277 __isl_keep isl_point *pnt);
2278 void isl_point_free(__isl_take isl_point *pnt);
2280 A singleton set can be created from a point using
2282 __isl_give isl_basic_set *isl_basic_set_from_point(
2283 __isl_take isl_point *pnt);
2284 __isl_give isl_set *isl_set_from_point(
2285 __isl_take isl_point *pnt);
2287 and a box can be created from two opposite extremal points using
2289 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2290 __isl_take isl_point *pnt1,
2291 __isl_take isl_point *pnt2);
2292 __isl_give isl_set *isl_set_box_from_points(
2293 __isl_take isl_point *pnt1,
2294 __isl_take isl_point *pnt2);
2296 All elements of a B<bounded> (union) set can be enumerated using
2297 the following functions.
2299 int isl_set_foreach_point(__isl_keep isl_set *set,
2300 int (*fn)(__isl_take isl_point *pnt, void *user),
2302 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2303 int (*fn)(__isl_take isl_point *pnt, void *user),
2306 The function C<fn> is called for each integer point in
2307 C<set> with as second argument the last argument of
2308 the C<isl_set_foreach_point> call. The function C<fn>
2309 should return C<0> on success and C<-1> on failure.
2310 In the latter case, C<isl_set_foreach_point> will stop
2311 enumerating and return C<-1> as well.
2312 If the enumeration is performed successfully and to completion,
2313 then C<isl_set_foreach_point> returns C<0>.
2315 To obtain a single point of a (basic) set, use
2317 __isl_give isl_point *isl_basic_set_sample_point(
2318 __isl_take isl_basic_set *bset);
2319 __isl_give isl_point *isl_set_sample_point(
2320 __isl_take isl_set *set);
2322 If C<set> does not contain any (integer) points, then the
2323 resulting point will be ``void'', a property that can be
2326 int isl_point_is_void(__isl_keep isl_point *pnt);
2328 =head2 Piecewise Quasipolynomials
2330 A piecewise quasipolynomial is a particular kind of function that maps
2331 a parametric point to a rational value.
2332 More specifically, a quasipolynomial is a polynomial expression in greatest
2333 integer parts of affine expressions of parameters and variables.
2334 A piecewise quasipolynomial is a subdivision of a given parametric
2335 domain into disjoint cells with a quasipolynomial associated to
2336 each cell. The value of the piecewise quasipolynomial at a given
2337 point is the value of the quasipolynomial associated to the cell
2338 that contains the point. Outside of the union of cells,
2339 the value is assumed to be zero.
2340 For example, the piecewise quasipolynomial
2342 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2344 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2345 A given piecewise quasipolynomial has a fixed domain dimension.
2346 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2347 defined over different domains.
2348 Piecewise quasipolynomials are mainly used by the C<barvinok>
2349 library for representing the number of elements in a parametric set or map.
2350 For example, the piecewise quasipolynomial above represents
2351 the number of points in the map
2353 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2355 =head3 Printing (Piecewise) Quasipolynomials
2357 Quasipolynomials and piecewise quasipolynomials can be printed
2358 using the following functions.
2360 __isl_give isl_printer *isl_printer_print_qpolynomial(
2361 __isl_take isl_printer *p,
2362 __isl_keep isl_qpolynomial *qp);
2364 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2365 __isl_take isl_printer *p,
2366 __isl_keep isl_pw_qpolynomial *pwqp);
2368 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2369 __isl_take isl_printer *p,
2370 __isl_keep isl_union_pw_qpolynomial *upwqp);
2372 The output format of the printer
2373 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2374 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2376 In case of printing in C<ISL_FORMAT_C>, the user may want
2377 to set the names of all dimensions
2379 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2380 __isl_take isl_qpolynomial *qp,
2381 enum isl_dim_type type, unsigned pos,
2383 __isl_give isl_pw_qpolynomial *
2384 isl_pw_qpolynomial_set_dim_name(
2385 __isl_take isl_pw_qpolynomial *pwqp,
2386 enum isl_dim_type type, unsigned pos,
2389 =head3 Creating New (Piecewise) Quasipolynomials
2391 Some simple quasipolynomials can be created using the following functions.
2392 More complicated quasipolynomials can be created by applying
2393 operations such as addition and multiplication
2394 on the resulting quasipolynomials
2396 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2397 __isl_take isl_dim *dim);
2398 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2399 __isl_take isl_dim *dim);
2400 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2401 __isl_take isl_dim *dim);
2402 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2403 __isl_take isl_dim *dim);
2404 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2405 __isl_take isl_dim *dim);
2406 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2407 __isl_take isl_dim *dim,
2408 const isl_int n, const isl_int d);
2409 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2410 __isl_take isl_div *div);
2411 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2412 __isl_take isl_dim *dim,
2413 enum isl_dim_type type, unsigned pos);
2414 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2415 __isl_take isl_aff *aff);
2417 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2418 with a single cell can be created using the following functions.
2419 Multiple of these single cell piecewise quasipolynomials can
2420 be combined to create more complicated piecewise quasipolynomials.
2422 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2423 __isl_take isl_dim *dim);
2424 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2425 __isl_take isl_set *set,
2426 __isl_take isl_qpolynomial *qp);
2428 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2429 __isl_take isl_dim *dim);
2430 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2431 __isl_take isl_pw_qpolynomial *pwqp);
2432 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2433 __isl_take isl_union_pw_qpolynomial *upwqp,
2434 __isl_take isl_pw_qpolynomial *pwqp);
2436 Quasipolynomials can be copied and freed again using the following
2439 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2440 __isl_keep isl_qpolynomial *qp);
2441 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2443 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2444 __isl_keep isl_pw_qpolynomial *pwqp);
2445 void isl_pw_qpolynomial_free(
2446 __isl_take isl_pw_qpolynomial *pwqp);
2448 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2449 __isl_keep isl_union_pw_qpolynomial *upwqp);
2450 void isl_union_pw_qpolynomial_free(
2451 __isl_take isl_union_pw_qpolynomial *upwqp);
2453 =head3 Inspecting (Piecewise) Quasipolynomials
2455 To iterate over all piecewise quasipolynomials in a union
2456 piecewise quasipolynomial, use the following function
2458 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2459 __isl_keep isl_union_pw_qpolynomial *upwqp,
2460 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2463 To extract the piecewise quasipolynomial from a union with a given dimension
2466 __isl_give isl_pw_qpolynomial *
2467 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2468 __isl_keep isl_union_pw_qpolynomial *upwqp,
2469 __isl_take isl_dim *dim);
2471 To iterate over the cells in a piecewise quasipolynomial,
2472 use either of the following two functions
2474 int isl_pw_qpolynomial_foreach_piece(
2475 __isl_keep isl_pw_qpolynomial *pwqp,
2476 int (*fn)(__isl_take isl_set *set,
2477 __isl_take isl_qpolynomial *qp,
2478 void *user), void *user);
2479 int isl_pw_qpolynomial_foreach_lifted_piece(
2480 __isl_keep isl_pw_qpolynomial *pwqp,
2481 int (*fn)(__isl_take isl_set *set,
2482 __isl_take isl_qpolynomial *qp,
2483 void *user), void *user);
2485 As usual, the function C<fn> should return C<0> on success
2486 and C<-1> on failure. The difference between
2487 C<isl_pw_qpolynomial_foreach_piece> and
2488 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2489 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2490 compute unique representations for all existentially quantified
2491 variables and then turn these existentially quantified variables
2492 into extra set variables, adapting the associated quasipolynomial
2493 accordingly. This means that the C<set> passed to C<fn>
2494 will not have any existentially quantified variables, but that
2495 the dimensions of the sets may be different for different
2496 invocations of C<fn>.
2498 To iterate over all terms in a quasipolynomial,
2501 int isl_qpolynomial_foreach_term(
2502 __isl_keep isl_qpolynomial *qp,
2503 int (*fn)(__isl_take isl_term *term,
2504 void *user), void *user);
2506 The terms themselves can be inspected and freed using
2509 unsigned isl_term_dim(__isl_keep isl_term *term,
2510 enum isl_dim_type type);
2511 void isl_term_get_num(__isl_keep isl_term *term,
2513 void isl_term_get_den(__isl_keep isl_term *term,
2515 int isl_term_get_exp(__isl_keep isl_term *term,
2516 enum isl_dim_type type, unsigned pos);
2517 __isl_give isl_div *isl_term_get_div(
2518 __isl_keep isl_term *term, unsigned pos);
2519 void isl_term_free(__isl_take isl_term *term);
2521 Each term is a product of parameters, set variables and
2522 integer divisions. The function C<isl_term_get_exp>
2523 returns the exponent of a given dimensions in the given term.
2524 The C<isl_int>s in the arguments of C<isl_term_get_num>
2525 and C<isl_term_get_den> need to have been initialized
2526 using C<isl_int_init> before calling these functions.
2528 =head3 Properties of (Piecewise) Quasipolynomials
2530 To check whether a quasipolynomial is actually a constant,
2531 use the following function.
2533 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2534 isl_int *n, isl_int *d);
2536 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2537 then the numerator and denominator of the constant
2538 are returned in C<*n> and C<*d>, respectively.
2540 =head3 Operations on (Piecewise) Quasipolynomials
2542 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2543 __isl_take isl_qpolynomial *qp);
2544 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2545 __isl_take isl_qpolynomial *qp1,
2546 __isl_take isl_qpolynomial *qp2);
2547 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2548 __isl_take isl_qpolynomial *qp1,
2549 __isl_take isl_qpolynomial *qp2);
2550 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2551 __isl_take isl_qpolynomial *qp1,
2552 __isl_take isl_qpolynomial *qp2);
2553 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2554 __isl_take isl_qpolynomial *qp, unsigned exponent);
2556 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2557 __isl_take isl_pw_qpolynomial *pwqp1,
2558 __isl_take isl_pw_qpolynomial *pwqp2);
2559 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2560 __isl_take isl_pw_qpolynomial *pwqp1,
2561 __isl_take isl_pw_qpolynomial *pwqp2);
2562 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2563 __isl_take isl_pw_qpolynomial *pwqp1,
2564 __isl_take isl_pw_qpolynomial *pwqp2);
2565 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2566 __isl_take isl_pw_qpolynomial *pwqp);
2567 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2568 __isl_take isl_pw_qpolynomial *pwqp1,
2569 __isl_take isl_pw_qpolynomial *pwqp2);
2571 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2572 __isl_take isl_union_pw_qpolynomial *upwqp1,
2573 __isl_take isl_union_pw_qpolynomial *upwqp2);
2574 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2575 __isl_take isl_union_pw_qpolynomial *upwqp1,
2576 __isl_take isl_union_pw_qpolynomial *upwqp2);
2577 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2578 __isl_take isl_union_pw_qpolynomial *upwqp1,
2579 __isl_take isl_union_pw_qpolynomial *upwqp2);
2581 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2582 __isl_take isl_pw_qpolynomial *pwqp,
2583 __isl_take isl_point *pnt);
2585 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2586 __isl_take isl_union_pw_qpolynomial *upwqp,
2587 __isl_take isl_point *pnt);
2589 __isl_give isl_set *isl_pw_qpolynomial_domain(
2590 __isl_take isl_pw_qpolynomial *pwqp);
2591 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2592 __isl_take isl_pw_qpolynomial *pwpq,
2593 __isl_take isl_set *set);
2595 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2596 __isl_take isl_union_pw_qpolynomial *upwqp);
2597 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2598 __isl_take isl_union_pw_qpolynomial *upwpq,
2599 __isl_take isl_union_set *uset);
2601 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2602 __isl_take isl_qpolynomial *qp,
2603 __isl_take isl_dim *model);
2605 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2606 __isl_take isl_union_pw_qpolynomial *upwqp);
2608 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2609 __isl_take isl_qpolynomial *qp,
2610 __isl_take isl_set *context);
2612 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2613 __isl_take isl_pw_qpolynomial *pwqp,
2614 __isl_take isl_set *context);
2616 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2617 __isl_take isl_union_pw_qpolynomial *upwqp,
2618 __isl_take isl_union_set *context);
2620 The gist operation applies the gist operation to each of
2621 the cells in the domain of the input piecewise quasipolynomial.
2622 The context is also exploited
2623 to simplify the quasipolynomials associated to each cell.
2625 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2626 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2627 __isl_give isl_union_pw_qpolynomial *
2628 isl_union_pw_qpolynomial_to_polynomial(
2629 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2631 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2632 the polynomial will be an overapproximation. If C<sign> is negative,
2633 it will be an underapproximation. If C<sign> is zero, the approximation
2634 will lie somewhere in between.
2636 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2638 A piecewise quasipolynomial reduction is a piecewise
2639 reduction (or fold) of quasipolynomials.
2640 In particular, the reduction can be maximum or a minimum.
2641 The objects are mainly used to represent the result of
2642 an upper or lower bound on a quasipolynomial over its domain,
2643 i.e., as the result of the following function.
2645 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2646 __isl_take isl_pw_qpolynomial *pwqp,
2647 enum isl_fold type, int *tight);
2649 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2650 __isl_take isl_union_pw_qpolynomial *upwqp,
2651 enum isl_fold type, int *tight);
2653 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2654 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2655 is the returned bound is known be tight, i.e., for each value
2656 of the parameters there is at least
2657 one element in the domain that reaches the bound.
2658 If the domain of C<pwqp> is not wrapping, then the bound is computed
2659 over all elements in that domain and the result has a purely parametric
2660 domain. If the domain of C<pwqp> is wrapping, then the bound is
2661 computed over the range of the wrapped relation. The domain of the
2662 wrapped relation becomes the domain of the result.
2664 A (piecewise) quasipolynomial reduction can be copied or freed using the
2665 following functions.
2667 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2668 __isl_keep isl_qpolynomial_fold *fold);
2669 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2670 __isl_keep isl_pw_qpolynomial_fold *pwf);
2671 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2672 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2673 void isl_qpolynomial_fold_free(
2674 __isl_take isl_qpolynomial_fold *fold);
2675 void isl_pw_qpolynomial_fold_free(
2676 __isl_take isl_pw_qpolynomial_fold *pwf);
2677 void isl_union_pw_qpolynomial_fold_free(
2678 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2680 =head3 Printing Piecewise Quasipolynomial Reductions
2682 Piecewise quasipolynomial reductions can be printed
2683 using the following function.
2685 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2686 __isl_take isl_printer *p,
2687 __isl_keep isl_pw_qpolynomial_fold *pwf);
2688 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2689 __isl_take isl_printer *p,
2690 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2692 For C<isl_printer_print_pw_qpolynomial_fold>,
2693 output format of the printer
2694 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2695 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2696 output format of the printer
2697 needs to be set to C<ISL_FORMAT_ISL>.
2698 In case of printing in C<ISL_FORMAT_C>, the user may want
2699 to set the names of all dimensions
2701 __isl_give isl_pw_qpolynomial_fold *
2702 isl_pw_qpolynomial_fold_set_dim_name(
2703 __isl_take isl_pw_qpolynomial_fold *pwf,
2704 enum isl_dim_type type, unsigned pos,
2707 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2709 To iterate over all piecewise quasipolynomial reductions in a union
2710 piecewise quasipolynomial reduction, use the following function
2712 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2713 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2714 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2715 void *user), void *user);
2717 To iterate over the cells in a piecewise quasipolynomial reduction,
2718 use either of the following two functions
2720 int isl_pw_qpolynomial_fold_foreach_piece(
2721 __isl_keep isl_pw_qpolynomial_fold *pwf,
2722 int (*fn)(__isl_take isl_set *set,
2723 __isl_take isl_qpolynomial_fold *fold,
2724 void *user), void *user);
2725 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2726 __isl_keep isl_pw_qpolynomial_fold *pwf,
2727 int (*fn)(__isl_take isl_set *set,
2728 __isl_take isl_qpolynomial_fold *fold,
2729 void *user), void *user);
2731 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2732 of the difference between these two functions.
2734 To iterate over all quasipolynomials in a reduction, use
2736 int isl_qpolynomial_fold_foreach_qpolynomial(
2737 __isl_keep isl_qpolynomial_fold *fold,
2738 int (*fn)(__isl_take isl_qpolynomial *qp,
2739 void *user), void *user);
2741 =head3 Operations on Piecewise Quasipolynomial Reductions
2743 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2744 __isl_take isl_pw_qpolynomial_fold *pwf1,
2745 __isl_take isl_pw_qpolynomial_fold *pwf2);
2747 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2748 __isl_take isl_pw_qpolynomial_fold *pwf1,
2749 __isl_take isl_pw_qpolynomial_fold *pwf2);
2751 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2752 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2753 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2755 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2756 __isl_take isl_pw_qpolynomial_fold *pwf,
2757 __isl_take isl_point *pnt);
2759 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2760 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2761 __isl_take isl_point *pnt);
2763 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2764 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2765 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2766 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2767 __isl_take isl_union_set *uset);
2769 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2770 __isl_take isl_pw_qpolynomial_fold *pwf);
2772 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2773 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2775 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2776 __isl_take isl_pw_qpolynomial_fold *pwf,
2777 __isl_take isl_set *context);
2779 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2780 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2781 __isl_take isl_union_set *context);
2783 The gist operation applies the gist operation to each of
2784 the cells in the domain of the input piecewise quasipolynomial reduction.
2785 In future, the operation will also exploit the context
2786 to simplify the quasipolynomial reductions associated to each cell.
2788 __isl_give isl_pw_qpolynomial_fold *
2789 isl_set_apply_pw_qpolynomial_fold(
2790 __isl_take isl_set *set,
2791 __isl_take isl_pw_qpolynomial_fold *pwf,
2793 __isl_give isl_pw_qpolynomial_fold *
2794 isl_map_apply_pw_qpolynomial_fold(
2795 __isl_take isl_map *map,
2796 __isl_take isl_pw_qpolynomial_fold *pwf,
2798 __isl_give isl_union_pw_qpolynomial_fold *
2799 isl_union_set_apply_union_pw_qpolynomial_fold(
2800 __isl_take isl_union_set *uset,
2801 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2803 __isl_give isl_union_pw_qpolynomial_fold *
2804 isl_union_map_apply_union_pw_qpolynomial_fold(
2805 __isl_take isl_union_map *umap,
2806 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2809 The functions taking a map
2810 compose the given map with the given piecewise quasipolynomial reduction.
2811 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2812 over all elements in the intersection of the range of the map
2813 and the domain of the piecewise quasipolynomial reduction
2814 as a function of an element in the domain of the map.
2815 The functions taking a set compute a bound over all elements in the
2816 intersection of the set and the domain of the
2817 piecewise quasipolynomial reduction.
2819 =head2 Dependence Analysis
2821 C<isl> contains specialized functionality for performing
2822 array dataflow analysis. That is, given a I<sink> access relation
2823 and a collection of possible I<source> access relations,
2824 C<isl> can compute relations that describe
2825 for each iteration of the sink access, which iteration
2826 of which of the source access relations was the last
2827 to access the same data element before the given iteration
2829 To compute standard flow dependences, the sink should be
2830 a read, while the sources should be writes.
2831 If any of the source accesses are marked as being I<may>
2832 accesses, then there will be a dependence to the last
2833 I<must> access B<and> to any I<may> access that follows
2834 this last I<must> access.
2835 In particular, if I<all> sources are I<may> accesses,
2836 then memory based dependence analysis is performed.
2837 If, on the other hand, all sources are I<must> accesses,
2838 then value based dependence analysis is performed.
2840 #include <isl/flow.h>
2842 typedef int (*isl_access_level_before)(void *first, void *second);
2844 __isl_give isl_access_info *isl_access_info_alloc(
2845 __isl_take isl_map *sink,
2846 void *sink_user, isl_access_level_before fn,
2848 __isl_give isl_access_info *isl_access_info_add_source(
2849 __isl_take isl_access_info *acc,
2850 __isl_take isl_map *source, int must,
2852 void isl_access_info_free(__isl_take isl_access_info *acc);
2854 __isl_give isl_flow *isl_access_info_compute_flow(
2855 __isl_take isl_access_info *acc);
2857 int isl_flow_foreach(__isl_keep isl_flow *deps,
2858 int (*fn)(__isl_take isl_map *dep, int must,
2859 void *dep_user, void *user),
2861 __isl_give isl_map *isl_flow_get_no_source(
2862 __isl_keep isl_flow *deps, int must);
2863 void isl_flow_free(__isl_take isl_flow *deps);
2865 The function C<isl_access_info_compute_flow> performs the actual
2866 dependence analysis. The other functions are used to construct
2867 the input for this function or to read off the output.
2869 The input is collected in an C<isl_access_info>, which can
2870 be created through a call to C<isl_access_info_alloc>.
2871 The arguments to this functions are the sink access relation
2872 C<sink>, a token C<sink_user> used to identify the sink
2873 access to the user, a callback function for specifying the
2874 relative order of source and sink accesses, and the number
2875 of source access relations that will be added.
2876 The callback function has type C<int (*)(void *first, void *second)>.
2877 The function is called with two user supplied tokens identifying
2878 either a source or the sink and it should return the shared nesting
2879 level and the relative order of the two accesses.
2880 In particular, let I<n> be the number of loops shared by
2881 the two accesses. If C<first> precedes C<second> textually,
2882 then the function should return I<2 * n + 1>; otherwise,
2883 it should return I<2 * n>.
2884 The sources can be added to the C<isl_access_info> by performing
2885 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2886 C<must> indicates whether the source is a I<must> access
2887 or a I<may> access. Note that a multi-valued access relation
2888 should only be marked I<must> if every iteration in the domain
2889 of the relation accesses I<all> elements in its image.
2890 The C<source_user> token is again used to identify
2891 the source access. The range of the source access relation
2892 C<source> should have the same dimension as the range
2893 of the sink access relation.
2894 The C<isl_access_info_free> function should usually not be
2895 called explicitly, because it is called implicitly by
2896 C<isl_access_info_compute_flow>.
2898 The result of the dependence analysis is collected in an
2899 C<isl_flow>. There may be elements of
2900 the sink access for which no preceding source access could be
2901 found or for which all preceding sources are I<may> accesses.
2902 The relations containing these elements can be obtained through
2903 calls to C<isl_flow_get_no_source>, the first with C<must> set
2904 and the second with C<must> unset.
2905 In the case of standard flow dependence analysis,
2906 with the sink a read and the sources I<must> writes,
2907 the first relation corresponds to the reads from uninitialized
2908 array elements and the second relation is empty.
2909 The actual flow dependences can be extracted using
2910 C<isl_flow_foreach>. This function will call the user-specified
2911 callback function C<fn> for each B<non-empty> dependence between
2912 a source and the sink. The callback function is called
2913 with four arguments, the actual flow dependence relation
2914 mapping source iterations to sink iterations, a boolean that
2915 indicates whether it is a I<must> or I<may> dependence, a token
2916 identifying the source and an additional C<void *> with value
2917 equal to the third argument of the C<isl_flow_foreach> call.
2918 A dependence is marked I<must> if it originates from a I<must>
2919 source and if it is not followed by any I<may> sources.
2921 After finishing with an C<isl_flow>, the user should call
2922 C<isl_flow_free> to free all associated memory.
2924 A higher-level interface to dependence analysis is provided
2925 by the following function.
2927 #include <isl/flow.h>
2929 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2930 __isl_take isl_union_map *must_source,
2931 __isl_take isl_union_map *may_source,
2932 __isl_take isl_union_map *schedule,
2933 __isl_give isl_union_map **must_dep,
2934 __isl_give isl_union_map **may_dep,
2935 __isl_give isl_union_map **must_no_source,
2936 __isl_give isl_union_map **may_no_source);
2938 The arrays are identified by the tuple names of the ranges
2939 of the accesses. The iteration domains by the tuple names
2940 of the domains of the accesses and of the schedule.
2941 The relative order of the iteration domains is given by the
2942 schedule. The relations returned through C<must_no_source>
2943 and C<may_no_source> are subsets of C<sink>.
2944 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2945 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2946 any of the other arguments is treated as an error.
2950 B<The functionality described in this section is fairly new
2951 and may be subject to change.>
2953 The following function can be used to compute a schedule
2954 for a union of domains. The generated schedule respects
2955 all C<validity> dependences. That is, all dependence distances
2956 over these dependences in the scheduled space are lexicographically
2957 positive. The generated schedule schedule also tries to minimize
2958 the dependence distances over C<proximity> dependences.
2959 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2960 for groups of domains where the dependence distances have only
2961 non-negative values.
2962 The algorithm used to construct the schedule is similar to that
2965 #include <isl/schedule.h>
2966 __isl_give isl_schedule *isl_union_set_compute_schedule(
2967 __isl_take isl_union_set *domain,
2968 __isl_take isl_union_map *validity,
2969 __isl_take isl_union_map *proximity);
2970 void *isl_schedule_free(__isl_take isl_schedule *sched);
2972 A mapping from the domains to the scheduled space can be obtained
2973 from an C<isl_schedule> using the following function.
2975 __isl_give isl_union_map *isl_schedule_get_map(
2976 __isl_keep isl_schedule *sched);
2978 A representation of the schedule can be printed using
2980 __isl_give isl_printer *isl_printer_print_schedule(
2981 __isl_take isl_printer *p,
2982 __isl_keep isl_schedule *schedule);
2984 A representation of the schedule as a forest of bands can be obtained
2985 using the following function.
2987 __isl_give isl_band_list *isl_schedule_get_band_forest(
2988 __isl_keep isl_schedule *schedule);
2990 The list can be manipulated as explained in L<"Lists">.
2991 The bands inside the list can be copied and freed using the following
2994 #include <isl/band.h>
2995 __isl_give isl_band *isl_band_copy(
2996 __isl_keep isl_band *band);
2997 void *isl_band_free(__isl_take isl_band *band);
2999 Each band contains zero or more scheduling dimensions.
3000 These are referred to as the members of the band.
3001 The section of the schedule that corresponds to the band is
3002 referred to as the partial schedule of the band.
3003 For those nodes that participate in a band, the outer scheduling
3004 dimensions form the prefix schedule, while the inner scheduling
3005 dimensions form the suffix schedule.
3006 That is, if we take a cut of the band forest, then the union of
3007 the concatenations of the prefix, partial and suffix schedules of
3008 each band in the cut is equal to the entire schedule (modulo
3009 some possible padding at the end with zero scheduling dimensions).
3010 The properties of a band can be inspected using the following functions.
3012 #include <isl/band.h>
3013 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3015 int isl_band_has_children(__isl_keep isl_band *band);
3016 __isl_give isl_band_list *isl_band_get_children(
3017 __isl_keep isl_band *band);
3019 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3020 __isl_keep isl_band *band);
3021 __isl_give isl_union_map *isl_band_get_partial_schedule(
3022 __isl_keep isl_band *band);
3023 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3024 __isl_keep isl_band *band);
3026 int isl_band_n_member(__isl_keep isl_band *band);
3027 int isl_band_member_is_zero_distance(
3028 __isl_keep isl_band *band, int pos);
3030 Note that a scheduling dimension is considered to be ``zero
3031 distance'' if it does not carry any proximity dependences
3033 That is, if the dependence distances of the proximity
3034 dependences are all zero in that direction (for fixed
3035 iterations of outer bands).
3037 A representation of the band can be printed using
3039 #include <isl/band.h>
3040 __isl_give isl_printer *isl_printer_print_band(
3041 __isl_take isl_printer *p,
3042 __isl_keep isl_band *band);
3044 Alternatively, the schedule mapping
3045 can also be obtained in pieces using the following functions.
3047 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3048 __isl_give isl_union_map *isl_schedule_get_band(
3049 __isl_keep isl_schedule *sched, unsigned band);
3051 C<isl_schedule_n_band> returns the maximal number of bands.
3052 C<isl_schedule_get_band> returns a union of mappings from a domain to
3053 the band of consecutive schedule dimensions with the given sequence
3054 number for that domain. Bands with the same sequence number but for
3055 different domains may be completely unrelated.
3056 Within a band, the corresponding coordinates of the distance vectors
3057 are all non-negative, assuming that the coordinates for all previous
3060 =head2 Parametric Vertex Enumeration
3062 The parametric vertex enumeration described in this section
3063 is mainly intended to be used internally and by the C<barvinok>
3066 #include <isl/vertices.h>
3067 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3068 __isl_keep isl_basic_set *bset);
3070 The function C<isl_basic_set_compute_vertices> performs the
3071 actual computation of the parametric vertices and the chamber
3072 decomposition and store the result in an C<isl_vertices> object.
3073 This information can be queried by either iterating over all
3074 the vertices or iterating over all the chambers or cells
3075 and then iterating over all vertices that are active on the chamber.
3077 int isl_vertices_foreach_vertex(
3078 __isl_keep isl_vertices *vertices,
3079 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3082 int isl_vertices_foreach_cell(
3083 __isl_keep isl_vertices *vertices,
3084 int (*fn)(__isl_take isl_cell *cell, void *user),
3086 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3087 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3090 Other operations that can be performed on an C<isl_vertices> object are
3093 isl_ctx *isl_vertices_get_ctx(
3094 __isl_keep isl_vertices *vertices);
3095 int isl_vertices_get_n_vertices(
3096 __isl_keep isl_vertices *vertices);
3097 void isl_vertices_free(__isl_take isl_vertices *vertices);
3099 Vertices can be inspected and destroyed using the following functions.
3101 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3102 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3103 __isl_give isl_basic_set *isl_vertex_get_domain(
3104 __isl_keep isl_vertex *vertex);
3105 __isl_give isl_basic_set *isl_vertex_get_expr(
3106 __isl_keep isl_vertex *vertex);
3107 void isl_vertex_free(__isl_take isl_vertex *vertex);
3109 C<isl_vertex_get_expr> returns a singleton parametric set describing
3110 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3112 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3113 B<rational> basic sets, so they should mainly be used for inspection
3114 and should not be mixed with integer sets.
3116 Chambers can be inspected and destroyed using the following functions.
3118 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3119 __isl_give isl_basic_set *isl_cell_get_domain(
3120 __isl_keep isl_cell *cell);
3121 void isl_cell_free(__isl_take isl_cell *cell);
3125 Although C<isl> is mainly meant to be used as a library,
3126 it also contains some basic applications that use some
3127 of the functionality of C<isl>.
3128 The input may be specified in either the L<isl format>
3129 or the L<PolyLib format>.
3131 =head2 C<isl_polyhedron_sample>
3133 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3134 an integer element of the polyhedron, if there is any.
3135 The first column in the output is the denominator and is always
3136 equal to 1. If the polyhedron contains no integer points,
3137 then a vector of length zero is printed.
3141 C<isl_pip> takes the same input as the C<example> program
3142 from the C<piplib> distribution, i.e., a set of constraints
3143 on the parameters, a line containing only -1 and finally a set
3144 of constraints on a parametric polyhedron.
3145 The coefficients of the parameters appear in the last columns
3146 (but before the final constant column).
3147 The output is the lexicographic minimum of the parametric polyhedron.
3148 As C<isl> currently does not have its own output format, the output
3149 is just a dump of the internal state.
3151 =head2 C<isl_polyhedron_minimize>
3153 C<isl_polyhedron_minimize> computes the minimum of some linear
3154 or affine objective function over the integer points in a polyhedron.
3155 If an affine objective function
3156 is given, then the constant should appear in the last column.
3158 =head2 C<isl_polytope_scan>
3160 Given a polytope, C<isl_polytope_scan> prints
3161 all integer points in the polytope.