3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
477 __isl_keep isl_qpolynomial_fold *fold);
478 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
479 __isl_keep isl_pw_qpolynomial *pwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
481 __isl_keep isl_union_pw_qpolynomial *upwqp);
482 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
483 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
486 __isl_give isl_dim *isl_aff_get_dim(
487 __isl_keep isl_aff *aff);
489 #include <isl/point.h>
490 __isl_give isl_dim *isl_point_get_dim(
491 __isl_keep isl_point *pnt);
493 The names of the individual dimensions may be set or read off
494 using the following functions.
497 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
498 enum isl_dim_type type, unsigned pos,
499 __isl_keep const char *name);
500 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
501 enum isl_dim_type type, unsigned pos);
503 Note that C<isl_dim_get_name> returns a pointer to some internal
504 data structure, so the result can only be used while the
505 corresponding C<isl_dim> is alive.
506 Also note that every function that operates on two sets or relations
507 requires that both arguments have the same parameters. This also
508 means that if one of the arguments has named parameters, then the
509 other needs to have named parameters too and the names need to match.
510 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
511 have different parameters (as long as they are named), in which case
512 the result will have as parameters the union of the parameters of
515 The names of entire spaces may be set or read off
516 using the following functions.
519 __isl_give isl_dim *isl_dim_set_tuple_name(
520 __isl_take isl_dim *dim,
521 enum isl_dim_type type, const char *s);
522 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
523 enum isl_dim_type type);
525 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
526 or C<isl_dim_set>. As with C<isl_dim_get_name>,
527 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
529 Binary operations require the corresponding spaces of their arguments
530 to have the same name.
532 Spaces can be nested. In particular, the domain of a set or
533 the domain or range of a relation can be a nested relation.
534 The following functions can be used to construct and deconstruct
535 such nested dimension specifications.
538 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
539 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
540 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
542 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
543 be the dimension specification of a set, while that of
544 C<isl_dim_wrap> should be the dimension specification of a relation.
545 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
546 of a relation, while that of C<isl_dim_wrap> is the dimension specification
549 Dimension specifications can be created from other dimension
550 specifications using the following functions.
552 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
553 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
554 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
555 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
556 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
557 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
558 __isl_take isl_dim *right);
559 __isl_give isl_dim *isl_dim_align_params(
560 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
561 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
562 enum isl_dim_type type, unsigned pos, unsigned n);
563 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
564 enum isl_dim_type type, unsigned n);
565 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
566 enum isl_dim_type type, unsigned first, unsigned n);
567 __isl_give isl_dim *isl_dim_map_from_set(
568 __isl_take isl_dim *dim);
569 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
571 Note that if dimensions are added or removed from a space, then
572 the name and the internal structure are lost.
576 A local space is essentially a dimension specification with
577 zero or more existentially quantified variables.
578 The local space of a basic set or relation can be obtained
579 using the following functions.
582 __isl_give isl_local_space *isl_basic_set_get_local_space(
583 __isl_keep isl_basic_set *bset);
586 __isl_give isl_local_space *isl_basic_map_get_local_space(
587 __isl_keep isl_basic_map *bmap);
589 A new local space can be created from a dimension specification using
591 #include <isl/local_space.h>
592 __isl_give isl_local_space *isl_local_space_from_dim(
593 __isl_take isl_dim *dim);
595 They can be inspected, copied and freed using the following functions.
597 #include <isl/local_space.h>
598 isl_ctx *isl_local_space_get_ctx(
599 __isl_keep isl_local_space *ls);
600 int isl_local_space_dim(__isl_keep isl_local_space *ls,
601 enum isl_dim_type type);
602 const char *isl_local_space_get_dim_name(
603 __isl_keep isl_local_space *ls,
604 enum isl_dim_type type, unsigned pos);
605 __isl_give isl_local_space *isl_local_space_set_dim_name(
606 __isl_take isl_local_space *ls,
607 enum isl_dim_type type, unsigned pos, const char *s);
608 __isl_give isl_dim *isl_local_space_get_dim(
609 __isl_keep isl_local_space *ls);
610 __isl_give isl_div *isl_local_space_get_div(
611 __isl_keep isl_local_space *ls, int pos);
612 __isl_give isl_local_space *isl_local_space_copy(
613 __isl_keep isl_local_space *ls);
614 void *isl_local_space_free(__isl_take isl_local_space *ls);
616 Two local spaces can be compared using
618 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
619 __isl_keep isl_local_space *ls2);
621 Local spaces can be created from other local spaces
622 using the following functions.
624 __isl_give isl_local_space *isl_local_space_from_domain(
625 __isl_take isl_local_space *ls);
626 __isl_give isl_local_space *isl_local_space_add_dim(
627 __isl_take isl_local_space *ls,
628 enum isl_dim_type type, unsigned n);
630 =head2 Input and Output
632 C<isl> supports its own input/output format, which is similar
633 to the C<Omega> format, but also supports the C<PolyLib> format
638 The C<isl> format is similar to that of C<Omega>, but has a different
639 syntax for describing the parameters and allows for the definition
640 of an existentially quantified variable as the integer division
641 of an affine expression.
642 For example, the set of integers C<i> between C<0> and C<n>
643 such that C<i % 10 <= 6> can be described as
645 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
648 A set or relation can have several disjuncts, separated
649 by the keyword C<or>. Each disjunct is either a conjunction
650 of constraints or a projection (C<exists>) of a conjunction
651 of constraints. The constraints are separated by the keyword
654 =head3 C<PolyLib> format
656 If the represented set is a union, then the first line
657 contains a single number representing the number of disjuncts.
658 Otherwise, a line containing the number C<1> is optional.
660 Each disjunct is represented by a matrix of constraints.
661 The first line contains two numbers representing
662 the number of rows and columns,
663 where the number of rows is equal to the number of constraints
664 and the number of columns is equal to two plus the number of variables.
665 The following lines contain the actual rows of the constraint matrix.
666 In each row, the first column indicates whether the constraint
667 is an equality (C<0>) or inequality (C<1>). The final column
668 corresponds to the constant term.
670 If the set is parametric, then the coefficients of the parameters
671 appear in the last columns before the constant column.
672 The coefficients of any existentially quantified variables appear
673 between those of the set variables and those of the parameters.
675 =head3 Extended C<PolyLib> format
677 The extended C<PolyLib> format is nearly identical to the
678 C<PolyLib> format. The only difference is that the line
679 containing the number of rows and columns of a constraint matrix
680 also contains four additional numbers:
681 the number of output dimensions, the number of input dimensions,
682 the number of local dimensions (i.e., the number of existentially
683 quantified variables) and the number of parameters.
684 For sets, the number of ``output'' dimensions is equal
685 to the number of set dimensions, while the number of ``input''
691 __isl_give isl_basic_set *isl_basic_set_read_from_file(
692 isl_ctx *ctx, FILE *input, int nparam);
693 __isl_give isl_basic_set *isl_basic_set_read_from_str(
694 isl_ctx *ctx, const char *str, int nparam);
695 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
696 FILE *input, int nparam);
697 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
698 const char *str, int nparam);
701 __isl_give isl_basic_map *isl_basic_map_read_from_file(
702 isl_ctx *ctx, FILE *input, int nparam);
703 __isl_give isl_basic_map *isl_basic_map_read_from_str(
704 isl_ctx *ctx, const char *str, int nparam);
705 __isl_give isl_map *isl_map_read_from_file(
706 struct isl_ctx *ctx, FILE *input, int nparam);
707 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
708 const char *str, int nparam);
710 #include <isl/union_set.h>
711 __isl_give isl_union_set *isl_union_set_read_from_file(
712 isl_ctx *ctx, FILE *input);
713 __isl_give isl_union_set *isl_union_set_read_from_str(
714 struct isl_ctx *ctx, const char *str);
716 #include <isl/union_map.h>
717 __isl_give isl_union_map *isl_union_map_read_from_file(
718 isl_ctx *ctx, FILE *input);
719 __isl_give isl_union_map *isl_union_map_read_from_str(
720 struct isl_ctx *ctx, const char *str);
722 The input format is autodetected and may be either the C<PolyLib> format
723 or the C<isl> format.
724 C<nparam> specifies how many of the final columns in
725 the C<PolyLib> format correspond to parameters.
726 If input is given in the C<isl> format, then the number
727 of parameters needs to be equal to C<nparam>.
728 If C<nparam> is negative, then any number of parameters
729 is accepted in the C<isl> format and zero parameters
730 are assumed in the C<PolyLib> format.
734 Before anything can be printed, an C<isl_printer> needs to
737 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
739 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
740 void isl_printer_free(__isl_take isl_printer *printer);
741 __isl_give char *isl_printer_get_str(
742 __isl_keep isl_printer *printer);
744 The behavior of the printer can be modified in various ways
746 __isl_give isl_printer *isl_printer_set_output_format(
747 __isl_take isl_printer *p, int output_format);
748 __isl_give isl_printer *isl_printer_set_indent(
749 __isl_take isl_printer *p, int indent);
750 __isl_give isl_printer *isl_printer_indent(
751 __isl_take isl_printer *p, int indent);
752 __isl_give isl_printer *isl_printer_set_prefix(
753 __isl_take isl_printer *p, const char *prefix);
754 __isl_give isl_printer *isl_printer_set_suffix(
755 __isl_take isl_printer *p, const char *suffix);
757 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
758 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
759 and defaults to C<ISL_FORMAT_ISL>.
760 Each line in the output is indented by C<indent> (set by
761 C<isl_printer_set_indent>) spaces
762 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
763 In the C<PolyLib> format output,
764 the coefficients of the existentially quantified variables
765 appear between those of the set variables and those
767 The function C<isl_printer_indent> increases the indentation
768 by the specified amount (which may be negative).
770 To actually print something, use
773 __isl_give isl_printer *isl_printer_print_basic_set(
774 __isl_take isl_printer *printer,
775 __isl_keep isl_basic_set *bset);
776 __isl_give isl_printer *isl_printer_print_set(
777 __isl_take isl_printer *printer,
778 __isl_keep isl_set *set);
781 __isl_give isl_printer *isl_printer_print_basic_map(
782 __isl_take isl_printer *printer,
783 __isl_keep isl_basic_map *bmap);
784 __isl_give isl_printer *isl_printer_print_map(
785 __isl_take isl_printer *printer,
786 __isl_keep isl_map *map);
788 #include <isl/union_set.h>
789 __isl_give isl_printer *isl_printer_print_union_set(
790 __isl_take isl_printer *p,
791 __isl_keep isl_union_set *uset);
793 #include <isl/union_map.h>
794 __isl_give isl_printer *isl_printer_print_union_map(
795 __isl_take isl_printer *p,
796 __isl_keep isl_union_map *umap);
798 When called on a file printer, the following function flushes
799 the file. When called on a string printer, the buffer is cleared.
801 __isl_give isl_printer *isl_printer_flush(
802 __isl_take isl_printer *p);
804 =head2 Creating New Sets and Relations
806 C<isl> has functions for creating some standard sets and relations.
810 =item * Empty sets and relations
812 __isl_give isl_basic_set *isl_basic_set_empty(
813 __isl_take isl_dim *dim);
814 __isl_give isl_basic_map *isl_basic_map_empty(
815 __isl_take isl_dim *dim);
816 __isl_give isl_set *isl_set_empty(
817 __isl_take isl_dim *dim);
818 __isl_give isl_map *isl_map_empty(
819 __isl_take isl_dim *dim);
820 __isl_give isl_union_set *isl_union_set_empty(
821 __isl_take isl_dim *dim);
822 __isl_give isl_union_map *isl_union_map_empty(
823 __isl_take isl_dim *dim);
825 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
826 is only used to specify the parameters.
828 =item * Universe sets and relations
830 __isl_give isl_basic_set *isl_basic_set_universe(
831 __isl_take isl_dim *dim);
832 __isl_give isl_basic_map *isl_basic_map_universe(
833 __isl_take isl_dim *dim);
834 __isl_give isl_set *isl_set_universe(
835 __isl_take isl_dim *dim);
836 __isl_give isl_map *isl_map_universe(
837 __isl_take isl_dim *dim);
838 __isl_give isl_union_set *isl_union_set_universe(
839 __isl_take isl_union_set *uset);
840 __isl_give isl_union_map *isl_union_map_universe(
841 __isl_take isl_union_map *umap);
843 The sets and relations constructed by the functions above
844 contain all integer values, while those constructed by the
845 functions below only contain non-negative values.
847 __isl_give isl_basic_set *isl_basic_set_nat_universe(
848 __isl_take isl_dim *dim);
849 __isl_give isl_basic_map *isl_basic_map_nat_universe(
850 __isl_take isl_dim *dim);
851 __isl_give isl_set *isl_set_nat_universe(
852 __isl_take isl_dim *dim);
853 __isl_give isl_map *isl_map_nat_universe(
854 __isl_take isl_dim *dim);
856 =item * Identity relations
858 __isl_give isl_basic_map *isl_basic_map_identity(
859 __isl_take isl_dim *dim);
860 __isl_give isl_map *isl_map_identity(
861 __isl_take isl_dim *dim);
863 The number of input and output dimensions in C<dim> needs
866 =item * Lexicographic order
868 __isl_give isl_map *isl_map_lex_lt(
869 __isl_take isl_dim *set_dim);
870 __isl_give isl_map *isl_map_lex_le(
871 __isl_take isl_dim *set_dim);
872 __isl_give isl_map *isl_map_lex_gt(
873 __isl_take isl_dim *set_dim);
874 __isl_give isl_map *isl_map_lex_ge(
875 __isl_take isl_dim *set_dim);
876 __isl_give isl_map *isl_map_lex_lt_first(
877 __isl_take isl_dim *dim, unsigned n);
878 __isl_give isl_map *isl_map_lex_le_first(
879 __isl_take isl_dim *dim, unsigned n);
880 __isl_give isl_map *isl_map_lex_gt_first(
881 __isl_take isl_dim *dim, unsigned n);
882 __isl_give isl_map *isl_map_lex_ge_first(
883 __isl_take isl_dim *dim, unsigned n);
885 The first four functions take a dimension specification for a B<set>
886 and return relations that express that the elements in the domain
887 are lexicographically less
888 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
889 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
890 than the elements in the range.
891 The last four functions take a dimension specification for a map
892 and return relations that express that the first C<n> dimensions
893 in the domain are lexicographically less
894 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
895 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
896 than the first C<n> dimensions in the range.
900 A basic set or relation can be converted to a set or relation
901 using the following functions.
903 __isl_give isl_set *isl_set_from_basic_set(
904 __isl_take isl_basic_set *bset);
905 __isl_give isl_map *isl_map_from_basic_map(
906 __isl_take isl_basic_map *bmap);
908 Sets and relations can be converted to union sets and relations
909 using the following functions.
911 __isl_give isl_union_map *isl_union_map_from_map(
912 __isl_take isl_map *map);
913 __isl_give isl_union_set *isl_union_set_from_set(
914 __isl_take isl_set *set);
916 Sets and relations can be copied and freed again using the following
919 __isl_give isl_basic_set *isl_basic_set_copy(
920 __isl_keep isl_basic_set *bset);
921 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
922 __isl_give isl_union_set *isl_union_set_copy(
923 __isl_keep isl_union_set *uset);
924 __isl_give isl_basic_map *isl_basic_map_copy(
925 __isl_keep isl_basic_map *bmap);
926 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
927 __isl_give isl_union_map *isl_union_map_copy(
928 __isl_keep isl_union_map *umap);
929 void isl_basic_set_free(__isl_take isl_basic_set *bset);
930 void isl_set_free(__isl_take isl_set *set);
931 void isl_union_set_free(__isl_take isl_union_set *uset);
932 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
933 void isl_map_free(__isl_take isl_map *map);
934 void isl_union_map_free(__isl_take isl_union_map *umap);
936 Other sets and relations can be constructed by starting
937 from a universe set or relation, adding equality and/or
938 inequality constraints and then projecting out the
939 existentially quantified variables, if any.
940 Constraints can be constructed, manipulated and
941 added to (basic) sets and relations using the following functions.
943 #include <isl/constraint.h>
944 __isl_give isl_constraint *isl_equality_alloc(
945 __isl_take isl_dim *dim);
946 __isl_give isl_constraint *isl_inequality_alloc(
947 __isl_take isl_dim *dim);
948 void isl_constraint_set_constant(
949 __isl_keep isl_constraint *constraint, isl_int v);
950 void isl_constraint_set_coefficient(
951 __isl_keep isl_constraint *constraint,
952 enum isl_dim_type type, int pos, isl_int v);
953 __isl_give isl_basic_map *isl_basic_map_add_constraint(
954 __isl_take isl_basic_map *bmap,
955 __isl_take isl_constraint *constraint);
956 __isl_give isl_basic_set *isl_basic_set_add_constraint(
957 __isl_take isl_basic_set *bset,
958 __isl_take isl_constraint *constraint);
959 __isl_give isl_map *isl_map_add_constraint(
960 __isl_take isl_map *map,
961 __isl_take isl_constraint *constraint);
962 __isl_give isl_set *isl_set_add_constraint(
963 __isl_take isl_set *set,
964 __isl_take isl_constraint *constraint);
966 For example, to create a set containing the even integers
967 between 10 and 42, you would use the following code.
971 struct isl_constraint *c;
972 struct isl_basic_set *bset;
975 dim = isl_dim_set_alloc(ctx, 0, 2);
976 bset = isl_basic_set_universe(isl_dim_copy(dim));
978 c = isl_equality_alloc(isl_dim_copy(dim));
979 isl_int_set_si(v, -1);
980 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
981 isl_int_set_si(v, 2);
982 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
983 bset = isl_basic_set_add_constraint(bset, c);
985 c = isl_inequality_alloc(isl_dim_copy(dim));
986 isl_int_set_si(v, -10);
987 isl_constraint_set_constant(c, v);
988 isl_int_set_si(v, 1);
989 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
990 bset = isl_basic_set_add_constraint(bset, c);
992 c = isl_inequality_alloc(dim);
993 isl_int_set_si(v, 42);
994 isl_constraint_set_constant(c, v);
995 isl_int_set_si(v, -1);
996 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
997 bset = isl_basic_set_add_constraint(bset, c);
999 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1005 struct isl_basic_set *bset;
1006 bset = isl_basic_set_read_from_str(ctx,
1007 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1009 A basic set or relation can also be constructed from two matrices
1010 describing the equalities and the inequalities.
1012 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1013 __isl_take isl_dim *dim,
1014 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1015 enum isl_dim_type c1,
1016 enum isl_dim_type c2, enum isl_dim_type c3,
1017 enum isl_dim_type c4);
1018 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1019 __isl_take isl_dim *dim,
1020 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1021 enum isl_dim_type c1,
1022 enum isl_dim_type c2, enum isl_dim_type c3,
1023 enum isl_dim_type c4, enum isl_dim_type c5);
1025 The C<isl_dim_type> arguments indicate the order in which
1026 different kinds of variables appear in the input matrices
1027 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1028 C<isl_dim_set> and C<isl_dim_div> for sets and
1029 of C<isl_dim_cst>, C<isl_dim_param>,
1030 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1032 A (basic) relation can also be constructed from a (piecewise) affine expression
1033 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1035 __isl_give isl_basic_map *isl_basic_map_from_aff(
1036 __isl_take isl_aff *aff);
1037 __isl_give isl_map *isl_map_from_pw_aff(
1038 __isl_take isl_pw_aff *pwaff);
1039 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1040 __isl_take isl_dim *domain_dim,
1041 __isl_take isl_aff_list *list);
1043 The C<domain_dim> argument describes the domain of the resulting
1044 basic relation. It is required because the C<list> may consist
1045 of zero affine expressions.
1047 =head2 Inspecting Sets and Relations
1049 Usually, the user should not have to care about the actual constraints
1050 of the sets and maps, but should instead apply the abstract operations
1051 explained in the following sections.
1052 Occasionally, however, it may be required to inspect the individual
1053 coefficients of the constraints. This section explains how to do so.
1054 In these cases, it may also be useful to have C<isl> compute
1055 an explicit representation of the existentially quantified variables.
1057 __isl_give isl_set *isl_set_compute_divs(
1058 __isl_take isl_set *set);
1059 __isl_give isl_map *isl_map_compute_divs(
1060 __isl_take isl_map *map);
1061 __isl_give isl_union_set *isl_union_set_compute_divs(
1062 __isl_take isl_union_set *uset);
1063 __isl_give isl_union_map *isl_union_map_compute_divs(
1064 __isl_take isl_union_map *umap);
1066 This explicit representation defines the existentially quantified
1067 variables as integer divisions of the other variables, possibly
1068 including earlier existentially quantified variables.
1069 An explicitly represented existentially quantified variable therefore
1070 has a unique value when the values of the other variables are known.
1071 If, furthermore, the same existentials, i.e., existentials
1072 with the same explicit representations, should appear in the
1073 same order in each of the disjuncts of a set or map, then the user should call
1074 either of the following functions.
1076 __isl_give isl_set *isl_set_align_divs(
1077 __isl_take isl_set *set);
1078 __isl_give isl_map *isl_map_align_divs(
1079 __isl_take isl_map *map);
1081 Alternatively, the existentially quantified variables can be removed
1082 using the following functions, which compute an overapproximation.
1084 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1085 __isl_take isl_basic_set *bset);
1086 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1087 __isl_take isl_basic_map *bmap);
1088 __isl_give isl_set *isl_set_remove_divs(
1089 __isl_take isl_set *set);
1090 __isl_give isl_map *isl_map_remove_divs(
1091 __isl_take isl_map *map);
1093 To iterate over all the sets or maps in a union set or map, use
1095 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1096 int (*fn)(__isl_take isl_set *set, void *user),
1098 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1099 int (*fn)(__isl_take isl_map *map, void *user),
1102 The number of sets or maps in a union set or map can be obtained
1105 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1106 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1108 To extract the set or map from a union with a given dimension
1111 __isl_give isl_set *isl_union_set_extract_set(
1112 __isl_keep isl_union_set *uset,
1113 __isl_take isl_dim *dim);
1114 __isl_give isl_map *isl_union_map_extract_map(
1115 __isl_keep isl_union_map *umap,
1116 __isl_take isl_dim *dim);
1118 To iterate over all the basic sets or maps in a set or map, use
1120 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1121 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1123 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1124 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1127 The callback function C<fn> should return 0 if successful and
1128 -1 if an error occurs. In the latter case, or if any other error
1129 occurs, the above functions will return -1.
1131 It should be noted that C<isl> does not guarantee that
1132 the basic sets or maps passed to C<fn> are disjoint.
1133 If this is required, then the user should call one of
1134 the following functions first.
1136 __isl_give isl_set *isl_set_make_disjoint(
1137 __isl_take isl_set *set);
1138 __isl_give isl_map *isl_map_make_disjoint(
1139 __isl_take isl_map *map);
1141 The number of basic sets in a set can be obtained
1144 int isl_set_n_basic_set(__isl_keep isl_set *set);
1146 To iterate over the constraints of a basic set or map, use
1148 #include <isl/constraint.h>
1150 int isl_basic_map_foreach_constraint(
1151 __isl_keep isl_basic_map *bmap,
1152 int (*fn)(__isl_take isl_constraint *c, void *user),
1154 void isl_constraint_free(struct isl_constraint *c);
1156 Again, the callback function C<fn> should return 0 if successful and
1157 -1 if an error occurs. In the latter case, or if any other error
1158 occurs, the above functions will return -1.
1159 The constraint C<c> represents either an equality or an inequality.
1160 Use the following function to find out whether a constraint
1161 represents an equality. If not, it represents an inequality.
1163 int isl_constraint_is_equality(
1164 __isl_keep isl_constraint *constraint);
1166 The coefficients of the constraints can be inspected using
1167 the following functions.
1169 void isl_constraint_get_constant(
1170 __isl_keep isl_constraint *constraint, isl_int *v);
1171 void isl_constraint_get_coefficient(
1172 __isl_keep isl_constraint *constraint,
1173 enum isl_dim_type type, int pos, isl_int *v);
1174 int isl_constraint_involves_dims(
1175 __isl_keep isl_constraint *constraint,
1176 enum isl_dim_type type, unsigned first, unsigned n);
1178 The explicit representations of the existentially quantified
1179 variables can be inspected using the following functions.
1180 Note that the user is only allowed to use these functions
1181 if the inspected set or map is the result of a call
1182 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1184 __isl_give isl_div *isl_constraint_div(
1185 __isl_keep isl_constraint *constraint, int pos);
1186 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1187 void isl_div_get_constant(__isl_keep isl_div *div,
1189 void isl_div_get_denominator(__isl_keep isl_div *div,
1191 void isl_div_get_coefficient(__isl_keep isl_div *div,
1192 enum isl_dim_type type, int pos, isl_int *v);
1194 To obtain the constraints of a basic set or map in matrix
1195 form, use the following functions.
1197 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1198 __isl_keep isl_basic_set *bset,
1199 enum isl_dim_type c1, enum isl_dim_type c2,
1200 enum isl_dim_type c3, enum isl_dim_type c4);
1201 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1202 __isl_keep isl_basic_set *bset,
1203 enum isl_dim_type c1, enum isl_dim_type c2,
1204 enum isl_dim_type c3, enum isl_dim_type c4);
1205 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1206 __isl_keep isl_basic_map *bmap,
1207 enum isl_dim_type c1,
1208 enum isl_dim_type c2, enum isl_dim_type c3,
1209 enum isl_dim_type c4, enum isl_dim_type c5);
1210 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1211 __isl_keep isl_basic_map *bmap,
1212 enum isl_dim_type c1,
1213 enum isl_dim_type c2, enum isl_dim_type c3,
1214 enum isl_dim_type c4, enum isl_dim_type c5);
1216 The C<isl_dim_type> arguments dictate the order in which
1217 different kinds of variables appear in the resulting matrix
1218 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1219 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1221 The names of the domain and range spaces of a set or relation can be
1222 read off using the following functions.
1224 const char *isl_basic_set_get_tuple_name(
1225 __isl_keep isl_basic_set *bset);
1226 const char *isl_set_get_tuple_name(
1227 __isl_keep isl_set *set);
1228 const char *isl_basic_map_get_tuple_name(
1229 __isl_keep isl_basic_map *bmap,
1230 enum isl_dim_type type);
1231 const char *isl_map_get_tuple_name(
1232 __isl_keep isl_map *map,
1233 enum isl_dim_type type);
1235 As with C<isl_dim_get_tuple_name>, the value returned points to
1236 an internal data structure.
1237 The names of individual dimensions can be read off using
1238 the following functions.
1240 const char *isl_constraint_get_dim_name(
1241 __isl_keep isl_constraint *constraint,
1242 enum isl_dim_type type, unsigned pos);
1243 const char *isl_basic_set_get_dim_name(
1244 __isl_keep isl_basic_set *bset,
1245 enum isl_dim_type type, unsigned pos);
1246 const char *isl_set_get_dim_name(
1247 __isl_keep isl_set *set,
1248 enum isl_dim_type type, unsigned pos);
1249 const char *isl_basic_map_get_dim_name(
1250 __isl_keep isl_basic_map *bmap,
1251 enum isl_dim_type type, unsigned pos);
1252 const char *isl_map_get_dim_name(
1253 __isl_keep isl_map *map,
1254 enum isl_dim_type type, unsigned pos);
1256 These functions are mostly useful to obtain the names
1261 =head3 Unary Properties
1267 The following functions test whether the given set or relation
1268 contains any integer points. The ``plain'' variants do not perform
1269 any computations, but simply check if the given set or relation
1270 is already known to be empty.
1272 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1273 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1274 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1275 int isl_set_is_empty(__isl_keep isl_set *set);
1276 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1277 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1278 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1279 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1280 int isl_map_is_empty(__isl_keep isl_map *map);
1281 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1283 =item * Universality
1285 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1286 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1287 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1289 =item * Single-valuedness
1291 int isl_map_is_single_valued(__isl_keep isl_map *map);
1292 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1296 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1297 int isl_map_is_injective(__isl_keep isl_map *map);
1298 int isl_union_map_plain_is_injective(
1299 __isl_keep isl_union_map *umap);
1300 int isl_union_map_is_injective(
1301 __isl_keep isl_union_map *umap);
1305 int isl_map_is_bijective(__isl_keep isl_map *map);
1306 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1310 The following functions check whether the domain of the given
1311 (basic) set is a wrapped relation.
1313 int isl_basic_set_is_wrapping(
1314 __isl_keep isl_basic_set *bset);
1315 int isl_set_is_wrapping(__isl_keep isl_set *set);
1317 =item * Internal Product
1319 int isl_basic_map_can_zip(
1320 __isl_keep isl_basic_map *bmap);
1321 int isl_map_can_zip(__isl_keep isl_map *map);
1323 Check whether the product of domain and range of the given relation
1325 i.e., whether both domain and range are nested relations.
1329 =head3 Binary Properties
1335 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1336 __isl_keep isl_set *set2);
1337 int isl_set_is_equal(__isl_keep isl_set *set1,
1338 __isl_keep isl_set *set2);
1339 int isl_union_set_is_equal(
1340 __isl_keep isl_union_set *uset1,
1341 __isl_keep isl_union_set *uset2);
1342 int isl_basic_map_is_equal(
1343 __isl_keep isl_basic_map *bmap1,
1344 __isl_keep isl_basic_map *bmap2);
1345 int isl_map_is_equal(__isl_keep isl_map *map1,
1346 __isl_keep isl_map *map2);
1347 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1348 __isl_keep isl_map *map2);
1349 int isl_union_map_is_equal(
1350 __isl_keep isl_union_map *umap1,
1351 __isl_keep isl_union_map *umap2);
1353 =item * Disjointness
1355 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1356 __isl_keep isl_set *set2);
1360 int isl_set_is_subset(__isl_keep isl_set *set1,
1361 __isl_keep isl_set *set2);
1362 int isl_set_is_strict_subset(
1363 __isl_keep isl_set *set1,
1364 __isl_keep isl_set *set2);
1365 int isl_union_set_is_subset(
1366 __isl_keep isl_union_set *uset1,
1367 __isl_keep isl_union_set *uset2);
1368 int isl_union_set_is_strict_subset(
1369 __isl_keep isl_union_set *uset1,
1370 __isl_keep isl_union_set *uset2);
1371 int isl_basic_map_is_subset(
1372 __isl_keep isl_basic_map *bmap1,
1373 __isl_keep isl_basic_map *bmap2);
1374 int isl_basic_map_is_strict_subset(
1375 __isl_keep isl_basic_map *bmap1,
1376 __isl_keep isl_basic_map *bmap2);
1377 int isl_map_is_subset(
1378 __isl_keep isl_map *map1,
1379 __isl_keep isl_map *map2);
1380 int isl_map_is_strict_subset(
1381 __isl_keep isl_map *map1,
1382 __isl_keep isl_map *map2);
1383 int isl_union_map_is_subset(
1384 __isl_keep isl_union_map *umap1,
1385 __isl_keep isl_union_map *umap2);
1386 int isl_union_map_is_strict_subset(
1387 __isl_keep isl_union_map *umap1,
1388 __isl_keep isl_union_map *umap2);
1392 =head2 Unary Operations
1398 __isl_give isl_set *isl_set_complement(
1399 __isl_take isl_set *set);
1403 __isl_give isl_basic_map *isl_basic_map_reverse(
1404 __isl_take isl_basic_map *bmap);
1405 __isl_give isl_map *isl_map_reverse(
1406 __isl_take isl_map *map);
1407 __isl_give isl_union_map *isl_union_map_reverse(
1408 __isl_take isl_union_map *umap);
1412 __isl_give isl_basic_set *isl_basic_set_project_out(
1413 __isl_take isl_basic_set *bset,
1414 enum isl_dim_type type, unsigned first, unsigned n);
1415 __isl_give isl_basic_map *isl_basic_map_project_out(
1416 __isl_take isl_basic_map *bmap,
1417 enum isl_dim_type type, unsigned first, unsigned n);
1418 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1419 enum isl_dim_type type, unsigned first, unsigned n);
1420 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1421 enum isl_dim_type type, unsigned first, unsigned n);
1422 __isl_give isl_basic_set *isl_basic_map_domain(
1423 __isl_take isl_basic_map *bmap);
1424 __isl_give isl_basic_set *isl_basic_map_range(
1425 __isl_take isl_basic_map *bmap);
1426 __isl_give isl_set *isl_map_domain(
1427 __isl_take isl_map *bmap);
1428 __isl_give isl_set *isl_map_range(
1429 __isl_take isl_map *map);
1430 __isl_give isl_union_set *isl_union_map_domain(
1431 __isl_take isl_union_map *umap);
1432 __isl_give isl_union_set *isl_union_map_range(
1433 __isl_take isl_union_map *umap);
1435 __isl_give isl_basic_map *isl_basic_map_domain_map(
1436 __isl_take isl_basic_map *bmap);
1437 __isl_give isl_basic_map *isl_basic_map_range_map(
1438 __isl_take isl_basic_map *bmap);
1439 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1440 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1441 __isl_give isl_union_map *isl_union_map_domain_map(
1442 __isl_take isl_union_map *umap);
1443 __isl_give isl_union_map *isl_union_map_range_map(
1444 __isl_take isl_union_map *umap);
1446 The functions above construct a (basic, regular or union) relation
1447 that maps (a wrapped version of) the input relation to its domain or range.
1451 __isl_give isl_set *isl_set_eliminate(
1452 __isl_take isl_set *set, enum isl_dim_type type,
1453 unsigned first, unsigned n);
1455 Eliminate the coefficients for the given dimensions from the constraints,
1456 without removing the dimensions.
1460 __isl_give isl_basic_set *isl_basic_set_fix(
1461 __isl_take isl_basic_set *bset,
1462 enum isl_dim_type type, unsigned pos,
1464 __isl_give isl_basic_set *isl_basic_set_fix_si(
1465 __isl_take isl_basic_set *bset,
1466 enum isl_dim_type type, unsigned pos, int value);
1467 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1468 enum isl_dim_type type, unsigned pos,
1470 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1471 enum isl_dim_type type, unsigned pos, int value);
1472 __isl_give isl_basic_map *isl_basic_map_fix_si(
1473 __isl_take isl_basic_map *bmap,
1474 enum isl_dim_type type, unsigned pos, int value);
1475 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1476 enum isl_dim_type type, unsigned pos, int value);
1478 Intersect the set or relation with the hyperplane where the given
1479 dimension has the fixed given value.
1483 __isl_give isl_map *isl_set_identity(
1484 __isl_take isl_set *set);
1485 __isl_give isl_union_map *isl_union_set_identity(
1486 __isl_take isl_union_set *uset);
1488 Construct an identity relation on the given (union) set.
1492 __isl_give isl_basic_set *isl_basic_map_deltas(
1493 __isl_take isl_basic_map *bmap);
1494 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1495 __isl_give isl_union_set *isl_union_map_deltas(
1496 __isl_take isl_union_map *umap);
1498 These functions return a (basic) set containing the differences
1499 between image elements and corresponding domain elements in the input.
1501 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1502 __isl_take isl_basic_map *bmap);
1503 __isl_give isl_map *isl_map_deltas_map(
1504 __isl_take isl_map *map);
1505 __isl_give isl_union_map *isl_union_map_deltas_map(
1506 __isl_take isl_union_map *umap);
1508 The functions above construct a (basic, regular or union) relation
1509 that maps (a wrapped version of) the input relation to its delta set.
1513 Simplify the representation of a set or relation by trying
1514 to combine pairs of basic sets or relations into a single
1515 basic set or relation.
1517 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1518 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1519 __isl_give isl_union_set *isl_union_set_coalesce(
1520 __isl_take isl_union_set *uset);
1521 __isl_give isl_union_map *isl_union_map_coalesce(
1522 __isl_take isl_union_map *umap);
1524 =item * Detecting equalities
1526 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1527 __isl_take isl_basic_set *bset);
1528 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1529 __isl_take isl_basic_map *bmap);
1530 __isl_give isl_set *isl_set_detect_equalities(
1531 __isl_take isl_set *set);
1532 __isl_give isl_map *isl_map_detect_equalities(
1533 __isl_take isl_map *map);
1534 __isl_give isl_union_set *isl_union_set_detect_equalities(
1535 __isl_take isl_union_set *uset);
1536 __isl_give isl_union_map *isl_union_map_detect_equalities(
1537 __isl_take isl_union_map *umap);
1539 Simplify the representation of a set or relation by detecting implicit
1542 =item * Removing redundant constraints
1544 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1545 __isl_take isl_basic_set *bset);
1546 __isl_give isl_set *isl_set_remove_redundancies(
1547 __isl_take isl_set *set);
1548 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1549 __isl_take isl_basic_map *bmap);
1550 __isl_give isl_map *isl_map_remove_redundancies(
1551 __isl_take isl_map *map);
1555 __isl_give isl_basic_set *isl_set_convex_hull(
1556 __isl_take isl_set *set);
1557 __isl_give isl_basic_map *isl_map_convex_hull(
1558 __isl_take isl_map *map);
1560 If the input set or relation has any existentially quantified
1561 variables, then the result of these operations is currently undefined.
1565 __isl_give isl_basic_set *isl_set_simple_hull(
1566 __isl_take isl_set *set);
1567 __isl_give isl_basic_map *isl_map_simple_hull(
1568 __isl_take isl_map *map);
1569 __isl_give isl_union_map *isl_union_map_simple_hull(
1570 __isl_take isl_union_map *umap);
1572 These functions compute a single basic set or relation
1573 that contains the whole input set or relation.
1574 In particular, the output is described by translates
1575 of the constraints describing the basic sets or relations in the input.
1579 (See \autoref{s:simple hull}.)
1585 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1586 __isl_take isl_basic_set *bset);
1587 __isl_give isl_basic_set *isl_set_affine_hull(
1588 __isl_take isl_set *set);
1589 __isl_give isl_union_set *isl_union_set_affine_hull(
1590 __isl_take isl_union_set *uset);
1591 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1592 __isl_take isl_basic_map *bmap);
1593 __isl_give isl_basic_map *isl_map_affine_hull(
1594 __isl_take isl_map *map);
1595 __isl_give isl_union_map *isl_union_map_affine_hull(
1596 __isl_take isl_union_map *umap);
1598 In case of union sets and relations, the affine hull is computed
1601 =item * Polyhedral hull
1603 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1604 __isl_take isl_set *set);
1605 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1606 __isl_take isl_map *map);
1607 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1608 __isl_take isl_union_set *uset);
1609 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1610 __isl_take isl_union_map *umap);
1612 These functions compute a single basic set or relation
1613 not involving any existentially quantified variables
1614 that contains the whole input set or relation.
1615 In case of union sets and relations, the polyhedral hull is computed
1618 =item * Optimization
1620 #include <isl/ilp.h>
1621 enum isl_lp_result isl_basic_set_max(
1622 __isl_keep isl_basic_set *bset,
1623 __isl_keep isl_aff *obj, isl_int *opt)
1624 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1625 __isl_keep isl_aff *obj, isl_int *opt);
1627 Compute the maximum of the integer affine expression C<obj>
1628 over the points in C<set>, returning the result in C<opt>.
1629 The return value may be one of C<isl_lp_error>,
1630 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1632 =item * Parametric optimization
1634 __isl_give isl_pw_aff *isl_set_dim_max(
1635 __isl_take isl_set *set, int pos);
1637 Compute the maximum of the given set dimension as a function of the
1638 parameters, but independently of the other set dimensions.
1639 For lexicographic optimization, see L<"Lexicographic Optimization">.
1643 The following functions compute either the set of (rational) coefficient
1644 values of valid constraints for the given set or the set of (rational)
1645 values satisfying the constraints with coefficients from the given set.
1646 Internally, these two sets of functions perform essentially the
1647 same operations, except that the set of coefficients is assumed to
1648 be a cone, while the set of values may be any polyhedron.
1649 The current implementation is based on the Farkas lemma and
1650 Fourier-Motzkin elimination, but this may change or be made optional
1651 in future. In particular, future implementations may use different
1652 dualization algorithms or skip the elimination step.
1654 __isl_give isl_basic_set *isl_basic_set_coefficients(
1655 __isl_take isl_basic_set *bset);
1656 __isl_give isl_basic_set *isl_set_coefficients(
1657 __isl_take isl_set *set);
1658 __isl_give isl_union_set *isl_union_set_coefficients(
1659 __isl_take isl_union_set *bset);
1660 __isl_give isl_basic_set *isl_basic_set_solutions(
1661 __isl_take isl_basic_set *bset);
1662 __isl_give isl_basic_set *isl_set_solutions(
1663 __isl_take isl_set *set);
1664 __isl_give isl_union_set *isl_union_set_solutions(
1665 __isl_take isl_union_set *bset);
1669 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1671 __isl_give isl_union_map *isl_union_map_power(
1672 __isl_take isl_union_map *umap, int *exact);
1674 Compute a parametric representation for all positive powers I<k> of C<map>.
1675 The result maps I<k> to a nested relation corresponding to the
1676 I<k>th power of C<map>.
1677 The result may be an overapproximation. If the result is known to be exact,
1678 then C<*exact> is set to C<1>.
1680 =item * Transitive closure
1682 __isl_give isl_map *isl_map_transitive_closure(
1683 __isl_take isl_map *map, int *exact);
1684 __isl_give isl_union_map *isl_union_map_transitive_closure(
1685 __isl_take isl_union_map *umap, int *exact);
1687 Compute the transitive closure of C<map>.
1688 The result may be an overapproximation. If the result is known to be exact,
1689 then C<*exact> is set to C<1>.
1691 =item * Reaching path lengths
1693 __isl_give isl_map *isl_map_reaching_path_lengths(
1694 __isl_take isl_map *map, int *exact);
1696 Compute a relation that maps each element in the range of C<map>
1697 to the lengths of all paths composed of edges in C<map> that
1698 end up in the given element.
1699 The result may be an overapproximation. If the result is known to be exact,
1700 then C<*exact> is set to C<1>.
1701 To compute the I<maximal> path length, the resulting relation
1702 should be postprocessed by C<isl_map_lexmax>.
1703 In particular, if the input relation is a dependence relation
1704 (mapping sources to sinks), then the maximal path length corresponds
1705 to the free schedule.
1706 Note, however, that C<isl_map_lexmax> expects the maximum to be
1707 finite, so if the path lengths are unbounded (possibly due to
1708 the overapproximation), then you will get an error message.
1712 __isl_give isl_basic_set *isl_basic_map_wrap(
1713 __isl_take isl_basic_map *bmap);
1714 __isl_give isl_set *isl_map_wrap(
1715 __isl_take isl_map *map);
1716 __isl_give isl_union_set *isl_union_map_wrap(
1717 __isl_take isl_union_map *umap);
1718 __isl_give isl_basic_map *isl_basic_set_unwrap(
1719 __isl_take isl_basic_set *bset);
1720 __isl_give isl_map *isl_set_unwrap(
1721 __isl_take isl_set *set);
1722 __isl_give isl_union_map *isl_union_set_unwrap(
1723 __isl_take isl_union_set *uset);
1727 Remove any internal structure of domain (and range) of the given
1728 set or relation. If there is any such internal structure in the input,
1729 then the name of the space is also removed.
1731 __isl_give isl_basic_set *isl_basic_set_flatten(
1732 __isl_take isl_basic_set *bset);
1733 __isl_give isl_set *isl_set_flatten(
1734 __isl_take isl_set *set);
1735 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1736 __isl_take isl_basic_map *bmap);
1737 __isl_give isl_map *isl_map_flatten_range(
1738 __isl_take isl_map *map);
1739 __isl_give isl_basic_map *isl_basic_map_flatten(
1740 __isl_take isl_basic_map *bmap);
1741 __isl_give isl_map *isl_map_flatten(
1742 __isl_take isl_map *map);
1744 __isl_give isl_map *isl_set_flatten_map(
1745 __isl_take isl_set *set);
1747 The function above constructs a relation
1748 that maps the input set to a flattened version of the set.
1752 Lift the input set to a space with extra dimensions corresponding
1753 to the existentially quantified variables in the input.
1754 In particular, the result lives in a wrapped map where the domain
1755 is the original space and the range corresponds to the original
1756 existentially quantified variables.
1758 __isl_give isl_basic_set *isl_basic_set_lift(
1759 __isl_take isl_basic_set *bset);
1760 __isl_give isl_set *isl_set_lift(
1761 __isl_take isl_set *set);
1762 __isl_give isl_union_set *isl_union_set_lift(
1763 __isl_take isl_union_set *uset);
1765 =item * Internal Product
1767 __isl_give isl_basic_map *isl_basic_map_zip(
1768 __isl_take isl_basic_map *bmap);
1769 __isl_give isl_map *isl_map_zip(
1770 __isl_take isl_map *map);
1771 __isl_give isl_union_map *isl_union_map_zip(
1772 __isl_take isl_union_map *umap);
1774 Given a relation with nested relations for domain and range,
1775 interchange the range of the domain with the domain of the range.
1777 =item * Aligning parameters
1779 __isl_give isl_set *isl_set_align_params(
1780 __isl_take isl_set *set,
1781 __isl_take isl_dim *model);
1782 __isl_give isl_map *isl_map_align_params(
1783 __isl_take isl_map *map,
1784 __isl_take isl_dim *model);
1786 Change the order of the parameters of the given set or relation
1787 such that the first parameters match those of C<model>.
1788 This may involve the introduction of extra parameters.
1789 All parameters need to be named.
1791 =item * Dimension manipulation
1793 __isl_give isl_set *isl_set_add_dims(
1794 __isl_take isl_set *set,
1795 enum isl_dim_type type, unsigned n);
1796 __isl_give isl_map *isl_map_add_dims(
1797 __isl_take isl_map *map,
1798 enum isl_dim_type type, unsigned n);
1800 It is usually not advisable to directly change the (input or output)
1801 space of a set or a relation as this removes the name and the internal
1802 structure of the space. However, the above functions can be useful
1803 to add new parameters, assuming
1804 C<isl_set_align_params> and C<isl_map_align_params>
1809 =head2 Binary Operations
1811 The two arguments of a binary operation not only need to live
1812 in the same C<isl_ctx>, they currently also need to have
1813 the same (number of) parameters.
1815 =head3 Basic Operations
1819 =item * Intersection
1821 __isl_give isl_basic_set *isl_basic_set_intersect(
1822 __isl_take isl_basic_set *bset1,
1823 __isl_take isl_basic_set *bset2);
1824 __isl_give isl_set *isl_set_intersect(
1825 __isl_take isl_set *set1,
1826 __isl_take isl_set *set2);
1827 __isl_give isl_union_set *isl_union_set_intersect(
1828 __isl_take isl_union_set *uset1,
1829 __isl_take isl_union_set *uset2);
1830 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1831 __isl_take isl_basic_map *bmap,
1832 __isl_take isl_basic_set *bset);
1833 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1834 __isl_take isl_basic_map *bmap,
1835 __isl_take isl_basic_set *bset);
1836 __isl_give isl_basic_map *isl_basic_map_intersect(
1837 __isl_take isl_basic_map *bmap1,
1838 __isl_take isl_basic_map *bmap2);
1839 __isl_give isl_map *isl_map_intersect_domain(
1840 __isl_take isl_map *map,
1841 __isl_take isl_set *set);
1842 __isl_give isl_map *isl_map_intersect_range(
1843 __isl_take isl_map *map,
1844 __isl_take isl_set *set);
1845 __isl_give isl_map *isl_map_intersect(
1846 __isl_take isl_map *map1,
1847 __isl_take isl_map *map2);
1848 __isl_give isl_union_map *isl_union_map_intersect_domain(
1849 __isl_take isl_union_map *umap,
1850 __isl_take isl_union_set *uset);
1851 __isl_give isl_union_map *isl_union_map_intersect_range(
1852 __isl_take isl_union_map *umap,
1853 __isl_take isl_union_set *uset);
1854 __isl_give isl_union_map *isl_union_map_intersect(
1855 __isl_take isl_union_map *umap1,
1856 __isl_take isl_union_map *umap2);
1860 __isl_give isl_set *isl_basic_set_union(
1861 __isl_take isl_basic_set *bset1,
1862 __isl_take isl_basic_set *bset2);
1863 __isl_give isl_map *isl_basic_map_union(
1864 __isl_take isl_basic_map *bmap1,
1865 __isl_take isl_basic_map *bmap2);
1866 __isl_give isl_set *isl_set_union(
1867 __isl_take isl_set *set1,
1868 __isl_take isl_set *set2);
1869 __isl_give isl_map *isl_map_union(
1870 __isl_take isl_map *map1,
1871 __isl_take isl_map *map2);
1872 __isl_give isl_union_set *isl_union_set_union(
1873 __isl_take isl_union_set *uset1,
1874 __isl_take isl_union_set *uset2);
1875 __isl_give isl_union_map *isl_union_map_union(
1876 __isl_take isl_union_map *umap1,
1877 __isl_take isl_union_map *umap2);
1879 =item * Set difference
1881 __isl_give isl_set *isl_set_subtract(
1882 __isl_take isl_set *set1,
1883 __isl_take isl_set *set2);
1884 __isl_give isl_map *isl_map_subtract(
1885 __isl_take isl_map *map1,
1886 __isl_take isl_map *map2);
1887 __isl_give isl_union_set *isl_union_set_subtract(
1888 __isl_take isl_union_set *uset1,
1889 __isl_take isl_union_set *uset2);
1890 __isl_give isl_union_map *isl_union_map_subtract(
1891 __isl_take isl_union_map *umap1,
1892 __isl_take isl_union_map *umap2);
1896 __isl_give isl_basic_set *isl_basic_set_apply(
1897 __isl_take isl_basic_set *bset,
1898 __isl_take isl_basic_map *bmap);
1899 __isl_give isl_set *isl_set_apply(
1900 __isl_take isl_set *set,
1901 __isl_take isl_map *map);
1902 __isl_give isl_union_set *isl_union_set_apply(
1903 __isl_take isl_union_set *uset,
1904 __isl_take isl_union_map *umap);
1905 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1906 __isl_take isl_basic_map *bmap1,
1907 __isl_take isl_basic_map *bmap2);
1908 __isl_give isl_basic_map *isl_basic_map_apply_range(
1909 __isl_take isl_basic_map *bmap1,
1910 __isl_take isl_basic_map *bmap2);
1911 __isl_give isl_map *isl_map_apply_domain(
1912 __isl_take isl_map *map1,
1913 __isl_take isl_map *map2);
1914 __isl_give isl_union_map *isl_union_map_apply_domain(
1915 __isl_take isl_union_map *umap1,
1916 __isl_take isl_union_map *umap2);
1917 __isl_give isl_map *isl_map_apply_range(
1918 __isl_take isl_map *map1,
1919 __isl_take isl_map *map2);
1920 __isl_give isl_union_map *isl_union_map_apply_range(
1921 __isl_take isl_union_map *umap1,
1922 __isl_take isl_union_map *umap2);
1924 =item * Cartesian Product
1926 __isl_give isl_set *isl_set_product(
1927 __isl_take isl_set *set1,
1928 __isl_take isl_set *set2);
1929 __isl_give isl_union_set *isl_union_set_product(
1930 __isl_take isl_union_set *uset1,
1931 __isl_take isl_union_set *uset2);
1932 __isl_give isl_basic_map *isl_basic_map_range_product(
1933 __isl_take isl_basic_map *bmap1,
1934 __isl_take isl_basic_map *bmap2);
1935 __isl_give isl_map *isl_map_range_product(
1936 __isl_take isl_map *map1,
1937 __isl_take isl_map *map2);
1938 __isl_give isl_union_map *isl_union_map_range_product(
1939 __isl_take isl_union_map *umap1,
1940 __isl_take isl_union_map *umap2);
1941 __isl_give isl_map *isl_map_product(
1942 __isl_take isl_map *map1,
1943 __isl_take isl_map *map2);
1944 __isl_give isl_union_map *isl_union_map_product(
1945 __isl_take isl_union_map *umap1,
1946 __isl_take isl_union_map *umap2);
1948 The above functions compute the cross product of the given
1949 sets or relations. The domains and ranges of the results
1950 are wrapped maps between domains and ranges of the inputs.
1951 To obtain a ``flat'' product, use the following functions
1954 __isl_give isl_basic_set *isl_basic_set_flat_product(
1955 __isl_take isl_basic_set *bset1,
1956 __isl_take isl_basic_set *bset2);
1957 __isl_give isl_set *isl_set_flat_product(
1958 __isl_take isl_set *set1,
1959 __isl_take isl_set *set2);
1960 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1961 __isl_take isl_basic_map *bmap1,
1962 __isl_take isl_basic_map *bmap2);
1963 __isl_give isl_map *isl_map_flat_range_product(
1964 __isl_take isl_map *map1,
1965 __isl_take isl_map *map2);
1966 __isl_give isl_union_map *isl_union_map_flat_range_product(
1967 __isl_take isl_union_map *umap1,
1968 __isl_take isl_union_map *umap2);
1969 __isl_give isl_basic_map *isl_basic_map_flat_product(
1970 __isl_take isl_basic_map *bmap1,
1971 __isl_take isl_basic_map *bmap2);
1972 __isl_give isl_map *isl_map_flat_product(
1973 __isl_take isl_map *map1,
1974 __isl_take isl_map *map2);
1976 =item * Simplification
1978 __isl_give isl_basic_set *isl_basic_set_gist(
1979 __isl_take isl_basic_set *bset,
1980 __isl_take isl_basic_set *context);
1981 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1982 __isl_take isl_set *context);
1983 __isl_give isl_union_set *isl_union_set_gist(
1984 __isl_take isl_union_set *uset,
1985 __isl_take isl_union_set *context);
1986 __isl_give isl_basic_map *isl_basic_map_gist(
1987 __isl_take isl_basic_map *bmap,
1988 __isl_take isl_basic_map *context);
1989 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1990 __isl_take isl_map *context);
1991 __isl_give isl_union_map *isl_union_map_gist(
1992 __isl_take isl_union_map *umap,
1993 __isl_take isl_union_map *context);
1995 The gist operation returns a set or relation that has the
1996 same intersection with the context as the input set or relation.
1997 Any implicit equality in the intersection is made explicit in the result,
1998 while all inequalities that are redundant with respect to the intersection
2000 In case of union sets and relations, the gist operation is performed
2005 =head3 Lexicographic Optimization
2007 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2008 the following functions
2009 compute a set that contains the lexicographic minimum or maximum
2010 of the elements in C<set> (or C<bset>) for those values of the parameters
2011 that satisfy C<dom>.
2012 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2013 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2015 In other words, the union of the parameter values
2016 for which the result is non-empty and of C<*empty>
2019 __isl_give isl_set *isl_basic_set_partial_lexmin(
2020 __isl_take isl_basic_set *bset,
2021 __isl_take isl_basic_set *dom,
2022 __isl_give isl_set **empty);
2023 __isl_give isl_set *isl_basic_set_partial_lexmax(
2024 __isl_take isl_basic_set *bset,
2025 __isl_take isl_basic_set *dom,
2026 __isl_give isl_set **empty);
2027 __isl_give isl_set *isl_set_partial_lexmin(
2028 __isl_take isl_set *set, __isl_take isl_set *dom,
2029 __isl_give isl_set **empty);
2030 __isl_give isl_set *isl_set_partial_lexmax(
2031 __isl_take isl_set *set, __isl_take isl_set *dom,
2032 __isl_give isl_set **empty);
2034 Given a (basic) set C<set> (or C<bset>), the following functions simply
2035 return a set containing the lexicographic minimum or maximum
2036 of the elements in C<set> (or C<bset>).
2037 In case of union sets, the optimum is computed per space.
2039 __isl_give isl_set *isl_basic_set_lexmin(
2040 __isl_take isl_basic_set *bset);
2041 __isl_give isl_set *isl_basic_set_lexmax(
2042 __isl_take isl_basic_set *bset);
2043 __isl_give isl_set *isl_set_lexmin(
2044 __isl_take isl_set *set);
2045 __isl_give isl_set *isl_set_lexmax(
2046 __isl_take isl_set *set);
2047 __isl_give isl_union_set *isl_union_set_lexmin(
2048 __isl_take isl_union_set *uset);
2049 __isl_give isl_union_set *isl_union_set_lexmax(
2050 __isl_take isl_union_set *uset);
2052 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2053 the following functions
2054 compute a relation that maps each element of C<dom>
2055 to the single lexicographic minimum or maximum
2056 of the elements that are associated to that same
2057 element in C<map> (or C<bmap>).
2058 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2059 that contains the elements in C<dom> that do not map
2060 to any elements in C<map> (or C<bmap>).
2061 In other words, the union of the domain of the result and of C<*empty>
2064 __isl_give isl_map *isl_basic_map_partial_lexmax(
2065 __isl_take isl_basic_map *bmap,
2066 __isl_take isl_basic_set *dom,
2067 __isl_give isl_set **empty);
2068 __isl_give isl_map *isl_basic_map_partial_lexmin(
2069 __isl_take isl_basic_map *bmap,
2070 __isl_take isl_basic_set *dom,
2071 __isl_give isl_set **empty);
2072 __isl_give isl_map *isl_map_partial_lexmax(
2073 __isl_take isl_map *map, __isl_take isl_set *dom,
2074 __isl_give isl_set **empty);
2075 __isl_give isl_map *isl_map_partial_lexmin(
2076 __isl_take isl_map *map, __isl_take isl_set *dom,
2077 __isl_give isl_set **empty);
2079 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2080 return a map mapping each element in the domain of
2081 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2082 of all elements associated to that element.
2083 In case of union relations, the optimum is computed per space.
2085 __isl_give isl_map *isl_basic_map_lexmin(
2086 __isl_take isl_basic_map *bmap);
2087 __isl_give isl_map *isl_basic_map_lexmax(
2088 __isl_take isl_basic_map *bmap);
2089 __isl_give isl_map *isl_map_lexmin(
2090 __isl_take isl_map *map);
2091 __isl_give isl_map *isl_map_lexmax(
2092 __isl_take isl_map *map);
2093 __isl_give isl_union_map *isl_union_map_lexmin(
2094 __isl_take isl_union_map *umap);
2095 __isl_give isl_union_map *isl_union_map_lexmax(
2096 __isl_take isl_union_map *umap);
2100 Lists are defined over several element types, including
2101 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2102 Here we take lists of C<isl_set>s as an example.
2103 Lists can be created, copied and freed using the following functions.
2105 #include <isl/list.h>
2106 __isl_give isl_set_list *isl_set_list_alloc(
2107 isl_ctx *ctx, int n);
2108 __isl_give isl_set_list *isl_set_list_copy(
2109 __isl_keep isl_set_list *list);
2110 __isl_give isl_set_list *isl_set_list_add(
2111 __isl_take isl_set_list *list,
2112 __isl_take isl_set *el);
2113 void isl_set_list_free(__isl_take isl_set_list *list);
2115 C<isl_set_list_alloc> creates an empty list with a capacity for
2118 Lists can be inspected using the following functions.
2120 #include <isl/list.h>
2121 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2122 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2123 __isl_give struct isl_set *isl_set_list_get_set(
2124 __isl_keep isl_set_list *list, int index);
2125 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2126 int (*fn)(__isl_take struct isl_set *el, void *user),
2129 Lists can be printed using
2131 #include <isl/list.h>
2132 __isl_give isl_printer *isl_printer_print_set_list(
2133 __isl_take isl_printer *p,
2134 __isl_keep isl_set_list *list);
2138 Matrices can be created, copied and freed using the following functions.
2140 #include <isl/mat.h>
2141 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2142 unsigned n_row, unsigned n_col);
2143 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2144 void isl_mat_free(__isl_take isl_mat *mat);
2146 Note that the elements of a newly created matrix may have arbitrary values.
2147 The elements can be changed and inspected using the following functions.
2149 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2150 int isl_mat_rows(__isl_keep isl_mat *mat);
2151 int isl_mat_cols(__isl_keep isl_mat *mat);
2152 int isl_mat_get_element(__isl_keep isl_mat *mat,
2153 int row, int col, isl_int *v);
2154 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2155 int row, int col, isl_int v);
2156 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2157 int row, int col, int v);
2159 C<isl_mat_get_element> will return a negative value if anything went wrong.
2160 In that case, the value of C<*v> is undefined.
2162 The following function can be used to compute the (right) inverse
2163 of a matrix, i.e., a matrix such that the product of the original
2164 and the inverse (in that order) is a multiple of the identity matrix.
2165 The input matrix is assumed to be of full row-rank.
2167 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2169 The following function can be used to compute the (right) kernel
2170 (or null space) of a matrix, i.e., a matrix such that the product of
2171 the original and the kernel (in that order) is the zero matrix.
2173 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2175 =head2 Piecewise Quasi Affine Expressions
2177 The zero quasi affine expression can be created using
2179 __isl_give isl_aff *isl_aff_zero(
2180 __isl_take isl_local_space *ls);
2182 An empty piecewise quasi affine expression (one with no cells)
2183 or a piecewise quasi affine expression with a single cell can
2184 be created using the following functions.
2186 #include <isl/aff.h>
2187 __isl_give isl_pw_aff *isl_pw_aff_empty(
2188 __isl_take isl_dim *dim);
2189 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2190 __isl_take isl_set *set, __isl_take isl_aff *aff);
2192 Quasi affine expressions can be copied and free using
2194 #include <isl/aff.h>
2195 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2196 void *isl_aff_free(__isl_take isl_aff *aff);
2198 __isl_give isl_pw_aff *isl_pw_aff_copy(
2199 __isl_keep isl_pw_aff *pwaff);
2200 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2202 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2203 using the following function. The constraint is required to have
2204 a non-zero coefficient for the specified dimension.
2206 #include <isl/constraint.h>
2207 __isl_give isl_aff *isl_constraint_get_bound(
2208 __isl_keep isl_constraint *constraint,
2209 enum isl_dim_type type, int pos);
2211 Conversely, an equality constraint equating
2212 the affine expression to zero or an inequality constraint enforcing
2213 the affine expression to be non-negative, can be constructed using
2215 __isl_give isl_constraint *isl_equality_from_aff(
2216 __isl_take isl_aff *aff);
2217 __isl_give isl_constraint *isl_inequality_from_aff(
2218 __isl_take isl_aff *aff);
2220 The expression can be inspected using
2222 #include <isl/aff.h>
2223 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2224 int isl_aff_dim(__isl_keep isl_aff *aff,
2225 enum isl_dim_type type);
2226 __isl_give isl_local_space *isl_aff_get_local_space(
2227 __isl_keep isl_aff *aff);
2228 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2229 enum isl_dim_type type, unsigned pos);
2230 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2232 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2233 enum isl_dim_type type, int pos, isl_int *v);
2234 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2236 __isl_give isl_div *isl_aff_get_div(
2237 __isl_keep isl_aff *aff, int pos);
2239 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2240 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2242 It can be modified using
2244 #include <isl/aff.h>
2245 __isl_give isl_aff *isl_aff_set_dim_name(
2246 __isl_take isl_aff *aff, enum isl_dim_type type,
2247 unsigned pos, const char *s);
2248 __isl_give isl_aff *isl_aff_set_constant(
2249 __isl_take isl_aff *aff, isl_int v);
2250 __isl_give isl_aff *isl_aff_set_constant_si(
2251 __isl_take isl_aff *aff, int v);
2252 __isl_give isl_aff *isl_aff_set_coefficient(
2253 __isl_take isl_aff *aff,
2254 enum isl_dim_type type, int pos, isl_int v);
2255 __isl_give isl_aff *isl_aff_set_coefficient_si(
2256 __isl_take isl_aff *aff,
2257 enum isl_dim_type type, int pos, int v);
2258 __isl_give isl_aff *isl_aff_set_denominator(
2259 __isl_take isl_aff *aff, isl_int v);
2261 __isl_give isl_aff *isl_aff_add_constant(
2262 __isl_take isl_aff *aff, isl_int v);
2263 __isl_give isl_aff *isl_aff_add_constant_si(
2264 __isl_take isl_aff *aff, int v);
2265 __isl_give isl_aff *isl_aff_add_coefficient_si(
2266 __isl_take isl_aff *aff,
2267 enum isl_dim_type type, int pos, int v);
2269 Note that the C<set_constant> and C<set_coefficient> functions
2270 set the I<numerator> of the constant or coefficient, while
2271 C<add_constant> and C<add_coefficient> add an integer value to
2272 the possibly rational constant or coefficient.
2274 To check whether an affine expressions is obviously zero
2275 or obviously equal to some other affine expression, use
2277 #include <isl/aff.h>
2278 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2279 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2280 __isl_keep isl_aff *aff2);
2284 #include <isl/aff.h>
2285 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2286 __isl_take isl_aff *aff2);
2287 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2288 __isl_take isl_aff *aff2);
2289 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2290 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2291 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2292 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2294 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2296 __isl_give isl_aff *isl_aff_scale_down_ui(
2297 __isl_take isl_aff *aff, unsigned f);
2299 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2300 __isl_take isl_set *context);
2302 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2303 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2305 The function C<isl_aff_ge_basic_set> returns a basic set
2306 containing those elements in the shared space
2307 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2309 #include <isl/aff.h>
2310 __isl_give isl_pw_aff *isl_pw_aff_max(
2311 __isl_take isl_pw_aff *pwaff1,
2312 __isl_take isl_pw_aff *pwaff2);
2314 The function C<isl_pw_aff_max> computes a piecewise quasi-affine
2315 expression with a domain that is the union of those of C<pwaff1> and
2316 C<pwaff2> and such that on each cell, the quasi-affine expression is
2317 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2318 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2319 associated expression is the defined one.
2321 An expression can be printed using
2323 #include <isl/aff.h>
2324 __isl_give isl_printer *isl_printer_print_aff(
2325 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2327 __isl_give isl_printer *isl_printer_print_pw_aff(
2328 __isl_take isl_printer *p,
2329 __isl_keep isl_pw_aff *pwaff);
2333 Points are elements of a set. They can be used to construct
2334 simple sets (boxes) or they can be used to represent the
2335 individual elements of a set.
2336 The zero point (the origin) can be created using
2338 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2340 The coordinates of a point can be inspected, set and changed
2343 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2344 enum isl_dim_type type, int pos, isl_int *v);
2345 __isl_give isl_point *isl_point_set_coordinate(
2346 __isl_take isl_point *pnt,
2347 enum isl_dim_type type, int pos, isl_int v);
2349 __isl_give isl_point *isl_point_add_ui(
2350 __isl_take isl_point *pnt,
2351 enum isl_dim_type type, int pos, unsigned val);
2352 __isl_give isl_point *isl_point_sub_ui(
2353 __isl_take isl_point *pnt,
2354 enum isl_dim_type type, int pos, unsigned val);
2356 Other properties can be obtained using
2358 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2360 Points can be copied or freed using
2362 __isl_give isl_point *isl_point_copy(
2363 __isl_keep isl_point *pnt);
2364 void isl_point_free(__isl_take isl_point *pnt);
2366 A singleton set can be created from a point using
2368 __isl_give isl_basic_set *isl_basic_set_from_point(
2369 __isl_take isl_point *pnt);
2370 __isl_give isl_set *isl_set_from_point(
2371 __isl_take isl_point *pnt);
2373 and a box can be created from two opposite extremal points using
2375 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2376 __isl_take isl_point *pnt1,
2377 __isl_take isl_point *pnt2);
2378 __isl_give isl_set *isl_set_box_from_points(
2379 __isl_take isl_point *pnt1,
2380 __isl_take isl_point *pnt2);
2382 All elements of a B<bounded> (union) set can be enumerated using
2383 the following functions.
2385 int isl_set_foreach_point(__isl_keep isl_set *set,
2386 int (*fn)(__isl_take isl_point *pnt, void *user),
2388 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2389 int (*fn)(__isl_take isl_point *pnt, void *user),
2392 The function C<fn> is called for each integer point in
2393 C<set> with as second argument the last argument of
2394 the C<isl_set_foreach_point> call. The function C<fn>
2395 should return C<0> on success and C<-1> on failure.
2396 In the latter case, C<isl_set_foreach_point> will stop
2397 enumerating and return C<-1> as well.
2398 If the enumeration is performed successfully and to completion,
2399 then C<isl_set_foreach_point> returns C<0>.
2401 To obtain a single point of a (basic) set, use
2403 __isl_give isl_point *isl_basic_set_sample_point(
2404 __isl_take isl_basic_set *bset);
2405 __isl_give isl_point *isl_set_sample_point(
2406 __isl_take isl_set *set);
2408 If C<set> does not contain any (integer) points, then the
2409 resulting point will be ``void'', a property that can be
2412 int isl_point_is_void(__isl_keep isl_point *pnt);
2414 =head2 Piecewise Quasipolynomials
2416 A piecewise quasipolynomial is a particular kind of function that maps
2417 a parametric point to a rational value.
2418 More specifically, a quasipolynomial is a polynomial expression in greatest
2419 integer parts of affine expressions of parameters and variables.
2420 A piecewise quasipolynomial is a subdivision of a given parametric
2421 domain into disjoint cells with a quasipolynomial associated to
2422 each cell. The value of the piecewise quasipolynomial at a given
2423 point is the value of the quasipolynomial associated to the cell
2424 that contains the point. Outside of the union of cells,
2425 the value is assumed to be zero.
2426 For example, the piecewise quasipolynomial
2428 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2430 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2431 A given piecewise quasipolynomial has a fixed domain dimension.
2432 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2433 defined over different domains.
2434 Piecewise quasipolynomials are mainly used by the C<barvinok>
2435 library for representing the number of elements in a parametric set or map.
2436 For example, the piecewise quasipolynomial above represents
2437 the number of points in the map
2439 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2441 =head3 Printing (Piecewise) Quasipolynomials
2443 Quasipolynomials and piecewise quasipolynomials can be printed
2444 using the following functions.
2446 __isl_give isl_printer *isl_printer_print_qpolynomial(
2447 __isl_take isl_printer *p,
2448 __isl_keep isl_qpolynomial *qp);
2450 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2451 __isl_take isl_printer *p,
2452 __isl_keep isl_pw_qpolynomial *pwqp);
2454 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2455 __isl_take isl_printer *p,
2456 __isl_keep isl_union_pw_qpolynomial *upwqp);
2458 The output format of the printer
2459 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2460 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2462 In case of printing in C<ISL_FORMAT_C>, the user may want
2463 to set the names of all dimensions
2465 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2466 __isl_take isl_qpolynomial *qp,
2467 enum isl_dim_type type, unsigned pos,
2469 __isl_give isl_pw_qpolynomial *
2470 isl_pw_qpolynomial_set_dim_name(
2471 __isl_take isl_pw_qpolynomial *pwqp,
2472 enum isl_dim_type type, unsigned pos,
2475 =head3 Creating New (Piecewise) Quasipolynomials
2477 Some simple quasipolynomials can be created using the following functions.
2478 More complicated quasipolynomials can be created by applying
2479 operations such as addition and multiplication
2480 on the resulting quasipolynomials
2482 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2483 __isl_take isl_dim *dim);
2484 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2485 __isl_take isl_dim *dim);
2486 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2487 __isl_take isl_dim *dim);
2488 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2489 __isl_take isl_dim *dim);
2490 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2491 __isl_take isl_dim *dim);
2492 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2493 __isl_take isl_dim *dim,
2494 const isl_int n, const isl_int d);
2495 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2496 __isl_take isl_div *div);
2497 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2498 __isl_take isl_dim *dim,
2499 enum isl_dim_type type, unsigned pos);
2500 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2501 __isl_take isl_aff *aff);
2503 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2504 with a single cell can be created using the following functions.
2505 Multiple of these single cell piecewise quasipolynomials can
2506 be combined to create more complicated piecewise quasipolynomials.
2508 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2509 __isl_take isl_dim *dim);
2510 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2511 __isl_take isl_set *set,
2512 __isl_take isl_qpolynomial *qp);
2514 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2515 __isl_take isl_dim *dim);
2516 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2517 __isl_take isl_pw_qpolynomial *pwqp);
2518 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2519 __isl_take isl_union_pw_qpolynomial *upwqp,
2520 __isl_take isl_pw_qpolynomial *pwqp);
2522 Quasipolynomials can be copied and freed again using the following
2525 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2526 __isl_keep isl_qpolynomial *qp);
2527 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2529 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2530 __isl_keep isl_pw_qpolynomial *pwqp);
2531 void *isl_pw_qpolynomial_free(
2532 __isl_take isl_pw_qpolynomial *pwqp);
2534 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2535 __isl_keep isl_union_pw_qpolynomial *upwqp);
2536 void isl_union_pw_qpolynomial_free(
2537 __isl_take isl_union_pw_qpolynomial *upwqp);
2539 =head3 Inspecting (Piecewise) Quasipolynomials
2541 To iterate over all piecewise quasipolynomials in a union
2542 piecewise quasipolynomial, use the following function
2544 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2545 __isl_keep isl_union_pw_qpolynomial *upwqp,
2546 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2549 To extract the piecewise quasipolynomial from a union with a given dimension
2552 __isl_give isl_pw_qpolynomial *
2553 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2554 __isl_keep isl_union_pw_qpolynomial *upwqp,
2555 __isl_take isl_dim *dim);
2557 To iterate over the cells in a piecewise quasipolynomial,
2558 use either of the following two functions
2560 int isl_pw_qpolynomial_foreach_piece(
2561 __isl_keep isl_pw_qpolynomial *pwqp,
2562 int (*fn)(__isl_take isl_set *set,
2563 __isl_take isl_qpolynomial *qp,
2564 void *user), void *user);
2565 int isl_pw_qpolynomial_foreach_lifted_piece(
2566 __isl_keep isl_pw_qpolynomial *pwqp,
2567 int (*fn)(__isl_take isl_set *set,
2568 __isl_take isl_qpolynomial *qp,
2569 void *user), void *user);
2571 As usual, the function C<fn> should return C<0> on success
2572 and C<-1> on failure. The difference between
2573 C<isl_pw_qpolynomial_foreach_piece> and
2574 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2575 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2576 compute unique representations for all existentially quantified
2577 variables and then turn these existentially quantified variables
2578 into extra set variables, adapting the associated quasipolynomial
2579 accordingly. This means that the C<set> passed to C<fn>
2580 will not have any existentially quantified variables, but that
2581 the dimensions of the sets may be different for different
2582 invocations of C<fn>.
2584 To iterate over all terms in a quasipolynomial,
2587 int isl_qpolynomial_foreach_term(
2588 __isl_keep isl_qpolynomial *qp,
2589 int (*fn)(__isl_take isl_term *term,
2590 void *user), void *user);
2592 The terms themselves can be inspected and freed using
2595 unsigned isl_term_dim(__isl_keep isl_term *term,
2596 enum isl_dim_type type);
2597 void isl_term_get_num(__isl_keep isl_term *term,
2599 void isl_term_get_den(__isl_keep isl_term *term,
2601 int isl_term_get_exp(__isl_keep isl_term *term,
2602 enum isl_dim_type type, unsigned pos);
2603 __isl_give isl_div *isl_term_get_div(
2604 __isl_keep isl_term *term, unsigned pos);
2605 void isl_term_free(__isl_take isl_term *term);
2607 Each term is a product of parameters, set variables and
2608 integer divisions. The function C<isl_term_get_exp>
2609 returns the exponent of a given dimensions in the given term.
2610 The C<isl_int>s in the arguments of C<isl_term_get_num>
2611 and C<isl_term_get_den> need to have been initialized
2612 using C<isl_int_init> before calling these functions.
2614 =head3 Properties of (Piecewise) Quasipolynomials
2616 To check whether a quasipolynomial is actually a constant,
2617 use the following function.
2619 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2620 isl_int *n, isl_int *d);
2622 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2623 then the numerator and denominator of the constant
2624 are returned in C<*n> and C<*d>, respectively.
2626 =head3 Operations on (Piecewise) Quasipolynomials
2628 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2629 __isl_take isl_qpolynomial *qp, isl_int v);
2630 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2631 __isl_take isl_qpolynomial *qp);
2632 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2633 __isl_take isl_qpolynomial *qp1,
2634 __isl_take isl_qpolynomial *qp2);
2635 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2636 __isl_take isl_qpolynomial *qp1,
2637 __isl_take isl_qpolynomial *qp2);
2638 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2639 __isl_take isl_qpolynomial *qp1,
2640 __isl_take isl_qpolynomial *qp2);
2641 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2642 __isl_take isl_qpolynomial *qp, unsigned exponent);
2644 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2645 __isl_take isl_pw_qpolynomial *pwqp1,
2646 __isl_take isl_pw_qpolynomial *pwqp2);
2647 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2648 __isl_take isl_pw_qpolynomial *pwqp1,
2649 __isl_take isl_pw_qpolynomial *pwqp2);
2650 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2651 __isl_take isl_pw_qpolynomial *pwqp1,
2652 __isl_take isl_pw_qpolynomial *pwqp2);
2653 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2654 __isl_take isl_pw_qpolynomial *pwqp);
2655 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2656 __isl_take isl_pw_qpolynomial *pwqp1,
2657 __isl_take isl_pw_qpolynomial *pwqp2);
2659 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2660 __isl_take isl_union_pw_qpolynomial *upwqp1,
2661 __isl_take isl_union_pw_qpolynomial *upwqp2);
2662 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2663 __isl_take isl_union_pw_qpolynomial *upwqp1,
2664 __isl_take isl_union_pw_qpolynomial *upwqp2);
2665 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2666 __isl_take isl_union_pw_qpolynomial *upwqp1,
2667 __isl_take isl_union_pw_qpolynomial *upwqp2);
2669 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2670 __isl_take isl_pw_qpolynomial *pwqp,
2671 __isl_take isl_point *pnt);
2673 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2674 __isl_take isl_union_pw_qpolynomial *upwqp,
2675 __isl_take isl_point *pnt);
2677 __isl_give isl_set *isl_pw_qpolynomial_domain(
2678 __isl_take isl_pw_qpolynomial *pwqp);
2679 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2680 __isl_take isl_pw_qpolynomial *pwpq,
2681 __isl_take isl_set *set);
2683 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2684 __isl_take isl_union_pw_qpolynomial *upwqp);
2685 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2686 __isl_take isl_union_pw_qpolynomial *upwpq,
2687 __isl_take isl_union_set *uset);
2689 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2690 __isl_take isl_qpolynomial *qp,
2691 __isl_take isl_dim *model);
2693 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2694 __isl_take isl_union_pw_qpolynomial *upwqp);
2696 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2697 __isl_take isl_qpolynomial *qp,
2698 __isl_take isl_set *context);
2700 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2701 __isl_take isl_pw_qpolynomial *pwqp,
2702 __isl_take isl_set *context);
2704 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2705 __isl_take isl_union_pw_qpolynomial *upwqp,
2706 __isl_take isl_union_set *context);
2708 The gist operation applies the gist operation to each of
2709 the cells in the domain of the input piecewise quasipolynomial.
2710 The context is also exploited
2711 to simplify the quasipolynomials associated to each cell.
2713 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2714 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2715 __isl_give isl_union_pw_qpolynomial *
2716 isl_union_pw_qpolynomial_to_polynomial(
2717 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2719 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2720 the polynomial will be an overapproximation. If C<sign> is negative,
2721 it will be an underapproximation. If C<sign> is zero, the approximation
2722 will lie somewhere in between.
2724 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2726 A piecewise quasipolynomial reduction is a piecewise
2727 reduction (or fold) of quasipolynomials.
2728 In particular, the reduction can be maximum or a minimum.
2729 The objects are mainly used to represent the result of
2730 an upper or lower bound on a quasipolynomial over its domain,
2731 i.e., as the result of the following function.
2733 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2734 __isl_take isl_pw_qpolynomial *pwqp,
2735 enum isl_fold type, int *tight);
2737 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2738 __isl_take isl_union_pw_qpolynomial *upwqp,
2739 enum isl_fold type, int *tight);
2741 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2742 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2743 is the returned bound is known be tight, i.e., for each value
2744 of the parameters there is at least
2745 one element in the domain that reaches the bound.
2746 If the domain of C<pwqp> is not wrapping, then the bound is computed
2747 over all elements in that domain and the result has a purely parametric
2748 domain. If the domain of C<pwqp> is wrapping, then the bound is
2749 computed over the range of the wrapped relation. The domain of the
2750 wrapped relation becomes the domain of the result.
2752 A (piecewise) quasipolynomial reduction can be copied or freed using the
2753 following functions.
2755 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2756 __isl_keep isl_qpolynomial_fold *fold);
2757 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2758 __isl_keep isl_pw_qpolynomial_fold *pwf);
2759 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2760 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2761 void isl_qpolynomial_fold_free(
2762 __isl_take isl_qpolynomial_fold *fold);
2763 void *isl_pw_qpolynomial_fold_free(
2764 __isl_take isl_pw_qpolynomial_fold *pwf);
2765 void isl_union_pw_qpolynomial_fold_free(
2766 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2768 =head3 Printing Piecewise Quasipolynomial Reductions
2770 Piecewise quasipolynomial reductions can be printed
2771 using the following function.
2773 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2774 __isl_take isl_printer *p,
2775 __isl_keep isl_pw_qpolynomial_fold *pwf);
2776 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2777 __isl_take isl_printer *p,
2778 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2780 For C<isl_printer_print_pw_qpolynomial_fold>,
2781 output format of the printer
2782 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2783 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2784 output format of the printer
2785 needs to be set to C<ISL_FORMAT_ISL>.
2786 In case of printing in C<ISL_FORMAT_C>, the user may want
2787 to set the names of all dimensions
2789 __isl_give isl_pw_qpolynomial_fold *
2790 isl_pw_qpolynomial_fold_set_dim_name(
2791 __isl_take isl_pw_qpolynomial_fold *pwf,
2792 enum isl_dim_type type, unsigned pos,
2795 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2797 To iterate over all piecewise quasipolynomial reductions in a union
2798 piecewise quasipolynomial reduction, use the following function
2800 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2801 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2802 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2803 void *user), void *user);
2805 To iterate over the cells in a piecewise quasipolynomial reduction,
2806 use either of the following two functions
2808 int isl_pw_qpolynomial_fold_foreach_piece(
2809 __isl_keep isl_pw_qpolynomial_fold *pwf,
2810 int (*fn)(__isl_take isl_set *set,
2811 __isl_take isl_qpolynomial_fold *fold,
2812 void *user), void *user);
2813 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2814 __isl_keep isl_pw_qpolynomial_fold *pwf,
2815 int (*fn)(__isl_take isl_set *set,
2816 __isl_take isl_qpolynomial_fold *fold,
2817 void *user), void *user);
2819 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2820 of the difference between these two functions.
2822 To iterate over all quasipolynomials in a reduction, use
2824 int isl_qpolynomial_fold_foreach_qpolynomial(
2825 __isl_keep isl_qpolynomial_fold *fold,
2826 int (*fn)(__isl_take isl_qpolynomial *qp,
2827 void *user), void *user);
2829 =head3 Operations on Piecewise Quasipolynomial Reductions
2831 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
2832 __isl_take isl_qpolynomial_fold *fold, isl_int v);
2834 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2835 __isl_take isl_pw_qpolynomial_fold *pwf1,
2836 __isl_take isl_pw_qpolynomial_fold *pwf2);
2838 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2839 __isl_take isl_pw_qpolynomial_fold *pwf1,
2840 __isl_take isl_pw_qpolynomial_fold *pwf2);
2842 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2843 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2844 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2846 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2847 __isl_take isl_pw_qpolynomial_fold *pwf,
2848 __isl_take isl_point *pnt);
2850 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2851 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2852 __isl_take isl_point *pnt);
2854 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2855 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2856 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2857 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2858 __isl_take isl_union_set *uset);
2860 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2861 __isl_take isl_pw_qpolynomial_fold *pwf);
2863 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2864 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2866 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2867 __isl_take isl_pw_qpolynomial_fold *pwf,
2868 __isl_take isl_set *context);
2870 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2871 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2872 __isl_take isl_union_set *context);
2874 The gist operation applies the gist operation to each of
2875 the cells in the domain of the input piecewise quasipolynomial reduction.
2876 In future, the operation will also exploit the context
2877 to simplify the quasipolynomial reductions associated to each cell.
2879 __isl_give isl_pw_qpolynomial_fold *
2880 isl_set_apply_pw_qpolynomial_fold(
2881 __isl_take isl_set *set,
2882 __isl_take isl_pw_qpolynomial_fold *pwf,
2884 __isl_give isl_pw_qpolynomial_fold *
2885 isl_map_apply_pw_qpolynomial_fold(
2886 __isl_take isl_map *map,
2887 __isl_take isl_pw_qpolynomial_fold *pwf,
2889 __isl_give isl_union_pw_qpolynomial_fold *
2890 isl_union_set_apply_union_pw_qpolynomial_fold(
2891 __isl_take isl_union_set *uset,
2892 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2894 __isl_give isl_union_pw_qpolynomial_fold *
2895 isl_union_map_apply_union_pw_qpolynomial_fold(
2896 __isl_take isl_union_map *umap,
2897 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2900 The functions taking a map
2901 compose the given map with the given piecewise quasipolynomial reduction.
2902 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2903 over all elements in the intersection of the range of the map
2904 and the domain of the piecewise quasipolynomial reduction
2905 as a function of an element in the domain of the map.
2906 The functions taking a set compute a bound over all elements in the
2907 intersection of the set and the domain of the
2908 piecewise quasipolynomial reduction.
2910 =head2 Dependence Analysis
2912 C<isl> contains specialized functionality for performing
2913 array dataflow analysis. That is, given a I<sink> access relation
2914 and a collection of possible I<source> access relations,
2915 C<isl> can compute relations that describe
2916 for each iteration of the sink access, which iteration
2917 of which of the source access relations was the last
2918 to access the same data element before the given iteration
2920 To compute standard flow dependences, the sink should be
2921 a read, while the sources should be writes.
2922 If any of the source accesses are marked as being I<may>
2923 accesses, then there will be a dependence to the last
2924 I<must> access B<and> to any I<may> access that follows
2925 this last I<must> access.
2926 In particular, if I<all> sources are I<may> accesses,
2927 then memory based dependence analysis is performed.
2928 If, on the other hand, all sources are I<must> accesses,
2929 then value based dependence analysis is performed.
2931 #include <isl/flow.h>
2933 typedef int (*isl_access_level_before)(void *first, void *second);
2935 __isl_give isl_access_info *isl_access_info_alloc(
2936 __isl_take isl_map *sink,
2937 void *sink_user, isl_access_level_before fn,
2939 __isl_give isl_access_info *isl_access_info_add_source(
2940 __isl_take isl_access_info *acc,
2941 __isl_take isl_map *source, int must,
2943 void isl_access_info_free(__isl_take isl_access_info *acc);
2945 __isl_give isl_flow *isl_access_info_compute_flow(
2946 __isl_take isl_access_info *acc);
2948 int isl_flow_foreach(__isl_keep isl_flow *deps,
2949 int (*fn)(__isl_take isl_map *dep, int must,
2950 void *dep_user, void *user),
2952 __isl_give isl_map *isl_flow_get_no_source(
2953 __isl_keep isl_flow *deps, int must);
2954 void isl_flow_free(__isl_take isl_flow *deps);
2956 The function C<isl_access_info_compute_flow> performs the actual
2957 dependence analysis. The other functions are used to construct
2958 the input for this function or to read off the output.
2960 The input is collected in an C<isl_access_info>, which can
2961 be created through a call to C<isl_access_info_alloc>.
2962 The arguments to this functions are the sink access relation
2963 C<sink>, a token C<sink_user> used to identify the sink
2964 access to the user, a callback function for specifying the
2965 relative order of source and sink accesses, and the number
2966 of source access relations that will be added.
2967 The callback function has type C<int (*)(void *first, void *second)>.
2968 The function is called with two user supplied tokens identifying
2969 either a source or the sink and it should return the shared nesting
2970 level and the relative order of the two accesses.
2971 In particular, let I<n> be the number of loops shared by
2972 the two accesses. If C<first> precedes C<second> textually,
2973 then the function should return I<2 * n + 1>; otherwise,
2974 it should return I<2 * n>.
2975 The sources can be added to the C<isl_access_info> by performing
2976 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2977 C<must> indicates whether the source is a I<must> access
2978 or a I<may> access. Note that a multi-valued access relation
2979 should only be marked I<must> if every iteration in the domain
2980 of the relation accesses I<all> elements in its image.
2981 The C<source_user> token is again used to identify
2982 the source access. The range of the source access relation
2983 C<source> should have the same dimension as the range
2984 of the sink access relation.
2985 The C<isl_access_info_free> function should usually not be
2986 called explicitly, because it is called implicitly by
2987 C<isl_access_info_compute_flow>.
2989 The result of the dependence analysis is collected in an
2990 C<isl_flow>. There may be elements of
2991 the sink access for which no preceding source access could be
2992 found or for which all preceding sources are I<may> accesses.
2993 The relations containing these elements can be obtained through
2994 calls to C<isl_flow_get_no_source>, the first with C<must> set
2995 and the second with C<must> unset.
2996 In the case of standard flow dependence analysis,
2997 with the sink a read and the sources I<must> writes,
2998 the first relation corresponds to the reads from uninitialized
2999 array elements and the second relation is empty.
3000 The actual flow dependences can be extracted using
3001 C<isl_flow_foreach>. This function will call the user-specified
3002 callback function C<fn> for each B<non-empty> dependence between
3003 a source and the sink. The callback function is called
3004 with four arguments, the actual flow dependence relation
3005 mapping source iterations to sink iterations, a boolean that
3006 indicates whether it is a I<must> or I<may> dependence, a token
3007 identifying the source and an additional C<void *> with value
3008 equal to the third argument of the C<isl_flow_foreach> call.
3009 A dependence is marked I<must> if it originates from a I<must>
3010 source and if it is not followed by any I<may> sources.
3012 After finishing with an C<isl_flow>, the user should call
3013 C<isl_flow_free> to free all associated memory.
3015 A higher-level interface to dependence analysis is provided
3016 by the following function.
3018 #include <isl/flow.h>
3020 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3021 __isl_take isl_union_map *must_source,
3022 __isl_take isl_union_map *may_source,
3023 __isl_take isl_union_map *schedule,
3024 __isl_give isl_union_map **must_dep,
3025 __isl_give isl_union_map **may_dep,
3026 __isl_give isl_union_map **must_no_source,
3027 __isl_give isl_union_map **may_no_source);
3029 The arrays are identified by the tuple names of the ranges
3030 of the accesses. The iteration domains by the tuple names
3031 of the domains of the accesses and of the schedule.
3032 The relative order of the iteration domains is given by the
3033 schedule. The relations returned through C<must_no_source>
3034 and C<may_no_source> are subsets of C<sink>.
3035 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3036 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3037 any of the other arguments is treated as an error.
3041 B<The functionality described in this section is fairly new
3042 and may be subject to change.>
3044 The following function can be used to compute a schedule
3045 for a union of domains. The generated schedule respects
3046 all C<validity> dependences. That is, all dependence distances
3047 over these dependences in the scheduled space are lexicographically
3048 positive. The generated schedule schedule also tries to minimize
3049 the dependence distances over C<proximity> dependences.
3050 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3051 for groups of domains where the dependence distances have only
3052 non-negative values.
3053 The algorithm used to construct the schedule is similar to that
3056 #include <isl/schedule.h>
3057 __isl_give isl_schedule *isl_union_set_compute_schedule(
3058 __isl_take isl_union_set *domain,
3059 __isl_take isl_union_map *validity,
3060 __isl_take isl_union_map *proximity);
3061 void *isl_schedule_free(__isl_take isl_schedule *sched);
3063 A mapping from the domains to the scheduled space can be obtained
3064 from an C<isl_schedule> using the following function.
3066 __isl_give isl_union_map *isl_schedule_get_map(
3067 __isl_keep isl_schedule *sched);
3069 A representation of the schedule can be printed using
3071 __isl_give isl_printer *isl_printer_print_schedule(
3072 __isl_take isl_printer *p,
3073 __isl_keep isl_schedule *schedule);
3075 A representation of the schedule as a forest of bands can be obtained
3076 using the following function.
3078 __isl_give isl_band_list *isl_schedule_get_band_forest(
3079 __isl_keep isl_schedule *schedule);
3081 The list can be manipulated as explained in L<"Lists">.
3082 The bands inside the list can be copied and freed using the following
3085 #include <isl/band.h>
3086 __isl_give isl_band *isl_band_copy(
3087 __isl_keep isl_band *band);
3088 void *isl_band_free(__isl_take isl_band *band);
3090 Each band contains zero or more scheduling dimensions.
3091 These are referred to as the members of the band.
3092 The section of the schedule that corresponds to the band is
3093 referred to as the partial schedule of the band.
3094 For those nodes that participate in a band, the outer scheduling
3095 dimensions form the prefix schedule, while the inner scheduling
3096 dimensions form the suffix schedule.
3097 That is, if we take a cut of the band forest, then the union of
3098 the concatenations of the prefix, partial and suffix schedules of
3099 each band in the cut is equal to the entire schedule (modulo
3100 some possible padding at the end with zero scheduling dimensions).
3101 The properties of a band can be inspected using the following functions.
3103 #include <isl/band.h>
3104 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3106 int isl_band_has_children(__isl_keep isl_band *band);
3107 __isl_give isl_band_list *isl_band_get_children(
3108 __isl_keep isl_band *band);
3110 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3111 __isl_keep isl_band *band);
3112 __isl_give isl_union_map *isl_band_get_partial_schedule(
3113 __isl_keep isl_band *band);
3114 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3115 __isl_keep isl_band *band);
3117 int isl_band_n_member(__isl_keep isl_band *band);
3118 int isl_band_member_is_zero_distance(
3119 __isl_keep isl_band *band, int pos);
3121 Note that a scheduling dimension is considered to be ``zero
3122 distance'' if it does not carry any proximity dependences
3124 That is, if the dependence distances of the proximity
3125 dependences are all zero in that direction (for fixed
3126 iterations of outer bands).
3128 A representation of the band can be printed using
3130 #include <isl/band.h>
3131 __isl_give isl_printer *isl_printer_print_band(
3132 __isl_take isl_printer *p,
3133 __isl_keep isl_band *band);
3135 Alternatively, the schedule mapping
3136 can also be obtained in pieces using the following functions.
3138 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3139 __isl_give isl_union_map *isl_schedule_get_band(
3140 __isl_keep isl_schedule *sched, unsigned band);
3142 C<isl_schedule_n_band> returns the maximal number of bands.
3143 C<isl_schedule_get_band> returns a union of mappings from a domain to
3144 the band of consecutive schedule dimensions with the given sequence
3145 number for that domain. Bands with the same sequence number but for
3146 different domains may be completely unrelated.
3147 Within a band, the corresponding coordinates of the distance vectors
3148 are all non-negative, assuming that the coordinates for all previous
3151 =head2 Parametric Vertex Enumeration
3153 The parametric vertex enumeration described in this section
3154 is mainly intended to be used internally and by the C<barvinok>
3157 #include <isl/vertices.h>
3158 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3159 __isl_keep isl_basic_set *bset);
3161 The function C<isl_basic_set_compute_vertices> performs the
3162 actual computation of the parametric vertices and the chamber
3163 decomposition and store the result in an C<isl_vertices> object.
3164 This information can be queried by either iterating over all
3165 the vertices or iterating over all the chambers or cells
3166 and then iterating over all vertices that are active on the chamber.
3168 int isl_vertices_foreach_vertex(
3169 __isl_keep isl_vertices *vertices,
3170 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3173 int isl_vertices_foreach_cell(
3174 __isl_keep isl_vertices *vertices,
3175 int (*fn)(__isl_take isl_cell *cell, void *user),
3177 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3178 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3181 Other operations that can be performed on an C<isl_vertices> object are
3184 isl_ctx *isl_vertices_get_ctx(
3185 __isl_keep isl_vertices *vertices);
3186 int isl_vertices_get_n_vertices(
3187 __isl_keep isl_vertices *vertices);
3188 void isl_vertices_free(__isl_take isl_vertices *vertices);
3190 Vertices can be inspected and destroyed using the following functions.
3192 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3193 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3194 __isl_give isl_basic_set *isl_vertex_get_domain(
3195 __isl_keep isl_vertex *vertex);
3196 __isl_give isl_basic_set *isl_vertex_get_expr(
3197 __isl_keep isl_vertex *vertex);
3198 void isl_vertex_free(__isl_take isl_vertex *vertex);
3200 C<isl_vertex_get_expr> returns a singleton parametric set describing
3201 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3203 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3204 B<rational> basic sets, so they should mainly be used for inspection
3205 and should not be mixed with integer sets.
3207 Chambers can be inspected and destroyed using the following functions.
3209 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3210 __isl_give isl_basic_set *isl_cell_get_domain(
3211 __isl_keep isl_cell *cell);
3212 void isl_cell_free(__isl_take isl_cell *cell);
3216 Although C<isl> is mainly meant to be used as a library,
3217 it also contains some basic applications that use some
3218 of the functionality of C<isl>.
3219 The input may be specified in either the L<isl format>
3220 or the L<PolyLib format>.
3222 =head2 C<isl_polyhedron_sample>
3224 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3225 an integer element of the polyhedron, if there is any.
3226 The first column in the output is the denominator and is always
3227 equal to 1. If the polyhedron contains no integer points,
3228 then a vector of length zero is printed.
3232 C<isl_pip> takes the same input as the C<example> program
3233 from the C<piplib> distribution, i.e., a set of constraints
3234 on the parameters, a line containing only -1 and finally a set
3235 of constraints on a parametric polyhedron.
3236 The coefficients of the parameters appear in the last columns
3237 (but before the final constant column).
3238 The output is the lexicographic minimum of the parametric polyhedron.
3239 As C<isl> currently does not have its own output format, the output
3240 is just a dump of the internal state.
3242 =head2 C<isl_polyhedron_minimize>
3244 C<isl_polyhedron_minimize> computes the minimum of some linear
3245 or affine objective function over the integer points in a polyhedron.
3246 If an affine objective function
3247 is given, then the constant should appear in the last column.
3249 =head2 C<isl_polytope_scan>
3251 Given a polytope, C<isl_polytope_scan> prints
3252 all integer points in the polytope.