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_dims(
627 __isl_take isl_local_space *ls,
628 enum isl_dim_type type, unsigned n);
629 __isl_give isl_local_space *isl_local_space_drop_dims(
630 __isl_take isl_local_space *ls,
631 enum isl_dim_type type, unsigned first, unsigned n);
633 =head2 Input and Output
635 C<isl> supports its own input/output format, which is similar
636 to the C<Omega> format, but also supports the C<PolyLib> format
641 The C<isl> format is similar to that of C<Omega>, but has a different
642 syntax for describing the parameters and allows for the definition
643 of an existentially quantified variable as the integer division
644 of an affine expression.
645 For example, the set of integers C<i> between C<0> and C<n>
646 such that C<i % 10 <= 6> can be described as
648 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
651 A set or relation can have several disjuncts, separated
652 by the keyword C<or>. Each disjunct is either a conjunction
653 of constraints or a projection (C<exists>) of a conjunction
654 of constraints. The constraints are separated by the keyword
657 =head3 C<PolyLib> format
659 If the represented set is a union, then the first line
660 contains a single number representing the number of disjuncts.
661 Otherwise, a line containing the number C<1> is optional.
663 Each disjunct is represented by a matrix of constraints.
664 The first line contains two numbers representing
665 the number of rows and columns,
666 where the number of rows is equal to the number of constraints
667 and the number of columns is equal to two plus the number of variables.
668 The following lines contain the actual rows of the constraint matrix.
669 In each row, the first column indicates whether the constraint
670 is an equality (C<0>) or inequality (C<1>). The final column
671 corresponds to the constant term.
673 If the set is parametric, then the coefficients of the parameters
674 appear in the last columns before the constant column.
675 The coefficients of any existentially quantified variables appear
676 between those of the set variables and those of the parameters.
678 =head3 Extended C<PolyLib> format
680 The extended C<PolyLib> format is nearly identical to the
681 C<PolyLib> format. The only difference is that the line
682 containing the number of rows and columns of a constraint matrix
683 also contains four additional numbers:
684 the number of output dimensions, the number of input dimensions,
685 the number of local dimensions (i.e., the number of existentially
686 quantified variables) and the number of parameters.
687 For sets, the number of ``output'' dimensions is equal
688 to the number of set dimensions, while the number of ``input''
694 __isl_give isl_basic_set *isl_basic_set_read_from_file(
695 isl_ctx *ctx, FILE *input, int nparam);
696 __isl_give isl_basic_set *isl_basic_set_read_from_str(
697 isl_ctx *ctx, const char *str, int nparam);
698 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
699 FILE *input, int nparam);
700 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
701 const char *str, int nparam);
704 __isl_give isl_basic_map *isl_basic_map_read_from_file(
705 isl_ctx *ctx, FILE *input, int nparam);
706 __isl_give isl_basic_map *isl_basic_map_read_from_str(
707 isl_ctx *ctx, const char *str, int nparam);
708 __isl_give isl_map *isl_map_read_from_file(
709 struct isl_ctx *ctx, FILE *input, int nparam);
710 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
711 const char *str, int nparam);
713 #include <isl/union_set.h>
714 __isl_give isl_union_set *isl_union_set_read_from_file(
715 isl_ctx *ctx, FILE *input);
716 __isl_give isl_union_set *isl_union_set_read_from_str(
717 struct isl_ctx *ctx, const char *str);
719 #include <isl/union_map.h>
720 __isl_give isl_union_map *isl_union_map_read_from_file(
721 isl_ctx *ctx, FILE *input);
722 __isl_give isl_union_map *isl_union_map_read_from_str(
723 struct isl_ctx *ctx, const char *str);
725 The input format is autodetected and may be either the C<PolyLib> format
726 or the C<isl> format.
727 C<nparam> specifies how many of the final columns in
728 the C<PolyLib> format correspond to parameters.
729 If input is given in the C<isl> format, then the number
730 of parameters needs to be equal to C<nparam>.
731 If C<nparam> is negative, then any number of parameters
732 is accepted in the C<isl> format and zero parameters
733 are assumed in the C<PolyLib> format.
737 Before anything can be printed, an C<isl_printer> needs to
740 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
742 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
743 void isl_printer_free(__isl_take isl_printer *printer);
744 __isl_give char *isl_printer_get_str(
745 __isl_keep isl_printer *printer);
747 The behavior of the printer can be modified in various ways
749 __isl_give isl_printer *isl_printer_set_output_format(
750 __isl_take isl_printer *p, int output_format);
751 __isl_give isl_printer *isl_printer_set_indent(
752 __isl_take isl_printer *p, int indent);
753 __isl_give isl_printer *isl_printer_indent(
754 __isl_take isl_printer *p, int indent);
755 __isl_give isl_printer *isl_printer_set_prefix(
756 __isl_take isl_printer *p, const char *prefix);
757 __isl_give isl_printer *isl_printer_set_suffix(
758 __isl_take isl_printer *p, const char *suffix);
760 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
761 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
762 and defaults to C<ISL_FORMAT_ISL>.
763 Each line in the output is indented by C<indent> (set by
764 C<isl_printer_set_indent>) spaces
765 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
766 In the C<PolyLib> format output,
767 the coefficients of the existentially quantified variables
768 appear between those of the set variables and those
770 The function C<isl_printer_indent> increases the indentation
771 by the specified amount (which may be negative).
773 To actually print something, use
776 __isl_give isl_printer *isl_printer_print_basic_set(
777 __isl_take isl_printer *printer,
778 __isl_keep isl_basic_set *bset);
779 __isl_give isl_printer *isl_printer_print_set(
780 __isl_take isl_printer *printer,
781 __isl_keep isl_set *set);
784 __isl_give isl_printer *isl_printer_print_basic_map(
785 __isl_take isl_printer *printer,
786 __isl_keep isl_basic_map *bmap);
787 __isl_give isl_printer *isl_printer_print_map(
788 __isl_take isl_printer *printer,
789 __isl_keep isl_map *map);
791 #include <isl/union_set.h>
792 __isl_give isl_printer *isl_printer_print_union_set(
793 __isl_take isl_printer *p,
794 __isl_keep isl_union_set *uset);
796 #include <isl/union_map.h>
797 __isl_give isl_printer *isl_printer_print_union_map(
798 __isl_take isl_printer *p,
799 __isl_keep isl_union_map *umap);
801 When called on a file printer, the following function flushes
802 the file. When called on a string printer, the buffer is cleared.
804 __isl_give isl_printer *isl_printer_flush(
805 __isl_take isl_printer *p);
807 =head2 Creating New Sets and Relations
809 C<isl> has functions for creating some standard sets and relations.
813 =item * Empty sets and relations
815 __isl_give isl_basic_set *isl_basic_set_empty(
816 __isl_take isl_dim *dim);
817 __isl_give isl_basic_map *isl_basic_map_empty(
818 __isl_take isl_dim *dim);
819 __isl_give isl_set *isl_set_empty(
820 __isl_take isl_dim *dim);
821 __isl_give isl_map *isl_map_empty(
822 __isl_take isl_dim *dim);
823 __isl_give isl_union_set *isl_union_set_empty(
824 __isl_take isl_dim *dim);
825 __isl_give isl_union_map *isl_union_map_empty(
826 __isl_take isl_dim *dim);
828 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
829 is only used to specify the parameters.
831 =item * Universe sets and relations
833 __isl_give isl_basic_set *isl_basic_set_universe(
834 __isl_take isl_dim *dim);
835 __isl_give isl_basic_map *isl_basic_map_universe(
836 __isl_take isl_dim *dim);
837 __isl_give isl_set *isl_set_universe(
838 __isl_take isl_dim *dim);
839 __isl_give isl_map *isl_map_universe(
840 __isl_take isl_dim *dim);
841 __isl_give isl_union_set *isl_union_set_universe(
842 __isl_take isl_union_set *uset);
843 __isl_give isl_union_map *isl_union_map_universe(
844 __isl_take isl_union_map *umap);
846 The sets and relations constructed by the functions above
847 contain all integer values, while those constructed by the
848 functions below only contain non-negative values.
850 __isl_give isl_basic_set *isl_basic_set_nat_universe(
851 __isl_take isl_dim *dim);
852 __isl_give isl_basic_map *isl_basic_map_nat_universe(
853 __isl_take isl_dim *dim);
854 __isl_give isl_set *isl_set_nat_universe(
855 __isl_take isl_dim *dim);
856 __isl_give isl_map *isl_map_nat_universe(
857 __isl_take isl_dim *dim);
859 =item * Identity relations
861 __isl_give isl_basic_map *isl_basic_map_identity(
862 __isl_take isl_dim *dim);
863 __isl_give isl_map *isl_map_identity(
864 __isl_take isl_dim *dim);
866 The number of input and output dimensions in C<dim> needs
869 =item * Lexicographic order
871 __isl_give isl_map *isl_map_lex_lt(
872 __isl_take isl_dim *set_dim);
873 __isl_give isl_map *isl_map_lex_le(
874 __isl_take isl_dim *set_dim);
875 __isl_give isl_map *isl_map_lex_gt(
876 __isl_take isl_dim *set_dim);
877 __isl_give isl_map *isl_map_lex_ge(
878 __isl_take isl_dim *set_dim);
879 __isl_give isl_map *isl_map_lex_lt_first(
880 __isl_take isl_dim *dim, unsigned n);
881 __isl_give isl_map *isl_map_lex_le_first(
882 __isl_take isl_dim *dim, unsigned n);
883 __isl_give isl_map *isl_map_lex_gt_first(
884 __isl_take isl_dim *dim, unsigned n);
885 __isl_give isl_map *isl_map_lex_ge_first(
886 __isl_take isl_dim *dim, unsigned n);
888 The first four functions take a dimension specification for a B<set>
889 and return relations that express that the elements in the domain
890 are lexicographically less
891 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
892 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
893 than the elements in the range.
894 The last four functions take a dimension specification for a map
895 and return relations that express that the first C<n> dimensions
896 in the domain are lexicographically less
897 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
898 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
899 than the first C<n> dimensions in the range.
903 A basic set or relation can be converted to a set or relation
904 using the following functions.
906 __isl_give isl_set *isl_set_from_basic_set(
907 __isl_take isl_basic_set *bset);
908 __isl_give isl_map *isl_map_from_basic_map(
909 __isl_take isl_basic_map *bmap);
911 Sets and relations can be converted to union sets and relations
912 using the following functions.
914 __isl_give isl_union_map *isl_union_map_from_map(
915 __isl_take isl_map *map);
916 __isl_give isl_union_set *isl_union_set_from_set(
917 __isl_take isl_set *set);
919 Sets and relations can be copied and freed again using the following
922 __isl_give isl_basic_set *isl_basic_set_copy(
923 __isl_keep isl_basic_set *bset);
924 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
925 __isl_give isl_union_set *isl_union_set_copy(
926 __isl_keep isl_union_set *uset);
927 __isl_give isl_basic_map *isl_basic_map_copy(
928 __isl_keep isl_basic_map *bmap);
929 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
930 __isl_give isl_union_map *isl_union_map_copy(
931 __isl_keep isl_union_map *umap);
932 void isl_basic_set_free(__isl_take isl_basic_set *bset);
933 void isl_set_free(__isl_take isl_set *set);
934 void isl_union_set_free(__isl_take isl_union_set *uset);
935 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
936 void isl_map_free(__isl_take isl_map *map);
937 void isl_union_map_free(__isl_take isl_union_map *umap);
939 Other sets and relations can be constructed by starting
940 from a universe set or relation, adding equality and/or
941 inequality constraints and then projecting out the
942 existentially quantified variables, if any.
943 Constraints can be constructed, manipulated and
944 added to (basic) sets and relations using the following functions.
946 #include <isl/constraint.h>
947 __isl_give isl_constraint *isl_equality_alloc(
948 __isl_take isl_dim *dim);
949 __isl_give isl_constraint *isl_inequality_alloc(
950 __isl_take isl_dim *dim);
951 void isl_constraint_set_constant(
952 __isl_keep isl_constraint *constraint, isl_int v);
953 void isl_constraint_set_coefficient(
954 __isl_keep isl_constraint *constraint,
955 enum isl_dim_type type, int pos, isl_int v);
956 __isl_give isl_basic_map *isl_basic_map_add_constraint(
957 __isl_take isl_basic_map *bmap,
958 __isl_take isl_constraint *constraint);
959 __isl_give isl_basic_set *isl_basic_set_add_constraint(
960 __isl_take isl_basic_set *bset,
961 __isl_take isl_constraint *constraint);
962 __isl_give isl_map *isl_map_add_constraint(
963 __isl_take isl_map *map,
964 __isl_take isl_constraint *constraint);
965 __isl_give isl_set *isl_set_add_constraint(
966 __isl_take isl_set *set,
967 __isl_take isl_constraint *constraint);
969 For example, to create a set containing the even integers
970 between 10 and 42, you would use the following code.
974 struct isl_constraint *c;
975 struct isl_basic_set *bset;
978 dim = isl_dim_set_alloc(ctx, 0, 2);
979 bset = isl_basic_set_universe(isl_dim_copy(dim));
981 c = isl_equality_alloc(isl_dim_copy(dim));
982 isl_int_set_si(v, -1);
983 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
984 isl_int_set_si(v, 2);
985 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
986 bset = isl_basic_set_add_constraint(bset, c);
988 c = isl_inequality_alloc(isl_dim_copy(dim));
989 isl_int_set_si(v, -10);
990 isl_constraint_set_constant(c, v);
991 isl_int_set_si(v, 1);
992 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
993 bset = isl_basic_set_add_constraint(bset, c);
995 c = isl_inequality_alloc(dim);
996 isl_int_set_si(v, 42);
997 isl_constraint_set_constant(c, v);
998 isl_int_set_si(v, -1);
999 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1000 bset = isl_basic_set_add_constraint(bset, c);
1002 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1008 struct isl_basic_set *bset;
1009 bset = isl_basic_set_read_from_str(ctx,
1010 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1012 A basic set or relation can also be constructed from two matrices
1013 describing the equalities and the inequalities.
1015 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1016 __isl_take isl_dim *dim,
1017 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1018 enum isl_dim_type c1,
1019 enum isl_dim_type c2, enum isl_dim_type c3,
1020 enum isl_dim_type c4);
1021 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1022 __isl_take isl_dim *dim,
1023 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1024 enum isl_dim_type c1,
1025 enum isl_dim_type c2, enum isl_dim_type c3,
1026 enum isl_dim_type c4, enum isl_dim_type c5);
1028 The C<isl_dim_type> arguments indicate the order in which
1029 different kinds of variables appear in the input matrices
1030 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1031 C<isl_dim_set> and C<isl_dim_div> for sets and
1032 of C<isl_dim_cst>, C<isl_dim_param>,
1033 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1035 A (basic) relation can also be constructed from a (piecewise) affine expression
1036 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1038 __isl_give isl_basic_map *isl_basic_map_from_aff(
1039 __isl_take isl_aff *aff);
1040 __isl_give isl_map *isl_map_from_pw_aff(
1041 __isl_take isl_pw_aff *pwaff);
1042 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1043 __isl_take isl_dim *domain_dim,
1044 __isl_take isl_aff_list *list);
1046 The C<domain_dim> argument describes the domain of the resulting
1047 basic relation. It is required because the C<list> may consist
1048 of zero affine expressions.
1050 =head2 Inspecting Sets and Relations
1052 Usually, the user should not have to care about the actual constraints
1053 of the sets and maps, but should instead apply the abstract operations
1054 explained in the following sections.
1055 Occasionally, however, it may be required to inspect the individual
1056 coefficients of the constraints. This section explains how to do so.
1057 In these cases, it may also be useful to have C<isl> compute
1058 an explicit representation of the existentially quantified variables.
1060 __isl_give isl_set *isl_set_compute_divs(
1061 __isl_take isl_set *set);
1062 __isl_give isl_map *isl_map_compute_divs(
1063 __isl_take isl_map *map);
1064 __isl_give isl_union_set *isl_union_set_compute_divs(
1065 __isl_take isl_union_set *uset);
1066 __isl_give isl_union_map *isl_union_map_compute_divs(
1067 __isl_take isl_union_map *umap);
1069 This explicit representation defines the existentially quantified
1070 variables as integer divisions of the other variables, possibly
1071 including earlier existentially quantified variables.
1072 An explicitly represented existentially quantified variable therefore
1073 has a unique value when the values of the other variables are known.
1074 If, furthermore, the same existentials, i.e., existentials
1075 with the same explicit representations, should appear in the
1076 same order in each of the disjuncts of a set or map, then the user should call
1077 either of the following functions.
1079 __isl_give isl_set *isl_set_align_divs(
1080 __isl_take isl_set *set);
1081 __isl_give isl_map *isl_map_align_divs(
1082 __isl_take isl_map *map);
1084 Alternatively, the existentially quantified variables can be removed
1085 using the following functions, which compute an overapproximation.
1087 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1088 __isl_take isl_basic_set *bset);
1089 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1090 __isl_take isl_basic_map *bmap);
1091 __isl_give isl_set *isl_set_remove_divs(
1092 __isl_take isl_set *set);
1093 __isl_give isl_map *isl_map_remove_divs(
1094 __isl_take isl_map *map);
1096 To iterate over all the sets or maps in a union set or map, use
1098 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1099 int (*fn)(__isl_take isl_set *set, void *user),
1101 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1102 int (*fn)(__isl_take isl_map *map, void *user),
1105 The number of sets or maps in a union set or map can be obtained
1108 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1109 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1111 To extract the set or map from a union with a given dimension
1114 __isl_give isl_set *isl_union_set_extract_set(
1115 __isl_keep isl_union_set *uset,
1116 __isl_take isl_dim *dim);
1117 __isl_give isl_map *isl_union_map_extract_map(
1118 __isl_keep isl_union_map *umap,
1119 __isl_take isl_dim *dim);
1121 To iterate over all the basic sets or maps in a set or map, use
1123 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1124 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1126 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1127 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1130 The callback function C<fn> should return 0 if successful and
1131 -1 if an error occurs. In the latter case, or if any other error
1132 occurs, the above functions will return -1.
1134 It should be noted that C<isl> does not guarantee that
1135 the basic sets or maps passed to C<fn> are disjoint.
1136 If this is required, then the user should call one of
1137 the following functions first.
1139 __isl_give isl_set *isl_set_make_disjoint(
1140 __isl_take isl_set *set);
1141 __isl_give isl_map *isl_map_make_disjoint(
1142 __isl_take isl_map *map);
1144 The number of basic sets in a set can be obtained
1147 int isl_set_n_basic_set(__isl_keep isl_set *set);
1149 To iterate over the constraints of a basic set or map, use
1151 #include <isl/constraint.h>
1153 int isl_basic_map_foreach_constraint(
1154 __isl_keep isl_basic_map *bmap,
1155 int (*fn)(__isl_take isl_constraint *c, void *user),
1157 void isl_constraint_free(struct isl_constraint *c);
1159 Again, the callback function C<fn> should return 0 if successful and
1160 -1 if an error occurs. In the latter case, or if any other error
1161 occurs, the above functions will return -1.
1162 The constraint C<c> represents either an equality or an inequality.
1163 Use the following function to find out whether a constraint
1164 represents an equality. If not, it represents an inequality.
1166 int isl_constraint_is_equality(
1167 __isl_keep isl_constraint *constraint);
1169 The coefficients of the constraints can be inspected using
1170 the following functions.
1172 void isl_constraint_get_constant(
1173 __isl_keep isl_constraint *constraint, isl_int *v);
1174 void isl_constraint_get_coefficient(
1175 __isl_keep isl_constraint *constraint,
1176 enum isl_dim_type type, int pos, isl_int *v);
1177 int isl_constraint_involves_dims(
1178 __isl_keep isl_constraint *constraint,
1179 enum isl_dim_type type, unsigned first, unsigned n);
1181 The explicit representations of the existentially quantified
1182 variables can be inspected using the following functions.
1183 Note that the user is only allowed to use these functions
1184 if the inspected set or map is the result of a call
1185 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1187 __isl_give isl_div *isl_constraint_div(
1188 __isl_keep isl_constraint *constraint, int pos);
1189 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1190 void isl_div_get_constant(__isl_keep isl_div *div,
1192 void isl_div_get_denominator(__isl_keep isl_div *div,
1194 void isl_div_get_coefficient(__isl_keep isl_div *div,
1195 enum isl_dim_type type, int pos, isl_int *v);
1197 To obtain the constraints of a basic set or map in matrix
1198 form, use the following functions.
1200 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1201 __isl_keep isl_basic_set *bset,
1202 enum isl_dim_type c1, enum isl_dim_type c2,
1203 enum isl_dim_type c3, enum isl_dim_type c4);
1204 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1205 __isl_keep isl_basic_set *bset,
1206 enum isl_dim_type c1, enum isl_dim_type c2,
1207 enum isl_dim_type c3, enum isl_dim_type c4);
1208 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1209 __isl_keep isl_basic_map *bmap,
1210 enum isl_dim_type c1,
1211 enum isl_dim_type c2, enum isl_dim_type c3,
1212 enum isl_dim_type c4, enum isl_dim_type c5);
1213 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1214 __isl_keep isl_basic_map *bmap,
1215 enum isl_dim_type c1,
1216 enum isl_dim_type c2, enum isl_dim_type c3,
1217 enum isl_dim_type c4, enum isl_dim_type c5);
1219 The C<isl_dim_type> arguments dictate the order in which
1220 different kinds of variables appear in the resulting matrix
1221 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1222 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1224 The names of the domain and range spaces of a set or relation can be
1225 read off or set using the following functions.
1227 const char *isl_basic_set_get_tuple_name(
1228 __isl_keep isl_basic_set *bset);
1229 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1230 __isl_take isl_basic_set *set, const char *s);
1231 const char *isl_set_get_tuple_name(
1232 __isl_keep isl_set *set);
1233 const char *isl_basic_map_get_tuple_name(
1234 __isl_keep isl_basic_map *bmap,
1235 enum isl_dim_type type);
1236 const char *isl_map_get_tuple_name(
1237 __isl_keep isl_map *map,
1238 enum isl_dim_type type);
1240 As with C<isl_dim_get_tuple_name>, the value returned points to
1241 an internal data structure.
1242 The names of individual dimensions can be read off using
1243 the following functions.
1245 const char *isl_constraint_get_dim_name(
1246 __isl_keep isl_constraint *constraint,
1247 enum isl_dim_type type, unsigned pos);
1248 const char *isl_basic_set_get_dim_name(
1249 __isl_keep isl_basic_set *bset,
1250 enum isl_dim_type type, unsigned pos);
1251 const char *isl_set_get_dim_name(
1252 __isl_keep isl_set *set,
1253 enum isl_dim_type type, unsigned pos);
1254 const char *isl_basic_map_get_dim_name(
1255 __isl_keep isl_basic_map *bmap,
1256 enum isl_dim_type type, unsigned pos);
1257 const char *isl_map_get_dim_name(
1258 __isl_keep isl_map *map,
1259 enum isl_dim_type type, unsigned pos);
1261 These functions are mostly useful to obtain the names
1266 =head3 Unary Properties
1272 The following functions test whether the given set or relation
1273 contains any integer points. The ``plain'' variants do not perform
1274 any computations, but simply check if the given set or relation
1275 is already known to be empty.
1277 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1278 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1279 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1280 int isl_set_is_empty(__isl_keep isl_set *set);
1281 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1282 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1283 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1284 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1285 int isl_map_is_empty(__isl_keep isl_map *map);
1286 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1288 =item * Universality
1290 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1291 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1292 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1294 =item * Single-valuedness
1296 int isl_map_is_single_valued(__isl_keep isl_map *map);
1297 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1301 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1302 int isl_map_is_injective(__isl_keep isl_map *map);
1303 int isl_union_map_plain_is_injective(
1304 __isl_keep isl_union_map *umap);
1305 int isl_union_map_is_injective(
1306 __isl_keep isl_union_map *umap);
1310 int isl_map_is_bijective(__isl_keep isl_map *map);
1311 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1315 The following functions check whether the domain of the given
1316 (basic) set is a wrapped relation.
1318 int isl_basic_set_is_wrapping(
1319 __isl_keep isl_basic_set *bset);
1320 int isl_set_is_wrapping(__isl_keep isl_set *set);
1322 =item * Internal Product
1324 int isl_basic_map_can_zip(
1325 __isl_keep isl_basic_map *bmap);
1326 int isl_map_can_zip(__isl_keep isl_map *map);
1328 Check whether the product of domain and range of the given relation
1330 i.e., whether both domain and range are nested relations.
1334 =head3 Binary Properties
1340 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1341 __isl_keep isl_set *set2);
1342 int isl_set_is_equal(__isl_keep isl_set *set1,
1343 __isl_keep isl_set *set2);
1344 int isl_union_set_is_equal(
1345 __isl_keep isl_union_set *uset1,
1346 __isl_keep isl_union_set *uset2);
1347 int isl_basic_map_is_equal(
1348 __isl_keep isl_basic_map *bmap1,
1349 __isl_keep isl_basic_map *bmap2);
1350 int isl_map_is_equal(__isl_keep isl_map *map1,
1351 __isl_keep isl_map *map2);
1352 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1353 __isl_keep isl_map *map2);
1354 int isl_union_map_is_equal(
1355 __isl_keep isl_union_map *umap1,
1356 __isl_keep isl_union_map *umap2);
1358 =item * Disjointness
1360 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1361 __isl_keep isl_set *set2);
1365 int isl_set_is_subset(__isl_keep isl_set *set1,
1366 __isl_keep isl_set *set2);
1367 int isl_set_is_strict_subset(
1368 __isl_keep isl_set *set1,
1369 __isl_keep isl_set *set2);
1370 int isl_union_set_is_subset(
1371 __isl_keep isl_union_set *uset1,
1372 __isl_keep isl_union_set *uset2);
1373 int isl_union_set_is_strict_subset(
1374 __isl_keep isl_union_set *uset1,
1375 __isl_keep isl_union_set *uset2);
1376 int isl_basic_map_is_subset(
1377 __isl_keep isl_basic_map *bmap1,
1378 __isl_keep isl_basic_map *bmap2);
1379 int isl_basic_map_is_strict_subset(
1380 __isl_keep isl_basic_map *bmap1,
1381 __isl_keep isl_basic_map *bmap2);
1382 int isl_map_is_subset(
1383 __isl_keep isl_map *map1,
1384 __isl_keep isl_map *map2);
1385 int isl_map_is_strict_subset(
1386 __isl_keep isl_map *map1,
1387 __isl_keep isl_map *map2);
1388 int isl_union_map_is_subset(
1389 __isl_keep isl_union_map *umap1,
1390 __isl_keep isl_union_map *umap2);
1391 int isl_union_map_is_strict_subset(
1392 __isl_keep isl_union_map *umap1,
1393 __isl_keep isl_union_map *umap2);
1397 =head2 Unary Operations
1403 __isl_give isl_set *isl_set_complement(
1404 __isl_take isl_set *set);
1408 __isl_give isl_basic_map *isl_basic_map_reverse(
1409 __isl_take isl_basic_map *bmap);
1410 __isl_give isl_map *isl_map_reverse(
1411 __isl_take isl_map *map);
1412 __isl_give isl_union_map *isl_union_map_reverse(
1413 __isl_take isl_union_map *umap);
1417 __isl_give isl_basic_set *isl_basic_set_project_out(
1418 __isl_take isl_basic_set *bset,
1419 enum isl_dim_type type, unsigned first, unsigned n);
1420 __isl_give isl_basic_map *isl_basic_map_project_out(
1421 __isl_take isl_basic_map *bmap,
1422 enum isl_dim_type type, unsigned first, unsigned n);
1423 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1424 enum isl_dim_type type, unsigned first, unsigned n);
1425 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1426 enum isl_dim_type type, unsigned first, unsigned n);
1427 __isl_give isl_basic_set *isl_basic_map_domain(
1428 __isl_take isl_basic_map *bmap);
1429 __isl_give isl_basic_set *isl_basic_map_range(
1430 __isl_take isl_basic_map *bmap);
1431 __isl_give isl_set *isl_map_domain(
1432 __isl_take isl_map *bmap);
1433 __isl_give isl_set *isl_map_range(
1434 __isl_take isl_map *map);
1435 __isl_give isl_union_set *isl_union_map_domain(
1436 __isl_take isl_union_map *umap);
1437 __isl_give isl_union_set *isl_union_map_range(
1438 __isl_take isl_union_map *umap);
1440 __isl_give isl_basic_map *isl_basic_map_domain_map(
1441 __isl_take isl_basic_map *bmap);
1442 __isl_give isl_basic_map *isl_basic_map_range_map(
1443 __isl_take isl_basic_map *bmap);
1444 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1445 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1446 __isl_give isl_union_map *isl_union_map_domain_map(
1447 __isl_take isl_union_map *umap);
1448 __isl_give isl_union_map *isl_union_map_range_map(
1449 __isl_take isl_union_map *umap);
1451 The functions above construct a (basic, regular or union) relation
1452 that maps (a wrapped version of) the input relation to its domain or range.
1456 __isl_give isl_set *isl_set_eliminate(
1457 __isl_take isl_set *set, enum isl_dim_type type,
1458 unsigned first, unsigned n);
1460 Eliminate the coefficients for the given dimensions from the constraints,
1461 without removing the dimensions.
1465 __isl_give isl_basic_set *isl_basic_set_fix(
1466 __isl_take isl_basic_set *bset,
1467 enum isl_dim_type type, unsigned pos,
1469 __isl_give isl_basic_set *isl_basic_set_fix_si(
1470 __isl_take isl_basic_set *bset,
1471 enum isl_dim_type type, unsigned pos, int value);
1472 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1473 enum isl_dim_type type, unsigned pos,
1475 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1476 enum isl_dim_type type, unsigned pos, int value);
1477 __isl_give isl_basic_map *isl_basic_map_fix_si(
1478 __isl_take isl_basic_map *bmap,
1479 enum isl_dim_type type, unsigned pos, int value);
1480 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1481 enum isl_dim_type type, unsigned pos, int value);
1483 Intersect the set or relation with the hyperplane where the given
1484 dimension has the fixed given value.
1488 __isl_give isl_map *isl_set_identity(
1489 __isl_take isl_set *set);
1490 __isl_give isl_union_map *isl_union_set_identity(
1491 __isl_take isl_union_set *uset);
1493 Construct an identity relation on the given (union) set.
1497 __isl_give isl_basic_set *isl_basic_map_deltas(
1498 __isl_take isl_basic_map *bmap);
1499 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1500 __isl_give isl_union_set *isl_union_map_deltas(
1501 __isl_take isl_union_map *umap);
1503 These functions return a (basic) set containing the differences
1504 between image elements and corresponding domain elements in the input.
1506 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1507 __isl_take isl_basic_map *bmap);
1508 __isl_give isl_map *isl_map_deltas_map(
1509 __isl_take isl_map *map);
1510 __isl_give isl_union_map *isl_union_map_deltas_map(
1511 __isl_take isl_union_map *umap);
1513 The functions above construct a (basic, regular or union) relation
1514 that maps (a wrapped version of) the input relation to its delta set.
1518 Simplify the representation of a set or relation by trying
1519 to combine pairs of basic sets or relations into a single
1520 basic set or relation.
1522 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1523 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1524 __isl_give isl_union_set *isl_union_set_coalesce(
1525 __isl_take isl_union_set *uset);
1526 __isl_give isl_union_map *isl_union_map_coalesce(
1527 __isl_take isl_union_map *umap);
1529 =item * Detecting equalities
1531 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1532 __isl_take isl_basic_set *bset);
1533 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1534 __isl_take isl_basic_map *bmap);
1535 __isl_give isl_set *isl_set_detect_equalities(
1536 __isl_take isl_set *set);
1537 __isl_give isl_map *isl_map_detect_equalities(
1538 __isl_take isl_map *map);
1539 __isl_give isl_union_set *isl_union_set_detect_equalities(
1540 __isl_take isl_union_set *uset);
1541 __isl_give isl_union_map *isl_union_map_detect_equalities(
1542 __isl_take isl_union_map *umap);
1544 Simplify the representation of a set or relation by detecting implicit
1547 =item * Removing redundant constraints
1549 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1550 __isl_take isl_basic_set *bset);
1551 __isl_give isl_set *isl_set_remove_redundancies(
1552 __isl_take isl_set *set);
1553 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1554 __isl_take isl_basic_map *bmap);
1555 __isl_give isl_map *isl_map_remove_redundancies(
1556 __isl_take isl_map *map);
1560 __isl_give isl_basic_set *isl_set_convex_hull(
1561 __isl_take isl_set *set);
1562 __isl_give isl_basic_map *isl_map_convex_hull(
1563 __isl_take isl_map *map);
1565 If the input set or relation has any existentially quantified
1566 variables, then the result of these operations is currently undefined.
1570 __isl_give isl_basic_set *isl_set_simple_hull(
1571 __isl_take isl_set *set);
1572 __isl_give isl_basic_map *isl_map_simple_hull(
1573 __isl_take isl_map *map);
1574 __isl_give isl_union_map *isl_union_map_simple_hull(
1575 __isl_take isl_union_map *umap);
1577 These functions compute a single basic set or relation
1578 that contains the whole input set or relation.
1579 In particular, the output is described by translates
1580 of the constraints describing the basic sets or relations in the input.
1584 (See \autoref{s:simple hull}.)
1590 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1591 __isl_take isl_basic_set *bset);
1592 __isl_give isl_basic_set *isl_set_affine_hull(
1593 __isl_take isl_set *set);
1594 __isl_give isl_union_set *isl_union_set_affine_hull(
1595 __isl_take isl_union_set *uset);
1596 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1597 __isl_take isl_basic_map *bmap);
1598 __isl_give isl_basic_map *isl_map_affine_hull(
1599 __isl_take isl_map *map);
1600 __isl_give isl_union_map *isl_union_map_affine_hull(
1601 __isl_take isl_union_map *umap);
1603 In case of union sets and relations, the affine hull is computed
1606 =item * Polyhedral hull
1608 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1609 __isl_take isl_set *set);
1610 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1611 __isl_take isl_map *map);
1612 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1613 __isl_take isl_union_set *uset);
1614 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1615 __isl_take isl_union_map *umap);
1617 These functions compute a single basic set or relation
1618 not involving any existentially quantified variables
1619 that contains the whole input set or relation.
1620 In case of union sets and relations, the polyhedral hull is computed
1623 =item * Optimization
1625 #include <isl/ilp.h>
1626 enum isl_lp_result isl_basic_set_max(
1627 __isl_keep isl_basic_set *bset,
1628 __isl_keep isl_aff *obj, isl_int *opt)
1629 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1630 __isl_keep isl_aff *obj, isl_int *opt);
1632 Compute the maximum of the integer affine expression C<obj>
1633 over the points in C<set>, returning the result in C<opt>.
1634 The return value may be one of C<isl_lp_error>,
1635 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1637 =item * Parametric optimization
1639 __isl_give isl_pw_aff *isl_set_dim_max(
1640 __isl_take isl_set *set, int pos);
1642 Compute the maximum of the given set dimension as a function of the
1643 parameters, but independently of the other set dimensions.
1644 For lexicographic optimization, see L<"Lexicographic Optimization">.
1648 The following functions compute either the set of (rational) coefficient
1649 values of valid constraints for the given set or the set of (rational)
1650 values satisfying the constraints with coefficients from the given set.
1651 Internally, these two sets of functions perform essentially the
1652 same operations, except that the set of coefficients is assumed to
1653 be a cone, while the set of values may be any polyhedron.
1654 The current implementation is based on the Farkas lemma and
1655 Fourier-Motzkin elimination, but this may change or be made optional
1656 in future. In particular, future implementations may use different
1657 dualization algorithms or skip the elimination step.
1659 __isl_give isl_basic_set *isl_basic_set_coefficients(
1660 __isl_take isl_basic_set *bset);
1661 __isl_give isl_basic_set *isl_set_coefficients(
1662 __isl_take isl_set *set);
1663 __isl_give isl_union_set *isl_union_set_coefficients(
1664 __isl_take isl_union_set *bset);
1665 __isl_give isl_basic_set *isl_basic_set_solutions(
1666 __isl_take isl_basic_set *bset);
1667 __isl_give isl_basic_set *isl_set_solutions(
1668 __isl_take isl_set *set);
1669 __isl_give isl_union_set *isl_union_set_solutions(
1670 __isl_take isl_union_set *bset);
1674 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1676 __isl_give isl_union_map *isl_union_map_power(
1677 __isl_take isl_union_map *umap, int *exact);
1679 Compute a parametric representation for all positive powers I<k> of C<map>.
1680 The result maps I<k> to a nested relation corresponding to the
1681 I<k>th power of C<map>.
1682 The result may be an overapproximation. If the result is known to be exact,
1683 then C<*exact> is set to C<1>.
1685 =item * Transitive closure
1687 __isl_give isl_map *isl_map_transitive_closure(
1688 __isl_take isl_map *map, int *exact);
1689 __isl_give isl_union_map *isl_union_map_transitive_closure(
1690 __isl_take isl_union_map *umap, int *exact);
1692 Compute the transitive closure of C<map>.
1693 The result may be an overapproximation. If the result is known to be exact,
1694 then C<*exact> is set to C<1>.
1696 =item * Reaching path lengths
1698 __isl_give isl_map *isl_map_reaching_path_lengths(
1699 __isl_take isl_map *map, int *exact);
1701 Compute a relation that maps each element in the range of C<map>
1702 to the lengths of all paths composed of edges in C<map> that
1703 end up in the given element.
1704 The result may be an overapproximation. If the result is known to be exact,
1705 then C<*exact> is set to C<1>.
1706 To compute the I<maximal> path length, the resulting relation
1707 should be postprocessed by C<isl_map_lexmax>.
1708 In particular, if the input relation is a dependence relation
1709 (mapping sources to sinks), then the maximal path length corresponds
1710 to the free schedule.
1711 Note, however, that C<isl_map_lexmax> expects the maximum to be
1712 finite, so if the path lengths are unbounded (possibly due to
1713 the overapproximation), then you will get an error message.
1717 __isl_give isl_basic_set *isl_basic_map_wrap(
1718 __isl_take isl_basic_map *bmap);
1719 __isl_give isl_set *isl_map_wrap(
1720 __isl_take isl_map *map);
1721 __isl_give isl_union_set *isl_union_map_wrap(
1722 __isl_take isl_union_map *umap);
1723 __isl_give isl_basic_map *isl_basic_set_unwrap(
1724 __isl_take isl_basic_set *bset);
1725 __isl_give isl_map *isl_set_unwrap(
1726 __isl_take isl_set *set);
1727 __isl_give isl_union_map *isl_union_set_unwrap(
1728 __isl_take isl_union_set *uset);
1732 Remove any internal structure of domain (and range) of the given
1733 set or relation. If there is any such internal structure in the input,
1734 then the name of the space is also removed.
1736 __isl_give isl_basic_set *isl_basic_set_flatten(
1737 __isl_take isl_basic_set *bset);
1738 __isl_give isl_set *isl_set_flatten(
1739 __isl_take isl_set *set);
1740 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1741 __isl_take isl_basic_map *bmap);
1742 __isl_give isl_map *isl_map_flatten_range(
1743 __isl_take isl_map *map);
1744 __isl_give isl_basic_map *isl_basic_map_flatten(
1745 __isl_take isl_basic_map *bmap);
1746 __isl_give isl_map *isl_map_flatten(
1747 __isl_take isl_map *map);
1749 __isl_give isl_map *isl_set_flatten_map(
1750 __isl_take isl_set *set);
1752 The function above constructs a relation
1753 that maps the input set to a flattened version of the set.
1757 Lift the input set to a space with extra dimensions corresponding
1758 to the existentially quantified variables in the input.
1759 In particular, the result lives in a wrapped map where the domain
1760 is the original space and the range corresponds to the original
1761 existentially quantified variables.
1763 __isl_give isl_basic_set *isl_basic_set_lift(
1764 __isl_take isl_basic_set *bset);
1765 __isl_give isl_set *isl_set_lift(
1766 __isl_take isl_set *set);
1767 __isl_give isl_union_set *isl_union_set_lift(
1768 __isl_take isl_union_set *uset);
1770 =item * Internal Product
1772 __isl_give isl_basic_map *isl_basic_map_zip(
1773 __isl_take isl_basic_map *bmap);
1774 __isl_give isl_map *isl_map_zip(
1775 __isl_take isl_map *map);
1776 __isl_give isl_union_map *isl_union_map_zip(
1777 __isl_take isl_union_map *umap);
1779 Given a relation with nested relations for domain and range,
1780 interchange the range of the domain with the domain of the range.
1782 =item * Aligning parameters
1784 __isl_give isl_set *isl_set_align_params(
1785 __isl_take isl_set *set,
1786 __isl_take isl_dim *model);
1787 __isl_give isl_map *isl_map_align_params(
1788 __isl_take isl_map *map,
1789 __isl_take isl_dim *model);
1791 Change the order of the parameters of the given set or relation
1792 such that the first parameters match those of C<model>.
1793 This may involve the introduction of extra parameters.
1794 All parameters need to be named.
1796 =item * Dimension manipulation
1798 __isl_give isl_set *isl_set_add_dims(
1799 __isl_take isl_set *set,
1800 enum isl_dim_type type, unsigned n);
1801 __isl_give isl_map *isl_map_add_dims(
1802 __isl_take isl_map *map,
1803 enum isl_dim_type type, unsigned n);
1805 It is usually not advisable to directly change the (input or output)
1806 space of a set or a relation as this removes the name and the internal
1807 structure of the space. However, the above functions can be useful
1808 to add new parameters, assuming
1809 C<isl_set_align_params> and C<isl_map_align_params>
1814 =head2 Binary Operations
1816 The two arguments of a binary operation not only need to live
1817 in the same C<isl_ctx>, they currently also need to have
1818 the same (number of) parameters.
1820 =head3 Basic Operations
1824 =item * Intersection
1826 __isl_give isl_basic_set *isl_basic_set_intersect(
1827 __isl_take isl_basic_set *bset1,
1828 __isl_take isl_basic_set *bset2);
1829 __isl_give isl_set *isl_set_intersect(
1830 __isl_take isl_set *set1,
1831 __isl_take isl_set *set2);
1832 __isl_give isl_union_set *isl_union_set_intersect(
1833 __isl_take isl_union_set *uset1,
1834 __isl_take isl_union_set *uset2);
1835 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1836 __isl_take isl_basic_map *bmap,
1837 __isl_take isl_basic_set *bset);
1838 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1839 __isl_take isl_basic_map *bmap,
1840 __isl_take isl_basic_set *bset);
1841 __isl_give isl_basic_map *isl_basic_map_intersect(
1842 __isl_take isl_basic_map *bmap1,
1843 __isl_take isl_basic_map *bmap2);
1844 __isl_give isl_map *isl_map_intersect_domain(
1845 __isl_take isl_map *map,
1846 __isl_take isl_set *set);
1847 __isl_give isl_map *isl_map_intersect_range(
1848 __isl_take isl_map *map,
1849 __isl_take isl_set *set);
1850 __isl_give isl_map *isl_map_intersect(
1851 __isl_take isl_map *map1,
1852 __isl_take isl_map *map2);
1853 __isl_give isl_union_map *isl_union_map_intersect_domain(
1854 __isl_take isl_union_map *umap,
1855 __isl_take isl_union_set *uset);
1856 __isl_give isl_union_map *isl_union_map_intersect_range(
1857 __isl_take isl_union_map *umap,
1858 __isl_take isl_union_set *uset);
1859 __isl_give isl_union_map *isl_union_map_intersect(
1860 __isl_take isl_union_map *umap1,
1861 __isl_take isl_union_map *umap2);
1865 __isl_give isl_set *isl_basic_set_union(
1866 __isl_take isl_basic_set *bset1,
1867 __isl_take isl_basic_set *bset2);
1868 __isl_give isl_map *isl_basic_map_union(
1869 __isl_take isl_basic_map *bmap1,
1870 __isl_take isl_basic_map *bmap2);
1871 __isl_give isl_set *isl_set_union(
1872 __isl_take isl_set *set1,
1873 __isl_take isl_set *set2);
1874 __isl_give isl_map *isl_map_union(
1875 __isl_take isl_map *map1,
1876 __isl_take isl_map *map2);
1877 __isl_give isl_union_set *isl_union_set_union(
1878 __isl_take isl_union_set *uset1,
1879 __isl_take isl_union_set *uset2);
1880 __isl_give isl_union_map *isl_union_map_union(
1881 __isl_take isl_union_map *umap1,
1882 __isl_take isl_union_map *umap2);
1884 =item * Set difference
1886 __isl_give isl_set *isl_set_subtract(
1887 __isl_take isl_set *set1,
1888 __isl_take isl_set *set2);
1889 __isl_give isl_map *isl_map_subtract(
1890 __isl_take isl_map *map1,
1891 __isl_take isl_map *map2);
1892 __isl_give isl_union_set *isl_union_set_subtract(
1893 __isl_take isl_union_set *uset1,
1894 __isl_take isl_union_set *uset2);
1895 __isl_give isl_union_map *isl_union_map_subtract(
1896 __isl_take isl_union_map *umap1,
1897 __isl_take isl_union_map *umap2);
1901 __isl_give isl_basic_set *isl_basic_set_apply(
1902 __isl_take isl_basic_set *bset,
1903 __isl_take isl_basic_map *bmap);
1904 __isl_give isl_set *isl_set_apply(
1905 __isl_take isl_set *set,
1906 __isl_take isl_map *map);
1907 __isl_give isl_union_set *isl_union_set_apply(
1908 __isl_take isl_union_set *uset,
1909 __isl_take isl_union_map *umap);
1910 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1911 __isl_take isl_basic_map *bmap1,
1912 __isl_take isl_basic_map *bmap2);
1913 __isl_give isl_basic_map *isl_basic_map_apply_range(
1914 __isl_take isl_basic_map *bmap1,
1915 __isl_take isl_basic_map *bmap2);
1916 __isl_give isl_map *isl_map_apply_domain(
1917 __isl_take isl_map *map1,
1918 __isl_take isl_map *map2);
1919 __isl_give isl_union_map *isl_union_map_apply_domain(
1920 __isl_take isl_union_map *umap1,
1921 __isl_take isl_union_map *umap2);
1922 __isl_give isl_map *isl_map_apply_range(
1923 __isl_take isl_map *map1,
1924 __isl_take isl_map *map2);
1925 __isl_give isl_union_map *isl_union_map_apply_range(
1926 __isl_take isl_union_map *umap1,
1927 __isl_take isl_union_map *umap2);
1929 =item * Cartesian Product
1931 __isl_give isl_set *isl_set_product(
1932 __isl_take isl_set *set1,
1933 __isl_take isl_set *set2);
1934 __isl_give isl_union_set *isl_union_set_product(
1935 __isl_take isl_union_set *uset1,
1936 __isl_take isl_union_set *uset2);
1937 __isl_give isl_basic_map *isl_basic_map_range_product(
1938 __isl_take isl_basic_map *bmap1,
1939 __isl_take isl_basic_map *bmap2);
1940 __isl_give isl_map *isl_map_range_product(
1941 __isl_take isl_map *map1,
1942 __isl_take isl_map *map2);
1943 __isl_give isl_union_map *isl_union_map_range_product(
1944 __isl_take isl_union_map *umap1,
1945 __isl_take isl_union_map *umap2);
1946 __isl_give isl_map *isl_map_product(
1947 __isl_take isl_map *map1,
1948 __isl_take isl_map *map2);
1949 __isl_give isl_union_map *isl_union_map_product(
1950 __isl_take isl_union_map *umap1,
1951 __isl_take isl_union_map *umap2);
1953 The above functions compute the cross product of the given
1954 sets or relations. The domains and ranges of the results
1955 are wrapped maps between domains and ranges of the inputs.
1956 To obtain a ``flat'' product, use the following functions
1959 __isl_give isl_basic_set *isl_basic_set_flat_product(
1960 __isl_take isl_basic_set *bset1,
1961 __isl_take isl_basic_set *bset2);
1962 __isl_give isl_set *isl_set_flat_product(
1963 __isl_take isl_set *set1,
1964 __isl_take isl_set *set2);
1965 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1966 __isl_take isl_basic_map *bmap1,
1967 __isl_take isl_basic_map *bmap2);
1968 __isl_give isl_map *isl_map_flat_range_product(
1969 __isl_take isl_map *map1,
1970 __isl_take isl_map *map2);
1971 __isl_give isl_union_map *isl_union_map_flat_range_product(
1972 __isl_take isl_union_map *umap1,
1973 __isl_take isl_union_map *umap2);
1974 __isl_give isl_basic_map *isl_basic_map_flat_product(
1975 __isl_take isl_basic_map *bmap1,
1976 __isl_take isl_basic_map *bmap2);
1977 __isl_give isl_map *isl_map_flat_product(
1978 __isl_take isl_map *map1,
1979 __isl_take isl_map *map2);
1981 =item * Simplification
1983 __isl_give isl_basic_set *isl_basic_set_gist(
1984 __isl_take isl_basic_set *bset,
1985 __isl_take isl_basic_set *context);
1986 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1987 __isl_take isl_set *context);
1988 __isl_give isl_union_set *isl_union_set_gist(
1989 __isl_take isl_union_set *uset,
1990 __isl_take isl_union_set *context);
1991 __isl_give isl_basic_map *isl_basic_map_gist(
1992 __isl_take isl_basic_map *bmap,
1993 __isl_take isl_basic_map *context);
1994 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1995 __isl_take isl_map *context);
1996 __isl_give isl_union_map *isl_union_map_gist(
1997 __isl_take isl_union_map *umap,
1998 __isl_take isl_union_map *context);
2000 The gist operation returns a set or relation that has the
2001 same intersection with the context as the input set or relation.
2002 Any implicit equality in the intersection is made explicit in the result,
2003 while all inequalities that are redundant with respect to the intersection
2005 In case of union sets and relations, the gist operation is performed
2010 =head3 Lexicographic Optimization
2012 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2013 the following functions
2014 compute a set that contains the lexicographic minimum or maximum
2015 of the elements in C<set> (or C<bset>) for those values of the parameters
2016 that satisfy C<dom>.
2017 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2018 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2020 In other words, the union of the parameter values
2021 for which the result is non-empty and of C<*empty>
2024 __isl_give isl_set *isl_basic_set_partial_lexmin(
2025 __isl_take isl_basic_set *bset,
2026 __isl_take isl_basic_set *dom,
2027 __isl_give isl_set **empty);
2028 __isl_give isl_set *isl_basic_set_partial_lexmax(
2029 __isl_take isl_basic_set *bset,
2030 __isl_take isl_basic_set *dom,
2031 __isl_give isl_set **empty);
2032 __isl_give isl_set *isl_set_partial_lexmin(
2033 __isl_take isl_set *set, __isl_take isl_set *dom,
2034 __isl_give isl_set **empty);
2035 __isl_give isl_set *isl_set_partial_lexmax(
2036 __isl_take isl_set *set, __isl_take isl_set *dom,
2037 __isl_give isl_set **empty);
2039 Given a (basic) set C<set> (or C<bset>), the following functions simply
2040 return a set containing the lexicographic minimum or maximum
2041 of the elements in C<set> (or C<bset>).
2042 In case of union sets, the optimum is computed per space.
2044 __isl_give isl_set *isl_basic_set_lexmin(
2045 __isl_take isl_basic_set *bset);
2046 __isl_give isl_set *isl_basic_set_lexmax(
2047 __isl_take isl_basic_set *bset);
2048 __isl_give isl_set *isl_set_lexmin(
2049 __isl_take isl_set *set);
2050 __isl_give isl_set *isl_set_lexmax(
2051 __isl_take isl_set *set);
2052 __isl_give isl_union_set *isl_union_set_lexmin(
2053 __isl_take isl_union_set *uset);
2054 __isl_give isl_union_set *isl_union_set_lexmax(
2055 __isl_take isl_union_set *uset);
2057 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2058 the following functions
2059 compute a relation that maps each element of C<dom>
2060 to the single lexicographic minimum or maximum
2061 of the elements that are associated to that same
2062 element in C<map> (or C<bmap>).
2063 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2064 that contains the elements in C<dom> that do not map
2065 to any elements in C<map> (or C<bmap>).
2066 In other words, the union of the domain of the result and of C<*empty>
2069 __isl_give isl_map *isl_basic_map_partial_lexmax(
2070 __isl_take isl_basic_map *bmap,
2071 __isl_take isl_basic_set *dom,
2072 __isl_give isl_set **empty);
2073 __isl_give isl_map *isl_basic_map_partial_lexmin(
2074 __isl_take isl_basic_map *bmap,
2075 __isl_take isl_basic_set *dom,
2076 __isl_give isl_set **empty);
2077 __isl_give isl_map *isl_map_partial_lexmax(
2078 __isl_take isl_map *map, __isl_take isl_set *dom,
2079 __isl_give isl_set **empty);
2080 __isl_give isl_map *isl_map_partial_lexmin(
2081 __isl_take isl_map *map, __isl_take isl_set *dom,
2082 __isl_give isl_set **empty);
2084 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2085 return a map mapping each element in the domain of
2086 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2087 of all elements associated to that element.
2088 In case of union relations, the optimum is computed per space.
2090 __isl_give isl_map *isl_basic_map_lexmin(
2091 __isl_take isl_basic_map *bmap);
2092 __isl_give isl_map *isl_basic_map_lexmax(
2093 __isl_take isl_basic_map *bmap);
2094 __isl_give isl_map *isl_map_lexmin(
2095 __isl_take isl_map *map);
2096 __isl_give isl_map *isl_map_lexmax(
2097 __isl_take isl_map *map);
2098 __isl_give isl_union_map *isl_union_map_lexmin(
2099 __isl_take isl_union_map *umap);
2100 __isl_give isl_union_map *isl_union_map_lexmax(
2101 __isl_take isl_union_map *umap);
2105 Lists are defined over several element types, including
2106 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2107 Here we take lists of C<isl_set>s as an example.
2108 Lists can be created, copied and freed using the following functions.
2110 #include <isl/list.h>
2111 __isl_give isl_set_list *isl_set_list_alloc(
2112 isl_ctx *ctx, int n);
2113 __isl_give isl_set_list *isl_set_list_copy(
2114 __isl_keep isl_set_list *list);
2115 __isl_give isl_set_list *isl_set_list_add(
2116 __isl_take isl_set_list *list,
2117 __isl_take isl_set *el);
2118 void isl_set_list_free(__isl_take isl_set_list *list);
2120 C<isl_set_list_alloc> creates an empty list with a capacity for
2123 Lists can be inspected using the following functions.
2125 #include <isl/list.h>
2126 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2127 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2128 __isl_give struct isl_set *isl_set_list_get_set(
2129 __isl_keep isl_set_list *list, int index);
2130 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2131 int (*fn)(__isl_take struct isl_set *el, void *user),
2134 Lists can be printed using
2136 #include <isl/list.h>
2137 __isl_give isl_printer *isl_printer_print_set_list(
2138 __isl_take isl_printer *p,
2139 __isl_keep isl_set_list *list);
2143 Matrices can be created, copied and freed using the following functions.
2145 #include <isl/mat.h>
2146 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2147 unsigned n_row, unsigned n_col);
2148 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2149 void isl_mat_free(__isl_take isl_mat *mat);
2151 Note that the elements of a newly created matrix may have arbitrary values.
2152 The elements can be changed and inspected using the following functions.
2154 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2155 int isl_mat_rows(__isl_keep isl_mat *mat);
2156 int isl_mat_cols(__isl_keep isl_mat *mat);
2157 int isl_mat_get_element(__isl_keep isl_mat *mat,
2158 int row, int col, isl_int *v);
2159 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2160 int row, int col, isl_int v);
2161 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2162 int row, int col, int v);
2164 C<isl_mat_get_element> will return a negative value if anything went wrong.
2165 In that case, the value of C<*v> is undefined.
2167 The following function can be used to compute the (right) inverse
2168 of a matrix, i.e., a matrix such that the product of the original
2169 and the inverse (in that order) is a multiple of the identity matrix.
2170 The input matrix is assumed to be of full row-rank.
2172 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2174 The following function can be used to compute the (right) kernel
2175 (or null space) of a matrix, i.e., a matrix such that the product of
2176 the original and the kernel (in that order) is the zero matrix.
2178 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2180 =head2 Piecewise Quasi Affine Expressions
2182 The zero quasi affine expression can be created using
2184 __isl_give isl_aff *isl_aff_zero(
2185 __isl_take isl_local_space *ls);
2187 An empty piecewise quasi affine expression (one with no cells)
2188 or a piecewise quasi affine expression with a single cell can
2189 be created using the following functions.
2191 #include <isl/aff.h>
2192 __isl_give isl_pw_aff *isl_pw_aff_empty(
2193 __isl_take isl_dim *dim);
2194 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2195 __isl_take isl_set *set, __isl_take isl_aff *aff);
2197 Quasi affine expressions can be copied and free using
2199 #include <isl/aff.h>
2200 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2201 void *isl_aff_free(__isl_take isl_aff *aff);
2203 __isl_give isl_pw_aff *isl_pw_aff_copy(
2204 __isl_keep isl_pw_aff *pwaff);
2205 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2207 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2208 using the following function. The constraint is required to have
2209 a non-zero coefficient for the specified dimension.
2211 #include <isl/constraint.h>
2212 __isl_give isl_aff *isl_constraint_get_bound(
2213 __isl_keep isl_constraint *constraint,
2214 enum isl_dim_type type, int pos);
2216 Conversely, an equality constraint equating
2217 the affine expression to zero or an inequality constraint enforcing
2218 the affine expression to be non-negative, can be constructed using
2220 __isl_give isl_constraint *isl_equality_from_aff(
2221 __isl_take isl_aff *aff);
2222 __isl_give isl_constraint *isl_inequality_from_aff(
2223 __isl_take isl_aff *aff);
2225 The expression can be inspected using
2227 #include <isl/aff.h>
2228 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2229 int isl_aff_dim(__isl_keep isl_aff *aff,
2230 enum isl_dim_type type);
2231 __isl_give isl_local_space *isl_aff_get_local_space(
2232 __isl_keep isl_aff *aff);
2233 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2234 enum isl_dim_type type, unsigned pos);
2235 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2237 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2238 enum isl_dim_type type, int pos, isl_int *v);
2239 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2241 __isl_give isl_div *isl_aff_get_div(
2242 __isl_keep isl_aff *aff, int pos);
2244 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2245 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2247 It can be modified using
2249 #include <isl/aff.h>
2250 __isl_give isl_aff *isl_aff_set_dim_name(
2251 __isl_take isl_aff *aff, enum isl_dim_type type,
2252 unsigned pos, const char *s);
2253 __isl_give isl_aff *isl_aff_set_constant(
2254 __isl_take isl_aff *aff, isl_int v);
2255 __isl_give isl_aff *isl_aff_set_constant_si(
2256 __isl_take isl_aff *aff, int v);
2257 __isl_give isl_aff *isl_aff_set_coefficient(
2258 __isl_take isl_aff *aff,
2259 enum isl_dim_type type, int pos, isl_int v);
2260 __isl_give isl_aff *isl_aff_set_coefficient_si(
2261 __isl_take isl_aff *aff,
2262 enum isl_dim_type type, int pos, int v);
2263 __isl_give isl_aff *isl_aff_set_denominator(
2264 __isl_take isl_aff *aff, isl_int v);
2266 __isl_give isl_aff *isl_aff_add_constant(
2267 __isl_take isl_aff *aff, isl_int v);
2268 __isl_give isl_aff *isl_aff_add_constant_si(
2269 __isl_take isl_aff *aff, int v);
2270 __isl_give isl_aff *isl_aff_add_coefficient_si(
2271 __isl_take isl_aff *aff,
2272 enum isl_dim_type type, int pos, int v);
2274 Note that the C<set_constant> and C<set_coefficient> functions
2275 set the I<numerator> of the constant or coefficient, while
2276 C<add_constant> and C<add_coefficient> add an integer value to
2277 the possibly rational constant or coefficient.
2279 To check whether an affine expressions is obviously zero
2280 or obviously equal to some other affine expression, use
2282 #include <isl/aff.h>
2283 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2284 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2285 __isl_keep isl_aff *aff2);
2289 #include <isl/aff.h>
2290 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2291 __isl_take isl_aff *aff2);
2292 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2293 __isl_take isl_aff *aff2);
2294 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2295 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2296 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2297 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2299 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2301 __isl_give isl_aff *isl_aff_scale_down_ui(
2302 __isl_take isl_aff *aff, unsigned f);
2304 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2305 __isl_take isl_set *context);
2307 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2308 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2310 The function C<isl_aff_ge_basic_set> returns a basic set
2311 containing those elements in the shared space
2312 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2314 #include <isl/aff.h>
2315 __isl_give isl_pw_aff *isl_pw_aff_max(
2316 __isl_take isl_pw_aff *pwaff1,
2317 __isl_take isl_pw_aff *pwaff2);
2319 The function C<isl_pw_aff_max> computes a piecewise quasi-affine
2320 expression with a domain that is the union of those of C<pwaff1> and
2321 C<pwaff2> and such that on each cell, the quasi-affine expression is
2322 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2323 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2324 associated expression is the defined one.
2326 An expression can be printed using
2328 #include <isl/aff.h>
2329 __isl_give isl_printer *isl_printer_print_aff(
2330 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2332 __isl_give isl_printer *isl_printer_print_pw_aff(
2333 __isl_take isl_printer *p,
2334 __isl_keep isl_pw_aff *pwaff);
2338 Points are elements of a set. They can be used to construct
2339 simple sets (boxes) or they can be used to represent the
2340 individual elements of a set.
2341 The zero point (the origin) can be created using
2343 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2345 The coordinates of a point can be inspected, set and changed
2348 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2349 enum isl_dim_type type, int pos, isl_int *v);
2350 __isl_give isl_point *isl_point_set_coordinate(
2351 __isl_take isl_point *pnt,
2352 enum isl_dim_type type, int pos, isl_int v);
2354 __isl_give isl_point *isl_point_add_ui(
2355 __isl_take isl_point *pnt,
2356 enum isl_dim_type type, int pos, unsigned val);
2357 __isl_give isl_point *isl_point_sub_ui(
2358 __isl_take isl_point *pnt,
2359 enum isl_dim_type type, int pos, unsigned val);
2361 Other properties can be obtained using
2363 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2365 Points can be copied or freed using
2367 __isl_give isl_point *isl_point_copy(
2368 __isl_keep isl_point *pnt);
2369 void isl_point_free(__isl_take isl_point *pnt);
2371 A singleton set can be created from a point using
2373 __isl_give isl_basic_set *isl_basic_set_from_point(
2374 __isl_take isl_point *pnt);
2375 __isl_give isl_set *isl_set_from_point(
2376 __isl_take isl_point *pnt);
2378 and a box can be created from two opposite extremal points using
2380 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2381 __isl_take isl_point *pnt1,
2382 __isl_take isl_point *pnt2);
2383 __isl_give isl_set *isl_set_box_from_points(
2384 __isl_take isl_point *pnt1,
2385 __isl_take isl_point *pnt2);
2387 All elements of a B<bounded> (union) set can be enumerated using
2388 the following functions.
2390 int isl_set_foreach_point(__isl_keep isl_set *set,
2391 int (*fn)(__isl_take isl_point *pnt, void *user),
2393 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2394 int (*fn)(__isl_take isl_point *pnt, void *user),
2397 The function C<fn> is called for each integer point in
2398 C<set> with as second argument the last argument of
2399 the C<isl_set_foreach_point> call. The function C<fn>
2400 should return C<0> on success and C<-1> on failure.
2401 In the latter case, C<isl_set_foreach_point> will stop
2402 enumerating and return C<-1> as well.
2403 If the enumeration is performed successfully and to completion,
2404 then C<isl_set_foreach_point> returns C<0>.
2406 To obtain a single point of a (basic) set, use
2408 __isl_give isl_point *isl_basic_set_sample_point(
2409 __isl_take isl_basic_set *bset);
2410 __isl_give isl_point *isl_set_sample_point(
2411 __isl_take isl_set *set);
2413 If C<set> does not contain any (integer) points, then the
2414 resulting point will be ``void'', a property that can be
2417 int isl_point_is_void(__isl_keep isl_point *pnt);
2419 =head2 Piecewise Quasipolynomials
2421 A piecewise quasipolynomial is a particular kind of function that maps
2422 a parametric point to a rational value.
2423 More specifically, a quasipolynomial is a polynomial expression in greatest
2424 integer parts of affine expressions of parameters and variables.
2425 A piecewise quasipolynomial is a subdivision of a given parametric
2426 domain into disjoint cells with a quasipolynomial associated to
2427 each cell. The value of the piecewise quasipolynomial at a given
2428 point is the value of the quasipolynomial associated to the cell
2429 that contains the point. Outside of the union of cells,
2430 the value is assumed to be zero.
2431 For example, the piecewise quasipolynomial
2433 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2435 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2436 A given piecewise quasipolynomial has a fixed domain dimension.
2437 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2438 defined over different domains.
2439 Piecewise quasipolynomials are mainly used by the C<barvinok>
2440 library for representing the number of elements in a parametric set or map.
2441 For example, the piecewise quasipolynomial above represents
2442 the number of points in the map
2444 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2446 =head3 Printing (Piecewise) Quasipolynomials
2448 Quasipolynomials and piecewise quasipolynomials can be printed
2449 using the following functions.
2451 __isl_give isl_printer *isl_printer_print_qpolynomial(
2452 __isl_take isl_printer *p,
2453 __isl_keep isl_qpolynomial *qp);
2455 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2456 __isl_take isl_printer *p,
2457 __isl_keep isl_pw_qpolynomial *pwqp);
2459 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2460 __isl_take isl_printer *p,
2461 __isl_keep isl_union_pw_qpolynomial *upwqp);
2463 The output format of the printer
2464 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2465 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2467 In case of printing in C<ISL_FORMAT_C>, the user may want
2468 to set the names of all dimensions
2470 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2471 __isl_take isl_qpolynomial *qp,
2472 enum isl_dim_type type, unsigned pos,
2474 __isl_give isl_pw_qpolynomial *
2475 isl_pw_qpolynomial_set_dim_name(
2476 __isl_take isl_pw_qpolynomial *pwqp,
2477 enum isl_dim_type type, unsigned pos,
2480 =head3 Creating New (Piecewise) Quasipolynomials
2482 Some simple quasipolynomials can be created using the following functions.
2483 More complicated quasipolynomials can be created by applying
2484 operations such as addition and multiplication
2485 on the resulting quasipolynomials
2487 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2488 __isl_take isl_dim *dim);
2489 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2490 __isl_take isl_dim *dim);
2491 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2492 __isl_take isl_dim *dim);
2493 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2494 __isl_take isl_dim *dim);
2495 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2496 __isl_take isl_dim *dim);
2497 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2498 __isl_take isl_dim *dim,
2499 const isl_int n, const isl_int d);
2500 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2501 __isl_take isl_div *div);
2502 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2503 __isl_take isl_dim *dim,
2504 enum isl_dim_type type, unsigned pos);
2505 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2506 __isl_take isl_aff *aff);
2508 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2509 with a single cell can be created using the following functions.
2510 Multiple of these single cell piecewise quasipolynomials can
2511 be combined to create more complicated piecewise quasipolynomials.
2513 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2514 __isl_take isl_dim *dim);
2515 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2516 __isl_take isl_set *set,
2517 __isl_take isl_qpolynomial *qp);
2519 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2520 __isl_take isl_dim *dim);
2521 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2522 __isl_take isl_pw_qpolynomial *pwqp);
2523 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2524 __isl_take isl_union_pw_qpolynomial *upwqp,
2525 __isl_take isl_pw_qpolynomial *pwqp);
2527 Quasipolynomials can be copied and freed again using the following
2530 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2531 __isl_keep isl_qpolynomial *qp);
2532 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2534 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2535 __isl_keep isl_pw_qpolynomial *pwqp);
2536 void *isl_pw_qpolynomial_free(
2537 __isl_take isl_pw_qpolynomial *pwqp);
2539 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2540 __isl_keep isl_union_pw_qpolynomial *upwqp);
2541 void isl_union_pw_qpolynomial_free(
2542 __isl_take isl_union_pw_qpolynomial *upwqp);
2544 =head3 Inspecting (Piecewise) Quasipolynomials
2546 To iterate over all piecewise quasipolynomials in a union
2547 piecewise quasipolynomial, use the following function
2549 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2550 __isl_keep isl_union_pw_qpolynomial *upwqp,
2551 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2554 To extract the piecewise quasipolynomial from a union with a given dimension
2557 __isl_give isl_pw_qpolynomial *
2558 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2559 __isl_keep isl_union_pw_qpolynomial *upwqp,
2560 __isl_take isl_dim *dim);
2562 To iterate over the cells in a piecewise quasipolynomial,
2563 use either of the following two functions
2565 int isl_pw_qpolynomial_foreach_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);
2570 int isl_pw_qpolynomial_foreach_lifted_piece(
2571 __isl_keep isl_pw_qpolynomial *pwqp,
2572 int (*fn)(__isl_take isl_set *set,
2573 __isl_take isl_qpolynomial *qp,
2574 void *user), void *user);
2576 As usual, the function C<fn> should return C<0> on success
2577 and C<-1> on failure. The difference between
2578 C<isl_pw_qpolynomial_foreach_piece> and
2579 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2580 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2581 compute unique representations for all existentially quantified
2582 variables and then turn these existentially quantified variables
2583 into extra set variables, adapting the associated quasipolynomial
2584 accordingly. This means that the C<set> passed to C<fn>
2585 will not have any existentially quantified variables, but that
2586 the dimensions of the sets may be different for different
2587 invocations of C<fn>.
2589 To iterate over all terms in a quasipolynomial,
2592 int isl_qpolynomial_foreach_term(
2593 __isl_keep isl_qpolynomial *qp,
2594 int (*fn)(__isl_take isl_term *term,
2595 void *user), void *user);
2597 The terms themselves can be inspected and freed using
2600 unsigned isl_term_dim(__isl_keep isl_term *term,
2601 enum isl_dim_type type);
2602 void isl_term_get_num(__isl_keep isl_term *term,
2604 void isl_term_get_den(__isl_keep isl_term *term,
2606 int isl_term_get_exp(__isl_keep isl_term *term,
2607 enum isl_dim_type type, unsigned pos);
2608 __isl_give isl_div *isl_term_get_div(
2609 __isl_keep isl_term *term, unsigned pos);
2610 void isl_term_free(__isl_take isl_term *term);
2612 Each term is a product of parameters, set variables and
2613 integer divisions. The function C<isl_term_get_exp>
2614 returns the exponent of a given dimensions in the given term.
2615 The C<isl_int>s in the arguments of C<isl_term_get_num>
2616 and C<isl_term_get_den> need to have been initialized
2617 using C<isl_int_init> before calling these functions.
2619 =head3 Properties of (Piecewise) Quasipolynomials
2621 To check whether a quasipolynomial is actually a constant,
2622 use the following function.
2624 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2625 isl_int *n, isl_int *d);
2627 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2628 then the numerator and denominator of the constant
2629 are returned in C<*n> and C<*d>, respectively.
2631 =head3 Operations on (Piecewise) Quasipolynomials
2633 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2634 __isl_take isl_qpolynomial *qp, isl_int v);
2635 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2636 __isl_take isl_qpolynomial *qp);
2637 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2638 __isl_take isl_qpolynomial *qp1,
2639 __isl_take isl_qpolynomial *qp2);
2640 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2641 __isl_take isl_qpolynomial *qp1,
2642 __isl_take isl_qpolynomial *qp2);
2643 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2644 __isl_take isl_qpolynomial *qp1,
2645 __isl_take isl_qpolynomial *qp2);
2646 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2647 __isl_take isl_qpolynomial *qp, unsigned exponent);
2649 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2650 __isl_take isl_pw_qpolynomial *pwqp1,
2651 __isl_take isl_pw_qpolynomial *pwqp2);
2652 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2653 __isl_take isl_pw_qpolynomial *pwqp1,
2654 __isl_take isl_pw_qpolynomial *pwqp2);
2655 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2656 __isl_take isl_pw_qpolynomial *pwqp1,
2657 __isl_take isl_pw_qpolynomial *pwqp2);
2658 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2659 __isl_take isl_pw_qpolynomial *pwqp);
2660 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2661 __isl_take isl_pw_qpolynomial *pwqp1,
2662 __isl_take isl_pw_qpolynomial *pwqp2);
2664 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2665 __isl_take isl_union_pw_qpolynomial *upwqp1,
2666 __isl_take isl_union_pw_qpolynomial *upwqp2);
2667 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2668 __isl_take isl_union_pw_qpolynomial *upwqp1,
2669 __isl_take isl_union_pw_qpolynomial *upwqp2);
2670 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2671 __isl_take isl_union_pw_qpolynomial *upwqp1,
2672 __isl_take isl_union_pw_qpolynomial *upwqp2);
2674 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2675 __isl_take isl_pw_qpolynomial *pwqp,
2676 __isl_take isl_point *pnt);
2678 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2679 __isl_take isl_union_pw_qpolynomial *upwqp,
2680 __isl_take isl_point *pnt);
2682 __isl_give isl_set *isl_pw_qpolynomial_domain(
2683 __isl_take isl_pw_qpolynomial *pwqp);
2684 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2685 __isl_take isl_pw_qpolynomial *pwpq,
2686 __isl_take isl_set *set);
2688 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2689 __isl_take isl_union_pw_qpolynomial *upwqp);
2690 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2691 __isl_take isl_union_pw_qpolynomial *upwpq,
2692 __isl_take isl_union_set *uset);
2694 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2695 __isl_take isl_qpolynomial *qp,
2696 __isl_take isl_dim *model);
2698 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2699 __isl_take isl_union_pw_qpolynomial *upwqp);
2701 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2702 __isl_take isl_qpolynomial *qp,
2703 __isl_take isl_set *context);
2705 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2706 __isl_take isl_pw_qpolynomial *pwqp,
2707 __isl_take isl_set *context);
2709 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2710 __isl_take isl_union_pw_qpolynomial *upwqp,
2711 __isl_take isl_union_set *context);
2713 The gist operation applies the gist operation to each of
2714 the cells in the domain of the input piecewise quasipolynomial.
2715 The context is also exploited
2716 to simplify the quasipolynomials associated to each cell.
2718 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2719 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2720 __isl_give isl_union_pw_qpolynomial *
2721 isl_union_pw_qpolynomial_to_polynomial(
2722 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2724 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2725 the polynomial will be an overapproximation. If C<sign> is negative,
2726 it will be an underapproximation. If C<sign> is zero, the approximation
2727 will lie somewhere in between.
2729 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2731 A piecewise quasipolynomial reduction is a piecewise
2732 reduction (or fold) of quasipolynomials.
2733 In particular, the reduction can be maximum or a minimum.
2734 The objects are mainly used to represent the result of
2735 an upper or lower bound on a quasipolynomial over its domain,
2736 i.e., as the result of the following function.
2738 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2739 __isl_take isl_pw_qpolynomial *pwqp,
2740 enum isl_fold type, int *tight);
2742 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2743 __isl_take isl_union_pw_qpolynomial *upwqp,
2744 enum isl_fold type, int *tight);
2746 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2747 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2748 is the returned bound is known be tight, i.e., for each value
2749 of the parameters there is at least
2750 one element in the domain that reaches the bound.
2751 If the domain of C<pwqp> is not wrapping, then the bound is computed
2752 over all elements in that domain and the result has a purely parametric
2753 domain. If the domain of C<pwqp> is wrapping, then the bound is
2754 computed over the range of the wrapped relation. The domain of the
2755 wrapped relation becomes the domain of the result.
2757 A (piecewise) quasipolynomial reduction can be copied or freed using the
2758 following functions.
2760 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2761 __isl_keep isl_qpolynomial_fold *fold);
2762 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2763 __isl_keep isl_pw_qpolynomial_fold *pwf);
2764 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2765 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2766 void isl_qpolynomial_fold_free(
2767 __isl_take isl_qpolynomial_fold *fold);
2768 void *isl_pw_qpolynomial_fold_free(
2769 __isl_take isl_pw_qpolynomial_fold *pwf);
2770 void isl_union_pw_qpolynomial_fold_free(
2771 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2773 =head3 Printing Piecewise Quasipolynomial Reductions
2775 Piecewise quasipolynomial reductions can be printed
2776 using the following function.
2778 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2779 __isl_take isl_printer *p,
2780 __isl_keep isl_pw_qpolynomial_fold *pwf);
2781 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2782 __isl_take isl_printer *p,
2783 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2785 For C<isl_printer_print_pw_qpolynomial_fold>,
2786 output format of the printer
2787 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2788 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2789 output format of the printer
2790 needs to be set to C<ISL_FORMAT_ISL>.
2791 In case of printing in C<ISL_FORMAT_C>, the user may want
2792 to set the names of all dimensions
2794 __isl_give isl_pw_qpolynomial_fold *
2795 isl_pw_qpolynomial_fold_set_dim_name(
2796 __isl_take isl_pw_qpolynomial_fold *pwf,
2797 enum isl_dim_type type, unsigned pos,
2800 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2802 To iterate over all piecewise quasipolynomial reductions in a union
2803 piecewise quasipolynomial reduction, use the following function
2805 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2806 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2807 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2808 void *user), void *user);
2810 To iterate over the cells in a piecewise quasipolynomial reduction,
2811 use either of the following two functions
2813 int isl_pw_qpolynomial_fold_foreach_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);
2818 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2819 __isl_keep isl_pw_qpolynomial_fold *pwf,
2820 int (*fn)(__isl_take isl_set *set,
2821 __isl_take isl_qpolynomial_fold *fold,
2822 void *user), void *user);
2824 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2825 of the difference between these two functions.
2827 To iterate over all quasipolynomials in a reduction, use
2829 int isl_qpolynomial_fold_foreach_qpolynomial(
2830 __isl_keep isl_qpolynomial_fold *fold,
2831 int (*fn)(__isl_take isl_qpolynomial *qp,
2832 void *user), void *user);
2834 =head3 Operations on Piecewise Quasipolynomial Reductions
2836 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
2837 __isl_take isl_qpolynomial_fold *fold, isl_int v);
2839 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2840 __isl_take isl_pw_qpolynomial_fold *pwf1,
2841 __isl_take isl_pw_qpolynomial_fold *pwf2);
2843 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2844 __isl_take isl_pw_qpolynomial_fold *pwf1,
2845 __isl_take isl_pw_qpolynomial_fold *pwf2);
2847 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2848 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2849 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2851 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2852 __isl_take isl_pw_qpolynomial_fold *pwf,
2853 __isl_take isl_point *pnt);
2855 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2856 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2857 __isl_take isl_point *pnt);
2859 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2860 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2861 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2862 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2863 __isl_take isl_union_set *uset);
2865 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2866 __isl_take isl_pw_qpolynomial_fold *pwf);
2868 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2869 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2871 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2872 __isl_take isl_pw_qpolynomial_fold *pwf,
2873 __isl_take isl_set *context);
2875 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2876 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2877 __isl_take isl_union_set *context);
2879 The gist operation applies the gist operation to each of
2880 the cells in the domain of the input piecewise quasipolynomial reduction.
2881 In future, the operation will also exploit the context
2882 to simplify the quasipolynomial reductions associated to each cell.
2884 __isl_give isl_pw_qpolynomial_fold *
2885 isl_set_apply_pw_qpolynomial_fold(
2886 __isl_take isl_set *set,
2887 __isl_take isl_pw_qpolynomial_fold *pwf,
2889 __isl_give isl_pw_qpolynomial_fold *
2890 isl_map_apply_pw_qpolynomial_fold(
2891 __isl_take isl_map *map,
2892 __isl_take isl_pw_qpolynomial_fold *pwf,
2894 __isl_give isl_union_pw_qpolynomial_fold *
2895 isl_union_set_apply_union_pw_qpolynomial_fold(
2896 __isl_take isl_union_set *uset,
2897 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2899 __isl_give isl_union_pw_qpolynomial_fold *
2900 isl_union_map_apply_union_pw_qpolynomial_fold(
2901 __isl_take isl_union_map *umap,
2902 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2905 The functions taking a map
2906 compose the given map with the given piecewise quasipolynomial reduction.
2907 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2908 over all elements in the intersection of the range of the map
2909 and the domain of the piecewise quasipolynomial reduction
2910 as a function of an element in the domain of the map.
2911 The functions taking a set compute a bound over all elements in the
2912 intersection of the set and the domain of the
2913 piecewise quasipolynomial reduction.
2915 =head2 Dependence Analysis
2917 C<isl> contains specialized functionality for performing
2918 array dataflow analysis. That is, given a I<sink> access relation
2919 and a collection of possible I<source> access relations,
2920 C<isl> can compute relations that describe
2921 for each iteration of the sink access, which iteration
2922 of which of the source access relations was the last
2923 to access the same data element before the given iteration
2925 To compute standard flow dependences, the sink should be
2926 a read, while the sources should be writes.
2927 If any of the source accesses are marked as being I<may>
2928 accesses, then there will be a dependence to the last
2929 I<must> access B<and> to any I<may> access that follows
2930 this last I<must> access.
2931 In particular, if I<all> sources are I<may> accesses,
2932 then memory based dependence analysis is performed.
2933 If, on the other hand, all sources are I<must> accesses,
2934 then value based dependence analysis is performed.
2936 #include <isl/flow.h>
2938 typedef int (*isl_access_level_before)(void *first, void *second);
2940 __isl_give isl_access_info *isl_access_info_alloc(
2941 __isl_take isl_map *sink,
2942 void *sink_user, isl_access_level_before fn,
2944 __isl_give isl_access_info *isl_access_info_add_source(
2945 __isl_take isl_access_info *acc,
2946 __isl_take isl_map *source, int must,
2948 void isl_access_info_free(__isl_take isl_access_info *acc);
2950 __isl_give isl_flow *isl_access_info_compute_flow(
2951 __isl_take isl_access_info *acc);
2953 int isl_flow_foreach(__isl_keep isl_flow *deps,
2954 int (*fn)(__isl_take isl_map *dep, int must,
2955 void *dep_user, void *user),
2957 __isl_give isl_map *isl_flow_get_no_source(
2958 __isl_keep isl_flow *deps, int must);
2959 void isl_flow_free(__isl_take isl_flow *deps);
2961 The function C<isl_access_info_compute_flow> performs the actual
2962 dependence analysis. The other functions are used to construct
2963 the input for this function or to read off the output.
2965 The input is collected in an C<isl_access_info>, which can
2966 be created through a call to C<isl_access_info_alloc>.
2967 The arguments to this functions are the sink access relation
2968 C<sink>, a token C<sink_user> used to identify the sink
2969 access to the user, a callback function for specifying the
2970 relative order of source and sink accesses, and the number
2971 of source access relations that will be added.
2972 The callback function has type C<int (*)(void *first, void *second)>.
2973 The function is called with two user supplied tokens identifying
2974 either a source or the sink and it should return the shared nesting
2975 level and the relative order of the two accesses.
2976 In particular, let I<n> be the number of loops shared by
2977 the two accesses. If C<first> precedes C<second> textually,
2978 then the function should return I<2 * n + 1>; otherwise,
2979 it should return I<2 * n>.
2980 The sources can be added to the C<isl_access_info> by performing
2981 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2982 C<must> indicates whether the source is a I<must> access
2983 or a I<may> access. Note that a multi-valued access relation
2984 should only be marked I<must> if every iteration in the domain
2985 of the relation accesses I<all> elements in its image.
2986 The C<source_user> token is again used to identify
2987 the source access. The range of the source access relation
2988 C<source> should have the same dimension as the range
2989 of the sink access relation.
2990 The C<isl_access_info_free> function should usually not be
2991 called explicitly, because it is called implicitly by
2992 C<isl_access_info_compute_flow>.
2994 The result of the dependence analysis is collected in an
2995 C<isl_flow>. There may be elements of
2996 the sink access for which no preceding source access could be
2997 found or for which all preceding sources are I<may> accesses.
2998 The relations containing these elements can be obtained through
2999 calls to C<isl_flow_get_no_source>, the first with C<must> set
3000 and the second with C<must> unset.
3001 In the case of standard flow dependence analysis,
3002 with the sink a read and the sources I<must> writes,
3003 the first relation corresponds to the reads from uninitialized
3004 array elements and the second relation is empty.
3005 The actual flow dependences can be extracted using
3006 C<isl_flow_foreach>. This function will call the user-specified
3007 callback function C<fn> for each B<non-empty> dependence between
3008 a source and the sink. The callback function is called
3009 with four arguments, the actual flow dependence relation
3010 mapping source iterations to sink iterations, a boolean that
3011 indicates whether it is a I<must> or I<may> dependence, a token
3012 identifying the source and an additional C<void *> with value
3013 equal to the third argument of the C<isl_flow_foreach> call.
3014 A dependence is marked I<must> if it originates from a I<must>
3015 source and if it is not followed by any I<may> sources.
3017 After finishing with an C<isl_flow>, the user should call
3018 C<isl_flow_free> to free all associated memory.
3020 A higher-level interface to dependence analysis is provided
3021 by the following function.
3023 #include <isl/flow.h>
3025 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3026 __isl_take isl_union_map *must_source,
3027 __isl_take isl_union_map *may_source,
3028 __isl_take isl_union_map *schedule,
3029 __isl_give isl_union_map **must_dep,
3030 __isl_give isl_union_map **may_dep,
3031 __isl_give isl_union_map **must_no_source,
3032 __isl_give isl_union_map **may_no_source);
3034 The arrays are identified by the tuple names of the ranges
3035 of the accesses. The iteration domains by the tuple names
3036 of the domains of the accesses and of the schedule.
3037 The relative order of the iteration domains is given by the
3038 schedule. The relations returned through C<must_no_source>
3039 and C<may_no_source> are subsets of C<sink>.
3040 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3041 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3042 any of the other arguments is treated as an error.
3046 B<The functionality described in this section is fairly new
3047 and may be subject to change.>
3049 The following function can be used to compute a schedule
3050 for a union of domains. The generated schedule respects
3051 all C<validity> dependences. That is, all dependence distances
3052 over these dependences in the scheduled space are lexicographically
3053 positive. The generated schedule schedule also tries to minimize
3054 the dependence distances over C<proximity> dependences.
3055 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3056 for groups of domains where the dependence distances have only
3057 non-negative values.
3058 The algorithm used to construct the schedule is similar to that
3061 #include <isl/schedule.h>
3062 __isl_give isl_schedule *isl_union_set_compute_schedule(
3063 __isl_take isl_union_set *domain,
3064 __isl_take isl_union_map *validity,
3065 __isl_take isl_union_map *proximity);
3066 void *isl_schedule_free(__isl_take isl_schedule *sched);
3068 A mapping from the domains to the scheduled space can be obtained
3069 from an C<isl_schedule> using the following function.
3071 __isl_give isl_union_map *isl_schedule_get_map(
3072 __isl_keep isl_schedule *sched);
3074 A representation of the schedule can be printed using
3076 __isl_give isl_printer *isl_printer_print_schedule(
3077 __isl_take isl_printer *p,
3078 __isl_keep isl_schedule *schedule);
3080 A representation of the schedule as a forest of bands can be obtained
3081 using the following function.
3083 __isl_give isl_band_list *isl_schedule_get_band_forest(
3084 __isl_keep isl_schedule *schedule);
3086 The list can be manipulated as explained in L<"Lists">.
3087 The bands inside the list can be copied and freed using the following
3090 #include <isl/band.h>
3091 __isl_give isl_band *isl_band_copy(
3092 __isl_keep isl_band *band);
3093 void *isl_band_free(__isl_take isl_band *band);
3095 Each band contains zero or more scheduling dimensions.
3096 These are referred to as the members of the band.
3097 The section of the schedule that corresponds to the band is
3098 referred to as the partial schedule of the band.
3099 For those nodes that participate in a band, the outer scheduling
3100 dimensions form the prefix schedule, while the inner scheduling
3101 dimensions form the suffix schedule.
3102 That is, if we take a cut of the band forest, then the union of
3103 the concatenations of the prefix, partial and suffix schedules of
3104 each band in the cut is equal to the entire schedule (modulo
3105 some possible padding at the end with zero scheduling dimensions).
3106 The properties of a band can be inspected using the following functions.
3108 #include <isl/band.h>
3109 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3111 int isl_band_has_children(__isl_keep isl_band *band);
3112 __isl_give isl_band_list *isl_band_get_children(
3113 __isl_keep isl_band *band);
3115 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3116 __isl_keep isl_band *band);
3117 __isl_give isl_union_map *isl_band_get_partial_schedule(
3118 __isl_keep isl_band *band);
3119 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3120 __isl_keep isl_band *band);
3122 int isl_band_n_member(__isl_keep isl_band *band);
3123 int isl_band_member_is_zero_distance(
3124 __isl_keep isl_band *band, int pos);
3126 Note that a scheduling dimension is considered to be ``zero
3127 distance'' if it does not carry any proximity dependences
3129 That is, if the dependence distances of the proximity
3130 dependences are all zero in that direction (for fixed
3131 iterations of outer bands).
3133 A representation of the band can be printed using
3135 #include <isl/band.h>
3136 __isl_give isl_printer *isl_printer_print_band(
3137 __isl_take isl_printer *p,
3138 __isl_keep isl_band *band);
3140 Alternatively, the schedule mapping
3141 can also be obtained in pieces using the following functions.
3143 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3144 __isl_give isl_union_map *isl_schedule_get_band(
3145 __isl_keep isl_schedule *sched, unsigned band);
3147 C<isl_schedule_n_band> returns the maximal number of bands.
3148 C<isl_schedule_get_band> returns a union of mappings from a domain to
3149 the band of consecutive schedule dimensions with the given sequence
3150 number for that domain. Bands with the same sequence number but for
3151 different domains may be completely unrelated.
3152 Within a band, the corresponding coordinates of the distance vectors
3153 are all non-negative, assuming that the coordinates for all previous
3156 =head2 Parametric Vertex Enumeration
3158 The parametric vertex enumeration described in this section
3159 is mainly intended to be used internally and by the C<barvinok>
3162 #include <isl/vertices.h>
3163 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3164 __isl_keep isl_basic_set *bset);
3166 The function C<isl_basic_set_compute_vertices> performs the
3167 actual computation of the parametric vertices and the chamber
3168 decomposition and store the result in an C<isl_vertices> object.
3169 This information can be queried by either iterating over all
3170 the vertices or iterating over all the chambers or cells
3171 and then iterating over all vertices that are active on the chamber.
3173 int isl_vertices_foreach_vertex(
3174 __isl_keep isl_vertices *vertices,
3175 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3178 int isl_vertices_foreach_cell(
3179 __isl_keep isl_vertices *vertices,
3180 int (*fn)(__isl_take isl_cell *cell, void *user),
3182 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3183 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3186 Other operations that can be performed on an C<isl_vertices> object are
3189 isl_ctx *isl_vertices_get_ctx(
3190 __isl_keep isl_vertices *vertices);
3191 int isl_vertices_get_n_vertices(
3192 __isl_keep isl_vertices *vertices);
3193 void isl_vertices_free(__isl_take isl_vertices *vertices);
3195 Vertices can be inspected and destroyed using the following functions.
3197 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3198 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3199 __isl_give isl_basic_set *isl_vertex_get_domain(
3200 __isl_keep isl_vertex *vertex);
3201 __isl_give isl_basic_set *isl_vertex_get_expr(
3202 __isl_keep isl_vertex *vertex);
3203 void isl_vertex_free(__isl_take isl_vertex *vertex);
3205 C<isl_vertex_get_expr> returns a singleton parametric set describing
3206 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3208 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3209 B<rational> basic sets, so they should mainly be used for inspection
3210 and should not be mixed with integer sets.
3212 Chambers can be inspected and destroyed using the following functions.
3214 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3215 __isl_give isl_basic_set *isl_cell_get_domain(
3216 __isl_keep isl_cell *cell);
3217 void isl_cell_free(__isl_take isl_cell *cell);
3221 Although C<isl> is mainly meant to be used as a library,
3222 it also contains some basic applications that use some
3223 of the functionality of C<isl>.
3224 The input may be specified in either the L<isl format>
3225 or the L<PolyLib format>.
3227 =head2 C<isl_polyhedron_sample>
3229 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3230 an integer element of the polyhedron, if there is any.
3231 The first column in the output is the denominator and is always
3232 equal to 1. If the polyhedron contains no integer points,
3233 then a vector of length zero is printed.
3237 C<isl_pip> takes the same input as the C<example> program
3238 from the C<piplib> distribution, i.e., a set of constraints
3239 on the parameters, a line containing only -1 and finally a set
3240 of constraints on a parametric polyhedron.
3241 The coefficients of the parameters appear in the last columns
3242 (but before the final constant column).
3243 The output is the lexicographic minimum of the parametric polyhedron.
3244 As C<isl> currently does not have its own output format, the output
3245 is just a dump of the internal state.
3247 =head2 C<isl_polyhedron_minimize>
3249 C<isl_polyhedron_minimize> computes the minimum of some linear
3250 or affine objective function over the integer points in a polyhedron.
3251 If an affine objective function
3252 is given, then the constant should appear in the last column.
3254 =head2 C<isl_polytope_scan>
3256 Given a polytope, C<isl_polytope_scan> prints
3257 all integer points in the polytope.