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_insert_dims(
630 __isl_take isl_local_space *ls,
631 enum isl_dim_type type, unsigned first, unsigned n);
632 __isl_give isl_local_space *isl_local_space_drop_dims(
633 __isl_take isl_local_space *ls,
634 enum isl_dim_type type, unsigned first, unsigned n);
636 =head2 Input and Output
638 C<isl> supports its own input/output format, which is similar
639 to the C<Omega> format, but also supports the C<PolyLib> format
644 The C<isl> format is similar to that of C<Omega>, but has a different
645 syntax for describing the parameters and allows for the definition
646 of an existentially quantified variable as the integer division
647 of an affine expression.
648 For example, the set of integers C<i> between C<0> and C<n>
649 such that C<i % 10 <= 6> can be described as
651 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
654 A set or relation can have several disjuncts, separated
655 by the keyword C<or>. Each disjunct is either a conjunction
656 of constraints or a projection (C<exists>) of a conjunction
657 of constraints. The constraints are separated by the keyword
660 =head3 C<PolyLib> format
662 If the represented set is a union, then the first line
663 contains a single number representing the number of disjuncts.
664 Otherwise, a line containing the number C<1> is optional.
666 Each disjunct is represented by a matrix of constraints.
667 The first line contains two numbers representing
668 the number of rows and columns,
669 where the number of rows is equal to the number of constraints
670 and the number of columns is equal to two plus the number of variables.
671 The following lines contain the actual rows of the constraint matrix.
672 In each row, the first column indicates whether the constraint
673 is an equality (C<0>) or inequality (C<1>). The final column
674 corresponds to the constant term.
676 If the set is parametric, then the coefficients of the parameters
677 appear in the last columns before the constant column.
678 The coefficients of any existentially quantified variables appear
679 between those of the set variables and those of the parameters.
681 =head3 Extended C<PolyLib> format
683 The extended C<PolyLib> format is nearly identical to the
684 C<PolyLib> format. The only difference is that the line
685 containing the number of rows and columns of a constraint matrix
686 also contains four additional numbers:
687 the number of output dimensions, the number of input dimensions,
688 the number of local dimensions (i.e., the number of existentially
689 quantified variables) and the number of parameters.
690 For sets, the number of ``output'' dimensions is equal
691 to the number of set dimensions, while the number of ``input''
697 __isl_give isl_basic_set *isl_basic_set_read_from_file(
698 isl_ctx *ctx, FILE *input, int nparam);
699 __isl_give isl_basic_set *isl_basic_set_read_from_str(
700 isl_ctx *ctx, const char *str, int nparam);
701 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
702 FILE *input, int nparam);
703 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
704 const char *str, int nparam);
707 __isl_give isl_basic_map *isl_basic_map_read_from_file(
708 isl_ctx *ctx, FILE *input, int nparam);
709 __isl_give isl_basic_map *isl_basic_map_read_from_str(
710 isl_ctx *ctx, const char *str, int nparam);
711 __isl_give isl_map *isl_map_read_from_file(
712 struct isl_ctx *ctx, FILE *input, int nparam);
713 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
714 const char *str, int nparam);
716 #include <isl/union_set.h>
717 __isl_give isl_union_set *isl_union_set_read_from_file(
718 isl_ctx *ctx, FILE *input);
719 __isl_give isl_union_set *isl_union_set_read_from_str(
720 struct isl_ctx *ctx, const char *str);
722 #include <isl/union_map.h>
723 __isl_give isl_union_map *isl_union_map_read_from_file(
724 isl_ctx *ctx, FILE *input);
725 __isl_give isl_union_map *isl_union_map_read_from_str(
726 struct isl_ctx *ctx, const char *str);
728 The input format is autodetected and may be either the C<PolyLib> format
729 or the C<isl> format.
730 C<nparam> specifies how many of the final columns in
731 the C<PolyLib> format correspond to parameters.
732 If input is given in the C<isl> format, then the number
733 of parameters needs to be equal to C<nparam>.
734 If C<nparam> is negative, then any number of parameters
735 is accepted in the C<isl> format and zero parameters
736 are assumed in the C<PolyLib> format.
740 Before anything can be printed, an C<isl_printer> needs to
743 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
745 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
746 void isl_printer_free(__isl_take isl_printer *printer);
747 __isl_give char *isl_printer_get_str(
748 __isl_keep isl_printer *printer);
750 The behavior of the printer can be modified in various ways
752 __isl_give isl_printer *isl_printer_set_output_format(
753 __isl_take isl_printer *p, int output_format);
754 __isl_give isl_printer *isl_printer_set_indent(
755 __isl_take isl_printer *p, int indent);
756 __isl_give isl_printer *isl_printer_indent(
757 __isl_take isl_printer *p, int indent);
758 __isl_give isl_printer *isl_printer_set_prefix(
759 __isl_take isl_printer *p, const char *prefix);
760 __isl_give isl_printer *isl_printer_set_suffix(
761 __isl_take isl_printer *p, const char *suffix);
763 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
764 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
765 and defaults to C<ISL_FORMAT_ISL>.
766 Each line in the output is indented by C<indent> (set by
767 C<isl_printer_set_indent>) spaces
768 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
769 In the C<PolyLib> format output,
770 the coefficients of the existentially quantified variables
771 appear between those of the set variables and those
773 The function C<isl_printer_indent> increases the indentation
774 by the specified amount (which may be negative).
776 To actually print something, use
779 __isl_give isl_printer *isl_printer_print_basic_set(
780 __isl_take isl_printer *printer,
781 __isl_keep isl_basic_set *bset);
782 __isl_give isl_printer *isl_printer_print_set(
783 __isl_take isl_printer *printer,
784 __isl_keep isl_set *set);
787 __isl_give isl_printer *isl_printer_print_basic_map(
788 __isl_take isl_printer *printer,
789 __isl_keep isl_basic_map *bmap);
790 __isl_give isl_printer *isl_printer_print_map(
791 __isl_take isl_printer *printer,
792 __isl_keep isl_map *map);
794 #include <isl/union_set.h>
795 __isl_give isl_printer *isl_printer_print_union_set(
796 __isl_take isl_printer *p,
797 __isl_keep isl_union_set *uset);
799 #include <isl/union_map.h>
800 __isl_give isl_printer *isl_printer_print_union_map(
801 __isl_take isl_printer *p,
802 __isl_keep isl_union_map *umap);
804 When called on a file printer, the following function flushes
805 the file. When called on a string printer, the buffer is cleared.
807 __isl_give isl_printer *isl_printer_flush(
808 __isl_take isl_printer *p);
810 =head2 Creating New Sets and Relations
812 C<isl> has functions for creating some standard sets and relations.
816 =item * Empty sets and relations
818 __isl_give isl_basic_set *isl_basic_set_empty(
819 __isl_take isl_dim *dim);
820 __isl_give isl_basic_map *isl_basic_map_empty(
821 __isl_take isl_dim *dim);
822 __isl_give isl_set *isl_set_empty(
823 __isl_take isl_dim *dim);
824 __isl_give isl_map *isl_map_empty(
825 __isl_take isl_dim *dim);
826 __isl_give isl_union_set *isl_union_set_empty(
827 __isl_take isl_dim *dim);
828 __isl_give isl_union_map *isl_union_map_empty(
829 __isl_take isl_dim *dim);
831 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
832 is only used to specify the parameters.
834 =item * Universe sets and relations
836 __isl_give isl_basic_set *isl_basic_set_universe(
837 __isl_take isl_dim *dim);
838 __isl_give isl_basic_map *isl_basic_map_universe(
839 __isl_take isl_dim *dim);
840 __isl_give isl_set *isl_set_universe(
841 __isl_take isl_dim *dim);
842 __isl_give isl_map *isl_map_universe(
843 __isl_take isl_dim *dim);
844 __isl_give isl_union_set *isl_union_set_universe(
845 __isl_take isl_union_set *uset);
846 __isl_give isl_union_map *isl_union_map_universe(
847 __isl_take isl_union_map *umap);
849 The sets and relations constructed by the functions above
850 contain all integer values, while those constructed by the
851 functions below only contain non-negative values.
853 __isl_give isl_basic_set *isl_basic_set_nat_universe(
854 __isl_take isl_dim *dim);
855 __isl_give isl_basic_map *isl_basic_map_nat_universe(
856 __isl_take isl_dim *dim);
857 __isl_give isl_set *isl_set_nat_universe(
858 __isl_take isl_dim *dim);
859 __isl_give isl_map *isl_map_nat_universe(
860 __isl_take isl_dim *dim);
862 =item * Identity relations
864 __isl_give isl_basic_map *isl_basic_map_identity(
865 __isl_take isl_dim *dim);
866 __isl_give isl_map *isl_map_identity(
867 __isl_take isl_dim *dim);
869 The number of input and output dimensions in C<dim> needs
872 =item * Lexicographic order
874 __isl_give isl_map *isl_map_lex_lt(
875 __isl_take isl_dim *set_dim);
876 __isl_give isl_map *isl_map_lex_le(
877 __isl_take isl_dim *set_dim);
878 __isl_give isl_map *isl_map_lex_gt(
879 __isl_take isl_dim *set_dim);
880 __isl_give isl_map *isl_map_lex_ge(
881 __isl_take isl_dim *set_dim);
882 __isl_give isl_map *isl_map_lex_lt_first(
883 __isl_take isl_dim *dim, unsigned n);
884 __isl_give isl_map *isl_map_lex_le_first(
885 __isl_take isl_dim *dim, unsigned n);
886 __isl_give isl_map *isl_map_lex_gt_first(
887 __isl_take isl_dim *dim, unsigned n);
888 __isl_give isl_map *isl_map_lex_ge_first(
889 __isl_take isl_dim *dim, unsigned n);
891 The first four functions take a dimension specification for a B<set>
892 and return relations that express that the elements in the domain
893 are lexicographically less
894 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
895 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
896 than the elements in the range.
897 The last four functions take a dimension specification for a map
898 and return relations that express that the first C<n> dimensions
899 in the domain are lexicographically less
900 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
901 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
902 than the first C<n> dimensions in the range.
906 A basic set or relation can be converted to a set or relation
907 using the following functions.
909 __isl_give isl_set *isl_set_from_basic_set(
910 __isl_take isl_basic_set *bset);
911 __isl_give isl_map *isl_map_from_basic_map(
912 __isl_take isl_basic_map *bmap);
914 Sets and relations can be converted to union sets and relations
915 using the following functions.
917 __isl_give isl_union_map *isl_union_map_from_map(
918 __isl_take isl_map *map);
919 __isl_give isl_union_set *isl_union_set_from_set(
920 __isl_take isl_set *set);
922 Sets and relations can be copied and freed again using the following
925 __isl_give isl_basic_set *isl_basic_set_copy(
926 __isl_keep isl_basic_set *bset);
927 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
928 __isl_give isl_union_set *isl_union_set_copy(
929 __isl_keep isl_union_set *uset);
930 __isl_give isl_basic_map *isl_basic_map_copy(
931 __isl_keep isl_basic_map *bmap);
932 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
933 __isl_give isl_union_map *isl_union_map_copy(
934 __isl_keep isl_union_map *umap);
935 void isl_basic_set_free(__isl_take isl_basic_set *bset);
936 void isl_set_free(__isl_take isl_set *set);
937 void isl_union_set_free(__isl_take isl_union_set *uset);
938 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
939 void isl_map_free(__isl_take isl_map *map);
940 void isl_union_map_free(__isl_take isl_union_map *umap);
942 Other sets and relations can be constructed by starting
943 from a universe set or relation, adding equality and/or
944 inequality constraints and then projecting out the
945 existentially quantified variables, if any.
946 Constraints can be constructed, manipulated and
947 added to (basic) sets and relations using the following functions.
949 #include <isl/constraint.h>
950 __isl_give isl_constraint *isl_equality_alloc(
951 __isl_take isl_dim *dim);
952 __isl_give isl_constraint *isl_inequality_alloc(
953 __isl_take isl_dim *dim);
954 void isl_constraint_set_constant(
955 __isl_keep isl_constraint *constraint, isl_int v);
956 void isl_constraint_set_coefficient(
957 __isl_keep isl_constraint *constraint,
958 enum isl_dim_type type, int pos, isl_int v);
959 __isl_give isl_basic_map *isl_basic_map_add_constraint(
960 __isl_take isl_basic_map *bmap,
961 __isl_take isl_constraint *constraint);
962 __isl_give isl_basic_set *isl_basic_set_add_constraint(
963 __isl_take isl_basic_set *bset,
964 __isl_take isl_constraint *constraint);
965 __isl_give isl_map *isl_map_add_constraint(
966 __isl_take isl_map *map,
967 __isl_take isl_constraint *constraint);
968 __isl_give isl_set *isl_set_add_constraint(
969 __isl_take isl_set *set,
970 __isl_take isl_constraint *constraint);
972 For example, to create a set containing the even integers
973 between 10 and 42, you would use the following code.
977 struct isl_constraint *c;
978 struct isl_basic_set *bset;
981 dim = isl_dim_set_alloc(ctx, 0, 2);
982 bset = isl_basic_set_universe(isl_dim_copy(dim));
984 c = isl_equality_alloc(isl_dim_copy(dim));
985 isl_int_set_si(v, -1);
986 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
987 isl_int_set_si(v, 2);
988 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
989 bset = isl_basic_set_add_constraint(bset, c);
991 c = isl_inequality_alloc(isl_dim_copy(dim));
992 isl_int_set_si(v, -10);
993 isl_constraint_set_constant(c, v);
994 isl_int_set_si(v, 1);
995 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
996 bset = isl_basic_set_add_constraint(bset, c);
998 c = isl_inequality_alloc(dim);
999 isl_int_set_si(v, 42);
1000 isl_constraint_set_constant(c, v);
1001 isl_int_set_si(v, -1);
1002 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1003 bset = isl_basic_set_add_constraint(bset, c);
1005 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1011 struct isl_basic_set *bset;
1012 bset = isl_basic_set_read_from_str(ctx,
1013 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1015 A basic set or relation can also be constructed from two matrices
1016 describing the equalities and the inequalities.
1018 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1019 __isl_take isl_dim *dim,
1020 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1021 enum isl_dim_type c1,
1022 enum isl_dim_type c2, enum isl_dim_type c3,
1023 enum isl_dim_type c4);
1024 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1025 __isl_take isl_dim *dim,
1026 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1027 enum isl_dim_type c1,
1028 enum isl_dim_type c2, enum isl_dim_type c3,
1029 enum isl_dim_type c4, enum isl_dim_type c5);
1031 The C<isl_dim_type> arguments indicate the order in which
1032 different kinds of variables appear in the input matrices
1033 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1034 C<isl_dim_set> and C<isl_dim_div> for sets and
1035 of C<isl_dim_cst>, C<isl_dim_param>,
1036 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1038 A (basic) relation can also be constructed from a (piecewise) affine expression
1039 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1041 __isl_give isl_basic_map *isl_basic_map_from_aff(
1042 __isl_take isl_aff *aff);
1043 __isl_give isl_map *isl_map_from_pw_aff(
1044 __isl_take isl_pw_aff *pwaff);
1045 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1046 __isl_take isl_dim *domain_dim,
1047 __isl_take isl_aff_list *list);
1049 The C<domain_dim> argument describes the domain of the resulting
1050 basic relation. It is required because the C<list> may consist
1051 of zero affine expressions.
1053 =head2 Inspecting Sets and Relations
1055 Usually, the user should not have to care about the actual constraints
1056 of the sets and maps, but should instead apply the abstract operations
1057 explained in the following sections.
1058 Occasionally, however, it may be required to inspect the individual
1059 coefficients of the constraints. This section explains how to do so.
1060 In these cases, it may also be useful to have C<isl> compute
1061 an explicit representation of the existentially quantified variables.
1063 __isl_give isl_set *isl_set_compute_divs(
1064 __isl_take isl_set *set);
1065 __isl_give isl_map *isl_map_compute_divs(
1066 __isl_take isl_map *map);
1067 __isl_give isl_union_set *isl_union_set_compute_divs(
1068 __isl_take isl_union_set *uset);
1069 __isl_give isl_union_map *isl_union_map_compute_divs(
1070 __isl_take isl_union_map *umap);
1072 This explicit representation defines the existentially quantified
1073 variables as integer divisions of the other variables, possibly
1074 including earlier existentially quantified variables.
1075 An explicitly represented existentially quantified variable therefore
1076 has a unique value when the values of the other variables are known.
1077 If, furthermore, the same existentials, i.e., existentials
1078 with the same explicit representations, should appear in the
1079 same order in each of the disjuncts of a set or map, then the user should call
1080 either of the following functions.
1082 __isl_give isl_set *isl_set_align_divs(
1083 __isl_take isl_set *set);
1084 __isl_give isl_map *isl_map_align_divs(
1085 __isl_take isl_map *map);
1087 Alternatively, the existentially quantified variables can be removed
1088 using the following functions, which compute an overapproximation.
1090 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1091 __isl_take isl_basic_set *bset);
1092 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1093 __isl_take isl_basic_map *bmap);
1094 __isl_give isl_set *isl_set_remove_divs(
1095 __isl_take isl_set *set);
1096 __isl_give isl_map *isl_map_remove_divs(
1097 __isl_take isl_map *map);
1099 To iterate over all the sets or maps in a union set or map, use
1101 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1102 int (*fn)(__isl_take isl_set *set, void *user),
1104 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1105 int (*fn)(__isl_take isl_map *map, void *user),
1108 The number of sets or maps in a union set or map can be obtained
1111 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1112 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1114 To extract the set or map from a union with a given dimension
1117 __isl_give isl_set *isl_union_set_extract_set(
1118 __isl_keep isl_union_set *uset,
1119 __isl_take isl_dim *dim);
1120 __isl_give isl_map *isl_union_map_extract_map(
1121 __isl_keep isl_union_map *umap,
1122 __isl_take isl_dim *dim);
1124 To iterate over all the basic sets or maps in a set or map, use
1126 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1127 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1129 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1130 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1133 The callback function C<fn> should return 0 if successful and
1134 -1 if an error occurs. In the latter case, or if any other error
1135 occurs, the above functions will return -1.
1137 It should be noted that C<isl> does not guarantee that
1138 the basic sets or maps passed to C<fn> are disjoint.
1139 If this is required, then the user should call one of
1140 the following functions first.
1142 __isl_give isl_set *isl_set_make_disjoint(
1143 __isl_take isl_set *set);
1144 __isl_give isl_map *isl_map_make_disjoint(
1145 __isl_take isl_map *map);
1147 The number of basic sets in a set can be obtained
1150 int isl_set_n_basic_set(__isl_keep isl_set *set);
1152 To iterate over the constraints of a basic set or map, use
1154 #include <isl/constraint.h>
1156 int isl_basic_map_foreach_constraint(
1157 __isl_keep isl_basic_map *bmap,
1158 int (*fn)(__isl_take isl_constraint *c, void *user),
1160 void isl_constraint_free(struct isl_constraint *c);
1162 Again, the callback function C<fn> should return 0 if successful and
1163 -1 if an error occurs. In the latter case, or if any other error
1164 occurs, the above functions will return -1.
1165 The constraint C<c> represents either an equality or an inequality.
1166 Use the following function to find out whether a constraint
1167 represents an equality. If not, it represents an inequality.
1169 int isl_constraint_is_equality(
1170 __isl_keep isl_constraint *constraint);
1172 The coefficients of the constraints can be inspected using
1173 the following functions.
1175 void isl_constraint_get_constant(
1176 __isl_keep isl_constraint *constraint, isl_int *v);
1177 void isl_constraint_get_coefficient(
1178 __isl_keep isl_constraint *constraint,
1179 enum isl_dim_type type, int pos, isl_int *v);
1180 int isl_constraint_involves_dims(
1181 __isl_keep isl_constraint *constraint,
1182 enum isl_dim_type type, unsigned first, unsigned n);
1184 The explicit representations of the existentially quantified
1185 variables can be inspected using the following functions.
1186 Note that the user is only allowed to use these functions
1187 if the inspected set or map is the result of a call
1188 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1190 __isl_give isl_div *isl_constraint_div(
1191 __isl_keep isl_constraint *constraint, int pos);
1192 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1193 void isl_div_get_constant(__isl_keep isl_div *div,
1195 void isl_div_get_denominator(__isl_keep isl_div *div,
1197 void isl_div_get_coefficient(__isl_keep isl_div *div,
1198 enum isl_dim_type type, int pos, isl_int *v);
1200 To obtain the constraints of a basic set or map in matrix
1201 form, use the following functions.
1203 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1204 __isl_keep isl_basic_set *bset,
1205 enum isl_dim_type c1, enum isl_dim_type c2,
1206 enum isl_dim_type c3, enum isl_dim_type c4);
1207 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1208 __isl_keep isl_basic_set *bset,
1209 enum isl_dim_type c1, enum isl_dim_type c2,
1210 enum isl_dim_type c3, enum isl_dim_type c4);
1211 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1212 __isl_keep isl_basic_map *bmap,
1213 enum isl_dim_type c1,
1214 enum isl_dim_type c2, enum isl_dim_type c3,
1215 enum isl_dim_type c4, enum isl_dim_type c5);
1216 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1217 __isl_keep isl_basic_map *bmap,
1218 enum isl_dim_type c1,
1219 enum isl_dim_type c2, enum isl_dim_type c3,
1220 enum isl_dim_type c4, enum isl_dim_type c5);
1222 The C<isl_dim_type> arguments dictate the order in which
1223 different kinds of variables appear in the resulting matrix
1224 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1225 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1227 The names of the domain and range spaces of a set or relation can be
1228 read off or set using the following functions.
1230 const char *isl_basic_set_get_tuple_name(
1231 __isl_keep isl_basic_set *bset);
1232 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1233 __isl_take isl_basic_set *set, const char *s);
1234 const char *isl_set_get_tuple_name(
1235 __isl_keep isl_set *set);
1236 const char *isl_basic_map_get_tuple_name(
1237 __isl_keep isl_basic_map *bmap,
1238 enum isl_dim_type type);
1239 const char *isl_map_get_tuple_name(
1240 __isl_keep isl_map *map,
1241 enum isl_dim_type type);
1243 As with C<isl_dim_get_tuple_name>, the value returned points to
1244 an internal data structure.
1245 The names of individual dimensions can be read off using
1246 the following functions.
1248 const char *isl_constraint_get_dim_name(
1249 __isl_keep isl_constraint *constraint,
1250 enum isl_dim_type type, unsigned pos);
1251 const char *isl_basic_set_get_dim_name(
1252 __isl_keep isl_basic_set *bset,
1253 enum isl_dim_type type, unsigned pos);
1254 const char *isl_set_get_dim_name(
1255 __isl_keep isl_set *set,
1256 enum isl_dim_type type, unsigned pos);
1257 const char *isl_basic_map_get_dim_name(
1258 __isl_keep isl_basic_map *bmap,
1259 enum isl_dim_type type, unsigned pos);
1260 const char *isl_map_get_dim_name(
1261 __isl_keep isl_map *map,
1262 enum isl_dim_type type, unsigned pos);
1264 These functions are mostly useful to obtain the names
1269 =head3 Unary Properties
1275 The following functions test whether the given set or relation
1276 contains any integer points. The ``plain'' variants do not perform
1277 any computations, but simply check if the given set or relation
1278 is already known to be empty.
1280 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1281 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1282 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1283 int isl_set_is_empty(__isl_keep isl_set *set);
1284 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1285 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1286 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1287 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1288 int isl_map_is_empty(__isl_keep isl_map *map);
1289 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1291 =item * Universality
1293 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1294 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1295 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1297 =item * Single-valuedness
1299 int isl_map_is_single_valued(__isl_keep isl_map *map);
1300 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1304 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1305 int isl_map_is_injective(__isl_keep isl_map *map);
1306 int isl_union_map_plain_is_injective(
1307 __isl_keep isl_union_map *umap);
1308 int isl_union_map_is_injective(
1309 __isl_keep isl_union_map *umap);
1313 int isl_map_is_bijective(__isl_keep isl_map *map);
1314 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1318 The following functions check whether the domain of the given
1319 (basic) set is a wrapped relation.
1321 int isl_basic_set_is_wrapping(
1322 __isl_keep isl_basic_set *bset);
1323 int isl_set_is_wrapping(__isl_keep isl_set *set);
1325 =item * Internal Product
1327 int isl_basic_map_can_zip(
1328 __isl_keep isl_basic_map *bmap);
1329 int isl_map_can_zip(__isl_keep isl_map *map);
1331 Check whether the product of domain and range of the given relation
1333 i.e., whether both domain and range are nested relations.
1337 =head3 Binary Properties
1343 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1344 __isl_keep isl_set *set2);
1345 int isl_set_is_equal(__isl_keep isl_set *set1,
1346 __isl_keep isl_set *set2);
1347 int isl_union_set_is_equal(
1348 __isl_keep isl_union_set *uset1,
1349 __isl_keep isl_union_set *uset2);
1350 int isl_basic_map_is_equal(
1351 __isl_keep isl_basic_map *bmap1,
1352 __isl_keep isl_basic_map *bmap2);
1353 int isl_map_is_equal(__isl_keep isl_map *map1,
1354 __isl_keep isl_map *map2);
1355 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1356 __isl_keep isl_map *map2);
1357 int isl_union_map_is_equal(
1358 __isl_keep isl_union_map *umap1,
1359 __isl_keep isl_union_map *umap2);
1361 =item * Disjointness
1363 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1364 __isl_keep isl_set *set2);
1368 int isl_set_is_subset(__isl_keep isl_set *set1,
1369 __isl_keep isl_set *set2);
1370 int isl_set_is_strict_subset(
1371 __isl_keep isl_set *set1,
1372 __isl_keep isl_set *set2);
1373 int isl_union_set_is_subset(
1374 __isl_keep isl_union_set *uset1,
1375 __isl_keep isl_union_set *uset2);
1376 int isl_union_set_is_strict_subset(
1377 __isl_keep isl_union_set *uset1,
1378 __isl_keep isl_union_set *uset2);
1379 int isl_basic_map_is_subset(
1380 __isl_keep isl_basic_map *bmap1,
1381 __isl_keep isl_basic_map *bmap2);
1382 int isl_basic_map_is_strict_subset(
1383 __isl_keep isl_basic_map *bmap1,
1384 __isl_keep isl_basic_map *bmap2);
1385 int isl_map_is_subset(
1386 __isl_keep isl_map *map1,
1387 __isl_keep isl_map *map2);
1388 int isl_map_is_strict_subset(
1389 __isl_keep isl_map *map1,
1390 __isl_keep isl_map *map2);
1391 int isl_union_map_is_subset(
1392 __isl_keep isl_union_map *umap1,
1393 __isl_keep isl_union_map *umap2);
1394 int isl_union_map_is_strict_subset(
1395 __isl_keep isl_union_map *umap1,
1396 __isl_keep isl_union_map *umap2);
1400 =head2 Unary Operations
1406 __isl_give isl_set *isl_set_complement(
1407 __isl_take isl_set *set);
1411 __isl_give isl_basic_map *isl_basic_map_reverse(
1412 __isl_take isl_basic_map *bmap);
1413 __isl_give isl_map *isl_map_reverse(
1414 __isl_take isl_map *map);
1415 __isl_give isl_union_map *isl_union_map_reverse(
1416 __isl_take isl_union_map *umap);
1420 __isl_give isl_basic_set *isl_basic_set_project_out(
1421 __isl_take isl_basic_set *bset,
1422 enum isl_dim_type type, unsigned first, unsigned n);
1423 __isl_give isl_basic_map *isl_basic_map_project_out(
1424 __isl_take isl_basic_map *bmap,
1425 enum isl_dim_type type, unsigned first, unsigned n);
1426 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1427 enum isl_dim_type type, unsigned first, unsigned n);
1428 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1429 enum isl_dim_type type, unsigned first, unsigned n);
1430 __isl_give isl_basic_set *isl_basic_map_domain(
1431 __isl_take isl_basic_map *bmap);
1432 __isl_give isl_basic_set *isl_basic_map_range(
1433 __isl_take isl_basic_map *bmap);
1434 __isl_give isl_set *isl_map_domain(
1435 __isl_take isl_map *bmap);
1436 __isl_give isl_set *isl_map_range(
1437 __isl_take isl_map *map);
1438 __isl_give isl_union_set *isl_union_map_domain(
1439 __isl_take isl_union_map *umap);
1440 __isl_give isl_union_set *isl_union_map_range(
1441 __isl_take isl_union_map *umap);
1443 __isl_give isl_basic_map *isl_basic_map_domain_map(
1444 __isl_take isl_basic_map *bmap);
1445 __isl_give isl_basic_map *isl_basic_map_range_map(
1446 __isl_take isl_basic_map *bmap);
1447 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1448 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1449 __isl_give isl_union_map *isl_union_map_domain_map(
1450 __isl_take isl_union_map *umap);
1451 __isl_give isl_union_map *isl_union_map_range_map(
1452 __isl_take isl_union_map *umap);
1454 The functions above construct a (basic, regular or union) relation
1455 that maps (a wrapped version of) the input relation to its domain or range.
1459 __isl_give isl_set *isl_set_eliminate(
1460 __isl_take isl_set *set, enum isl_dim_type type,
1461 unsigned first, unsigned n);
1463 Eliminate the coefficients for the given dimensions from the constraints,
1464 without removing the dimensions.
1468 __isl_give isl_basic_set *isl_basic_set_fix(
1469 __isl_take isl_basic_set *bset,
1470 enum isl_dim_type type, unsigned pos,
1472 __isl_give isl_basic_set *isl_basic_set_fix_si(
1473 __isl_take isl_basic_set *bset,
1474 enum isl_dim_type type, unsigned pos, int value);
1475 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1476 enum isl_dim_type type, unsigned pos,
1478 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1479 enum isl_dim_type type, unsigned pos, int value);
1480 __isl_give isl_basic_map *isl_basic_map_fix_si(
1481 __isl_take isl_basic_map *bmap,
1482 enum isl_dim_type type, unsigned pos, int value);
1483 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1484 enum isl_dim_type type, unsigned pos, int value);
1486 Intersect the set or relation with the hyperplane where the given
1487 dimension has the fixed given value.
1491 __isl_give isl_map *isl_set_identity(
1492 __isl_take isl_set *set);
1493 __isl_give isl_union_map *isl_union_set_identity(
1494 __isl_take isl_union_set *uset);
1496 Construct an identity relation on the given (union) set.
1500 __isl_give isl_basic_set *isl_basic_map_deltas(
1501 __isl_take isl_basic_map *bmap);
1502 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1503 __isl_give isl_union_set *isl_union_map_deltas(
1504 __isl_take isl_union_map *umap);
1506 These functions return a (basic) set containing the differences
1507 between image elements and corresponding domain elements in the input.
1509 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1510 __isl_take isl_basic_map *bmap);
1511 __isl_give isl_map *isl_map_deltas_map(
1512 __isl_take isl_map *map);
1513 __isl_give isl_union_map *isl_union_map_deltas_map(
1514 __isl_take isl_union_map *umap);
1516 The functions above construct a (basic, regular or union) relation
1517 that maps (a wrapped version of) the input relation to its delta set.
1521 Simplify the representation of a set or relation by trying
1522 to combine pairs of basic sets or relations into a single
1523 basic set or relation.
1525 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1526 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1527 __isl_give isl_union_set *isl_union_set_coalesce(
1528 __isl_take isl_union_set *uset);
1529 __isl_give isl_union_map *isl_union_map_coalesce(
1530 __isl_take isl_union_map *umap);
1532 =item * Detecting equalities
1534 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1535 __isl_take isl_basic_set *bset);
1536 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1537 __isl_take isl_basic_map *bmap);
1538 __isl_give isl_set *isl_set_detect_equalities(
1539 __isl_take isl_set *set);
1540 __isl_give isl_map *isl_map_detect_equalities(
1541 __isl_take isl_map *map);
1542 __isl_give isl_union_set *isl_union_set_detect_equalities(
1543 __isl_take isl_union_set *uset);
1544 __isl_give isl_union_map *isl_union_map_detect_equalities(
1545 __isl_take isl_union_map *umap);
1547 Simplify the representation of a set or relation by detecting implicit
1550 =item * Removing redundant constraints
1552 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1553 __isl_take isl_basic_set *bset);
1554 __isl_give isl_set *isl_set_remove_redundancies(
1555 __isl_take isl_set *set);
1556 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1557 __isl_take isl_basic_map *bmap);
1558 __isl_give isl_map *isl_map_remove_redundancies(
1559 __isl_take isl_map *map);
1563 __isl_give isl_basic_set *isl_set_convex_hull(
1564 __isl_take isl_set *set);
1565 __isl_give isl_basic_map *isl_map_convex_hull(
1566 __isl_take isl_map *map);
1568 If the input set or relation has any existentially quantified
1569 variables, then the result of these operations is currently undefined.
1573 __isl_give isl_basic_set *isl_set_simple_hull(
1574 __isl_take isl_set *set);
1575 __isl_give isl_basic_map *isl_map_simple_hull(
1576 __isl_take isl_map *map);
1577 __isl_give isl_union_map *isl_union_map_simple_hull(
1578 __isl_take isl_union_map *umap);
1580 These functions compute a single basic set or relation
1581 that contains the whole input set or relation.
1582 In particular, the output is described by translates
1583 of the constraints describing the basic sets or relations in the input.
1587 (See \autoref{s:simple hull}.)
1593 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1594 __isl_take isl_basic_set *bset);
1595 __isl_give isl_basic_set *isl_set_affine_hull(
1596 __isl_take isl_set *set);
1597 __isl_give isl_union_set *isl_union_set_affine_hull(
1598 __isl_take isl_union_set *uset);
1599 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1600 __isl_take isl_basic_map *bmap);
1601 __isl_give isl_basic_map *isl_map_affine_hull(
1602 __isl_take isl_map *map);
1603 __isl_give isl_union_map *isl_union_map_affine_hull(
1604 __isl_take isl_union_map *umap);
1606 In case of union sets and relations, the affine hull is computed
1609 =item * Polyhedral hull
1611 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1612 __isl_take isl_set *set);
1613 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1614 __isl_take isl_map *map);
1615 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1616 __isl_take isl_union_set *uset);
1617 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1618 __isl_take isl_union_map *umap);
1620 These functions compute a single basic set or relation
1621 not involving any existentially quantified variables
1622 that contains the whole input set or relation.
1623 In case of union sets and relations, the polyhedral hull is computed
1626 =item * Optimization
1628 #include <isl/ilp.h>
1629 enum isl_lp_result isl_basic_set_max(
1630 __isl_keep isl_basic_set *bset,
1631 __isl_keep isl_aff *obj, isl_int *opt)
1632 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1633 __isl_keep isl_aff *obj, isl_int *opt);
1635 Compute the maximum of the integer affine expression C<obj>
1636 over the points in C<set>, returning the result in C<opt>.
1637 The return value may be one of C<isl_lp_error>,
1638 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1640 =item * Parametric optimization
1642 __isl_give isl_pw_aff *isl_set_dim_max(
1643 __isl_take isl_set *set, int pos);
1645 Compute the maximum of the given set dimension as a function of the
1646 parameters, but independently of the other set dimensions.
1647 For lexicographic optimization, see L<"Lexicographic Optimization">.
1651 The following functions compute either the set of (rational) coefficient
1652 values of valid constraints for the given set or the set of (rational)
1653 values satisfying the constraints with coefficients from the given set.
1654 Internally, these two sets of functions perform essentially the
1655 same operations, except that the set of coefficients is assumed to
1656 be a cone, while the set of values may be any polyhedron.
1657 The current implementation is based on the Farkas lemma and
1658 Fourier-Motzkin elimination, but this may change or be made optional
1659 in future. In particular, future implementations may use different
1660 dualization algorithms or skip the elimination step.
1662 __isl_give isl_basic_set *isl_basic_set_coefficients(
1663 __isl_take isl_basic_set *bset);
1664 __isl_give isl_basic_set *isl_set_coefficients(
1665 __isl_take isl_set *set);
1666 __isl_give isl_union_set *isl_union_set_coefficients(
1667 __isl_take isl_union_set *bset);
1668 __isl_give isl_basic_set *isl_basic_set_solutions(
1669 __isl_take isl_basic_set *bset);
1670 __isl_give isl_basic_set *isl_set_solutions(
1671 __isl_take isl_set *set);
1672 __isl_give isl_union_set *isl_union_set_solutions(
1673 __isl_take isl_union_set *bset);
1677 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1679 __isl_give isl_union_map *isl_union_map_power(
1680 __isl_take isl_union_map *umap, int *exact);
1682 Compute a parametric representation for all positive powers I<k> of C<map>.
1683 The result maps I<k> to a nested relation corresponding to the
1684 I<k>th power of C<map>.
1685 The result may be an overapproximation. If the result is known to be exact,
1686 then C<*exact> is set to C<1>.
1688 =item * Transitive closure
1690 __isl_give isl_map *isl_map_transitive_closure(
1691 __isl_take isl_map *map, int *exact);
1692 __isl_give isl_union_map *isl_union_map_transitive_closure(
1693 __isl_take isl_union_map *umap, int *exact);
1695 Compute the transitive closure of C<map>.
1696 The result may be an overapproximation. If the result is known to be exact,
1697 then C<*exact> is set to C<1>.
1699 =item * Reaching path lengths
1701 __isl_give isl_map *isl_map_reaching_path_lengths(
1702 __isl_take isl_map *map, int *exact);
1704 Compute a relation that maps each element in the range of C<map>
1705 to the lengths of all paths composed of edges in C<map> that
1706 end up in the given element.
1707 The result may be an overapproximation. If the result is known to be exact,
1708 then C<*exact> is set to C<1>.
1709 To compute the I<maximal> path length, the resulting relation
1710 should be postprocessed by C<isl_map_lexmax>.
1711 In particular, if the input relation is a dependence relation
1712 (mapping sources to sinks), then the maximal path length corresponds
1713 to the free schedule.
1714 Note, however, that C<isl_map_lexmax> expects the maximum to be
1715 finite, so if the path lengths are unbounded (possibly due to
1716 the overapproximation), then you will get an error message.
1720 __isl_give isl_basic_set *isl_basic_map_wrap(
1721 __isl_take isl_basic_map *bmap);
1722 __isl_give isl_set *isl_map_wrap(
1723 __isl_take isl_map *map);
1724 __isl_give isl_union_set *isl_union_map_wrap(
1725 __isl_take isl_union_map *umap);
1726 __isl_give isl_basic_map *isl_basic_set_unwrap(
1727 __isl_take isl_basic_set *bset);
1728 __isl_give isl_map *isl_set_unwrap(
1729 __isl_take isl_set *set);
1730 __isl_give isl_union_map *isl_union_set_unwrap(
1731 __isl_take isl_union_set *uset);
1735 Remove any internal structure of domain (and range) of the given
1736 set or relation. If there is any such internal structure in the input,
1737 then the name of the space is also removed.
1739 __isl_give isl_basic_set *isl_basic_set_flatten(
1740 __isl_take isl_basic_set *bset);
1741 __isl_give isl_set *isl_set_flatten(
1742 __isl_take isl_set *set);
1743 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1744 __isl_take isl_basic_map *bmap);
1745 __isl_give isl_map *isl_map_flatten_range(
1746 __isl_take isl_map *map);
1747 __isl_give isl_basic_map *isl_basic_map_flatten(
1748 __isl_take isl_basic_map *bmap);
1749 __isl_give isl_map *isl_map_flatten(
1750 __isl_take isl_map *map);
1752 __isl_give isl_map *isl_set_flatten_map(
1753 __isl_take isl_set *set);
1755 The function above constructs a relation
1756 that maps the input set to a flattened version of the set.
1760 Lift the input set to a space with extra dimensions corresponding
1761 to the existentially quantified variables in the input.
1762 In particular, the result lives in a wrapped map where the domain
1763 is the original space and the range corresponds to the original
1764 existentially quantified variables.
1766 __isl_give isl_basic_set *isl_basic_set_lift(
1767 __isl_take isl_basic_set *bset);
1768 __isl_give isl_set *isl_set_lift(
1769 __isl_take isl_set *set);
1770 __isl_give isl_union_set *isl_union_set_lift(
1771 __isl_take isl_union_set *uset);
1773 =item * Internal Product
1775 __isl_give isl_basic_map *isl_basic_map_zip(
1776 __isl_take isl_basic_map *bmap);
1777 __isl_give isl_map *isl_map_zip(
1778 __isl_take isl_map *map);
1779 __isl_give isl_union_map *isl_union_map_zip(
1780 __isl_take isl_union_map *umap);
1782 Given a relation with nested relations for domain and range,
1783 interchange the range of the domain with the domain of the range.
1785 =item * Aligning parameters
1787 __isl_give isl_set *isl_set_align_params(
1788 __isl_take isl_set *set,
1789 __isl_take isl_dim *model);
1790 __isl_give isl_map *isl_map_align_params(
1791 __isl_take isl_map *map,
1792 __isl_take isl_dim *model);
1794 Change the order of the parameters of the given set or relation
1795 such that the first parameters match those of C<model>.
1796 This may involve the introduction of extra parameters.
1797 All parameters need to be named.
1799 =item * Dimension manipulation
1801 __isl_give isl_set *isl_set_add_dims(
1802 __isl_take isl_set *set,
1803 enum isl_dim_type type, unsigned n);
1804 __isl_give isl_map *isl_map_add_dims(
1805 __isl_take isl_map *map,
1806 enum isl_dim_type type, unsigned n);
1808 It is usually not advisable to directly change the (input or output)
1809 space of a set or a relation as this removes the name and the internal
1810 structure of the space. However, the above functions can be useful
1811 to add new parameters, assuming
1812 C<isl_set_align_params> and C<isl_map_align_params>
1817 =head2 Binary Operations
1819 The two arguments of a binary operation not only need to live
1820 in the same C<isl_ctx>, they currently also need to have
1821 the same (number of) parameters.
1823 =head3 Basic Operations
1827 =item * Intersection
1829 __isl_give isl_basic_set *isl_basic_set_intersect(
1830 __isl_take isl_basic_set *bset1,
1831 __isl_take isl_basic_set *bset2);
1832 __isl_give isl_set *isl_set_intersect(
1833 __isl_take isl_set *set1,
1834 __isl_take isl_set *set2);
1835 __isl_give isl_union_set *isl_union_set_intersect(
1836 __isl_take isl_union_set *uset1,
1837 __isl_take isl_union_set *uset2);
1838 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1839 __isl_take isl_basic_map *bmap,
1840 __isl_take isl_basic_set *bset);
1841 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1842 __isl_take isl_basic_map *bmap,
1843 __isl_take isl_basic_set *bset);
1844 __isl_give isl_basic_map *isl_basic_map_intersect(
1845 __isl_take isl_basic_map *bmap1,
1846 __isl_take isl_basic_map *bmap2);
1847 __isl_give isl_map *isl_map_intersect_domain(
1848 __isl_take isl_map *map,
1849 __isl_take isl_set *set);
1850 __isl_give isl_map *isl_map_intersect_range(
1851 __isl_take isl_map *map,
1852 __isl_take isl_set *set);
1853 __isl_give isl_map *isl_map_intersect(
1854 __isl_take isl_map *map1,
1855 __isl_take isl_map *map2);
1856 __isl_give isl_union_map *isl_union_map_intersect_domain(
1857 __isl_take isl_union_map *umap,
1858 __isl_take isl_union_set *uset);
1859 __isl_give isl_union_map *isl_union_map_intersect_range(
1860 __isl_take isl_union_map *umap,
1861 __isl_take isl_union_set *uset);
1862 __isl_give isl_union_map *isl_union_map_intersect(
1863 __isl_take isl_union_map *umap1,
1864 __isl_take isl_union_map *umap2);
1868 __isl_give isl_set *isl_basic_set_union(
1869 __isl_take isl_basic_set *bset1,
1870 __isl_take isl_basic_set *bset2);
1871 __isl_give isl_map *isl_basic_map_union(
1872 __isl_take isl_basic_map *bmap1,
1873 __isl_take isl_basic_map *bmap2);
1874 __isl_give isl_set *isl_set_union(
1875 __isl_take isl_set *set1,
1876 __isl_take isl_set *set2);
1877 __isl_give isl_map *isl_map_union(
1878 __isl_take isl_map *map1,
1879 __isl_take isl_map *map2);
1880 __isl_give isl_union_set *isl_union_set_union(
1881 __isl_take isl_union_set *uset1,
1882 __isl_take isl_union_set *uset2);
1883 __isl_give isl_union_map *isl_union_map_union(
1884 __isl_take isl_union_map *umap1,
1885 __isl_take isl_union_map *umap2);
1887 =item * Set difference
1889 __isl_give isl_set *isl_set_subtract(
1890 __isl_take isl_set *set1,
1891 __isl_take isl_set *set2);
1892 __isl_give isl_map *isl_map_subtract(
1893 __isl_take isl_map *map1,
1894 __isl_take isl_map *map2);
1895 __isl_give isl_union_set *isl_union_set_subtract(
1896 __isl_take isl_union_set *uset1,
1897 __isl_take isl_union_set *uset2);
1898 __isl_give isl_union_map *isl_union_map_subtract(
1899 __isl_take isl_union_map *umap1,
1900 __isl_take isl_union_map *umap2);
1904 __isl_give isl_basic_set *isl_basic_set_apply(
1905 __isl_take isl_basic_set *bset,
1906 __isl_take isl_basic_map *bmap);
1907 __isl_give isl_set *isl_set_apply(
1908 __isl_take isl_set *set,
1909 __isl_take isl_map *map);
1910 __isl_give isl_union_set *isl_union_set_apply(
1911 __isl_take isl_union_set *uset,
1912 __isl_take isl_union_map *umap);
1913 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1914 __isl_take isl_basic_map *bmap1,
1915 __isl_take isl_basic_map *bmap2);
1916 __isl_give isl_basic_map *isl_basic_map_apply_range(
1917 __isl_take isl_basic_map *bmap1,
1918 __isl_take isl_basic_map *bmap2);
1919 __isl_give isl_map *isl_map_apply_domain(
1920 __isl_take isl_map *map1,
1921 __isl_take isl_map *map2);
1922 __isl_give isl_union_map *isl_union_map_apply_domain(
1923 __isl_take isl_union_map *umap1,
1924 __isl_take isl_union_map *umap2);
1925 __isl_give isl_map *isl_map_apply_range(
1926 __isl_take isl_map *map1,
1927 __isl_take isl_map *map2);
1928 __isl_give isl_union_map *isl_union_map_apply_range(
1929 __isl_take isl_union_map *umap1,
1930 __isl_take isl_union_map *umap2);
1932 =item * Cartesian Product
1934 __isl_give isl_set *isl_set_product(
1935 __isl_take isl_set *set1,
1936 __isl_take isl_set *set2);
1937 __isl_give isl_union_set *isl_union_set_product(
1938 __isl_take isl_union_set *uset1,
1939 __isl_take isl_union_set *uset2);
1940 __isl_give isl_basic_map *isl_basic_map_range_product(
1941 __isl_take isl_basic_map *bmap1,
1942 __isl_take isl_basic_map *bmap2);
1943 __isl_give isl_map *isl_map_range_product(
1944 __isl_take isl_map *map1,
1945 __isl_take isl_map *map2);
1946 __isl_give isl_union_map *isl_union_map_range_product(
1947 __isl_take isl_union_map *umap1,
1948 __isl_take isl_union_map *umap2);
1949 __isl_give isl_map *isl_map_product(
1950 __isl_take isl_map *map1,
1951 __isl_take isl_map *map2);
1952 __isl_give isl_union_map *isl_union_map_product(
1953 __isl_take isl_union_map *umap1,
1954 __isl_take isl_union_map *umap2);
1956 The above functions compute the cross product of the given
1957 sets or relations. The domains and ranges of the results
1958 are wrapped maps between domains and ranges of the inputs.
1959 To obtain a ``flat'' product, use the following functions
1962 __isl_give isl_basic_set *isl_basic_set_flat_product(
1963 __isl_take isl_basic_set *bset1,
1964 __isl_take isl_basic_set *bset2);
1965 __isl_give isl_set *isl_set_flat_product(
1966 __isl_take isl_set *set1,
1967 __isl_take isl_set *set2);
1968 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1969 __isl_take isl_basic_map *bmap1,
1970 __isl_take isl_basic_map *bmap2);
1971 __isl_give isl_map *isl_map_flat_range_product(
1972 __isl_take isl_map *map1,
1973 __isl_take isl_map *map2);
1974 __isl_give isl_union_map *isl_union_map_flat_range_product(
1975 __isl_take isl_union_map *umap1,
1976 __isl_take isl_union_map *umap2);
1977 __isl_give isl_basic_map *isl_basic_map_flat_product(
1978 __isl_take isl_basic_map *bmap1,
1979 __isl_take isl_basic_map *bmap2);
1980 __isl_give isl_map *isl_map_flat_product(
1981 __isl_take isl_map *map1,
1982 __isl_take isl_map *map2);
1984 =item * Simplification
1986 __isl_give isl_basic_set *isl_basic_set_gist(
1987 __isl_take isl_basic_set *bset,
1988 __isl_take isl_basic_set *context);
1989 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1990 __isl_take isl_set *context);
1991 __isl_give isl_union_set *isl_union_set_gist(
1992 __isl_take isl_union_set *uset,
1993 __isl_take isl_union_set *context);
1994 __isl_give isl_basic_map *isl_basic_map_gist(
1995 __isl_take isl_basic_map *bmap,
1996 __isl_take isl_basic_map *context);
1997 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1998 __isl_take isl_map *context);
1999 __isl_give isl_union_map *isl_union_map_gist(
2000 __isl_take isl_union_map *umap,
2001 __isl_take isl_union_map *context);
2003 The gist operation returns a set or relation that has the
2004 same intersection with the context as the input set or relation.
2005 Any implicit equality in the intersection is made explicit in the result,
2006 while all inequalities that are redundant with respect to the intersection
2008 In case of union sets and relations, the gist operation is performed
2013 =head3 Lexicographic Optimization
2015 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2016 the following functions
2017 compute a set that contains the lexicographic minimum or maximum
2018 of the elements in C<set> (or C<bset>) for those values of the parameters
2019 that satisfy C<dom>.
2020 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2021 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2023 In other words, the union of the parameter values
2024 for which the result is non-empty and of C<*empty>
2027 __isl_give isl_set *isl_basic_set_partial_lexmin(
2028 __isl_take isl_basic_set *bset,
2029 __isl_take isl_basic_set *dom,
2030 __isl_give isl_set **empty);
2031 __isl_give isl_set *isl_basic_set_partial_lexmax(
2032 __isl_take isl_basic_set *bset,
2033 __isl_take isl_basic_set *dom,
2034 __isl_give isl_set **empty);
2035 __isl_give isl_set *isl_set_partial_lexmin(
2036 __isl_take isl_set *set, __isl_take isl_set *dom,
2037 __isl_give isl_set **empty);
2038 __isl_give isl_set *isl_set_partial_lexmax(
2039 __isl_take isl_set *set, __isl_take isl_set *dom,
2040 __isl_give isl_set **empty);
2042 Given a (basic) set C<set> (or C<bset>), the following functions simply
2043 return a set containing the lexicographic minimum or maximum
2044 of the elements in C<set> (or C<bset>).
2045 In case of union sets, the optimum is computed per space.
2047 __isl_give isl_set *isl_basic_set_lexmin(
2048 __isl_take isl_basic_set *bset);
2049 __isl_give isl_set *isl_basic_set_lexmax(
2050 __isl_take isl_basic_set *bset);
2051 __isl_give isl_set *isl_set_lexmin(
2052 __isl_take isl_set *set);
2053 __isl_give isl_set *isl_set_lexmax(
2054 __isl_take isl_set *set);
2055 __isl_give isl_union_set *isl_union_set_lexmin(
2056 __isl_take isl_union_set *uset);
2057 __isl_give isl_union_set *isl_union_set_lexmax(
2058 __isl_take isl_union_set *uset);
2060 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2061 the following functions
2062 compute a relation that maps each element of C<dom>
2063 to the single lexicographic minimum or maximum
2064 of the elements that are associated to that same
2065 element in C<map> (or C<bmap>).
2066 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2067 that contains the elements in C<dom> that do not map
2068 to any elements in C<map> (or C<bmap>).
2069 In other words, the union of the domain of the result and of C<*empty>
2072 __isl_give isl_map *isl_basic_map_partial_lexmax(
2073 __isl_take isl_basic_map *bmap,
2074 __isl_take isl_basic_set *dom,
2075 __isl_give isl_set **empty);
2076 __isl_give isl_map *isl_basic_map_partial_lexmin(
2077 __isl_take isl_basic_map *bmap,
2078 __isl_take isl_basic_set *dom,
2079 __isl_give isl_set **empty);
2080 __isl_give isl_map *isl_map_partial_lexmax(
2081 __isl_take isl_map *map, __isl_take isl_set *dom,
2082 __isl_give isl_set **empty);
2083 __isl_give isl_map *isl_map_partial_lexmin(
2084 __isl_take isl_map *map, __isl_take isl_set *dom,
2085 __isl_give isl_set **empty);
2087 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2088 return a map mapping each element in the domain of
2089 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2090 of all elements associated to that element.
2091 In case of union relations, the optimum is computed per space.
2093 __isl_give isl_map *isl_basic_map_lexmin(
2094 __isl_take isl_basic_map *bmap);
2095 __isl_give isl_map *isl_basic_map_lexmax(
2096 __isl_take isl_basic_map *bmap);
2097 __isl_give isl_map *isl_map_lexmin(
2098 __isl_take isl_map *map);
2099 __isl_give isl_map *isl_map_lexmax(
2100 __isl_take isl_map *map);
2101 __isl_give isl_union_map *isl_union_map_lexmin(
2102 __isl_take isl_union_map *umap);
2103 __isl_give isl_union_map *isl_union_map_lexmax(
2104 __isl_take isl_union_map *umap);
2108 Lists are defined over several element types, including
2109 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2110 Here we take lists of C<isl_set>s as an example.
2111 Lists can be created, copied and freed using the following functions.
2113 #include <isl/list.h>
2114 __isl_give isl_set_list *isl_set_list_alloc(
2115 isl_ctx *ctx, int n);
2116 __isl_give isl_set_list *isl_set_list_copy(
2117 __isl_keep isl_set_list *list);
2118 __isl_give isl_set_list *isl_set_list_add(
2119 __isl_take isl_set_list *list,
2120 __isl_take isl_set *el);
2121 void isl_set_list_free(__isl_take isl_set_list *list);
2123 C<isl_set_list_alloc> creates an empty list with a capacity for
2126 Lists can be inspected using the following functions.
2128 #include <isl/list.h>
2129 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2130 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2131 __isl_give struct isl_set *isl_set_list_get_set(
2132 __isl_keep isl_set_list *list, int index);
2133 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2134 int (*fn)(__isl_take struct isl_set *el, void *user),
2137 Lists can be printed using
2139 #include <isl/list.h>
2140 __isl_give isl_printer *isl_printer_print_set_list(
2141 __isl_take isl_printer *p,
2142 __isl_keep isl_set_list *list);
2146 Matrices can be created, copied and freed using the following functions.
2148 #include <isl/mat.h>
2149 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2150 unsigned n_row, unsigned n_col);
2151 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2152 void isl_mat_free(__isl_take isl_mat *mat);
2154 Note that the elements of a newly created matrix may have arbitrary values.
2155 The elements can be changed and inspected using the following functions.
2157 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2158 int isl_mat_rows(__isl_keep isl_mat *mat);
2159 int isl_mat_cols(__isl_keep isl_mat *mat);
2160 int isl_mat_get_element(__isl_keep isl_mat *mat,
2161 int row, int col, isl_int *v);
2162 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2163 int row, int col, isl_int v);
2164 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2165 int row, int col, int v);
2167 C<isl_mat_get_element> will return a negative value if anything went wrong.
2168 In that case, the value of C<*v> is undefined.
2170 The following function can be used to compute the (right) inverse
2171 of a matrix, i.e., a matrix such that the product of the original
2172 and the inverse (in that order) is a multiple of the identity matrix.
2173 The input matrix is assumed to be of full row-rank.
2175 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2177 The following function can be used to compute the (right) kernel
2178 (or null space) of a matrix, i.e., a matrix such that the product of
2179 the original and the kernel (in that order) is the zero matrix.
2181 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2183 =head2 Piecewise Quasi Affine Expressions
2185 The zero quasi affine expression can be created using
2187 __isl_give isl_aff *isl_aff_zero(
2188 __isl_take isl_local_space *ls);
2190 An empty piecewise quasi affine expression (one with no cells)
2191 or a piecewise quasi affine expression with a single cell can
2192 be created using the following functions.
2194 #include <isl/aff.h>
2195 __isl_give isl_pw_aff *isl_pw_aff_empty(
2196 __isl_take isl_dim *dim);
2197 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2198 __isl_take isl_set *set, __isl_take isl_aff *aff);
2200 Quasi affine expressions can be copied and free using
2202 #include <isl/aff.h>
2203 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2204 void *isl_aff_free(__isl_take isl_aff *aff);
2206 __isl_give isl_pw_aff *isl_pw_aff_copy(
2207 __isl_keep isl_pw_aff *pwaff);
2208 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2210 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2211 using the following function. The constraint is required to have
2212 a non-zero coefficient for the specified dimension.
2214 #include <isl/constraint.h>
2215 __isl_give isl_aff *isl_constraint_get_bound(
2216 __isl_keep isl_constraint *constraint,
2217 enum isl_dim_type type, int pos);
2219 Conversely, an equality constraint equating
2220 the affine expression to zero or an inequality constraint enforcing
2221 the affine expression to be non-negative, can be constructed using
2223 __isl_give isl_constraint *isl_equality_from_aff(
2224 __isl_take isl_aff *aff);
2225 __isl_give isl_constraint *isl_inequality_from_aff(
2226 __isl_take isl_aff *aff);
2228 The expression can be inspected using
2230 #include <isl/aff.h>
2231 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2232 int isl_aff_dim(__isl_keep isl_aff *aff,
2233 enum isl_dim_type type);
2234 __isl_give isl_local_space *isl_aff_get_local_space(
2235 __isl_keep isl_aff *aff);
2236 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2237 enum isl_dim_type type, unsigned pos);
2238 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2240 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2241 enum isl_dim_type type, int pos, isl_int *v);
2242 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2244 __isl_give isl_div *isl_aff_get_div(
2245 __isl_keep isl_aff *aff, int pos);
2247 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2248 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2249 enum isl_dim_type type);
2250 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2252 It can be modified using
2254 #include <isl/aff.h>
2255 __isl_give isl_aff *isl_aff_set_dim_name(
2256 __isl_take isl_aff *aff, enum isl_dim_type type,
2257 unsigned pos, const char *s);
2258 __isl_give isl_aff *isl_aff_set_constant(
2259 __isl_take isl_aff *aff, isl_int v);
2260 __isl_give isl_aff *isl_aff_set_constant_si(
2261 __isl_take isl_aff *aff, int v);
2262 __isl_give isl_aff *isl_aff_set_coefficient(
2263 __isl_take isl_aff *aff,
2264 enum isl_dim_type type, int pos, isl_int v);
2265 __isl_give isl_aff *isl_aff_set_coefficient_si(
2266 __isl_take isl_aff *aff,
2267 enum isl_dim_type type, int pos, int v);
2268 __isl_give isl_aff *isl_aff_set_denominator(
2269 __isl_take isl_aff *aff, isl_int v);
2271 __isl_give isl_aff *isl_aff_add_constant(
2272 __isl_take isl_aff *aff, isl_int v);
2273 __isl_give isl_aff *isl_aff_add_constant_si(
2274 __isl_take isl_aff *aff, int v);
2275 __isl_give isl_aff *isl_aff_add_coefficient_si(
2276 __isl_take isl_aff *aff,
2277 enum isl_dim_type type, int pos, int v);
2279 Note that the C<set_constant> and C<set_coefficient> functions
2280 set the I<numerator> of the constant or coefficient, while
2281 C<add_constant> and C<add_coefficient> add an integer value to
2282 the possibly rational constant or coefficient.
2284 To check whether an affine expressions is obviously zero
2285 or obviously equal to some other affine expression, use
2287 #include <isl/aff.h>
2288 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2289 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2290 __isl_keep isl_aff *aff2);
2294 #include <isl/aff.h>
2295 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2296 __isl_take isl_aff *aff2);
2297 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2298 __isl_take isl_aff *aff2);
2299 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2300 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2301 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2302 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2304 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2306 __isl_give isl_aff *isl_aff_scale_down_ui(
2307 __isl_take isl_aff *aff, unsigned f);
2309 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2310 __isl_take isl_pw_aff *pwqp);
2312 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2313 __isl_take isl_set *context);
2314 __isl_give isl_pw_aff *isl_pw_aff_gist(
2315 __isl_take isl_pw_aff *pwaff,
2316 __isl_take isl_set *context);
2318 __isl_give isl_set *isl_pw_aff_domain(
2319 __isl_take isl_pw_aff *pwaff);
2321 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2322 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2324 The function C<isl_aff_ge_basic_set> returns a basic set
2325 containing those elements in the shared space
2326 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2328 #include <isl/aff.h>
2329 __isl_give isl_pw_aff *isl_pw_aff_max(
2330 __isl_take isl_pw_aff *pwaff1,
2331 __isl_take isl_pw_aff *pwaff2);
2333 The function C<isl_pw_aff_max> computes a piecewise quasi-affine
2334 expression with a domain that is the union of those of C<pwaff1> and
2335 C<pwaff2> and such that on each cell, the quasi-affine expression is
2336 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2337 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2338 associated expression is the defined one.
2340 An expression can be printed using
2342 #include <isl/aff.h>
2343 __isl_give isl_printer *isl_printer_print_aff(
2344 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2346 __isl_give isl_printer *isl_printer_print_pw_aff(
2347 __isl_take isl_printer *p,
2348 __isl_keep isl_pw_aff *pwaff);
2352 Points are elements of a set. They can be used to construct
2353 simple sets (boxes) or they can be used to represent the
2354 individual elements of a set.
2355 The zero point (the origin) can be created using
2357 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2359 The coordinates of a point can be inspected, set and changed
2362 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2363 enum isl_dim_type type, int pos, isl_int *v);
2364 __isl_give isl_point *isl_point_set_coordinate(
2365 __isl_take isl_point *pnt,
2366 enum isl_dim_type type, int pos, isl_int v);
2368 __isl_give isl_point *isl_point_add_ui(
2369 __isl_take isl_point *pnt,
2370 enum isl_dim_type type, int pos, unsigned val);
2371 __isl_give isl_point *isl_point_sub_ui(
2372 __isl_take isl_point *pnt,
2373 enum isl_dim_type type, int pos, unsigned val);
2375 Other properties can be obtained using
2377 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2379 Points can be copied or freed using
2381 __isl_give isl_point *isl_point_copy(
2382 __isl_keep isl_point *pnt);
2383 void isl_point_free(__isl_take isl_point *pnt);
2385 A singleton set can be created from a point using
2387 __isl_give isl_basic_set *isl_basic_set_from_point(
2388 __isl_take isl_point *pnt);
2389 __isl_give isl_set *isl_set_from_point(
2390 __isl_take isl_point *pnt);
2392 and a box can be created from two opposite extremal points using
2394 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2395 __isl_take isl_point *pnt1,
2396 __isl_take isl_point *pnt2);
2397 __isl_give isl_set *isl_set_box_from_points(
2398 __isl_take isl_point *pnt1,
2399 __isl_take isl_point *pnt2);
2401 All elements of a B<bounded> (union) set can be enumerated using
2402 the following functions.
2404 int isl_set_foreach_point(__isl_keep isl_set *set,
2405 int (*fn)(__isl_take isl_point *pnt, void *user),
2407 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2408 int (*fn)(__isl_take isl_point *pnt, void *user),
2411 The function C<fn> is called for each integer point in
2412 C<set> with as second argument the last argument of
2413 the C<isl_set_foreach_point> call. The function C<fn>
2414 should return C<0> on success and C<-1> on failure.
2415 In the latter case, C<isl_set_foreach_point> will stop
2416 enumerating and return C<-1> as well.
2417 If the enumeration is performed successfully and to completion,
2418 then C<isl_set_foreach_point> returns C<0>.
2420 To obtain a single point of a (basic) set, use
2422 __isl_give isl_point *isl_basic_set_sample_point(
2423 __isl_take isl_basic_set *bset);
2424 __isl_give isl_point *isl_set_sample_point(
2425 __isl_take isl_set *set);
2427 If C<set> does not contain any (integer) points, then the
2428 resulting point will be ``void'', a property that can be
2431 int isl_point_is_void(__isl_keep isl_point *pnt);
2433 =head2 Piecewise Quasipolynomials
2435 A piecewise quasipolynomial is a particular kind of function that maps
2436 a parametric point to a rational value.
2437 More specifically, a quasipolynomial is a polynomial expression in greatest
2438 integer parts of affine expressions of parameters and variables.
2439 A piecewise quasipolynomial is a subdivision of a given parametric
2440 domain into disjoint cells with a quasipolynomial associated to
2441 each cell. The value of the piecewise quasipolynomial at a given
2442 point is the value of the quasipolynomial associated to the cell
2443 that contains the point. Outside of the union of cells,
2444 the value is assumed to be zero.
2445 For example, the piecewise quasipolynomial
2447 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2449 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2450 A given piecewise quasipolynomial has a fixed domain dimension.
2451 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2452 defined over different domains.
2453 Piecewise quasipolynomials are mainly used by the C<barvinok>
2454 library for representing the number of elements in a parametric set or map.
2455 For example, the piecewise quasipolynomial above represents
2456 the number of points in the map
2458 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2460 =head3 Printing (Piecewise) Quasipolynomials
2462 Quasipolynomials and piecewise quasipolynomials can be printed
2463 using the following functions.
2465 __isl_give isl_printer *isl_printer_print_qpolynomial(
2466 __isl_take isl_printer *p,
2467 __isl_keep isl_qpolynomial *qp);
2469 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2470 __isl_take isl_printer *p,
2471 __isl_keep isl_pw_qpolynomial *pwqp);
2473 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2474 __isl_take isl_printer *p,
2475 __isl_keep isl_union_pw_qpolynomial *upwqp);
2477 The output format of the printer
2478 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2479 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2481 In case of printing in C<ISL_FORMAT_C>, the user may want
2482 to set the names of all dimensions
2484 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2485 __isl_take isl_qpolynomial *qp,
2486 enum isl_dim_type type, unsigned pos,
2488 __isl_give isl_pw_qpolynomial *
2489 isl_pw_qpolynomial_set_dim_name(
2490 __isl_take isl_pw_qpolynomial *pwqp,
2491 enum isl_dim_type type, unsigned pos,
2494 =head3 Creating New (Piecewise) Quasipolynomials
2496 Some simple quasipolynomials can be created using the following functions.
2497 More complicated quasipolynomials can be created by applying
2498 operations such as addition and multiplication
2499 on the resulting quasipolynomials
2501 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2502 __isl_take isl_dim *dim);
2503 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2504 __isl_take isl_dim *dim);
2505 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2506 __isl_take isl_dim *dim);
2507 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2508 __isl_take isl_dim *dim);
2509 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2510 __isl_take isl_dim *dim);
2511 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2512 __isl_take isl_dim *dim,
2513 const isl_int n, const isl_int d);
2514 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2515 __isl_take isl_div *div);
2516 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2517 __isl_take isl_dim *dim,
2518 enum isl_dim_type type, unsigned pos);
2519 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2520 __isl_take isl_aff *aff);
2522 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2523 with a single cell can be created using the following functions.
2524 Multiple of these single cell piecewise quasipolynomials can
2525 be combined to create more complicated piecewise quasipolynomials.
2527 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2528 __isl_take isl_dim *dim);
2529 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2530 __isl_take isl_set *set,
2531 __isl_take isl_qpolynomial *qp);
2533 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2534 __isl_take isl_dim *dim);
2535 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2536 __isl_take isl_pw_qpolynomial *pwqp);
2537 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2538 __isl_take isl_union_pw_qpolynomial *upwqp,
2539 __isl_take isl_pw_qpolynomial *pwqp);
2541 Quasipolynomials can be copied and freed again using the following
2544 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2545 __isl_keep isl_qpolynomial *qp);
2546 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2548 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2549 __isl_keep isl_pw_qpolynomial *pwqp);
2550 void *isl_pw_qpolynomial_free(
2551 __isl_take isl_pw_qpolynomial *pwqp);
2553 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2554 __isl_keep isl_union_pw_qpolynomial *upwqp);
2555 void isl_union_pw_qpolynomial_free(
2556 __isl_take isl_union_pw_qpolynomial *upwqp);
2558 =head3 Inspecting (Piecewise) Quasipolynomials
2560 To iterate over all piecewise quasipolynomials in a union
2561 piecewise quasipolynomial, use the following function
2563 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2564 __isl_keep isl_union_pw_qpolynomial *upwqp,
2565 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2568 To extract the piecewise quasipolynomial from a union with a given dimension
2571 __isl_give isl_pw_qpolynomial *
2572 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2573 __isl_keep isl_union_pw_qpolynomial *upwqp,
2574 __isl_take isl_dim *dim);
2576 To iterate over the cells in a piecewise quasipolynomial,
2577 use either of the following two functions
2579 int isl_pw_qpolynomial_foreach_piece(
2580 __isl_keep isl_pw_qpolynomial *pwqp,
2581 int (*fn)(__isl_take isl_set *set,
2582 __isl_take isl_qpolynomial *qp,
2583 void *user), void *user);
2584 int isl_pw_qpolynomial_foreach_lifted_piece(
2585 __isl_keep isl_pw_qpolynomial *pwqp,
2586 int (*fn)(__isl_take isl_set *set,
2587 __isl_take isl_qpolynomial *qp,
2588 void *user), void *user);
2590 As usual, the function C<fn> should return C<0> on success
2591 and C<-1> on failure. The difference between
2592 C<isl_pw_qpolynomial_foreach_piece> and
2593 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2594 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2595 compute unique representations for all existentially quantified
2596 variables and then turn these existentially quantified variables
2597 into extra set variables, adapting the associated quasipolynomial
2598 accordingly. This means that the C<set> passed to C<fn>
2599 will not have any existentially quantified variables, but that
2600 the dimensions of the sets may be different for different
2601 invocations of C<fn>.
2603 To iterate over all terms in a quasipolynomial,
2606 int isl_qpolynomial_foreach_term(
2607 __isl_keep isl_qpolynomial *qp,
2608 int (*fn)(__isl_take isl_term *term,
2609 void *user), void *user);
2611 The terms themselves can be inspected and freed using
2614 unsigned isl_term_dim(__isl_keep isl_term *term,
2615 enum isl_dim_type type);
2616 void isl_term_get_num(__isl_keep isl_term *term,
2618 void isl_term_get_den(__isl_keep isl_term *term,
2620 int isl_term_get_exp(__isl_keep isl_term *term,
2621 enum isl_dim_type type, unsigned pos);
2622 __isl_give isl_div *isl_term_get_div(
2623 __isl_keep isl_term *term, unsigned pos);
2624 void isl_term_free(__isl_take isl_term *term);
2626 Each term is a product of parameters, set variables and
2627 integer divisions. The function C<isl_term_get_exp>
2628 returns the exponent of a given dimensions in the given term.
2629 The C<isl_int>s in the arguments of C<isl_term_get_num>
2630 and C<isl_term_get_den> need to have been initialized
2631 using C<isl_int_init> before calling these functions.
2633 =head3 Properties of (Piecewise) Quasipolynomials
2635 To check whether a quasipolynomial is actually a constant,
2636 use the following function.
2638 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2639 isl_int *n, isl_int *d);
2641 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2642 then the numerator and denominator of the constant
2643 are returned in C<*n> and C<*d>, respectively.
2645 =head3 Operations on (Piecewise) Quasipolynomials
2647 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2648 __isl_take isl_qpolynomial *qp, isl_int v);
2649 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2650 __isl_take isl_qpolynomial *qp);
2651 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2652 __isl_take isl_qpolynomial *qp1,
2653 __isl_take isl_qpolynomial *qp2);
2654 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2655 __isl_take isl_qpolynomial *qp1,
2656 __isl_take isl_qpolynomial *qp2);
2657 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2658 __isl_take isl_qpolynomial *qp1,
2659 __isl_take isl_qpolynomial *qp2);
2660 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2661 __isl_take isl_qpolynomial *qp, unsigned exponent);
2663 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2664 __isl_take isl_pw_qpolynomial *pwqp1,
2665 __isl_take isl_pw_qpolynomial *pwqp2);
2666 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2667 __isl_take isl_pw_qpolynomial *pwqp1,
2668 __isl_take isl_pw_qpolynomial *pwqp2);
2669 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2670 __isl_take isl_pw_qpolynomial *pwqp1,
2671 __isl_take isl_pw_qpolynomial *pwqp2);
2672 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2673 __isl_take isl_pw_qpolynomial *pwqp);
2674 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2675 __isl_take isl_pw_qpolynomial *pwqp1,
2676 __isl_take isl_pw_qpolynomial *pwqp2);
2678 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2679 __isl_take isl_union_pw_qpolynomial *upwqp1,
2680 __isl_take isl_union_pw_qpolynomial *upwqp2);
2681 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2682 __isl_take isl_union_pw_qpolynomial *upwqp1,
2683 __isl_take isl_union_pw_qpolynomial *upwqp2);
2684 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2685 __isl_take isl_union_pw_qpolynomial *upwqp1,
2686 __isl_take isl_union_pw_qpolynomial *upwqp2);
2688 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2689 __isl_take isl_pw_qpolynomial *pwqp,
2690 __isl_take isl_point *pnt);
2692 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2693 __isl_take isl_union_pw_qpolynomial *upwqp,
2694 __isl_take isl_point *pnt);
2696 __isl_give isl_set *isl_pw_qpolynomial_domain(
2697 __isl_take isl_pw_qpolynomial *pwqp);
2698 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2699 __isl_take isl_pw_qpolynomial *pwpq,
2700 __isl_take isl_set *set);
2702 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2703 __isl_take isl_union_pw_qpolynomial *upwqp);
2704 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2705 __isl_take isl_union_pw_qpolynomial *upwpq,
2706 __isl_take isl_union_set *uset);
2708 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2709 __isl_take isl_qpolynomial *qp,
2710 __isl_take isl_dim *model);
2712 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2713 __isl_take isl_union_pw_qpolynomial *upwqp);
2715 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2716 __isl_take isl_qpolynomial *qp,
2717 __isl_take isl_set *context);
2719 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2720 __isl_take isl_pw_qpolynomial *pwqp,
2721 __isl_take isl_set *context);
2723 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2724 __isl_take isl_union_pw_qpolynomial *upwqp,
2725 __isl_take isl_union_set *context);
2727 The gist operation applies the gist operation to each of
2728 the cells in the domain of the input piecewise quasipolynomial.
2729 The context is also exploited
2730 to simplify the quasipolynomials associated to each cell.
2732 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2733 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2734 __isl_give isl_union_pw_qpolynomial *
2735 isl_union_pw_qpolynomial_to_polynomial(
2736 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2738 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2739 the polynomial will be an overapproximation. If C<sign> is negative,
2740 it will be an underapproximation. If C<sign> is zero, the approximation
2741 will lie somewhere in between.
2743 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2745 A piecewise quasipolynomial reduction is a piecewise
2746 reduction (or fold) of quasipolynomials.
2747 In particular, the reduction can be maximum or a minimum.
2748 The objects are mainly used to represent the result of
2749 an upper or lower bound on a quasipolynomial over its domain,
2750 i.e., as the result of the following function.
2752 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2753 __isl_take isl_pw_qpolynomial *pwqp,
2754 enum isl_fold type, int *tight);
2756 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2757 __isl_take isl_union_pw_qpolynomial *upwqp,
2758 enum isl_fold type, int *tight);
2760 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2761 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2762 is the returned bound is known be tight, i.e., for each value
2763 of the parameters there is at least
2764 one element in the domain that reaches the bound.
2765 If the domain of C<pwqp> is not wrapping, then the bound is computed
2766 over all elements in that domain and the result has a purely parametric
2767 domain. If the domain of C<pwqp> is wrapping, then the bound is
2768 computed over the range of the wrapped relation. The domain of the
2769 wrapped relation becomes the domain of the result.
2771 A (piecewise) quasipolynomial reduction can be copied or freed using the
2772 following functions.
2774 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2775 __isl_keep isl_qpolynomial_fold *fold);
2776 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2777 __isl_keep isl_pw_qpolynomial_fold *pwf);
2778 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2779 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2780 void isl_qpolynomial_fold_free(
2781 __isl_take isl_qpolynomial_fold *fold);
2782 void *isl_pw_qpolynomial_fold_free(
2783 __isl_take isl_pw_qpolynomial_fold *pwf);
2784 void isl_union_pw_qpolynomial_fold_free(
2785 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2787 =head3 Printing Piecewise Quasipolynomial Reductions
2789 Piecewise quasipolynomial reductions can be printed
2790 using the following function.
2792 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2793 __isl_take isl_printer *p,
2794 __isl_keep isl_pw_qpolynomial_fold *pwf);
2795 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2796 __isl_take isl_printer *p,
2797 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2799 For C<isl_printer_print_pw_qpolynomial_fold>,
2800 output format of the printer
2801 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2802 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2803 output format of the printer
2804 needs to be set to C<ISL_FORMAT_ISL>.
2805 In case of printing in C<ISL_FORMAT_C>, the user may want
2806 to set the names of all dimensions
2808 __isl_give isl_pw_qpolynomial_fold *
2809 isl_pw_qpolynomial_fold_set_dim_name(
2810 __isl_take isl_pw_qpolynomial_fold *pwf,
2811 enum isl_dim_type type, unsigned pos,
2814 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2816 To iterate over all piecewise quasipolynomial reductions in a union
2817 piecewise quasipolynomial reduction, use the following function
2819 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2820 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2821 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2822 void *user), void *user);
2824 To iterate over the cells in a piecewise quasipolynomial reduction,
2825 use either of the following two functions
2827 int isl_pw_qpolynomial_fold_foreach_piece(
2828 __isl_keep isl_pw_qpolynomial_fold *pwf,
2829 int (*fn)(__isl_take isl_set *set,
2830 __isl_take isl_qpolynomial_fold *fold,
2831 void *user), void *user);
2832 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2833 __isl_keep isl_pw_qpolynomial_fold *pwf,
2834 int (*fn)(__isl_take isl_set *set,
2835 __isl_take isl_qpolynomial_fold *fold,
2836 void *user), void *user);
2838 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2839 of the difference between these two functions.
2841 To iterate over all quasipolynomials in a reduction, use
2843 int isl_qpolynomial_fold_foreach_qpolynomial(
2844 __isl_keep isl_qpolynomial_fold *fold,
2845 int (*fn)(__isl_take isl_qpolynomial *qp,
2846 void *user), void *user);
2848 =head3 Operations on Piecewise Quasipolynomial Reductions
2850 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
2851 __isl_take isl_qpolynomial_fold *fold, isl_int v);
2853 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2854 __isl_take isl_pw_qpolynomial_fold *pwf1,
2855 __isl_take isl_pw_qpolynomial_fold *pwf2);
2857 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2858 __isl_take isl_pw_qpolynomial_fold *pwf1,
2859 __isl_take isl_pw_qpolynomial_fold *pwf2);
2861 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2862 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2863 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2865 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2866 __isl_take isl_pw_qpolynomial_fold *pwf,
2867 __isl_take isl_point *pnt);
2869 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2870 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2871 __isl_take isl_point *pnt);
2873 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2874 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2875 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2876 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2877 __isl_take isl_union_set *uset);
2879 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2880 __isl_take isl_pw_qpolynomial_fold *pwf);
2882 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2883 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2885 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2886 __isl_take isl_pw_qpolynomial_fold *pwf,
2887 __isl_take isl_set *context);
2889 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2890 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2891 __isl_take isl_union_set *context);
2893 The gist operation applies the gist operation to each of
2894 the cells in the domain of the input piecewise quasipolynomial reduction.
2895 In future, the operation will also exploit the context
2896 to simplify the quasipolynomial reductions associated to each cell.
2898 __isl_give isl_pw_qpolynomial_fold *
2899 isl_set_apply_pw_qpolynomial_fold(
2900 __isl_take isl_set *set,
2901 __isl_take isl_pw_qpolynomial_fold *pwf,
2903 __isl_give isl_pw_qpolynomial_fold *
2904 isl_map_apply_pw_qpolynomial_fold(
2905 __isl_take isl_map *map,
2906 __isl_take isl_pw_qpolynomial_fold *pwf,
2908 __isl_give isl_union_pw_qpolynomial_fold *
2909 isl_union_set_apply_union_pw_qpolynomial_fold(
2910 __isl_take isl_union_set *uset,
2911 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2913 __isl_give isl_union_pw_qpolynomial_fold *
2914 isl_union_map_apply_union_pw_qpolynomial_fold(
2915 __isl_take isl_union_map *umap,
2916 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2919 The functions taking a map
2920 compose the given map with the given piecewise quasipolynomial reduction.
2921 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2922 over all elements in the intersection of the range of the map
2923 and the domain of the piecewise quasipolynomial reduction
2924 as a function of an element in the domain of the map.
2925 The functions taking a set compute a bound over all elements in the
2926 intersection of the set and the domain of the
2927 piecewise quasipolynomial reduction.
2929 =head2 Dependence Analysis
2931 C<isl> contains specialized functionality for performing
2932 array dataflow analysis. That is, given a I<sink> access relation
2933 and a collection of possible I<source> access relations,
2934 C<isl> can compute relations that describe
2935 for each iteration of the sink access, which iteration
2936 of which of the source access relations was the last
2937 to access the same data element before the given iteration
2939 To compute standard flow dependences, the sink should be
2940 a read, while the sources should be writes.
2941 If any of the source accesses are marked as being I<may>
2942 accesses, then there will be a dependence to the last
2943 I<must> access B<and> to any I<may> access that follows
2944 this last I<must> access.
2945 In particular, if I<all> sources are I<may> accesses,
2946 then memory based dependence analysis is performed.
2947 If, on the other hand, all sources are I<must> accesses,
2948 then value based dependence analysis is performed.
2950 #include <isl/flow.h>
2952 typedef int (*isl_access_level_before)(void *first, void *second);
2954 __isl_give isl_access_info *isl_access_info_alloc(
2955 __isl_take isl_map *sink,
2956 void *sink_user, isl_access_level_before fn,
2958 __isl_give isl_access_info *isl_access_info_add_source(
2959 __isl_take isl_access_info *acc,
2960 __isl_take isl_map *source, int must,
2962 void isl_access_info_free(__isl_take isl_access_info *acc);
2964 __isl_give isl_flow *isl_access_info_compute_flow(
2965 __isl_take isl_access_info *acc);
2967 int isl_flow_foreach(__isl_keep isl_flow *deps,
2968 int (*fn)(__isl_take isl_map *dep, int must,
2969 void *dep_user, void *user),
2971 __isl_give isl_map *isl_flow_get_no_source(
2972 __isl_keep isl_flow *deps, int must);
2973 void isl_flow_free(__isl_take isl_flow *deps);
2975 The function C<isl_access_info_compute_flow> performs the actual
2976 dependence analysis. The other functions are used to construct
2977 the input for this function or to read off the output.
2979 The input is collected in an C<isl_access_info>, which can
2980 be created through a call to C<isl_access_info_alloc>.
2981 The arguments to this functions are the sink access relation
2982 C<sink>, a token C<sink_user> used to identify the sink
2983 access to the user, a callback function for specifying the
2984 relative order of source and sink accesses, and the number
2985 of source access relations that will be added.
2986 The callback function has type C<int (*)(void *first, void *second)>.
2987 The function is called with two user supplied tokens identifying
2988 either a source or the sink and it should return the shared nesting
2989 level and the relative order of the two accesses.
2990 In particular, let I<n> be the number of loops shared by
2991 the two accesses. If C<first> precedes C<second> textually,
2992 then the function should return I<2 * n + 1>; otherwise,
2993 it should return I<2 * n>.
2994 The sources can be added to the C<isl_access_info> by performing
2995 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2996 C<must> indicates whether the source is a I<must> access
2997 or a I<may> access. Note that a multi-valued access relation
2998 should only be marked I<must> if every iteration in the domain
2999 of the relation accesses I<all> elements in its image.
3000 The C<source_user> token is again used to identify
3001 the source access. The range of the source access relation
3002 C<source> should have the same dimension as the range
3003 of the sink access relation.
3004 The C<isl_access_info_free> function should usually not be
3005 called explicitly, because it is called implicitly by
3006 C<isl_access_info_compute_flow>.
3008 The result of the dependence analysis is collected in an
3009 C<isl_flow>. There may be elements of
3010 the sink access for which no preceding source access could be
3011 found or for which all preceding sources are I<may> accesses.
3012 The relations containing these elements can be obtained through
3013 calls to C<isl_flow_get_no_source>, the first with C<must> set
3014 and the second with C<must> unset.
3015 In the case of standard flow dependence analysis,
3016 with the sink a read and the sources I<must> writes,
3017 the first relation corresponds to the reads from uninitialized
3018 array elements and the second relation is empty.
3019 The actual flow dependences can be extracted using
3020 C<isl_flow_foreach>. This function will call the user-specified
3021 callback function C<fn> for each B<non-empty> dependence between
3022 a source and the sink. The callback function is called
3023 with four arguments, the actual flow dependence relation
3024 mapping source iterations to sink iterations, a boolean that
3025 indicates whether it is a I<must> or I<may> dependence, a token
3026 identifying the source and an additional C<void *> with value
3027 equal to the third argument of the C<isl_flow_foreach> call.
3028 A dependence is marked I<must> if it originates from a I<must>
3029 source and if it is not followed by any I<may> sources.
3031 After finishing with an C<isl_flow>, the user should call
3032 C<isl_flow_free> to free all associated memory.
3034 A higher-level interface to dependence analysis is provided
3035 by the following function.
3037 #include <isl/flow.h>
3039 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3040 __isl_take isl_union_map *must_source,
3041 __isl_take isl_union_map *may_source,
3042 __isl_take isl_union_map *schedule,
3043 __isl_give isl_union_map **must_dep,
3044 __isl_give isl_union_map **may_dep,
3045 __isl_give isl_union_map **must_no_source,
3046 __isl_give isl_union_map **may_no_source);
3048 The arrays are identified by the tuple names of the ranges
3049 of the accesses. The iteration domains by the tuple names
3050 of the domains of the accesses and of the schedule.
3051 The relative order of the iteration domains is given by the
3052 schedule. The relations returned through C<must_no_source>
3053 and C<may_no_source> are subsets of C<sink>.
3054 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3055 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3056 any of the other arguments is treated as an error.
3060 B<The functionality described in this section is fairly new
3061 and may be subject to change.>
3063 The following function can be used to compute a schedule
3064 for a union of domains. The generated schedule respects
3065 all C<validity> dependences. That is, all dependence distances
3066 over these dependences in the scheduled space are lexicographically
3067 positive. The generated schedule schedule also tries to minimize
3068 the dependence distances over C<proximity> dependences.
3069 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3070 for groups of domains where the dependence distances have only
3071 non-negative values.
3072 The algorithm used to construct the schedule is similar to that
3075 #include <isl/schedule.h>
3076 __isl_give isl_schedule *isl_union_set_compute_schedule(
3077 __isl_take isl_union_set *domain,
3078 __isl_take isl_union_map *validity,
3079 __isl_take isl_union_map *proximity);
3080 void *isl_schedule_free(__isl_take isl_schedule *sched);
3082 A mapping from the domains to the scheduled space can be obtained
3083 from an C<isl_schedule> using the following function.
3085 __isl_give isl_union_map *isl_schedule_get_map(
3086 __isl_keep isl_schedule *sched);
3088 A representation of the schedule can be printed using
3090 __isl_give isl_printer *isl_printer_print_schedule(
3091 __isl_take isl_printer *p,
3092 __isl_keep isl_schedule *schedule);
3094 A representation of the schedule as a forest of bands can be obtained
3095 using the following function.
3097 __isl_give isl_band_list *isl_schedule_get_band_forest(
3098 __isl_keep isl_schedule *schedule);
3100 The list can be manipulated as explained in L<"Lists">.
3101 The bands inside the list can be copied and freed using the following
3104 #include <isl/band.h>
3105 __isl_give isl_band *isl_band_copy(
3106 __isl_keep isl_band *band);
3107 void *isl_band_free(__isl_take isl_band *band);
3109 Each band contains zero or more scheduling dimensions.
3110 These are referred to as the members of the band.
3111 The section of the schedule that corresponds to the band is
3112 referred to as the partial schedule of the band.
3113 For those nodes that participate in a band, the outer scheduling
3114 dimensions form the prefix schedule, while the inner scheduling
3115 dimensions form the suffix schedule.
3116 That is, if we take a cut of the band forest, then the union of
3117 the concatenations of the prefix, partial and suffix schedules of
3118 each band in the cut is equal to the entire schedule (modulo
3119 some possible padding at the end with zero scheduling dimensions).
3120 The properties of a band can be inspected using the following functions.
3122 #include <isl/band.h>
3123 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3125 int isl_band_has_children(__isl_keep isl_band *band);
3126 __isl_give isl_band_list *isl_band_get_children(
3127 __isl_keep isl_band *band);
3129 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3130 __isl_keep isl_band *band);
3131 __isl_give isl_union_map *isl_band_get_partial_schedule(
3132 __isl_keep isl_band *band);
3133 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3134 __isl_keep isl_band *band);
3136 int isl_band_n_member(__isl_keep isl_band *band);
3137 int isl_band_member_is_zero_distance(
3138 __isl_keep isl_band *band, int pos);
3140 Note that a scheduling dimension is considered to be ``zero
3141 distance'' if it does not carry any proximity dependences
3143 That is, if the dependence distances of the proximity
3144 dependences are all zero in that direction (for fixed
3145 iterations of outer bands).
3147 A representation of the band can be printed using
3149 #include <isl/band.h>
3150 __isl_give isl_printer *isl_printer_print_band(
3151 __isl_take isl_printer *p,
3152 __isl_keep isl_band *band);
3154 Alternatively, the schedule mapping
3155 can also be obtained in pieces using the following functions.
3157 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3158 __isl_give isl_union_map *isl_schedule_get_band(
3159 __isl_keep isl_schedule *sched, unsigned band);
3161 C<isl_schedule_n_band> returns the maximal number of bands.
3162 C<isl_schedule_get_band> returns a union of mappings from a domain to
3163 the band of consecutive schedule dimensions with the given sequence
3164 number for that domain. Bands with the same sequence number but for
3165 different domains may be completely unrelated.
3166 Within a band, the corresponding coordinates of the distance vectors
3167 are all non-negative, assuming that the coordinates for all previous
3170 =head2 Parametric Vertex Enumeration
3172 The parametric vertex enumeration described in this section
3173 is mainly intended to be used internally and by the C<barvinok>
3176 #include <isl/vertices.h>
3177 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3178 __isl_keep isl_basic_set *bset);
3180 The function C<isl_basic_set_compute_vertices> performs the
3181 actual computation of the parametric vertices and the chamber
3182 decomposition and store the result in an C<isl_vertices> object.
3183 This information can be queried by either iterating over all
3184 the vertices or iterating over all the chambers or cells
3185 and then iterating over all vertices that are active on the chamber.
3187 int isl_vertices_foreach_vertex(
3188 __isl_keep isl_vertices *vertices,
3189 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3192 int isl_vertices_foreach_cell(
3193 __isl_keep isl_vertices *vertices,
3194 int (*fn)(__isl_take isl_cell *cell, void *user),
3196 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3197 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3200 Other operations that can be performed on an C<isl_vertices> object are
3203 isl_ctx *isl_vertices_get_ctx(
3204 __isl_keep isl_vertices *vertices);
3205 int isl_vertices_get_n_vertices(
3206 __isl_keep isl_vertices *vertices);
3207 void isl_vertices_free(__isl_take isl_vertices *vertices);
3209 Vertices can be inspected and destroyed using the following functions.
3211 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3212 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3213 __isl_give isl_basic_set *isl_vertex_get_domain(
3214 __isl_keep isl_vertex *vertex);
3215 __isl_give isl_basic_set *isl_vertex_get_expr(
3216 __isl_keep isl_vertex *vertex);
3217 void isl_vertex_free(__isl_take isl_vertex *vertex);
3219 C<isl_vertex_get_expr> returns a singleton parametric set describing
3220 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3222 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3223 B<rational> basic sets, so they should mainly be used for inspection
3224 and should not be mixed with integer sets.
3226 Chambers can be inspected and destroyed using the following functions.
3228 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3229 __isl_give isl_basic_set *isl_cell_get_domain(
3230 __isl_keep isl_cell *cell);
3231 void isl_cell_free(__isl_take isl_cell *cell);
3235 Although C<isl> is mainly meant to be used as a library,
3236 it also contains some basic applications that use some
3237 of the functionality of C<isl>.
3238 The input may be specified in either the L<isl format>
3239 or the L<PolyLib format>.
3241 =head2 C<isl_polyhedron_sample>
3243 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3244 an integer element of the polyhedron, if there is any.
3245 The first column in the output is the denominator and is always
3246 equal to 1. If the polyhedron contains no integer points,
3247 then a vector of length zero is printed.
3251 C<isl_pip> takes the same input as the C<example> program
3252 from the C<piplib> distribution, i.e., a set of constraints
3253 on the parameters, a line containing only -1 and finally a set
3254 of constraints on a parametric polyhedron.
3255 The coefficients of the parameters appear in the last columns
3256 (but before the final constant column).
3257 The output is the lexicographic minimum of the parametric polyhedron.
3258 As C<isl> currently does not have its own output format, the output
3259 is just a dump of the internal state.
3261 =head2 C<isl_polyhedron_minimize>
3263 C<isl_polyhedron_minimize> computes the minimum of some linear
3264 or affine objective function over the integer points in a polyhedron.
3265 If an affine objective function
3266 is given, then the constant should appear in the last column.
3268 =head2 C<isl_polytope_scan>
3270 Given a polytope, C<isl_polytope_scan> prints
3271 all integer points in the polytope.