3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
477 __isl_keep isl_qpolynomial_fold *fold);
478 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
479 __isl_keep isl_pw_qpolynomial *pwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
481 __isl_keep isl_union_pw_qpolynomial *upwqp);
482 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
483 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
486 __isl_give isl_dim *isl_aff_get_dim(
487 __isl_keep isl_aff *aff);
489 #include <isl/point.h>
490 __isl_give isl_dim *isl_point_get_dim(
491 __isl_keep isl_point *pnt);
493 The names of the individual dimensions may be set or read off
494 using the following functions.
497 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
498 enum isl_dim_type type, unsigned pos,
499 __isl_keep const char *name);
500 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
501 enum isl_dim_type type, unsigned pos);
503 Note that C<isl_dim_get_name> returns a pointer to some internal
504 data structure, so the result can only be used while the
505 corresponding C<isl_dim> is alive.
506 Also note that every function that operates on two sets or relations
507 requires that both arguments have the same parameters. This also
508 means that if one of the arguments has named parameters, then the
509 other needs to have named parameters too and the names need to match.
510 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
511 have different parameters (as long as they are named), in which case
512 the result will have as parameters the union of the parameters of
515 The names of entire spaces may be set or read off
516 using the following functions.
519 __isl_give isl_dim *isl_dim_set_tuple_name(
520 __isl_take isl_dim *dim,
521 enum isl_dim_type type, const char *s);
522 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
523 enum isl_dim_type type);
525 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
526 or C<isl_dim_set>. As with C<isl_dim_get_name>,
527 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
529 Binary operations require the corresponding spaces of their arguments
530 to have the same name.
532 Spaces can be nested. In particular, the domain of a set or
533 the domain or range of a relation can be a nested relation.
534 The following functions can be used to construct and deconstruct
535 such nested dimension specifications.
538 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
539 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
540 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
542 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
543 be the dimension specification of a set, while that of
544 C<isl_dim_wrap> should be the dimension specification of a relation.
545 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
546 of a relation, while that of C<isl_dim_wrap> is the dimension specification
549 Dimension specifications can be created from other dimension
550 specifications using the following functions.
552 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
553 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
554 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
555 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
556 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
557 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
558 __isl_take isl_dim *right);
559 __isl_give isl_dim *isl_dim_align_params(
560 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
561 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
562 enum isl_dim_type type, unsigned pos, unsigned n);
563 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
564 enum isl_dim_type type, unsigned n);
565 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
566 enum isl_dim_type type, unsigned first, unsigned n);
567 __isl_give isl_dim *isl_dim_map_from_set(
568 __isl_take isl_dim *dim);
569 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
571 Note that if dimensions are added or removed from a space, then
572 the name and the internal structure are lost.
576 A local space is essentially a dimension specification with
577 zero or more existentially quantified variables.
578 The local space of a basic set or relation can be obtained
579 using the following functions.
582 __isl_give isl_local_space *isl_basic_set_get_local_space(
583 __isl_keep isl_basic_set *bset);
586 __isl_give isl_local_space *isl_basic_map_get_local_space(
587 __isl_keep isl_basic_map *bmap);
589 A new local space can be created from a dimension specification using
591 #include <isl/local_space.h>
592 __isl_give isl_local_space *isl_local_space_from_dim(
593 __isl_take isl_dim *dim);
595 They can be inspected, copied and freed using the following functions.
597 #include <isl/local_space.h>
598 isl_ctx *isl_local_space_get_ctx(
599 __isl_keep isl_local_space *ls);
600 int isl_local_space_dim(__isl_keep isl_local_space *ls,
601 enum isl_dim_type type);
602 const char *isl_local_space_get_dim_name(
603 __isl_keep isl_local_space *ls,
604 enum isl_dim_type type, unsigned pos);
605 __isl_give isl_local_space *isl_local_space_set_dim_name(
606 __isl_take isl_local_space *ls,
607 enum isl_dim_type type, unsigned pos, const char *s);
608 __isl_give isl_dim *isl_local_space_get_dim(
609 __isl_keep isl_local_space *ls);
610 __isl_give isl_div *isl_local_space_get_div(
611 __isl_keep isl_local_space *ls, int pos);
612 __isl_give isl_local_space *isl_local_space_copy(
613 __isl_keep isl_local_space *ls);
614 void *isl_local_space_free(__isl_take isl_local_space *ls);
616 Two local spaces can be compared using
618 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
619 __isl_keep isl_local_space *ls2);
621 Local spaces can be created from other local spaces
622 using the following functions.
624 __isl_give isl_local_space *isl_local_space_from_domain(
625 __isl_take isl_local_space *ls);
626 __isl_give isl_local_space *isl_local_space_add_dim(
627 __isl_take isl_local_space *ls,
628 enum isl_dim_type type, unsigned n);
630 =head2 Input and Output
632 C<isl> supports its own input/output format, which is similar
633 to the C<Omega> format, but also supports the C<PolyLib> format
638 The C<isl> format is similar to that of C<Omega>, but has a different
639 syntax for describing the parameters and allows for the definition
640 of an existentially quantified variable as the integer division
641 of an affine expression.
642 For example, the set of integers C<i> between C<0> and C<n>
643 such that C<i % 10 <= 6> can be described as
645 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
648 A set or relation can have several disjuncts, separated
649 by the keyword C<or>. Each disjunct is either a conjunction
650 of constraints or a projection (C<exists>) of a conjunction
651 of constraints. The constraints are separated by the keyword
654 =head3 C<PolyLib> format
656 If the represented set is a union, then the first line
657 contains a single number representing the number of disjuncts.
658 Otherwise, a line containing the number C<1> is optional.
660 Each disjunct is represented by a matrix of constraints.
661 The first line contains two numbers representing
662 the number of rows and columns,
663 where the number of rows is equal to the number of constraints
664 and the number of columns is equal to two plus the number of variables.
665 The following lines contain the actual rows of the constraint matrix.
666 In each row, the first column indicates whether the constraint
667 is an equality (C<0>) or inequality (C<1>). The final column
668 corresponds to the constant term.
670 If the set is parametric, then the coefficients of the parameters
671 appear in the last columns before the constant column.
672 The coefficients of any existentially quantified variables appear
673 between those of the set variables and those of the parameters.
675 =head3 Extended C<PolyLib> format
677 The extended C<PolyLib> format is nearly identical to the
678 C<PolyLib> format. The only difference is that the line
679 containing the number of rows and columns of a constraint matrix
680 also contains four additional numbers:
681 the number of output dimensions, the number of input dimensions,
682 the number of local dimensions (i.e., the number of existentially
683 quantified variables) and the number of parameters.
684 For sets, the number of ``output'' dimensions is equal
685 to the number of set dimensions, while the number of ``input''
691 __isl_give isl_basic_set *isl_basic_set_read_from_file(
692 isl_ctx *ctx, FILE *input, int nparam);
693 __isl_give isl_basic_set *isl_basic_set_read_from_str(
694 isl_ctx *ctx, const char *str, int nparam);
695 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
696 FILE *input, int nparam);
697 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
698 const char *str, int nparam);
701 __isl_give isl_basic_map *isl_basic_map_read_from_file(
702 isl_ctx *ctx, FILE *input, int nparam);
703 __isl_give isl_basic_map *isl_basic_map_read_from_str(
704 isl_ctx *ctx, const char *str, int nparam);
705 __isl_give isl_map *isl_map_read_from_file(
706 struct isl_ctx *ctx, FILE *input, int nparam);
707 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
708 const char *str, int nparam);
710 #include <isl/union_set.h>
711 __isl_give isl_union_set *isl_union_set_read_from_file(
712 isl_ctx *ctx, FILE *input);
713 __isl_give isl_union_set *isl_union_set_read_from_str(
714 struct isl_ctx *ctx, const char *str);
716 #include <isl/union_map.h>
717 __isl_give isl_union_map *isl_union_map_read_from_file(
718 isl_ctx *ctx, FILE *input);
719 __isl_give isl_union_map *isl_union_map_read_from_str(
720 struct isl_ctx *ctx, const char *str);
722 The input format is autodetected and may be either the C<PolyLib> format
723 or the C<isl> format.
724 C<nparam> specifies how many of the final columns in
725 the C<PolyLib> format correspond to parameters.
726 If input is given in the C<isl> format, then the number
727 of parameters needs to be equal to C<nparam>.
728 If C<nparam> is negative, then any number of parameters
729 is accepted in the C<isl> format and zero parameters
730 are assumed in the C<PolyLib> format.
734 Before anything can be printed, an C<isl_printer> needs to
737 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
739 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
740 void isl_printer_free(__isl_take isl_printer *printer);
741 __isl_give char *isl_printer_get_str(
742 __isl_keep isl_printer *printer);
744 The behavior of the printer can be modified in various ways
746 __isl_give isl_printer *isl_printer_set_output_format(
747 __isl_take isl_printer *p, int output_format);
748 __isl_give isl_printer *isl_printer_set_indent(
749 __isl_take isl_printer *p, int indent);
750 __isl_give isl_printer *isl_printer_indent(
751 __isl_take isl_printer *p, int indent);
752 __isl_give isl_printer *isl_printer_set_prefix(
753 __isl_take isl_printer *p, const char *prefix);
754 __isl_give isl_printer *isl_printer_set_suffix(
755 __isl_take isl_printer *p, const char *suffix);
757 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
758 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
759 and defaults to C<ISL_FORMAT_ISL>.
760 Each line in the output is indented by C<indent> (set by
761 C<isl_printer_set_indent>) spaces
762 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
763 In the C<PolyLib> format output,
764 the coefficients of the existentially quantified variables
765 appear between those of the set variables and those
767 The function C<isl_printer_indent> increases the indentation
768 by the specified amount (which may be negative).
770 To actually print something, use
773 __isl_give isl_printer *isl_printer_print_basic_set(
774 __isl_take isl_printer *printer,
775 __isl_keep isl_basic_set *bset);
776 __isl_give isl_printer *isl_printer_print_set(
777 __isl_take isl_printer *printer,
778 __isl_keep isl_set *set);
781 __isl_give isl_printer *isl_printer_print_basic_map(
782 __isl_take isl_printer *printer,
783 __isl_keep isl_basic_map *bmap);
784 __isl_give isl_printer *isl_printer_print_map(
785 __isl_take isl_printer *printer,
786 __isl_keep isl_map *map);
788 #include <isl/union_set.h>
789 __isl_give isl_printer *isl_printer_print_union_set(
790 __isl_take isl_printer *p,
791 __isl_keep isl_union_set *uset);
793 #include <isl/union_map.h>
794 __isl_give isl_printer *isl_printer_print_union_map(
795 __isl_take isl_printer *p,
796 __isl_keep isl_union_map *umap);
798 When called on a file printer, the following function flushes
799 the file. When called on a string printer, the buffer is cleared.
801 __isl_give isl_printer *isl_printer_flush(
802 __isl_take isl_printer *p);
804 =head2 Creating New Sets and Relations
806 C<isl> has functions for creating some standard sets and relations.
810 =item * Empty sets and relations
812 __isl_give isl_basic_set *isl_basic_set_empty(
813 __isl_take isl_dim *dim);
814 __isl_give isl_basic_map *isl_basic_map_empty(
815 __isl_take isl_dim *dim);
816 __isl_give isl_set *isl_set_empty(
817 __isl_take isl_dim *dim);
818 __isl_give isl_map *isl_map_empty(
819 __isl_take isl_dim *dim);
820 __isl_give isl_union_set *isl_union_set_empty(
821 __isl_take isl_dim *dim);
822 __isl_give isl_union_map *isl_union_map_empty(
823 __isl_take isl_dim *dim);
825 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
826 is only used to specify the parameters.
828 =item * Universe sets and relations
830 __isl_give isl_basic_set *isl_basic_set_universe(
831 __isl_take isl_dim *dim);
832 __isl_give isl_basic_map *isl_basic_map_universe(
833 __isl_take isl_dim *dim);
834 __isl_give isl_set *isl_set_universe(
835 __isl_take isl_dim *dim);
836 __isl_give isl_map *isl_map_universe(
837 __isl_take isl_dim *dim);
838 __isl_give isl_union_set *isl_union_set_universe(
839 __isl_take isl_union_set *uset);
840 __isl_give isl_union_map *isl_union_map_universe(
841 __isl_take isl_union_map *umap);
843 The sets and relations constructed by the functions above
844 contain all integer values, while those constructed by the
845 functions below only contain non-negative values.
847 __isl_give isl_basic_set *isl_basic_set_nat_universe(
848 __isl_take isl_dim *dim);
849 __isl_give isl_basic_map *isl_basic_map_nat_universe(
850 __isl_take isl_dim *dim);
851 __isl_give isl_set *isl_set_nat_universe(
852 __isl_take isl_dim *dim);
853 __isl_give isl_map *isl_map_nat_universe(
854 __isl_take isl_dim *dim);
856 =item * Identity relations
858 __isl_give isl_basic_map *isl_basic_map_identity(
859 __isl_take isl_dim *dim);
860 __isl_give isl_map *isl_map_identity(
861 __isl_take isl_dim *dim);
863 The number of input and output dimensions in C<dim> needs
866 =item * Lexicographic order
868 __isl_give isl_map *isl_map_lex_lt(
869 __isl_take isl_dim *set_dim);
870 __isl_give isl_map *isl_map_lex_le(
871 __isl_take isl_dim *set_dim);
872 __isl_give isl_map *isl_map_lex_gt(
873 __isl_take isl_dim *set_dim);
874 __isl_give isl_map *isl_map_lex_ge(
875 __isl_take isl_dim *set_dim);
876 __isl_give isl_map *isl_map_lex_lt_first(
877 __isl_take isl_dim *dim, unsigned n);
878 __isl_give isl_map *isl_map_lex_le_first(
879 __isl_take isl_dim *dim, unsigned n);
880 __isl_give isl_map *isl_map_lex_gt_first(
881 __isl_take isl_dim *dim, unsigned n);
882 __isl_give isl_map *isl_map_lex_ge_first(
883 __isl_take isl_dim *dim, unsigned n);
885 The first four functions take a dimension specification for a B<set>
886 and return relations that express that the elements in the domain
887 are lexicographically less
888 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
889 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
890 than the elements in the range.
891 The last four functions take a dimension specification for a map
892 and return relations that express that the first C<n> dimensions
893 in the domain are lexicographically less
894 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
895 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
896 than the first C<n> dimensions in the range.
900 A basic set or relation can be converted to a set or relation
901 using the following functions.
903 __isl_give isl_set *isl_set_from_basic_set(
904 __isl_take isl_basic_set *bset);
905 __isl_give isl_map *isl_map_from_basic_map(
906 __isl_take isl_basic_map *bmap);
908 Sets and relations can be converted to union sets and relations
909 using the following functions.
911 __isl_give isl_union_map *isl_union_map_from_map(
912 __isl_take isl_map *map);
913 __isl_give isl_union_set *isl_union_set_from_set(
914 __isl_take isl_set *set);
916 Sets and relations can be copied and freed again using the following
919 __isl_give isl_basic_set *isl_basic_set_copy(
920 __isl_keep isl_basic_set *bset);
921 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
922 __isl_give isl_union_set *isl_union_set_copy(
923 __isl_keep isl_union_set *uset);
924 __isl_give isl_basic_map *isl_basic_map_copy(
925 __isl_keep isl_basic_map *bmap);
926 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
927 __isl_give isl_union_map *isl_union_map_copy(
928 __isl_keep isl_union_map *umap);
929 void isl_basic_set_free(__isl_take isl_basic_set *bset);
930 void isl_set_free(__isl_take isl_set *set);
931 void isl_union_set_free(__isl_take isl_union_set *uset);
932 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
933 void isl_map_free(__isl_take isl_map *map);
934 void isl_union_map_free(__isl_take isl_union_map *umap);
936 Other sets and relations can be constructed by starting
937 from a universe set or relation, adding equality and/or
938 inequality constraints and then projecting out the
939 existentially quantified variables, if any.
940 Constraints can be constructed, manipulated and
941 added to (basic) sets and relations using the following functions.
943 #include <isl/constraint.h>
944 __isl_give isl_constraint *isl_equality_alloc(
945 __isl_take isl_dim *dim);
946 __isl_give isl_constraint *isl_inequality_alloc(
947 __isl_take isl_dim *dim);
948 void isl_constraint_set_constant(
949 __isl_keep isl_constraint *constraint, isl_int v);
950 void isl_constraint_set_coefficient(
951 __isl_keep isl_constraint *constraint,
952 enum isl_dim_type type, int pos, isl_int v);
953 __isl_give isl_basic_map *isl_basic_map_add_constraint(
954 __isl_take isl_basic_map *bmap,
955 __isl_take isl_constraint *constraint);
956 __isl_give isl_basic_set *isl_basic_set_add_constraint(
957 __isl_take isl_basic_set *bset,
958 __isl_take isl_constraint *constraint);
959 __isl_give isl_map *isl_map_add_constraint(
960 __isl_take isl_map *map,
961 __isl_take isl_constraint *constraint);
962 __isl_give isl_set *isl_set_add_constraint(
963 __isl_take isl_set *set,
964 __isl_take isl_constraint *constraint);
966 For example, to create a set containing the even integers
967 between 10 and 42, you would use the following code.
971 struct isl_constraint *c;
972 struct isl_basic_set *bset;
975 dim = isl_dim_set_alloc(ctx, 0, 2);
976 bset = isl_basic_set_universe(isl_dim_copy(dim));
978 c = isl_equality_alloc(isl_dim_copy(dim));
979 isl_int_set_si(v, -1);
980 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
981 isl_int_set_si(v, 2);
982 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
983 bset = isl_basic_set_add_constraint(bset, c);
985 c = isl_inequality_alloc(isl_dim_copy(dim));
986 isl_int_set_si(v, -10);
987 isl_constraint_set_constant(c, v);
988 isl_int_set_si(v, 1);
989 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
990 bset = isl_basic_set_add_constraint(bset, c);
992 c = isl_inequality_alloc(dim);
993 isl_int_set_si(v, 42);
994 isl_constraint_set_constant(c, v);
995 isl_int_set_si(v, -1);
996 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
997 bset = isl_basic_set_add_constraint(bset, c);
999 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1005 struct isl_basic_set *bset;
1006 bset = isl_basic_set_read_from_str(ctx,
1007 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1009 A basic set or relation can also be constructed from two matrices
1010 describing the equalities and the inequalities.
1012 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1013 __isl_take isl_dim *dim,
1014 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1015 enum isl_dim_type c1,
1016 enum isl_dim_type c2, enum isl_dim_type c3,
1017 enum isl_dim_type c4);
1018 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1019 __isl_take isl_dim *dim,
1020 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1021 enum isl_dim_type c1,
1022 enum isl_dim_type c2, enum isl_dim_type c3,
1023 enum isl_dim_type c4, enum isl_dim_type c5);
1025 The C<isl_dim_type> arguments indicate the order in which
1026 different kinds of variables appear in the input matrices
1027 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1028 C<isl_dim_set> and C<isl_dim_div> for sets and
1029 of C<isl_dim_cst>, C<isl_dim_param>,
1030 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1032 A (basic) relation can also be constructed from a (piecewise) affine expression
1033 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1035 __isl_give isl_basic_map *isl_basic_map_from_aff(
1036 __isl_take isl_aff *aff);
1037 __isl_give isl_map *isl_map_from_pw_aff(
1038 __isl_take isl_pw_aff *pwaff);
1039 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1040 __isl_take isl_dim *domain_dim,
1041 __isl_take isl_aff_list *list);
1043 The C<domain_dim> argument describes the domain of the resulting
1044 basic relation. It is required because the C<list> may consist
1045 of zero affine expressions.
1047 =head2 Inspecting Sets and Relations
1049 Usually, the user should not have to care about the actual constraints
1050 of the sets and maps, but should instead apply the abstract operations
1051 explained in the following sections.
1052 Occasionally, however, it may be required to inspect the individual
1053 coefficients of the constraints. This section explains how to do so.
1054 In these cases, it may also be useful to have C<isl> compute
1055 an explicit representation of the existentially quantified variables.
1057 __isl_give isl_set *isl_set_compute_divs(
1058 __isl_take isl_set *set);
1059 __isl_give isl_map *isl_map_compute_divs(
1060 __isl_take isl_map *map);
1061 __isl_give isl_union_set *isl_union_set_compute_divs(
1062 __isl_take isl_union_set *uset);
1063 __isl_give isl_union_map *isl_union_map_compute_divs(
1064 __isl_take isl_union_map *umap);
1066 This explicit representation defines the existentially quantified
1067 variables as integer divisions of the other variables, possibly
1068 including earlier existentially quantified variables.
1069 An explicitly represented existentially quantified variable therefore
1070 has a unique value when the values of the other variables are known.
1071 If, furthermore, the same existentials, i.e., existentials
1072 with the same explicit representations, should appear in the
1073 same order in each of the disjuncts of a set or map, then the user should call
1074 either of the following functions.
1076 __isl_give isl_set *isl_set_align_divs(
1077 __isl_take isl_set *set);
1078 __isl_give isl_map *isl_map_align_divs(
1079 __isl_take isl_map *map);
1081 Alternatively, the existentially quantified variables can be removed
1082 using the following functions, which compute an overapproximation.
1084 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1085 __isl_take isl_basic_set *bset);
1086 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1087 __isl_take isl_basic_map *bmap);
1088 __isl_give isl_set *isl_set_remove_divs(
1089 __isl_take isl_set *set);
1090 __isl_give isl_map *isl_map_remove_divs(
1091 __isl_take isl_map *map);
1093 To iterate over all the sets or maps in a union set or map, use
1095 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1096 int (*fn)(__isl_take isl_set *set, void *user),
1098 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1099 int (*fn)(__isl_take isl_map *map, void *user),
1102 The number of sets or maps in a union set or map can be obtained
1105 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1106 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1108 To extract the set or map from a union with a given dimension
1111 __isl_give isl_set *isl_union_set_extract_set(
1112 __isl_keep isl_union_set *uset,
1113 __isl_take isl_dim *dim);
1114 __isl_give isl_map *isl_union_map_extract_map(
1115 __isl_keep isl_union_map *umap,
1116 __isl_take isl_dim *dim);
1118 To iterate over all the basic sets or maps in a set or map, use
1120 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1121 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1123 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1124 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1127 The callback function C<fn> should return 0 if successful and
1128 -1 if an error occurs. In the latter case, or if any other error
1129 occurs, the above functions will return -1.
1131 It should be noted that C<isl> does not guarantee that
1132 the basic sets or maps passed to C<fn> are disjoint.
1133 If this is required, then the user should call one of
1134 the following functions first.
1136 __isl_give isl_set *isl_set_make_disjoint(
1137 __isl_take isl_set *set);
1138 __isl_give isl_map *isl_map_make_disjoint(
1139 __isl_take isl_map *map);
1141 The number of basic sets in a set can be obtained
1144 int isl_set_n_basic_set(__isl_keep isl_set *set);
1146 To iterate over the constraints of a basic set or map, use
1148 #include <isl/constraint.h>
1150 int isl_basic_map_foreach_constraint(
1151 __isl_keep isl_basic_map *bmap,
1152 int (*fn)(__isl_take isl_constraint *c, void *user),
1154 void isl_constraint_free(struct isl_constraint *c);
1156 Again, the callback function C<fn> should return 0 if successful and
1157 -1 if an error occurs. In the latter case, or if any other error
1158 occurs, the above functions will return -1.
1159 The constraint C<c> represents either an equality or an inequality.
1160 Use the following function to find out whether a constraint
1161 represents an equality. If not, it represents an inequality.
1163 int isl_constraint_is_equality(
1164 __isl_keep isl_constraint *constraint);
1166 The coefficients of the constraints can be inspected using
1167 the following functions.
1169 void isl_constraint_get_constant(
1170 __isl_keep isl_constraint *constraint, isl_int *v);
1171 void isl_constraint_get_coefficient(
1172 __isl_keep isl_constraint *constraint,
1173 enum isl_dim_type type, int pos, isl_int *v);
1174 int isl_constraint_involves_dims(
1175 __isl_keep isl_constraint *constraint,
1176 enum isl_dim_type type, unsigned first, unsigned n);
1178 The explicit representations of the existentially quantified
1179 variables can be inspected using the following functions.
1180 Note that the user is only allowed to use these functions
1181 if the inspected set or map is the result of a call
1182 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1184 __isl_give isl_div *isl_constraint_div(
1185 __isl_keep isl_constraint *constraint, int pos);
1186 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1187 void isl_div_get_constant(__isl_keep isl_div *div,
1189 void isl_div_get_denominator(__isl_keep isl_div *div,
1191 void isl_div_get_coefficient(__isl_keep isl_div *div,
1192 enum isl_dim_type type, int pos, isl_int *v);
1194 To obtain the constraints of a basic set or map in matrix
1195 form, use the following functions.
1197 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1198 __isl_keep isl_basic_set *bset,
1199 enum isl_dim_type c1, enum isl_dim_type c2,
1200 enum isl_dim_type c3, enum isl_dim_type c4);
1201 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1202 __isl_keep isl_basic_set *bset,
1203 enum isl_dim_type c1, enum isl_dim_type c2,
1204 enum isl_dim_type c3, enum isl_dim_type c4);
1205 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1206 __isl_keep isl_basic_map *bmap,
1207 enum isl_dim_type c1,
1208 enum isl_dim_type c2, enum isl_dim_type c3,
1209 enum isl_dim_type c4, enum isl_dim_type c5);
1210 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1211 __isl_keep isl_basic_map *bmap,
1212 enum isl_dim_type c1,
1213 enum isl_dim_type c2, enum isl_dim_type c3,
1214 enum isl_dim_type c4, enum isl_dim_type c5);
1216 The C<isl_dim_type> arguments dictate the order in which
1217 different kinds of variables appear in the resulting matrix
1218 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1219 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1221 The names of the domain and range spaces of a set or relation can be
1222 read off using the following functions.
1224 const char *isl_basic_set_get_tuple_name(
1225 __isl_keep isl_basic_set *bset);
1226 const char *isl_set_get_tuple_name(
1227 __isl_keep isl_set *set);
1228 const char *isl_basic_map_get_tuple_name(
1229 __isl_keep isl_basic_map *bmap,
1230 enum isl_dim_type type);
1231 const char *isl_map_get_tuple_name(
1232 __isl_keep isl_map *map,
1233 enum isl_dim_type type);
1235 As with C<isl_dim_get_tuple_name>, the value returned points to
1236 an internal data structure.
1237 The names of individual dimensions can be read off using
1238 the following functions.
1240 const char *isl_constraint_get_dim_name(
1241 __isl_keep isl_constraint *constraint,
1242 enum isl_dim_type type, unsigned pos);
1243 const char *isl_basic_set_get_dim_name(
1244 __isl_keep isl_basic_set *bset,
1245 enum isl_dim_type type, unsigned pos);
1246 const char *isl_set_get_dim_name(
1247 __isl_keep isl_set *set,
1248 enum isl_dim_type type, unsigned pos);
1249 const char *isl_basic_map_get_dim_name(
1250 __isl_keep isl_basic_map *bmap,
1251 enum isl_dim_type type, unsigned pos);
1252 const char *isl_map_get_dim_name(
1253 __isl_keep isl_map *map,
1254 enum isl_dim_type type, unsigned pos);
1256 These functions are mostly useful to obtain the names
1261 =head3 Unary Properties
1267 The following functions test whether the given set or relation
1268 contains any integer points. The ``plain'' variants do not perform
1269 any computations, but simply check if the given set or relation
1270 is already known to be empty.
1272 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1273 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1274 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1275 int isl_set_is_empty(__isl_keep isl_set *set);
1276 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1277 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1278 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1279 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1280 int isl_map_is_empty(__isl_keep isl_map *map);
1281 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1283 =item * Universality
1285 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1286 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1287 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1289 =item * Single-valuedness
1291 int isl_map_is_single_valued(__isl_keep isl_map *map);
1292 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1296 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1297 int isl_map_is_injective(__isl_keep isl_map *map);
1298 int isl_union_map_plain_is_injective(
1299 __isl_keep isl_union_map *umap);
1300 int isl_union_map_is_injective(
1301 __isl_keep isl_union_map *umap);
1305 int isl_map_is_bijective(__isl_keep isl_map *map);
1306 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1310 The following functions check whether the domain of the given
1311 (basic) set is a wrapped relation.
1313 int isl_basic_set_is_wrapping(
1314 __isl_keep isl_basic_set *bset);
1315 int isl_set_is_wrapping(__isl_keep isl_set *set);
1317 =item * Internal Product
1319 int isl_basic_map_can_zip(
1320 __isl_keep isl_basic_map *bmap);
1321 int isl_map_can_zip(__isl_keep isl_map *map);
1323 Check whether the product of domain and range of the given relation
1325 i.e., whether both domain and range are nested relations.
1329 =head3 Binary Properties
1335 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1336 __isl_keep isl_set *set2);
1337 int isl_set_is_equal(__isl_keep isl_set *set1,
1338 __isl_keep isl_set *set2);
1339 int isl_union_set_is_equal(
1340 __isl_keep isl_union_set *uset1,
1341 __isl_keep isl_union_set *uset2);
1342 int isl_basic_map_is_equal(
1343 __isl_keep isl_basic_map *bmap1,
1344 __isl_keep isl_basic_map *bmap2);
1345 int isl_map_is_equal(__isl_keep isl_map *map1,
1346 __isl_keep isl_map *map2);
1347 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1348 __isl_keep isl_map *map2);
1349 int isl_union_map_is_equal(
1350 __isl_keep isl_union_map *umap1,
1351 __isl_keep isl_union_map *umap2);
1353 =item * Disjointness
1355 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1356 __isl_keep isl_set *set2);
1360 int isl_set_is_subset(__isl_keep isl_set *set1,
1361 __isl_keep isl_set *set2);
1362 int isl_set_is_strict_subset(
1363 __isl_keep isl_set *set1,
1364 __isl_keep isl_set *set2);
1365 int isl_union_set_is_subset(
1366 __isl_keep isl_union_set *uset1,
1367 __isl_keep isl_union_set *uset2);
1368 int isl_union_set_is_strict_subset(
1369 __isl_keep isl_union_set *uset1,
1370 __isl_keep isl_union_set *uset2);
1371 int isl_basic_map_is_subset(
1372 __isl_keep isl_basic_map *bmap1,
1373 __isl_keep isl_basic_map *bmap2);
1374 int isl_basic_map_is_strict_subset(
1375 __isl_keep isl_basic_map *bmap1,
1376 __isl_keep isl_basic_map *bmap2);
1377 int isl_map_is_subset(
1378 __isl_keep isl_map *map1,
1379 __isl_keep isl_map *map2);
1380 int isl_map_is_strict_subset(
1381 __isl_keep isl_map *map1,
1382 __isl_keep isl_map *map2);
1383 int isl_union_map_is_subset(
1384 __isl_keep isl_union_map *umap1,
1385 __isl_keep isl_union_map *umap2);
1386 int isl_union_map_is_strict_subset(
1387 __isl_keep isl_union_map *umap1,
1388 __isl_keep isl_union_map *umap2);
1392 =head2 Unary Operations
1398 __isl_give isl_set *isl_set_complement(
1399 __isl_take isl_set *set);
1403 __isl_give isl_basic_map *isl_basic_map_reverse(
1404 __isl_take isl_basic_map *bmap);
1405 __isl_give isl_map *isl_map_reverse(
1406 __isl_take isl_map *map);
1407 __isl_give isl_union_map *isl_union_map_reverse(
1408 __isl_take isl_union_map *umap);
1412 __isl_give isl_basic_set *isl_basic_set_project_out(
1413 __isl_take isl_basic_set *bset,
1414 enum isl_dim_type type, unsigned first, unsigned n);
1415 __isl_give isl_basic_map *isl_basic_map_project_out(
1416 __isl_take isl_basic_map *bmap,
1417 enum isl_dim_type type, unsigned first, unsigned n);
1418 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1419 enum isl_dim_type type, unsigned first, unsigned n);
1420 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1421 enum isl_dim_type type, unsigned first, unsigned n);
1422 __isl_give isl_basic_set *isl_basic_map_domain(
1423 __isl_take isl_basic_map *bmap);
1424 __isl_give isl_basic_set *isl_basic_map_range(
1425 __isl_take isl_basic_map *bmap);
1426 __isl_give isl_set *isl_map_domain(
1427 __isl_take isl_map *bmap);
1428 __isl_give isl_set *isl_map_range(
1429 __isl_take isl_map *map);
1430 __isl_give isl_union_set *isl_union_map_domain(
1431 __isl_take isl_union_map *umap);
1432 __isl_give isl_union_set *isl_union_map_range(
1433 __isl_take isl_union_map *umap);
1435 __isl_give isl_basic_map *isl_basic_map_domain_map(
1436 __isl_take isl_basic_map *bmap);
1437 __isl_give isl_basic_map *isl_basic_map_range_map(
1438 __isl_take isl_basic_map *bmap);
1439 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1440 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1441 __isl_give isl_union_map *isl_union_map_domain_map(
1442 __isl_take isl_union_map *umap);
1443 __isl_give isl_union_map *isl_union_map_range_map(
1444 __isl_take isl_union_map *umap);
1446 The functions above construct a (basic, regular or union) relation
1447 that maps (a wrapped version of) the input relation to its domain or range.
1451 __isl_give isl_set *isl_set_eliminate(
1452 __isl_take isl_set *set, enum isl_dim_type type,
1453 unsigned first, unsigned n);
1455 Eliminate the coefficients for the given dimensions from the constraints,
1456 without removing the dimensions.
1460 __isl_give isl_basic_set *isl_basic_set_fix(
1461 __isl_take isl_basic_set *bset,
1462 enum isl_dim_type type, unsigned pos,
1464 __isl_give isl_basic_set *isl_basic_set_fix_si(
1465 __isl_take isl_basic_set *bset,
1466 enum isl_dim_type type, unsigned pos, int value);
1467 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1468 enum isl_dim_type type, unsigned pos,
1470 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1471 enum isl_dim_type type, unsigned pos, int value);
1472 __isl_give isl_basic_map *isl_basic_map_fix_si(
1473 __isl_take isl_basic_map *bmap,
1474 enum isl_dim_type type, unsigned pos, int value);
1475 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1476 enum isl_dim_type type, unsigned pos, int value);
1478 Intersect the set or relation with the hyperplane where the given
1479 dimension has the fixed given value.
1483 __isl_give isl_map *isl_set_identity(
1484 __isl_take isl_set *set);
1485 __isl_give isl_union_map *isl_union_set_identity(
1486 __isl_take isl_union_set *uset);
1488 Construct an identity relation on the given (union) set.
1492 __isl_give isl_basic_set *isl_basic_map_deltas(
1493 __isl_take isl_basic_map *bmap);
1494 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1495 __isl_give isl_union_set *isl_union_map_deltas(
1496 __isl_take isl_union_map *umap);
1498 These functions return a (basic) set containing the differences
1499 between image elements and corresponding domain elements in the input.
1501 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1502 __isl_take isl_basic_map *bmap);
1503 __isl_give isl_map *isl_map_deltas_map(
1504 __isl_take isl_map *map);
1505 __isl_give isl_union_map *isl_union_map_deltas_map(
1506 __isl_take isl_union_map *umap);
1508 The functions above construct a (basic, regular or union) relation
1509 that maps (a wrapped version of) the input relation to its delta set.
1513 Simplify the representation of a set or relation by trying
1514 to combine pairs of basic sets or relations into a single
1515 basic set or relation.
1517 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1518 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1519 __isl_give isl_union_set *isl_union_set_coalesce(
1520 __isl_take isl_union_set *uset);
1521 __isl_give isl_union_map *isl_union_map_coalesce(
1522 __isl_take isl_union_map *umap);
1524 =item * Detecting equalities
1526 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1527 __isl_take isl_basic_set *bset);
1528 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1529 __isl_take isl_basic_map *bmap);
1530 __isl_give isl_set *isl_set_detect_equalities(
1531 __isl_take isl_set *set);
1532 __isl_give isl_map *isl_map_detect_equalities(
1533 __isl_take isl_map *map);
1534 __isl_give isl_union_set *isl_union_set_detect_equalities(
1535 __isl_take isl_union_set *uset);
1536 __isl_give isl_union_map *isl_union_map_detect_equalities(
1537 __isl_take isl_union_map *umap);
1539 Simplify the representation of a set or relation by detecting implicit
1542 =item * Removing redundant constraints
1544 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1545 __isl_take isl_basic_set *bset);
1546 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1547 __isl_take isl_basic_map *bmap);
1551 __isl_give isl_basic_set *isl_set_convex_hull(
1552 __isl_take isl_set *set);
1553 __isl_give isl_basic_map *isl_map_convex_hull(
1554 __isl_take isl_map *map);
1556 If the input set or relation has any existentially quantified
1557 variables, then the result of these operations is currently undefined.
1561 __isl_give isl_basic_set *isl_set_simple_hull(
1562 __isl_take isl_set *set);
1563 __isl_give isl_basic_map *isl_map_simple_hull(
1564 __isl_take isl_map *map);
1565 __isl_give isl_union_map *isl_union_map_simple_hull(
1566 __isl_take isl_union_map *umap);
1568 These functions compute a single basic set or relation
1569 that contains the whole input set or relation.
1570 In particular, the output is described by translates
1571 of the constraints describing the basic sets or relations in the input.
1575 (See \autoref{s:simple hull}.)
1581 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1582 __isl_take isl_basic_set *bset);
1583 __isl_give isl_basic_set *isl_set_affine_hull(
1584 __isl_take isl_set *set);
1585 __isl_give isl_union_set *isl_union_set_affine_hull(
1586 __isl_take isl_union_set *uset);
1587 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1588 __isl_take isl_basic_map *bmap);
1589 __isl_give isl_basic_map *isl_map_affine_hull(
1590 __isl_take isl_map *map);
1591 __isl_give isl_union_map *isl_union_map_affine_hull(
1592 __isl_take isl_union_map *umap);
1594 In case of union sets and relations, the affine hull is computed
1597 =item * Polyhedral hull
1599 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1600 __isl_take isl_set *set);
1601 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1602 __isl_take isl_map *map);
1603 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1604 __isl_take isl_union_set *uset);
1605 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1606 __isl_take isl_union_map *umap);
1608 These functions compute a single basic set or relation
1609 not involving any existentially quantified variables
1610 that contains the whole input set or relation.
1611 In case of union sets and relations, the polyhedral hull is computed
1614 =item * Optimization
1616 #include <isl/ilp.h>
1617 enum isl_lp_result isl_basic_set_max(
1618 __isl_keep isl_basic_set *bset,
1619 __isl_keep isl_aff *obj, isl_int *opt)
1620 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1621 __isl_keep isl_aff *obj, isl_int *opt);
1623 Compute the maximum of the integer affine expression C<obj>
1624 over the points in C<set>, returning the result in C<opt>.
1625 The return value may be one of C<isl_lp_error>,
1626 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1628 =item * Parametric optimization
1630 __isl_give isl_pw_aff *isl_set_dim_max(
1631 __isl_take isl_set *set, int pos);
1633 Compute the maximum of the given set dimension as a function of the
1634 parameters, but independently of the other set dimensions.
1635 For lexicographic optimization, see L<"Lexicographic Optimization">.
1639 The following functions compute either the set of (rational) coefficient
1640 values of valid constraints for the given set or the set of (rational)
1641 values satisfying the constraints with coefficients from the given set.
1642 Internally, these two sets of functions perform essentially the
1643 same operations, except that the set of coefficients is assumed to
1644 be a cone, while the set of values may be any polyhedron.
1645 The current implementation is based on the Farkas lemma and
1646 Fourier-Motzkin elimination, but this may change or be made optional
1647 in future. In particular, future implementations may use different
1648 dualization algorithms or skip the elimination step.
1650 __isl_give isl_basic_set *isl_basic_set_coefficients(
1651 __isl_take isl_basic_set *bset);
1652 __isl_give isl_basic_set *isl_set_coefficients(
1653 __isl_take isl_set *set);
1654 __isl_give isl_union_set *isl_union_set_coefficients(
1655 __isl_take isl_union_set *bset);
1656 __isl_give isl_basic_set *isl_basic_set_solutions(
1657 __isl_take isl_basic_set *bset);
1658 __isl_give isl_basic_set *isl_set_solutions(
1659 __isl_take isl_set *set);
1660 __isl_give isl_union_set *isl_union_set_solutions(
1661 __isl_take isl_union_set *bset);
1665 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1667 __isl_give isl_union_map *isl_union_map_power(
1668 __isl_take isl_union_map *umap, int *exact);
1670 Compute a parametric representation for all positive powers I<k> of C<map>.
1671 The result maps I<k> to a nested relation corresponding to the
1672 I<k>th power of C<map>.
1673 The result may be an overapproximation. If the result is known to be exact,
1674 then C<*exact> is set to C<1>.
1676 =item * Transitive closure
1678 __isl_give isl_map *isl_map_transitive_closure(
1679 __isl_take isl_map *map, int *exact);
1680 __isl_give isl_union_map *isl_union_map_transitive_closure(
1681 __isl_take isl_union_map *umap, int *exact);
1683 Compute the transitive closure of C<map>.
1684 The result may be an overapproximation. If the result is known to be exact,
1685 then C<*exact> is set to C<1>.
1687 =item * Reaching path lengths
1689 __isl_give isl_map *isl_map_reaching_path_lengths(
1690 __isl_take isl_map *map, int *exact);
1692 Compute a relation that maps each element in the range of C<map>
1693 to the lengths of all paths composed of edges in C<map> that
1694 end up in the given element.
1695 The result may be an overapproximation. If the result is known to be exact,
1696 then C<*exact> is set to C<1>.
1697 To compute the I<maximal> path length, the resulting relation
1698 should be postprocessed by C<isl_map_lexmax>.
1699 In particular, if the input relation is a dependence relation
1700 (mapping sources to sinks), then the maximal path length corresponds
1701 to the free schedule.
1702 Note, however, that C<isl_map_lexmax> expects the maximum to be
1703 finite, so if the path lengths are unbounded (possibly due to
1704 the overapproximation), then you will get an error message.
1708 __isl_give isl_basic_set *isl_basic_map_wrap(
1709 __isl_take isl_basic_map *bmap);
1710 __isl_give isl_set *isl_map_wrap(
1711 __isl_take isl_map *map);
1712 __isl_give isl_union_set *isl_union_map_wrap(
1713 __isl_take isl_union_map *umap);
1714 __isl_give isl_basic_map *isl_basic_set_unwrap(
1715 __isl_take isl_basic_set *bset);
1716 __isl_give isl_map *isl_set_unwrap(
1717 __isl_take isl_set *set);
1718 __isl_give isl_union_map *isl_union_set_unwrap(
1719 __isl_take isl_union_set *uset);
1723 Remove any internal structure of domain (and range) of the given
1724 set or relation. If there is any such internal structure in the input,
1725 then the name of the space is also removed.
1727 __isl_give isl_basic_set *isl_basic_set_flatten(
1728 __isl_take isl_basic_set *bset);
1729 __isl_give isl_set *isl_set_flatten(
1730 __isl_take isl_set *set);
1731 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1732 __isl_take isl_basic_map *bmap);
1733 __isl_give isl_map *isl_map_flatten_range(
1734 __isl_take isl_map *map);
1735 __isl_give isl_basic_map *isl_basic_map_flatten(
1736 __isl_take isl_basic_map *bmap);
1737 __isl_give isl_map *isl_map_flatten(
1738 __isl_take isl_map *map);
1740 __isl_give isl_map *isl_set_flatten_map(
1741 __isl_take isl_set *set);
1743 The function above constructs a relation
1744 that maps the input set to a flattened version of the set.
1748 Lift the input set to a space with extra dimensions corresponding
1749 to the existentially quantified variables in the input.
1750 In particular, the result lives in a wrapped map where the domain
1751 is the original space and the range corresponds to the original
1752 existentially quantified variables.
1754 __isl_give isl_basic_set *isl_basic_set_lift(
1755 __isl_take isl_basic_set *bset);
1756 __isl_give isl_set *isl_set_lift(
1757 __isl_take isl_set *set);
1758 __isl_give isl_union_set *isl_union_set_lift(
1759 __isl_take isl_union_set *uset);
1761 =item * Internal Product
1763 __isl_give isl_basic_map *isl_basic_map_zip(
1764 __isl_take isl_basic_map *bmap);
1765 __isl_give isl_map *isl_map_zip(
1766 __isl_take isl_map *map);
1767 __isl_give isl_union_map *isl_union_map_zip(
1768 __isl_take isl_union_map *umap);
1770 Given a relation with nested relations for domain and range,
1771 interchange the range of the domain with the domain of the range.
1773 =item * Aligning parameters
1775 __isl_give isl_set *isl_set_align_params(
1776 __isl_take isl_set *set,
1777 __isl_take isl_dim *model);
1778 __isl_give isl_map *isl_map_align_params(
1779 __isl_take isl_map *map,
1780 __isl_take isl_dim *model);
1782 Change the order of the parameters of the given set or relation
1783 such that the first parameters match those of C<model>.
1784 This may involve the introduction of extra parameters.
1785 All parameters need to be named.
1787 =item * Dimension manipulation
1789 __isl_give isl_set *isl_set_add_dims(
1790 __isl_take isl_set *set,
1791 enum isl_dim_type type, unsigned n);
1792 __isl_give isl_map *isl_map_add_dims(
1793 __isl_take isl_map *map,
1794 enum isl_dim_type type, unsigned n);
1796 It is usually not advisable to directly change the (input or output)
1797 space of a set or a relation as this removes the name and the internal
1798 structure of the space. However, the above functions can be useful
1799 to add new parameters, assuming
1800 C<isl_set_align_params> and C<isl_map_align_params>
1805 =head2 Binary Operations
1807 The two arguments of a binary operation not only need to live
1808 in the same C<isl_ctx>, they currently also need to have
1809 the same (number of) parameters.
1811 =head3 Basic Operations
1815 =item * Intersection
1817 __isl_give isl_basic_set *isl_basic_set_intersect(
1818 __isl_take isl_basic_set *bset1,
1819 __isl_take isl_basic_set *bset2);
1820 __isl_give isl_set *isl_set_intersect(
1821 __isl_take isl_set *set1,
1822 __isl_take isl_set *set2);
1823 __isl_give isl_union_set *isl_union_set_intersect(
1824 __isl_take isl_union_set *uset1,
1825 __isl_take isl_union_set *uset2);
1826 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1827 __isl_take isl_basic_map *bmap,
1828 __isl_take isl_basic_set *bset);
1829 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1830 __isl_take isl_basic_map *bmap,
1831 __isl_take isl_basic_set *bset);
1832 __isl_give isl_basic_map *isl_basic_map_intersect(
1833 __isl_take isl_basic_map *bmap1,
1834 __isl_take isl_basic_map *bmap2);
1835 __isl_give isl_map *isl_map_intersect_domain(
1836 __isl_take isl_map *map,
1837 __isl_take isl_set *set);
1838 __isl_give isl_map *isl_map_intersect_range(
1839 __isl_take isl_map *map,
1840 __isl_take isl_set *set);
1841 __isl_give isl_map *isl_map_intersect(
1842 __isl_take isl_map *map1,
1843 __isl_take isl_map *map2);
1844 __isl_give isl_union_map *isl_union_map_intersect_domain(
1845 __isl_take isl_union_map *umap,
1846 __isl_take isl_union_set *uset);
1847 __isl_give isl_union_map *isl_union_map_intersect_range(
1848 __isl_take isl_union_map *umap,
1849 __isl_take isl_union_set *uset);
1850 __isl_give isl_union_map *isl_union_map_intersect(
1851 __isl_take isl_union_map *umap1,
1852 __isl_take isl_union_map *umap2);
1856 __isl_give isl_set *isl_basic_set_union(
1857 __isl_take isl_basic_set *bset1,
1858 __isl_take isl_basic_set *bset2);
1859 __isl_give isl_map *isl_basic_map_union(
1860 __isl_take isl_basic_map *bmap1,
1861 __isl_take isl_basic_map *bmap2);
1862 __isl_give isl_set *isl_set_union(
1863 __isl_take isl_set *set1,
1864 __isl_take isl_set *set2);
1865 __isl_give isl_map *isl_map_union(
1866 __isl_take isl_map *map1,
1867 __isl_take isl_map *map2);
1868 __isl_give isl_union_set *isl_union_set_union(
1869 __isl_take isl_union_set *uset1,
1870 __isl_take isl_union_set *uset2);
1871 __isl_give isl_union_map *isl_union_map_union(
1872 __isl_take isl_union_map *umap1,
1873 __isl_take isl_union_map *umap2);
1875 =item * Set difference
1877 __isl_give isl_set *isl_set_subtract(
1878 __isl_take isl_set *set1,
1879 __isl_take isl_set *set2);
1880 __isl_give isl_map *isl_map_subtract(
1881 __isl_take isl_map *map1,
1882 __isl_take isl_map *map2);
1883 __isl_give isl_union_set *isl_union_set_subtract(
1884 __isl_take isl_union_set *uset1,
1885 __isl_take isl_union_set *uset2);
1886 __isl_give isl_union_map *isl_union_map_subtract(
1887 __isl_take isl_union_map *umap1,
1888 __isl_take isl_union_map *umap2);
1892 __isl_give isl_basic_set *isl_basic_set_apply(
1893 __isl_take isl_basic_set *bset,
1894 __isl_take isl_basic_map *bmap);
1895 __isl_give isl_set *isl_set_apply(
1896 __isl_take isl_set *set,
1897 __isl_take isl_map *map);
1898 __isl_give isl_union_set *isl_union_set_apply(
1899 __isl_take isl_union_set *uset,
1900 __isl_take isl_union_map *umap);
1901 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1902 __isl_take isl_basic_map *bmap1,
1903 __isl_take isl_basic_map *bmap2);
1904 __isl_give isl_basic_map *isl_basic_map_apply_range(
1905 __isl_take isl_basic_map *bmap1,
1906 __isl_take isl_basic_map *bmap2);
1907 __isl_give isl_map *isl_map_apply_domain(
1908 __isl_take isl_map *map1,
1909 __isl_take isl_map *map2);
1910 __isl_give isl_union_map *isl_union_map_apply_domain(
1911 __isl_take isl_union_map *umap1,
1912 __isl_take isl_union_map *umap2);
1913 __isl_give isl_map *isl_map_apply_range(
1914 __isl_take isl_map *map1,
1915 __isl_take isl_map *map2);
1916 __isl_give isl_union_map *isl_union_map_apply_range(
1917 __isl_take isl_union_map *umap1,
1918 __isl_take isl_union_map *umap2);
1920 =item * Cartesian Product
1922 __isl_give isl_set *isl_set_product(
1923 __isl_take isl_set *set1,
1924 __isl_take isl_set *set2);
1925 __isl_give isl_union_set *isl_union_set_product(
1926 __isl_take isl_union_set *uset1,
1927 __isl_take isl_union_set *uset2);
1928 __isl_give isl_basic_map *isl_basic_map_range_product(
1929 __isl_take isl_basic_map *bmap1,
1930 __isl_take isl_basic_map *bmap2);
1931 __isl_give isl_map *isl_map_range_product(
1932 __isl_take isl_map *map1,
1933 __isl_take isl_map *map2);
1934 __isl_give isl_union_map *isl_union_map_range_product(
1935 __isl_take isl_union_map *umap1,
1936 __isl_take isl_union_map *umap2);
1937 __isl_give isl_map *isl_map_product(
1938 __isl_take isl_map *map1,
1939 __isl_take isl_map *map2);
1940 __isl_give isl_union_map *isl_union_map_product(
1941 __isl_take isl_union_map *umap1,
1942 __isl_take isl_union_map *umap2);
1944 The above functions compute the cross product of the given
1945 sets or relations. The domains and ranges of the results
1946 are wrapped maps between domains and ranges of the inputs.
1947 To obtain a ``flat'' product, use the following functions
1950 __isl_give isl_basic_set *isl_basic_set_flat_product(
1951 __isl_take isl_basic_set *bset1,
1952 __isl_take isl_basic_set *bset2);
1953 __isl_give isl_set *isl_set_flat_product(
1954 __isl_take isl_set *set1,
1955 __isl_take isl_set *set2);
1956 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1957 __isl_take isl_basic_map *bmap1,
1958 __isl_take isl_basic_map *bmap2);
1959 __isl_give isl_map *isl_map_flat_range_product(
1960 __isl_take isl_map *map1,
1961 __isl_take isl_map *map2);
1962 __isl_give isl_union_map *isl_union_map_flat_range_product(
1963 __isl_take isl_union_map *umap1,
1964 __isl_take isl_union_map *umap2);
1965 __isl_give isl_basic_map *isl_basic_map_flat_product(
1966 __isl_take isl_basic_map *bmap1,
1967 __isl_take isl_basic_map *bmap2);
1968 __isl_give isl_map *isl_map_flat_product(
1969 __isl_take isl_map *map1,
1970 __isl_take isl_map *map2);
1972 =item * Simplification
1974 __isl_give isl_basic_set *isl_basic_set_gist(
1975 __isl_take isl_basic_set *bset,
1976 __isl_take isl_basic_set *context);
1977 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1978 __isl_take isl_set *context);
1979 __isl_give isl_union_set *isl_union_set_gist(
1980 __isl_take isl_union_set *uset,
1981 __isl_take isl_union_set *context);
1982 __isl_give isl_basic_map *isl_basic_map_gist(
1983 __isl_take isl_basic_map *bmap,
1984 __isl_take isl_basic_map *context);
1985 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1986 __isl_take isl_map *context);
1987 __isl_give isl_union_map *isl_union_map_gist(
1988 __isl_take isl_union_map *umap,
1989 __isl_take isl_union_map *context);
1991 The gist operation returns a set or relation that has the
1992 same intersection with the context as the input set or relation.
1993 Any implicit equality in the intersection is made explicit in the result,
1994 while all inequalities that are redundant with respect to the intersection
1996 In case of union sets and relations, the gist operation is performed
2001 =head3 Lexicographic Optimization
2003 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2004 the following functions
2005 compute a set that contains the lexicographic minimum or maximum
2006 of the elements in C<set> (or C<bset>) for those values of the parameters
2007 that satisfy C<dom>.
2008 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2009 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2011 In other words, the union of the parameter values
2012 for which the result is non-empty and of C<*empty>
2015 __isl_give isl_set *isl_basic_set_partial_lexmin(
2016 __isl_take isl_basic_set *bset,
2017 __isl_take isl_basic_set *dom,
2018 __isl_give isl_set **empty);
2019 __isl_give isl_set *isl_basic_set_partial_lexmax(
2020 __isl_take isl_basic_set *bset,
2021 __isl_take isl_basic_set *dom,
2022 __isl_give isl_set **empty);
2023 __isl_give isl_set *isl_set_partial_lexmin(
2024 __isl_take isl_set *set, __isl_take isl_set *dom,
2025 __isl_give isl_set **empty);
2026 __isl_give isl_set *isl_set_partial_lexmax(
2027 __isl_take isl_set *set, __isl_take isl_set *dom,
2028 __isl_give isl_set **empty);
2030 Given a (basic) set C<set> (or C<bset>), the following functions simply
2031 return a set containing the lexicographic minimum or maximum
2032 of the elements in C<set> (or C<bset>).
2033 In case of union sets, the optimum is computed per space.
2035 __isl_give isl_set *isl_basic_set_lexmin(
2036 __isl_take isl_basic_set *bset);
2037 __isl_give isl_set *isl_basic_set_lexmax(
2038 __isl_take isl_basic_set *bset);
2039 __isl_give isl_set *isl_set_lexmin(
2040 __isl_take isl_set *set);
2041 __isl_give isl_set *isl_set_lexmax(
2042 __isl_take isl_set *set);
2043 __isl_give isl_union_set *isl_union_set_lexmin(
2044 __isl_take isl_union_set *uset);
2045 __isl_give isl_union_set *isl_union_set_lexmax(
2046 __isl_take isl_union_set *uset);
2048 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2049 the following functions
2050 compute a relation that maps each element of C<dom>
2051 to the single lexicographic minimum or maximum
2052 of the elements that are associated to that same
2053 element in C<map> (or C<bmap>).
2054 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2055 that contains the elements in C<dom> that do not map
2056 to any elements in C<map> (or C<bmap>).
2057 In other words, the union of the domain of the result and of C<*empty>
2060 __isl_give isl_map *isl_basic_map_partial_lexmax(
2061 __isl_take isl_basic_map *bmap,
2062 __isl_take isl_basic_set *dom,
2063 __isl_give isl_set **empty);
2064 __isl_give isl_map *isl_basic_map_partial_lexmin(
2065 __isl_take isl_basic_map *bmap,
2066 __isl_take isl_basic_set *dom,
2067 __isl_give isl_set **empty);
2068 __isl_give isl_map *isl_map_partial_lexmax(
2069 __isl_take isl_map *map, __isl_take isl_set *dom,
2070 __isl_give isl_set **empty);
2071 __isl_give isl_map *isl_map_partial_lexmin(
2072 __isl_take isl_map *map, __isl_take isl_set *dom,
2073 __isl_give isl_set **empty);
2075 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2076 return a map mapping each element in the domain of
2077 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2078 of all elements associated to that element.
2079 In case of union relations, the optimum is computed per space.
2081 __isl_give isl_map *isl_basic_map_lexmin(
2082 __isl_take isl_basic_map *bmap);
2083 __isl_give isl_map *isl_basic_map_lexmax(
2084 __isl_take isl_basic_map *bmap);
2085 __isl_give isl_map *isl_map_lexmin(
2086 __isl_take isl_map *map);
2087 __isl_give isl_map *isl_map_lexmax(
2088 __isl_take isl_map *map);
2089 __isl_give isl_union_map *isl_union_map_lexmin(
2090 __isl_take isl_union_map *umap);
2091 __isl_give isl_union_map *isl_union_map_lexmax(
2092 __isl_take isl_union_map *umap);
2096 Lists are defined over several element types, including
2097 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2098 Here we take lists of C<isl_set>s as an example.
2099 Lists can be created, copied and freed using the following functions.
2101 #include <isl/list.h>
2102 __isl_give isl_set_list *isl_set_list_alloc(
2103 isl_ctx *ctx, int n);
2104 __isl_give isl_set_list *isl_set_list_copy(
2105 __isl_keep isl_set_list *list);
2106 __isl_give isl_set_list *isl_set_list_add(
2107 __isl_take isl_set_list *list,
2108 __isl_take isl_set *el);
2109 void isl_set_list_free(__isl_take isl_set_list *list);
2111 C<isl_set_list_alloc> creates an empty list with a capacity for
2114 Lists can be inspected using the following functions.
2116 #include <isl/list.h>
2117 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2118 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2119 __isl_give struct isl_set *isl_set_list_get_set(
2120 __isl_keep isl_set_list *list, int index);
2121 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2122 int (*fn)(__isl_take struct isl_set *el, void *user),
2125 Lists can be printed using
2127 #include <isl/list.h>
2128 __isl_give isl_printer *isl_printer_print_set_list(
2129 __isl_take isl_printer *p,
2130 __isl_keep isl_set_list *list);
2134 Matrices can be created, copied and freed using the following functions.
2136 #include <isl/mat.h>
2137 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2138 unsigned n_row, unsigned n_col);
2139 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2140 void isl_mat_free(__isl_take isl_mat *mat);
2142 Note that the elements of a newly created matrix may have arbitrary values.
2143 The elements can be changed and inspected using the following functions.
2145 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2146 int isl_mat_rows(__isl_keep isl_mat *mat);
2147 int isl_mat_cols(__isl_keep isl_mat *mat);
2148 int isl_mat_get_element(__isl_keep isl_mat *mat,
2149 int row, int col, isl_int *v);
2150 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2151 int row, int col, isl_int v);
2152 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2153 int row, int col, int v);
2155 C<isl_mat_get_element> will return a negative value if anything went wrong.
2156 In that case, the value of C<*v> is undefined.
2158 The following function can be used to compute the (right) inverse
2159 of a matrix, i.e., a matrix such that the product of the original
2160 and the inverse (in that order) is a multiple of the identity matrix.
2161 The input matrix is assumed to be of full row-rank.
2163 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2165 The following function can be used to compute the (right) kernel
2166 (or null space) of a matrix, i.e., a matrix such that the product of
2167 the original and the kernel (in that order) is the zero matrix.
2169 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2171 =head2 Piecewise Quasi Affine Expressions
2173 The zero quasi affine expression can be created using
2175 __isl_give isl_aff *isl_aff_zero(
2176 __isl_take isl_local_space *ls);
2178 An empty piecewise quasi affine expression (one with no cells)
2179 or a piecewise quasi affine expression with a single cell can
2180 be created using the following functions.
2182 #include <isl/aff.h>
2183 __isl_give isl_pw_aff *isl_pw_aff_empty(
2184 __isl_take isl_dim *dim);
2185 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2186 __isl_take isl_set *set, __isl_take isl_aff *aff);
2188 Quasi affine expressions can be copied and free using
2190 #include <isl/aff.h>
2191 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2192 void *isl_aff_free(__isl_take isl_aff *aff);
2194 __isl_give isl_pw_aff *isl_pw_aff_copy(
2195 __isl_keep isl_pw_aff *pwaff);
2196 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2198 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2199 using the following function. The constraint is required to have
2200 a non-zero coefficient for the specified dimension.
2202 #include <isl/constraint.h>
2203 __isl_give isl_aff *isl_constraint_get_bound(
2204 __isl_keep isl_constraint *constraint,
2205 enum isl_dim_type type, int pos);
2207 Conversely, an equality constraint equating
2208 the affine expression to zero or an inequality constraint enforcing
2209 the affine expression to be non-negative, can be constructed using
2211 __isl_give isl_constraint *isl_equality_from_aff(
2212 __isl_take isl_aff *aff);
2213 __isl_give isl_constraint *isl_inequality_from_aff(
2214 __isl_take isl_aff *aff);
2216 The expression can be inspected using
2218 #include <isl/aff.h>
2219 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2220 int isl_aff_dim(__isl_keep isl_aff *aff,
2221 enum isl_dim_type type);
2222 __isl_give isl_local_space *isl_aff_get_local_space(
2223 __isl_keep isl_aff *aff);
2224 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2225 enum isl_dim_type type, unsigned pos);
2226 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2228 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2229 enum isl_dim_type type, int pos, isl_int *v);
2230 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2232 __isl_give isl_div *isl_aff_get_div(
2233 __isl_keep isl_aff *aff, int pos);
2235 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2236 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2238 It can be modified using
2240 #include <isl/aff.h>
2241 __isl_give isl_aff *isl_aff_set_dim_name(
2242 __isl_take isl_aff *aff, enum isl_dim_type type,
2243 unsigned pos, const char *s);
2244 __isl_give isl_aff *isl_aff_set_constant(
2245 __isl_take isl_aff *aff, isl_int v);
2246 __isl_give isl_aff *isl_aff_set_constant_si(
2247 __isl_take isl_aff *aff, int v);
2248 __isl_give isl_aff *isl_aff_set_coefficient(
2249 __isl_take isl_aff *aff,
2250 enum isl_dim_type type, int pos, isl_int v);
2251 __isl_give isl_aff *isl_aff_set_coefficient_si(
2252 __isl_take isl_aff *aff,
2253 enum isl_dim_type type, int pos, int v);
2254 __isl_give isl_aff *isl_aff_set_denominator(
2255 __isl_take isl_aff *aff, isl_int v);
2257 __isl_give isl_aff *isl_aff_add_constant(
2258 __isl_take isl_aff *aff, isl_int v);
2259 __isl_give isl_aff *isl_aff_add_constant_si(
2260 __isl_take isl_aff *aff, int v);
2261 __isl_give isl_aff *isl_aff_add_coefficient_si(
2262 __isl_take isl_aff *aff,
2263 enum isl_dim_type type, int pos, int v);
2265 Note that the C<set_constant> and C<set_coefficient> functions
2266 set the I<numerator> of the constant or coefficient, while
2267 C<add_constant> and C<add_coefficient> add an integer value to
2268 the possibly rational constant or coefficient.
2270 To check whether an affine expressions is obviously zero
2271 or obviously equal to some other affine expression, use
2273 #include <isl/aff.h>
2274 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2275 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2276 __isl_keep isl_aff *aff2);
2280 #include <isl/aff.h>
2281 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2282 __isl_take isl_aff *aff2);
2283 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2284 __isl_take isl_aff *aff2);
2285 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2286 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2287 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2288 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2290 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2292 __isl_give isl_aff *isl_aff_scale_down_ui(
2293 __isl_take isl_aff *aff, unsigned f);
2295 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2296 __isl_take isl_set *context);
2298 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2299 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2301 The function C<isl_aff_ge_basic_set> returns a basic set
2302 containing those elements in the shared space
2303 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2305 #include <isl/aff.h>
2306 __isl_give isl_pw_aff *isl_pw_aff_max(
2307 __isl_take isl_pw_aff *pwaff1,
2308 __isl_take isl_pw_aff *pwaff2);
2310 The function C<isl_pw_aff_max> computes a piecewise quasi-affine
2311 expression with a domain that is the union of those of C<pwaff1> and
2312 C<pwaff2> and such that on each cell, the quasi-affine expression is
2313 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2314 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2315 associated expression is the defined one.
2317 An expression can be printed using
2319 #include <isl/aff.h>
2320 __isl_give isl_printer *isl_printer_print_aff(
2321 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2323 __isl_give isl_printer *isl_printer_print_pw_aff(
2324 __isl_take isl_printer *p,
2325 __isl_keep isl_pw_aff *pwaff);
2329 Points are elements of a set. They can be used to construct
2330 simple sets (boxes) or they can be used to represent the
2331 individual elements of a set.
2332 The zero point (the origin) can be created using
2334 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2336 The coordinates of a point can be inspected, set and changed
2339 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2340 enum isl_dim_type type, int pos, isl_int *v);
2341 __isl_give isl_point *isl_point_set_coordinate(
2342 __isl_take isl_point *pnt,
2343 enum isl_dim_type type, int pos, isl_int v);
2345 __isl_give isl_point *isl_point_add_ui(
2346 __isl_take isl_point *pnt,
2347 enum isl_dim_type type, int pos, unsigned val);
2348 __isl_give isl_point *isl_point_sub_ui(
2349 __isl_take isl_point *pnt,
2350 enum isl_dim_type type, int pos, unsigned val);
2352 Other properties can be obtained using
2354 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2356 Points can be copied or freed using
2358 __isl_give isl_point *isl_point_copy(
2359 __isl_keep isl_point *pnt);
2360 void isl_point_free(__isl_take isl_point *pnt);
2362 A singleton set can be created from a point using
2364 __isl_give isl_basic_set *isl_basic_set_from_point(
2365 __isl_take isl_point *pnt);
2366 __isl_give isl_set *isl_set_from_point(
2367 __isl_take isl_point *pnt);
2369 and a box can be created from two opposite extremal points using
2371 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2372 __isl_take isl_point *pnt1,
2373 __isl_take isl_point *pnt2);
2374 __isl_give isl_set *isl_set_box_from_points(
2375 __isl_take isl_point *pnt1,
2376 __isl_take isl_point *pnt2);
2378 All elements of a B<bounded> (union) set can be enumerated using
2379 the following functions.
2381 int isl_set_foreach_point(__isl_keep isl_set *set,
2382 int (*fn)(__isl_take isl_point *pnt, void *user),
2384 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2385 int (*fn)(__isl_take isl_point *pnt, void *user),
2388 The function C<fn> is called for each integer point in
2389 C<set> with as second argument the last argument of
2390 the C<isl_set_foreach_point> call. The function C<fn>
2391 should return C<0> on success and C<-1> on failure.
2392 In the latter case, C<isl_set_foreach_point> will stop
2393 enumerating and return C<-1> as well.
2394 If the enumeration is performed successfully and to completion,
2395 then C<isl_set_foreach_point> returns C<0>.
2397 To obtain a single point of a (basic) set, use
2399 __isl_give isl_point *isl_basic_set_sample_point(
2400 __isl_take isl_basic_set *bset);
2401 __isl_give isl_point *isl_set_sample_point(
2402 __isl_take isl_set *set);
2404 If C<set> does not contain any (integer) points, then the
2405 resulting point will be ``void'', a property that can be
2408 int isl_point_is_void(__isl_keep isl_point *pnt);
2410 =head2 Piecewise Quasipolynomials
2412 A piecewise quasipolynomial is a particular kind of function that maps
2413 a parametric point to a rational value.
2414 More specifically, a quasipolynomial is a polynomial expression in greatest
2415 integer parts of affine expressions of parameters and variables.
2416 A piecewise quasipolynomial is a subdivision of a given parametric
2417 domain into disjoint cells with a quasipolynomial associated to
2418 each cell. The value of the piecewise quasipolynomial at a given
2419 point is the value of the quasipolynomial associated to the cell
2420 that contains the point. Outside of the union of cells,
2421 the value is assumed to be zero.
2422 For example, the piecewise quasipolynomial
2424 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2426 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2427 A given piecewise quasipolynomial has a fixed domain dimension.
2428 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2429 defined over different domains.
2430 Piecewise quasipolynomials are mainly used by the C<barvinok>
2431 library for representing the number of elements in a parametric set or map.
2432 For example, the piecewise quasipolynomial above represents
2433 the number of points in the map
2435 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2437 =head3 Printing (Piecewise) Quasipolynomials
2439 Quasipolynomials and piecewise quasipolynomials can be printed
2440 using the following functions.
2442 __isl_give isl_printer *isl_printer_print_qpolynomial(
2443 __isl_take isl_printer *p,
2444 __isl_keep isl_qpolynomial *qp);
2446 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2447 __isl_take isl_printer *p,
2448 __isl_keep isl_pw_qpolynomial *pwqp);
2450 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2451 __isl_take isl_printer *p,
2452 __isl_keep isl_union_pw_qpolynomial *upwqp);
2454 The output format of the printer
2455 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2456 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2458 In case of printing in C<ISL_FORMAT_C>, the user may want
2459 to set the names of all dimensions
2461 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2462 __isl_take isl_qpolynomial *qp,
2463 enum isl_dim_type type, unsigned pos,
2465 __isl_give isl_pw_qpolynomial *
2466 isl_pw_qpolynomial_set_dim_name(
2467 __isl_take isl_pw_qpolynomial *pwqp,
2468 enum isl_dim_type type, unsigned pos,
2471 =head3 Creating New (Piecewise) Quasipolynomials
2473 Some simple quasipolynomials can be created using the following functions.
2474 More complicated quasipolynomials can be created by applying
2475 operations such as addition and multiplication
2476 on the resulting quasipolynomials
2478 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2479 __isl_take isl_dim *dim);
2480 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2481 __isl_take isl_dim *dim);
2482 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2483 __isl_take isl_dim *dim);
2484 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2485 __isl_take isl_dim *dim);
2486 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2487 __isl_take isl_dim *dim);
2488 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2489 __isl_take isl_dim *dim,
2490 const isl_int n, const isl_int d);
2491 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2492 __isl_take isl_div *div);
2493 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2494 __isl_take isl_dim *dim,
2495 enum isl_dim_type type, unsigned pos);
2496 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2497 __isl_take isl_aff *aff);
2499 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2500 with a single cell can be created using the following functions.
2501 Multiple of these single cell piecewise quasipolynomials can
2502 be combined to create more complicated piecewise quasipolynomials.
2504 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2505 __isl_take isl_dim *dim);
2506 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2507 __isl_take isl_set *set,
2508 __isl_take isl_qpolynomial *qp);
2510 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2511 __isl_take isl_dim *dim);
2512 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2513 __isl_take isl_pw_qpolynomial *pwqp);
2514 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2515 __isl_take isl_union_pw_qpolynomial *upwqp,
2516 __isl_take isl_pw_qpolynomial *pwqp);
2518 Quasipolynomials can be copied and freed again using the following
2521 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2522 __isl_keep isl_qpolynomial *qp);
2523 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2525 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2526 __isl_keep isl_pw_qpolynomial *pwqp);
2527 void *isl_pw_qpolynomial_free(
2528 __isl_take isl_pw_qpolynomial *pwqp);
2530 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2531 __isl_keep isl_union_pw_qpolynomial *upwqp);
2532 void isl_union_pw_qpolynomial_free(
2533 __isl_take isl_union_pw_qpolynomial *upwqp);
2535 =head3 Inspecting (Piecewise) Quasipolynomials
2537 To iterate over all piecewise quasipolynomials in a union
2538 piecewise quasipolynomial, use the following function
2540 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2541 __isl_keep isl_union_pw_qpolynomial *upwqp,
2542 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2545 To extract the piecewise quasipolynomial from a union with a given dimension
2548 __isl_give isl_pw_qpolynomial *
2549 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2550 __isl_keep isl_union_pw_qpolynomial *upwqp,
2551 __isl_take isl_dim *dim);
2553 To iterate over the cells in a piecewise quasipolynomial,
2554 use either of the following two functions
2556 int isl_pw_qpolynomial_foreach_piece(
2557 __isl_keep isl_pw_qpolynomial *pwqp,
2558 int (*fn)(__isl_take isl_set *set,
2559 __isl_take isl_qpolynomial *qp,
2560 void *user), void *user);
2561 int isl_pw_qpolynomial_foreach_lifted_piece(
2562 __isl_keep isl_pw_qpolynomial *pwqp,
2563 int (*fn)(__isl_take isl_set *set,
2564 __isl_take isl_qpolynomial *qp,
2565 void *user), void *user);
2567 As usual, the function C<fn> should return C<0> on success
2568 and C<-1> on failure. The difference between
2569 C<isl_pw_qpolynomial_foreach_piece> and
2570 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2571 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2572 compute unique representations for all existentially quantified
2573 variables and then turn these existentially quantified variables
2574 into extra set variables, adapting the associated quasipolynomial
2575 accordingly. This means that the C<set> passed to C<fn>
2576 will not have any existentially quantified variables, but that
2577 the dimensions of the sets may be different for different
2578 invocations of C<fn>.
2580 To iterate over all terms in a quasipolynomial,
2583 int isl_qpolynomial_foreach_term(
2584 __isl_keep isl_qpolynomial *qp,
2585 int (*fn)(__isl_take isl_term *term,
2586 void *user), void *user);
2588 The terms themselves can be inspected and freed using
2591 unsigned isl_term_dim(__isl_keep isl_term *term,
2592 enum isl_dim_type type);
2593 void isl_term_get_num(__isl_keep isl_term *term,
2595 void isl_term_get_den(__isl_keep isl_term *term,
2597 int isl_term_get_exp(__isl_keep isl_term *term,
2598 enum isl_dim_type type, unsigned pos);
2599 __isl_give isl_div *isl_term_get_div(
2600 __isl_keep isl_term *term, unsigned pos);
2601 void isl_term_free(__isl_take isl_term *term);
2603 Each term is a product of parameters, set variables and
2604 integer divisions. The function C<isl_term_get_exp>
2605 returns the exponent of a given dimensions in the given term.
2606 The C<isl_int>s in the arguments of C<isl_term_get_num>
2607 and C<isl_term_get_den> need to have been initialized
2608 using C<isl_int_init> before calling these functions.
2610 =head3 Properties of (Piecewise) Quasipolynomials
2612 To check whether a quasipolynomial is actually a constant,
2613 use the following function.
2615 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2616 isl_int *n, isl_int *d);
2618 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2619 then the numerator and denominator of the constant
2620 are returned in C<*n> and C<*d>, respectively.
2622 =head3 Operations on (Piecewise) Quasipolynomials
2624 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2625 __isl_take isl_qpolynomial *qp, isl_int v);
2626 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2627 __isl_take isl_qpolynomial *qp);
2628 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2629 __isl_take isl_qpolynomial *qp1,
2630 __isl_take isl_qpolynomial *qp2);
2631 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2632 __isl_take isl_qpolynomial *qp1,
2633 __isl_take isl_qpolynomial *qp2);
2634 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2635 __isl_take isl_qpolynomial *qp1,
2636 __isl_take isl_qpolynomial *qp2);
2637 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2638 __isl_take isl_qpolynomial *qp, unsigned exponent);
2640 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2641 __isl_take isl_pw_qpolynomial *pwqp1,
2642 __isl_take isl_pw_qpolynomial *pwqp2);
2643 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2644 __isl_take isl_pw_qpolynomial *pwqp1,
2645 __isl_take isl_pw_qpolynomial *pwqp2);
2646 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2647 __isl_take isl_pw_qpolynomial *pwqp1,
2648 __isl_take isl_pw_qpolynomial *pwqp2);
2649 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2650 __isl_take isl_pw_qpolynomial *pwqp);
2651 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2652 __isl_take isl_pw_qpolynomial *pwqp1,
2653 __isl_take isl_pw_qpolynomial *pwqp2);
2655 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2656 __isl_take isl_union_pw_qpolynomial *upwqp1,
2657 __isl_take isl_union_pw_qpolynomial *upwqp2);
2658 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2659 __isl_take isl_union_pw_qpolynomial *upwqp1,
2660 __isl_take isl_union_pw_qpolynomial *upwqp2);
2661 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2662 __isl_take isl_union_pw_qpolynomial *upwqp1,
2663 __isl_take isl_union_pw_qpolynomial *upwqp2);
2665 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2666 __isl_take isl_pw_qpolynomial *pwqp,
2667 __isl_take isl_point *pnt);
2669 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2670 __isl_take isl_union_pw_qpolynomial *upwqp,
2671 __isl_take isl_point *pnt);
2673 __isl_give isl_set *isl_pw_qpolynomial_domain(
2674 __isl_take isl_pw_qpolynomial *pwqp);
2675 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2676 __isl_take isl_pw_qpolynomial *pwpq,
2677 __isl_take isl_set *set);
2679 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2680 __isl_take isl_union_pw_qpolynomial *upwqp);
2681 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2682 __isl_take isl_union_pw_qpolynomial *upwpq,
2683 __isl_take isl_union_set *uset);
2685 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2686 __isl_take isl_qpolynomial *qp,
2687 __isl_take isl_dim *model);
2689 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2690 __isl_take isl_union_pw_qpolynomial *upwqp);
2692 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2693 __isl_take isl_qpolynomial *qp,
2694 __isl_take isl_set *context);
2696 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2697 __isl_take isl_pw_qpolynomial *pwqp,
2698 __isl_take isl_set *context);
2700 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2701 __isl_take isl_union_pw_qpolynomial *upwqp,
2702 __isl_take isl_union_set *context);
2704 The gist operation applies the gist operation to each of
2705 the cells in the domain of the input piecewise quasipolynomial.
2706 The context is also exploited
2707 to simplify the quasipolynomials associated to each cell.
2709 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2710 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2711 __isl_give isl_union_pw_qpolynomial *
2712 isl_union_pw_qpolynomial_to_polynomial(
2713 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2715 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2716 the polynomial will be an overapproximation. If C<sign> is negative,
2717 it will be an underapproximation. If C<sign> is zero, the approximation
2718 will lie somewhere in between.
2720 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2722 A piecewise quasipolynomial reduction is a piecewise
2723 reduction (or fold) of quasipolynomials.
2724 In particular, the reduction can be maximum or a minimum.
2725 The objects are mainly used to represent the result of
2726 an upper or lower bound on a quasipolynomial over its domain,
2727 i.e., as the result of the following function.
2729 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2730 __isl_take isl_pw_qpolynomial *pwqp,
2731 enum isl_fold type, int *tight);
2733 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2734 __isl_take isl_union_pw_qpolynomial *upwqp,
2735 enum isl_fold type, int *tight);
2737 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2738 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2739 is the returned bound is known be tight, i.e., for each value
2740 of the parameters there is at least
2741 one element in the domain that reaches the bound.
2742 If the domain of C<pwqp> is not wrapping, then the bound is computed
2743 over all elements in that domain and the result has a purely parametric
2744 domain. If the domain of C<pwqp> is wrapping, then the bound is
2745 computed over the range of the wrapped relation. The domain of the
2746 wrapped relation becomes the domain of the result.
2748 A (piecewise) quasipolynomial reduction can be copied or freed using the
2749 following functions.
2751 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2752 __isl_keep isl_qpolynomial_fold *fold);
2753 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2754 __isl_keep isl_pw_qpolynomial_fold *pwf);
2755 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2756 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2757 void isl_qpolynomial_fold_free(
2758 __isl_take isl_qpolynomial_fold *fold);
2759 void *isl_pw_qpolynomial_fold_free(
2760 __isl_take isl_pw_qpolynomial_fold *pwf);
2761 void isl_union_pw_qpolynomial_fold_free(
2762 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2764 =head3 Printing Piecewise Quasipolynomial Reductions
2766 Piecewise quasipolynomial reductions can be printed
2767 using the following function.
2769 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2770 __isl_take isl_printer *p,
2771 __isl_keep isl_pw_qpolynomial_fold *pwf);
2772 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2773 __isl_take isl_printer *p,
2774 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2776 For C<isl_printer_print_pw_qpolynomial_fold>,
2777 output format of the printer
2778 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2779 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2780 output format of the printer
2781 needs to be set to C<ISL_FORMAT_ISL>.
2782 In case of printing in C<ISL_FORMAT_C>, the user may want
2783 to set the names of all dimensions
2785 __isl_give isl_pw_qpolynomial_fold *
2786 isl_pw_qpolynomial_fold_set_dim_name(
2787 __isl_take isl_pw_qpolynomial_fold *pwf,
2788 enum isl_dim_type type, unsigned pos,
2791 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2793 To iterate over all piecewise quasipolynomial reductions in a union
2794 piecewise quasipolynomial reduction, use the following function
2796 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2797 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2798 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2799 void *user), void *user);
2801 To iterate over the cells in a piecewise quasipolynomial reduction,
2802 use either of the following two functions
2804 int isl_pw_qpolynomial_fold_foreach_piece(
2805 __isl_keep isl_pw_qpolynomial_fold *pwf,
2806 int (*fn)(__isl_take isl_set *set,
2807 __isl_take isl_qpolynomial_fold *fold,
2808 void *user), void *user);
2809 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2810 __isl_keep isl_pw_qpolynomial_fold *pwf,
2811 int (*fn)(__isl_take isl_set *set,
2812 __isl_take isl_qpolynomial_fold *fold,
2813 void *user), void *user);
2815 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2816 of the difference between these two functions.
2818 To iterate over all quasipolynomials in a reduction, use
2820 int isl_qpolynomial_fold_foreach_qpolynomial(
2821 __isl_keep isl_qpolynomial_fold *fold,
2822 int (*fn)(__isl_take isl_qpolynomial *qp,
2823 void *user), void *user);
2825 =head3 Operations on Piecewise Quasipolynomial Reductions
2827 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
2828 __isl_take isl_qpolynomial_fold *fold, isl_int v);
2830 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2831 __isl_take isl_pw_qpolynomial_fold *pwf1,
2832 __isl_take isl_pw_qpolynomial_fold *pwf2);
2834 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2835 __isl_take isl_pw_qpolynomial_fold *pwf1,
2836 __isl_take isl_pw_qpolynomial_fold *pwf2);
2838 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2839 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2840 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2842 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2843 __isl_take isl_pw_qpolynomial_fold *pwf,
2844 __isl_take isl_point *pnt);
2846 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2847 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2848 __isl_take isl_point *pnt);
2850 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2851 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2852 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2853 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2854 __isl_take isl_union_set *uset);
2856 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2857 __isl_take isl_pw_qpolynomial_fold *pwf);
2859 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2860 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2862 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2863 __isl_take isl_pw_qpolynomial_fold *pwf,
2864 __isl_take isl_set *context);
2866 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2867 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2868 __isl_take isl_union_set *context);
2870 The gist operation applies the gist operation to each of
2871 the cells in the domain of the input piecewise quasipolynomial reduction.
2872 In future, the operation will also exploit the context
2873 to simplify the quasipolynomial reductions associated to each cell.
2875 __isl_give isl_pw_qpolynomial_fold *
2876 isl_set_apply_pw_qpolynomial_fold(
2877 __isl_take isl_set *set,
2878 __isl_take isl_pw_qpolynomial_fold *pwf,
2880 __isl_give isl_pw_qpolynomial_fold *
2881 isl_map_apply_pw_qpolynomial_fold(
2882 __isl_take isl_map *map,
2883 __isl_take isl_pw_qpolynomial_fold *pwf,
2885 __isl_give isl_union_pw_qpolynomial_fold *
2886 isl_union_set_apply_union_pw_qpolynomial_fold(
2887 __isl_take isl_union_set *uset,
2888 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2890 __isl_give isl_union_pw_qpolynomial_fold *
2891 isl_union_map_apply_union_pw_qpolynomial_fold(
2892 __isl_take isl_union_map *umap,
2893 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2896 The functions taking a map
2897 compose the given map with the given piecewise quasipolynomial reduction.
2898 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2899 over all elements in the intersection of the range of the map
2900 and the domain of the piecewise quasipolynomial reduction
2901 as a function of an element in the domain of the map.
2902 The functions taking a set compute a bound over all elements in the
2903 intersection of the set and the domain of the
2904 piecewise quasipolynomial reduction.
2906 =head2 Dependence Analysis
2908 C<isl> contains specialized functionality for performing
2909 array dataflow analysis. That is, given a I<sink> access relation
2910 and a collection of possible I<source> access relations,
2911 C<isl> can compute relations that describe
2912 for each iteration of the sink access, which iteration
2913 of which of the source access relations was the last
2914 to access the same data element before the given iteration
2916 To compute standard flow dependences, the sink should be
2917 a read, while the sources should be writes.
2918 If any of the source accesses are marked as being I<may>
2919 accesses, then there will be a dependence to the last
2920 I<must> access B<and> to any I<may> access that follows
2921 this last I<must> access.
2922 In particular, if I<all> sources are I<may> accesses,
2923 then memory based dependence analysis is performed.
2924 If, on the other hand, all sources are I<must> accesses,
2925 then value based dependence analysis is performed.
2927 #include <isl/flow.h>
2929 typedef int (*isl_access_level_before)(void *first, void *second);
2931 __isl_give isl_access_info *isl_access_info_alloc(
2932 __isl_take isl_map *sink,
2933 void *sink_user, isl_access_level_before fn,
2935 __isl_give isl_access_info *isl_access_info_add_source(
2936 __isl_take isl_access_info *acc,
2937 __isl_take isl_map *source, int must,
2939 void isl_access_info_free(__isl_take isl_access_info *acc);
2941 __isl_give isl_flow *isl_access_info_compute_flow(
2942 __isl_take isl_access_info *acc);
2944 int isl_flow_foreach(__isl_keep isl_flow *deps,
2945 int (*fn)(__isl_take isl_map *dep, int must,
2946 void *dep_user, void *user),
2948 __isl_give isl_map *isl_flow_get_no_source(
2949 __isl_keep isl_flow *deps, int must);
2950 void isl_flow_free(__isl_take isl_flow *deps);
2952 The function C<isl_access_info_compute_flow> performs the actual
2953 dependence analysis. The other functions are used to construct
2954 the input for this function or to read off the output.
2956 The input is collected in an C<isl_access_info>, which can
2957 be created through a call to C<isl_access_info_alloc>.
2958 The arguments to this functions are the sink access relation
2959 C<sink>, a token C<sink_user> used to identify the sink
2960 access to the user, a callback function for specifying the
2961 relative order of source and sink accesses, and the number
2962 of source access relations that will be added.
2963 The callback function has type C<int (*)(void *first, void *second)>.
2964 The function is called with two user supplied tokens identifying
2965 either a source or the sink and it should return the shared nesting
2966 level and the relative order of the two accesses.
2967 In particular, let I<n> be the number of loops shared by
2968 the two accesses. If C<first> precedes C<second> textually,
2969 then the function should return I<2 * n + 1>; otherwise,
2970 it should return I<2 * n>.
2971 The sources can be added to the C<isl_access_info> by performing
2972 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2973 C<must> indicates whether the source is a I<must> access
2974 or a I<may> access. Note that a multi-valued access relation
2975 should only be marked I<must> if every iteration in the domain
2976 of the relation accesses I<all> elements in its image.
2977 The C<source_user> token is again used to identify
2978 the source access. The range of the source access relation
2979 C<source> should have the same dimension as the range
2980 of the sink access relation.
2981 The C<isl_access_info_free> function should usually not be
2982 called explicitly, because it is called implicitly by
2983 C<isl_access_info_compute_flow>.
2985 The result of the dependence analysis is collected in an
2986 C<isl_flow>. There may be elements of
2987 the sink access for which no preceding source access could be
2988 found or for which all preceding sources are I<may> accesses.
2989 The relations containing these elements can be obtained through
2990 calls to C<isl_flow_get_no_source>, the first with C<must> set
2991 and the second with C<must> unset.
2992 In the case of standard flow dependence analysis,
2993 with the sink a read and the sources I<must> writes,
2994 the first relation corresponds to the reads from uninitialized
2995 array elements and the second relation is empty.
2996 The actual flow dependences can be extracted using
2997 C<isl_flow_foreach>. This function will call the user-specified
2998 callback function C<fn> for each B<non-empty> dependence between
2999 a source and the sink. The callback function is called
3000 with four arguments, the actual flow dependence relation
3001 mapping source iterations to sink iterations, a boolean that
3002 indicates whether it is a I<must> or I<may> dependence, a token
3003 identifying the source and an additional C<void *> with value
3004 equal to the third argument of the C<isl_flow_foreach> call.
3005 A dependence is marked I<must> if it originates from a I<must>
3006 source and if it is not followed by any I<may> sources.
3008 After finishing with an C<isl_flow>, the user should call
3009 C<isl_flow_free> to free all associated memory.
3011 A higher-level interface to dependence analysis is provided
3012 by the following function.
3014 #include <isl/flow.h>
3016 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3017 __isl_take isl_union_map *must_source,
3018 __isl_take isl_union_map *may_source,
3019 __isl_take isl_union_map *schedule,
3020 __isl_give isl_union_map **must_dep,
3021 __isl_give isl_union_map **may_dep,
3022 __isl_give isl_union_map **must_no_source,
3023 __isl_give isl_union_map **may_no_source);
3025 The arrays are identified by the tuple names of the ranges
3026 of the accesses. The iteration domains by the tuple names
3027 of the domains of the accesses and of the schedule.
3028 The relative order of the iteration domains is given by the
3029 schedule. The relations returned through C<must_no_source>
3030 and C<may_no_source> are subsets of C<sink>.
3031 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3032 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3033 any of the other arguments is treated as an error.
3037 B<The functionality described in this section is fairly new
3038 and may be subject to change.>
3040 The following function can be used to compute a schedule
3041 for a union of domains. The generated schedule respects
3042 all C<validity> dependences. That is, all dependence distances
3043 over these dependences in the scheduled space are lexicographically
3044 positive. The generated schedule schedule also tries to minimize
3045 the dependence distances over C<proximity> dependences.
3046 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3047 for groups of domains where the dependence distances have only
3048 non-negative values.
3049 The algorithm used to construct the schedule is similar to that
3052 #include <isl/schedule.h>
3053 __isl_give isl_schedule *isl_union_set_compute_schedule(
3054 __isl_take isl_union_set *domain,
3055 __isl_take isl_union_map *validity,
3056 __isl_take isl_union_map *proximity);
3057 void *isl_schedule_free(__isl_take isl_schedule *sched);
3059 A mapping from the domains to the scheduled space can be obtained
3060 from an C<isl_schedule> using the following function.
3062 __isl_give isl_union_map *isl_schedule_get_map(
3063 __isl_keep isl_schedule *sched);
3065 A representation of the schedule can be printed using
3067 __isl_give isl_printer *isl_printer_print_schedule(
3068 __isl_take isl_printer *p,
3069 __isl_keep isl_schedule *schedule);
3071 A representation of the schedule as a forest of bands can be obtained
3072 using the following function.
3074 __isl_give isl_band_list *isl_schedule_get_band_forest(
3075 __isl_keep isl_schedule *schedule);
3077 The list can be manipulated as explained in L<"Lists">.
3078 The bands inside the list can be copied and freed using the following
3081 #include <isl/band.h>
3082 __isl_give isl_band *isl_band_copy(
3083 __isl_keep isl_band *band);
3084 void *isl_band_free(__isl_take isl_band *band);
3086 Each band contains zero or more scheduling dimensions.
3087 These are referred to as the members of the band.
3088 The section of the schedule that corresponds to the band is
3089 referred to as the partial schedule of the band.
3090 For those nodes that participate in a band, the outer scheduling
3091 dimensions form the prefix schedule, while the inner scheduling
3092 dimensions form the suffix schedule.
3093 That is, if we take a cut of the band forest, then the union of
3094 the concatenations of the prefix, partial and suffix schedules of
3095 each band in the cut is equal to the entire schedule (modulo
3096 some possible padding at the end with zero scheduling dimensions).
3097 The properties of a band can be inspected using the following functions.
3099 #include <isl/band.h>
3100 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3102 int isl_band_has_children(__isl_keep isl_band *band);
3103 __isl_give isl_band_list *isl_band_get_children(
3104 __isl_keep isl_band *band);
3106 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3107 __isl_keep isl_band *band);
3108 __isl_give isl_union_map *isl_band_get_partial_schedule(
3109 __isl_keep isl_band *band);
3110 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3111 __isl_keep isl_band *band);
3113 int isl_band_n_member(__isl_keep isl_band *band);
3114 int isl_band_member_is_zero_distance(
3115 __isl_keep isl_band *band, int pos);
3117 Note that a scheduling dimension is considered to be ``zero
3118 distance'' if it does not carry any proximity dependences
3120 That is, if the dependence distances of the proximity
3121 dependences are all zero in that direction (for fixed
3122 iterations of outer bands).
3124 A representation of the band can be printed using
3126 #include <isl/band.h>
3127 __isl_give isl_printer *isl_printer_print_band(
3128 __isl_take isl_printer *p,
3129 __isl_keep isl_band *band);
3131 Alternatively, the schedule mapping
3132 can also be obtained in pieces using the following functions.
3134 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3135 __isl_give isl_union_map *isl_schedule_get_band(
3136 __isl_keep isl_schedule *sched, unsigned band);
3138 C<isl_schedule_n_band> returns the maximal number of bands.
3139 C<isl_schedule_get_band> returns a union of mappings from a domain to
3140 the band of consecutive schedule dimensions with the given sequence
3141 number for that domain. Bands with the same sequence number but for
3142 different domains may be completely unrelated.
3143 Within a band, the corresponding coordinates of the distance vectors
3144 are all non-negative, assuming that the coordinates for all previous
3147 =head2 Parametric Vertex Enumeration
3149 The parametric vertex enumeration described in this section
3150 is mainly intended to be used internally and by the C<barvinok>
3153 #include <isl/vertices.h>
3154 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3155 __isl_keep isl_basic_set *bset);
3157 The function C<isl_basic_set_compute_vertices> performs the
3158 actual computation of the parametric vertices and the chamber
3159 decomposition and store the result in an C<isl_vertices> object.
3160 This information can be queried by either iterating over all
3161 the vertices or iterating over all the chambers or cells
3162 and then iterating over all vertices that are active on the chamber.
3164 int isl_vertices_foreach_vertex(
3165 __isl_keep isl_vertices *vertices,
3166 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3169 int isl_vertices_foreach_cell(
3170 __isl_keep isl_vertices *vertices,
3171 int (*fn)(__isl_take isl_cell *cell, void *user),
3173 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3174 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3177 Other operations that can be performed on an C<isl_vertices> object are
3180 isl_ctx *isl_vertices_get_ctx(
3181 __isl_keep isl_vertices *vertices);
3182 int isl_vertices_get_n_vertices(
3183 __isl_keep isl_vertices *vertices);
3184 void isl_vertices_free(__isl_take isl_vertices *vertices);
3186 Vertices can be inspected and destroyed using the following functions.
3188 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3189 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3190 __isl_give isl_basic_set *isl_vertex_get_domain(
3191 __isl_keep isl_vertex *vertex);
3192 __isl_give isl_basic_set *isl_vertex_get_expr(
3193 __isl_keep isl_vertex *vertex);
3194 void isl_vertex_free(__isl_take isl_vertex *vertex);
3196 C<isl_vertex_get_expr> returns a singleton parametric set describing
3197 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3199 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3200 B<rational> basic sets, so they should mainly be used for inspection
3201 and should not be mixed with integer sets.
3203 Chambers can be inspected and destroyed using the following functions.
3205 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3206 __isl_give isl_basic_set *isl_cell_get_domain(
3207 __isl_keep isl_cell *cell);
3208 void isl_cell_free(__isl_take isl_cell *cell);
3212 Although C<isl> is mainly meant to be used as a library,
3213 it also contains some basic applications that use some
3214 of the functionality of C<isl>.
3215 The input may be specified in either the L<isl format>
3216 or the L<PolyLib format>.
3218 =head2 C<isl_polyhedron_sample>
3220 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3221 an integer element of the polyhedron, if there is any.
3222 The first column in the output is the denominator and is always
3223 equal to 1. If the polyhedron contains no integer points,
3224 then a vector of length zero is printed.
3228 C<isl_pip> takes the same input as the C<example> program
3229 from the C<piplib> distribution, i.e., a set of constraints
3230 on the parameters, a line containing only -1 and finally a set
3231 of constraints on a parametric polyhedron.
3232 The coefficients of the parameters appear in the last columns
3233 (but before the final constant column).
3234 The output is the lexicographic minimum of the parametric polyhedron.
3235 As C<isl> currently does not have its own output format, the output
3236 is just a dump of the internal state.
3238 =head2 C<isl_polyhedron_minimize>
3240 C<isl_polyhedron_minimize> computes the minimum of some linear
3241 or affine objective function over the integer points in a polyhedron.
3242 If an affine objective function
3243 is given, then the constant should appear in the last column.
3245 =head2 C<isl_polytope_scan>
3247 Given a polytope, C<isl_polytope_scan> prints
3248 all integer points in the polytope.