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);
488 __isl_give isl_dim *isl_pw_aff_get_dim(
489 __isl_keep isl_pw_aff *pwaff);
491 #include <isl/point.h>
492 __isl_give isl_dim *isl_point_get_dim(
493 __isl_keep isl_point *pnt);
495 The names of the individual dimensions may be set or read off
496 using the following functions.
499 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
500 enum isl_dim_type type, unsigned pos,
501 __isl_keep const char *name);
502 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
503 enum isl_dim_type type, unsigned pos);
505 Note that C<isl_dim_get_name> returns a pointer to some internal
506 data structure, so the result can only be used while the
507 corresponding C<isl_dim> is alive.
508 Also note that every function that operates on two sets or relations
509 requires that both arguments have the same parameters. This also
510 means that if one of the arguments has named parameters, then the
511 other needs to have named parameters too and the names need to match.
512 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
513 have different parameters (as long as they are named), in which case
514 the result will have as parameters the union of the parameters of
517 The names of entire spaces may be set or read off
518 using the following functions.
521 __isl_give isl_dim *isl_dim_set_tuple_name(
522 __isl_take isl_dim *dim,
523 enum isl_dim_type type, const char *s);
524 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
525 enum isl_dim_type type);
527 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
528 or C<isl_dim_set>. As with C<isl_dim_get_name>,
529 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
531 Binary operations require the corresponding spaces of their arguments
532 to have the same name.
534 Spaces can be nested. In particular, the domain of a set or
535 the domain or range of a relation can be a nested relation.
536 The following functions can be used to construct and deconstruct
537 such nested dimension specifications.
540 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
541 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
542 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
544 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
545 be the dimension specification of a set, while that of
546 C<isl_dim_wrap> should be the dimension specification of a relation.
547 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
548 of a relation, while that of C<isl_dim_wrap> is the dimension specification
551 Dimension specifications can be created from other dimension
552 specifications using the following functions.
554 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
555 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
556 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
557 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
558 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
559 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
560 __isl_take isl_dim *right);
561 __isl_give isl_dim *isl_dim_align_params(
562 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
563 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
564 enum isl_dim_type type, unsigned pos, unsigned n);
565 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
566 enum isl_dim_type type, unsigned n);
567 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
568 enum isl_dim_type type, unsigned first, unsigned n);
569 __isl_give isl_dim *isl_dim_map_from_set(
570 __isl_take isl_dim *dim);
571 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
573 Note that if dimensions are added or removed from a space, then
574 the name and the internal structure are lost.
578 A local space is essentially a dimension specification with
579 zero or more existentially quantified variables.
580 The local space of a basic set or relation can be obtained
581 using the following functions.
584 __isl_give isl_local_space *isl_basic_set_get_local_space(
585 __isl_keep isl_basic_set *bset);
588 __isl_give isl_local_space *isl_basic_map_get_local_space(
589 __isl_keep isl_basic_map *bmap);
591 A new local space can be created from a dimension specification using
593 #include <isl/local_space.h>
594 __isl_give isl_local_space *isl_local_space_from_dim(
595 __isl_take isl_dim *dim);
597 They can be inspected, copied and freed using the following functions.
599 #include <isl/local_space.h>
600 isl_ctx *isl_local_space_get_ctx(
601 __isl_keep isl_local_space *ls);
602 int isl_local_space_dim(__isl_keep isl_local_space *ls,
603 enum isl_dim_type type);
604 const char *isl_local_space_get_dim_name(
605 __isl_keep isl_local_space *ls,
606 enum isl_dim_type type, unsigned pos);
607 __isl_give isl_local_space *isl_local_space_set_dim_name(
608 __isl_take isl_local_space *ls,
609 enum isl_dim_type type, unsigned pos, const char *s);
610 __isl_give isl_dim *isl_local_space_get_dim(
611 __isl_keep isl_local_space *ls);
612 __isl_give isl_div *isl_local_space_get_div(
613 __isl_keep isl_local_space *ls, int pos);
614 __isl_give isl_local_space *isl_local_space_copy(
615 __isl_keep isl_local_space *ls);
616 void *isl_local_space_free(__isl_take isl_local_space *ls);
618 Two local spaces can be compared using
620 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
621 __isl_keep isl_local_space *ls2);
623 Local spaces can be created from other local spaces
624 using the following functions.
626 __isl_give isl_local_space *isl_local_space_from_domain(
627 __isl_take isl_local_space *ls);
628 __isl_give isl_local_space *isl_local_space_add_dims(
629 __isl_take isl_local_space *ls,
630 enum isl_dim_type type, unsigned n);
631 __isl_give isl_local_space *isl_local_space_insert_dims(
632 __isl_take isl_local_space *ls,
633 enum isl_dim_type type, unsigned first, unsigned n);
634 __isl_give isl_local_space *isl_local_space_drop_dims(
635 __isl_take isl_local_space *ls,
636 enum isl_dim_type type, unsigned first, unsigned n);
638 =head2 Input and Output
640 C<isl> supports its own input/output format, which is similar
641 to the C<Omega> format, but also supports the C<PolyLib> format
646 The C<isl> format is similar to that of C<Omega>, but has a different
647 syntax for describing the parameters and allows for the definition
648 of an existentially quantified variable as the integer division
649 of an affine expression.
650 For example, the set of integers C<i> between C<0> and C<n>
651 such that C<i % 10 <= 6> can be described as
653 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
656 A set or relation can have several disjuncts, separated
657 by the keyword C<or>. Each disjunct is either a conjunction
658 of constraints or a projection (C<exists>) of a conjunction
659 of constraints. The constraints are separated by the keyword
662 =head3 C<PolyLib> format
664 If the represented set is a union, then the first line
665 contains a single number representing the number of disjuncts.
666 Otherwise, a line containing the number C<1> is optional.
668 Each disjunct is represented by a matrix of constraints.
669 The first line contains two numbers representing
670 the number of rows and columns,
671 where the number of rows is equal to the number of constraints
672 and the number of columns is equal to two plus the number of variables.
673 The following lines contain the actual rows of the constraint matrix.
674 In each row, the first column indicates whether the constraint
675 is an equality (C<0>) or inequality (C<1>). The final column
676 corresponds to the constant term.
678 If the set is parametric, then the coefficients of the parameters
679 appear in the last columns before the constant column.
680 The coefficients of any existentially quantified variables appear
681 between those of the set variables and those of the parameters.
683 =head3 Extended C<PolyLib> format
685 The extended C<PolyLib> format is nearly identical to the
686 C<PolyLib> format. The only difference is that the line
687 containing the number of rows and columns of a constraint matrix
688 also contains four additional numbers:
689 the number of output dimensions, the number of input dimensions,
690 the number of local dimensions (i.e., the number of existentially
691 quantified variables) and the number of parameters.
692 For sets, the number of ``output'' dimensions is equal
693 to the number of set dimensions, while the number of ``input''
699 __isl_give isl_basic_set *isl_basic_set_read_from_file(
700 isl_ctx *ctx, FILE *input, int nparam);
701 __isl_give isl_basic_set *isl_basic_set_read_from_str(
702 isl_ctx *ctx, const char *str, int nparam);
703 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
704 FILE *input, int nparam);
705 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
706 const char *str, int nparam);
709 __isl_give isl_basic_map *isl_basic_map_read_from_file(
710 isl_ctx *ctx, FILE *input, int nparam);
711 __isl_give isl_basic_map *isl_basic_map_read_from_str(
712 isl_ctx *ctx, const char *str, int nparam);
713 __isl_give isl_map *isl_map_read_from_file(
714 struct isl_ctx *ctx, FILE *input, int nparam);
715 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
716 const char *str, int nparam);
718 #include <isl/union_set.h>
719 __isl_give isl_union_set *isl_union_set_read_from_file(
720 isl_ctx *ctx, FILE *input);
721 __isl_give isl_union_set *isl_union_set_read_from_str(
722 struct isl_ctx *ctx, const char *str);
724 #include <isl/union_map.h>
725 __isl_give isl_union_map *isl_union_map_read_from_file(
726 isl_ctx *ctx, FILE *input);
727 __isl_give isl_union_map *isl_union_map_read_from_str(
728 struct isl_ctx *ctx, const char *str);
730 The input format is autodetected and may be either the C<PolyLib> format
731 or the C<isl> format.
732 C<nparam> specifies how many of the final columns in
733 the C<PolyLib> format correspond to parameters.
734 If input is given in the C<isl> format, then the number
735 of parameters needs to be equal to C<nparam>.
736 If C<nparam> is negative, then any number of parameters
737 is accepted in the C<isl> format and zero parameters
738 are assumed in the C<PolyLib> format.
742 Before anything can be printed, an C<isl_printer> needs to
745 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
747 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
748 void isl_printer_free(__isl_take isl_printer *printer);
749 __isl_give char *isl_printer_get_str(
750 __isl_keep isl_printer *printer);
752 The behavior of the printer can be modified in various ways
754 __isl_give isl_printer *isl_printer_set_output_format(
755 __isl_take isl_printer *p, int output_format);
756 __isl_give isl_printer *isl_printer_set_indent(
757 __isl_take isl_printer *p, int indent);
758 __isl_give isl_printer *isl_printer_indent(
759 __isl_take isl_printer *p, int indent);
760 __isl_give isl_printer *isl_printer_set_prefix(
761 __isl_take isl_printer *p, const char *prefix);
762 __isl_give isl_printer *isl_printer_set_suffix(
763 __isl_take isl_printer *p, const char *suffix);
765 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
766 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
767 and defaults to C<ISL_FORMAT_ISL>.
768 Each line in the output is indented by C<indent> (set by
769 C<isl_printer_set_indent>) spaces
770 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
771 In the C<PolyLib> format output,
772 the coefficients of the existentially quantified variables
773 appear between those of the set variables and those
775 The function C<isl_printer_indent> increases the indentation
776 by the specified amount (which may be negative).
778 To actually print something, use
781 __isl_give isl_printer *isl_printer_print_basic_set(
782 __isl_take isl_printer *printer,
783 __isl_keep isl_basic_set *bset);
784 __isl_give isl_printer *isl_printer_print_set(
785 __isl_take isl_printer *printer,
786 __isl_keep isl_set *set);
789 __isl_give isl_printer *isl_printer_print_basic_map(
790 __isl_take isl_printer *printer,
791 __isl_keep isl_basic_map *bmap);
792 __isl_give isl_printer *isl_printer_print_map(
793 __isl_take isl_printer *printer,
794 __isl_keep isl_map *map);
796 #include <isl/union_set.h>
797 __isl_give isl_printer *isl_printer_print_union_set(
798 __isl_take isl_printer *p,
799 __isl_keep isl_union_set *uset);
801 #include <isl/union_map.h>
802 __isl_give isl_printer *isl_printer_print_union_map(
803 __isl_take isl_printer *p,
804 __isl_keep isl_union_map *umap);
806 When called on a file printer, the following function flushes
807 the file. When called on a string printer, the buffer is cleared.
809 __isl_give isl_printer *isl_printer_flush(
810 __isl_take isl_printer *p);
812 =head2 Creating New Sets and Relations
814 C<isl> has functions for creating some standard sets and relations.
818 =item * Empty sets and relations
820 __isl_give isl_basic_set *isl_basic_set_empty(
821 __isl_take isl_dim *dim);
822 __isl_give isl_basic_map *isl_basic_map_empty(
823 __isl_take isl_dim *dim);
824 __isl_give isl_set *isl_set_empty(
825 __isl_take isl_dim *dim);
826 __isl_give isl_map *isl_map_empty(
827 __isl_take isl_dim *dim);
828 __isl_give isl_union_set *isl_union_set_empty(
829 __isl_take isl_dim *dim);
830 __isl_give isl_union_map *isl_union_map_empty(
831 __isl_take isl_dim *dim);
833 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
834 is only used to specify the parameters.
836 =item * Universe sets and relations
838 __isl_give isl_basic_set *isl_basic_set_universe(
839 __isl_take isl_dim *dim);
840 __isl_give isl_basic_map *isl_basic_map_universe(
841 __isl_take isl_dim *dim);
842 __isl_give isl_set *isl_set_universe(
843 __isl_take isl_dim *dim);
844 __isl_give isl_map *isl_map_universe(
845 __isl_take isl_dim *dim);
846 __isl_give isl_union_set *isl_union_set_universe(
847 __isl_take isl_union_set *uset);
848 __isl_give isl_union_map *isl_union_map_universe(
849 __isl_take isl_union_map *umap);
851 The sets and relations constructed by the functions above
852 contain all integer values, while those constructed by the
853 functions below only contain non-negative values.
855 __isl_give isl_basic_set *isl_basic_set_nat_universe(
856 __isl_take isl_dim *dim);
857 __isl_give isl_basic_map *isl_basic_map_nat_universe(
858 __isl_take isl_dim *dim);
859 __isl_give isl_set *isl_set_nat_universe(
860 __isl_take isl_dim *dim);
861 __isl_give isl_map *isl_map_nat_universe(
862 __isl_take isl_dim *dim);
864 =item * Identity relations
866 __isl_give isl_basic_map *isl_basic_map_identity(
867 __isl_take isl_dim *dim);
868 __isl_give isl_map *isl_map_identity(
869 __isl_take isl_dim *dim);
871 The number of input and output dimensions in C<dim> needs
874 =item * Lexicographic order
876 __isl_give isl_map *isl_map_lex_lt(
877 __isl_take isl_dim *set_dim);
878 __isl_give isl_map *isl_map_lex_le(
879 __isl_take isl_dim *set_dim);
880 __isl_give isl_map *isl_map_lex_gt(
881 __isl_take isl_dim *set_dim);
882 __isl_give isl_map *isl_map_lex_ge(
883 __isl_take isl_dim *set_dim);
884 __isl_give isl_map *isl_map_lex_lt_first(
885 __isl_take isl_dim *dim, unsigned n);
886 __isl_give isl_map *isl_map_lex_le_first(
887 __isl_take isl_dim *dim, unsigned n);
888 __isl_give isl_map *isl_map_lex_gt_first(
889 __isl_take isl_dim *dim, unsigned n);
890 __isl_give isl_map *isl_map_lex_ge_first(
891 __isl_take isl_dim *dim, unsigned n);
893 The first four functions take a dimension specification for a B<set>
894 and return relations that express that the elements in the domain
895 are lexicographically less
896 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
897 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
898 than the elements in the range.
899 The last four functions take a dimension specification for a map
900 and return relations that express that the first C<n> dimensions
901 in the domain are lexicographically less
902 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
903 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
904 than the first C<n> dimensions in the range.
908 A basic set or relation can be converted to a set or relation
909 using the following functions.
911 __isl_give isl_set *isl_set_from_basic_set(
912 __isl_take isl_basic_set *bset);
913 __isl_give isl_map *isl_map_from_basic_map(
914 __isl_take isl_basic_map *bmap);
916 Sets and relations can be converted to union sets and relations
917 using the following functions.
919 __isl_give isl_union_map *isl_union_map_from_map(
920 __isl_take isl_map *map);
921 __isl_give isl_union_set *isl_union_set_from_set(
922 __isl_take isl_set *set);
924 Sets and relations can be copied and freed again using the following
927 __isl_give isl_basic_set *isl_basic_set_copy(
928 __isl_keep isl_basic_set *bset);
929 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
930 __isl_give isl_union_set *isl_union_set_copy(
931 __isl_keep isl_union_set *uset);
932 __isl_give isl_basic_map *isl_basic_map_copy(
933 __isl_keep isl_basic_map *bmap);
934 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
935 __isl_give isl_union_map *isl_union_map_copy(
936 __isl_keep isl_union_map *umap);
937 void isl_basic_set_free(__isl_take isl_basic_set *bset);
938 void isl_set_free(__isl_take isl_set *set);
939 void isl_union_set_free(__isl_take isl_union_set *uset);
940 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
941 void isl_map_free(__isl_take isl_map *map);
942 void isl_union_map_free(__isl_take isl_union_map *umap);
944 Other sets and relations can be constructed by starting
945 from a universe set or relation, adding equality and/or
946 inequality constraints and then projecting out the
947 existentially quantified variables, if any.
948 Constraints can be constructed, manipulated and
949 added to (or removed from) (basic) sets and relations
950 using the following functions.
952 #include <isl/constraint.h>
953 __isl_give isl_constraint *isl_equality_alloc(
954 __isl_take isl_dim *dim);
955 __isl_give isl_constraint *isl_inequality_alloc(
956 __isl_take isl_dim *dim);
957 void isl_constraint_set_constant(
958 __isl_keep isl_constraint *constraint, isl_int v);
959 void isl_constraint_set_coefficient(
960 __isl_keep isl_constraint *constraint,
961 enum isl_dim_type type, int pos, isl_int v);
962 __isl_give isl_basic_map *isl_basic_map_add_constraint(
963 __isl_take isl_basic_map *bmap,
964 __isl_take isl_constraint *constraint);
965 __isl_give isl_basic_set *isl_basic_set_add_constraint(
966 __isl_take isl_basic_set *bset,
967 __isl_take isl_constraint *constraint);
968 __isl_give isl_map *isl_map_add_constraint(
969 __isl_take isl_map *map,
970 __isl_take isl_constraint *constraint);
971 __isl_give isl_set *isl_set_add_constraint(
972 __isl_take isl_set *set,
973 __isl_take isl_constraint *constraint);
974 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
975 __isl_take isl_basic_set *bset,
976 __isl_take isl_constraint *constraint);
978 For example, to create a set containing the even integers
979 between 10 and 42, you would use the following code.
983 struct isl_constraint *c;
984 struct isl_basic_set *bset;
987 dim = isl_dim_set_alloc(ctx, 0, 2);
988 bset = isl_basic_set_universe(isl_dim_copy(dim));
990 c = isl_equality_alloc(isl_dim_copy(dim));
991 isl_int_set_si(v, -1);
992 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
993 isl_int_set_si(v, 2);
994 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
995 bset = isl_basic_set_add_constraint(bset, c);
997 c = isl_inequality_alloc(isl_dim_copy(dim));
998 isl_int_set_si(v, -10);
999 isl_constraint_set_constant(c, v);
1000 isl_int_set_si(v, 1);
1001 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1002 bset = isl_basic_set_add_constraint(bset, c);
1004 c = isl_inequality_alloc(dim);
1005 isl_int_set_si(v, 42);
1006 isl_constraint_set_constant(c, v);
1007 isl_int_set_si(v, -1);
1008 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1009 bset = isl_basic_set_add_constraint(bset, c);
1011 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1017 struct isl_basic_set *bset;
1018 bset = isl_basic_set_read_from_str(ctx,
1019 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1021 A basic set or relation can also be constructed from two matrices
1022 describing the equalities and the inequalities.
1024 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1025 __isl_take isl_dim *dim,
1026 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1027 enum isl_dim_type c1,
1028 enum isl_dim_type c2, enum isl_dim_type c3,
1029 enum isl_dim_type c4);
1030 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1031 __isl_take isl_dim *dim,
1032 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1033 enum isl_dim_type c1,
1034 enum isl_dim_type c2, enum isl_dim_type c3,
1035 enum isl_dim_type c4, enum isl_dim_type c5);
1037 The C<isl_dim_type> arguments indicate the order in which
1038 different kinds of variables appear in the input matrices
1039 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1040 C<isl_dim_set> and C<isl_dim_div> for sets and
1041 of C<isl_dim_cst>, C<isl_dim_param>,
1042 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1044 A (basic) relation can also be constructed from a (piecewise) affine expression
1045 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1047 __isl_give isl_basic_map *isl_basic_map_from_aff(
1048 __isl_take isl_aff *aff);
1049 __isl_give isl_map *isl_map_from_pw_aff(
1050 __isl_take isl_pw_aff *pwaff);
1051 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1052 __isl_take isl_dim *domain_dim,
1053 __isl_take isl_aff_list *list);
1055 The C<domain_dim> argument describes the domain of the resulting
1056 basic relation. It is required because the C<list> may consist
1057 of zero affine expressions.
1059 =head2 Inspecting Sets and Relations
1061 Usually, the user should not have to care about the actual constraints
1062 of the sets and maps, but should instead apply the abstract operations
1063 explained in the following sections.
1064 Occasionally, however, it may be required to inspect the individual
1065 coefficients of the constraints. This section explains how to do so.
1066 In these cases, it may also be useful to have C<isl> compute
1067 an explicit representation of the existentially quantified variables.
1069 __isl_give isl_set *isl_set_compute_divs(
1070 __isl_take isl_set *set);
1071 __isl_give isl_map *isl_map_compute_divs(
1072 __isl_take isl_map *map);
1073 __isl_give isl_union_set *isl_union_set_compute_divs(
1074 __isl_take isl_union_set *uset);
1075 __isl_give isl_union_map *isl_union_map_compute_divs(
1076 __isl_take isl_union_map *umap);
1078 This explicit representation defines the existentially quantified
1079 variables as integer divisions of the other variables, possibly
1080 including earlier existentially quantified variables.
1081 An explicitly represented existentially quantified variable therefore
1082 has a unique value when the values of the other variables are known.
1083 If, furthermore, the same existentials, i.e., existentials
1084 with the same explicit representations, should appear in the
1085 same order in each of the disjuncts of a set or map, then the user should call
1086 either of the following functions.
1088 __isl_give isl_set *isl_set_align_divs(
1089 __isl_take isl_set *set);
1090 __isl_give isl_map *isl_map_align_divs(
1091 __isl_take isl_map *map);
1093 Alternatively, the existentially quantified variables can be removed
1094 using the following functions, which compute an overapproximation.
1096 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1097 __isl_take isl_basic_set *bset);
1098 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1099 __isl_take isl_basic_map *bmap);
1100 __isl_give isl_set *isl_set_remove_divs(
1101 __isl_take isl_set *set);
1102 __isl_give isl_map *isl_map_remove_divs(
1103 __isl_take isl_map *map);
1105 To iterate over all the sets or maps in a union set or map, use
1107 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1108 int (*fn)(__isl_take isl_set *set, void *user),
1110 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1111 int (*fn)(__isl_take isl_map *map, void *user),
1114 The number of sets or maps in a union set or map can be obtained
1117 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1118 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1120 To extract the set or map from a union with a given dimension
1123 __isl_give isl_set *isl_union_set_extract_set(
1124 __isl_keep isl_union_set *uset,
1125 __isl_take isl_dim *dim);
1126 __isl_give isl_map *isl_union_map_extract_map(
1127 __isl_keep isl_union_map *umap,
1128 __isl_take isl_dim *dim);
1130 To iterate over all the basic sets or maps in a set or map, use
1132 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1133 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1135 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1136 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1139 The callback function C<fn> should return 0 if successful and
1140 -1 if an error occurs. In the latter case, or if any other error
1141 occurs, the above functions will return -1.
1143 It should be noted that C<isl> does not guarantee that
1144 the basic sets or maps passed to C<fn> are disjoint.
1145 If this is required, then the user should call one of
1146 the following functions first.
1148 __isl_give isl_set *isl_set_make_disjoint(
1149 __isl_take isl_set *set);
1150 __isl_give isl_map *isl_map_make_disjoint(
1151 __isl_take isl_map *map);
1153 The number of basic sets in a set can be obtained
1156 int isl_set_n_basic_set(__isl_keep isl_set *set);
1158 To iterate over the constraints of a basic set or map, use
1160 #include <isl/constraint.h>
1162 int isl_basic_map_foreach_constraint(
1163 __isl_keep isl_basic_map *bmap,
1164 int (*fn)(__isl_take isl_constraint *c, void *user),
1166 void isl_constraint_free(struct isl_constraint *c);
1168 Again, the callback function C<fn> should return 0 if successful and
1169 -1 if an error occurs. In the latter case, or if any other error
1170 occurs, the above functions will return -1.
1171 The constraint C<c> represents either an equality or an inequality.
1172 Use the following function to find out whether a constraint
1173 represents an equality. If not, it represents an inequality.
1175 int isl_constraint_is_equality(
1176 __isl_keep isl_constraint *constraint);
1178 The coefficients of the constraints can be inspected using
1179 the following functions.
1181 void isl_constraint_get_constant(
1182 __isl_keep isl_constraint *constraint, isl_int *v);
1183 void isl_constraint_get_coefficient(
1184 __isl_keep isl_constraint *constraint,
1185 enum isl_dim_type type, int pos, isl_int *v);
1186 int isl_constraint_involves_dims(
1187 __isl_keep isl_constraint *constraint,
1188 enum isl_dim_type type, unsigned first, unsigned n);
1190 The explicit representations of the existentially quantified
1191 variables can be inspected using the following functions.
1192 Note that the user is only allowed to use these functions
1193 if the inspected set or map is the result of a call
1194 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1196 __isl_give isl_div *isl_constraint_div(
1197 __isl_keep isl_constraint *constraint, int pos);
1198 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1199 void isl_div_get_constant(__isl_keep isl_div *div,
1201 void isl_div_get_denominator(__isl_keep isl_div *div,
1203 void isl_div_get_coefficient(__isl_keep isl_div *div,
1204 enum isl_dim_type type, int pos, isl_int *v);
1206 To obtain the constraints of a basic set or map in matrix
1207 form, use the following functions.
1209 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1210 __isl_keep isl_basic_set *bset,
1211 enum isl_dim_type c1, enum isl_dim_type c2,
1212 enum isl_dim_type c3, enum isl_dim_type c4);
1213 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1214 __isl_keep isl_basic_set *bset,
1215 enum isl_dim_type c1, enum isl_dim_type c2,
1216 enum isl_dim_type c3, enum isl_dim_type c4);
1217 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1218 __isl_keep isl_basic_map *bmap,
1219 enum isl_dim_type c1,
1220 enum isl_dim_type c2, enum isl_dim_type c3,
1221 enum isl_dim_type c4, enum isl_dim_type c5);
1222 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1223 __isl_keep isl_basic_map *bmap,
1224 enum isl_dim_type c1,
1225 enum isl_dim_type c2, enum isl_dim_type c3,
1226 enum isl_dim_type c4, enum isl_dim_type c5);
1228 The C<isl_dim_type> arguments dictate the order in which
1229 different kinds of variables appear in the resulting matrix
1230 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1231 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1233 The names of the domain and range spaces of a set or relation can be
1234 read off or set using the following functions.
1236 const char *isl_basic_set_get_tuple_name(
1237 __isl_keep isl_basic_set *bset);
1238 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1239 __isl_take isl_basic_set *set, const char *s);
1240 const char *isl_set_get_tuple_name(
1241 __isl_keep isl_set *set);
1242 const char *isl_basic_map_get_tuple_name(
1243 __isl_keep isl_basic_map *bmap,
1244 enum isl_dim_type type);
1245 const char *isl_map_get_tuple_name(
1246 __isl_keep isl_map *map,
1247 enum isl_dim_type type);
1249 As with C<isl_dim_get_tuple_name>, the value returned points to
1250 an internal data structure.
1251 The names of individual dimensions can be read off using
1252 the following functions.
1254 const char *isl_constraint_get_dim_name(
1255 __isl_keep isl_constraint *constraint,
1256 enum isl_dim_type type, unsigned pos);
1257 const char *isl_basic_set_get_dim_name(
1258 __isl_keep isl_basic_set *bset,
1259 enum isl_dim_type type, unsigned pos);
1260 const char *isl_set_get_dim_name(
1261 __isl_keep isl_set *set,
1262 enum isl_dim_type type, unsigned pos);
1263 const char *isl_basic_map_get_dim_name(
1264 __isl_keep isl_basic_map *bmap,
1265 enum isl_dim_type type, unsigned pos);
1266 const char *isl_map_get_dim_name(
1267 __isl_keep isl_map *map,
1268 enum isl_dim_type type, unsigned pos);
1270 These functions are mostly useful to obtain the names
1275 =head3 Unary Properties
1281 The following functions test whether the given set or relation
1282 contains any integer points. The ``plain'' variants do not perform
1283 any computations, but simply check if the given set or relation
1284 is already known to be empty.
1286 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1287 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1288 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1289 int isl_set_is_empty(__isl_keep isl_set *set);
1290 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1291 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1292 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1293 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1294 int isl_map_is_empty(__isl_keep isl_map *map);
1295 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1297 =item * Universality
1299 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1300 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1301 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1303 =item * Single-valuedness
1305 int isl_map_is_single_valued(__isl_keep isl_map *map);
1306 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1310 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1311 int isl_map_is_injective(__isl_keep isl_map *map);
1312 int isl_union_map_plain_is_injective(
1313 __isl_keep isl_union_map *umap);
1314 int isl_union_map_is_injective(
1315 __isl_keep isl_union_map *umap);
1319 int isl_map_is_bijective(__isl_keep isl_map *map);
1320 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1324 The following functions check whether the domain of the given
1325 (basic) set is a wrapped relation.
1327 int isl_basic_set_is_wrapping(
1328 __isl_keep isl_basic_set *bset);
1329 int isl_set_is_wrapping(__isl_keep isl_set *set);
1331 =item * Internal Product
1333 int isl_basic_map_can_zip(
1334 __isl_keep isl_basic_map *bmap);
1335 int isl_map_can_zip(__isl_keep isl_map *map);
1337 Check whether the product of domain and range of the given relation
1339 i.e., whether both domain and range are nested relations.
1343 =head3 Binary Properties
1349 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1350 __isl_keep isl_set *set2);
1351 int isl_set_is_equal(__isl_keep isl_set *set1,
1352 __isl_keep isl_set *set2);
1353 int isl_union_set_is_equal(
1354 __isl_keep isl_union_set *uset1,
1355 __isl_keep isl_union_set *uset2);
1356 int isl_basic_map_is_equal(
1357 __isl_keep isl_basic_map *bmap1,
1358 __isl_keep isl_basic_map *bmap2);
1359 int isl_map_is_equal(__isl_keep isl_map *map1,
1360 __isl_keep isl_map *map2);
1361 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1362 __isl_keep isl_map *map2);
1363 int isl_union_map_is_equal(
1364 __isl_keep isl_union_map *umap1,
1365 __isl_keep isl_union_map *umap2);
1367 =item * Disjointness
1369 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1370 __isl_keep isl_set *set2);
1374 int isl_set_is_subset(__isl_keep isl_set *set1,
1375 __isl_keep isl_set *set2);
1376 int isl_set_is_strict_subset(
1377 __isl_keep isl_set *set1,
1378 __isl_keep isl_set *set2);
1379 int isl_union_set_is_subset(
1380 __isl_keep isl_union_set *uset1,
1381 __isl_keep isl_union_set *uset2);
1382 int isl_union_set_is_strict_subset(
1383 __isl_keep isl_union_set *uset1,
1384 __isl_keep isl_union_set *uset2);
1385 int isl_basic_map_is_subset(
1386 __isl_keep isl_basic_map *bmap1,
1387 __isl_keep isl_basic_map *bmap2);
1388 int isl_basic_map_is_strict_subset(
1389 __isl_keep isl_basic_map *bmap1,
1390 __isl_keep isl_basic_map *bmap2);
1391 int isl_map_is_subset(
1392 __isl_keep isl_map *map1,
1393 __isl_keep isl_map *map2);
1394 int isl_map_is_strict_subset(
1395 __isl_keep isl_map *map1,
1396 __isl_keep isl_map *map2);
1397 int isl_union_map_is_subset(
1398 __isl_keep isl_union_map *umap1,
1399 __isl_keep isl_union_map *umap2);
1400 int isl_union_map_is_strict_subset(
1401 __isl_keep isl_union_map *umap1,
1402 __isl_keep isl_union_map *umap2);
1406 =head2 Unary Operations
1412 __isl_give isl_set *isl_set_complement(
1413 __isl_take isl_set *set);
1417 __isl_give isl_basic_map *isl_basic_map_reverse(
1418 __isl_take isl_basic_map *bmap);
1419 __isl_give isl_map *isl_map_reverse(
1420 __isl_take isl_map *map);
1421 __isl_give isl_union_map *isl_union_map_reverse(
1422 __isl_take isl_union_map *umap);
1426 __isl_give isl_basic_set *isl_basic_set_project_out(
1427 __isl_take isl_basic_set *bset,
1428 enum isl_dim_type type, unsigned first, unsigned n);
1429 __isl_give isl_basic_map *isl_basic_map_project_out(
1430 __isl_take isl_basic_map *bmap,
1431 enum isl_dim_type type, unsigned first, unsigned n);
1432 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1433 enum isl_dim_type type, unsigned first, unsigned n);
1434 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1435 enum isl_dim_type type, unsigned first, unsigned n);
1436 __isl_give isl_basic_set *isl_basic_map_domain(
1437 __isl_take isl_basic_map *bmap);
1438 __isl_give isl_basic_set *isl_basic_map_range(
1439 __isl_take isl_basic_map *bmap);
1440 __isl_give isl_set *isl_map_domain(
1441 __isl_take isl_map *bmap);
1442 __isl_give isl_set *isl_map_range(
1443 __isl_take isl_map *map);
1444 __isl_give isl_union_set *isl_union_map_domain(
1445 __isl_take isl_union_map *umap);
1446 __isl_give isl_union_set *isl_union_map_range(
1447 __isl_take isl_union_map *umap);
1449 __isl_give isl_basic_map *isl_basic_map_domain_map(
1450 __isl_take isl_basic_map *bmap);
1451 __isl_give isl_basic_map *isl_basic_map_range_map(
1452 __isl_take isl_basic_map *bmap);
1453 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1454 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1455 __isl_give isl_union_map *isl_union_map_domain_map(
1456 __isl_take isl_union_map *umap);
1457 __isl_give isl_union_map *isl_union_map_range_map(
1458 __isl_take isl_union_map *umap);
1460 The functions above construct a (basic, regular or union) relation
1461 that maps (a wrapped version of) the input relation to its domain or range.
1465 __isl_give isl_set *isl_set_eliminate(
1466 __isl_take isl_set *set, enum isl_dim_type type,
1467 unsigned first, unsigned n);
1469 Eliminate the coefficients for the given dimensions from the constraints,
1470 without removing the dimensions.
1474 __isl_give isl_basic_set *isl_basic_set_fix(
1475 __isl_take isl_basic_set *bset,
1476 enum isl_dim_type type, unsigned pos,
1478 __isl_give isl_basic_set *isl_basic_set_fix_si(
1479 __isl_take isl_basic_set *bset,
1480 enum isl_dim_type type, unsigned pos, int value);
1481 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1482 enum isl_dim_type type, unsigned pos,
1484 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1485 enum isl_dim_type type, unsigned pos, int value);
1486 __isl_give isl_basic_map *isl_basic_map_fix_si(
1487 __isl_take isl_basic_map *bmap,
1488 enum isl_dim_type type, unsigned pos, int value);
1489 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1490 enum isl_dim_type type, unsigned pos, int value);
1492 Intersect the set or relation with the hyperplane where the given
1493 dimension has the fixed given value.
1497 __isl_give isl_map *isl_set_identity(
1498 __isl_take isl_set *set);
1499 __isl_give isl_union_map *isl_union_set_identity(
1500 __isl_take isl_union_set *uset);
1502 Construct an identity relation on the given (union) set.
1506 __isl_give isl_basic_set *isl_basic_map_deltas(
1507 __isl_take isl_basic_map *bmap);
1508 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1509 __isl_give isl_union_set *isl_union_map_deltas(
1510 __isl_take isl_union_map *umap);
1512 These functions return a (basic) set containing the differences
1513 between image elements and corresponding domain elements in the input.
1515 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1516 __isl_take isl_basic_map *bmap);
1517 __isl_give isl_map *isl_map_deltas_map(
1518 __isl_take isl_map *map);
1519 __isl_give isl_union_map *isl_union_map_deltas_map(
1520 __isl_take isl_union_map *umap);
1522 The functions above construct a (basic, regular or union) relation
1523 that maps (a wrapped version of) the input relation to its delta set.
1527 Simplify the representation of a set or relation by trying
1528 to combine pairs of basic sets or relations into a single
1529 basic set or relation.
1531 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1532 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1533 __isl_give isl_union_set *isl_union_set_coalesce(
1534 __isl_take isl_union_set *uset);
1535 __isl_give isl_union_map *isl_union_map_coalesce(
1536 __isl_take isl_union_map *umap);
1538 =item * Detecting equalities
1540 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1541 __isl_take isl_basic_set *bset);
1542 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1543 __isl_take isl_basic_map *bmap);
1544 __isl_give isl_set *isl_set_detect_equalities(
1545 __isl_take isl_set *set);
1546 __isl_give isl_map *isl_map_detect_equalities(
1547 __isl_take isl_map *map);
1548 __isl_give isl_union_set *isl_union_set_detect_equalities(
1549 __isl_take isl_union_set *uset);
1550 __isl_give isl_union_map *isl_union_map_detect_equalities(
1551 __isl_take isl_union_map *umap);
1553 Simplify the representation of a set or relation by detecting implicit
1556 =item * Removing redundant constraints
1558 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1559 __isl_take isl_basic_set *bset);
1560 __isl_give isl_set *isl_set_remove_redundancies(
1561 __isl_take isl_set *set);
1562 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1563 __isl_take isl_basic_map *bmap);
1564 __isl_give isl_map *isl_map_remove_redundancies(
1565 __isl_take isl_map *map);
1569 __isl_give isl_basic_set *isl_set_convex_hull(
1570 __isl_take isl_set *set);
1571 __isl_give isl_basic_map *isl_map_convex_hull(
1572 __isl_take isl_map *map);
1574 If the input set or relation has any existentially quantified
1575 variables, then the result of these operations is currently undefined.
1579 __isl_give isl_basic_set *isl_set_simple_hull(
1580 __isl_take isl_set *set);
1581 __isl_give isl_basic_map *isl_map_simple_hull(
1582 __isl_take isl_map *map);
1583 __isl_give isl_union_map *isl_union_map_simple_hull(
1584 __isl_take isl_union_map *umap);
1586 These functions compute a single basic set or relation
1587 that contains the whole input set or relation.
1588 In particular, the output is described by translates
1589 of the constraints describing the basic sets or relations in the input.
1593 (See \autoref{s:simple hull}.)
1599 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1600 __isl_take isl_basic_set *bset);
1601 __isl_give isl_basic_set *isl_set_affine_hull(
1602 __isl_take isl_set *set);
1603 __isl_give isl_union_set *isl_union_set_affine_hull(
1604 __isl_take isl_union_set *uset);
1605 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1606 __isl_take isl_basic_map *bmap);
1607 __isl_give isl_basic_map *isl_map_affine_hull(
1608 __isl_take isl_map *map);
1609 __isl_give isl_union_map *isl_union_map_affine_hull(
1610 __isl_take isl_union_map *umap);
1612 In case of union sets and relations, the affine hull is computed
1615 =item * Polyhedral hull
1617 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1618 __isl_take isl_set *set);
1619 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1620 __isl_take isl_map *map);
1621 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1622 __isl_take isl_union_set *uset);
1623 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1624 __isl_take isl_union_map *umap);
1626 These functions compute a single basic set or relation
1627 not involving any existentially quantified variables
1628 that contains the whole input set or relation.
1629 In case of union sets and relations, the polyhedral hull is computed
1632 =item * Optimization
1634 #include <isl/ilp.h>
1635 enum isl_lp_result isl_basic_set_max(
1636 __isl_keep isl_basic_set *bset,
1637 __isl_keep isl_aff *obj, isl_int *opt)
1638 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1639 __isl_keep isl_aff *obj, isl_int *opt);
1641 Compute the maximum of the integer affine expression C<obj>
1642 over the points in C<set>, returning the result in C<opt>.
1643 The return value may be one of C<isl_lp_error>,
1644 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1646 =item * Parametric optimization
1648 __isl_give isl_pw_aff *isl_set_dim_max(
1649 __isl_take isl_set *set, int pos);
1651 Compute the maximum of the given set dimension as a function of the
1652 parameters, but independently of the other set dimensions.
1653 For lexicographic optimization, see L<"Lexicographic Optimization">.
1657 The following functions compute either the set of (rational) coefficient
1658 values of valid constraints for the given set or the set of (rational)
1659 values satisfying the constraints with coefficients from the given set.
1660 Internally, these two sets of functions perform essentially the
1661 same operations, except that the set of coefficients is assumed to
1662 be a cone, while the set of values may be any polyhedron.
1663 The current implementation is based on the Farkas lemma and
1664 Fourier-Motzkin elimination, but this may change or be made optional
1665 in future. In particular, future implementations may use different
1666 dualization algorithms or skip the elimination step.
1668 __isl_give isl_basic_set *isl_basic_set_coefficients(
1669 __isl_take isl_basic_set *bset);
1670 __isl_give isl_basic_set *isl_set_coefficients(
1671 __isl_take isl_set *set);
1672 __isl_give isl_union_set *isl_union_set_coefficients(
1673 __isl_take isl_union_set *bset);
1674 __isl_give isl_basic_set *isl_basic_set_solutions(
1675 __isl_take isl_basic_set *bset);
1676 __isl_give isl_basic_set *isl_set_solutions(
1677 __isl_take isl_set *set);
1678 __isl_give isl_union_set *isl_union_set_solutions(
1679 __isl_take isl_union_set *bset);
1683 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1685 __isl_give isl_union_map *isl_union_map_power(
1686 __isl_take isl_union_map *umap, int *exact);
1688 Compute a parametric representation for all positive powers I<k> of C<map>.
1689 The result maps I<k> to a nested relation corresponding to the
1690 I<k>th power of C<map>.
1691 The result may be an overapproximation. If the result is known to be exact,
1692 then C<*exact> is set to C<1>.
1694 =item * Transitive closure
1696 __isl_give isl_map *isl_map_transitive_closure(
1697 __isl_take isl_map *map, int *exact);
1698 __isl_give isl_union_map *isl_union_map_transitive_closure(
1699 __isl_take isl_union_map *umap, int *exact);
1701 Compute the transitive closure of C<map>.
1702 The result may be an overapproximation. If the result is known to be exact,
1703 then C<*exact> is set to C<1>.
1705 =item * Reaching path lengths
1707 __isl_give isl_map *isl_map_reaching_path_lengths(
1708 __isl_take isl_map *map, int *exact);
1710 Compute a relation that maps each element in the range of C<map>
1711 to the lengths of all paths composed of edges in C<map> that
1712 end up in the given element.
1713 The result may be an overapproximation. If the result is known to be exact,
1714 then C<*exact> is set to C<1>.
1715 To compute the I<maximal> path length, the resulting relation
1716 should be postprocessed by C<isl_map_lexmax>.
1717 In particular, if the input relation is a dependence relation
1718 (mapping sources to sinks), then the maximal path length corresponds
1719 to the free schedule.
1720 Note, however, that C<isl_map_lexmax> expects the maximum to be
1721 finite, so if the path lengths are unbounded (possibly due to
1722 the overapproximation), then you will get an error message.
1726 __isl_give isl_basic_set *isl_basic_map_wrap(
1727 __isl_take isl_basic_map *bmap);
1728 __isl_give isl_set *isl_map_wrap(
1729 __isl_take isl_map *map);
1730 __isl_give isl_union_set *isl_union_map_wrap(
1731 __isl_take isl_union_map *umap);
1732 __isl_give isl_basic_map *isl_basic_set_unwrap(
1733 __isl_take isl_basic_set *bset);
1734 __isl_give isl_map *isl_set_unwrap(
1735 __isl_take isl_set *set);
1736 __isl_give isl_union_map *isl_union_set_unwrap(
1737 __isl_take isl_union_set *uset);
1741 Remove any internal structure of domain (and range) of the given
1742 set or relation. If there is any such internal structure in the input,
1743 then the name of the space is also removed.
1745 __isl_give isl_basic_set *isl_basic_set_flatten(
1746 __isl_take isl_basic_set *bset);
1747 __isl_give isl_set *isl_set_flatten(
1748 __isl_take isl_set *set);
1749 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1750 __isl_take isl_basic_map *bmap);
1751 __isl_give isl_map *isl_map_flatten_range(
1752 __isl_take isl_map *map);
1753 __isl_give isl_basic_map *isl_basic_map_flatten(
1754 __isl_take isl_basic_map *bmap);
1755 __isl_give isl_map *isl_map_flatten(
1756 __isl_take isl_map *map);
1758 __isl_give isl_map *isl_set_flatten_map(
1759 __isl_take isl_set *set);
1761 The function above constructs a relation
1762 that maps the input set to a flattened version of the set.
1766 Lift the input set to a space with extra dimensions corresponding
1767 to the existentially quantified variables in the input.
1768 In particular, the result lives in a wrapped map where the domain
1769 is the original space and the range corresponds to the original
1770 existentially quantified variables.
1772 __isl_give isl_basic_set *isl_basic_set_lift(
1773 __isl_take isl_basic_set *bset);
1774 __isl_give isl_set *isl_set_lift(
1775 __isl_take isl_set *set);
1776 __isl_give isl_union_set *isl_union_set_lift(
1777 __isl_take isl_union_set *uset);
1779 =item * Internal Product
1781 __isl_give isl_basic_map *isl_basic_map_zip(
1782 __isl_take isl_basic_map *bmap);
1783 __isl_give isl_map *isl_map_zip(
1784 __isl_take isl_map *map);
1785 __isl_give isl_union_map *isl_union_map_zip(
1786 __isl_take isl_union_map *umap);
1788 Given a relation with nested relations for domain and range,
1789 interchange the range of the domain with the domain of the range.
1791 =item * Aligning parameters
1793 __isl_give isl_set *isl_set_align_params(
1794 __isl_take isl_set *set,
1795 __isl_take isl_dim *model);
1796 __isl_give isl_map *isl_map_align_params(
1797 __isl_take isl_map *map,
1798 __isl_take isl_dim *model);
1800 Change the order of the parameters of the given set or relation
1801 such that the first parameters match those of C<model>.
1802 This may involve the introduction of extra parameters.
1803 All parameters need to be named.
1805 =item * Dimension manipulation
1807 __isl_give isl_set *isl_set_add_dims(
1808 __isl_take isl_set *set,
1809 enum isl_dim_type type, unsigned n);
1810 __isl_give isl_map *isl_map_add_dims(
1811 __isl_take isl_map *map,
1812 enum isl_dim_type type, unsigned n);
1814 It is usually not advisable to directly change the (input or output)
1815 space of a set or a relation as this removes the name and the internal
1816 structure of the space. However, the above functions can be useful
1817 to add new parameters, assuming
1818 C<isl_set_align_params> and C<isl_map_align_params>
1823 =head2 Binary Operations
1825 The two arguments of a binary operation not only need to live
1826 in the same C<isl_ctx>, they currently also need to have
1827 the same (number of) parameters.
1829 =head3 Basic Operations
1833 =item * Intersection
1835 __isl_give isl_basic_set *isl_basic_set_intersect(
1836 __isl_take isl_basic_set *bset1,
1837 __isl_take isl_basic_set *bset2);
1838 __isl_give isl_set *isl_set_intersect_params(
1839 __isl_take isl_set *set,
1840 __isl_take isl_set *params);
1841 __isl_give isl_set *isl_set_intersect(
1842 __isl_take isl_set *set1,
1843 __isl_take isl_set *set2);
1844 __isl_give isl_union_set *isl_union_set_intersect(
1845 __isl_take isl_union_set *uset1,
1846 __isl_take isl_union_set *uset2);
1847 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1848 __isl_take isl_basic_map *bmap,
1849 __isl_take isl_basic_set *bset);
1850 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1851 __isl_take isl_basic_map *bmap,
1852 __isl_take isl_basic_set *bset);
1853 __isl_give isl_basic_map *isl_basic_map_intersect(
1854 __isl_take isl_basic_map *bmap1,
1855 __isl_take isl_basic_map *bmap2);
1856 __isl_give isl_map *isl_map_intersect_params(
1857 __isl_take isl_map *map,
1858 __isl_take isl_set *params);
1859 __isl_give isl_map *isl_map_intersect_domain(
1860 __isl_take isl_map *map,
1861 __isl_take isl_set *set);
1862 __isl_give isl_map *isl_map_intersect_range(
1863 __isl_take isl_map *map,
1864 __isl_take isl_set *set);
1865 __isl_give isl_map *isl_map_intersect(
1866 __isl_take isl_map *map1,
1867 __isl_take isl_map *map2);
1868 __isl_give isl_union_map *isl_union_map_intersect_domain(
1869 __isl_take isl_union_map *umap,
1870 __isl_take isl_union_set *uset);
1871 __isl_give isl_union_map *isl_union_map_intersect_range(
1872 __isl_take isl_union_map *umap,
1873 __isl_take isl_union_set *uset);
1874 __isl_give isl_union_map *isl_union_map_intersect(
1875 __isl_take isl_union_map *umap1,
1876 __isl_take isl_union_map *umap2);
1880 __isl_give isl_set *isl_basic_set_union(
1881 __isl_take isl_basic_set *bset1,
1882 __isl_take isl_basic_set *bset2);
1883 __isl_give isl_map *isl_basic_map_union(
1884 __isl_take isl_basic_map *bmap1,
1885 __isl_take isl_basic_map *bmap2);
1886 __isl_give isl_set *isl_set_union(
1887 __isl_take isl_set *set1,
1888 __isl_take isl_set *set2);
1889 __isl_give isl_map *isl_map_union(
1890 __isl_take isl_map *map1,
1891 __isl_take isl_map *map2);
1892 __isl_give isl_union_set *isl_union_set_union(
1893 __isl_take isl_union_set *uset1,
1894 __isl_take isl_union_set *uset2);
1895 __isl_give isl_union_map *isl_union_map_union(
1896 __isl_take isl_union_map *umap1,
1897 __isl_take isl_union_map *umap2);
1899 =item * Set difference
1901 __isl_give isl_set *isl_set_subtract(
1902 __isl_take isl_set *set1,
1903 __isl_take isl_set *set2);
1904 __isl_give isl_map *isl_map_subtract(
1905 __isl_take isl_map *map1,
1906 __isl_take isl_map *map2);
1907 __isl_give isl_union_set *isl_union_set_subtract(
1908 __isl_take isl_union_set *uset1,
1909 __isl_take isl_union_set *uset2);
1910 __isl_give isl_union_map *isl_union_map_subtract(
1911 __isl_take isl_union_map *umap1,
1912 __isl_take isl_union_map *umap2);
1916 __isl_give isl_basic_set *isl_basic_set_apply(
1917 __isl_take isl_basic_set *bset,
1918 __isl_take isl_basic_map *bmap);
1919 __isl_give isl_set *isl_set_apply(
1920 __isl_take isl_set *set,
1921 __isl_take isl_map *map);
1922 __isl_give isl_union_set *isl_union_set_apply(
1923 __isl_take isl_union_set *uset,
1924 __isl_take isl_union_map *umap);
1925 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1926 __isl_take isl_basic_map *bmap1,
1927 __isl_take isl_basic_map *bmap2);
1928 __isl_give isl_basic_map *isl_basic_map_apply_range(
1929 __isl_take isl_basic_map *bmap1,
1930 __isl_take isl_basic_map *bmap2);
1931 __isl_give isl_map *isl_map_apply_domain(
1932 __isl_take isl_map *map1,
1933 __isl_take isl_map *map2);
1934 __isl_give isl_union_map *isl_union_map_apply_domain(
1935 __isl_take isl_union_map *umap1,
1936 __isl_take isl_union_map *umap2);
1937 __isl_give isl_map *isl_map_apply_range(
1938 __isl_take isl_map *map1,
1939 __isl_take isl_map *map2);
1940 __isl_give isl_union_map *isl_union_map_apply_range(
1941 __isl_take isl_union_map *umap1,
1942 __isl_take isl_union_map *umap2);
1944 =item * Cartesian Product
1946 __isl_give isl_set *isl_set_product(
1947 __isl_take isl_set *set1,
1948 __isl_take isl_set *set2);
1949 __isl_give isl_union_set *isl_union_set_product(
1950 __isl_take isl_union_set *uset1,
1951 __isl_take isl_union_set *uset2);
1952 __isl_give isl_basic_map *isl_basic_map_range_product(
1953 __isl_take isl_basic_map *bmap1,
1954 __isl_take isl_basic_map *bmap2);
1955 __isl_give isl_map *isl_map_range_product(
1956 __isl_take isl_map *map1,
1957 __isl_take isl_map *map2);
1958 __isl_give isl_union_map *isl_union_map_range_product(
1959 __isl_take isl_union_map *umap1,
1960 __isl_take isl_union_map *umap2);
1961 __isl_give isl_map *isl_map_product(
1962 __isl_take isl_map *map1,
1963 __isl_take isl_map *map2);
1964 __isl_give isl_union_map *isl_union_map_product(
1965 __isl_take isl_union_map *umap1,
1966 __isl_take isl_union_map *umap2);
1968 The above functions compute the cross product of the given
1969 sets or relations. The domains and ranges of the results
1970 are wrapped maps between domains and ranges of the inputs.
1971 To obtain a ``flat'' product, use the following functions
1974 __isl_give isl_basic_set *isl_basic_set_flat_product(
1975 __isl_take isl_basic_set *bset1,
1976 __isl_take isl_basic_set *bset2);
1977 __isl_give isl_set *isl_set_flat_product(
1978 __isl_take isl_set *set1,
1979 __isl_take isl_set *set2);
1980 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1981 __isl_take isl_basic_map *bmap1,
1982 __isl_take isl_basic_map *bmap2);
1983 __isl_give isl_map *isl_map_flat_range_product(
1984 __isl_take isl_map *map1,
1985 __isl_take isl_map *map2);
1986 __isl_give isl_union_map *isl_union_map_flat_range_product(
1987 __isl_take isl_union_map *umap1,
1988 __isl_take isl_union_map *umap2);
1989 __isl_give isl_basic_map *isl_basic_map_flat_product(
1990 __isl_take isl_basic_map *bmap1,
1991 __isl_take isl_basic_map *bmap2);
1992 __isl_give isl_map *isl_map_flat_product(
1993 __isl_take isl_map *map1,
1994 __isl_take isl_map *map2);
1996 =item * Simplification
1998 __isl_give isl_basic_set *isl_basic_set_gist(
1999 __isl_take isl_basic_set *bset,
2000 __isl_take isl_basic_set *context);
2001 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2002 __isl_take isl_set *context);
2003 __isl_give isl_union_set *isl_union_set_gist(
2004 __isl_take isl_union_set *uset,
2005 __isl_take isl_union_set *context);
2006 __isl_give isl_basic_map *isl_basic_map_gist(
2007 __isl_take isl_basic_map *bmap,
2008 __isl_take isl_basic_map *context);
2009 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2010 __isl_take isl_map *context);
2011 __isl_give isl_union_map *isl_union_map_gist(
2012 __isl_take isl_union_map *umap,
2013 __isl_take isl_union_map *context);
2015 The gist operation returns a set or relation that has the
2016 same intersection with the context as the input set or relation.
2017 Any implicit equality in the intersection is made explicit in the result,
2018 while all inequalities that are redundant with respect to the intersection
2020 In case of union sets and relations, the gist operation is performed
2025 =head3 Lexicographic Optimization
2027 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2028 the following functions
2029 compute a set that contains the lexicographic minimum or maximum
2030 of the elements in C<set> (or C<bset>) for those values of the parameters
2031 that satisfy C<dom>.
2032 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2033 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2035 In other words, the union of the parameter values
2036 for which the result is non-empty and of C<*empty>
2039 __isl_give isl_set *isl_basic_set_partial_lexmin(
2040 __isl_take isl_basic_set *bset,
2041 __isl_take isl_basic_set *dom,
2042 __isl_give isl_set **empty);
2043 __isl_give isl_set *isl_basic_set_partial_lexmax(
2044 __isl_take isl_basic_set *bset,
2045 __isl_take isl_basic_set *dom,
2046 __isl_give isl_set **empty);
2047 __isl_give isl_set *isl_set_partial_lexmin(
2048 __isl_take isl_set *set, __isl_take isl_set *dom,
2049 __isl_give isl_set **empty);
2050 __isl_give isl_set *isl_set_partial_lexmax(
2051 __isl_take isl_set *set, __isl_take isl_set *dom,
2052 __isl_give isl_set **empty);
2054 Given a (basic) set C<set> (or C<bset>), the following functions simply
2055 return a set containing the lexicographic minimum or maximum
2056 of the elements in C<set> (or C<bset>).
2057 In case of union sets, the optimum is computed per space.
2059 __isl_give isl_set *isl_basic_set_lexmin(
2060 __isl_take isl_basic_set *bset);
2061 __isl_give isl_set *isl_basic_set_lexmax(
2062 __isl_take isl_basic_set *bset);
2063 __isl_give isl_set *isl_set_lexmin(
2064 __isl_take isl_set *set);
2065 __isl_give isl_set *isl_set_lexmax(
2066 __isl_take isl_set *set);
2067 __isl_give isl_union_set *isl_union_set_lexmin(
2068 __isl_take isl_union_set *uset);
2069 __isl_give isl_union_set *isl_union_set_lexmax(
2070 __isl_take isl_union_set *uset);
2072 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2073 the following functions
2074 compute a relation that maps each element of C<dom>
2075 to the single lexicographic minimum or maximum
2076 of the elements that are associated to that same
2077 element in C<map> (or C<bmap>).
2078 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2079 that contains the elements in C<dom> that do not map
2080 to any elements in C<map> (or C<bmap>).
2081 In other words, the union of the domain of the result and of C<*empty>
2084 __isl_give isl_map *isl_basic_map_partial_lexmax(
2085 __isl_take isl_basic_map *bmap,
2086 __isl_take isl_basic_set *dom,
2087 __isl_give isl_set **empty);
2088 __isl_give isl_map *isl_basic_map_partial_lexmin(
2089 __isl_take isl_basic_map *bmap,
2090 __isl_take isl_basic_set *dom,
2091 __isl_give isl_set **empty);
2092 __isl_give isl_map *isl_map_partial_lexmax(
2093 __isl_take isl_map *map, __isl_take isl_set *dom,
2094 __isl_give isl_set **empty);
2095 __isl_give isl_map *isl_map_partial_lexmin(
2096 __isl_take isl_map *map, __isl_take isl_set *dom,
2097 __isl_give isl_set **empty);
2099 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2100 return a map mapping each element in the domain of
2101 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2102 of all elements associated to that element.
2103 In case of union relations, the optimum is computed per space.
2105 __isl_give isl_map *isl_basic_map_lexmin(
2106 __isl_take isl_basic_map *bmap);
2107 __isl_give isl_map *isl_basic_map_lexmax(
2108 __isl_take isl_basic_map *bmap);
2109 __isl_give isl_map *isl_map_lexmin(
2110 __isl_take isl_map *map);
2111 __isl_give isl_map *isl_map_lexmax(
2112 __isl_take isl_map *map);
2113 __isl_give isl_union_map *isl_union_map_lexmin(
2114 __isl_take isl_union_map *umap);
2115 __isl_give isl_union_map *isl_union_map_lexmax(
2116 __isl_take isl_union_map *umap);
2120 Lists are defined over several element types, including
2121 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2122 Here we take lists of C<isl_set>s as an example.
2123 Lists can be created, copied and freed using the following functions.
2125 #include <isl/list.h>
2126 __isl_give isl_set_list *isl_set_list_alloc(
2127 isl_ctx *ctx, int n);
2128 __isl_give isl_set_list *isl_set_list_copy(
2129 __isl_keep isl_set_list *list);
2130 __isl_give isl_set_list *isl_set_list_add(
2131 __isl_take isl_set_list *list,
2132 __isl_take isl_set *el);
2133 void isl_set_list_free(__isl_take isl_set_list *list);
2135 C<isl_set_list_alloc> creates an empty list with a capacity for
2138 Lists can be inspected using the following functions.
2140 #include <isl/list.h>
2141 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2142 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2143 __isl_give struct isl_set *isl_set_list_get_set(
2144 __isl_keep isl_set_list *list, int index);
2145 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2146 int (*fn)(__isl_take struct isl_set *el, void *user),
2149 Lists can be printed using
2151 #include <isl/list.h>
2152 __isl_give isl_printer *isl_printer_print_set_list(
2153 __isl_take isl_printer *p,
2154 __isl_keep isl_set_list *list);
2158 Matrices can be created, copied and freed using the following functions.
2160 #include <isl/mat.h>
2161 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2162 unsigned n_row, unsigned n_col);
2163 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2164 void isl_mat_free(__isl_take isl_mat *mat);
2166 Note that the elements of a newly created matrix may have arbitrary values.
2167 The elements can be changed and inspected using the following functions.
2169 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2170 int isl_mat_rows(__isl_keep isl_mat *mat);
2171 int isl_mat_cols(__isl_keep isl_mat *mat);
2172 int isl_mat_get_element(__isl_keep isl_mat *mat,
2173 int row, int col, isl_int *v);
2174 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2175 int row, int col, isl_int v);
2176 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2177 int row, int col, int v);
2179 C<isl_mat_get_element> will return a negative value if anything went wrong.
2180 In that case, the value of C<*v> is undefined.
2182 The following function can be used to compute the (right) inverse
2183 of a matrix, i.e., a matrix such that the product of the original
2184 and the inverse (in that order) is a multiple of the identity matrix.
2185 The input matrix is assumed to be of full row-rank.
2187 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2189 The following function can be used to compute the (right) kernel
2190 (or null space) of a matrix, i.e., a matrix such that the product of
2191 the original and the kernel (in that order) is the zero matrix.
2193 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2195 =head2 Piecewise Quasi Affine Expressions
2197 The zero quasi affine expression can be created using
2199 __isl_give isl_aff *isl_aff_zero(
2200 __isl_take isl_local_space *ls);
2202 A quasi affine expression can also be initialized from an C<isl_div>:
2204 #include <isl/div.h>
2205 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2207 An empty piecewise quasi affine expression (one with no cells)
2208 or a piecewise quasi affine expression with a single cell can
2209 be created using the following functions.
2211 #include <isl/aff.h>
2212 __isl_give isl_pw_aff *isl_pw_aff_empty(
2213 __isl_take isl_dim *dim);
2214 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2215 __isl_take isl_set *set, __isl_take isl_aff *aff);
2217 Quasi affine expressions can be copied and freed using
2219 #include <isl/aff.h>
2220 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2221 void *isl_aff_free(__isl_take isl_aff *aff);
2223 __isl_give isl_pw_aff *isl_pw_aff_copy(
2224 __isl_keep isl_pw_aff *pwaff);
2225 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2227 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2228 using the following function. The constraint is required to have
2229 a non-zero coefficient for the specified dimension.
2231 #include <isl/constraint.h>
2232 __isl_give isl_aff *isl_constraint_get_bound(
2233 __isl_keep isl_constraint *constraint,
2234 enum isl_dim_type type, int pos);
2236 The entire affine expression of the constraint can also be extracted
2237 using the following function.
2239 #include <isl/constraint.h>
2240 __isl_give isl_aff *isl_constraint_get_aff(
2241 __isl_keep isl_constraint *constraint);
2243 Conversely, an equality constraint equating
2244 the affine expression to zero or an inequality constraint enforcing
2245 the affine expression to be non-negative, can be constructed using
2247 __isl_give isl_constraint *isl_equality_from_aff(
2248 __isl_take isl_aff *aff);
2249 __isl_give isl_constraint *isl_inequality_from_aff(
2250 __isl_take isl_aff *aff);
2252 The expression can be inspected using
2254 #include <isl/aff.h>
2255 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2256 int isl_aff_dim(__isl_keep isl_aff *aff,
2257 enum isl_dim_type type);
2258 __isl_give isl_local_space *isl_aff_get_local_space(
2259 __isl_keep isl_aff *aff);
2260 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2261 enum isl_dim_type type, unsigned pos);
2262 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2264 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2265 enum isl_dim_type type, int pos, isl_int *v);
2266 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2268 __isl_give isl_div *isl_aff_get_div(
2269 __isl_keep isl_aff *aff, int pos);
2271 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2272 enum isl_dim_type type, unsigned first, unsigned n);
2273 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2274 enum isl_dim_type type, unsigned first, unsigned n);
2276 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2277 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2278 enum isl_dim_type type);
2279 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2281 It can be modified using
2283 #include <isl/aff.h>
2284 __isl_give isl_aff *isl_aff_set_dim_name(
2285 __isl_take isl_aff *aff, enum isl_dim_type type,
2286 unsigned pos, const char *s);
2287 __isl_give isl_aff *isl_aff_set_constant(
2288 __isl_take isl_aff *aff, isl_int v);
2289 __isl_give isl_aff *isl_aff_set_constant_si(
2290 __isl_take isl_aff *aff, int v);
2291 __isl_give isl_aff *isl_aff_set_coefficient(
2292 __isl_take isl_aff *aff,
2293 enum isl_dim_type type, int pos, isl_int v);
2294 __isl_give isl_aff *isl_aff_set_coefficient_si(
2295 __isl_take isl_aff *aff,
2296 enum isl_dim_type type, int pos, int v);
2297 __isl_give isl_aff *isl_aff_set_denominator(
2298 __isl_take isl_aff *aff, isl_int v);
2300 __isl_give isl_aff *isl_aff_add_constant(
2301 __isl_take isl_aff *aff, isl_int v);
2302 __isl_give isl_aff *isl_aff_add_constant_si(
2303 __isl_take isl_aff *aff, int v);
2304 __isl_give isl_aff *isl_aff_add_coefficient(
2305 __isl_take isl_aff *aff,
2306 enum isl_dim_type type, int pos, isl_int v);
2307 __isl_give isl_aff *isl_aff_add_coefficient_si(
2308 __isl_take isl_aff *aff,
2309 enum isl_dim_type type, int pos, int v);
2311 __isl_give isl_aff *isl_aff_insert_dims(
2312 __isl_take isl_aff *aff,
2313 enum isl_dim_type type, unsigned first, unsigned n);
2314 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2315 __isl_take isl_pw_aff *pwaff,
2316 enum isl_dim_type type, unsigned first, unsigned n);
2317 __isl_give isl_aff *isl_aff_add_dims(
2318 __isl_take isl_aff *aff,
2319 enum isl_dim_type type, unsigned n);
2320 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2321 __isl_take isl_pw_aff *pwaff,
2322 enum isl_dim_type type, unsigned n);
2323 __isl_give isl_aff *isl_aff_drop_dims(
2324 __isl_take isl_aff *aff,
2325 enum isl_dim_type type, unsigned first, unsigned n);
2326 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2327 __isl_take isl_pw_aff *pwaff,
2328 enum isl_dim_type type, unsigned first, unsigned n);
2330 Note that the C<set_constant> and C<set_coefficient> functions
2331 set the I<numerator> of the constant or coefficient, while
2332 C<add_constant> and C<add_coefficient> add an integer value to
2333 the possibly rational constant or coefficient.
2335 To check whether an affine expressions is obviously zero
2336 or obviously equal to some other affine expression, use
2338 #include <isl/aff.h>
2339 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2340 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2341 __isl_keep isl_aff *aff2);
2345 #include <isl/aff.h>
2346 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2347 __isl_take isl_aff *aff2);
2348 __isl_give isl_pw_aff *isl_pw_aff_add(
2349 __isl_take isl_pw_aff *pwaff1,
2350 __isl_take isl_pw_aff *pwaff2);
2351 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2352 __isl_take isl_aff *aff2);
2353 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2354 __isl_give isl_pw_aff *isl_pw_aff_neg(
2355 __isl_take isl_pw_aff *pwaff);
2356 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2357 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2358 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2360 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2362 __isl_give isl_aff *isl_aff_scale_down_ui(
2363 __isl_take isl_aff *aff, unsigned f);
2364 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2365 __isl_take isl_pw_aff *pwaff, isl_int f);
2367 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2368 __isl_take isl_pw_aff *pwqp);
2370 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2371 __isl_take isl_pw_aff *pwaff,
2372 __isl_take isl_dim *model);
2374 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2375 __isl_take isl_set *context);
2376 __isl_give isl_pw_aff *isl_pw_aff_gist(
2377 __isl_take isl_pw_aff *pwaff,
2378 __isl_take isl_set *context);
2380 __isl_give isl_set *isl_pw_aff_domain(
2381 __isl_take isl_pw_aff *pwaff);
2383 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2384 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2385 __isl_give isl_set *isl_pw_aff_lt_set(
2386 __isl_take isl_pw_aff *pwaff1,
2387 __isl_take isl_pw_aff *pwaff2);
2388 __isl_give isl_set *isl_pw_aff_ge_set(
2389 __isl_take isl_pw_aff *pwaff1,
2390 __isl_take isl_pw_aff *pwaff2);
2391 __isl_give isl_set *isl_pw_aff_gt_set(
2392 __isl_take isl_pw_aff *pwaff1,
2393 __isl_take isl_pw_aff *pwaff2);
2395 The function C<isl_aff_ge_basic_set> returns a basic set
2396 containing those elements in the shared space
2397 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2398 The function C<isl_aff_ge_set> returns a set
2399 containing those elements in the shared domain
2400 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2402 #include <isl/aff.h>
2403 __isl_give isl_set *isl_pw_aff_nonneg_set(
2404 __isl_take isl_pw_aff *pwaff);
2406 The function C<isl_pw_aff_nonneg_set> returns a set
2407 containing those elements in the domain
2408 of C<pwaff> where C<pwaff> is non-negative.
2410 #include <isl/aff.h>
2411 __isl_give isl_pw_aff *isl_pw_aff_max(
2412 __isl_take isl_pw_aff *pwaff1,
2413 __isl_take isl_pw_aff *pwaff2);
2415 The function C<isl_pw_aff_max> computes a piecewise quasi-affine
2416 expression with a domain that is the union of those of C<pwaff1> and
2417 C<pwaff2> and such that on each cell, the quasi-affine expression is
2418 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2419 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2420 associated expression is the defined one.
2422 An expression can be printed using
2424 #include <isl/aff.h>
2425 __isl_give isl_printer *isl_printer_print_aff(
2426 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2428 __isl_give isl_printer *isl_printer_print_pw_aff(
2429 __isl_take isl_printer *p,
2430 __isl_keep isl_pw_aff *pwaff);
2434 Points are elements of a set. They can be used to construct
2435 simple sets (boxes) or they can be used to represent the
2436 individual elements of a set.
2437 The zero point (the origin) can be created using
2439 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2441 The coordinates of a point can be inspected, set and changed
2444 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2445 enum isl_dim_type type, int pos, isl_int *v);
2446 __isl_give isl_point *isl_point_set_coordinate(
2447 __isl_take isl_point *pnt,
2448 enum isl_dim_type type, int pos, isl_int v);
2450 __isl_give isl_point *isl_point_add_ui(
2451 __isl_take isl_point *pnt,
2452 enum isl_dim_type type, int pos, unsigned val);
2453 __isl_give isl_point *isl_point_sub_ui(
2454 __isl_take isl_point *pnt,
2455 enum isl_dim_type type, int pos, unsigned val);
2457 Other properties can be obtained using
2459 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2461 Points can be copied or freed using
2463 __isl_give isl_point *isl_point_copy(
2464 __isl_keep isl_point *pnt);
2465 void isl_point_free(__isl_take isl_point *pnt);
2467 A singleton set can be created from a point using
2469 __isl_give isl_basic_set *isl_basic_set_from_point(
2470 __isl_take isl_point *pnt);
2471 __isl_give isl_set *isl_set_from_point(
2472 __isl_take isl_point *pnt);
2474 and a box can be created from two opposite extremal points using
2476 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2477 __isl_take isl_point *pnt1,
2478 __isl_take isl_point *pnt2);
2479 __isl_give isl_set *isl_set_box_from_points(
2480 __isl_take isl_point *pnt1,
2481 __isl_take isl_point *pnt2);
2483 All elements of a B<bounded> (union) set can be enumerated using
2484 the following functions.
2486 int isl_set_foreach_point(__isl_keep isl_set *set,
2487 int (*fn)(__isl_take isl_point *pnt, void *user),
2489 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2490 int (*fn)(__isl_take isl_point *pnt, void *user),
2493 The function C<fn> is called for each integer point in
2494 C<set> with as second argument the last argument of
2495 the C<isl_set_foreach_point> call. The function C<fn>
2496 should return C<0> on success and C<-1> on failure.
2497 In the latter case, C<isl_set_foreach_point> will stop
2498 enumerating and return C<-1> as well.
2499 If the enumeration is performed successfully and to completion,
2500 then C<isl_set_foreach_point> returns C<0>.
2502 To obtain a single point of a (basic) set, use
2504 __isl_give isl_point *isl_basic_set_sample_point(
2505 __isl_take isl_basic_set *bset);
2506 __isl_give isl_point *isl_set_sample_point(
2507 __isl_take isl_set *set);
2509 If C<set> does not contain any (integer) points, then the
2510 resulting point will be ``void'', a property that can be
2513 int isl_point_is_void(__isl_keep isl_point *pnt);
2515 =head2 Piecewise Quasipolynomials
2517 A piecewise quasipolynomial is a particular kind of function that maps
2518 a parametric point to a rational value.
2519 More specifically, a quasipolynomial is a polynomial expression in greatest
2520 integer parts of affine expressions of parameters and variables.
2521 A piecewise quasipolynomial is a subdivision of a given parametric
2522 domain into disjoint cells with a quasipolynomial associated to
2523 each cell. The value of the piecewise quasipolynomial at a given
2524 point is the value of the quasipolynomial associated to the cell
2525 that contains the point. Outside of the union of cells,
2526 the value is assumed to be zero.
2527 For example, the piecewise quasipolynomial
2529 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2531 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2532 A given piecewise quasipolynomial has a fixed domain dimension.
2533 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2534 defined over different domains.
2535 Piecewise quasipolynomials are mainly used by the C<barvinok>
2536 library for representing the number of elements in a parametric set or map.
2537 For example, the piecewise quasipolynomial above represents
2538 the number of points in the map
2540 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2542 =head3 Printing (Piecewise) Quasipolynomials
2544 Quasipolynomials and piecewise quasipolynomials can be printed
2545 using the following functions.
2547 __isl_give isl_printer *isl_printer_print_qpolynomial(
2548 __isl_take isl_printer *p,
2549 __isl_keep isl_qpolynomial *qp);
2551 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2552 __isl_take isl_printer *p,
2553 __isl_keep isl_pw_qpolynomial *pwqp);
2555 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2556 __isl_take isl_printer *p,
2557 __isl_keep isl_union_pw_qpolynomial *upwqp);
2559 The output format of the printer
2560 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2561 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2563 In case of printing in C<ISL_FORMAT_C>, the user may want
2564 to set the names of all dimensions
2566 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2567 __isl_take isl_qpolynomial *qp,
2568 enum isl_dim_type type, unsigned pos,
2570 __isl_give isl_pw_qpolynomial *
2571 isl_pw_qpolynomial_set_dim_name(
2572 __isl_take isl_pw_qpolynomial *pwqp,
2573 enum isl_dim_type type, unsigned pos,
2576 =head3 Creating New (Piecewise) Quasipolynomials
2578 Some simple quasipolynomials can be created using the following functions.
2579 More complicated quasipolynomials can be created by applying
2580 operations such as addition and multiplication
2581 on the resulting quasipolynomials
2583 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2584 __isl_take isl_dim *dim);
2585 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2586 __isl_take isl_dim *dim);
2587 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2588 __isl_take isl_dim *dim);
2589 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2590 __isl_take isl_dim *dim);
2591 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2592 __isl_take isl_dim *dim);
2593 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2594 __isl_take isl_dim *dim,
2595 const isl_int n, const isl_int d);
2596 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2597 __isl_take isl_div *div);
2598 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2599 __isl_take isl_dim *dim,
2600 enum isl_dim_type type, unsigned pos);
2601 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2602 __isl_take isl_aff *aff);
2604 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2605 with a single cell can be created using the following functions.
2606 Multiple of these single cell piecewise quasipolynomials can
2607 be combined to create more complicated piecewise quasipolynomials.
2609 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2610 __isl_take isl_dim *dim);
2611 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2612 __isl_take isl_set *set,
2613 __isl_take isl_qpolynomial *qp);
2615 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2616 __isl_take isl_dim *dim);
2617 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2618 __isl_take isl_pw_qpolynomial *pwqp);
2619 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2620 __isl_take isl_union_pw_qpolynomial *upwqp,
2621 __isl_take isl_pw_qpolynomial *pwqp);
2623 Quasipolynomials can be copied and freed again using the following
2626 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2627 __isl_keep isl_qpolynomial *qp);
2628 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2630 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2631 __isl_keep isl_pw_qpolynomial *pwqp);
2632 void *isl_pw_qpolynomial_free(
2633 __isl_take isl_pw_qpolynomial *pwqp);
2635 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2636 __isl_keep isl_union_pw_qpolynomial *upwqp);
2637 void isl_union_pw_qpolynomial_free(
2638 __isl_take isl_union_pw_qpolynomial *upwqp);
2640 =head3 Inspecting (Piecewise) Quasipolynomials
2642 To iterate over all piecewise quasipolynomials in a union
2643 piecewise quasipolynomial, use the following function
2645 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2646 __isl_keep isl_union_pw_qpolynomial *upwqp,
2647 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2650 To extract the piecewise quasipolynomial from a union with a given dimension
2653 __isl_give isl_pw_qpolynomial *
2654 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2655 __isl_keep isl_union_pw_qpolynomial *upwqp,
2656 __isl_take isl_dim *dim);
2658 To iterate over the cells in a piecewise quasipolynomial,
2659 use either of the following two functions
2661 int isl_pw_qpolynomial_foreach_piece(
2662 __isl_keep isl_pw_qpolynomial *pwqp,
2663 int (*fn)(__isl_take isl_set *set,
2664 __isl_take isl_qpolynomial *qp,
2665 void *user), void *user);
2666 int isl_pw_qpolynomial_foreach_lifted_piece(
2667 __isl_keep isl_pw_qpolynomial *pwqp,
2668 int (*fn)(__isl_take isl_set *set,
2669 __isl_take isl_qpolynomial *qp,
2670 void *user), void *user);
2672 As usual, the function C<fn> should return C<0> on success
2673 and C<-1> on failure. The difference between
2674 C<isl_pw_qpolynomial_foreach_piece> and
2675 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2676 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2677 compute unique representations for all existentially quantified
2678 variables and then turn these existentially quantified variables
2679 into extra set variables, adapting the associated quasipolynomial
2680 accordingly. This means that the C<set> passed to C<fn>
2681 will not have any existentially quantified variables, but that
2682 the dimensions of the sets may be different for different
2683 invocations of C<fn>.
2685 To iterate over all terms in a quasipolynomial,
2688 int isl_qpolynomial_foreach_term(
2689 __isl_keep isl_qpolynomial *qp,
2690 int (*fn)(__isl_take isl_term *term,
2691 void *user), void *user);
2693 The terms themselves can be inspected and freed using
2696 unsigned isl_term_dim(__isl_keep isl_term *term,
2697 enum isl_dim_type type);
2698 void isl_term_get_num(__isl_keep isl_term *term,
2700 void isl_term_get_den(__isl_keep isl_term *term,
2702 int isl_term_get_exp(__isl_keep isl_term *term,
2703 enum isl_dim_type type, unsigned pos);
2704 __isl_give isl_div *isl_term_get_div(
2705 __isl_keep isl_term *term, unsigned pos);
2706 void isl_term_free(__isl_take isl_term *term);
2708 Each term is a product of parameters, set variables and
2709 integer divisions. The function C<isl_term_get_exp>
2710 returns the exponent of a given dimensions in the given term.
2711 The C<isl_int>s in the arguments of C<isl_term_get_num>
2712 and C<isl_term_get_den> need to have been initialized
2713 using C<isl_int_init> before calling these functions.
2715 =head3 Properties of (Piecewise) Quasipolynomials
2717 To check whether a quasipolynomial is actually a constant,
2718 use the following function.
2720 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2721 isl_int *n, isl_int *d);
2723 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2724 then the numerator and denominator of the constant
2725 are returned in C<*n> and C<*d>, respectively.
2727 =head3 Operations on (Piecewise) Quasipolynomials
2729 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2730 __isl_take isl_qpolynomial *qp, isl_int v);
2731 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2732 __isl_take isl_qpolynomial *qp);
2733 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2734 __isl_take isl_qpolynomial *qp1,
2735 __isl_take isl_qpolynomial *qp2);
2736 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2737 __isl_take isl_qpolynomial *qp1,
2738 __isl_take isl_qpolynomial *qp2);
2739 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2740 __isl_take isl_qpolynomial *qp1,
2741 __isl_take isl_qpolynomial *qp2);
2742 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2743 __isl_take isl_qpolynomial *qp, unsigned exponent);
2745 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2746 __isl_take isl_pw_qpolynomial *pwqp1,
2747 __isl_take isl_pw_qpolynomial *pwqp2);
2748 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2749 __isl_take isl_pw_qpolynomial *pwqp1,
2750 __isl_take isl_pw_qpolynomial *pwqp2);
2751 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2752 __isl_take isl_pw_qpolynomial *pwqp1,
2753 __isl_take isl_pw_qpolynomial *pwqp2);
2754 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2755 __isl_take isl_pw_qpolynomial *pwqp);
2756 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2757 __isl_take isl_pw_qpolynomial *pwqp1,
2758 __isl_take isl_pw_qpolynomial *pwqp2);
2760 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2761 __isl_take isl_union_pw_qpolynomial *upwqp1,
2762 __isl_take isl_union_pw_qpolynomial *upwqp2);
2763 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2764 __isl_take isl_union_pw_qpolynomial *upwqp1,
2765 __isl_take isl_union_pw_qpolynomial *upwqp2);
2766 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2767 __isl_take isl_union_pw_qpolynomial *upwqp1,
2768 __isl_take isl_union_pw_qpolynomial *upwqp2);
2770 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2771 __isl_take isl_pw_qpolynomial *pwqp,
2772 __isl_take isl_point *pnt);
2774 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2775 __isl_take isl_union_pw_qpolynomial *upwqp,
2776 __isl_take isl_point *pnt);
2778 __isl_give isl_set *isl_pw_qpolynomial_domain(
2779 __isl_take isl_pw_qpolynomial *pwqp);
2780 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2781 __isl_take isl_pw_qpolynomial *pwpq,
2782 __isl_take isl_set *set);
2784 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2785 __isl_take isl_union_pw_qpolynomial *upwqp);
2786 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2787 __isl_take isl_union_pw_qpolynomial *upwpq,
2788 __isl_take isl_union_set *uset);
2790 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2791 __isl_take isl_qpolynomial *qp,
2792 __isl_take isl_dim *model);
2794 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2795 __isl_take isl_union_pw_qpolynomial *upwqp);
2797 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2798 __isl_take isl_qpolynomial *qp,
2799 __isl_take isl_set *context);
2801 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2802 __isl_take isl_pw_qpolynomial *pwqp,
2803 __isl_take isl_set *context);
2805 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2806 __isl_take isl_union_pw_qpolynomial *upwqp,
2807 __isl_take isl_union_set *context);
2809 The gist operation applies the gist operation to each of
2810 the cells in the domain of the input piecewise quasipolynomial.
2811 The context is also exploited
2812 to simplify the quasipolynomials associated to each cell.
2814 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2815 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2816 __isl_give isl_union_pw_qpolynomial *
2817 isl_union_pw_qpolynomial_to_polynomial(
2818 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2820 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2821 the polynomial will be an overapproximation. If C<sign> is negative,
2822 it will be an underapproximation. If C<sign> is zero, the approximation
2823 will lie somewhere in between.
2825 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2827 A piecewise quasipolynomial reduction is a piecewise
2828 reduction (or fold) of quasipolynomials.
2829 In particular, the reduction can be maximum or a minimum.
2830 The objects are mainly used to represent the result of
2831 an upper or lower bound on a quasipolynomial over its domain,
2832 i.e., as the result of the following function.
2834 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2835 __isl_take isl_pw_qpolynomial *pwqp,
2836 enum isl_fold type, int *tight);
2838 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2839 __isl_take isl_union_pw_qpolynomial *upwqp,
2840 enum isl_fold type, int *tight);
2842 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2843 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2844 is the returned bound is known be tight, i.e., for each value
2845 of the parameters there is at least
2846 one element in the domain that reaches the bound.
2847 If the domain of C<pwqp> is not wrapping, then the bound is computed
2848 over all elements in that domain and the result has a purely parametric
2849 domain. If the domain of C<pwqp> is wrapping, then the bound is
2850 computed over the range of the wrapped relation. The domain of the
2851 wrapped relation becomes the domain of the result.
2853 A (piecewise) quasipolynomial reduction can be copied or freed using the
2854 following functions.
2856 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2857 __isl_keep isl_qpolynomial_fold *fold);
2858 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2859 __isl_keep isl_pw_qpolynomial_fold *pwf);
2860 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2861 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2862 void isl_qpolynomial_fold_free(
2863 __isl_take isl_qpolynomial_fold *fold);
2864 void *isl_pw_qpolynomial_fold_free(
2865 __isl_take isl_pw_qpolynomial_fold *pwf);
2866 void isl_union_pw_qpolynomial_fold_free(
2867 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2869 =head3 Printing Piecewise Quasipolynomial Reductions
2871 Piecewise quasipolynomial reductions can be printed
2872 using the following function.
2874 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2875 __isl_take isl_printer *p,
2876 __isl_keep isl_pw_qpolynomial_fold *pwf);
2877 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2878 __isl_take isl_printer *p,
2879 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2881 For C<isl_printer_print_pw_qpolynomial_fold>,
2882 output format of the printer
2883 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2884 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2885 output format of the printer
2886 needs to be set to C<ISL_FORMAT_ISL>.
2887 In case of printing in C<ISL_FORMAT_C>, the user may want
2888 to set the names of all dimensions
2890 __isl_give isl_pw_qpolynomial_fold *
2891 isl_pw_qpolynomial_fold_set_dim_name(
2892 __isl_take isl_pw_qpolynomial_fold *pwf,
2893 enum isl_dim_type type, unsigned pos,
2896 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2898 To iterate over all piecewise quasipolynomial reductions in a union
2899 piecewise quasipolynomial reduction, use the following function
2901 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2902 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2903 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2904 void *user), void *user);
2906 To iterate over the cells in a piecewise quasipolynomial reduction,
2907 use either of the following two functions
2909 int isl_pw_qpolynomial_fold_foreach_piece(
2910 __isl_keep isl_pw_qpolynomial_fold *pwf,
2911 int (*fn)(__isl_take isl_set *set,
2912 __isl_take isl_qpolynomial_fold *fold,
2913 void *user), void *user);
2914 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2915 __isl_keep isl_pw_qpolynomial_fold *pwf,
2916 int (*fn)(__isl_take isl_set *set,
2917 __isl_take isl_qpolynomial_fold *fold,
2918 void *user), void *user);
2920 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2921 of the difference between these two functions.
2923 To iterate over all quasipolynomials in a reduction, use
2925 int isl_qpolynomial_fold_foreach_qpolynomial(
2926 __isl_keep isl_qpolynomial_fold *fold,
2927 int (*fn)(__isl_take isl_qpolynomial *qp,
2928 void *user), void *user);
2930 =head3 Operations on Piecewise Quasipolynomial Reductions
2932 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
2933 __isl_take isl_qpolynomial_fold *fold, isl_int v);
2935 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2936 __isl_take isl_pw_qpolynomial_fold *pwf1,
2937 __isl_take isl_pw_qpolynomial_fold *pwf2);
2939 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2940 __isl_take isl_pw_qpolynomial_fold *pwf1,
2941 __isl_take isl_pw_qpolynomial_fold *pwf2);
2943 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2944 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2945 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2947 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2948 __isl_take isl_pw_qpolynomial_fold *pwf,
2949 __isl_take isl_point *pnt);
2951 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2952 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2953 __isl_take isl_point *pnt);
2955 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2956 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2957 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2958 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2959 __isl_take isl_union_set *uset);
2961 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2962 __isl_take isl_pw_qpolynomial_fold *pwf);
2964 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2965 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2967 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2968 __isl_take isl_pw_qpolynomial_fold *pwf,
2969 __isl_take isl_set *context);
2971 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2972 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2973 __isl_take isl_union_set *context);
2975 The gist operation applies the gist operation to each of
2976 the cells in the domain of the input piecewise quasipolynomial reduction.
2977 In future, the operation will also exploit the context
2978 to simplify the quasipolynomial reductions associated to each cell.
2980 __isl_give isl_pw_qpolynomial_fold *
2981 isl_set_apply_pw_qpolynomial_fold(
2982 __isl_take isl_set *set,
2983 __isl_take isl_pw_qpolynomial_fold *pwf,
2985 __isl_give isl_pw_qpolynomial_fold *
2986 isl_map_apply_pw_qpolynomial_fold(
2987 __isl_take isl_map *map,
2988 __isl_take isl_pw_qpolynomial_fold *pwf,
2990 __isl_give isl_union_pw_qpolynomial_fold *
2991 isl_union_set_apply_union_pw_qpolynomial_fold(
2992 __isl_take isl_union_set *uset,
2993 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2995 __isl_give isl_union_pw_qpolynomial_fold *
2996 isl_union_map_apply_union_pw_qpolynomial_fold(
2997 __isl_take isl_union_map *umap,
2998 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3001 The functions taking a map
3002 compose the given map with the given piecewise quasipolynomial reduction.
3003 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3004 over all elements in the intersection of the range of the map
3005 and the domain of the piecewise quasipolynomial reduction
3006 as a function of an element in the domain of the map.
3007 The functions taking a set compute a bound over all elements in the
3008 intersection of the set and the domain of the
3009 piecewise quasipolynomial reduction.
3011 =head2 Dependence Analysis
3013 C<isl> contains specialized functionality for performing
3014 array dataflow analysis. That is, given a I<sink> access relation
3015 and a collection of possible I<source> access relations,
3016 C<isl> can compute relations that describe
3017 for each iteration of the sink access, which iteration
3018 of which of the source access relations was the last
3019 to access the same data element before the given iteration
3021 To compute standard flow dependences, the sink should be
3022 a read, while the sources should be writes.
3023 If any of the source accesses are marked as being I<may>
3024 accesses, then there will be a dependence to the last
3025 I<must> access B<and> to any I<may> access that follows
3026 this last I<must> access.
3027 In particular, if I<all> sources are I<may> accesses,
3028 then memory based dependence analysis is performed.
3029 If, on the other hand, all sources are I<must> accesses,
3030 then value based dependence analysis is performed.
3032 #include <isl/flow.h>
3034 typedef int (*isl_access_level_before)(void *first, void *second);
3036 __isl_give isl_access_info *isl_access_info_alloc(
3037 __isl_take isl_map *sink,
3038 void *sink_user, isl_access_level_before fn,
3040 __isl_give isl_access_info *isl_access_info_add_source(
3041 __isl_take isl_access_info *acc,
3042 __isl_take isl_map *source, int must,
3044 void isl_access_info_free(__isl_take isl_access_info *acc);
3046 __isl_give isl_flow *isl_access_info_compute_flow(
3047 __isl_take isl_access_info *acc);
3049 int isl_flow_foreach(__isl_keep isl_flow *deps,
3050 int (*fn)(__isl_take isl_map *dep, int must,
3051 void *dep_user, void *user),
3053 __isl_give isl_map *isl_flow_get_no_source(
3054 __isl_keep isl_flow *deps, int must);
3055 void isl_flow_free(__isl_take isl_flow *deps);
3057 The function C<isl_access_info_compute_flow> performs the actual
3058 dependence analysis. The other functions are used to construct
3059 the input for this function or to read off the output.
3061 The input is collected in an C<isl_access_info>, which can
3062 be created through a call to C<isl_access_info_alloc>.
3063 The arguments to this functions are the sink access relation
3064 C<sink>, a token C<sink_user> used to identify the sink
3065 access to the user, a callback function for specifying the
3066 relative order of source and sink accesses, and the number
3067 of source access relations that will be added.
3068 The callback function has type C<int (*)(void *first, void *second)>.
3069 The function is called with two user supplied tokens identifying
3070 either a source or the sink and it should return the shared nesting
3071 level and the relative order of the two accesses.
3072 In particular, let I<n> be the number of loops shared by
3073 the two accesses. If C<first> precedes C<second> textually,
3074 then the function should return I<2 * n + 1>; otherwise,
3075 it should return I<2 * n>.
3076 The sources can be added to the C<isl_access_info> by performing
3077 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3078 C<must> indicates whether the source is a I<must> access
3079 or a I<may> access. Note that a multi-valued access relation
3080 should only be marked I<must> if every iteration in the domain
3081 of the relation accesses I<all> elements in its image.
3082 The C<source_user> token is again used to identify
3083 the source access. The range of the source access relation
3084 C<source> should have the same dimension as the range
3085 of the sink access relation.
3086 The C<isl_access_info_free> function should usually not be
3087 called explicitly, because it is called implicitly by
3088 C<isl_access_info_compute_flow>.
3090 The result of the dependence analysis is collected in an
3091 C<isl_flow>. There may be elements of
3092 the sink access for which no preceding source access could be
3093 found or for which all preceding sources are I<may> accesses.
3094 The relations containing these elements can be obtained through
3095 calls to C<isl_flow_get_no_source>, the first with C<must> set
3096 and the second with C<must> unset.
3097 In the case of standard flow dependence analysis,
3098 with the sink a read and the sources I<must> writes,
3099 the first relation corresponds to the reads from uninitialized
3100 array elements and the second relation is empty.
3101 The actual flow dependences can be extracted using
3102 C<isl_flow_foreach>. This function will call the user-specified
3103 callback function C<fn> for each B<non-empty> dependence between
3104 a source and the sink. The callback function is called
3105 with four arguments, the actual flow dependence relation
3106 mapping source iterations to sink iterations, a boolean that
3107 indicates whether it is a I<must> or I<may> dependence, a token
3108 identifying the source and an additional C<void *> with value
3109 equal to the third argument of the C<isl_flow_foreach> call.
3110 A dependence is marked I<must> if it originates from a I<must>
3111 source and if it is not followed by any I<may> sources.
3113 After finishing with an C<isl_flow>, the user should call
3114 C<isl_flow_free> to free all associated memory.
3116 A higher-level interface to dependence analysis is provided
3117 by the following function.
3119 #include <isl/flow.h>
3121 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3122 __isl_take isl_union_map *must_source,
3123 __isl_take isl_union_map *may_source,
3124 __isl_take isl_union_map *schedule,
3125 __isl_give isl_union_map **must_dep,
3126 __isl_give isl_union_map **may_dep,
3127 __isl_give isl_union_map **must_no_source,
3128 __isl_give isl_union_map **may_no_source);
3130 The arrays are identified by the tuple names of the ranges
3131 of the accesses. The iteration domains by the tuple names
3132 of the domains of the accesses and of the schedule.
3133 The relative order of the iteration domains is given by the
3134 schedule. The relations returned through C<must_no_source>
3135 and C<may_no_source> are subsets of C<sink>.
3136 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3137 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3138 any of the other arguments is treated as an error.
3142 B<The functionality described in this section is fairly new
3143 and may be subject to change.>
3145 The following function can be used to compute a schedule
3146 for a union of domains. The generated schedule respects
3147 all C<validity> dependences. That is, all dependence distances
3148 over these dependences in the scheduled space are lexicographically
3149 positive. The generated schedule schedule also tries to minimize
3150 the dependence distances over C<proximity> dependences.
3151 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3152 for groups of domains where the dependence distances have only
3153 non-negative values.
3154 The algorithm used to construct the schedule is similar to that
3157 #include <isl/schedule.h>
3158 __isl_give isl_schedule *isl_union_set_compute_schedule(
3159 __isl_take isl_union_set *domain,
3160 __isl_take isl_union_map *validity,
3161 __isl_take isl_union_map *proximity);
3162 void *isl_schedule_free(__isl_take isl_schedule *sched);
3164 A mapping from the domains to the scheduled space can be obtained
3165 from an C<isl_schedule> using the following function.
3167 __isl_give isl_union_map *isl_schedule_get_map(
3168 __isl_keep isl_schedule *sched);
3170 A representation of the schedule can be printed using
3172 __isl_give isl_printer *isl_printer_print_schedule(
3173 __isl_take isl_printer *p,
3174 __isl_keep isl_schedule *schedule);
3176 A representation of the schedule as a forest of bands can be obtained
3177 using the following function.
3179 __isl_give isl_band_list *isl_schedule_get_band_forest(
3180 __isl_keep isl_schedule *schedule);
3182 The list can be manipulated as explained in L<"Lists">.
3183 The bands inside the list can be copied and freed using the following
3186 #include <isl/band.h>
3187 __isl_give isl_band *isl_band_copy(
3188 __isl_keep isl_band *band);
3189 void *isl_band_free(__isl_take isl_band *band);
3191 Each band contains zero or more scheduling dimensions.
3192 These are referred to as the members of the band.
3193 The section of the schedule that corresponds to the band is
3194 referred to as the partial schedule of the band.
3195 For those nodes that participate in a band, the outer scheduling
3196 dimensions form the prefix schedule, while the inner scheduling
3197 dimensions form the suffix schedule.
3198 That is, if we take a cut of the band forest, then the union of
3199 the concatenations of the prefix, partial and suffix schedules of
3200 each band in the cut is equal to the entire schedule (modulo
3201 some possible padding at the end with zero scheduling dimensions).
3202 The properties of a band can be inspected using the following functions.
3204 #include <isl/band.h>
3205 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3207 int isl_band_has_children(__isl_keep isl_band *band);
3208 __isl_give isl_band_list *isl_band_get_children(
3209 __isl_keep isl_band *band);
3211 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3212 __isl_keep isl_band *band);
3213 __isl_give isl_union_map *isl_band_get_partial_schedule(
3214 __isl_keep isl_band *band);
3215 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3216 __isl_keep isl_band *band);
3218 int isl_band_n_member(__isl_keep isl_band *band);
3219 int isl_band_member_is_zero_distance(
3220 __isl_keep isl_band *band, int pos);
3222 Note that a scheduling dimension is considered to be ``zero
3223 distance'' if it does not carry any proximity dependences
3225 That is, if the dependence distances of the proximity
3226 dependences are all zero in that direction (for fixed
3227 iterations of outer bands).
3229 A representation of the band can be printed using
3231 #include <isl/band.h>
3232 __isl_give isl_printer *isl_printer_print_band(
3233 __isl_take isl_printer *p,
3234 __isl_keep isl_band *band);
3236 =head2 Parametric Vertex Enumeration
3238 The parametric vertex enumeration described in this section
3239 is mainly intended to be used internally and by the C<barvinok>
3242 #include <isl/vertices.h>
3243 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3244 __isl_keep isl_basic_set *bset);
3246 The function C<isl_basic_set_compute_vertices> performs the
3247 actual computation of the parametric vertices and the chamber
3248 decomposition and store the result in an C<isl_vertices> object.
3249 This information can be queried by either iterating over all
3250 the vertices or iterating over all the chambers or cells
3251 and then iterating over all vertices that are active on the chamber.
3253 int isl_vertices_foreach_vertex(
3254 __isl_keep isl_vertices *vertices,
3255 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3258 int isl_vertices_foreach_cell(
3259 __isl_keep isl_vertices *vertices,
3260 int (*fn)(__isl_take isl_cell *cell, void *user),
3262 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3263 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3266 Other operations that can be performed on an C<isl_vertices> object are
3269 isl_ctx *isl_vertices_get_ctx(
3270 __isl_keep isl_vertices *vertices);
3271 int isl_vertices_get_n_vertices(
3272 __isl_keep isl_vertices *vertices);
3273 void isl_vertices_free(__isl_take isl_vertices *vertices);
3275 Vertices can be inspected and destroyed using the following functions.
3277 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3278 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3279 __isl_give isl_basic_set *isl_vertex_get_domain(
3280 __isl_keep isl_vertex *vertex);
3281 __isl_give isl_basic_set *isl_vertex_get_expr(
3282 __isl_keep isl_vertex *vertex);
3283 void isl_vertex_free(__isl_take isl_vertex *vertex);
3285 C<isl_vertex_get_expr> returns a singleton parametric set describing
3286 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3288 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3289 B<rational> basic sets, so they should mainly be used for inspection
3290 and should not be mixed with integer sets.
3292 Chambers can be inspected and destroyed using the following functions.
3294 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3295 __isl_give isl_basic_set *isl_cell_get_domain(
3296 __isl_keep isl_cell *cell);
3297 void isl_cell_free(__isl_take isl_cell *cell);
3301 Although C<isl> is mainly meant to be used as a library,
3302 it also contains some basic applications that use some
3303 of the functionality of C<isl>.
3304 The input may be specified in either the L<isl format>
3305 or the L<PolyLib format>.
3307 =head2 C<isl_polyhedron_sample>
3309 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3310 an integer element of the polyhedron, if there is any.
3311 The first column in the output is the denominator and is always
3312 equal to 1. If the polyhedron contains no integer points,
3313 then a vector of length zero is printed.
3317 C<isl_pip> takes the same input as the C<example> program
3318 from the C<piplib> distribution, i.e., a set of constraints
3319 on the parameters, a line containing only -1 and finally a set
3320 of constraints on a parametric polyhedron.
3321 The coefficients of the parameters appear in the last columns
3322 (but before the final constant column).
3323 The output is the lexicographic minimum of the parametric polyhedron.
3324 As C<isl> currently does not have its own output format, the output
3325 is just a dump of the internal state.
3327 =head2 C<isl_polyhedron_minimize>
3329 C<isl_polyhedron_minimize> computes the minimum of some linear
3330 or affine objective function over the integer points in a polyhedron.
3331 If an affine objective function
3332 is given, then the constant should appear in the last column.
3334 =head2 C<isl_polytope_scan>
3336 Given a polytope, C<isl_polytope_scan> prints
3337 all integer points in the polytope.