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(
1839 __isl_take isl_set *set1,
1840 __isl_take isl_set *set2);
1841 __isl_give isl_union_set *isl_union_set_intersect(
1842 __isl_take isl_union_set *uset1,
1843 __isl_take isl_union_set *uset2);
1844 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1845 __isl_take isl_basic_map *bmap,
1846 __isl_take isl_basic_set *bset);
1847 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1848 __isl_take isl_basic_map *bmap,
1849 __isl_take isl_basic_set *bset);
1850 __isl_give isl_basic_map *isl_basic_map_intersect(
1851 __isl_take isl_basic_map *bmap1,
1852 __isl_take isl_basic_map *bmap2);
1853 __isl_give isl_map *isl_map_intersect_domain(
1854 __isl_take isl_map *map,
1855 __isl_take isl_set *set);
1856 __isl_give isl_map *isl_map_intersect_range(
1857 __isl_take isl_map *map,
1858 __isl_take isl_set *set);
1859 __isl_give isl_map *isl_map_intersect(
1860 __isl_take isl_map *map1,
1861 __isl_take isl_map *map2);
1862 __isl_give isl_union_map *isl_union_map_intersect_domain(
1863 __isl_take isl_union_map *umap,
1864 __isl_take isl_union_set *uset);
1865 __isl_give isl_union_map *isl_union_map_intersect_range(
1866 __isl_take isl_union_map *umap,
1867 __isl_take isl_union_set *uset);
1868 __isl_give isl_union_map *isl_union_map_intersect(
1869 __isl_take isl_union_map *umap1,
1870 __isl_take isl_union_map *umap2);
1874 __isl_give isl_set *isl_basic_set_union(
1875 __isl_take isl_basic_set *bset1,
1876 __isl_take isl_basic_set *bset2);
1877 __isl_give isl_map *isl_basic_map_union(
1878 __isl_take isl_basic_map *bmap1,
1879 __isl_take isl_basic_map *bmap2);
1880 __isl_give isl_set *isl_set_union(
1881 __isl_take isl_set *set1,
1882 __isl_take isl_set *set2);
1883 __isl_give isl_map *isl_map_union(
1884 __isl_take isl_map *map1,
1885 __isl_take isl_map *map2);
1886 __isl_give isl_union_set *isl_union_set_union(
1887 __isl_take isl_union_set *uset1,
1888 __isl_take isl_union_set *uset2);
1889 __isl_give isl_union_map *isl_union_map_union(
1890 __isl_take isl_union_map *umap1,
1891 __isl_take isl_union_map *umap2);
1893 =item * Set difference
1895 __isl_give isl_set *isl_set_subtract(
1896 __isl_take isl_set *set1,
1897 __isl_take isl_set *set2);
1898 __isl_give isl_map *isl_map_subtract(
1899 __isl_take isl_map *map1,
1900 __isl_take isl_map *map2);
1901 __isl_give isl_union_set *isl_union_set_subtract(
1902 __isl_take isl_union_set *uset1,
1903 __isl_take isl_union_set *uset2);
1904 __isl_give isl_union_map *isl_union_map_subtract(
1905 __isl_take isl_union_map *umap1,
1906 __isl_take isl_union_map *umap2);
1910 __isl_give isl_basic_set *isl_basic_set_apply(
1911 __isl_take isl_basic_set *bset,
1912 __isl_take isl_basic_map *bmap);
1913 __isl_give isl_set *isl_set_apply(
1914 __isl_take isl_set *set,
1915 __isl_take isl_map *map);
1916 __isl_give isl_union_set *isl_union_set_apply(
1917 __isl_take isl_union_set *uset,
1918 __isl_take isl_union_map *umap);
1919 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1920 __isl_take isl_basic_map *bmap1,
1921 __isl_take isl_basic_map *bmap2);
1922 __isl_give isl_basic_map *isl_basic_map_apply_range(
1923 __isl_take isl_basic_map *bmap1,
1924 __isl_take isl_basic_map *bmap2);
1925 __isl_give isl_map *isl_map_apply_domain(
1926 __isl_take isl_map *map1,
1927 __isl_take isl_map *map2);
1928 __isl_give isl_union_map *isl_union_map_apply_domain(
1929 __isl_take isl_union_map *umap1,
1930 __isl_take isl_union_map *umap2);
1931 __isl_give isl_map *isl_map_apply_range(
1932 __isl_take isl_map *map1,
1933 __isl_take isl_map *map2);
1934 __isl_give isl_union_map *isl_union_map_apply_range(
1935 __isl_take isl_union_map *umap1,
1936 __isl_take isl_union_map *umap2);
1938 =item * Cartesian Product
1940 __isl_give isl_set *isl_set_product(
1941 __isl_take isl_set *set1,
1942 __isl_take isl_set *set2);
1943 __isl_give isl_union_set *isl_union_set_product(
1944 __isl_take isl_union_set *uset1,
1945 __isl_take isl_union_set *uset2);
1946 __isl_give isl_basic_map *isl_basic_map_range_product(
1947 __isl_take isl_basic_map *bmap1,
1948 __isl_take isl_basic_map *bmap2);
1949 __isl_give isl_map *isl_map_range_product(
1950 __isl_take isl_map *map1,
1951 __isl_take isl_map *map2);
1952 __isl_give isl_union_map *isl_union_map_range_product(
1953 __isl_take isl_union_map *umap1,
1954 __isl_take isl_union_map *umap2);
1955 __isl_give isl_map *isl_map_product(
1956 __isl_take isl_map *map1,
1957 __isl_take isl_map *map2);
1958 __isl_give isl_union_map *isl_union_map_product(
1959 __isl_take isl_union_map *umap1,
1960 __isl_take isl_union_map *umap2);
1962 The above functions compute the cross product of the given
1963 sets or relations. The domains and ranges of the results
1964 are wrapped maps between domains and ranges of the inputs.
1965 To obtain a ``flat'' product, use the following functions
1968 __isl_give isl_basic_set *isl_basic_set_flat_product(
1969 __isl_take isl_basic_set *bset1,
1970 __isl_take isl_basic_set *bset2);
1971 __isl_give isl_set *isl_set_flat_product(
1972 __isl_take isl_set *set1,
1973 __isl_take isl_set *set2);
1974 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1975 __isl_take isl_basic_map *bmap1,
1976 __isl_take isl_basic_map *bmap2);
1977 __isl_give isl_map *isl_map_flat_range_product(
1978 __isl_take isl_map *map1,
1979 __isl_take isl_map *map2);
1980 __isl_give isl_union_map *isl_union_map_flat_range_product(
1981 __isl_take isl_union_map *umap1,
1982 __isl_take isl_union_map *umap2);
1983 __isl_give isl_basic_map *isl_basic_map_flat_product(
1984 __isl_take isl_basic_map *bmap1,
1985 __isl_take isl_basic_map *bmap2);
1986 __isl_give isl_map *isl_map_flat_product(
1987 __isl_take isl_map *map1,
1988 __isl_take isl_map *map2);
1990 =item * Simplification
1992 __isl_give isl_basic_set *isl_basic_set_gist(
1993 __isl_take isl_basic_set *bset,
1994 __isl_take isl_basic_set *context);
1995 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1996 __isl_take isl_set *context);
1997 __isl_give isl_union_set *isl_union_set_gist(
1998 __isl_take isl_union_set *uset,
1999 __isl_take isl_union_set *context);
2000 __isl_give isl_basic_map *isl_basic_map_gist(
2001 __isl_take isl_basic_map *bmap,
2002 __isl_take isl_basic_map *context);
2003 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2004 __isl_take isl_map *context);
2005 __isl_give isl_union_map *isl_union_map_gist(
2006 __isl_take isl_union_map *umap,
2007 __isl_take isl_union_map *context);
2009 The gist operation returns a set or relation that has the
2010 same intersection with the context as the input set or relation.
2011 Any implicit equality in the intersection is made explicit in the result,
2012 while all inequalities that are redundant with respect to the intersection
2014 In case of union sets and relations, the gist operation is performed
2019 =head3 Lexicographic Optimization
2021 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2022 the following functions
2023 compute a set that contains the lexicographic minimum or maximum
2024 of the elements in C<set> (or C<bset>) for those values of the parameters
2025 that satisfy C<dom>.
2026 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2027 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2029 In other words, the union of the parameter values
2030 for which the result is non-empty and of C<*empty>
2033 __isl_give isl_set *isl_basic_set_partial_lexmin(
2034 __isl_take isl_basic_set *bset,
2035 __isl_take isl_basic_set *dom,
2036 __isl_give isl_set **empty);
2037 __isl_give isl_set *isl_basic_set_partial_lexmax(
2038 __isl_take isl_basic_set *bset,
2039 __isl_take isl_basic_set *dom,
2040 __isl_give isl_set **empty);
2041 __isl_give isl_set *isl_set_partial_lexmin(
2042 __isl_take isl_set *set, __isl_take isl_set *dom,
2043 __isl_give isl_set **empty);
2044 __isl_give isl_set *isl_set_partial_lexmax(
2045 __isl_take isl_set *set, __isl_take isl_set *dom,
2046 __isl_give isl_set **empty);
2048 Given a (basic) set C<set> (or C<bset>), the following functions simply
2049 return a set containing the lexicographic minimum or maximum
2050 of the elements in C<set> (or C<bset>).
2051 In case of union sets, the optimum is computed per space.
2053 __isl_give isl_set *isl_basic_set_lexmin(
2054 __isl_take isl_basic_set *bset);
2055 __isl_give isl_set *isl_basic_set_lexmax(
2056 __isl_take isl_basic_set *bset);
2057 __isl_give isl_set *isl_set_lexmin(
2058 __isl_take isl_set *set);
2059 __isl_give isl_set *isl_set_lexmax(
2060 __isl_take isl_set *set);
2061 __isl_give isl_union_set *isl_union_set_lexmin(
2062 __isl_take isl_union_set *uset);
2063 __isl_give isl_union_set *isl_union_set_lexmax(
2064 __isl_take isl_union_set *uset);
2066 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2067 the following functions
2068 compute a relation that maps each element of C<dom>
2069 to the single lexicographic minimum or maximum
2070 of the elements that are associated to that same
2071 element in C<map> (or C<bmap>).
2072 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2073 that contains the elements in C<dom> that do not map
2074 to any elements in C<map> (or C<bmap>).
2075 In other words, the union of the domain of the result and of C<*empty>
2078 __isl_give isl_map *isl_basic_map_partial_lexmax(
2079 __isl_take isl_basic_map *bmap,
2080 __isl_take isl_basic_set *dom,
2081 __isl_give isl_set **empty);
2082 __isl_give isl_map *isl_basic_map_partial_lexmin(
2083 __isl_take isl_basic_map *bmap,
2084 __isl_take isl_basic_set *dom,
2085 __isl_give isl_set **empty);
2086 __isl_give isl_map *isl_map_partial_lexmax(
2087 __isl_take isl_map *map, __isl_take isl_set *dom,
2088 __isl_give isl_set **empty);
2089 __isl_give isl_map *isl_map_partial_lexmin(
2090 __isl_take isl_map *map, __isl_take isl_set *dom,
2091 __isl_give isl_set **empty);
2093 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2094 return a map mapping each element in the domain of
2095 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2096 of all elements associated to that element.
2097 In case of union relations, the optimum is computed per space.
2099 __isl_give isl_map *isl_basic_map_lexmin(
2100 __isl_take isl_basic_map *bmap);
2101 __isl_give isl_map *isl_basic_map_lexmax(
2102 __isl_take isl_basic_map *bmap);
2103 __isl_give isl_map *isl_map_lexmin(
2104 __isl_take isl_map *map);
2105 __isl_give isl_map *isl_map_lexmax(
2106 __isl_take isl_map *map);
2107 __isl_give isl_union_map *isl_union_map_lexmin(
2108 __isl_take isl_union_map *umap);
2109 __isl_give isl_union_map *isl_union_map_lexmax(
2110 __isl_take isl_union_map *umap);
2114 Lists are defined over several element types, including
2115 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2116 Here we take lists of C<isl_set>s as an example.
2117 Lists can be created, copied and freed using the following functions.
2119 #include <isl/list.h>
2120 __isl_give isl_set_list *isl_set_list_alloc(
2121 isl_ctx *ctx, int n);
2122 __isl_give isl_set_list *isl_set_list_copy(
2123 __isl_keep isl_set_list *list);
2124 __isl_give isl_set_list *isl_set_list_add(
2125 __isl_take isl_set_list *list,
2126 __isl_take isl_set *el);
2127 void isl_set_list_free(__isl_take isl_set_list *list);
2129 C<isl_set_list_alloc> creates an empty list with a capacity for
2132 Lists can be inspected using the following functions.
2134 #include <isl/list.h>
2135 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2136 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2137 __isl_give struct isl_set *isl_set_list_get_set(
2138 __isl_keep isl_set_list *list, int index);
2139 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2140 int (*fn)(__isl_take struct isl_set *el, void *user),
2143 Lists can be printed using
2145 #include <isl/list.h>
2146 __isl_give isl_printer *isl_printer_print_set_list(
2147 __isl_take isl_printer *p,
2148 __isl_keep isl_set_list *list);
2152 Matrices can be created, copied and freed using the following functions.
2154 #include <isl/mat.h>
2155 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2156 unsigned n_row, unsigned n_col);
2157 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2158 void isl_mat_free(__isl_take isl_mat *mat);
2160 Note that the elements of a newly created matrix may have arbitrary values.
2161 The elements can be changed and inspected using the following functions.
2163 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2164 int isl_mat_rows(__isl_keep isl_mat *mat);
2165 int isl_mat_cols(__isl_keep isl_mat *mat);
2166 int isl_mat_get_element(__isl_keep isl_mat *mat,
2167 int row, int col, isl_int *v);
2168 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2169 int row, int col, isl_int v);
2170 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2171 int row, int col, int v);
2173 C<isl_mat_get_element> will return a negative value if anything went wrong.
2174 In that case, the value of C<*v> is undefined.
2176 The following function can be used to compute the (right) inverse
2177 of a matrix, i.e., a matrix such that the product of the original
2178 and the inverse (in that order) is a multiple of the identity matrix.
2179 The input matrix is assumed to be of full row-rank.
2181 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2183 The following function can be used to compute the (right) kernel
2184 (or null space) of a matrix, i.e., a matrix such that the product of
2185 the original and the kernel (in that order) is the zero matrix.
2187 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2189 =head2 Piecewise Quasi Affine Expressions
2191 The zero quasi affine expression can be created using
2193 __isl_give isl_aff *isl_aff_zero(
2194 __isl_take isl_local_space *ls);
2196 A quasi affine expression can also be initialized from an C<isl_div>:
2198 #include <isl/div.h>
2199 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2201 An empty piecewise quasi affine expression (one with no cells)
2202 or a piecewise quasi affine expression with a single cell can
2203 be created using the following functions.
2205 #include <isl/aff.h>
2206 __isl_give isl_pw_aff *isl_pw_aff_empty(
2207 __isl_take isl_dim *dim);
2208 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2209 __isl_take isl_set *set, __isl_take isl_aff *aff);
2211 Quasi affine expressions can be copied and free using
2213 #include <isl/aff.h>
2214 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2215 void *isl_aff_free(__isl_take isl_aff *aff);
2217 __isl_give isl_pw_aff *isl_pw_aff_copy(
2218 __isl_keep isl_pw_aff *pwaff);
2219 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2221 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2222 using the following function. The constraint is required to have
2223 a non-zero coefficient for the specified dimension.
2225 #include <isl/constraint.h>
2226 __isl_give isl_aff *isl_constraint_get_bound(
2227 __isl_keep isl_constraint *constraint,
2228 enum isl_dim_type type, int pos);
2230 The entire affine expression of the constraint can also be extracted
2231 using the following function.
2233 #include <isl/constraint.h>
2234 __isl_give isl_aff *isl_constraint_get_aff(
2235 __isl_keep isl_constraint *constraint);
2237 Conversely, an equality constraint equating
2238 the affine expression to zero or an inequality constraint enforcing
2239 the affine expression to be non-negative, can be constructed using
2241 __isl_give isl_constraint *isl_equality_from_aff(
2242 __isl_take isl_aff *aff);
2243 __isl_give isl_constraint *isl_inequality_from_aff(
2244 __isl_take isl_aff *aff);
2246 The expression can be inspected using
2248 #include <isl/aff.h>
2249 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2250 int isl_aff_dim(__isl_keep isl_aff *aff,
2251 enum isl_dim_type type);
2252 __isl_give isl_local_space *isl_aff_get_local_space(
2253 __isl_keep isl_aff *aff);
2254 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2255 enum isl_dim_type type, unsigned pos);
2256 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2258 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2259 enum isl_dim_type type, int pos, isl_int *v);
2260 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2262 __isl_give isl_div *isl_aff_get_div(
2263 __isl_keep isl_aff *aff, int pos);
2265 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2266 enum isl_dim_type type, unsigned first, unsigned n);
2267 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2268 enum isl_dim_type type, unsigned first, unsigned n);
2270 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2271 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2272 enum isl_dim_type type);
2273 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2275 It can be modified using
2277 #include <isl/aff.h>
2278 __isl_give isl_aff *isl_aff_set_dim_name(
2279 __isl_take isl_aff *aff, enum isl_dim_type type,
2280 unsigned pos, const char *s);
2281 __isl_give isl_aff *isl_aff_set_constant(
2282 __isl_take isl_aff *aff, isl_int v);
2283 __isl_give isl_aff *isl_aff_set_constant_si(
2284 __isl_take isl_aff *aff, int v);
2285 __isl_give isl_aff *isl_aff_set_coefficient(
2286 __isl_take isl_aff *aff,
2287 enum isl_dim_type type, int pos, isl_int v);
2288 __isl_give isl_aff *isl_aff_set_coefficient_si(
2289 __isl_take isl_aff *aff,
2290 enum isl_dim_type type, int pos, int v);
2291 __isl_give isl_aff *isl_aff_set_denominator(
2292 __isl_take isl_aff *aff, isl_int v);
2294 __isl_give isl_aff *isl_aff_add_constant(
2295 __isl_take isl_aff *aff, isl_int v);
2296 __isl_give isl_aff *isl_aff_add_constant_si(
2297 __isl_take isl_aff *aff, int v);
2298 __isl_give isl_aff *isl_aff_add_coefficient(
2299 __isl_take isl_aff *aff,
2300 enum isl_dim_type type, int pos, isl_int v);
2301 __isl_give isl_aff *isl_aff_add_coefficient_si(
2302 __isl_take isl_aff *aff,
2303 enum isl_dim_type type, int pos, int v);
2305 __isl_give isl_aff *isl_aff_insert_dims(
2306 __isl_take isl_aff *aff,
2307 enum isl_dim_type type, unsigned first, unsigned n);
2308 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2309 __isl_take isl_pw_aff *pwaff,
2310 enum isl_dim_type type, unsigned first, unsigned n);
2311 __isl_give isl_aff *isl_aff_add_dims(
2312 __isl_take isl_aff *aff,
2313 enum isl_dim_type type, unsigned n);
2314 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2315 __isl_take isl_pw_aff *pwaff,
2316 enum isl_dim_type type, unsigned n);
2317 __isl_give isl_aff *isl_aff_drop_dims(
2318 __isl_take isl_aff *aff,
2319 enum isl_dim_type type, unsigned first, unsigned n);
2320 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2321 __isl_take isl_pw_aff *pwaff,
2322 enum isl_dim_type type, unsigned first, unsigned n);
2324 Note that the C<set_constant> and C<set_coefficient> functions
2325 set the I<numerator> of the constant or coefficient, while
2326 C<add_constant> and C<add_coefficient> add an integer value to
2327 the possibly rational constant or coefficient.
2329 To check whether an affine expressions is obviously zero
2330 or obviously equal to some other affine expression, use
2332 #include <isl/aff.h>
2333 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2334 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2335 __isl_keep isl_aff *aff2);
2339 #include <isl/aff.h>
2340 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2341 __isl_take isl_aff *aff2);
2342 __isl_give isl_pw_aff *isl_pw_aff_add(
2343 __isl_take isl_pw_aff *pwaff1,
2344 __isl_take isl_pw_aff *pwaff2);
2345 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2346 __isl_take isl_aff *aff2);
2347 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2348 __isl_give isl_pw_aff *isl_pw_aff_neg(
2349 __isl_take isl_pw_aff *pwaff);
2350 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2351 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2352 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2354 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2356 __isl_give isl_aff *isl_aff_scale_down_ui(
2357 __isl_take isl_aff *aff, unsigned f);
2359 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2360 __isl_take isl_pw_aff *pwqp);
2362 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2363 __isl_take isl_set *context);
2364 __isl_give isl_pw_aff *isl_pw_aff_gist(
2365 __isl_take isl_pw_aff *pwaff,
2366 __isl_take isl_set *context);
2368 __isl_give isl_set *isl_pw_aff_domain(
2369 __isl_take isl_pw_aff *pwaff);
2371 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2372 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2373 __isl_give isl_set *isl_pw_aff_ge_set(
2374 __isl_take isl_pw_aff *pwaff1,
2375 __isl_take isl_pw_aff *pwaff2);
2377 The function C<isl_aff_ge_basic_set> returns a basic set
2378 containing those elements in the shared space
2379 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2380 The function C<isl_aff_ge_set> returns a set
2381 containing those elements in the shared domain
2382 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2384 #include <isl/aff.h>
2385 __isl_give isl_pw_aff *isl_pw_aff_max(
2386 __isl_take isl_pw_aff *pwaff1,
2387 __isl_take isl_pw_aff *pwaff2);
2389 The function C<isl_pw_aff_max> computes a piecewise quasi-affine
2390 expression with a domain that is the union of those of C<pwaff1> and
2391 C<pwaff2> and such that on each cell, the quasi-affine expression is
2392 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2393 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2394 associated expression is the defined one.
2396 An expression can be printed using
2398 #include <isl/aff.h>
2399 __isl_give isl_printer *isl_printer_print_aff(
2400 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2402 __isl_give isl_printer *isl_printer_print_pw_aff(
2403 __isl_take isl_printer *p,
2404 __isl_keep isl_pw_aff *pwaff);
2408 Points are elements of a set. They can be used to construct
2409 simple sets (boxes) or they can be used to represent the
2410 individual elements of a set.
2411 The zero point (the origin) can be created using
2413 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2415 The coordinates of a point can be inspected, set and changed
2418 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2419 enum isl_dim_type type, int pos, isl_int *v);
2420 __isl_give isl_point *isl_point_set_coordinate(
2421 __isl_take isl_point *pnt,
2422 enum isl_dim_type type, int pos, isl_int v);
2424 __isl_give isl_point *isl_point_add_ui(
2425 __isl_take isl_point *pnt,
2426 enum isl_dim_type type, int pos, unsigned val);
2427 __isl_give isl_point *isl_point_sub_ui(
2428 __isl_take isl_point *pnt,
2429 enum isl_dim_type type, int pos, unsigned val);
2431 Other properties can be obtained using
2433 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2435 Points can be copied or freed using
2437 __isl_give isl_point *isl_point_copy(
2438 __isl_keep isl_point *pnt);
2439 void isl_point_free(__isl_take isl_point *pnt);
2441 A singleton set can be created from a point using
2443 __isl_give isl_basic_set *isl_basic_set_from_point(
2444 __isl_take isl_point *pnt);
2445 __isl_give isl_set *isl_set_from_point(
2446 __isl_take isl_point *pnt);
2448 and a box can be created from two opposite extremal points using
2450 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2451 __isl_take isl_point *pnt1,
2452 __isl_take isl_point *pnt2);
2453 __isl_give isl_set *isl_set_box_from_points(
2454 __isl_take isl_point *pnt1,
2455 __isl_take isl_point *pnt2);
2457 All elements of a B<bounded> (union) set can be enumerated using
2458 the following functions.
2460 int isl_set_foreach_point(__isl_keep isl_set *set,
2461 int (*fn)(__isl_take isl_point *pnt, void *user),
2463 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2464 int (*fn)(__isl_take isl_point *pnt, void *user),
2467 The function C<fn> is called for each integer point in
2468 C<set> with as second argument the last argument of
2469 the C<isl_set_foreach_point> call. The function C<fn>
2470 should return C<0> on success and C<-1> on failure.
2471 In the latter case, C<isl_set_foreach_point> will stop
2472 enumerating and return C<-1> as well.
2473 If the enumeration is performed successfully and to completion,
2474 then C<isl_set_foreach_point> returns C<0>.
2476 To obtain a single point of a (basic) set, use
2478 __isl_give isl_point *isl_basic_set_sample_point(
2479 __isl_take isl_basic_set *bset);
2480 __isl_give isl_point *isl_set_sample_point(
2481 __isl_take isl_set *set);
2483 If C<set> does not contain any (integer) points, then the
2484 resulting point will be ``void'', a property that can be
2487 int isl_point_is_void(__isl_keep isl_point *pnt);
2489 =head2 Piecewise Quasipolynomials
2491 A piecewise quasipolynomial is a particular kind of function that maps
2492 a parametric point to a rational value.
2493 More specifically, a quasipolynomial is a polynomial expression in greatest
2494 integer parts of affine expressions of parameters and variables.
2495 A piecewise quasipolynomial is a subdivision of a given parametric
2496 domain into disjoint cells with a quasipolynomial associated to
2497 each cell. The value of the piecewise quasipolynomial at a given
2498 point is the value of the quasipolynomial associated to the cell
2499 that contains the point. Outside of the union of cells,
2500 the value is assumed to be zero.
2501 For example, the piecewise quasipolynomial
2503 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2505 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2506 A given piecewise quasipolynomial has a fixed domain dimension.
2507 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2508 defined over different domains.
2509 Piecewise quasipolynomials are mainly used by the C<barvinok>
2510 library for representing the number of elements in a parametric set or map.
2511 For example, the piecewise quasipolynomial above represents
2512 the number of points in the map
2514 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2516 =head3 Printing (Piecewise) Quasipolynomials
2518 Quasipolynomials and piecewise quasipolynomials can be printed
2519 using the following functions.
2521 __isl_give isl_printer *isl_printer_print_qpolynomial(
2522 __isl_take isl_printer *p,
2523 __isl_keep isl_qpolynomial *qp);
2525 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2526 __isl_take isl_printer *p,
2527 __isl_keep isl_pw_qpolynomial *pwqp);
2529 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2530 __isl_take isl_printer *p,
2531 __isl_keep isl_union_pw_qpolynomial *upwqp);
2533 The output format of the printer
2534 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2535 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2537 In case of printing in C<ISL_FORMAT_C>, the user may want
2538 to set the names of all dimensions
2540 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2541 __isl_take isl_qpolynomial *qp,
2542 enum isl_dim_type type, unsigned pos,
2544 __isl_give isl_pw_qpolynomial *
2545 isl_pw_qpolynomial_set_dim_name(
2546 __isl_take isl_pw_qpolynomial *pwqp,
2547 enum isl_dim_type type, unsigned pos,
2550 =head3 Creating New (Piecewise) Quasipolynomials
2552 Some simple quasipolynomials can be created using the following functions.
2553 More complicated quasipolynomials can be created by applying
2554 operations such as addition and multiplication
2555 on the resulting quasipolynomials
2557 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2558 __isl_take isl_dim *dim);
2559 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2560 __isl_take isl_dim *dim);
2561 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2562 __isl_take isl_dim *dim);
2563 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2564 __isl_take isl_dim *dim);
2565 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2566 __isl_take isl_dim *dim);
2567 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2568 __isl_take isl_dim *dim,
2569 const isl_int n, const isl_int d);
2570 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2571 __isl_take isl_div *div);
2572 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2573 __isl_take isl_dim *dim,
2574 enum isl_dim_type type, unsigned pos);
2575 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2576 __isl_take isl_aff *aff);
2578 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2579 with a single cell can be created using the following functions.
2580 Multiple of these single cell piecewise quasipolynomials can
2581 be combined to create more complicated piecewise quasipolynomials.
2583 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2584 __isl_take isl_dim *dim);
2585 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2586 __isl_take isl_set *set,
2587 __isl_take isl_qpolynomial *qp);
2589 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2590 __isl_take isl_dim *dim);
2591 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2592 __isl_take isl_pw_qpolynomial *pwqp);
2593 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2594 __isl_take isl_union_pw_qpolynomial *upwqp,
2595 __isl_take isl_pw_qpolynomial *pwqp);
2597 Quasipolynomials can be copied and freed again using the following
2600 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2601 __isl_keep isl_qpolynomial *qp);
2602 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2604 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2605 __isl_keep isl_pw_qpolynomial *pwqp);
2606 void *isl_pw_qpolynomial_free(
2607 __isl_take isl_pw_qpolynomial *pwqp);
2609 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2610 __isl_keep isl_union_pw_qpolynomial *upwqp);
2611 void isl_union_pw_qpolynomial_free(
2612 __isl_take isl_union_pw_qpolynomial *upwqp);
2614 =head3 Inspecting (Piecewise) Quasipolynomials
2616 To iterate over all piecewise quasipolynomials in a union
2617 piecewise quasipolynomial, use the following function
2619 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2620 __isl_keep isl_union_pw_qpolynomial *upwqp,
2621 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2624 To extract the piecewise quasipolynomial from a union with a given dimension
2627 __isl_give isl_pw_qpolynomial *
2628 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2629 __isl_keep isl_union_pw_qpolynomial *upwqp,
2630 __isl_take isl_dim *dim);
2632 To iterate over the cells in a piecewise quasipolynomial,
2633 use either of the following two functions
2635 int isl_pw_qpolynomial_foreach_piece(
2636 __isl_keep isl_pw_qpolynomial *pwqp,
2637 int (*fn)(__isl_take isl_set *set,
2638 __isl_take isl_qpolynomial *qp,
2639 void *user), void *user);
2640 int isl_pw_qpolynomial_foreach_lifted_piece(
2641 __isl_keep isl_pw_qpolynomial *pwqp,
2642 int (*fn)(__isl_take isl_set *set,
2643 __isl_take isl_qpolynomial *qp,
2644 void *user), void *user);
2646 As usual, the function C<fn> should return C<0> on success
2647 and C<-1> on failure. The difference between
2648 C<isl_pw_qpolynomial_foreach_piece> and
2649 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2650 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2651 compute unique representations for all existentially quantified
2652 variables and then turn these existentially quantified variables
2653 into extra set variables, adapting the associated quasipolynomial
2654 accordingly. This means that the C<set> passed to C<fn>
2655 will not have any existentially quantified variables, but that
2656 the dimensions of the sets may be different for different
2657 invocations of C<fn>.
2659 To iterate over all terms in a quasipolynomial,
2662 int isl_qpolynomial_foreach_term(
2663 __isl_keep isl_qpolynomial *qp,
2664 int (*fn)(__isl_take isl_term *term,
2665 void *user), void *user);
2667 The terms themselves can be inspected and freed using
2670 unsigned isl_term_dim(__isl_keep isl_term *term,
2671 enum isl_dim_type type);
2672 void isl_term_get_num(__isl_keep isl_term *term,
2674 void isl_term_get_den(__isl_keep isl_term *term,
2676 int isl_term_get_exp(__isl_keep isl_term *term,
2677 enum isl_dim_type type, unsigned pos);
2678 __isl_give isl_div *isl_term_get_div(
2679 __isl_keep isl_term *term, unsigned pos);
2680 void isl_term_free(__isl_take isl_term *term);
2682 Each term is a product of parameters, set variables and
2683 integer divisions. The function C<isl_term_get_exp>
2684 returns the exponent of a given dimensions in the given term.
2685 The C<isl_int>s in the arguments of C<isl_term_get_num>
2686 and C<isl_term_get_den> need to have been initialized
2687 using C<isl_int_init> before calling these functions.
2689 =head3 Properties of (Piecewise) Quasipolynomials
2691 To check whether a quasipolynomial is actually a constant,
2692 use the following function.
2694 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2695 isl_int *n, isl_int *d);
2697 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2698 then the numerator and denominator of the constant
2699 are returned in C<*n> and C<*d>, respectively.
2701 =head3 Operations on (Piecewise) Quasipolynomials
2703 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2704 __isl_take isl_qpolynomial *qp, isl_int v);
2705 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2706 __isl_take isl_qpolynomial *qp);
2707 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2708 __isl_take isl_qpolynomial *qp1,
2709 __isl_take isl_qpolynomial *qp2);
2710 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2711 __isl_take isl_qpolynomial *qp1,
2712 __isl_take isl_qpolynomial *qp2);
2713 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2714 __isl_take isl_qpolynomial *qp1,
2715 __isl_take isl_qpolynomial *qp2);
2716 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2717 __isl_take isl_qpolynomial *qp, unsigned exponent);
2719 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2720 __isl_take isl_pw_qpolynomial *pwqp1,
2721 __isl_take isl_pw_qpolynomial *pwqp2);
2722 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2723 __isl_take isl_pw_qpolynomial *pwqp1,
2724 __isl_take isl_pw_qpolynomial *pwqp2);
2725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2726 __isl_take isl_pw_qpolynomial *pwqp1,
2727 __isl_take isl_pw_qpolynomial *pwqp2);
2728 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2729 __isl_take isl_pw_qpolynomial *pwqp);
2730 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2731 __isl_take isl_pw_qpolynomial *pwqp1,
2732 __isl_take isl_pw_qpolynomial *pwqp2);
2734 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2735 __isl_take isl_union_pw_qpolynomial *upwqp1,
2736 __isl_take isl_union_pw_qpolynomial *upwqp2);
2737 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2738 __isl_take isl_union_pw_qpolynomial *upwqp1,
2739 __isl_take isl_union_pw_qpolynomial *upwqp2);
2740 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2741 __isl_take isl_union_pw_qpolynomial *upwqp1,
2742 __isl_take isl_union_pw_qpolynomial *upwqp2);
2744 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2745 __isl_take isl_pw_qpolynomial *pwqp,
2746 __isl_take isl_point *pnt);
2748 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2749 __isl_take isl_union_pw_qpolynomial *upwqp,
2750 __isl_take isl_point *pnt);
2752 __isl_give isl_set *isl_pw_qpolynomial_domain(
2753 __isl_take isl_pw_qpolynomial *pwqp);
2754 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2755 __isl_take isl_pw_qpolynomial *pwpq,
2756 __isl_take isl_set *set);
2758 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2759 __isl_take isl_union_pw_qpolynomial *upwqp);
2760 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2761 __isl_take isl_union_pw_qpolynomial *upwpq,
2762 __isl_take isl_union_set *uset);
2764 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2765 __isl_take isl_qpolynomial *qp,
2766 __isl_take isl_dim *model);
2768 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2769 __isl_take isl_union_pw_qpolynomial *upwqp);
2771 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2772 __isl_take isl_qpolynomial *qp,
2773 __isl_take isl_set *context);
2775 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2776 __isl_take isl_pw_qpolynomial *pwqp,
2777 __isl_take isl_set *context);
2779 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2780 __isl_take isl_union_pw_qpolynomial *upwqp,
2781 __isl_take isl_union_set *context);
2783 The gist operation applies the gist operation to each of
2784 the cells in the domain of the input piecewise quasipolynomial.
2785 The context is also exploited
2786 to simplify the quasipolynomials associated to each cell.
2788 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2789 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2790 __isl_give isl_union_pw_qpolynomial *
2791 isl_union_pw_qpolynomial_to_polynomial(
2792 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2794 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2795 the polynomial will be an overapproximation. If C<sign> is negative,
2796 it will be an underapproximation. If C<sign> is zero, the approximation
2797 will lie somewhere in between.
2799 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2801 A piecewise quasipolynomial reduction is a piecewise
2802 reduction (or fold) of quasipolynomials.
2803 In particular, the reduction can be maximum or a minimum.
2804 The objects are mainly used to represent the result of
2805 an upper or lower bound on a quasipolynomial over its domain,
2806 i.e., as the result of the following function.
2808 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2809 __isl_take isl_pw_qpolynomial *pwqp,
2810 enum isl_fold type, int *tight);
2812 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2813 __isl_take isl_union_pw_qpolynomial *upwqp,
2814 enum isl_fold type, int *tight);
2816 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2817 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2818 is the returned bound is known be tight, i.e., for each value
2819 of the parameters there is at least
2820 one element in the domain that reaches the bound.
2821 If the domain of C<pwqp> is not wrapping, then the bound is computed
2822 over all elements in that domain and the result has a purely parametric
2823 domain. If the domain of C<pwqp> is wrapping, then the bound is
2824 computed over the range of the wrapped relation. The domain of the
2825 wrapped relation becomes the domain of the result.
2827 A (piecewise) quasipolynomial reduction can be copied or freed using the
2828 following functions.
2830 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2831 __isl_keep isl_qpolynomial_fold *fold);
2832 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2833 __isl_keep isl_pw_qpolynomial_fold *pwf);
2834 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2835 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2836 void isl_qpolynomial_fold_free(
2837 __isl_take isl_qpolynomial_fold *fold);
2838 void *isl_pw_qpolynomial_fold_free(
2839 __isl_take isl_pw_qpolynomial_fold *pwf);
2840 void isl_union_pw_qpolynomial_fold_free(
2841 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2843 =head3 Printing Piecewise Quasipolynomial Reductions
2845 Piecewise quasipolynomial reductions can be printed
2846 using the following function.
2848 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2849 __isl_take isl_printer *p,
2850 __isl_keep isl_pw_qpolynomial_fold *pwf);
2851 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2852 __isl_take isl_printer *p,
2853 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2855 For C<isl_printer_print_pw_qpolynomial_fold>,
2856 output format of the printer
2857 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2858 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2859 output format of the printer
2860 needs to be set to C<ISL_FORMAT_ISL>.
2861 In case of printing in C<ISL_FORMAT_C>, the user may want
2862 to set the names of all dimensions
2864 __isl_give isl_pw_qpolynomial_fold *
2865 isl_pw_qpolynomial_fold_set_dim_name(
2866 __isl_take isl_pw_qpolynomial_fold *pwf,
2867 enum isl_dim_type type, unsigned pos,
2870 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2872 To iterate over all piecewise quasipolynomial reductions in a union
2873 piecewise quasipolynomial reduction, use the following function
2875 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2876 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2877 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2878 void *user), void *user);
2880 To iterate over the cells in a piecewise quasipolynomial reduction,
2881 use either of the following two functions
2883 int isl_pw_qpolynomial_fold_foreach_piece(
2884 __isl_keep isl_pw_qpolynomial_fold *pwf,
2885 int (*fn)(__isl_take isl_set *set,
2886 __isl_take isl_qpolynomial_fold *fold,
2887 void *user), void *user);
2888 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2889 __isl_keep isl_pw_qpolynomial_fold *pwf,
2890 int (*fn)(__isl_take isl_set *set,
2891 __isl_take isl_qpolynomial_fold *fold,
2892 void *user), void *user);
2894 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2895 of the difference between these two functions.
2897 To iterate over all quasipolynomials in a reduction, use
2899 int isl_qpolynomial_fold_foreach_qpolynomial(
2900 __isl_keep isl_qpolynomial_fold *fold,
2901 int (*fn)(__isl_take isl_qpolynomial *qp,
2902 void *user), void *user);
2904 =head3 Operations on Piecewise Quasipolynomial Reductions
2906 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
2907 __isl_take isl_qpolynomial_fold *fold, isl_int v);
2909 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2910 __isl_take isl_pw_qpolynomial_fold *pwf1,
2911 __isl_take isl_pw_qpolynomial_fold *pwf2);
2913 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2914 __isl_take isl_pw_qpolynomial_fold *pwf1,
2915 __isl_take isl_pw_qpolynomial_fold *pwf2);
2917 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2918 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2919 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2921 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2922 __isl_take isl_pw_qpolynomial_fold *pwf,
2923 __isl_take isl_point *pnt);
2925 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2926 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2927 __isl_take isl_point *pnt);
2929 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2930 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2931 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2932 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2933 __isl_take isl_union_set *uset);
2935 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2936 __isl_take isl_pw_qpolynomial_fold *pwf);
2938 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2939 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2941 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2942 __isl_take isl_pw_qpolynomial_fold *pwf,
2943 __isl_take isl_set *context);
2945 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2946 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2947 __isl_take isl_union_set *context);
2949 The gist operation applies the gist operation to each of
2950 the cells in the domain of the input piecewise quasipolynomial reduction.
2951 In future, the operation will also exploit the context
2952 to simplify the quasipolynomial reductions associated to each cell.
2954 __isl_give isl_pw_qpolynomial_fold *
2955 isl_set_apply_pw_qpolynomial_fold(
2956 __isl_take isl_set *set,
2957 __isl_take isl_pw_qpolynomial_fold *pwf,
2959 __isl_give isl_pw_qpolynomial_fold *
2960 isl_map_apply_pw_qpolynomial_fold(
2961 __isl_take isl_map *map,
2962 __isl_take isl_pw_qpolynomial_fold *pwf,
2964 __isl_give isl_union_pw_qpolynomial_fold *
2965 isl_union_set_apply_union_pw_qpolynomial_fold(
2966 __isl_take isl_union_set *uset,
2967 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2969 __isl_give isl_union_pw_qpolynomial_fold *
2970 isl_union_map_apply_union_pw_qpolynomial_fold(
2971 __isl_take isl_union_map *umap,
2972 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2975 The functions taking a map
2976 compose the given map with the given piecewise quasipolynomial reduction.
2977 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2978 over all elements in the intersection of the range of the map
2979 and the domain of the piecewise quasipolynomial reduction
2980 as a function of an element in the domain of the map.
2981 The functions taking a set compute a bound over all elements in the
2982 intersection of the set and the domain of the
2983 piecewise quasipolynomial reduction.
2985 =head2 Dependence Analysis
2987 C<isl> contains specialized functionality for performing
2988 array dataflow analysis. That is, given a I<sink> access relation
2989 and a collection of possible I<source> access relations,
2990 C<isl> can compute relations that describe
2991 for each iteration of the sink access, which iteration
2992 of which of the source access relations was the last
2993 to access the same data element before the given iteration
2995 To compute standard flow dependences, the sink should be
2996 a read, while the sources should be writes.
2997 If any of the source accesses are marked as being I<may>
2998 accesses, then there will be a dependence to the last
2999 I<must> access B<and> to any I<may> access that follows
3000 this last I<must> access.
3001 In particular, if I<all> sources are I<may> accesses,
3002 then memory based dependence analysis is performed.
3003 If, on the other hand, all sources are I<must> accesses,
3004 then value based dependence analysis is performed.
3006 #include <isl/flow.h>
3008 typedef int (*isl_access_level_before)(void *first, void *second);
3010 __isl_give isl_access_info *isl_access_info_alloc(
3011 __isl_take isl_map *sink,
3012 void *sink_user, isl_access_level_before fn,
3014 __isl_give isl_access_info *isl_access_info_add_source(
3015 __isl_take isl_access_info *acc,
3016 __isl_take isl_map *source, int must,
3018 void isl_access_info_free(__isl_take isl_access_info *acc);
3020 __isl_give isl_flow *isl_access_info_compute_flow(
3021 __isl_take isl_access_info *acc);
3023 int isl_flow_foreach(__isl_keep isl_flow *deps,
3024 int (*fn)(__isl_take isl_map *dep, int must,
3025 void *dep_user, void *user),
3027 __isl_give isl_map *isl_flow_get_no_source(
3028 __isl_keep isl_flow *deps, int must);
3029 void isl_flow_free(__isl_take isl_flow *deps);
3031 The function C<isl_access_info_compute_flow> performs the actual
3032 dependence analysis. The other functions are used to construct
3033 the input for this function or to read off the output.
3035 The input is collected in an C<isl_access_info>, which can
3036 be created through a call to C<isl_access_info_alloc>.
3037 The arguments to this functions are the sink access relation
3038 C<sink>, a token C<sink_user> used to identify the sink
3039 access to the user, a callback function for specifying the
3040 relative order of source and sink accesses, and the number
3041 of source access relations that will be added.
3042 The callback function has type C<int (*)(void *first, void *second)>.
3043 The function is called with two user supplied tokens identifying
3044 either a source or the sink and it should return the shared nesting
3045 level and the relative order of the two accesses.
3046 In particular, let I<n> be the number of loops shared by
3047 the two accesses. If C<first> precedes C<second> textually,
3048 then the function should return I<2 * n + 1>; otherwise,
3049 it should return I<2 * n>.
3050 The sources can be added to the C<isl_access_info> by performing
3051 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3052 C<must> indicates whether the source is a I<must> access
3053 or a I<may> access. Note that a multi-valued access relation
3054 should only be marked I<must> if every iteration in the domain
3055 of the relation accesses I<all> elements in its image.
3056 The C<source_user> token is again used to identify
3057 the source access. The range of the source access relation
3058 C<source> should have the same dimension as the range
3059 of the sink access relation.
3060 The C<isl_access_info_free> function should usually not be
3061 called explicitly, because it is called implicitly by
3062 C<isl_access_info_compute_flow>.
3064 The result of the dependence analysis is collected in an
3065 C<isl_flow>. There may be elements of
3066 the sink access for which no preceding source access could be
3067 found or for which all preceding sources are I<may> accesses.
3068 The relations containing these elements can be obtained through
3069 calls to C<isl_flow_get_no_source>, the first with C<must> set
3070 and the second with C<must> unset.
3071 In the case of standard flow dependence analysis,
3072 with the sink a read and the sources I<must> writes,
3073 the first relation corresponds to the reads from uninitialized
3074 array elements and the second relation is empty.
3075 The actual flow dependences can be extracted using
3076 C<isl_flow_foreach>. This function will call the user-specified
3077 callback function C<fn> for each B<non-empty> dependence between
3078 a source and the sink. The callback function is called
3079 with four arguments, the actual flow dependence relation
3080 mapping source iterations to sink iterations, a boolean that
3081 indicates whether it is a I<must> or I<may> dependence, a token
3082 identifying the source and an additional C<void *> with value
3083 equal to the third argument of the C<isl_flow_foreach> call.
3084 A dependence is marked I<must> if it originates from a I<must>
3085 source and if it is not followed by any I<may> sources.
3087 After finishing with an C<isl_flow>, the user should call
3088 C<isl_flow_free> to free all associated memory.
3090 A higher-level interface to dependence analysis is provided
3091 by the following function.
3093 #include <isl/flow.h>
3095 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3096 __isl_take isl_union_map *must_source,
3097 __isl_take isl_union_map *may_source,
3098 __isl_take isl_union_map *schedule,
3099 __isl_give isl_union_map **must_dep,
3100 __isl_give isl_union_map **may_dep,
3101 __isl_give isl_union_map **must_no_source,
3102 __isl_give isl_union_map **may_no_source);
3104 The arrays are identified by the tuple names of the ranges
3105 of the accesses. The iteration domains by the tuple names
3106 of the domains of the accesses and of the schedule.
3107 The relative order of the iteration domains is given by the
3108 schedule. The relations returned through C<must_no_source>
3109 and C<may_no_source> are subsets of C<sink>.
3110 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3111 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3112 any of the other arguments is treated as an error.
3116 B<The functionality described in this section is fairly new
3117 and may be subject to change.>
3119 The following function can be used to compute a schedule
3120 for a union of domains. The generated schedule respects
3121 all C<validity> dependences. That is, all dependence distances
3122 over these dependences in the scheduled space are lexicographically
3123 positive. The generated schedule schedule also tries to minimize
3124 the dependence distances over C<proximity> dependences.
3125 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3126 for groups of domains where the dependence distances have only
3127 non-negative values.
3128 The algorithm used to construct the schedule is similar to that
3131 #include <isl/schedule.h>
3132 __isl_give isl_schedule *isl_union_set_compute_schedule(
3133 __isl_take isl_union_set *domain,
3134 __isl_take isl_union_map *validity,
3135 __isl_take isl_union_map *proximity);
3136 void *isl_schedule_free(__isl_take isl_schedule *sched);
3138 A mapping from the domains to the scheduled space can be obtained
3139 from an C<isl_schedule> using the following function.
3141 __isl_give isl_union_map *isl_schedule_get_map(
3142 __isl_keep isl_schedule *sched);
3144 A representation of the schedule can be printed using
3146 __isl_give isl_printer *isl_printer_print_schedule(
3147 __isl_take isl_printer *p,
3148 __isl_keep isl_schedule *schedule);
3150 A representation of the schedule as a forest of bands can be obtained
3151 using the following function.
3153 __isl_give isl_band_list *isl_schedule_get_band_forest(
3154 __isl_keep isl_schedule *schedule);
3156 The list can be manipulated as explained in L<"Lists">.
3157 The bands inside the list can be copied and freed using the following
3160 #include <isl/band.h>
3161 __isl_give isl_band *isl_band_copy(
3162 __isl_keep isl_band *band);
3163 void *isl_band_free(__isl_take isl_band *band);
3165 Each band contains zero or more scheduling dimensions.
3166 These are referred to as the members of the band.
3167 The section of the schedule that corresponds to the band is
3168 referred to as the partial schedule of the band.
3169 For those nodes that participate in a band, the outer scheduling
3170 dimensions form the prefix schedule, while the inner scheduling
3171 dimensions form the suffix schedule.
3172 That is, if we take a cut of the band forest, then the union of
3173 the concatenations of the prefix, partial and suffix schedules of
3174 each band in the cut is equal to the entire schedule (modulo
3175 some possible padding at the end with zero scheduling dimensions).
3176 The properties of a band can be inspected using the following functions.
3178 #include <isl/band.h>
3179 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3181 int isl_band_has_children(__isl_keep isl_band *band);
3182 __isl_give isl_band_list *isl_band_get_children(
3183 __isl_keep isl_band *band);
3185 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3186 __isl_keep isl_band *band);
3187 __isl_give isl_union_map *isl_band_get_partial_schedule(
3188 __isl_keep isl_band *band);
3189 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3190 __isl_keep isl_band *band);
3192 int isl_band_n_member(__isl_keep isl_band *band);
3193 int isl_band_member_is_zero_distance(
3194 __isl_keep isl_band *band, int pos);
3196 Note that a scheduling dimension is considered to be ``zero
3197 distance'' if it does not carry any proximity dependences
3199 That is, if the dependence distances of the proximity
3200 dependences are all zero in that direction (for fixed
3201 iterations of outer bands).
3203 A representation of the band can be printed using
3205 #include <isl/band.h>
3206 __isl_give isl_printer *isl_printer_print_band(
3207 __isl_take isl_printer *p,
3208 __isl_keep isl_band *band);
3210 Alternatively, the schedule mapping
3211 can also be obtained in pieces using the following functions.
3213 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3214 __isl_give isl_union_map *isl_schedule_get_band(
3215 __isl_keep isl_schedule *sched, unsigned band);
3217 C<isl_schedule_n_band> returns the maximal number of bands.
3218 C<isl_schedule_get_band> returns a union of mappings from a domain to
3219 the band of consecutive schedule dimensions with the given sequence
3220 number for that domain. Bands with the same sequence number but for
3221 different domains may be completely unrelated.
3222 Within a band, the corresponding coordinates of the distance vectors
3223 are all non-negative, assuming that the coordinates for all previous
3226 =head2 Parametric Vertex Enumeration
3228 The parametric vertex enumeration described in this section
3229 is mainly intended to be used internally and by the C<barvinok>
3232 #include <isl/vertices.h>
3233 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3234 __isl_keep isl_basic_set *bset);
3236 The function C<isl_basic_set_compute_vertices> performs the
3237 actual computation of the parametric vertices and the chamber
3238 decomposition and store the result in an C<isl_vertices> object.
3239 This information can be queried by either iterating over all
3240 the vertices or iterating over all the chambers or cells
3241 and then iterating over all vertices that are active on the chamber.
3243 int isl_vertices_foreach_vertex(
3244 __isl_keep isl_vertices *vertices,
3245 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3248 int isl_vertices_foreach_cell(
3249 __isl_keep isl_vertices *vertices,
3250 int (*fn)(__isl_take isl_cell *cell, void *user),
3252 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3253 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3256 Other operations that can be performed on an C<isl_vertices> object are
3259 isl_ctx *isl_vertices_get_ctx(
3260 __isl_keep isl_vertices *vertices);
3261 int isl_vertices_get_n_vertices(
3262 __isl_keep isl_vertices *vertices);
3263 void isl_vertices_free(__isl_take isl_vertices *vertices);
3265 Vertices can be inspected and destroyed using the following functions.
3267 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3268 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3269 __isl_give isl_basic_set *isl_vertex_get_domain(
3270 __isl_keep isl_vertex *vertex);
3271 __isl_give isl_basic_set *isl_vertex_get_expr(
3272 __isl_keep isl_vertex *vertex);
3273 void isl_vertex_free(__isl_take isl_vertex *vertex);
3275 C<isl_vertex_get_expr> returns a singleton parametric set describing
3276 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3278 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3279 B<rational> basic sets, so they should mainly be used for inspection
3280 and should not be mixed with integer sets.
3282 Chambers can be inspected and destroyed using the following functions.
3284 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3285 __isl_give isl_basic_set *isl_cell_get_domain(
3286 __isl_keep isl_cell *cell);
3287 void isl_cell_free(__isl_take isl_cell *cell);
3291 Although C<isl> is mainly meant to be used as a library,
3292 it also contains some basic applications that use some
3293 of the functionality of C<isl>.
3294 The input may be specified in either the L<isl format>
3295 or the L<PolyLib format>.
3297 =head2 C<isl_polyhedron_sample>
3299 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3300 an integer element of the polyhedron, if there is any.
3301 The first column in the output is the denominator and is always
3302 equal to 1. If the polyhedron contains no integer points,
3303 then a vector of length zero is printed.
3307 C<isl_pip> takes the same input as the C<example> program
3308 from the C<piplib> distribution, i.e., a set of constraints
3309 on the parameters, a line containing only -1 and finally a set
3310 of constraints on a parametric polyhedron.
3311 The coefficients of the parameters appear in the last columns
3312 (but before the final constant column).
3313 The output is the lexicographic minimum of the parametric polyhedron.
3314 As C<isl> currently does not have its own output format, the output
3315 is just a dump of the internal state.
3317 =head2 C<isl_polyhedron_minimize>
3319 C<isl_polyhedron_minimize> computes the minimum of some linear
3320 or affine objective function over the integer points in a polyhedron.
3321 If an affine objective function
3322 is given, then the constant should appear in the last column.
3324 =head2 C<isl_polytope_scan>
3326 Given a polytope, C<isl_polytope_scan> prints
3327 all integer points in the polytope.