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.
90 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
91 Some of the old names have been kept for backward compatibility,
92 but they will be removed in the future.
98 The source of C<isl> can be obtained either as a tarball
99 or from the git repository. Both are available from
100 L<http://freshmeat.net/projects/isl/>.
101 The installation process depends on how you obtained
104 =head2 Installation from the git repository
108 =item 1 Clone or update the repository
110 The first time the source is obtained, you need to clone
113 git clone git://repo.or.cz/isl.git
115 To obtain updates, you need to pull in the latest changes
119 =item 2 Generate C<configure>
125 After performing the above steps, continue
126 with the L<Common installation instructions>.
128 =head2 Common installation instructions
132 =item 1 Obtain C<GMP>
134 Building C<isl> requires C<GMP>, including its headers files.
135 Your distribution may not provide these header files by default
136 and you may need to install a package called C<gmp-devel> or something
137 similar. Alternatively, C<GMP> can be built from
138 source, available from L<http://gmplib.org/>.
142 C<isl> uses the standard C<autoconf> C<configure> script.
147 optionally followed by some configure options.
148 A complete list of options can be obtained by running
152 Below we discuss some of the more common options.
154 C<isl> can optionally use C<piplib>, but no
155 C<piplib> functionality is currently used by default.
156 The C<--with-piplib> option can
157 be used to specify which C<piplib>
158 library to use, either an installed version (C<system>),
159 an externally built version (C<build>)
160 or no version (C<no>). The option C<build> is mostly useful
161 in C<configure> scripts of larger projects that bundle both C<isl>
168 Installation prefix for C<isl>
170 =item C<--with-gmp-prefix>
172 Installation prefix for C<GMP> (architecture-independent files).
174 =item C<--with-gmp-exec-prefix>
176 Installation prefix for C<GMP> (architecture-dependent files).
178 =item C<--with-piplib>
180 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
182 =item C<--with-piplib-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-independent files).
186 =item C<--with-piplib-exec-prefix>
188 Installation prefix for C<system> C<piplib> (architecture-dependent files).
190 =item C<--with-piplib-builddir>
192 Location where C<build> C<piplib> was built.
200 =item 4 Install (optional)
208 =head2 Initialization
210 All manipulations of integer sets and relations occur within
211 the context of an C<isl_ctx>.
212 A given C<isl_ctx> can only be used within a single thread.
213 All arguments of a function are required to have been allocated
214 within the same context.
215 There are currently no functions available for moving an object
216 from one C<isl_ctx> to another C<isl_ctx>. This means that
217 there is currently no way of safely moving an object from one
218 thread to another, unless the whole C<isl_ctx> is moved.
220 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
221 freed using C<isl_ctx_free>.
222 All objects allocated within an C<isl_ctx> should be freed
223 before the C<isl_ctx> itself is freed.
225 isl_ctx *isl_ctx_alloc();
226 void isl_ctx_free(isl_ctx *ctx);
230 All operations on integers, mainly the coefficients
231 of the constraints describing the sets and relations,
232 are performed in exact integer arithmetic using C<GMP>.
233 However, to allow future versions of C<isl> to optionally
234 support fixed integer arithmetic, all calls to C<GMP>
235 are wrapped inside C<isl> specific macros.
236 The basic type is C<isl_int> and the operations below
237 are available on this type.
238 The meanings of these operations are essentially the same
239 as their C<GMP> C<mpz_> counterparts.
240 As always with C<GMP> types, C<isl_int>s need to be
241 initialized with C<isl_int_init> before they can be used
242 and they need to be released with C<isl_int_clear>
244 The user should not assume that an C<isl_int> is represented
245 as a C<mpz_t>, but should instead explicitly convert between
246 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
247 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
251 =item isl_int_init(i)
253 =item isl_int_clear(i)
255 =item isl_int_set(r,i)
257 =item isl_int_set_si(r,i)
259 =item isl_int_set_gmp(r,g)
261 =item isl_int_get_gmp(i,g)
263 =item isl_int_abs(r,i)
265 =item isl_int_neg(r,i)
267 =item isl_int_swap(i,j)
269 =item isl_int_swap_or_set(i,j)
271 =item isl_int_add_ui(r,i,j)
273 =item isl_int_sub_ui(r,i,j)
275 =item isl_int_add(r,i,j)
277 =item isl_int_sub(r,i,j)
279 =item isl_int_mul(r,i,j)
281 =item isl_int_mul_ui(r,i,j)
283 =item isl_int_addmul(r,i,j)
285 =item isl_int_submul(r,i,j)
287 =item isl_int_gcd(r,i,j)
289 =item isl_int_lcm(r,i,j)
291 =item isl_int_divexact(r,i,j)
293 =item isl_int_cdiv_q(r,i,j)
295 =item isl_int_fdiv_q(r,i,j)
297 =item isl_int_fdiv_r(r,i,j)
299 =item isl_int_fdiv_q_ui(r,i,j)
301 =item isl_int_read(r,s)
303 =item isl_int_print(out,i,width)
307 =item isl_int_cmp(i,j)
309 =item isl_int_cmp_si(i,si)
311 =item isl_int_eq(i,j)
313 =item isl_int_ne(i,j)
315 =item isl_int_lt(i,j)
317 =item isl_int_le(i,j)
319 =item isl_int_gt(i,j)
321 =item isl_int_ge(i,j)
323 =item isl_int_abs_eq(i,j)
325 =item isl_int_abs_ne(i,j)
327 =item isl_int_abs_lt(i,j)
329 =item isl_int_abs_gt(i,j)
331 =item isl_int_abs_ge(i,j)
333 =item isl_int_is_zero(i)
335 =item isl_int_is_one(i)
337 =item isl_int_is_negone(i)
339 =item isl_int_is_pos(i)
341 =item isl_int_is_neg(i)
343 =item isl_int_is_nonpos(i)
345 =item isl_int_is_nonneg(i)
347 =item isl_int_is_divisible_by(i,j)
351 =head2 Sets and Relations
353 C<isl> uses six types of objects for representing sets and relations,
354 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
355 C<isl_union_set> and C<isl_union_map>.
356 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
357 can be described as a conjunction of affine constraints, while
358 C<isl_set> and C<isl_map> represent unions of
359 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
360 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
361 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
362 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
363 where dimensions with different space names
364 (see L<Dimension Specifications>) are considered different as well.
365 The difference between sets and relations (maps) is that sets have
366 one set of variables, while relations have two sets of variables,
367 input variables and output variables.
369 =head2 Memory Management
371 Since a high-level operation on sets and/or relations usually involves
372 several substeps and since the user is usually not interested in
373 the intermediate results, most functions that return a new object
374 will also release all the objects passed as arguments.
375 If the user still wants to use one or more of these arguments
376 after the function call, she should pass along a copy of the
377 object rather than the object itself.
378 The user is then responsible for making sure that the original
379 object gets used somewhere else or is explicitly freed.
381 The arguments and return values of all documents functions are
382 annotated to make clear which arguments are released and which
383 arguments are preserved. In particular, the following annotations
390 C<__isl_give> means that a new object is returned.
391 The user should make sure that the returned pointer is
392 used exactly once as a value for an C<__isl_take> argument.
393 In between, it can be used as a value for as many
394 C<__isl_keep> arguments as the user likes.
395 There is one exception, and that is the case where the
396 pointer returned is C<NULL>. Is this case, the user
397 is free to use it as an C<__isl_take> argument or not.
401 C<__isl_take> means that the object the argument points to
402 is taken over by the function and may no longer be used
403 by the user as an argument to any other function.
404 The pointer value must be one returned by a function
405 returning an C<__isl_give> pointer.
406 If the user passes in a C<NULL> value, then this will
407 be treated as an error in the sense that the function will
408 not perform its usual operation. However, it will still
409 make sure that all the the other C<__isl_take> arguments
414 C<__isl_keep> means that the function will only use the object
415 temporarily. After the function has finished, the user
416 can still use it as an argument to other functions.
417 A C<NULL> value will be treated in the same way as
418 a C<NULL> value for an C<__isl_take> argument.
422 =head2 Dimension Specifications
424 Whenever a new set or relation is created from scratch,
425 its dimension needs to be specified using an C<isl_dim>.
428 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
429 unsigned nparam, unsigned n_in, unsigned n_out);
430 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
431 unsigned nparam, unsigned dim);
432 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
433 void isl_dim_free(__isl_take isl_dim *dim);
434 unsigned isl_dim_size(__isl_keep isl_dim *dim,
435 enum isl_dim_type type);
437 The dimension specification used for creating a set
438 needs to be created using C<isl_dim_set_alloc>, while
439 that for creating a relation
440 needs to be created using C<isl_dim_alloc>.
441 C<isl_dim_size> can be used
442 to find out the number of dimensions of each type in
443 a dimension specification, where type may be
444 C<isl_dim_param>, C<isl_dim_in> (only for relations),
445 C<isl_dim_out> (only for relations), C<isl_dim_set>
446 (only for sets) or C<isl_dim_all>.
448 It is often useful to create objects that live in the
449 same space as some other object. This can be accomplished
450 by creating the new objects
451 (see L<Creating New Sets and Relations> or
452 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
453 specification of the original object.
456 __isl_give isl_dim *isl_basic_set_get_dim(
457 __isl_keep isl_basic_set *bset);
458 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
460 #include <isl/union_set.h>
461 __isl_give isl_dim *isl_union_set_get_dim(
462 __isl_keep isl_union_set *uset);
465 __isl_give isl_dim *isl_basic_map_get_dim(
466 __isl_keep isl_basic_map *bmap);
467 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
469 #include <isl/union_map.h>
470 __isl_give isl_dim *isl_union_map_get_dim(
471 __isl_keep isl_union_map *umap);
473 #include <isl/constraint.h>
474 __isl_give isl_dim *isl_constraint_get_dim(
475 __isl_keep isl_constraint *constraint);
477 #include <isl/polynomial.h>
478 __isl_give isl_dim *isl_qpolynomial_get_dim(
479 __isl_keep isl_qpolynomial *qp);
480 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
481 __isl_keep isl_qpolynomial_fold *fold);
482 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
483 __isl_keep isl_pw_qpolynomial *pwqp);
484 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
485 __isl_keep isl_union_pw_qpolynomial *upwqp);
486 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
487 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
490 __isl_give isl_dim *isl_aff_get_dim(
491 __isl_keep isl_aff *aff);
492 __isl_give isl_dim *isl_pw_aff_get_dim(
493 __isl_keep isl_pw_aff *pwaff);
495 #include <isl/point.h>
496 __isl_give isl_dim *isl_point_get_dim(
497 __isl_keep isl_point *pnt);
499 The names of the individual dimensions may be set or read off
500 using the following functions.
503 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
504 enum isl_dim_type type, unsigned pos,
505 __isl_keep const char *name);
506 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
507 enum isl_dim_type type, unsigned pos);
509 Note that C<isl_dim_get_name> returns a pointer to some internal
510 data structure, so the result can only be used while the
511 corresponding C<isl_dim> is alive.
512 Also note that every function that operates on two sets or relations
513 requires that both arguments have the same parameters. This also
514 means that if one of the arguments has named parameters, then the
515 other needs to have named parameters too and the names need to match.
516 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
517 have different parameters (as long as they are named), in which case
518 the result will have as parameters the union of the parameters of
521 The names of entire spaces may be set or read off
522 using the following functions.
525 __isl_give isl_dim *isl_dim_set_tuple_name(
526 __isl_take isl_dim *dim,
527 enum isl_dim_type type, const char *s);
528 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
529 enum isl_dim_type type);
531 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
532 or C<isl_dim_set>. As with C<isl_dim_get_name>,
533 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
535 Binary operations require the corresponding spaces of their arguments
536 to have the same name.
538 Spaces can be nested. In particular, the domain of a set or
539 the domain or range of a relation can be a nested relation.
540 The following functions can be used to construct and deconstruct
541 such nested dimension specifications.
544 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
545 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
546 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
548 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
549 be the dimension specification of a set, while that of
550 C<isl_dim_wrap> should be the dimension specification of a relation.
551 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
552 of a relation, while that of C<isl_dim_wrap> is the dimension specification
555 Dimension specifications can be created from other dimension
556 specifications using the following functions.
558 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
559 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
560 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
561 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
562 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
563 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
564 __isl_take isl_dim *right);
565 __isl_give isl_dim *isl_dim_align_params(
566 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
567 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
568 enum isl_dim_type type, unsigned pos, unsigned n);
569 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
570 enum isl_dim_type type, unsigned n);
571 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
572 enum isl_dim_type type, unsigned first, unsigned n);
573 __isl_give isl_dim *isl_dim_map_from_set(
574 __isl_take isl_dim *dim);
575 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
577 Note that if dimensions are added or removed from a space, then
578 the name and the internal structure are lost.
582 A local space is essentially a dimension specification with
583 zero or more existentially quantified variables.
584 The local space of a basic set or relation can be obtained
585 using the following functions.
588 __isl_give isl_local_space *isl_basic_set_get_local_space(
589 __isl_keep isl_basic_set *bset);
592 __isl_give isl_local_space *isl_basic_map_get_local_space(
593 __isl_keep isl_basic_map *bmap);
595 A new local space can be created from a dimension specification using
597 #include <isl/local_space.h>
598 __isl_give isl_local_space *isl_local_space_from_dim(
599 __isl_take isl_dim *dim);
601 They can be inspected, copied and freed using the following functions.
603 #include <isl/local_space.h>
604 isl_ctx *isl_local_space_get_ctx(
605 __isl_keep isl_local_space *ls);
606 int isl_local_space_dim(__isl_keep isl_local_space *ls,
607 enum isl_dim_type type);
608 const char *isl_local_space_get_dim_name(
609 __isl_keep isl_local_space *ls,
610 enum isl_dim_type type, unsigned pos);
611 __isl_give isl_local_space *isl_local_space_set_dim_name(
612 __isl_take isl_local_space *ls,
613 enum isl_dim_type type, unsigned pos, const char *s);
614 __isl_give isl_dim *isl_local_space_get_dim(
615 __isl_keep isl_local_space *ls);
616 __isl_give isl_div *isl_local_space_get_div(
617 __isl_keep isl_local_space *ls, int pos);
618 __isl_give isl_local_space *isl_local_space_copy(
619 __isl_keep isl_local_space *ls);
620 void *isl_local_space_free(__isl_take isl_local_space *ls);
622 Two local spaces can be compared using
624 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
625 __isl_keep isl_local_space *ls2);
627 Local spaces can be created from other local spaces
628 using the following functions.
630 __isl_give isl_local_space *isl_local_space_from_domain(
631 __isl_take isl_local_space *ls);
632 __isl_give isl_local_space *isl_local_space_add_dims(
633 __isl_take isl_local_space *ls,
634 enum isl_dim_type type, unsigned n);
635 __isl_give isl_local_space *isl_local_space_insert_dims(
636 __isl_take isl_local_space *ls,
637 enum isl_dim_type type, unsigned first, unsigned n);
638 __isl_give isl_local_space *isl_local_space_drop_dims(
639 __isl_take isl_local_space *ls,
640 enum isl_dim_type type, unsigned first, unsigned n);
642 =head2 Input and Output
644 C<isl> supports its own input/output format, which is similar
645 to the C<Omega> format, but also supports the C<PolyLib> format
650 The C<isl> format is similar to that of C<Omega>, but has a different
651 syntax for describing the parameters and allows for the definition
652 of an existentially quantified variable as the integer division
653 of an affine expression.
654 For example, the set of integers C<i> between C<0> and C<n>
655 such that C<i % 10 <= 6> can be described as
657 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
660 A set or relation can have several disjuncts, separated
661 by the keyword C<or>. Each disjunct is either a conjunction
662 of constraints or a projection (C<exists>) of a conjunction
663 of constraints. The constraints are separated by the keyword
666 =head3 C<PolyLib> format
668 If the represented set is a union, then the first line
669 contains a single number representing the number of disjuncts.
670 Otherwise, a line containing the number C<1> is optional.
672 Each disjunct is represented by a matrix of constraints.
673 The first line contains two numbers representing
674 the number of rows and columns,
675 where the number of rows is equal to the number of constraints
676 and the number of columns is equal to two plus the number of variables.
677 The following lines contain the actual rows of the constraint matrix.
678 In each row, the first column indicates whether the constraint
679 is an equality (C<0>) or inequality (C<1>). The final column
680 corresponds to the constant term.
682 If the set is parametric, then the coefficients of the parameters
683 appear in the last columns before the constant column.
684 The coefficients of any existentially quantified variables appear
685 between those of the set variables and those of the parameters.
687 =head3 Extended C<PolyLib> format
689 The extended C<PolyLib> format is nearly identical to the
690 C<PolyLib> format. The only difference is that the line
691 containing the number of rows and columns of a constraint matrix
692 also contains four additional numbers:
693 the number of output dimensions, the number of input dimensions,
694 the number of local dimensions (i.e., the number of existentially
695 quantified variables) and the number of parameters.
696 For sets, the number of ``output'' dimensions is equal
697 to the number of set dimensions, while the number of ``input''
703 __isl_give isl_basic_set *isl_basic_set_read_from_file(
704 isl_ctx *ctx, FILE *input, int nparam);
705 __isl_give isl_basic_set *isl_basic_set_read_from_str(
706 isl_ctx *ctx, const char *str, int nparam);
707 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
708 FILE *input, int nparam);
709 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
710 const char *str, int nparam);
713 __isl_give isl_basic_map *isl_basic_map_read_from_file(
714 isl_ctx *ctx, FILE *input, int nparam);
715 __isl_give isl_basic_map *isl_basic_map_read_from_str(
716 isl_ctx *ctx, const char *str, int nparam);
717 __isl_give isl_map *isl_map_read_from_file(
718 struct isl_ctx *ctx, FILE *input, int nparam);
719 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
720 const char *str, int nparam);
722 #include <isl/union_set.h>
723 __isl_give isl_union_set *isl_union_set_read_from_file(
724 isl_ctx *ctx, FILE *input);
725 __isl_give isl_union_set *isl_union_set_read_from_str(
726 struct isl_ctx *ctx, const char *str);
728 #include <isl/union_map.h>
729 __isl_give isl_union_map *isl_union_map_read_from_file(
730 isl_ctx *ctx, FILE *input);
731 __isl_give isl_union_map *isl_union_map_read_from_str(
732 struct isl_ctx *ctx, const char *str);
734 The input format is autodetected and may be either the C<PolyLib> format
735 or the C<isl> format.
736 C<nparam> specifies how many of the final columns in
737 the C<PolyLib> format correspond to parameters.
738 If input is given in the C<isl> format, then the number
739 of parameters needs to be equal to C<nparam>.
740 If C<nparam> is negative, then any number of parameters
741 is accepted in the C<isl> format and zero parameters
742 are assumed in the C<PolyLib> format.
746 Before anything can be printed, an C<isl_printer> needs to
749 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
751 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
752 void isl_printer_free(__isl_take isl_printer *printer);
753 __isl_give char *isl_printer_get_str(
754 __isl_keep isl_printer *printer);
756 The behavior of the printer can be modified in various ways
758 __isl_give isl_printer *isl_printer_set_output_format(
759 __isl_take isl_printer *p, int output_format);
760 __isl_give isl_printer *isl_printer_set_indent(
761 __isl_take isl_printer *p, int indent);
762 __isl_give isl_printer *isl_printer_indent(
763 __isl_take isl_printer *p, int indent);
764 __isl_give isl_printer *isl_printer_set_prefix(
765 __isl_take isl_printer *p, const char *prefix);
766 __isl_give isl_printer *isl_printer_set_suffix(
767 __isl_take isl_printer *p, const char *suffix);
769 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
770 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
771 and defaults to C<ISL_FORMAT_ISL>.
772 Each line in the output is indented by C<indent> (set by
773 C<isl_printer_set_indent>) spaces
774 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
775 In the C<PolyLib> format output,
776 the coefficients of the existentially quantified variables
777 appear between those of the set variables and those
779 The function C<isl_printer_indent> increases the indentation
780 by the specified amount (which may be negative).
782 To actually print something, use
785 __isl_give isl_printer *isl_printer_print_basic_set(
786 __isl_take isl_printer *printer,
787 __isl_keep isl_basic_set *bset);
788 __isl_give isl_printer *isl_printer_print_set(
789 __isl_take isl_printer *printer,
790 __isl_keep isl_set *set);
793 __isl_give isl_printer *isl_printer_print_basic_map(
794 __isl_take isl_printer *printer,
795 __isl_keep isl_basic_map *bmap);
796 __isl_give isl_printer *isl_printer_print_map(
797 __isl_take isl_printer *printer,
798 __isl_keep isl_map *map);
800 #include <isl/union_set.h>
801 __isl_give isl_printer *isl_printer_print_union_set(
802 __isl_take isl_printer *p,
803 __isl_keep isl_union_set *uset);
805 #include <isl/union_map.h>
806 __isl_give isl_printer *isl_printer_print_union_map(
807 __isl_take isl_printer *p,
808 __isl_keep isl_union_map *umap);
810 When called on a file printer, the following function flushes
811 the file. When called on a string printer, the buffer is cleared.
813 __isl_give isl_printer *isl_printer_flush(
814 __isl_take isl_printer *p);
816 =head2 Creating New Sets and Relations
818 C<isl> has functions for creating some standard sets and relations.
822 =item * Empty sets and relations
824 __isl_give isl_basic_set *isl_basic_set_empty(
825 __isl_take isl_dim *dim);
826 __isl_give isl_basic_map *isl_basic_map_empty(
827 __isl_take isl_dim *dim);
828 __isl_give isl_set *isl_set_empty(
829 __isl_take isl_dim *dim);
830 __isl_give isl_map *isl_map_empty(
831 __isl_take isl_dim *dim);
832 __isl_give isl_union_set *isl_union_set_empty(
833 __isl_take isl_dim *dim);
834 __isl_give isl_union_map *isl_union_map_empty(
835 __isl_take isl_dim *dim);
837 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
838 is only used to specify the parameters.
840 =item * Universe sets and relations
842 __isl_give isl_basic_set *isl_basic_set_universe(
843 __isl_take isl_dim *dim);
844 __isl_give isl_basic_map *isl_basic_map_universe(
845 __isl_take isl_dim *dim);
846 __isl_give isl_set *isl_set_universe(
847 __isl_take isl_dim *dim);
848 __isl_give isl_map *isl_map_universe(
849 __isl_take isl_dim *dim);
850 __isl_give isl_union_set *isl_union_set_universe(
851 __isl_take isl_union_set *uset);
852 __isl_give isl_union_map *isl_union_map_universe(
853 __isl_take isl_union_map *umap);
855 The sets and relations constructed by the functions above
856 contain all integer values, while those constructed by the
857 functions below only contain non-negative values.
859 __isl_give isl_basic_set *isl_basic_set_nat_universe(
860 __isl_take isl_dim *dim);
861 __isl_give isl_basic_map *isl_basic_map_nat_universe(
862 __isl_take isl_dim *dim);
863 __isl_give isl_set *isl_set_nat_universe(
864 __isl_take isl_dim *dim);
865 __isl_give isl_map *isl_map_nat_universe(
866 __isl_take isl_dim *dim);
868 =item * Identity relations
870 __isl_give isl_basic_map *isl_basic_map_identity(
871 __isl_take isl_dim *dim);
872 __isl_give isl_map *isl_map_identity(
873 __isl_take isl_dim *dim);
875 The number of input and output dimensions in C<dim> needs
878 =item * Lexicographic order
880 __isl_give isl_map *isl_map_lex_lt(
881 __isl_take isl_dim *set_dim);
882 __isl_give isl_map *isl_map_lex_le(
883 __isl_take isl_dim *set_dim);
884 __isl_give isl_map *isl_map_lex_gt(
885 __isl_take isl_dim *set_dim);
886 __isl_give isl_map *isl_map_lex_ge(
887 __isl_take isl_dim *set_dim);
888 __isl_give isl_map *isl_map_lex_lt_first(
889 __isl_take isl_dim *dim, unsigned n);
890 __isl_give isl_map *isl_map_lex_le_first(
891 __isl_take isl_dim *dim, unsigned n);
892 __isl_give isl_map *isl_map_lex_gt_first(
893 __isl_take isl_dim *dim, unsigned n);
894 __isl_give isl_map *isl_map_lex_ge_first(
895 __isl_take isl_dim *dim, unsigned n);
897 The first four functions take a dimension specification for a B<set>
898 and return relations that express that the elements in the domain
899 are lexicographically less
900 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
901 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
902 than the elements in the range.
903 The last four functions take a dimension specification for a map
904 and return relations that express that the first C<n> dimensions
905 in the domain are lexicographically less
906 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
907 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
908 than the first C<n> dimensions in the range.
912 A basic set or relation can be converted to a set or relation
913 using the following functions.
915 __isl_give isl_set *isl_set_from_basic_set(
916 __isl_take isl_basic_set *bset);
917 __isl_give isl_map *isl_map_from_basic_map(
918 __isl_take isl_basic_map *bmap);
920 Sets and relations can be converted to union sets and relations
921 using the following functions.
923 __isl_give isl_union_map *isl_union_map_from_map(
924 __isl_take isl_map *map);
925 __isl_give isl_union_set *isl_union_set_from_set(
926 __isl_take isl_set *set);
928 The inverse conversions below can only be used if the input
929 union set or relation is known to contain elements in exactly one
932 __isl_give isl_set *isl_set_from_union_set(
933 __isl_take isl_union_set *uset);
934 __isl_give isl_map *isl_map_from_union_map(
935 __isl_take isl_union_map *umap);
937 Sets and relations can be copied and freed again using the following
940 __isl_give isl_basic_set *isl_basic_set_copy(
941 __isl_keep isl_basic_set *bset);
942 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
943 __isl_give isl_union_set *isl_union_set_copy(
944 __isl_keep isl_union_set *uset);
945 __isl_give isl_basic_map *isl_basic_map_copy(
946 __isl_keep isl_basic_map *bmap);
947 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
948 __isl_give isl_union_map *isl_union_map_copy(
949 __isl_keep isl_union_map *umap);
950 void isl_basic_set_free(__isl_take isl_basic_set *bset);
951 void isl_set_free(__isl_take isl_set *set);
952 void *isl_union_set_free(__isl_take isl_union_set *uset);
953 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
954 void isl_map_free(__isl_take isl_map *map);
955 void *isl_union_map_free(__isl_take isl_union_map *umap);
957 Other sets and relations can be constructed by starting
958 from a universe set or relation, adding equality and/or
959 inequality constraints and then projecting out the
960 existentially quantified variables, if any.
961 Constraints can be constructed, manipulated and
962 added to (or removed from) (basic) sets and relations
963 using the following functions.
965 #include <isl/constraint.h>
966 __isl_give isl_constraint *isl_equality_alloc(
967 __isl_take isl_dim *dim);
968 __isl_give isl_constraint *isl_inequality_alloc(
969 __isl_take isl_dim *dim);
970 void isl_constraint_set_constant(
971 __isl_keep isl_constraint *constraint, isl_int v);
972 void isl_constraint_set_coefficient(
973 __isl_keep isl_constraint *constraint,
974 enum isl_dim_type type, int pos, isl_int v);
975 __isl_give isl_basic_map *isl_basic_map_add_constraint(
976 __isl_take isl_basic_map *bmap,
977 __isl_take isl_constraint *constraint);
978 __isl_give isl_basic_set *isl_basic_set_add_constraint(
979 __isl_take isl_basic_set *bset,
980 __isl_take isl_constraint *constraint);
981 __isl_give isl_map *isl_map_add_constraint(
982 __isl_take isl_map *map,
983 __isl_take isl_constraint *constraint);
984 __isl_give isl_set *isl_set_add_constraint(
985 __isl_take isl_set *set,
986 __isl_take isl_constraint *constraint);
987 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
988 __isl_take isl_basic_set *bset,
989 __isl_take isl_constraint *constraint);
991 For example, to create a set containing the even integers
992 between 10 and 42, you would use the following code.
996 struct isl_constraint *c;
997 struct isl_basic_set *bset;
1000 dim = isl_dim_set_alloc(ctx, 0, 2);
1001 bset = isl_basic_set_universe(isl_dim_copy(dim));
1003 c = isl_equality_alloc(isl_dim_copy(dim));
1004 isl_int_set_si(v, -1);
1005 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1006 isl_int_set_si(v, 2);
1007 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1008 bset = isl_basic_set_add_constraint(bset, c);
1010 c = isl_inequality_alloc(isl_dim_copy(dim));
1011 isl_int_set_si(v, -10);
1012 isl_constraint_set_constant(c, v);
1013 isl_int_set_si(v, 1);
1014 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1015 bset = isl_basic_set_add_constraint(bset, c);
1017 c = isl_inequality_alloc(dim);
1018 isl_int_set_si(v, 42);
1019 isl_constraint_set_constant(c, v);
1020 isl_int_set_si(v, -1);
1021 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1022 bset = isl_basic_set_add_constraint(bset, c);
1024 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1030 struct isl_basic_set *bset;
1031 bset = isl_basic_set_read_from_str(ctx,
1032 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1034 A basic set or relation can also be constructed from two matrices
1035 describing the equalities and the inequalities.
1037 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1038 __isl_take isl_dim *dim,
1039 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1040 enum isl_dim_type c1,
1041 enum isl_dim_type c2, enum isl_dim_type c3,
1042 enum isl_dim_type c4);
1043 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1044 __isl_take isl_dim *dim,
1045 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1046 enum isl_dim_type c1,
1047 enum isl_dim_type c2, enum isl_dim_type c3,
1048 enum isl_dim_type c4, enum isl_dim_type c5);
1050 The C<isl_dim_type> arguments indicate the order in which
1051 different kinds of variables appear in the input matrices
1052 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1053 C<isl_dim_set> and C<isl_dim_div> for sets and
1054 of C<isl_dim_cst>, C<isl_dim_param>,
1055 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1057 A (basic) relation can also be constructed from a (piecewise) affine expression
1058 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1060 __isl_give isl_basic_map *isl_basic_map_from_aff(
1061 __isl_take isl_aff *aff);
1062 __isl_give isl_map *isl_map_from_pw_aff(
1063 __isl_take isl_pw_aff *pwaff);
1064 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1065 __isl_take isl_dim *domain_dim,
1066 __isl_take isl_aff_list *list);
1068 The C<domain_dim> argument describes the domain of the resulting
1069 basic relation. It is required because the C<list> may consist
1070 of zero affine expressions.
1072 =head2 Inspecting Sets and Relations
1074 Usually, the user should not have to care about the actual constraints
1075 of the sets and maps, but should instead apply the abstract operations
1076 explained in the following sections.
1077 Occasionally, however, it may be required to inspect the individual
1078 coefficients of the constraints. This section explains how to do so.
1079 In these cases, it may also be useful to have C<isl> compute
1080 an explicit representation of the existentially quantified variables.
1082 __isl_give isl_set *isl_set_compute_divs(
1083 __isl_take isl_set *set);
1084 __isl_give isl_map *isl_map_compute_divs(
1085 __isl_take isl_map *map);
1086 __isl_give isl_union_set *isl_union_set_compute_divs(
1087 __isl_take isl_union_set *uset);
1088 __isl_give isl_union_map *isl_union_map_compute_divs(
1089 __isl_take isl_union_map *umap);
1091 This explicit representation defines the existentially quantified
1092 variables as integer divisions of the other variables, possibly
1093 including earlier existentially quantified variables.
1094 An explicitly represented existentially quantified variable therefore
1095 has a unique value when the values of the other variables are known.
1096 If, furthermore, the same existentials, i.e., existentials
1097 with the same explicit representations, should appear in the
1098 same order in each of the disjuncts of a set or map, then the user should call
1099 either of the following functions.
1101 __isl_give isl_set *isl_set_align_divs(
1102 __isl_take isl_set *set);
1103 __isl_give isl_map *isl_map_align_divs(
1104 __isl_take isl_map *map);
1106 Alternatively, the existentially quantified variables can be removed
1107 using the following functions, which compute an overapproximation.
1109 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1110 __isl_take isl_basic_set *bset);
1111 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1112 __isl_take isl_basic_map *bmap);
1113 __isl_give isl_set *isl_set_remove_divs(
1114 __isl_take isl_set *set);
1115 __isl_give isl_map *isl_map_remove_divs(
1116 __isl_take isl_map *map);
1118 To iterate over all the sets or maps in a union set or map, use
1120 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1121 int (*fn)(__isl_take isl_set *set, void *user),
1123 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1124 int (*fn)(__isl_take isl_map *map, void *user),
1127 The number of sets or maps in a union set or map can be obtained
1130 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1131 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1133 To extract the set or map from a union with a given dimension
1136 __isl_give isl_set *isl_union_set_extract_set(
1137 __isl_keep isl_union_set *uset,
1138 __isl_take isl_dim *dim);
1139 __isl_give isl_map *isl_union_map_extract_map(
1140 __isl_keep isl_union_map *umap,
1141 __isl_take isl_dim *dim);
1143 To iterate over all the basic sets or maps in a set or map, use
1145 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1146 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1148 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1149 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1152 The callback function C<fn> should return 0 if successful and
1153 -1 if an error occurs. In the latter case, or if any other error
1154 occurs, the above functions will return -1.
1156 It should be noted that C<isl> does not guarantee that
1157 the basic sets or maps passed to C<fn> are disjoint.
1158 If this is required, then the user should call one of
1159 the following functions first.
1161 __isl_give isl_set *isl_set_make_disjoint(
1162 __isl_take isl_set *set);
1163 __isl_give isl_map *isl_map_make_disjoint(
1164 __isl_take isl_map *map);
1166 The number of basic sets in a set can be obtained
1169 int isl_set_n_basic_set(__isl_keep isl_set *set);
1171 To iterate over the constraints of a basic set or map, use
1173 #include <isl/constraint.h>
1175 int isl_basic_map_foreach_constraint(
1176 __isl_keep isl_basic_map *bmap,
1177 int (*fn)(__isl_take isl_constraint *c, void *user),
1179 void isl_constraint_free(struct isl_constraint *c);
1181 Again, the callback function C<fn> should return 0 if successful and
1182 -1 if an error occurs. In the latter case, or if any other error
1183 occurs, the above functions will return -1.
1184 The constraint C<c> represents either an equality or an inequality.
1185 Use the following function to find out whether a constraint
1186 represents an equality. If not, it represents an inequality.
1188 int isl_constraint_is_equality(
1189 __isl_keep isl_constraint *constraint);
1191 The coefficients of the constraints can be inspected using
1192 the following functions.
1194 void isl_constraint_get_constant(
1195 __isl_keep isl_constraint *constraint, isl_int *v);
1196 void isl_constraint_get_coefficient(
1197 __isl_keep isl_constraint *constraint,
1198 enum isl_dim_type type, int pos, isl_int *v);
1199 int isl_constraint_involves_dims(
1200 __isl_keep isl_constraint *constraint,
1201 enum isl_dim_type type, unsigned first, unsigned n);
1203 The explicit representations of the existentially quantified
1204 variables can be inspected using the following functions.
1205 Note that the user is only allowed to use these functions
1206 if the inspected set or map is the result of a call
1207 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1209 __isl_give isl_div *isl_constraint_div(
1210 __isl_keep isl_constraint *constraint, int pos);
1211 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1212 void isl_div_get_constant(__isl_keep isl_div *div,
1214 void isl_div_get_denominator(__isl_keep isl_div *div,
1216 void isl_div_get_coefficient(__isl_keep isl_div *div,
1217 enum isl_dim_type type, int pos, isl_int *v);
1219 To obtain the constraints of a basic set or map in matrix
1220 form, use the following functions.
1222 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1223 __isl_keep isl_basic_set *bset,
1224 enum isl_dim_type c1, enum isl_dim_type c2,
1225 enum isl_dim_type c3, enum isl_dim_type c4);
1226 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1227 __isl_keep isl_basic_set *bset,
1228 enum isl_dim_type c1, enum isl_dim_type c2,
1229 enum isl_dim_type c3, enum isl_dim_type c4);
1230 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1231 __isl_keep isl_basic_map *bmap,
1232 enum isl_dim_type c1,
1233 enum isl_dim_type c2, enum isl_dim_type c3,
1234 enum isl_dim_type c4, enum isl_dim_type c5);
1235 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1236 __isl_keep isl_basic_map *bmap,
1237 enum isl_dim_type c1,
1238 enum isl_dim_type c2, enum isl_dim_type c3,
1239 enum isl_dim_type c4, enum isl_dim_type c5);
1241 The C<isl_dim_type> arguments dictate the order in which
1242 different kinds of variables appear in the resulting matrix
1243 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1244 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1246 To check whether the description of a set or relation depends
1247 on one or more given dimensions, it is not necessary to iterate over all
1248 constraints. Instead the following functions can be used.
1250 int isl_basic_set_involves_dims(
1251 __isl_keep isl_basic_set *bset,
1252 enum isl_dim_type type, unsigned first, unsigned n);
1253 int isl_set_involves_dims(__isl_keep isl_set *set,
1254 enum isl_dim_type type, unsigned first, unsigned n);
1255 int isl_basic_map_involves_dims(
1256 __isl_keep isl_basic_map *bmap,
1257 enum isl_dim_type type, unsigned first, unsigned n);
1258 int isl_map_involves_dims(__isl_keep isl_map *map,
1259 enum isl_dim_type type, unsigned first, unsigned n);
1261 The names of the domain and range spaces of a set or relation can be
1262 read off or set using the following functions.
1264 const char *isl_basic_set_get_tuple_name(
1265 __isl_keep isl_basic_set *bset);
1266 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1267 __isl_take isl_basic_set *set, const char *s);
1268 const char *isl_set_get_tuple_name(
1269 __isl_keep isl_set *set);
1270 const char *isl_basic_map_get_tuple_name(
1271 __isl_keep isl_basic_map *bmap,
1272 enum isl_dim_type type);
1273 const char *isl_map_get_tuple_name(
1274 __isl_keep isl_map *map,
1275 enum isl_dim_type type);
1277 As with C<isl_dim_get_tuple_name>, the value returned points to
1278 an internal data structure.
1279 The names of individual dimensions can be read off using
1280 the following functions.
1282 const char *isl_constraint_get_dim_name(
1283 __isl_keep isl_constraint *constraint,
1284 enum isl_dim_type type, unsigned pos);
1285 const char *isl_basic_set_get_dim_name(
1286 __isl_keep isl_basic_set *bset,
1287 enum isl_dim_type type, unsigned pos);
1288 const char *isl_set_get_dim_name(
1289 __isl_keep isl_set *set,
1290 enum isl_dim_type type, unsigned pos);
1291 const char *isl_basic_map_get_dim_name(
1292 __isl_keep isl_basic_map *bmap,
1293 enum isl_dim_type type, unsigned pos);
1294 const char *isl_map_get_dim_name(
1295 __isl_keep isl_map *map,
1296 enum isl_dim_type type, unsigned pos);
1298 These functions are mostly useful to obtain the names
1303 =head3 Unary Properties
1309 The following functions test whether the given set or relation
1310 contains any integer points. The ``plain'' variants do not perform
1311 any computations, but simply check if the given set or relation
1312 is already known to be empty.
1314 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1315 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1316 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1317 int isl_set_is_empty(__isl_keep isl_set *set);
1318 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1319 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1320 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1321 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1322 int isl_map_is_empty(__isl_keep isl_map *map);
1323 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1325 =item * Universality
1327 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1328 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1329 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1331 =item * Single-valuedness
1333 int isl_map_is_single_valued(__isl_keep isl_map *map);
1334 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1338 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1339 int isl_map_is_injective(__isl_keep isl_map *map);
1340 int isl_union_map_plain_is_injective(
1341 __isl_keep isl_union_map *umap);
1342 int isl_union_map_is_injective(
1343 __isl_keep isl_union_map *umap);
1347 int isl_map_is_bijective(__isl_keep isl_map *map);
1348 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1352 The following functions check whether the domain of the given
1353 (basic) set is a wrapped relation.
1355 int isl_basic_set_is_wrapping(
1356 __isl_keep isl_basic_set *bset);
1357 int isl_set_is_wrapping(__isl_keep isl_set *set);
1359 =item * Internal Product
1361 int isl_basic_map_can_zip(
1362 __isl_keep isl_basic_map *bmap);
1363 int isl_map_can_zip(__isl_keep isl_map *map);
1365 Check whether the product of domain and range of the given relation
1367 i.e., whether both domain and range are nested relations.
1371 =head3 Binary Properties
1377 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1378 __isl_keep isl_set *set2);
1379 int isl_set_is_equal(__isl_keep isl_set *set1,
1380 __isl_keep isl_set *set2);
1381 int isl_union_set_is_equal(
1382 __isl_keep isl_union_set *uset1,
1383 __isl_keep isl_union_set *uset2);
1384 int isl_basic_map_is_equal(
1385 __isl_keep isl_basic_map *bmap1,
1386 __isl_keep isl_basic_map *bmap2);
1387 int isl_map_is_equal(__isl_keep isl_map *map1,
1388 __isl_keep isl_map *map2);
1389 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1390 __isl_keep isl_map *map2);
1391 int isl_union_map_is_equal(
1392 __isl_keep isl_union_map *umap1,
1393 __isl_keep isl_union_map *umap2);
1395 =item * Disjointness
1397 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1398 __isl_keep isl_set *set2);
1402 int isl_set_is_subset(__isl_keep isl_set *set1,
1403 __isl_keep isl_set *set2);
1404 int isl_set_is_strict_subset(
1405 __isl_keep isl_set *set1,
1406 __isl_keep isl_set *set2);
1407 int isl_union_set_is_subset(
1408 __isl_keep isl_union_set *uset1,
1409 __isl_keep isl_union_set *uset2);
1410 int isl_union_set_is_strict_subset(
1411 __isl_keep isl_union_set *uset1,
1412 __isl_keep isl_union_set *uset2);
1413 int isl_basic_map_is_subset(
1414 __isl_keep isl_basic_map *bmap1,
1415 __isl_keep isl_basic_map *bmap2);
1416 int isl_basic_map_is_strict_subset(
1417 __isl_keep isl_basic_map *bmap1,
1418 __isl_keep isl_basic_map *bmap2);
1419 int isl_map_is_subset(
1420 __isl_keep isl_map *map1,
1421 __isl_keep isl_map *map2);
1422 int isl_map_is_strict_subset(
1423 __isl_keep isl_map *map1,
1424 __isl_keep isl_map *map2);
1425 int isl_union_map_is_subset(
1426 __isl_keep isl_union_map *umap1,
1427 __isl_keep isl_union_map *umap2);
1428 int isl_union_map_is_strict_subset(
1429 __isl_keep isl_union_map *umap1,
1430 __isl_keep isl_union_map *umap2);
1434 =head2 Unary Operations
1440 __isl_give isl_set *isl_set_complement(
1441 __isl_take isl_set *set);
1445 __isl_give isl_basic_map *isl_basic_map_reverse(
1446 __isl_take isl_basic_map *bmap);
1447 __isl_give isl_map *isl_map_reverse(
1448 __isl_take isl_map *map);
1449 __isl_give isl_union_map *isl_union_map_reverse(
1450 __isl_take isl_union_map *umap);
1454 __isl_give isl_basic_set *isl_basic_set_project_out(
1455 __isl_take isl_basic_set *bset,
1456 enum isl_dim_type type, unsigned first, unsigned n);
1457 __isl_give isl_basic_map *isl_basic_map_project_out(
1458 __isl_take isl_basic_map *bmap,
1459 enum isl_dim_type type, unsigned first, unsigned n);
1460 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1461 enum isl_dim_type type, unsigned first, unsigned n);
1462 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1463 enum isl_dim_type type, unsigned first, unsigned n);
1464 __isl_give isl_basic_set *isl_basic_map_domain(
1465 __isl_take isl_basic_map *bmap);
1466 __isl_give isl_basic_set *isl_basic_map_range(
1467 __isl_take isl_basic_map *bmap);
1468 __isl_give isl_set *isl_map_domain(
1469 __isl_take isl_map *bmap);
1470 __isl_give isl_set *isl_map_range(
1471 __isl_take isl_map *map);
1472 __isl_give isl_union_set *isl_union_map_domain(
1473 __isl_take isl_union_map *umap);
1474 __isl_give isl_union_set *isl_union_map_range(
1475 __isl_take isl_union_map *umap);
1477 __isl_give isl_basic_map *isl_basic_map_domain_map(
1478 __isl_take isl_basic_map *bmap);
1479 __isl_give isl_basic_map *isl_basic_map_range_map(
1480 __isl_take isl_basic_map *bmap);
1481 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1482 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1483 __isl_give isl_union_map *isl_union_map_domain_map(
1484 __isl_take isl_union_map *umap);
1485 __isl_give isl_union_map *isl_union_map_range_map(
1486 __isl_take isl_union_map *umap);
1488 The functions above construct a (basic, regular or union) relation
1489 that maps (a wrapped version of) the input relation to its domain or range.
1493 __isl_give isl_set *isl_set_eliminate(
1494 __isl_take isl_set *set, enum isl_dim_type type,
1495 unsigned first, unsigned n);
1497 Eliminate the coefficients for the given dimensions from the constraints,
1498 without removing the dimensions.
1502 __isl_give isl_basic_set *isl_basic_set_fix(
1503 __isl_take isl_basic_set *bset,
1504 enum isl_dim_type type, unsigned pos,
1506 __isl_give isl_basic_set *isl_basic_set_fix_si(
1507 __isl_take isl_basic_set *bset,
1508 enum isl_dim_type type, unsigned pos, int value);
1509 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1510 enum isl_dim_type type, unsigned pos,
1512 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1513 enum isl_dim_type type, unsigned pos, int value);
1514 __isl_give isl_basic_map *isl_basic_map_fix_si(
1515 __isl_take isl_basic_map *bmap,
1516 enum isl_dim_type type, unsigned pos, int value);
1517 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1518 enum isl_dim_type type, unsigned pos, int value);
1520 Intersect the set or relation with the hyperplane where the given
1521 dimension has the fixed given value.
1523 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1524 enum isl_dim_type type1, int pos1,
1525 enum isl_dim_type type2, int pos2);
1526 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1527 enum isl_dim_type type1, int pos1,
1528 enum isl_dim_type type2, int pos2);
1530 Intersect the set or relation with the hyperplane where the given
1531 dimensions are equal to each other.
1533 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1534 enum isl_dim_type type1, int pos1,
1535 enum isl_dim_type type2, int pos2);
1537 Intersect the relation with the hyperplane where the given
1538 dimensions have opposite values.
1542 __isl_give isl_map *isl_set_identity(
1543 __isl_take isl_set *set);
1544 __isl_give isl_union_map *isl_union_set_identity(
1545 __isl_take isl_union_set *uset);
1547 Construct an identity relation on the given (union) set.
1551 __isl_give isl_basic_set *isl_basic_map_deltas(
1552 __isl_take isl_basic_map *bmap);
1553 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1554 __isl_give isl_union_set *isl_union_map_deltas(
1555 __isl_take isl_union_map *umap);
1557 These functions return a (basic) set containing the differences
1558 between image elements and corresponding domain elements in the input.
1560 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1561 __isl_take isl_basic_map *bmap);
1562 __isl_give isl_map *isl_map_deltas_map(
1563 __isl_take isl_map *map);
1564 __isl_give isl_union_map *isl_union_map_deltas_map(
1565 __isl_take isl_union_map *umap);
1567 The functions above construct a (basic, regular or union) relation
1568 that maps (a wrapped version of) the input relation to its delta set.
1572 Simplify the representation of a set or relation by trying
1573 to combine pairs of basic sets or relations into a single
1574 basic set or relation.
1576 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1577 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1578 __isl_give isl_union_set *isl_union_set_coalesce(
1579 __isl_take isl_union_set *uset);
1580 __isl_give isl_union_map *isl_union_map_coalesce(
1581 __isl_take isl_union_map *umap);
1583 =item * Detecting equalities
1585 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1586 __isl_take isl_basic_set *bset);
1587 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1588 __isl_take isl_basic_map *bmap);
1589 __isl_give isl_set *isl_set_detect_equalities(
1590 __isl_take isl_set *set);
1591 __isl_give isl_map *isl_map_detect_equalities(
1592 __isl_take isl_map *map);
1593 __isl_give isl_union_set *isl_union_set_detect_equalities(
1594 __isl_take isl_union_set *uset);
1595 __isl_give isl_union_map *isl_union_map_detect_equalities(
1596 __isl_take isl_union_map *umap);
1598 Simplify the representation of a set or relation by detecting implicit
1601 =item * Removing redundant constraints
1603 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1604 __isl_take isl_basic_set *bset);
1605 __isl_give isl_set *isl_set_remove_redundancies(
1606 __isl_take isl_set *set);
1607 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1608 __isl_take isl_basic_map *bmap);
1609 __isl_give isl_map *isl_map_remove_redundancies(
1610 __isl_take isl_map *map);
1614 __isl_give isl_basic_set *isl_set_convex_hull(
1615 __isl_take isl_set *set);
1616 __isl_give isl_basic_map *isl_map_convex_hull(
1617 __isl_take isl_map *map);
1619 If the input set or relation has any existentially quantified
1620 variables, then the result of these operations is currently undefined.
1624 __isl_give isl_basic_set *isl_set_simple_hull(
1625 __isl_take isl_set *set);
1626 __isl_give isl_basic_map *isl_map_simple_hull(
1627 __isl_take isl_map *map);
1628 __isl_give isl_union_map *isl_union_map_simple_hull(
1629 __isl_take isl_union_map *umap);
1631 These functions compute a single basic set or relation
1632 that contains the whole input set or relation.
1633 In particular, the output is described by translates
1634 of the constraints describing the basic sets or relations in the input.
1638 (See \autoref{s:simple hull}.)
1644 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1645 __isl_take isl_basic_set *bset);
1646 __isl_give isl_basic_set *isl_set_affine_hull(
1647 __isl_take isl_set *set);
1648 __isl_give isl_union_set *isl_union_set_affine_hull(
1649 __isl_take isl_union_set *uset);
1650 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1651 __isl_take isl_basic_map *bmap);
1652 __isl_give isl_basic_map *isl_map_affine_hull(
1653 __isl_take isl_map *map);
1654 __isl_give isl_union_map *isl_union_map_affine_hull(
1655 __isl_take isl_union_map *umap);
1657 In case of union sets and relations, the affine hull is computed
1660 =item * Polyhedral hull
1662 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1663 __isl_take isl_set *set);
1664 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1665 __isl_take isl_map *map);
1666 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1667 __isl_take isl_union_set *uset);
1668 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1669 __isl_take isl_union_map *umap);
1671 These functions compute a single basic set or relation
1672 not involving any existentially quantified variables
1673 that contains the whole input set or relation.
1674 In case of union sets and relations, the polyhedral hull is computed
1677 =item * Optimization
1679 #include <isl/ilp.h>
1680 enum isl_lp_result isl_basic_set_max(
1681 __isl_keep isl_basic_set *bset,
1682 __isl_keep isl_aff *obj, isl_int *opt)
1683 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1684 __isl_keep isl_aff *obj, isl_int *opt);
1685 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1686 __isl_keep isl_aff *obj, isl_int *opt);
1688 Compute the minimum or maximum of the integer affine expression C<obj>
1689 over the points in C<set>, returning the result in C<opt>.
1690 The return value may be one of C<isl_lp_error>,
1691 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1693 =item * Parametric optimization
1695 __isl_give isl_pw_aff *isl_set_dim_max(
1696 __isl_take isl_set *set, int pos);
1698 Compute the maximum of the given set dimension as a function of the
1699 parameters, but independently of the other set dimensions.
1700 For lexicographic optimization, see L<"Lexicographic Optimization">.
1704 The following functions compute either the set of (rational) coefficient
1705 values of valid constraints for the given set or the set of (rational)
1706 values satisfying the constraints with coefficients from the given set.
1707 Internally, these two sets of functions perform essentially the
1708 same operations, except that the set of coefficients is assumed to
1709 be a cone, while the set of values may be any polyhedron.
1710 The current implementation is based on the Farkas lemma and
1711 Fourier-Motzkin elimination, but this may change or be made optional
1712 in future. In particular, future implementations may use different
1713 dualization algorithms or skip the elimination step.
1715 __isl_give isl_basic_set *isl_basic_set_coefficients(
1716 __isl_take isl_basic_set *bset);
1717 __isl_give isl_basic_set *isl_set_coefficients(
1718 __isl_take isl_set *set);
1719 __isl_give isl_union_set *isl_union_set_coefficients(
1720 __isl_take isl_union_set *bset);
1721 __isl_give isl_basic_set *isl_basic_set_solutions(
1722 __isl_take isl_basic_set *bset);
1723 __isl_give isl_basic_set *isl_set_solutions(
1724 __isl_take isl_set *set);
1725 __isl_give isl_union_set *isl_union_set_solutions(
1726 __isl_take isl_union_set *bset);
1730 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1732 __isl_give isl_union_map *isl_union_map_power(
1733 __isl_take isl_union_map *umap, int *exact);
1735 Compute a parametric representation for all positive powers I<k> of C<map>.
1736 The result maps I<k> to a nested relation corresponding to the
1737 I<k>th power of C<map>.
1738 The result may be an overapproximation. If the result is known to be exact,
1739 then C<*exact> is set to C<1>.
1741 =item * Transitive closure
1743 __isl_give isl_map *isl_map_transitive_closure(
1744 __isl_take isl_map *map, int *exact);
1745 __isl_give isl_union_map *isl_union_map_transitive_closure(
1746 __isl_take isl_union_map *umap, int *exact);
1748 Compute the transitive closure of C<map>.
1749 The result may be an overapproximation. If the result is known to be exact,
1750 then C<*exact> is set to C<1>.
1752 =item * Reaching path lengths
1754 __isl_give isl_map *isl_map_reaching_path_lengths(
1755 __isl_take isl_map *map, int *exact);
1757 Compute a relation that maps each element in the range of C<map>
1758 to the lengths of all paths composed of edges in C<map> that
1759 end up in the given element.
1760 The result may be an overapproximation. If the result is known to be exact,
1761 then C<*exact> is set to C<1>.
1762 To compute the I<maximal> path length, the resulting relation
1763 should be postprocessed by C<isl_map_lexmax>.
1764 In particular, if the input relation is a dependence relation
1765 (mapping sources to sinks), then the maximal path length corresponds
1766 to the free schedule.
1767 Note, however, that C<isl_map_lexmax> expects the maximum to be
1768 finite, so if the path lengths are unbounded (possibly due to
1769 the overapproximation), then you will get an error message.
1773 __isl_give isl_basic_set *isl_basic_map_wrap(
1774 __isl_take isl_basic_map *bmap);
1775 __isl_give isl_set *isl_map_wrap(
1776 __isl_take isl_map *map);
1777 __isl_give isl_union_set *isl_union_map_wrap(
1778 __isl_take isl_union_map *umap);
1779 __isl_give isl_basic_map *isl_basic_set_unwrap(
1780 __isl_take isl_basic_set *bset);
1781 __isl_give isl_map *isl_set_unwrap(
1782 __isl_take isl_set *set);
1783 __isl_give isl_union_map *isl_union_set_unwrap(
1784 __isl_take isl_union_set *uset);
1788 Remove any internal structure of domain (and range) of the given
1789 set or relation. If there is any such internal structure in the input,
1790 then the name of the space is also removed.
1792 __isl_give isl_basic_set *isl_basic_set_flatten(
1793 __isl_take isl_basic_set *bset);
1794 __isl_give isl_set *isl_set_flatten(
1795 __isl_take isl_set *set);
1796 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1797 __isl_take isl_basic_map *bmap);
1798 __isl_give isl_map *isl_map_flatten_range(
1799 __isl_take isl_map *map);
1800 __isl_give isl_basic_map *isl_basic_map_flatten(
1801 __isl_take isl_basic_map *bmap);
1802 __isl_give isl_map *isl_map_flatten(
1803 __isl_take isl_map *map);
1805 __isl_give isl_map *isl_set_flatten_map(
1806 __isl_take isl_set *set);
1808 The function above constructs a relation
1809 that maps the input set to a flattened version of the set.
1813 Lift the input set to a space with extra dimensions corresponding
1814 to the existentially quantified variables in the input.
1815 In particular, the result lives in a wrapped map where the domain
1816 is the original space and the range corresponds to the original
1817 existentially quantified variables.
1819 __isl_give isl_basic_set *isl_basic_set_lift(
1820 __isl_take isl_basic_set *bset);
1821 __isl_give isl_set *isl_set_lift(
1822 __isl_take isl_set *set);
1823 __isl_give isl_union_set *isl_union_set_lift(
1824 __isl_take isl_union_set *uset);
1826 =item * Internal Product
1828 __isl_give isl_basic_map *isl_basic_map_zip(
1829 __isl_take isl_basic_map *bmap);
1830 __isl_give isl_map *isl_map_zip(
1831 __isl_take isl_map *map);
1832 __isl_give isl_union_map *isl_union_map_zip(
1833 __isl_take isl_union_map *umap);
1835 Given a relation with nested relations for domain and range,
1836 interchange the range of the domain with the domain of the range.
1838 =item * Aligning parameters
1840 __isl_give isl_set *isl_set_align_params(
1841 __isl_take isl_set *set,
1842 __isl_take isl_dim *model);
1843 __isl_give isl_map *isl_map_align_params(
1844 __isl_take isl_map *map,
1845 __isl_take isl_dim *model);
1847 Change the order of the parameters of the given set or relation
1848 such that the first parameters match those of C<model>.
1849 This may involve the introduction of extra parameters.
1850 All parameters need to be named.
1852 =item * Dimension manipulation
1854 __isl_give isl_set *isl_set_add_dims(
1855 __isl_take isl_set *set,
1856 enum isl_dim_type type, unsigned n);
1857 __isl_give isl_map *isl_map_add_dims(
1858 __isl_take isl_map *map,
1859 enum isl_dim_type type, unsigned n);
1861 It is usually not advisable to directly change the (input or output)
1862 space of a set or a relation as this removes the name and the internal
1863 structure of the space. However, the above functions can be useful
1864 to add new parameters, assuming
1865 C<isl_set_align_params> and C<isl_map_align_params>
1870 =head2 Binary Operations
1872 The two arguments of a binary operation not only need to live
1873 in the same C<isl_ctx>, they currently also need to have
1874 the same (number of) parameters.
1876 =head3 Basic Operations
1880 =item * Intersection
1882 __isl_give isl_basic_set *isl_basic_set_intersect(
1883 __isl_take isl_basic_set *bset1,
1884 __isl_take isl_basic_set *bset2);
1885 __isl_give isl_set *isl_set_intersect_params(
1886 __isl_take isl_set *set,
1887 __isl_take isl_set *params);
1888 __isl_give isl_set *isl_set_intersect(
1889 __isl_take isl_set *set1,
1890 __isl_take isl_set *set2);
1891 __isl_give isl_union_set *isl_union_set_intersect(
1892 __isl_take isl_union_set *uset1,
1893 __isl_take isl_union_set *uset2);
1894 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1895 __isl_take isl_basic_map *bmap,
1896 __isl_take isl_basic_set *bset);
1897 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1898 __isl_take isl_basic_map *bmap,
1899 __isl_take isl_basic_set *bset);
1900 __isl_give isl_basic_map *isl_basic_map_intersect(
1901 __isl_take isl_basic_map *bmap1,
1902 __isl_take isl_basic_map *bmap2);
1903 __isl_give isl_map *isl_map_intersect_params(
1904 __isl_take isl_map *map,
1905 __isl_take isl_set *params);
1906 __isl_give isl_map *isl_map_intersect_domain(
1907 __isl_take isl_map *map,
1908 __isl_take isl_set *set);
1909 __isl_give isl_map *isl_map_intersect_range(
1910 __isl_take isl_map *map,
1911 __isl_take isl_set *set);
1912 __isl_give isl_map *isl_map_intersect(
1913 __isl_take isl_map *map1,
1914 __isl_take isl_map *map2);
1915 __isl_give isl_union_map *isl_union_map_intersect_domain(
1916 __isl_take isl_union_map *umap,
1917 __isl_take isl_union_set *uset);
1918 __isl_give isl_union_map *isl_union_map_intersect_range(
1919 __isl_take isl_union_map *umap,
1920 __isl_take isl_union_set *uset);
1921 __isl_give isl_union_map *isl_union_map_intersect(
1922 __isl_take isl_union_map *umap1,
1923 __isl_take isl_union_map *umap2);
1927 __isl_give isl_set *isl_basic_set_union(
1928 __isl_take isl_basic_set *bset1,
1929 __isl_take isl_basic_set *bset2);
1930 __isl_give isl_map *isl_basic_map_union(
1931 __isl_take isl_basic_map *bmap1,
1932 __isl_take isl_basic_map *bmap2);
1933 __isl_give isl_set *isl_set_union(
1934 __isl_take isl_set *set1,
1935 __isl_take isl_set *set2);
1936 __isl_give isl_map *isl_map_union(
1937 __isl_take isl_map *map1,
1938 __isl_take isl_map *map2);
1939 __isl_give isl_union_set *isl_union_set_union(
1940 __isl_take isl_union_set *uset1,
1941 __isl_take isl_union_set *uset2);
1942 __isl_give isl_union_map *isl_union_map_union(
1943 __isl_take isl_union_map *umap1,
1944 __isl_take isl_union_map *umap2);
1946 =item * Set difference
1948 __isl_give isl_set *isl_set_subtract(
1949 __isl_take isl_set *set1,
1950 __isl_take isl_set *set2);
1951 __isl_give isl_map *isl_map_subtract(
1952 __isl_take isl_map *map1,
1953 __isl_take isl_map *map2);
1954 __isl_give isl_union_set *isl_union_set_subtract(
1955 __isl_take isl_union_set *uset1,
1956 __isl_take isl_union_set *uset2);
1957 __isl_give isl_union_map *isl_union_map_subtract(
1958 __isl_take isl_union_map *umap1,
1959 __isl_take isl_union_map *umap2);
1963 __isl_give isl_basic_set *isl_basic_set_apply(
1964 __isl_take isl_basic_set *bset,
1965 __isl_take isl_basic_map *bmap);
1966 __isl_give isl_set *isl_set_apply(
1967 __isl_take isl_set *set,
1968 __isl_take isl_map *map);
1969 __isl_give isl_union_set *isl_union_set_apply(
1970 __isl_take isl_union_set *uset,
1971 __isl_take isl_union_map *umap);
1972 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1973 __isl_take isl_basic_map *bmap1,
1974 __isl_take isl_basic_map *bmap2);
1975 __isl_give isl_basic_map *isl_basic_map_apply_range(
1976 __isl_take isl_basic_map *bmap1,
1977 __isl_take isl_basic_map *bmap2);
1978 __isl_give isl_map *isl_map_apply_domain(
1979 __isl_take isl_map *map1,
1980 __isl_take isl_map *map2);
1981 __isl_give isl_union_map *isl_union_map_apply_domain(
1982 __isl_take isl_union_map *umap1,
1983 __isl_take isl_union_map *umap2);
1984 __isl_give isl_map *isl_map_apply_range(
1985 __isl_take isl_map *map1,
1986 __isl_take isl_map *map2);
1987 __isl_give isl_union_map *isl_union_map_apply_range(
1988 __isl_take isl_union_map *umap1,
1989 __isl_take isl_union_map *umap2);
1991 =item * Cartesian Product
1993 __isl_give isl_set *isl_set_product(
1994 __isl_take isl_set *set1,
1995 __isl_take isl_set *set2);
1996 __isl_give isl_union_set *isl_union_set_product(
1997 __isl_take isl_union_set *uset1,
1998 __isl_take isl_union_set *uset2);
1999 __isl_give isl_basic_map *isl_basic_map_range_product(
2000 __isl_take isl_basic_map *bmap1,
2001 __isl_take isl_basic_map *bmap2);
2002 __isl_give isl_map *isl_map_range_product(
2003 __isl_take isl_map *map1,
2004 __isl_take isl_map *map2);
2005 __isl_give isl_union_map *isl_union_map_range_product(
2006 __isl_take isl_union_map *umap1,
2007 __isl_take isl_union_map *umap2);
2008 __isl_give isl_map *isl_map_product(
2009 __isl_take isl_map *map1,
2010 __isl_take isl_map *map2);
2011 __isl_give isl_union_map *isl_union_map_product(
2012 __isl_take isl_union_map *umap1,
2013 __isl_take isl_union_map *umap2);
2015 The above functions compute the cross product of the given
2016 sets or relations. The domains and ranges of the results
2017 are wrapped maps between domains and ranges of the inputs.
2018 To obtain a ``flat'' product, use the following functions
2021 __isl_give isl_basic_set *isl_basic_set_flat_product(
2022 __isl_take isl_basic_set *bset1,
2023 __isl_take isl_basic_set *bset2);
2024 __isl_give isl_set *isl_set_flat_product(
2025 __isl_take isl_set *set1,
2026 __isl_take isl_set *set2);
2027 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2028 __isl_take isl_basic_map *bmap1,
2029 __isl_take isl_basic_map *bmap2);
2030 __isl_give isl_map *isl_map_flat_range_product(
2031 __isl_take isl_map *map1,
2032 __isl_take isl_map *map2);
2033 __isl_give isl_union_map *isl_union_map_flat_range_product(
2034 __isl_take isl_union_map *umap1,
2035 __isl_take isl_union_map *umap2);
2036 __isl_give isl_basic_map *isl_basic_map_flat_product(
2037 __isl_take isl_basic_map *bmap1,
2038 __isl_take isl_basic_map *bmap2);
2039 __isl_give isl_map *isl_map_flat_product(
2040 __isl_take isl_map *map1,
2041 __isl_take isl_map *map2);
2043 =item * Simplification
2045 __isl_give isl_basic_set *isl_basic_set_gist(
2046 __isl_take isl_basic_set *bset,
2047 __isl_take isl_basic_set *context);
2048 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2049 __isl_take isl_set *context);
2050 __isl_give isl_union_set *isl_union_set_gist(
2051 __isl_take isl_union_set *uset,
2052 __isl_take isl_union_set *context);
2053 __isl_give isl_basic_map *isl_basic_map_gist(
2054 __isl_take isl_basic_map *bmap,
2055 __isl_take isl_basic_map *context);
2056 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2057 __isl_take isl_map *context);
2058 __isl_give isl_union_map *isl_union_map_gist(
2059 __isl_take isl_union_map *umap,
2060 __isl_take isl_union_map *context);
2062 The gist operation returns a set or relation that has the
2063 same intersection with the context as the input set or relation.
2064 Any implicit equality in the intersection is made explicit in the result,
2065 while all inequalities that are redundant with respect to the intersection
2067 In case of union sets and relations, the gist operation is performed
2072 =head3 Lexicographic Optimization
2074 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2075 the following functions
2076 compute a set that contains the lexicographic minimum or maximum
2077 of the elements in C<set> (or C<bset>) for those values of the parameters
2078 that satisfy C<dom>.
2079 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2080 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2082 In other words, the union of the parameter values
2083 for which the result is non-empty and of C<*empty>
2086 __isl_give isl_set *isl_basic_set_partial_lexmin(
2087 __isl_take isl_basic_set *bset,
2088 __isl_take isl_basic_set *dom,
2089 __isl_give isl_set **empty);
2090 __isl_give isl_set *isl_basic_set_partial_lexmax(
2091 __isl_take isl_basic_set *bset,
2092 __isl_take isl_basic_set *dom,
2093 __isl_give isl_set **empty);
2094 __isl_give isl_set *isl_set_partial_lexmin(
2095 __isl_take isl_set *set, __isl_take isl_set *dom,
2096 __isl_give isl_set **empty);
2097 __isl_give isl_set *isl_set_partial_lexmax(
2098 __isl_take isl_set *set, __isl_take isl_set *dom,
2099 __isl_give isl_set **empty);
2101 Given a (basic) set C<set> (or C<bset>), the following functions simply
2102 return a set containing the lexicographic minimum or maximum
2103 of the elements in C<set> (or C<bset>).
2104 In case of union sets, the optimum is computed per space.
2106 __isl_give isl_set *isl_basic_set_lexmin(
2107 __isl_take isl_basic_set *bset);
2108 __isl_give isl_set *isl_basic_set_lexmax(
2109 __isl_take isl_basic_set *bset);
2110 __isl_give isl_set *isl_set_lexmin(
2111 __isl_take isl_set *set);
2112 __isl_give isl_set *isl_set_lexmax(
2113 __isl_take isl_set *set);
2114 __isl_give isl_union_set *isl_union_set_lexmin(
2115 __isl_take isl_union_set *uset);
2116 __isl_give isl_union_set *isl_union_set_lexmax(
2117 __isl_take isl_union_set *uset);
2119 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2120 the following functions
2121 compute a relation that maps each element of C<dom>
2122 to the single lexicographic minimum or maximum
2123 of the elements that are associated to that same
2124 element in C<map> (or C<bmap>).
2125 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2126 that contains the elements in C<dom> that do not map
2127 to any elements in C<map> (or C<bmap>).
2128 In other words, the union of the domain of the result and of C<*empty>
2131 __isl_give isl_map *isl_basic_map_partial_lexmax(
2132 __isl_take isl_basic_map *bmap,
2133 __isl_take isl_basic_set *dom,
2134 __isl_give isl_set **empty);
2135 __isl_give isl_map *isl_basic_map_partial_lexmin(
2136 __isl_take isl_basic_map *bmap,
2137 __isl_take isl_basic_set *dom,
2138 __isl_give isl_set **empty);
2139 __isl_give isl_map *isl_map_partial_lexmax(
2140 __isl_take isl_map *map, __isl_take isl_set *dom,
2141 __isl_give isl_set **empty);
2142 __isl_give isl_map *isl_map_partial_lexmin(
2143 __isl_take isl_map *map, __isl_take isl_set *dom,
2144 __isl_give isl_set **empty);
2146 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2147 return a map mapping each element in the domain of
2148 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2149 of all elements associated to that element.
2150 In case of union relations, the optimum is computed per space.
2152 __isl_give isl_map *isl_basic_map_lexmin(
2153 __isl_take isl_basic_map *bmap);
2154 __isl_give isl_map *isl_basic_map_lexmax(
2155 __isl_take isl_basic_map *bmap);
2156 __isl_give isl_map *isl_map_lexmin(
2157 __isl_take isl_map *map);
2158 __isl_give isl_map *isl_map_lexmax(
2159 __isl_take isl_map *map);
2160 __isl_give isl_union_map *isl_union_map_lexmin(
2161 __isl_take isl_union_map *umap);
2162 __isl_give isl_union_map *isl_union_map_lexmax(
2163 __isl_take isl_union_map *umap);
2167 Lists are defined over several element types, including
2168 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2169 Here we take lists of C<isl_set>s as an example.
2170 Lists can be created, copied and freed using the following functions.
2172 #include <isl/list.h>
2173 __isl_give isl_set_list *isl_set_list_alloc(
2174 isl_ctx *ctx, int n);
2175 __isl_give isl_set_list *isl_set_list_copy(
2176 __isl_keep isl_set_list *list);
2177 __isl_give isl_set_list *isl_set_list_add(
2178 __isl_take isl_set_list *list,
2179 __isl_take isl_set *el);
2180 void isl_set_list_free(__isl_take isl_set_list *list);
2182 C<isl_set_list_alloc> creates an empty list with a capacity for
2185 Lists can be inspected using the following functions.
2187 #include <isl/list.h>
2188 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2189 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2190 __isl_give struct isl_set *isl_set_list_get_set(
2191 __isl_keep isl_set_list *list, int index);
2192 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2193 int (*fn)(__isl_take struct isl_set *el, void *user),
2196 Lists can be printed using
2198 #include <isl/list.h>
2199 __isl_give isl_printer *isl_printer_print_set_list(
2200 __isl_take isl_printer *p,
2201 __isl_keep isl_set_list *list);
2205 Matrices can be created, copied and freed using the following functions.
2207 #include <isl/mat.h>
2208 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2209 unsigned n_row, unsigned n_col);
2210 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2211 void isl_mat_free(__isl_take isl_mat *mat);
2213 Note that the elements of a newly created matrix may have arbitrary values.
2214 The elements can be changed and inspected using the following functions.
2216 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2217 int isl_mat_rows(__isl_keep isl_mat *mat);
2218 int isl_mat_cols(__isl_keep isl_mat *mat);
2219 int isl_mat_get_element(__isl_keep isl_mat *mat,
2220 int row, int col, isl_int *v);
2221 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2222 int row, int col, isl_int v);
2223 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2224 int row, int col, int v);
2226 C<isl_mat_get_element> will return a negative value if anything went wrong.
2227 In that case, the value of C<*v> is undefined.
2229 The following function can be used to compute the (right) inverse
2230 of a matrix, i.e., a matrix such that the product of the original
2231 and the inverse (in that order) is a multiple of the identity matrix.
2232 The input matrix is assumed to be of full row-rank.
2234 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2236 The following function can be used to compute the (right) kernel
2237 (or null space) of a matrix, i.e., a matrix such that the product of
2238 the original and the kernel (in that order) is the zero matrix.
2240 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2242 =head2 Piecewise Quasi Affine Expressions
2244 The zero quasi affine expression can be created using
2246 __isl_give isl_aff *isl_aff_zero(
2247 __isl_take isl_local_space *ls);
2249 A quasi affine expression can also be initialized from an C<isl_div>:
2251 #include <isl/div.h>
2252 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2254 An empty piecewise quasi affine expression (one with no cells)
2255 or a piecewise quasi affine expression with a single cell can
2256 be created using the following functions.
2258 #include <isl/aff.h>
2259 __isl_give isl_pw_aff *isl_pw_aff_empty(
2260 __isl_take isl_dim *dim);
2261 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2262 __isl_take isl_set *set, __isl_take isl_aff *aff);
2264 Quasi affine expressions can be copied and freed using
2266 #include <isl/aff.h>
2267 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2268 void *isl_aff_free(__isl_take isl_aff *aff);
2270 __isl_give isl_pw_aff *isl_pw_aff_copy(
2271 __isl_keep isl_pw_aff *pwaff);
2272 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2274 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2275 using the following function. The constraint is required to have
2276 a non-zero coefficient for the specified dimension.
2278 #include <isl/constraint.h>
2279 __isl_give isl_aff *isl_constraint_get_bound(
2280 __isl_keep isl_constraint *constraint,
2281 enum isl_dim_type type, int pos);
2283 The entire affine expression of the constraint can also be extracted
2284 using the following function.
2286 #include <isl/constraint.h>
2287 __isl_give isl_aff *isl_constraint_get_aff(
2288 __isl_keep isl_constraint *constraint);
2290 Conversely, an equality constraint equating
2291 the affine expression to zero or an inequality constraint enforcing
2292 the affine expression to be non-negative, can be constructed using
2294 __isl_give isl_constraint *isl_equality_from_aff(
2295 __isl_take isl_aff *aff);
2296 __isl_give isl_constraint *isl_inequality_from_aff(
2297 __isl_take isl_aff *aff);
2299 The expression can be inspected using
2301 #include <isl/aff.h>
2302 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2303 int isl_aff_dim(__isl_keep isl_aff *aff,
2304 enum isl_dim_type type);
2305 __isl_give isl_local_space *isl_aff_get_local_space(
2306 __isl_keep isl_aff *aff);
2307 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2308 enum isl_dim_type type, unsigned pos);
2309 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2311 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2312 enum isl_dim_type type, int pos, isl_int *v);
2313 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2315 __isl_give isl_div *isl_aff_get_div(
2316 __isl_keep isl_aff *aff, int pos);
2318 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2319 enum isl_dim_type type, unsigned first, unsigned n);
2320 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2321 enum isl_dim_type type, unsigned first, unsigned n);
2323 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2324 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2325 enum isl_dim_type type);
2326 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2328 It can be modified using
2330 #include <isl/aff.h>
2331 __isl_give isl_aff *isl_aff_set_dim_name(
2332 __isl_take isl_aff *aff, enum isl_dim_type type,
2333 unsigned pos, const char *s);
2334 __isl_give isl_aff *isl_aff_set_constant(
2335 __isl_take isl_aff *aff, isl_int v);
2336 __isl_give isl_aff *isl_aff_set_constant_si(
2337 __isl_take isl_aff *aff, int v);
2338 __isl_give isl_aff *isl_aff_set_coefficient(
2339 __isl_take isl_aff *aff,
2340 enum isl_dim_type type, int pos, isl_int v);
2341 __isl_give isl_aff *isl_aff_set_coefficient_si(
2342 __isl_take isl_aff *aff,
2343 enum isl_dim_type type, int pos, int v);
2344 __isl_give isl_aff *isl_aff_set_denominator(
2345 __isl_take isl_aff *aff, isl_int v);
2347 __isl_give isl_aff *isl_aff_add_constant(
2348 __isl_take isl_aff *aff, isl_int v);
2349 __isl_give isl_aff *isl_aff_add_constant_si(
2350 __isl_take isl_aff *aff, int v);
2351 __isl_give isl_aff *isl_aff_add_coefficient(
2352 __isl_take isl_aff *aff,
2353 enum isl_dim_type type, int pos, isl_int v);
2354 __isl_give isl_aff *isl_aff_add_coefficient_si(
2355 __isl_take isl_aff *aff,
2356 enum isl_dim_type type, int pos, int v);
2358 __isl_give isl_aff *isl_aff_insert_dims(
2359 __isl_take isl_aff *aff,
2360 enum isl_dim_type type, unsigned first, unsigned n);
2361 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2362 __isl_take isl_pw_aff *pwaff,
2363 enum isl_dim_type type, unsigned first, unsigned n);
2364 __isl_give isl_aff *isl_aff_add_dims(
2365 __isl_take isl_aff *aff,
2366 enum isl_dim_type type, unsigned n);
2367 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2368 __isl_take isl_pw_aff *pwaff,
2369 enum isl_dim_type type, unsigned n);
2370 __isl_give isl_aff *isl_aff_drop_dims(
2371 __isl_take isl_aff *aff,
2372 enum isl_dim_type type, unsigned first, unsigned n);
2373 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2374 __isl_take isl_pw_aff *pwaff,
2375 enum isl_dim_type type, unsigned first, unsigned n);
2377 Note that the C<set_constant> and C<set_coefficient> functions
2378 set the I<numerator> of the constant or coefficient, while
2379 C<add_constant> and C<add_coefficient> add an integer value to
2380 the possibly rational constant or coefficient.
2382 To check whether an affine expressions is obviously zero
2383 or obviously equal to some other affine expression, use
2385 #include <isl/aff.h>
2386 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2387 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2388 __isl_keep isl_aff *aff2);
2392 #include <isl/aff.h>
2393 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2394 __isl_take isl_aff *aff2);
2395 __isl_give isl_pw_aff *isl_pw_aff_add(
2396 __isl_take isl_pw_aff *pwaff1,
2397 __isl_take isl_pw_aff *pwaff2);
2398 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2399 __isl_take isl_aff *aff2);
2400 __isl_give isl_pw_aff *isl_pw_aff_sub(
2401 __isl_take isl_pw_aff *pwaff1,
2402 __isl_take isl_pw_aff *pwaff2);
2403 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2404 __isl_give isl_pw_aff *isl_pw_aff_neg(
2405 __isl_take isl_pw_aff *pwaff);
2406 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2407 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2408 __isl_take isl_pw_aff *pwaff);
2409 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2410 __isl_give isl_pw_aff *isl_pw_aff_floor(
2411 __isl_take isl_pw_aff *pwaff);
2412 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2414 __isl_give isl_pw_aff *isl_pw_aff_scale(
2415 __isl_take isl_pw_aff *pwaff, isl_int f);
2416 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2418 __isl_give isl_aff *isl_aff_scale_down_ui(
2419 __isl_take isl_aff *aff, unsigned f);
2420 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2421 __isl_take isl_pw_aff *pwaff, isl_int f);
2423 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2424 __isl_take isl_pw_aff *pwqp);
2426 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2427 __isl_take isl_pw_aff *pwaff,
2428 __isl_take isl_dim *model);
2430 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2431 __isl_take isl_set *context);
2432 __isl_give isl_pw_aff *isl_pw_aff_gist(
2433 __isl_take isl_pw_aff *pwaff,
2434 __isl_take isl_set *context);
2436 __isl_give isl_set *isl_pw_aff_domain(
2437 __isl_take isl_pw_aff *pwaff);
2439 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2440 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2441 __isl_give isl_set *isl_pw_aff_eq_set(
2442 __isl_take isl_pw_aff *pwaff1,
2443 __isl_take isl_pw_aff *pwaff2);
2444 __isl_give isl_set *isl_pw_aff_le_set(
2445 __isl_take isl_pw_aff *pwaff1,
2446 __isl_take isl_pw_aff *pwaff2);
2447 __isl_give isl_set *isl_pw_aff_lt_set(
2448 __isl_take isl_pw_aff *pwaff1,
2449 __isl_take isl_pw_aff *pwaff2);
2450 __isl_give isl_set *isl_pw_aff_ge_set(
2451 __isl_take isl_pw_aff *pwaff1,
2452 __isl_take isl_pw_aff *pwaff2);
2453 __isl_give isl_set *isl_pw_aff_gt_set(
2454 __isl_take isl_pw_aff *pwaff1,
2455 __isl_take isl_pw_aff *pwaff2);
2457 The function C<isl_aff_ge_basic_set> returns a basic set
2458 containing those elements in the shared space
2459 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2460 The function C<isl_aff_ge_set> returns a set
2461 containing those elements in the shared domain
2462 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2464 #include <isl/aff.h>
2465 __isl_give isl_set *isl_pw_aff_nonneg_set(
2466 __isl_take isl_pw_aff *pwaff);
2468 The function C<isl_pw_aff_nonneg_set> returns a set
2469 containing those elements in the domain
2470 of C<pwaff> where C<pwaff> is non-negative.
2472 #include <isl/aff.h>
2473 __isl_give isl_pw_aff *isl_pw_aff_cond(
2474 __isl_take isl_set *cond,
2475 __isl_take isl_pw_aff *pwaff_true,
2476 __isl_take isl_pw_aff *pwaff_false);
2478 The function C<isl_pw_aff_cond> performs a conditional operator
2479 and returns an expression that is equal to C<pwaff_true>
2480 for elements in C<cond> and equal to C<pwaff_false> for elements
2483 #include <isl/aff.h>
2484 __isl_give isl_pw_aff *isl_pw_aff_max(
2485 __isl_take isl_pw_aff *pwaff1,
2486 __isl_take isl_pw_aff *pwaff2);
2488 The function C<isl_pw_aff_max> computes a piecewise quasi-affine
2489 expression with a domain that is the union of those of C<pwaff1> and
2490 C<pwaff2> and such that on each cell, the quasi-affine expression is
2491 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2492 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2493 associated expression is the defined one.
2495 An expression can be printed using
2497 #include <isl/aff.h>
2498 __isl_give isl_printer *isl_printer_print_aff(
2499 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2501 __isl_give isl_printer *isl_printer_print_pw_aff(
2502 __isl_take isl_printer *p,
2503 __isl_keep isl_pw_aff *pwaff);
2507 Points are elements of a set. They can be used to construct
2508 simple sets (boxes) or they can be used to represent the
2509 individual elements of a set.
2510 The zero point (the origin) can be created using
2512 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2514 The coordinates of a point can be inspected, set and changed
2517 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2518 enum isl_dim_type type, int pos, isl_int *v);
2519 __isl_give isl_point *isl_point_set_coordinate(
2520 __isl_take isl_point *pnt,
2521 enum isl_dim_type type, int pos, isl_int v);
2523 __isl_give isl_point *isl_point_add_ui(
2524 __isl_take isl_point *pnt,
2525 enum isl_dim_type type, int pos, unsigned val);
2526 __isl_give isl_point *isl_point_sub_ui(
2527 __isl_take isl_point *pnt,
2528 enum isl_dim_type type, int pos, unsigned val);
2530 Other properties can be obtained using
2532 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2534 Points can be copied or freed using
2536 __isl_give isl_point *isl_point_copy(
2537 __isl_keep isl_point *pnt);
2538 void isl_point_free(__isl_take isl_point *pnt);
2540 A singleton set can be created from a point using
2542 __isl_give isl_basic_set *isl_basic_set_from_point(
2543 __isl_take isl_point *pnt);
2544 __isl_give isl_set *isl_set_from_point(
2545 __isl_take isl_point *pnt);
2547 and a box can be created from two opposite extremal points using
2549 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2550 __isl_take isl_point *pnt1,
2551 __isl_take isl_point *pnt2);
2552 __isl_give isl_set *isl_set_box_from_points(
2553 __isl_take isl_point *pnt1,
2554 __isl_take isl_point *pnt2);
2556 All elements of a B<bounded> (union) set can be enumerated using
2557 the following functions.
2559 int isl_set_foreach_point(__isl_keep isl_set *set,
2560 int (*fn)(__isl_take isl_point *pnt, void *user),
2562 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2563 int (*fn)(__isl_take isl_point *pnt, void *user),
2566 The function C<fn> is called for each integer point in
2567 C<set> with as second argument the last argument of
2568 the C<isl_set_foreach_point> call. The function C<fn>
2569 should return C<0> on success and C<-1> on failure.
2570 In the latter case, C<isl_set_foreach_point> will stop
2571 enumerating and return C<-1> as well.
2572 If the enumeration is performed successfully and to completion,
2573 then C<isl_set_foreach_point> returns C<0>.
2575 To obtain a single point of a (basic) set, use
2577 __isl_give isl_point *isl_basic_set_sample_point(
2578 __isl_take isl_basic_set *bset);
2579 __isl_give isl_point *isl_set_sample_point(
2580 __isl_take isl_set *set);
2582 If C<set> does not contain any (integer) points, then the
2583 resulting point will be ``void'', a property that can be
2586 int isl_point_is_void(__isl_keep isl_point *pnt);
2588 =head2 Piecewise Quasipolynomials
2590 A piecewise quasipolynomial is a particular kind of function that maps
2591 a parametric point to a rational value.
2592 More specifically, a quasipolynomial is a polynomial expression in greatest
2593 integer parts of affine expressions of parameters and variables.
2594 A piecewise quasipolynomial is a subdivision of a given parametric
2595 domain into disjoint cells with a quasipolynomial associated to
2596 each cell. The value of the piecewise quasipolynomial at a given
2597 point is the value of the quasipolynomial associated to the cell
2598 that contains the point. Outside of the union of cells,
2599 the value is assumed to be zero.
2600 For example, the piecewise quasipolynomial
2602 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2604 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2605 A given piecewise quasipolynomial has a fixed domain dimension.
2606 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2607 defined over different domains.
2608 Piecewise quasipolynomials are mainly used by the C<barvinok>
2609 library for representing the number of elements in a parametric set or map.
2610 For example, the piecewise quasipolynomial above represents
2611 the number of points in the map
2613 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2615 =head3 Printing (Piecewise) Quasipolynomials
2617 Quasipolynomials and piecewise quasipolynomials can be printed
2618 using the following functions.
2620 __isl_give isl_printer *isl_printer_print_qpolynomial(
2621 __isl_take isl_printer *p,
2622 __isl_keep isl_qpolynomial *qp);
2624 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2625 __isl_take isl_printer *p,
2626 __isl_keep isl_pw_qpolynomial *pwqp);
2628 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2629 __isl_take isl_printer *p,
2630 __isl_keep isl_union_pw_qpolynomial *upwqp);
2632 The output format of the printer
2633 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2634 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2636 In case of printing in C<ISL_FORMAT_C>, the user may want
2637 to set the names of all dimensions
2639 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2640 __isl_take isl_qpolynomial *qp,
2641 enum isl_dim_type type, unsigned pos,
2643 __isl_give isl_pw_qpolynomial *
2644 isl_pw_qpolynomial_set_dim_name(
2645 __isl_take isl_pw_qpolynomial *pwqp,
2646 enum isl_dim_type type, unsigned pos,
2649 =head3 Creating New (Piecewise) Quasipolynomials
2651 Some simple quasipolynomials can be created using the following functions.
2652 More complicated quasipolynomials can be created by applying
2653 operations such as addition and multiplication
2654 on the resulting quasipolynomials
2656 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2657 __isl_take isl_dim *dim);
2658 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2659 __isl_take isl_dim *dim);
2660 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2661 __isl_take isl_dim *dim);
2662 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2663 __isl_take isl_dim *dim);
2664 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2665 __isl_take isl_dim *dim);
2666 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2667 __isl_take isl_dim *dim,
2668 const isl_int n, const isl_int d);
2669 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2670 __isl_take isl_div *div);
2671 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2672 __isl_take isl_dim *dim,
2673 enum isl_dim_type type, unsigned pos);
2674 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2675 __isl_take isl_aff *aff);
2677 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2678 with a single cell can be created using the following functions.
2679 Multiple of these single cell piecewise quasipolynomials can
2680 be combined to create more complicated piecewise quasipolynomials.
2682 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2683 __isl_take isl_dim *dim);
2684 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2685 __isl_take isl_set *set,
2686 __isl_take isl_qpolynomial *qp);
2688 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2689 __isl_take isl_dim *dim);
2690 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2691 __isl_take isl_pw_qpolynomial *pwqp);
2692 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2693 __isl_take isl_union_pw_qpolynomial *upwqp,
2694 __isl_take isl_pw_qpolynomial *pwqp);
2696 Quasipolynomials can be copied and freed again using the following
2699 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2700 __isl_keep isl_qpolynomial *qp);
2701 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2703 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2704 __isl_keep isl_pw_qpolynomial *pwqp);
2705 void *isl_pw_qpolynomial_free(
2706 __isl_take isl_pw_qpolynomial *pwqp);
2708 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2709 __isl_keep isl_union_pw_qpolynomial *upwqp);
2710 void isl_union_pw_qpolynomial_free(
2711 __isl_take isl_union_pw_qpolynomial *upwqp);
2713 =head3 Inspecting (Piecewise) Quasipolynomials
2715 To iterate over all piecewise quasipolynomials in a union
2716 piecewise quasipolynomial, use the following function
2718 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2719 __isl_keep isl_union_pw_qpolynomial *upwqp,
2720 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2723 To extract the piecewise quasipolynomial from a union with a given dimension
2726 __isl_give isl_pw_qpolynomial *
2727 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2728 __isl_keep isl_union_pw_qpolynomial *upwqp,
2729 __isl_take isl_dim *dim);
2731 To iterate over the cells in a piecewise quasipolynomial,
2732 use either of the following two functions
2734 int isl_pw_qpolynomial_foreach_piece(
2735 __isl_keep isl_pw_qpolynomial *pwqp,
2736 int (*fn)(__isl_take isl_set *set,
2737 __isl_take isl_qpolynomial *qp,
2738 void *user), void *user);
2739 int isl_pw_qpolynomial_foreach_lifted_piece(
2740 __isl_keep isl_pw_qpolynomial *pwqp,
2741 int (*fn)(__isl_take isl_set *set,
2742 __isl_take isl_qpolynomial *qp,
2743 void *user), void *user);
2745 As usual, the function C<fn> should return C<0> on success
2746 and C<-1> on failure. The difference between
2747 C<isl_pw_qpolynomial_foreach_piece> and
2748 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2749 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2750 compute unique representations for all existentially quantified
2751 variables and then turn these existentially quantified variables
2752 into extra set variables, adapting the associated quasipolynomial
2753 accordingly. This means that the C<set> passed to C<fn>
2754 will not have any existentially quantified variables, but that
2755 the dimensions of the sets may be different for different
2756 invocations of C<fn>.
2758 To iterate over all terms in a quasipolynomial,
2761 int isl_qpolynomial_foreach_term(
2762 __isl_keep isl_qpolynomial *qp,
2763 int (*fn)(__isl_take isl_term *term,
2764 void *user), void *user);
2766 The terms themselves can be inspected and freed using
2769 unsigned isl_term_dim(__isl_keep isl_term *term,
2770 enum isl_dim_type type);
2771 void isl_term_get_num(__isl_keep isl_term *term,
2773 void isl_term_get_den(__isl_keep isl_term *term,
2775 int isl_term_get_exp(__isl_keep isl_term *term,
2776 enum isl_dim_type type, unsigned pos);
2777 __isl_give isl_div *isl_term_get_div(
2778 __isl_keep isl_term *term, unsigned pos);
2779 void isl_term_free(__isl_take isl_term *term);
2781 Each term is a product of parameters, set variables and
2782 integer divisions. The function C<isl_term_get_exp>
2783 returns the exponent of a given dimensions in the given term.
2784 The C<isl_int>s in the arguments of C<isl_term_get_num>
2785 and C<isl_term_get_den> need to have been initialized
2786 using C<isl_int_init> before calling these functions.
2788 =head3 Properties of (Piecewise) Quasipolynomials
2790 To check whether a quasipolynomial is actually a constant,
2791 use the following function.
2793 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2794 isl_int *n, isl_int *d);
2796 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2797 then the numerator and denominator of the constant
2798 are returned in C<*n> and C<*d>, respectively.
2800 =head3 Operations on (Piecewise) Quasipolynomials
2802 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2803 __isl_take isl_qpolynomial *qp, isl_int v);
2804 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2805 __isl_take isl_qpolynomial *qp);
2806 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2807 __isl_take isl_qpolynomial *qp1,
2808 __isl_take isl_qpolynomial *qp2);
2809 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2810 __isl_take isl_qpolynomial *qp1,
2811 __isl_take isl_qpolynomial *qp2);
2812 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2813 __isl_take isl_qpolynomial *qp1,
2814 __isl_take isl_qpolynomial *qp2);
2815 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2816 __isl_take isl_qpolynomial *qp, unsigned exponent);
2818 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2819 __isl_take isl_pw_qpolynomial *pwqp1,
2820 __isl_take isl_pw_qpolynomial *pwqp2);
2821 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2822 __isl_take isl_pw_qpolynomial *pwqp1,
2823 __isl_take isl_pw_qpolynomial *pwqp2);
2824 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2825 __isl_take isl_pw_qpolynomial *pwqp1,
2826 __isl_take isl_pw_qpolynomial *pwqp2);
2827 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2828 __isl_take isl_pw_qpolynomial *pwqp);
2829 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2830 __isl_take isl_pw_qpolynomial *pwqp1,
2831 __isl_take isl_pw_qpolynomial *pwqp2);
2833 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2834 __isl_take isl_union_pw_qpolynomial *upwqp1,
2835 __isl_take isl_union_pw_qpolynomial *upwqp2);
2836 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2837 __isl_take isl_union_pw_qpolynomial *upwqp1,
2838 __isl_take isl_union_pw_qpolynomial *upwqp2);
2839 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2840 __isl_take isl_union_pw_qpolynomial *upwqp1,
2841 __isl_take isl_union_pw_qpolynomial *upwqp2);
2843 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2844 __isl_take isl_pw_qpolynomial *pwqp,
2845 __isl_take isl_point *pnt);
2847 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2848 __isl_take isl_union_pw_qpolynomial *upwqp,
2849 __isl_take isl_point *pnt);
2851 __isl_give isl_set *isl_pw_qpolynomial_domain(
2852 __isl_take isl_pw_qpolynomial *pwqp);
2853 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2854 __isl_take isl_pw_qpolynomial *pwpq,
2855 __isl_take isl_set *set);
2857 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2858 __isl_take isl_union_pw_qpolynomial *upwqp);
2859 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2860 __isl_take isl_union_pw_qpolynomial *upwpq,
2861 __isl_take isl_union_set *uset);
2863 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2864 __isl_take isl_qpolynomial *qp,
2865 __isl_take isl_dim *model);
2867 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2868 __isl_take isl_union_pw_qpolynomial *upwqp);
2870 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2871 __isl_take isl_qpolynomial *qp,
2872 __isl_take isl_set *context);
2874 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2875 __isl_take isl_pw_qpolynomial *pwqp,
2876 __isl_take isl_set *context);
2878 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2879 __isl_take isl_union_pw_qpolynomial *upwqp,
2880 __isl_take isl_union_set *context);
2882 The gist operation applies the gist operation to each of
2883 the cells in the domain of the input piecewise quasipolynomial.
2884 The context is also exploited
2885 to simplify the quasipolynomials associated to each cell.
2887 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2888 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2889 __isl_give isl_union_pw_qpolynomial *
2890 isl_union_pw_qpolynomial_to_polynomial(
2891 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2893 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2894 the polynomial will be an overapproximation. If C<sign> is negative,
2895 it will be an underapproximation. If C<sign> is zero, the approximation
2896 will lie somewhere in between.
2898 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2900 A piecewise quasipolynomial reduction is a piecewise
2901 reduction (or fold) of quasipolynomials.
2902 In particular, the reduction can be maximum or a minimum.
2903 The objects are mainly used to represent the result of
2904 an upper or lower bound on a quasipolynomial over its domain,
2905 i.e., as the result of the following function.
2907 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2908 __isl_take isl_pw_qpolynomial *pwqp,
2909 enum isl_fold type, int *tight);
2911 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2912 __isl_take isl_union_pw_qpolynomial *upwqp,
2913 enum isl_fold type, int *tight);
2915 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2916 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2917 is the returned bound is known be tight, i.e., for each value
2918 of the parameters there is at least
2919 one element in the domain that reaches the bound.
2920 If the domain of C<pwqp> is not wrapping, then the bound is computed
2921 over all elements in that domain and the result has a purely parametric
2922 domain. If the domain of C<pwqp> is wrapping, then the bound is
2923 computed over the range of the wrapped relation. The domain of the
2924 wrapped relation becomes the domain of the result.
2926 A (piecewise) quasipolynomial reduction can be copied or freed using the
2927 following functions.
2929 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2930 __isl_keep isl_qpolynomial_fold *fold);
2931 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2932 __isl_keep isl_pw_qpolynomial_fold *pwf);
2933 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2934 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2935 void isl_qpolynomial_fold_free(
2936 __isl_take isl_qpolynomial_fold *fold);
2937 void *isl_pw_qpolynomial_fold_free(
2938 __isl_take isl_pw_qpolynomial_fold *pwf);
2939 void isl_union_pw_qpolynomial_fold_free(
2940 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2942 =head3 Printing Piecewise Quasipolynomial Reductions
2944 Piecewise quasipolynomial reductions can be printed
2945 using the following function.
2947 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2948 __isl_take isl_printer *p,
2949 __isl_keep isl_pw_qpolynomial_fold *pwf);
2950 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2951 __isl_take isl_printer *p,
2952 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2954 For C<isl_printer_print_pw_qpolynomial_fold>,
2955 output format of the printer
2956 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2957 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2958 output format of the printer
2959 needs to be set to C<ISL_FORMAT_ISL>.
2960 In case of printing in C<ISL_FORMAT_C>, the user may want
2961 to set the names of all dimensions
2963 __isl_give isl_pw_qpolynomial_fold *
2964 isl_pw_qpolynomial_fold_set_dim_name(
2965 __isl_take isl_pw_qpolynomial_fold *pwf,
2966 enum isl_dim_type type, unsigned pos,
2969 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2971 To iterate over all piecewise quasipolynomial reductions in a union
2972 piecewise quasipolynomial reduction, use the following function
2974 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2975 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2976 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2977 void *user), void *user);
2979 To iterate over the cells in a piecewise quasipolynomial reduction,
2980 use either of the following two functions
2982 int isl_pw_qpolynomial_fold_foreach_piece(
2983 __isl_keep isl_pw_qpolynomial_fold *pwf,
2984 int (*fn)(__isl_take isl_set *set,
2985 __isl_take isl_qpolynomial_fold *fold,
2986 void *user), void *user);
2987 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2988 __isl_keep isl_pw_qpolynomial_fold *pwf,
2989 int (*fn)(__isl_take isl_set *set,
2990 __isl_take isl_qpolynomial_fold *fold,
2991 void *user), void *user);
2993 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2994 of the difference between these two functions.
2996 To iterate over all quasipolynomials in a reduction, use
2998 int isl_qpolynomial_fold_foreach_qpolynomial(
2999 __isl_keep isl_qpolynomial_fold *fold,
3000 int (*fn)(__isl_take isl_qpolynomial *qp,
3001 void *user), void *user);
3003 =head3 Operations on Piecewise Quasipolynomial Reductions
3005 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3006 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3008 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3009 __isl_take isl_pw_qpolynomial_fold *pwf1,
3010 __isl_take isl_pw_qpolynomial_fold *pwf2);
3012 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3013 __isl_take isl_pw_qpolynomial_fold *pwf1,
3014 __isl_take isl_pw_qpolynomial_fold *pwf2);
3016 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3017 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3018 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3020 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3021 __isl_take isl_pw_qpolynomial_fold *pwf,
3022 __isl_take isl_point *pnt);
3024 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3025 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3026 __isl_take isl_point *pnt);
3028 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3029 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3030 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3031 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3032 __isl_take isl_union_set *uset);
3034 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3035 __isl_take isl_pw_qpolynomial_fold *pwf);
3037 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3038 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3040 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3041 __isl_take isl_pw_qpolynomial_fold *pwf,
3042 __isl_take isl_set *context);
3044 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3045 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3046 __isl_take isl_union_set *context);
3048 The gist operation applies the gist operation to each of
3049 the cells in the domain of the input piecewise quasipolynomial reduction.
3050 In future, the operation will also exploit the context
3051 to simplify the quasipolynomial reductions associated to each cell.
3053 __isl_give isl_pw_qpolynomial_fold *
3054 isl_set_apply_pw_qpolynomial_fold(
3055 __isl_take isl_set *set,
3056 __isl_take isl_pw_qpolynomial_fold *pwf,
3058 __isl_give isl_pw_qpolynomial_fold *
3059 isl_map_apply_pw_qpolynomial_fold(
3060 __isl_take isl_map *map,
3061 __isl_take isl_pw_qpolynomial_fold *pwf,
3063 __isl_give isl_union_pw_qpolynomial_fold *
3064 isl_union_set_apply_union_pw_qpolynomial_fold(
3065 __isl_take isl_union_set *uset,
3066 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3068 __isl_give isl_union_pw_qpolynomial_fold *
3069 isl_union_map_apply_union_pw_qpolynomial_fold(
3070 __isl_take isl_union_map *umap,
3071 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3074 The functions taking a map
3075 compose the given map with the given piecewise quasipolynomial reduction.
3076 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3077 over all elements in the intersection of the range of the map
3078 and the domain of the piecewise quasipolynomial reduction
3079 as a function of an element in the domain of the map.
3080 The functions taking a set compute a bound over all elements in the
3081 intersection of the set and the domain of the
3082 piecewise quasipolynomial reduction.
3084 =head2 Dependence Analysis
3086 C<isl> contains specialized functionality for performing
3087 array dataflow analysis. That is, given a I<sink> access relation
3088 and a collection of possible I<source> access relations,
3089 C<isl> can compute relations that describe
3090 for each iteration of the sink access, which iteration
3091 of which of the source access relations was the last
3092 to access the same data element before the given iteration
3094 To compute standard flow dependences, the sink should be
3095 a read, while the sources should be writes.
3096 If any of the source accesses are marked as being I<may>
3097 accesses, then there will be a dependence to the last
3098 I<must> access B<and> to any I<may> access that follows
3099 this last I<must> access.
3100 In particular, if I<all> sources are I<may> accesses,
3101 then memory based dependence analysis is performed.
3102 If, on the other hand, all sources are I<must> accesses,
3103 then value based dependence analysis is performed.
3105 #include <isl/flow.h>
3107 typedef int (*isl_access_level_before)(void *first, void *second);
3109 __isl_give isl_access_info *isl_access_info_alloc(
3110 __isl_take isl_map *sink,
3111 void *sink_user, isl_access_level_before fn,
3113 __isl_give isl_access_info *isl_access_info_add_source(
3114 __isl_take isl_access_info *acc,
3115 __isl_take isl_map *source, int must,
3117 void isl_access_info_free(__isl_take isl_access_info *acc);
3119 __isl_give isl_flow *isl_access_info_compute_flow(
3120 __isl_take isl_access_info *acc);
3122 int isl_flow_foreach(__isl_keep isl_flow *deps,
3123 int (*fn)(__isl_take isl_map *dep, int must,
3124 void *dep_user, void *user),
3126 __isl_give isl_map *isl_flow_get_no_source(
3127 __isl_keep isl_flow *deps, int must);
3128 void isl_flow_free(__isl_take isl_flow *deps);
3130 The function C<isl_access_info_compute_flow> performs the actual
3131 dependence analysis. The other functions are used to construct
3132 the input for this function or to read off the output.
3134 The input is collected in an C<isl_access_info>, which can
3135 be created through a call to C<isl_access_info_alloc>.
3136 The arguments to this functions are the sink access relation
3137 C<sink>, a token C<sink_user> used to identify the sink
3138 access to the user, a callback function for specifying the
3139 relative order of source and sink accesses, and the number
3140 of source access relations that will be added.
3141 The callback function has type C<int (*)(void *first, void *second)>.
3142 The function is called with two user supplied tokens identifying
3143 either a source or the sink and it should return the shared nesting
3144 level and the relative order of the two accesses.
3145 In particular, let I<n> be the number of loops shared by
3146 the two accesses. If C<first> precedes C<second> textually,
3147 then the function should return I<2 * n + 1>; otherwise,
3148 it should return I<2 * n>.
3149 The sources can be added to the C<isl_access_info> by performing
3150 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3151 C<must> indicates whether the source is a I<must> access
3152 or a I<may> access. Note that a multi-valued access relation
3153 should only be marked I<must> if every iteration in the domain
3154 of the relation accesses I<all> elements in its image.
3155 The C<source_user> token is again used to identify
3156 the source access. The range of the source access relation
3157 C<source> should have the same dimension as the range
3158 of the sink access relation.
3159 The C<isl_access_info_free> function should usually not be
3160 called explicitly, because it is called implicitly by
3161 C<isl_access_info_compute_flow>.
3163 The result of the dependence analysis is collected in an
3164 C<isl_flow>. There may be elements of
3165 the sink access for which no preceding source access could be
3166 found or for which all preceding sources are I<may> accesses.
3167 The relations containing these elements can be obtained through
3168 calls to C<isl_flow_get_no_source>, the first with C<must> set
3169 and the second with C<must> unset.
3170 In the case of standard flow dependence analysis,
3171 with the sink a read and the sources I<must> writes,
3172 the first relation corresponds to the reads from uninitialized
3173 array elements and the second relation is empty.
3174 The actual flow dependences can be extracted using
3175 C<isl_flow_foreach>. This function will call the user-specified
3176 callback function C<fn> for each B<non-empty> dependence between
3177 a source and the sink. The callback function is called
3178 with four arguments, the actual flow dependence relation
3179 mapping source iterations to sink iterations, a boolean that
3180 indicates whether it is a I<must> or I<may> dependence, a token
3181 identifying the source and an additional C<void *> with value
3182 equal to the third argument of the C<isl_flow_foreach> call.
3183 A dependence is marked I<must> if it originates from a I<must>
3184 source and if it is not followed by any I<may> sources.
3186 After finishing with an C<isl_flow>, the user should call
3187 C<isl_flow_free> to free all associated memory.
3189 A higher-level interface to dependence analysis is provided
3190 by the following function.
3192 #include <isl/flow.h>
3194 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3195 __isl_take isl_union_map *must_source,
3196 __isl_take isl_union_map *may_source,
3197 __isl_take isl_union_map *schedule,
3198 __isl_give isl_union_map **must_dep,
3199 __isl_give isl_union_map **may_dep,
3200 __isl_give isl_union_map **must_no_source,
3201 __isl_give isl_union_map **may_no_source);
3203 The arrays are identified by the tuple names of the ranges
3204 of the accesses. The iteration domains by the tuple names
3205 of the domains of the accesses and of the schedule.
3206 The relative order of the iteration domains is given by the
3207 schedule. The relations returned through C<must_no_source>
3208 and C<may_no_source> are subsets of C<sink>.
3209 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3210 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3211 any of the other arguments is treated as an error.
3215 B<The functionality described in this section is fairly new
3216 and may be subject to change.>
3218 The following function can be used to compute a schedule
3219 for a union of domains. The generated schedule respects
3220 all C<validity> dependences. That is, all dependence distances
3221 over these dependences in the scheduled space are lexicographically
3222 positive. The generated schedule schedule also tries to minimize
3223 the dependence distances over C<proximity> dependences.
3224 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3225 for groups of domains where the dependence distances have only
3226 non-negative values.
3227 The algorithm used to construct the schedule is similar to that
3230 #include <isl/schedule.h>
3231 __isl_give isl_schedule *isl_union_set_compute_schedule(
3232 __isl_take isl_union_set *domain,
3233 __isl_take isl_union_map *validity,
3234 __isl_take isl_union_map *proximity);
3235 void *isl_schedule_free(__isl_take isl_schedule *sched);
3237 A mapping from the domains to the scheduled space can be obtained
3238 from an C<isl_schedule> using the following function.
3240 __isl_give isl_union_map *isl_schedule_get_map(
3241 __isl_keep isl_schedule *sched);
3243 A representation of the schedule can be printed using
3245 __isl_give isl_printer *isl_printer_print_schedule(
3246 __isl_take isl_printer *p,
3247 __isl_keep isl_schedule *schedule);
3249 A representation of the schedule as a forest of bands can be obtained
3250 using the following function.
3252 __isl_give isl_band_list *isl_schedule_get_band_forest(
3253 __isl_keep isl_schedule *schedule);
3255 The list can be manipulated as explained in L<"Lists">.
3256 The bands inside the list can be copied and freed using the following
3259 #include <isl/band.h>
3260 __isl_give isl_band *isl_band_copy(
3261 __isl_keep isl_band *band);
3262 void *isl_band_free(__isl_take isl_band *band);
3264 Each band contains zero or more scheduling dimensions.
3265 These are referred to as the members of the band.
3266 The section of the schedule that corresponds to the band is
3267 referred to as the partial schedule of the band.
3268 For those nodes that participate in a band, the outer scheduling
3269 dimensions form the prefix schedule, while the inner scheduling
3270 dimensions form the suffix schedule.
3271 That is, if we take a cut of the band forest, then the union of
3272 the concatenations of the prefix, partial and suffix schedules of
3273 each band in the cut is equal to the entire schedule (modulo
3274 some possible padding at the end with zero scheduling dimensions).
3275 The properties of a band can be inspected using the following functions.
3277 #include <isl/band.h>
3278 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3280 int isl_band_has_children(__isl_keep isl_band *band);
3281 __isl_give isl_band_list *isl_band_get_children(
3282 __isl_keep isl_band *band);
3284 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3285 __isl_keep isl_band *band);
3286 __isl_give isl_union_map *isl_band_get_partial_schedule(
3287 __isl_keep isl_band *band);
3288 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3289 __isl_keep isl_band *band);
3291 int isl_band_n_member(__isl_keep isl_band *band);
3292 int isl_band_member_is_zero_distance(
3293 __isl_keep isl_band *band, int pos);
3295 Note that a scheduling dimension is considered to be ``zero
3296 distance'' if it does not carry any proximity dependences
3298 That is, if the dependence distances of the proximity
3299 dependences are all zero in that direction (for fixed
3300 iterations of outer bands).
3302 A representation of the band can be printed using
3304 #include <isl/band.h>
3305 __isl_give isl_printer *isl_printer_print_band(
3306 __isl_take isl_printer *p,
3307 __isl_keep isl_band *band);
3309 =head2 Parametric Vertex Enumeration
3311 The parametric vertex enumeration described in this section
3312 is mainly intended to be used internally and by the C<barvinok>
3315 #include <isl/vertices.h>
3316 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3317 __isl_keep isl_basic_set *bset);
3319 The function C<isl_basic_set_compute_vertices> performs the
3320 actual computation of the parametric vertices and the chamber
3321 decomposition and store the result in an C<isl_vertices> object.
3322 This information can be queried by either iterating over all
3323 the vertices or iterating over all the chambers or cells
3324 and then iterating over all vertices that are active on the chamber.
3326 int isl_vertices_foreach_vertex(
3327 __isl_keep isl_vertices *vertices,
3328 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3331 int isl_vertices_foreach_cell(
3332 __isl_keep isl_vertices *vertices,
3333 int (*fn)(__isl_take isl_cell *cell, void *user),
3335 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3336 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3339 Other operations that can be performed on an C<isl_vertices> object are
3342 isl_ctx *isl_vertices_get_ctx(
3343 __isl_keep isl_vertices *vertices);
3344 int isl_vertices_get_n_vertices(
3345 __isl_keep isl_vertices *vertices);
3346 void isl_vertices_free(__isl_take isl_vertices *vertices);
3348 Vertices can be inspected and destroyed using the following functions.
3350 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3351 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3352 __isl_give isl_basic_set *isl_vertex_get_domain(
3353 __isl_keep isl_vertex *vertex);
3354 __isl_give isl_basic_set *isl_vertex_get_expr(
3355 __isl_keep isl_vertex *vertex);
3356 void isl_vertex_free(__isl_take isl_vertex *vertex);
3358 C<isl_vertex_get_expr> returns a singleton parametric set describing
3359 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3361 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3362 B<rational> basic sets, so they should mainly be used for inspection
3363 and should not be mixed with integer sets.
3365 Chambers can be inspected and destroyed using the following functions.
3367 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3368 __isl_give isl_basic_set *isl_cell_get_domain(
3369 __isl_keep isl_cell *cell);
3370 void isl_cell_free(__isl_take isl_cell *cell);
3374 Although C<isl> is mainly meant to be used as a library,
3375 it also contains some basic applications that use some
3376 of the functionality of C<isl>.
3377 The input may be specified in either the L<isl format>
3378 or the L<PolyLib format>.
3380 =head2 C<isl_polyhedron_sample>
3382 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3383 an integer element of the polyhedron, if there is any.
3384 The first column in the output is the denominator and is always
3385 equal to 1. If the polyhedron contains no integer points,
3386 then a vector of length zero is printed.
3390 C<isl_pip> takes the same input as the C<example> program
3391 from the C<piplib> distribution, i.e., a set of constraints
3392 on the parameters, a line containing only -1 and finally a set
3393 of constraints on a parametric polyhedron.
3394 The coefficients of the parameters appear in the last columns
3395 (but before the final constant column).
3396 The output is the lexicographic minimum of the parametric polyhedron.
3397 As C<isl> currently does not have its own output format, the output
3398 is just a dump of the internal state.
3400 =head2 C<isl_polyhedron_minimize>
3402 C<isl_polyhedron_minimize> computes the minimum of some linear
3403 or affine objective function over the integer points in a polyhedron.
3404 If an affine objective function
3405 is given, then the constant should appear in the last column.
3407 =head2 C<isl_polytope_scan>
3409 Given a polytope, C<isl_polytope_scan> prints
3410 all integer points in the polytope.