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 Sets and relations can be copied and freed again using the following
931 __isl_give isl_basic_set *isl_basic_set_copy(
932 __isl_keep isl_basic_set *bset);
933 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
934 __isl_give isl_union_set *isl_union_set_copy(
935 __isl_keep isl_union_set *uset);
936 __isl_give isl_basic_map *isl_basic_map_copy(
937 __isl_keep isl_basic_map *bmap);
938 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
939 __isl_give isl_union_map *isl_union_map_copy(
940 __isl_keep isl_union_map *umap);
941 void isl_basic_set_free(__isl_take isl_basic_set *bset);
942 void isl_set_free(__isl_take isl_set *set);
943 void *isl_union_set_free(__isl_take isl_union_set *uset);
944 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
945 void isl_map_free(__isl_take isl_map *map);
946 void *isl_union_map_free(__isl_take isl_union_map *umap);
948 Other sets and relations can be constructed by starting
949 from a universe set or relation, adding equality and/or
950 inequality constraints and then projecting out the
951 existentially quantified variables, if any.
952 Constraints can be constructed, manipulated and
953 added to (or removed from) (basic) sets and relations
954 using the following functions.
956 #include <isl/constraint.h>
957 __isl_give isl_constraint *isl_equality_alloc(
958 __isl_take isl_dim *dim);
959 __isl_give isl_constraint *isl_inequality_alloc(
960 __isl_take isl_dim *dim);
961 void isl_constraint_set_constant(
962 __isl_keep isl_constraint *constraint, isl_int v);
963 void isl_constraint_set_coefficient(
964 __isl_keep isl_constraint *constraint,
965 enum isl_dim_type type, int pos, isl_int v);
966 __isl_give isl_basic_map *isl_basic_map_add_constraint(
967 __isl_take isl_basic_map *bmap,
968 __isl_take isl_constraint *constraint);
969 __isl_give isl_basic_set *isl_basic_set_add_constraint(
970 __isl_take isl_basic_set *bset,
971 __isl_take isl_constraint *constraint);
972 __isl_give isl_map *isl_map_add_constraint(
973 __isl_take isl_map *map,
974 __isl_take isl_constraint *constraint);
975 __isl_give isl_set *isl_set_add_constraint(
976 __isl_take isl_set *set,
977 __isl_take isl_constraint *constraint);
978 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
979 __isl_take isl_basic_set *bset,
980 __isl_take isl_constraint *constraint);
982 For example, to create a set containing the even integers
983 between 10 and 42, you would use the following code.
987 struct isl_constraint *c;
988 struct isl_basic_set *bset;
991 dim = isl_dim_set_alloc(ctx, 0, 2);
992 bset = isl_basic_set_universe(isl_dim_copy(dim));
994 c = isl_equality_alloc(isl_dim_copy(dim));
995 isl_int_set_si(v, -1);
996 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
997 isl_int_set_si(v, 2);
998 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
999 bset = isl_basic_set_add_constraint(bset, c);
1001 c = isl_inequality_alloc(isl_dim_copy(dim));
1002 isl_int_set_si(v, -10);
1003 isl_constraint_set_constant(c, v);
1004 isl_int_set_si(v, 1);
1005 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1006 bset = isl_basic_set_add_constraint(bset, c);
1008 c = isl_inequality_alloc(dim);
1009 isl_int_set_si(v, 42);
1010 isl_constraint_set_constant(c, v);
1011 isl_int_set_si(v, -1);
1012 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1013 bset = isl_basic_set_add_constraint(bset, c);
1015 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1021 struct isl_basic_set *bset;
1022 bset = isl_basic_set_read_from_str(ctx,
1023 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1025 A basic set or relation can also be constructed from two matrices
1026 describing the equalities and the inequalities.
1028 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1029 __isl_take isl_dim *dim,
1030 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1031 enum isl_dim_type c1,
1032 enum isl_dim_type c2, enum isl_dim_type c3,
1033 enum isl_dim_type c4);
1034 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1035 __isl_take isl_dim *dim,
1036 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1037 enum isl_dim_type c1,
1038 enum isl_dim_type c2, enum isl_dim_type c3,
1039 enum isl_dim_type c4, enum isl_dim_type c5);
1041 The C<isl_dim_type> arguments indicate the order in which
1042 different kinds of variables appear in the input matrices
1043 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1044 C<isl_dim_set> and C<isl_dim_div> for sets and
1045 of C<isl_dim_cst>, C<isl_dim_param>,
1046 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1048 A (basic) relation can also be constructed from a (piecewise) affine expression
1049 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1051 __isl_give isl_basic_map *isl_basic_map_from_aff(
1052 __isl_take isl_aff *aff);
1053 __isl_give isl_map *isl_map_from_pw_aff(
1054 __isl_take isl_pw_aff *pwaff);
1055 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1056 __isl_take isl_dim *domain_dim,
1057 __isl_take isl_aff_list *list);
1059 The C<domain_dim> argument describes the domain of the resulting
1060 basic relation. It is required because the C<list> may consist
1061 of zero affine expressions.
1063 =head2 Inspecting Sets and Relations
1065 Usually, the user should not have to care about the actual constraints
1066 of the sets and maps, but should instead apply the abstract operations
1067 explained in the following sections.
1068 Occasionally, however, it may be required to inspect the individual
1069 coefficients of the constraints. This section explains how to do so.
1070 In these cases, it may also be useful to have C<isl> compute
1071 an explicit representation of the existentially quantified variables.
1073 __isl_give isl_set *isl_set_compute_divs(
1074 __isl_take isl_set *set);
1075 __isl_give isl_map *isl_map_compute_divs(
1076 __isl_take isl_map *map);
1077 __isl_give isl_union_set *isl_union_set_compute_divs(
1078 __isl_take isl_union_set *uset);
1079 __isl_give isl_union_map *isl_union_map_compute_divs(
1080 __isl_take isl_union_map *umap);
1082 This explicit representation defines the existentially quantified
1083 variables as integer divisions of the other variables, possibly
1084 including earlier existentially quantified variables.
1085 An explicitly represented existentially quantified variable therefore
1086 has a unique value when the values of the other variables are known.
1087 If, furthermore, the same existentials, i.e., existentials
1088 with the same explicit representations, should appear in the
1089 same order in each of the disjuncts of a set or map, then the user should call
1090 either of the following functions.
1092 __isl_give isl_set *isl_set_align_divs(
1093 __isl_take isl_set *set);
1094 __isl_give isl_map *isl_map_align_divs(
1095 __isl_take isl_map *map);
1097 Alternatively, the existentially quantified variables can be removed
1098 using the following functions, which compute an overapproximation.
1100 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1101 __isl_take isl_basic_set *bset);
1102 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1103 __isl_take isl_basic_map *bmap);
1104 __isl_give isl_set *isl_set_remove_divs(
1105 __isl_take isl_set *set);
1106 __isl_give isl_map *isl_map_remove_divs(
1107 __isl_take isl_map *map);
1109 To iterate over all the sets or maps in a union set or map, use
1111 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1112 int (*fn)(__isl_take isl_set *set, void *user),
1114 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1115 int (*fn)(__isl_take isl_map *map, void *user),
1118 The number of sets or maps in a union set or map can be obtained
1121 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1122 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1124 To extract the set or map from a union with a given dimension
1127 __isl_give isl_set *isl_union_set_extract_set(
1128 __isl_keep isl_union_set *uset,
1129 __isl_take isl_dim *dim);
1130 __isl_give isl_map *isl_union_map_extract_map(
1131 __isl_keep isl_union_map *umap,
1132 __isl_take isl_dim *dim);
1134 To iterate over all the basic sets or maps in a set or map, use
1136 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1137 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1139 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1140 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1143 The callback function C<fn> should return 0 if successful and
1144 -1 if an error occurs. In the latter case, or if any other error
1145 occurs, the above functions will return -1.
1147 It should be noted that C<isl> does not guarantee that
1148 the basic sets or maps passed to C<fn> are disjoint.
1149 If this is required, then the user should call one of
1150 the following functions first.
1152 __isl_give isl_set *isl_set_make_disjoint(
1153 __isl_take isl_set *set);
1154 __isl_give isl_map *isl_map_make_disjoint(
1155 __isl_take isl_map *map);
1157 The number of basic sets in a set can be obtained
1160 int isl_set_n_basic_set(__isl_keep isl_set *set);
1162 To iterate over the constraints of a basic set or map, use
1164 #include <isl/constraint.h>
1166 int isl_basic_map_foreach_constraint(
1167 __isl_keep isl_basic_map *bmap,
1168 int (*fn)(__isl_take isl_constraint *c, void *user),
1170 void isl_constraint_free(struct isl_constraint *c);
1172 Again, the callback function C<fn> should return 0 if successful and
1173 -1 if an error occurs. In the latter case, or if any other error
1174 occurs, the above functions will return -1.
1175 The constraint C<c> represents either an equality or an inequality.
1176 Use the following function to find out whether a constraint
1177 represents an equality. If not, it represents an inequality.
1179 int isl_constraint_is_equality(
1180 __isl_keep isl_constraint *constraint);
1182 The coefficients of the constraints can be inspected using
1183 the following functions.
1185 void isl_constraint_get_constant(
1186 __isl_keep isl_constraint *constraint, isl_int *v);
1187 void isl_constraint_get_coefficient(
1188 __isl_keep isl_constraint *constraint,
1189 enum isl_dim_type type, int pos, isl_int *v);
1190 int isl_constraint_involves_dims(
1191 __isl_keep isl_constraint *constraint,
1192 enum isl_dim_type type, unsigned first, unsigned n);
1194 The explicit representations of the existentially quantified
1195 variables can be inspected using the following functions.
1196 Note that the user is only allowed to use these functions
1197 if the inspected set or map is the result of a call
1198 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1200 __isl_give isl_div *isl_constraint_div(
1201 __isl_keep isl_constraint *constraint, int pos);
1202 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1203 void isl_div_get_constant(__isl_keep isl_div *div,
1205 void isl_div_get_denominator(__isl_keep isl_div *div,
1207 void isl_div_get_coefficient(__isl_keep isl_div *div,
1208 enum isl_dim_type type, int pos, isl_int *v);
1210 To obtain the constraints of a basic set or map in matrix
1211 form, use the following functions.
1213 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1214 __isl_keep isl_basic_set *bset,
1215 enum isl_dim_type c1, enum isl_dim_type c2,
1216 enum isl_dim_type c3, enum isl_dim_type c4);
1217 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1218 __isl_keep isl_basic_set *bset,
1219 enum isl_dim_type c1, enum isl_dim_type c2,
1220 enum isl_dim_type c3, enum isl_dim_type c4);
1221 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1222 __isl_keep isl_basic_map *bmap,
1223 enum isl_dim_type c1,
1224 enum isl_dim_type c2, enum isl_dim_type c3,
1225 enum isl_dim_type c4, enum isl_dim_type c5);
1226 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1227 __isl_keep isl_basic_map *bmap,
1228 enum isl_dim_type c1,
1229 enum isl_dim_type c2, enum isl_dim_type c3,
1230 enum isl_dim_type c4, enum isl_dim_type c5);
1232 The C<isl_dim_type> arguments dictate the order in which
1233 different kinds of variables appear in the resulting matrix
1234 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1235 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1237 The names of the domain and range spaces of a set or relation can be
1238 read off or set using the following functions.
1240 const char *isl_basic_set_get_tuple_name(
1241 __isl_keep isl_basic_set *bset);
1242 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1243 __isl_take isl_basic_set *set, const char *s);
1244 const char *isl_set_get_tuple_name(
1245 __isl_keep isl_set *set);
1246 const char *isl_basic_map_get_tuple_name(
1247 __isl_keep isl_basic_map *bmap,
1248 enum isl_dim_type type);
1249 const char *isl_map_get_tuple_name(
1250 __isl_keep isl_map *map,
1251 enum isl_dim_type type);
1253 As with C<isl_dim_get_tuple_name>, the value returned points to
1254 an internal data structure.
1255 The names of individual dimensions can be read off using
1256 the following functions.
1258 const char *isl_constraint_get_dim_name(
1259 __isl_keep isl_constraint *constraint,
1260 enum isl_dim_type type, unsigned pos);
1261 const char *isl_basic_set_get_dim_name(
1262 __isl_keep isl_basic_set *bset,
1263 enum isl_dim_type type, unsigned pos);
1264 const char *isl_set_get_dim_name(
1265 __isl_keep isl_set *set,
1266 enum isl_dim_type type, unsigned pos);
1267 const char *isl_basic_map_get_dim_name(
1268 __isl_keep isl_basic_map *bmap,
1269 enum isl_dim_type type, unsigned pos);
1270 const char *isl_map_get_dim_name(
1271 __isl_keep isl_map *map,
1272 enum isl_dim_type type, unsigned pos);
1274 These functions are mostly useful to obtain the names
1279 =head3 Unary Properties
1285 The following functions test whether the given set or relation
1286 contains any integer points. The ``plain'' variants do not perform
1287 any computations, but simply check if the given set or relation
1288 is already known to be empty.
1290 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1291 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1292 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1293 int isl_set_is_empty(__isl_keep isl_set *set);
1294 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1295 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1296 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1297 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1298 int isl_map_is_empty(__isl_keep isl_map *map);
1299 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1301 =item * Universality
1303 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1304 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1305 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1307 =item * Single-valuedness
1309 int isl_map_is_single_valued(__isl_keep isl_map *map);
1310 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1314 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1315 int isl_map_is_injective(__isl_keep isl_map *map);
1316 int isl_union_map_plain_is_injective(
1317 __isl_keep isl_union_map *umap);
1318 int isl_union_map_is_injective(
1319 __isl_keep isl_union_map *umap);
1323 int isl_map_is_bijective(__isl_keep isl_map *map);
1324 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1328 The following functions check whether the domain of the given
1329 (basic) set is a wrapped relation.
1331 int isl_basic_set_is_wrapping(
1332 __isl_keep isl_basic_set *bset);
1333 int isl_set_is_wrapping(__isl_keep isl_set *set);
1335 =item * Internal Product
1337 int isl_basic_map_can_zip(
1338 __isl_keep isl_basic_map *bmap);
1339 int isl_map_can_zip(__isl_keep isl_map *map);
1341 Check whether the product of domain and range of the given relation
1343 i.e., whether both domain and range are nested relations.
1347 =head3 Binary Properties
1353 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1354 __isl_keep isl_set *set2);
1355 int isl_set_is_equal(__isl_keep isl_set *set1,
1356 __isl_keep isl_set *set2);
1357 int isl_union_set_is_equal(
1358 __isl_keep isl_union_set *uset1,
1359 __isl_keep isl_union_set *uset2);
1360 int isl_basic_map_is_equal(
1361 __isl_keep isl_basic_map *bmap1,
1362 __isl_keep isl_basic_map *bmap2);
1363 int isl_map_is_equal(__isl_keep isl_map *map1,
1364 __isl_keep isl_map *map2);
1365 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1366 __isl_keep isl_map *map2);
1367 int isl_union_map_is_equal(
1368 __isl_keep isl_union_map *umap1,
1369 __isl_keep isl_union_map *umap2);
1371 =item * Disjointness
1373 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1374 __isl_keep isl_set *set2);
1378 int isl_set_is_subset(__isl_keep isl_set *set1,
1379 __isl_keep isl_set *set2);
1380 int isl_set_is_strict_subset(
1381 __isl_keep isl_set *set1,
1382 __isl_keep isl_set *set2);
1383 int isl_union_set_is_subset(
1384 __isl_keep isl_union_set *uset1,
1385 __isl_keep isl_union_set *uset2);
1386 int isl_union_set_is_strict_subset(
1387 __isl_keep isl_union_set *uset1,
1388 __isl_keep isl_union_set *uset2);
1389 int isl_basic_map_is_subset(
1390 __isl_keep isl_basic_map *bmap1,
1391 __isl_keep isl_basic_map *bmap2);
1392 int isl_basic_map_is_strict_subset(
1393 __isl_keep isl_basic_map *bmap1,
1394 __isl_keep isl_basic_map *bmap2);
1395 int isl_map_is_subset(
1396 __isl_keep isl_map *map1,
1397 __isl_keep isl_map *map2);
1398 int isl_map_is_strict_subset(
1399 __isl_keep isl_map *map1,
1400 __isl_keep isl_map *map2);
1401 int isl_union_map_is_subset(
1402 __isl_keep isl_union_map *umap1,
1403 __isl_keep isl_union_map *umap2);
1404 int isl_union_map_is_strict_subset(
1405 __isl_keep isl_union_map *umap1,
1406 __isl_keep isl_union_map *umap2);
1410 =head2 Unary Operations
1416 __isl_give isl_set *isl_set_complement(
1417 __isl_take isl_set *set);
1421 __isl_give isl_basic_map *isl_basic_map_reverse(
1422 __isl_take isl_basic_map *bmap);
1423 __isl_give isl_map *isl_map_reverse(
1424 __isl_take isl_map *map);
1425 __isl_give isl_union_map *isl_union_map_reverse(
1426 __isl_take isl_union_map *umap);
1430 __isl_give isl_basic_set *isl_basic_set_project_out(
1431 __isl_take isl_basic_set *bset,
1432 enum isl_dim_type type, unsigned first, unsigned n);
1433 __isl_give isl_basic_map *isl_basic_map_project_out(
1434 __isl_take isl_basic_map *bmap,
1435 enum isl_dim_type type, unsigned first, unsigned n);
1436 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1437 enum isl_dim_type type, unsigned first, unsigned n);
1438 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1439 enum isl_dim_type type, unsigned first, unsigned n);
1440 __isl_give isl_basic_set *isl_basic_map_domain(
1441 __isl_take isl_basic_map *bmap);
1442 __isl_give isl_basic_set *isl_basic_map_range(
1443 __isl_take isl_basic_map *bmap);
1444 __isl_give isl_set *isl_map_domain(
1445 __isl_take isl_map *bmap);
1446 __isl_give isl_set *isl_map_range(
1447 __isl_take isl_map *map);
1448 __isl_give isl_union_set *isl_union_map_domain(
1449 __isl_take isl_union_map *umap);
1450 __isl_give isl_union_set *isl_union_map_range(
1451 __isl_take isl_union_map *umap);
1453 __isl_give isl_basic_map *isl_basic_map_domain_map(
1454 __isl_take isl_basic_map *bmap);
1455 __isl_give isl_basic_map *isl_basic_map_range_map(
1456 __isl_take isl_basic_map *bmap);
1457 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1458 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1459 __isl_give isl_union_map *isl_union_map_domain_map(
1460 __isl_take isl_union_map *umap);
1461 __isl_give isl_union_map *isl_union_map_range_map(
1462 __isl_take isl_union_map *umap);
1464 The functions above construct a (basic, regular or union) relation
1465 that maps (a wrapped version of) the input relation to its domain or range.
1469 __isl_give isl_set *isl_set_eliminate(
1470 __isl_take isl_set *set, enum isl_dim_type type,
1471 unsigned first, unsigned n);
1473 Eliminate the coefficients for the given dimensions from the constraints,
1474 without removing the dimensions.
1478 __isl_give isl_basic_set *isl_basic_set_fix(
1479 __isl_take isl_basic_set *bset,
1480 enum isl_dim_type type, unsigned pos,
1482 __isl_give isl_basic_set *isl_basic_set_fix_si(
1483 __isl_take isl_basic_set *bset,
1484 enum isl_dim_type type, unsigned pos, int value);
1485 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1486 enum isl_dim_type type, unsigned pos,
1488 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1489 enum isl_dim_type type, unsigned pos, int value);
1490 __isl_give isl_basic_map *isl_basic_map_fix_si(
1491 __isl_take isl_basic_map *bmap,
1492 enum isl_dim_type type, unsigned pos, int value);
1493 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1494 enum isl_dim_type type, unsigned pos, int value);
1496 Intersect the set or relation with the hyperplane where the given
1497 dimension has the fixed given value.
1501 __isl_give isl_map *isl_set_identity(
1502 __isl_take isl_set *set);
1503 __isl_give isl_union_map *isl_union_set_identity(
1504 __isl_take isl_union_set *uset);
1506 Construct an identity relation on the given (union) set.
1510 __isl_give isl_basic_set *isl_basic_map_deltas(
1511 __isl_take isl_basic_map *bmap);
1512 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1513 __isl_give isl_union_set *isl_union_map_deltas(
1514 __isl_take isl_union_map *umap);
1516 These functions return a (basic) set containing the differences
1517 between image elements and corresponding domain elements in the input.
1519 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1520 __isl_take isl_basic_map *bmap);
1521 __isl_give isl_map *isl_map_deltas_map(
1522 __isl_take isl_map *map);
1523 __isl_give isl_union_map *isl_union_map_deltas_map(
1524 __isl_take isl_union_map *umap);
1526 The functions above construct a (basic, regular or union) relation
1527 that maps (a wrapped version of) the input relation to its delta set.
1531 Simplify the representation of a set or relation by trying
1532 to combine pairs of basic sets or relations into a single
1533 basic set or relation.
1535 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1536 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1537 __isl_give isl_union_set *isl_union_set_coalesce(
1538 __isl_take isl_union_set *uset);
1539 __isl_give isl_union_map *isl_union_map_coalesce(
1540 __isl_take isl_union_map *umap);
1542 =item * Detecting equalities
1544 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1545 __isl_take isl_basic_set *bset);
1546 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1547 __isl_take isl_basic_map *bmap);
1548 __isl_give isl_set *isl_set_detect_equalities(
1549 __isl_take isl_set *set);
1550 __isl_give isl_map *isl_map_detect_equalities(
1551 __isl_take isl_map *map);
1552 __isl_give isl_union_set *isl_union_set_detect_equalities(
1553 __isl_take isl_union_set *uset);
1554 __isl_give isl_union_map *isl_union_map_detect_equalities(
1555 __isl_take isl_union_map *umap);
1557 Simplify the representation of a set or relation by detecting implicit
1560 =item * Removing redundant constraints
1562 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1563 __isl_take isl_basic_set *bset);
1564 __isl_give isl_set *isl_set_remove_redundancies(
1565 __isl_take isl_set *set);
1566 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1567 __isl_take isl_basic_map *bmap);
1568 __isl_give isl_map *isl_map_remove_redundancies(
1569 __isl_take isl_map *map);
1573 __isl_give isl_basic_set *isl_set_convex_hull(
1574 __isl_take isl_set *set);
1575 __isl_give isl_basic_map *isl_map_convex_hull(
1576 __isl_take isl_map *map);
1578 If the input set or relation has any existentially quantified
1579 variables, then the result of these operations is currently undefined.
1583 __isl_give isl_basic_set *isl_set_simple_hull(
1584 __isl_take isl_set *set);
1585 __isl_give isl_basic_map *isl_map_simple_hull(
1586 __isl_take isl_map *map);
1587 __isl_give isl_union_map *isl_union_map_simple_hull(
1588 __isl_take isl_union_map *umap);
1590 These functions compute a single basic set or relation
1591 that contains the whole input set or relation.
1592 In particular, the output is described by translates
1593 of the constraints describing the basic sets or relations in the input.
1597 (See \autoref{s:simple hull}.)
1603 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1604 __isl_take isl_basic_set *bset);
1605 __isl_give isl_basic_set *isl_set_affine_hull(
1606 __isl_take isl_set *set);
1607 __isl_give isl_union_set *isl_union_set_affine_hull(
1608 __isl_take isl_union_set *uset);
1609 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1610 __isl_take isl_basic_map *bmap);
1611 __isl_give isl_basic_map *isl_map_affine_hull(
1612 __isl_take isl_map *map);
1613 __isl_give isl_union_map *isl_union_map_affine_hull(
1614 __isl_take isl_union_map *umap);
1616 In case of union sets and relations, the affine hull is computed
1619 =item * Polyhedral hull
1621 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1622 __isl_take isl_set *set);
1623 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1624 __isl_take isl_map *map);
1625 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1626 __isl_take isl_union_set *uset);
1627 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1628 __isl_take isl_union_map *umap);
1630 These functions compute a single basic set or relation
1631 not involving any existentially quantified variables
1632 that contains the whole input set or relation.
1633 In case of union sets and relations, the polyhedral hull is computed
1636 =item * Optimization
1638 #include <isl/ilp.h>
1639 enum isl_lp_result isl_basic_set_max(
1640 __isl_keep isl_basic_set *bset,
1641 __isl_keep isl_aff *obj, isl_int *opt)
1642 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1643 __isl_keep isl_aff *obj, isl_int *opt);
1645 Compute the maximum of the integer affine expression C<obj>
1646 over the points in C<set>, returning the result in C<opt>.
1647 The return value may be one of C<isl_lp_error>,
1648 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1650 =item * Parametric optimization
1652 __isl_give isl_pw_aff *isl_set_dim_max(
1653 __isl_take isl_set *set, int pos);
1655 Compute the maximum of the given set dimension as a function of the
1656 parameters, but independently of the other set dimensions.
1657 For lexicographic optimization, see L<"Lexicographic Optimization">.
1661 The following functions compute either the set of (rational) coefficient
1662 values of valid constraints for the given set or the set of (rational)
1663 values satisfying the constraints with coefficients from the given set.
1664 Internally, these two sets of functions perform essentially the
1665 same operations, except that the set of coefficients is assumed to
1666 be a cone, while the set of values may be any polyhedron.
1667 The current implementation is based on the Farkas lemma and
1668 Fourier-Motzkin elimination, but this may change or be made optional
1669 in future. In particular, future implementations may use different
1670 dualization algorithms or skip the elimination step.
1672 __isl_give isl_basic_set *isl_basic_set_coefficients(
1673 __isl_take isl_basic_set *bset);
1674 __isl_give isl_basic_set *isl_set_coefficients(
1675 __isl_take isl_set *set);
1676 __isl_give isl_union_set *isl_union_set_coefficients(
1677 __isl_take isl_union_set *bset);
1678 __isl_give isl_basic_set *isl_basic_set_solutions(
1679 __isl_take isl_basic_set *bset);
1680 __isl_give isl_basic_set *isl_set_solutions(
1681 __isl_take isl_set *set);
1682 __isl_give isl_union_set *isl_union_set_solutions(
1683 __isl_take isl_union_set *bset);
1687 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1689 __isl_give isl_union_map *isl_union_map_power(
1690 __isl_take isl_union_map *umap, int *exact);
1692 Compute a parametric representation for all positive powers I<k> of C<map>.
1693 The result maps I<k> to a nested relation corresponding to the
1694 I<k>th power of C<map>.
1695 The result may be an overapproximation. If the result is known to be exact,
1696 then C<*exact> is set to C<1>.
1698 =item * Transitive closure
1700 __isl_give isl_map *isl_map_transitive_closure(
1701 __isl_take isl_map *map, int *exact);
1702 __isl_give isl_union_map *isl_union_map_transitive_closure(
1703 __isl_take isl_union_map *umap, int *exact);
1705 Compute the transitive closure of C<map>.
1706 The result may be an overapproximation. If the result is known to be exact,
1707 then C<*exact> is set to C<1>.
1709 =item * Reaching path lengths
1711 __isl_give isl_map *isl_map_reaching_path_lengths(
1712 __isl_take isl_map *map, int *exact);
1714 Compute a relation that maps each element in the range of C<map>
1715 to the lengths of all paths composed of edges in C<map> that
1716 end up in the given element.
1717 The result may be an overapproximation. If the result is known to be exact,
1718 then C<*exact> is set to C<1>.
1719 To compute the I<maximal> path length, the resulting relation
1720 should be postprocessed by C<isl_map_lexmax>.
1721 In particular, if the input relation is a dependence relation
1722 (mapping sources to sinks), then the maximal path length corresponds
1723 to the free schedule.
1724 Note, however, that C<isl_map_lexmax> expects the maximum to be
1725 finite, so if the path lengths are unbounded (possibly due to
1726 the overapproximation), then you will get an error message.
1730 __isl_give isl_basic_set *isl_basic_map_wrap(
1731 __isl_take isl_basic_map *bmap);
1732 __isl_give isl_set *isl_map_wrap(
1733 __isl_take isl_map *map);
1734 __isl_give isl_union_set *isl_union_map_wrap(
1735 __isl_take isl_union_map *umap);
1736 __isl_give isl_basic_map *isl_basic_set_unwrap(
1737 __isl_take isl_basic_set *bset);
1738 __isl_give isl_map *isl_set_unwrap(
1739 __isl_take isl_set *set);
1740 __isl_give isl_union_map *isl_union_set_unwrap(
1741 __isl_take isl_union_set *uset);
1745 Remove any internal structure of domain (and range) of the given
1746 set or relation. If there is any such internal structure in the input,
1747 then the name of the space is also removed.
1749 __isl_give isl_basic_set *isl_basic_set_flatten(
1750 __isl_take isl_basic_set *bset);
1751 __isl_give isl_set *isl_set_flatten(
1752 __isl_take isl_set *set);
1753 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1754 __isl_take isl_basic_map *bmap);
1755 __isl_give isl_map *isl_map_flatten_range(
1756 __isl_take isl_map *map);
1757 __isl_give isl_basic_map *isl_basic_map_flatten(
1758 __isl_take isl_basic_map *bmap);
1759 __isl_give isl_map *isl_map_flatten(
1760 __isl_take isl_map *map);
1762 __isl_give isl_map *isl_set_flatten_map(
1763 __isl_take isl_set *set);
1765 The function above constructs a relation
1766 that maps the input set to a flattened version of the set.
1770 Lift the input set to a space with extra dimensions corresponding
1771 to the existentially quantified variables in the input.
1772 In particular, the result lives in a wrapped map where the domain
1773 is the original space and the range corresponds to the original
1774 existentially quantified variables.
1776 __isl_give isl_basic_set *isl_basic_set_lift(
1777 __isl_take isl_basic_set *bset);
1778 __isl_give isl_set *isl_set_lift(
1779 __isl_take isl_set *set);
1780 __isl_give isl_union_set *isl_union_set_lift(
1781 __isl_take isl_union_set *uset);
1783 =item * Internal Product
1785 __isl_give isl_basic_map *isl_basic_map_zip(
1786 __isl_take isl_basic_map *bmap);
1787 __isl_give isl_map *isl_map_zip(
1788 __isl_take isl_map *map);
1789 __isl_give isl_union_map *isl_union_map_zip(
1790 __isl_take isl_union_map *umap);
1792 Given a relation with nested relations for domain and range,
1793 interchange the range of the domain with the domain of the range.
1795 =item * Aligning parameters
1797 __isl_give isl_set *isl_set_align_params(
1798 __isl_take isl_set *set,
1799 __isl_take isl_dim *model);
1800 __isl_give isl_map *isl_map_align_params(
1801 __isl_take isl_map *map,
1802 __isl_take isl_dim *model);
1804 Change the order of the parameters of the given set or relation
1805 such that the first parameters match those of C<model>.
1806 This may involve the introduction of extra parameters.
1807 All parameters need to be named.
1809 =item * Dimension manipulation
1811 __isl_give isl_set *isl_set_add_dims(
1812 __isl_take isl_set *set,
1813 enum isl_dim_type type, unsigned n);
1814 __isl_give isl_map *isl_map_add_dims(
1815 __isl_take isl_map *map,
1816 enum isl_dim_type type, unsigned n);
1818 It is usually not advisable to directly change the (input or output)
1819 space of a set or a relation as this removes the name and the internal
1820 structure of the space. However, the above functions can be useful
1821 to add new parameters, assuming
1822 C<isl_set_align_params> and C<isl_map_align_params>
1827 =head2 Binary Operations
1829 The two arguments of a binary operation not only need to live
1830 in the same C<isl_ctx>, they currently also need to have
1831 the same (number of) parameters.
1833 =head3 Basic Operations
1837 =item * Intersection
1839 __isl_give isl_basic_set *isl_basic_set_intersect(
1840 __isl_take isl_basic_set *bset1,
1841 __isl_take isl_basic_set *bset2);
1842 __isl_give isl_set *isl_set_intersect_params(
1843 __isl_take isl_set *set,
1844 __isl_take isl_set *params);
1845 __isl_give isl_set *isl_set_intersect(
1846 __isl_take isl_set *set1,
1847 __isl_take isl_set *set2);
1848 __isl_give isl_union_set *isl_union_set_intersect(
1849 __isl_take isl_union_set *uset1,
1850 __isl_take isl_union_set *uset2);
1851 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1852 __isl_take isl_basic_map *bmap,
1853 __isl_take isl_basic_set *bset);
1854 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1855 __isl_take isl_basic_map *bmap,
1856 __isl_take isl_basic_set *bset);
1857 __isl_give isl_basic_map *isl_basic_map_intersect(
1858 __isl_take isl_basic_map *bmap1,
1859 __isl_take isl_basic_map *bmap2);
1860 __isl_give isl_map *isl_map_intersect_params(
1861 __isl_take isl_map *map,
1862 __isl_take isl_set *params);
1863 __isl_give isl_map *isl_map_intersect_domain(
1864 __isl_take isl_map *map,
1865 __isl_take isl_set *set);
1866 __isl_give isl_map *isl_map_intersect_range(
1867 __isl_take isl_map *map,
1868 __isl_take isl_set *set);
1869 __isl_give isl_map *isl_map_intersect(
1870 __isl_take isl_map *map1,
1871 __isl_take isl_map *map2);
1872 __isl_give isl_union_map *isl_union_map_intersect_domain(
1873 __isl_take isl_union_map *umap,
1874 __isl_take isl_union_set *uset);
1875 __isl_give isl_union_map *isl_union_map_intersect_range(
1876 __isl_take isl_union_map *umap,
1877 __isl_take isl_union_set *uset);
1878 __isl_give isl_union_map *isl_union_map_intersect(
1879 __isl_take isl_union_map *umap1,
1880 __isl_take isl_union_map *umap2);
1884 __isl_give isl_set *isl_basic_set_union(
1885 __isl_take isl_basic_set *bset1,
1886 __isl_take isl_basic_set *bset2);
1887 __isl_give isl_map *isl_basic_map_union(
1888 __isl_take isl_basic_map *bmap1,
1889 __isl_take isl_basic_map *bmap2);
1890 __isl_give isl_set *isl_set_union(
1891 __isl_take isl_set *set1,
1892 __isl_take isl_set *set2);
1893 __isl_give isl_map *isl_map_union(
1894 __isl_take isl_map *map1,
1895 __isl_take isl_map *map2);
1896 __isl_give isl_union_set *isl_union_set_union(
1897 __isl_take isl_union_set *uset1,
1898 __isl_take isl_union_set *uset2);
1899 __isl_give isl_union_map *isl_union_map_union(
1900 __isl_take isl_union_map *umap1,
1901 __isl_take isl_union_map *umap2);
1903 =item * Set difference
1905 __isl_give isl_set *isl_set_subtract(
1906 __isl_take isl_set *set1,
1907 __isl_take isl_set *set2);
1908 __isl_give isl_map *isl_map_subtract(
1909 __isl_take isl_map *map1,
1910 __isl_take isl_map *map2);
1911 __isl_give isl_union_set *isl_union_set_subtract(
1912 __isl_take isl_union_set *uset1,
1913 __isl_take isl_union_set *uset2);
1914 __isl_give isl_union_map *isl_union_map_subtract(
1915 __isl_take isl_union_map *umap1,
1916 __isl_take isl_union_map *umap2);
1920 __isl_give isl_basic_set *isl_basic_set_apply(
1921 __isl_take isl_basic_set *bset,
1922 __isl_take isl_basic_map *bmap);
1923 __isl_give isl_set *isl_set_apply(
1924 __isl_take isl_set *set,
1925 __isl_take isl_map *map);
1926 __isl_give isl_union_set *isl_union_set_apply(
1927 __isl_take isl_union_set *uset,
1928 __isl_take isl_union_map *umap);
1929 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1930 __isl_take isl_basic_map *bmap1,
1931 __isl_take isl_basic_map *bmap2);
1932 __isl_give isl_basic_map *isl_basic_map_apply_range(
1933 __isl_take isl_basic_map *bmap1,
1934 __isl_take isl_basic_map *bmap2);
1935 __isl_give isl_map *isl_map_apply_domain(
1936 __isl_take isl_map *map1,
1937 __isl_take isl_map *map2);
1938 __isl_give isl_union_map *isl_union_map_apply_domain(
1939 __isl_take isl_union_map *umap1,
1940 __isl_take isl_union_map *umap2);
1941 __isl_give isl_map *isl_map_apply_range(
1942 __isl_take isl_map *map1,
1943 __isl_take isl_map *map2);
1944 __isl_give isl_union_map *isl_union_map_apply_range(
1945 __isl_take isl_union_map *umap1,
1946 __isl_take isl_union_map *umap2);
1948 =item * Cartesian Product
1950 __isl_give isl_set *isl_set_product(
1951 __isl_take isl_set *set1,
1952 __isl_take isl_set *set2);
1953 __isl_give isl_union_set *isl_union_set_product(
1954 __isl_take isl_union_set *uset1,
1955 __isl_take isl_union_set *uset2);
1956 __isl_give isl_basic_map *isl_basic_map_range_product(
1957 __isl_take isl_basic_map *bmap1,
1958 __isl_take isl_basic_map *bmap2);
1959 __isl_give isl_map *isl_map_range_product(
1960 __isl_take isl_map *map1,
1961 __isl_take isl_map *map2);
1962 __isl_give isl_union_map *isl_union_map_range_product(
1963 __isl_take isl_union_map *umap1,
1964 __isl_take isl_union_map *umap2);
1965 __isl_give isl_map *isl_map_product(
1966 __isl_take isl_map *map1,
1967 __isl_take isl_map *map2);
1968 __isl_give isl_union_map *isl_union_map_product(
1969 __isl_take isl_union_map *umap1,
1970 __isl_take isl_union_map *umap2);
1972 The above functions compute the cross product of the given
1973 sets or relations. The domains and ranges of the results
1974 are wrapped maps between domains and ranges of the inputs.
1975 To obtain a ``flat'' product, use the following functions
1978 __isl_give isl_basic_set *isl_basic_set_flat_product(
1979 __isl_take isl_basic_set *bset1,
1980 __isl_take isl_basic_set *bset2);
1981 __isl_give isl_set *isl_set_flat_product(
1982 __isl_take isl_set *set1,
1983 __isl_take isl_set *set2);
1984 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1985 __isl_take isl_basic_map *bmap1,
1986 __isl_take isl_basic_map *bmap2);
1987 __isl_give isl_map *isl_map_flat_range_product(
1988 __isl_take isl_map *map1,
1989 __isl_take isl_map *map2);
1990 __isl_give isl_union_map *isl_union_map_flat_range_product(
1991 __isl_take isl_union_map *umap1,
1992 __isl_take isl_union_map *umap2);
1993 __isl_give isl_basic_map *isl_basic_map_flat_product(
1994 __isl_take isl_basic_map *bmap1,
1995 __isl_take isl_basic_map *bmap2);
1996 __isl_give isl_map *isl_map_flat_product(
1997 __isl_take isl_map *map1,
1998 __isl_take isl_map *map2);
2000 =item * Simplification
2002 __isl_give isl_basic_set *isl_basic_set_gist(
2003 __isl_take isl_basic_set *bset,
2004 __isl_take isl_basic_set *context);
2005 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2006 __isl_take isl_set *context);
2007 __isl_give isl_union_set *isl_union_set_gist(
2008 __isl_take isl_union_set *uset,
2009 __isl_take isl_union_set *context);
2010 __isl_give isl_basic_map *isl_basic_map_gist(
2011 __isl_take isl_basic_map *bmap,
2012 __isl_take isl_basic_map *context);
2013 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2014 __isl_take isl_map *context);
2015 __isl_give isl_union_map *isl_union_map_gist(
2016 __isl_take isl_union_map *umap,
2017 __isl_take isl_union_map *context);
2019 The gist operation returns a set or relation that has the
2020 same intersection with the context as the input set or relation.
2021 Any implicit equality in the intersection is made explicit in the result,
2022 while all inequalities that are redundant with respect to the intersection
2024 In case of union sets and relations, the gist operation is performed
2029 =head3 Lexicographic Optimization
2031 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2032 the following functions
2033 compute a set that contains the lexicographic minimum or maximum
2034 of the elements in C<set> (or C<bset>) for those values of the parameters
2035 that satisfy C<dom>.
2036 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2037 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2039 In other words, the union of the parameter values
2040 for which the result is non-empty and of C<*empty>
2043 __isl_give isl_set *isl_basic_set_partial_lexmin(
2044 __isl_take isl_basic_set *bset,
2045 __isl_take isl_basic_set *dom,
2046 __isl_give isl_set **empty);
2047 __isl_give isl_set *isl_basic_set_partial_lexmax(
2048 __isl_take isl_basic_set *bset,
2049 __isl_take isl_basic_set *dom,
2050 __isl_give isl_set **empty);
2051 __isl_give isl_set *isl_set_partial_lexmin(
2052 __isl_take isl_set *set, __isl_take isl_set *dom,
2053 __isl_give isl_set **empty);
2054 __isl_give isl_set *isl_set_partial_lexmax(
2055 __isl_take isl_set *set, __isl_take isl_set *dom,
2056 __isl_give isl_set **empty);
2058 Given a (basic) set C<set> (or C<bset>), the following functions simply
2059 return a set containing the lexicographic minimum or maximum
2060 of the elements in C<set> (or C<bset>).
2061 In case of union sets, the optimum is computed per space.
2063 __isl_give isl_set *isl_basic_set_lexmin(
2064 __isl_take isl_basic_set *bset);
2065 __isl_give isl_set *isl_basic_set_lexmax(
2066 __isl_take isl_basic_set *bset);
2067 __isl_give isl_set *isl_set_lexmin(
2068 __isl_take isl_set *set);
2069 __isl_give isl_set *isl_set_lexmax(
2070 __isl_take isl_set *set);
2071 __isl_give isl_union_set *isl_union_set_lexmin(
2072 __isl_take isl_union_set *uset);
2073 __isl_give isl_union_set *isl_union_set_lexmax(
2074 __isl_take isl_union_set *uset);
2076 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2077 the following functions
2078 compute a relation that maps each element of C<dom>
2079 to the single lexicographic minimum or maximum
2080 of the elements that are associated to that same
2081 element in C<map> (or C<bmap>).
2082 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2083 that contains the elements in C<dom> that do not map
2084 to any elements in C<map> (or C<bmap>).
2085 In other words, the union of the domain of the result and of C<*empty>
2088 __isl_give isl_map *isl_basic_map_partial_lexmax(
2089 __isl_take isl_basic_map *bmap,
2090 __isl_take isl_basic_set *dom,
2091 __isl_give isl_set **empty);
2092 __isl_give isl_map *isl_basic_map_partial_lexmin(
2093 __isl_take isl_basic_map *bmap,
2094 __isl_take isl_basic_set *dom,
2095 __isl_give isl_set **empty);
2096 __isl_give isl_map *isl_map_partial_lexmax(
2097 __isl_take isl_map *map, __isl_take isl_set *dom,
2098 __isl_give isl_set **empty);
2099 __isl_give isl_map *isl_map_partial_lexmin(
2100 __isl_take isl_map *map, __isl_take isl_set *dom,
2101 __isl_give isl_set **empty);
2103 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2104 return a map mapping each element in the domain of
2105 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2106 of all elements associated to that element.
2107 In case of union relations, the optimum is computed per space.
2109 __isl_give isl_map *isl_basic_map_lexmin(
2110 __isl_take isl_basic_map *bmap);
2111 __isl_give isl_map *isl_basic_map_lexmax(
2112 __isl_take isl_basic_map *bmap);
2113 __isl_give isl_map *isl_map_lexmin(
2114 __isl_take isl_map *map);
2115 __isl_give isl_map *isl_map_lexmax(
2116 __isl_take isl_map *map);
2117 __isl_give isl_union_map *isl_union_map_lexmin(
2118 __isl_take isl_union_map *umap);
2119 __isl_give isl_union_map *isl_union_map_lexmax(
2120 __isl_take isl_union_map *umap);
2124 Lists are defined over several element types, including
2125 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2126 Here we take lists of C<isl_set>s as an example.
2127 Lists can be created, copied and freed using the following functions.
2129 #include <isl/list.h>
2130 __isl_give isl_set_list *isl_set_list_alloc(
2131 isl_ctx *ctx, int n);
2132 __isl_give isl_set_list *isl_set_list_copy(
2133 __isl_keep isl_set_list *list);
2134 __isl_give isl_set_list *isl_set_list_add(
2135 __isl_take isl_set_list *list,
2136 __isl_take isl_set *el);
2137 void isl_set_list_free(__isl_take isl_set_list *list);
2139 C<isl_set_list_alloc> creates an empty list with a capacity for
2142 Lists can be inspected using the following functions.
2144 #include <isl/list.h>
2145 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2146 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2147 __isl_give struct isl_set *isl_set_list_get_set(
2148 __isl_keep isl_set_list *list, int index);
2149 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2150 int (*fn)(__isl_take struct isl_set *el, void *user),
2153 Lists can be printed using
2155 #include <isl/list.h>
2156 __isl_give isl_printer *isl_printer_print_set_list(
2157 __isl_take isl_printer *p,
2158 __isl_keep isl_set_list *list);
2162 Matrices can be created, copied and freed using the following functions.
2164 #include <isl/mat.h>
2165 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2166 unsigned n_row, unsigned n_col);
2167 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2168 void isl_mat_free(__isl_take isl_mat *mat);
2170 Note that the elements of a newly created matrix may have arbitrary values.
2171 The elements can be changed and inspected using the following functions.
2173 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2174 int isl_mat_rows(__isl_keep isl_mat *mat);
2175 int isl_mat_cols(__isl_keep isl_mat *mat);
2176 int isl_mat_get_element(__isl_keep isl_mat *mat,
2177 int row, int col, isl_int *v);
2178 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2179 int row, int col, isl_int v);
2180 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2181 int row, int col, int v);
2183 C<isl_mat_get_element> will return a negative value if anything went wrong.
2184 In that case, the value of C<*v> is undefined.
2186 The following function can be used to compute the (right) inverse
2187 of a matrix, i.e., a matrix such that the product of the original
2188 and the inverse (in that order) is a multiple of the identity matrix.
2189 The input matrix is assumed to be of full row-rank.
2191 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2193 The following function can be used to compute the (right) kernel
2194 (or null space) of a matrix, i.e., a matrix such that the product of
2195 the original and the kernel (in that order) is the zero matrix.
2197 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2199 =head2 Piecewise Quasi Affine Expressions
2201 The zero quasi affine expression can be created using
2203 __isl_give isl_aff *isl_aff_zero(
2204 __isl_take isl_local_space *ls);
2206 A quasi affine expression can also be initialized from an C<isl_div>:
2208 #include <isl/div.h>
2209 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2211 An empty piecewise quasi affine expression (one with no cells)
2212 or a piecewise quasi affine expression with a single cell can
2213 be created using the following functions.
2215 #include <isl/aff.h>
2216 __isl_give isl_pw_aff *isl_pw_aff_empty(
2217 __isl_take isl_dim *dim);
2218 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2219 __isl_take isl_set *set, __isl_take isl_aff *aff);
2221 Quasi affine expressions can be copied and freed using
2223 #include <isl/aff.h>
2224 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2225 void *isl_aff_free(__isl_take isl_aff *aff);
2227 __isl_give isl_pw_aff *isl_pw_aff_copy(
2228 __isl_keep isl_pw_aff *pwaff);
2229 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2231 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2232 using the following function. The constraint is required to have
2233 a non-zero coefficient for the specified dimension.
2235 #include <isl/constraint.h>
2236 __isl_give isl_aff *isl_constraint_get_bound(
2237 __isl_keep isl_constraint *constraint,
2238 enum isl_dim_type type, int pos);
2240 The entire affine expression of the constraint can also be extracted
2241 using the following function.
2243 #include <isl/constraint.h>
2244 __isl_give isl_aff *isl_constraint_get_aff(
2245 __isl_keep isl_constraint *constraint);
2247 Conversely, an equality constraint equating
2248 the affine expression to zero or an inequality constraint enforcing
2249 the affine expression to be non-negative, can be constructed using
2251 __isl_give isl_constraint *isl_equality_from_aff(
2252 __isl_take isl_aff *aff);
2253 __isl_give isl_constraint *isl_inequality_from_aff(
2254 __isl_take isl_aff *aff);
2256 The expression can be inspected using
2258 #include <isl/aff.h>
2259 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2260 int isl_aff_dim(__isl_keep isl_aff *aff,
2261 enum isl_dim_type type);
2262 __isl_give isl_local_space *isl_aff_get_local_space(
2263 __isl_keep isl_aff *aff);
2264 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2265 enum isl_dim_type type, unsigned pos);
2266 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2268 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2269 enum isl_dim_type type, int pos, isl_int *v);
2270 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2272 __isl_give isl_div *isl_aff_get_div(
2273 __isl_keep isl_aff *aff, int pos);
2275 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2276 enum isl_dim_type type, unsigned first, unsigned n);
2277 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2278 enum isl_dim_type type, unsigned first, unsigned n);
2280 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2281 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2282 enum isl_dim_type type);
2283 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2285 It can be modified using
2287 #include <isl/aff.h>
2288 __isl_give isl_aff *isl_aff_set_dim_name(
2289 __isl_take isl_aff *aff, enum isl_dim_type type,
2290 unsigned pos, const char *s);
2291 __isl_give isl_aff *isl_aff_set_constant(
2292 __isl_take isl_aff *aff, isl_int v);
2293 __isl_give isl_aff *isl_aff_set_constant_si(
2294 __isl_take isl_aff *aff, int v);
2295 __isl_give isl_aff *isl_aff_set_coefficient(
2296 __isl_take isl_aff *aff,
2297 enum isl_dim_type type, int pos, isl_int v);
2298 __isl_give isl_aff *isl_aff_set_coefficient_si(
2299 __isl_take isl_aff *aff,
2300 enum isl_dim_type type, int pos, int v);
2301 __isl_give isl_aff *isl_aff_set_denominator(
2302 __isl_take isl_aff *aff, isl_int v);
2304 __isl_give isl_aff *isl_aff_add_constant(
2305 __isl_take isl_aff *aff, isl_int v);
2306 __isl_give isl_aff *isl_aff_add_constant_si(
2307 __isl_take isl_aff *aff, int v);
2308 __isl_give isl_aff *isl_aff_add_coefficient(
2309 __isl_take isl_aff *aff,
2310 enum isl_dim_type type, int pos, isl_int v);
2311 __isl_give isl_aff *isl_aff_add_coefficient_si(
2312 __isl_take isl_aff *aff,
2313 enum isl_dim_type type, int pos, int v);
2315 __isl_give isl_aff *isl_aff_insert_dims(
2316 __isl_take isl_aff *aff,
2317 enum isl_dim_type type, unsigned first, unsigned n);
2318 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2319 __isl_take isl_pw_aff *pwaff,
2320 enum isl_dim_type type, unsigned first, unsigned n);
2321 __isl_give isl_aff *isl_aff_add_dims(
2322 __isl_take isl_aff *aff,
2323 enum isl_dim_type type, unsigned n);
2324 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2325 __isl_take isl_pw_aff *pwaff,
2326 enum isl_dim_type type, unsigned n);
2327 __isl_give isl_aff *isl_aff_drop_dims(
2328 __isl_take isl_aff *aff,
2329 enum isl_dim_type type, unsigned first, unsigned n);
2330 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2331 __isl_take isl_pw_aff *pwaff,
2332 enum isl_dim_type type, unsigned first, unsigned n);
2334 Note that the C<set_constant> and C<set_coefficient> functions
2335 set the I<numerator> of the constant or coefficient, while
2336 C<add_constant> and C<add_coefficient> add an integer value to
2337 the possibly rational constant or coefficient.
2339 To check whether an affine expressions is obviously zero
2340 or obviously equal to some other affine expression, use
2342 #include <isl/aff.h>
2343 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2344 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2345 __isl_keep isl_aff *aff2);
2349 #include <isl/aff.h>
2350 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2351 __isl_take isl_aff *aff2);
2352 __isl_give isl_pw_aff *isl_pw_aff_add(
2353 __isl_take isl_pw_aff *pwaff1,
2354 __isl_take isl_pw_aff *pwaff2);
2355 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2356 __isl_take isl_aff *aff2);
2357 __isl_give isl_pw_aff *isl_pw_aff_sub(
2358 __isl_take isl_pw_aff *pwaff1,
2359 __isl_take isl_pw_aff *pwaff2);
2360 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2361 __isl_give isl_pw_aff *isl_pw_aff_neg(
2362 __isl_take isl_pw_aff *pwaff);
2363 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2364 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2365 __isl_take isl_pw_aff *pwaff);
2366 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2367 __isl_give isl_pw_aff *isl_pw_aff_floor(
2368 __isl_take isl_pw_aff *pwaff);
2369 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2371 __isl_give isl_pw_aff *isl_pw_aff_scale(
2372 __isl_take isl_pw_aff *pwaff, isl_int f);
2373 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2375 __isl_give isl_aff *isl_aff_scale_down_ui(
2376 __isl_take isl_aff *aff, unsigned f);
2377 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2378 __isl_take isl_pw_aff *pwaff, isl_int f);
2380 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2381 __isl_take isl_pw_aff *pwqp);
2383 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2384 __isl_take isl_pw_aff *pwaff,
2385 __isl_take isl_dim *model);
2387 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2388 __isl_take isl_set *context);
2389 __isl_give isl_pw_aff *isl_pw_aff_gist(
2390 __isl_take isl_pw_aff *pwaff,
2391 __isl_take isl_set *context);
2393 __isl_give isl_set *isl_pw_aff_domain(
2394 __isl_take isl_pw_aff *pwaff);
2396 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2397 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2398 __isl_give isl_set *isl_pw_aff_eq_set(
2399 __isl_take isl_pw_aff *pwaff1,
2400 __isl_take isl_pw_aff *pwaff2);
2401 __isl_give isl_set *isl_pw_aff_le_set(
2402 __isl_take isl_pw_aff *pwaff1,
2403 __isl_take isl_pw_aff *pwaff2);
2404 __isl_give isl_set *isl_pw_aff_lt_set(
2405 __isl_take isl_pw_aff *pwaff1,
2406 __isl_take isl_pw_aff *pwaff2);
2407 __isl_give isl_set *isl_pw_aff_ge_set(
2408 __isl_take isl_pw_aff *pwaff1,
2409 __isl_take isl_pw_aff *pwaff2);
2410 __isl_give isl_set *isl_pw_aff_gt_set(
2411 __isl_take isl_pw_aff *pwaff1,
2412 __isl_take isl_pw_aff *pwaff2);
2414 The function C<isl_aff_ge_basic_set> returns a basic set
2415 containing those elements in the shared space
2416 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2417 The function C<isl_aff_ge_set> returns a set
2418 containing those elements in the shared domain
2419 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2421 #include <isl/aff.h>
2422 __isl_give isl_set *isl_pw_aff_nonneg_set(
2423 __isl_take isl_pw_aff *pwaff);
2425 The function C<isl_pw_aff_nonneg_set> returns a set
2426 containing those elements in the domain
2427 of C<pwaff> where C<pwaff> is non-negative.
2429 #include <isl/aff.h>
2430 __isl_give isl_pw_aff *isl_pw_aff_cond(
2431 __isl_take isl_set *cond,
2432 __isl_take isl_pw_aff *pwaff_true,
2433 __isl_take isl_pw_aff *pwaff_false);
2435 The function C<isl_pw_aff_cond> performs a conditional operator
2436 and returns an expression that is equal to C<pwaff_true>
2437 for elements in C<cond> and equal to C<pwaff_false> for elements
2440 #include <isl/aff.h>
2441 __isl_give isl_pw_aff *isl_pw_aff_max(
2442 __isl_take isl_pw_aff *pwaff1,
2443 __isl_take isl_pw_aff *pwaff2);
2445 The function C<isl_pw_aff_max> computes a piecewise quasi-affine
2446 expression with a domain that is the union of those of C<pwaff1> and
2447 C<pwaff2> and such that on each cell, the quasi-affine expression is
2448 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2449 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2450 associated expression is the defined one.
2452 An expression can be printed using
2454 #include <isl/aff.h>
2455 __isl_give isl_printer *isl_printer_print_aff(
2456 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2458 __isl_give isl_printer *isl_printer_print_pw_aff(
2459 __isl_take isl_printer *p,
2460 __isl_keep isl_pw_aff *pwaff);
2464 Points are elements of a set. They can be used to construct
2465 simple sets (boxes) or they can be used to represent the
2466 individual elements of a set.
2467 The zero point (the origin) can be created using
2469 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2471 The coordinates of a point can be inspected, set and changed
2474 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2475 enum isl_dim_type type, int pos, isl_int *v);
2476 __isl_give isl_point *isl_point_set_coordinate(
2477 __isl_take isl_point *pnt,
2478 enum isl_dim_type type, int pos, isl_int v);
2480 __isl_give isl_point *isl_point_add_ui(
2481 __isl_take isl_point *pnt,
2482 enum isl_dim_type type, int pos, unsigned val);
2483 __isl_give isl_point *isl_point_sub_ui(
2484 __isl_take isl_point *pnt,
2485 enum isl_dim_type type, int pos, unsigned val);
2487 Other properties can be obtained using
2489 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2491 Points can be copied or freed using
2493 __isl_give isl_point *isl_point_copy(
2494 __isl_keep isl_point *pnt);
2495 void isl_point_free(__isl_take isl_point *pnt);
2497 A singleton set can be created from a point using
2499 __isl_give isl_basic_set *isl_basic_set_from_point(
2500 __isl_take isl_point *pnt);
2501 __isl_give isl_set *isl_set_from_point(
2502 __isl_take isl_point *pnt);
2504 and a box can be created from two opposite extremal points using
2506 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2507 __isl_take isl_point *pnt1,
2508 __isl_take isl_point *pnt2);
2509 __isl_give isl_set *isl_set_box_from_points(
2510 __isl_take isl_point *pnt1,
2511 __isl_take isl_point *pnt2);
2513 All elements of a B<bounded> (union) set can be enumerated using
2514 the following functions.
2516 int isl_set_foreach_point(__isl_keep isl_set *set,
2517 int (*fn)(__isl_take isl_point *pnt, void *user),
2519 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2520 int (*fn)(__isl_take isl_point *pnt, void *user),
2523 The function C<fn> is called for each integer point in
2524 C<set> with as second argument the last argument of
2525 the C<isl_set_foreach_point> call. The function C<fn>
2526 should return C<0> on success and C<-1> on failure.
2527 In the latter case, C<isl_set_foreach_point> will stop
2528 enumerating and return C<-1> as well.
2529 If the enumeration is performed successfully and to completion,
2530 then C<isl_set_foreach_point> returns C<0>.
2532 To obtain a single point of a (basic) set, use
2534 __isl_give isl_point *isl_basic_set_sample_point(
2535 __isl_take isl_basic_set *bset);
2536 __isl_give isl_point *isl_set_sample_point(
2537 __isl_take isl_set *set);
2539 If C<set> does not contain any (integer) points, then the
2540 resulting point will be ``void'', a property that can be
2543 int isl_point_is_void(__isl_keep isl_point *pnt);
2545 =head2 Piecewise Quasipolynomials
2547 A piecewise quasipolynomial is a particular kind of function that maps
2548 a parametric point to a rational value.
2549 More specifically, a quasipolynomial is a polynomial expression in greatest
2550 integer parts of affine expressions of parameters and variables.
2551 A piecewise quasipolynomial is a subdivision of a given parametric
2552 domain into disjoint cells with a quasipolynomial associated to
2553 each cell. The value of the piecewise quasipolynomial at a given
2554 point is the value of the quasipolynomial associated to the cell
2555 that contains the point. Outside of the union of cells,
2556 the value is assumed to be zero.
2557 For example, the piecewise quasipolynomial
2559 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2561 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2562 A given piecewise quasipolynomial has a fixed domain dimension.
2563 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2564 defined over different domains.
2565 Piecewise quasipolynomials are mainly used by the C<barvinok>
2566 library for representing the number of elements in a parametric set or map.
2567 For example, the piecewise quasipolynomial above represents
2568 the number of points in the map
2570 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2572 =head3 Printing (Piecewise) Quasipolynomials
2574 Quasipolynomials and piecewise quasipolynomials can be printed
2575 using the following functions.
2577 __isl_give isl_printer *isl_printer_print_qpolynomial(
2578 __isl_take isl_printer *p,
2579 __isl_keep isl_qpolynomial *qp);
2581 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2582 __isl_take isl_printer *p,
2583 __isl_keep isl_pw_qpolynomial *pwqp);
2585 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2586 __isl_take isl_printer *p,
2587 __isl_keep isl_union_pw_qpolynomial *upwqp);
2589 The output format of the printer
2590 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2591 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2593 In case of printing in C<ISL_FORMAT_C>, the user may want
2594 to set the names of all dimensions
2596 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2597 __isl_take isl_qpolynomial *qp,
2598 enum isl_dim_type type, unsigned pos,
2600 __isl_give isl_pw_qpolynomial *
2601 isl_pw_qpolynomial_set_dim_name(
2602 __isl_take isl_pw_qpolynomial *pwqp,
2603 enum isl_dim_type type, unsigned pos,
2606 =head3 Creating New (Piecewise) Quasipolynomials
2608 Some simple quasipolynomials can be created using the following functions.
2609 More complicated quasipolynomials can be created by applying
2610 operations such as addition and multiplication
2611 on the resulting quasipolynomials
2613 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2614 __isl_take isl_dim *dim);
2615 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2616 __isl_take isl_dim *dim);
2617 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2618 __isl_take isl_dim *dim);
2619 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2620 __isl_take isl_dim *dim);
2621 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2622 __isl_take isl_dim *dim);
2623 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2624 __isl_take isl_dim *dim,
2625 const isl_int n, const isl_int d);
2626 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2627 __isl_take isl_div *div);
2628 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2629 __isl_take isl_dim *dim,
2630 enum isl_dim_type type, unsigned pos);
2631 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2632 __isl_take isl_aff *aff);
2634 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2635 with a single cell can be created using the following functions.
2636 Multiple of these single cell piecewise quasipolynomials can
2637 be combined to create more complicated piecewise quasipolynomials.
2639 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2640 __isl_take isl_dim *dim);
2641 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2642 __isl_take isl_set *set,
2643 __isl_take isl_qpolynomial *qp);
2645 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2646 __isl_take isl_dim *dim);
2647 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2648 __isl_take isl_pw_qpolynomial *pwqp);
2649 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2650 __isl_take isl_union_pw_qpolynomial *upwqp,
2651 __isl_take isl_pw_qpolynomial *pwqp);
2653 Quasipolynomials can be copied and freed again using the following
2656 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2657 __isl_keep isl_qpolynomial *qp);
2658 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2660 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2661 __isl_keep isl_pw_qpolynomial *pwqp);
2662 void *isl_pw_qpolynomial_free(
2663 __isl_take isl_pw_qpolynomial *pwqp);
2665 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2666 __isl_keep isl_union_pw_qpolynomial *upwqp);
2667 void isl_union_pw_qpolynomial_free(
2668 __isl_take isl_union_pw_qpolynomial *upwqp);
2670 =head3 Inspecting (Piecewise) Quasipolynomials
2672 To iterate over all piecewise quasipolynomials in a union
2673 piecewise quasipolynomial, use the following function
2675 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2676 __isl_keep isl_union_pw_qpolynomial *upwqp,
2677 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2680 To extract the piecewise quasipolynomial from a union with a given dimension
2683 __isl_give isl_pw_qpolynomial *
2684 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2685 __isl_keep isl_union_pw_qpolynomial *upwqp,
2686 __isl_take isl_dim *dim);
2688 To iterate over the cells in a piecewise quasipolynomial,
2689 use either of the following two functions
2691 int isl_pw_qpolynomial_foreach_piece(
2692 __isl_keep isl_pw_qpolynomial *pwqp,
2693 int (*fn)(__isl_take isl_set *set,
2694 __isl_take isl_qpolynomial *qp,
2695 void *user), void *user);
2696 int isl_pw_qpolynomial_foreach_lifted_piece(
2697 __isl_keep isl_pw_qpolynomial *pwqp,
2698 int (*fn)(__isl_take isl_set *set,
2699 __isl_take isl_qpolynomial *qp,
2700 void *user), void *user);
2702 As usual, the function C<fn> should return C<0> on success
2703 and C<-1> on failure. The difference between
2704 C<isl_pw_qpolynomial_foreach_piece> and
2705 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2706 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2707 compute unique representations for all existentially quantified
2708 variables and then turn these existentially quantified variables
2709 into extra set variables, adapting the associated quasipolynomial
2710 accordingly. This means that the C<set> passed to C<fn>
2711 will not have any existentially quantified variables, but that
2712 the dimensions of the sets may be different for different
2713 invocations of C<fn>.
2715 To iterate over all terms in a quasipolynomial,
2718 int isl_qpolynomial_foreach_term(
2719 __isl_keep isl_qpolynomial *qp,
2720 int (*fn)(__isl_take isl_term *term,
2721 void *user), void *user);
2723 The terms themselves can be inspected and freed using
2726 unsigned isl_term_dim(__isl_keep isl_term *term,
2727 enum isl_dim_type type);
2728 void isl_term_get_num(__isl_keep isl_term *term,
2730 void isl_term_get_den(__isl_keep isl_term *term,
2732 int isl_term_get_exp(__isl_keep isl_term *term,
2733 enum isl_dim_type type, unsigned pos);
2734 __isl_give isl_div *isl_term_get_div(
2735 __isl_keep isl_term *term, unsigned pos);
2736 void isl_term_free(__isl_take isl_term *term);
2738 Each term is a product of parameters, set variables and
2739 integer divisions. The function C<isl_term_get_exp>
2740 returns the exponent of a given dimensions in the given term.
2741 The C<isl_int>s in the arguments of C<isl_term_get_num>
2742 and C<isl_term_get_den> need to have been initialized
2743 using C<isl_int_init> before calling these functions.
2745 =head3 Properties of (Piecewise) Quasipolynomials
2747 To check whether a quasipolynomial is actually a constant,
2748 use the following function.
2750 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2751 isl_int *n, isl_int *d);
2753 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2754 then the numerator and denominator of the constant
2755 are returned in C<*n> and C<*d>, respectively.
2757 =head3 Operations on (Piecewise) Quasipolynomials
2759 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2760 __isl_take isl_qpolynomial *qp, isl_int v);
2761 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2762 __isl_take isl_qpolynomial *qp);
2763 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2764 __isl_take isl_qpolynomial *qp1,
2765 __isl_take isl_qpolynomial *qp2);
2766 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2767 __isl_take isl_qpolynomial *qp1,
2768 __isl_take isl_qpolynomial *qp2);
2769 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2770 __isl_take isl_qpolynomial *qp1,
2771 __isl_take isl_qpolynomial *qp2);
2772 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2773 __isl_take isl_qpolynomial *qp, unsigned exponent);
2775 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2776 __isl_take isl_pw_qpolynomial *pwqp1,
2777 __isl_take isl_pw_qpolynomial *pwqp2);
2778 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2779 __isl_take isl_pw_qpolynomial *pwqp1,
2780 __isl_take isl_pw_qpolynomial *pwqp2);
2781 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2782 __isl_take isl_pw_qpolynomial *pwqp1,
2783 __isl_take isl_pw_qpolynomial *pwqp2);
2784 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2785 __isl_take isl_pw_qpolynomial *pwqp);
2786 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2787 __isl_take isl_pw_qpolynomial *pwqp1,
2788 __isl_take isl_pw_qpolynomial *pwqp2);
2790 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2791 __isl_take isl_union_pw_qpolynomial *upwqp1,
2792 __isl_take isl_union_pw_qpolynomial *upwqp2);
2793 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2794 __isl_take isl_union_pw_qpolynomial *upwqp1,
2795 __isl_take isl_union_pw_qpolynomial *upwqp2);
2796 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2797 __isl_take isl_union_pw_qpolynomial *upwqp1,
2798 __isl_take isl_union_pw_qpolynomial *upwqp2);
2800 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2801 __isl_take isl_pw_qpolynomial *pwqp,
2802 __isl_take isl_point *pnt);
2804 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2805 __isl_take isl_union_pw_qpolynomial *upwqp,
2806 __isl_take isl_point *pnt);
2808 __isl_give isl_set *isl_pw_qpolynomial_domain(
2809 __isl_take isl_pw_qpolynomial *pwqp);
2810 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2811 __isl_take isl_pw_qpolynomial *pwpq,
2812 __isl_take isl_set *set);
2814 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2815 __isl_take isl_union_pw_qpolynomial *upwqp);
2816 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2817 __isl_take isl_union_pw_qpolynomial *upwpq,
2818 __isl_take isl_union_set *uset);
2820 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2821 __isl_take isl_qpolynomial *qp,
2822 __isl_take isl_dim *model);
2824 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2825 __isl_take isl_union_pw_qpolynomial *upwqp);
2827 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2828 __isl_take isl_qpolynomial *qp,
2829 __isl_take isl_set *context);
2831 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2832 __isl_take isl_pw_qpolynomial *pwqp,
2833 __isl_take isl_set *context);
2835 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2836 __isl_take isl_union_pw_qpolynomial *upwqp,
2837 __isl_take isl_union_set *context);
2839 The gist operation applies the gist operation to each of
2840 the cells in the domain of the input piecewise quasipolynomial.
2841 The context is also exploited
2842 to simplify the quasipolynomials associated to each cell.
2844 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2845 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2846 __isl_give isl_union_pw_qpolynomial *
2847 isl_union_pw_qpolynomial_to_polynomial(
2848 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2850 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2851 the polynomial will be an overapproximation. If C<sign> is negative,
2852 it will be an underapproximation. If C<sign> is zero, the approximation
2853 will lie somewhere in between.
2855 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2857 A piecewise quasipolynomial reduction is a piecewise
2858 reduction (or fold) of quasipolynomials.
2859 In particular, the reduction can be maximum or a minimum.
2860 The objects are mainly used to represent the result of
2861 an upper or lower bound on a quasipolynomial over its domain,
2862 i.e., as the result of the following function.
2864 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2865 __isl_take isl_pw_qpolynomial *pwqp,
2866 enum isl_fold type, int *tight);
2868 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2869 __isl_take isl_union_pw_qpolynomial *upwqp,
2870 enum isl_fold type, int *tight);
2872 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2873 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2874 is the returned bound is known be tight, i.e., for each value
2875 of the parameters there is at least
2876 one element in the domain that reaches the bound.
2877 If the domain of C<pwqp> is not wrapping, then the bound is computed
2878 over all elements in that domain and the result has a purely parametric
2879 domain. If the domain of C<pwqp> is wrapping, then the bound is
2880 computed over the range of the wrapped relation. The domain of the
2881 wrapped relation becomes the domain of the result.
2883 A (piecewise) quasipolynomial reduction can be copied or freed using the
2884 following functions.
2886 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2887 __isl_keep isl_qpolynomial_fold *fold);
2888 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2889 __isl_keep isl_pw_qpolynomial_fold *pwf);
2890 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2891 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2892 void isl_qpolynomial_fold_free(
2893 __isl_take isl_qpolynomial_fold *fold);
2894 void *isl_pw_qpolynomial_fold_free(
2895 __isl_take isl_pw_qpolynomial_fold *pwf);
2896 void isl_union_pw_qpolynomial_fold_free(
2897 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2899 =head3 Printing Piecewise Quasipolynomial Reductions
2901 Piecewise quasipolynomial reductions can be printed
2902 using the following function.
2904 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2905 __isl_take isl_printer *p,
2906 __isl_keep isl_pw_qpolynomial_fold *pwf);
2907 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2908 __isl_take isl_printer *p,
2909 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2911 For C<isl_printer_print_pw_qpolynomial_fold>,
2912 output format of the printer
2913 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2914 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2915 output format of the printer
2916 needs to be set to C<ISL_FORMAT_ISL>.
2917 In case of printing in C<ISL_FORMAT_C>, the user may want
2918 to set the names of all dimensions
2920 __isl_give isl_pw_qpolynomial_fold *
2921 isl_pw_qpolynomial_fold_set_dim_name(
2922 __isl_take isl_pw_qpolynomial_fold *pwf,
2923 enum isl_dim_type type, unsigned pos,
2926 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2928 To iterate over all piecewise quasipolynomial reductions in a union
2929 piecewise quasipolynomial reduction, use the following function
2931 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2932 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2933 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2934 void *user), void *user);
2936 To iterate over the cells in a piecewise quasipolynomial reduction,
2937 use either of the following two functions
2939 int isl_pw_qpolynomial_fold_foreach_piece(
2940 __isl_keep isl_pw_qpolynomial_fold *pwf,
2941 int (*fn)(__isl_take isl_set *set,
2942 __isl_take isl_qpolynomial_fold *fold,
2943 void *user), void *user);
2944 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2945 __isl_keep isl_pw_qpolynomial_fold *pwf,
2946 int (*fn)(__isl_take isl_set *set,
2947 __isl_take isl_qpolynomial_fold *fold,
2948 void *user), void *user);
2950 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2951 of the difference between these two functions.
2953 To iterate over all quasipolynomials in a reduction, use
2955 int isl_qpolynomial_fold_foreach_qpolynomial(
2956 __isl_keep isl_qpolynomial_fold *fold,
2957 int (*fn)(__isl_take isl_qpolynomial *qp,
2958 void *user), void *user);
2960 =head3 Operations on Piecewise Quasipolynomial Reductions
2962 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
2963 __isl_take isl_qpolynomial_fold *fold, isl_int v);
2965 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2966 __isl_take isl_pw_qpolynomial_fold *pwf1,
2967 __isl_take isl_pw_qpolynomial_fold *pwf2);
2969 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2970 __isl_take isl_pw_qpolynomial_fold *pwf1,
2971 __isl_take isl_pw_qpolynomial_fold *pwf2);
2973 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2974 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2975 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2977 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2978 __isl_take isl_pw_qpolynomial_fold *pwf,
2979 __isl_take isl_point *pnt);
2981 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2982 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2983 __isl_take isl_point *pnt);
2985 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2986 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2987 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2988 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2989 __isl_take isl_union_set *uset);
2991 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2992 __isl_take isl_pw_qpolynomial_fold *pwf);
2994 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2995 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2997 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2998 __isl_take isl_pw_qpolynomial_fold *pwf,
2999 __isl_take isl_set *context);
3001 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3002 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3003 __isl_take isl_union_set *context);
3005 The gist operation applies the gist operation to each of
3006 the cells in the domain of the input piecewise quasipolynomial reduction.
3007 In future, the operation will also exploit the context
3008 to simplify the quasipolynomial reductions associated to each cell.
3010 __isl_give isl_pw_qpolynomial_fold *
3011 isl_set_apply_pw_qpolynomial_fold(
3012 __isl_take isl_set *set,
3013 __isl_take isl_pw_qpolynomial_fold *pwf,
3015 __isl_give isl_pw_qpolynomial_fold *
3016 isl_map_apply_pw_qpolynomial_fold(
3017 __isl_take isl_map *map,
3018 __isl_take isl_pw_qpolynomial_fold *pwf,
3020 __isl_give isl_union_pw_qpolynomial_fold *
3021 isl_union_set_apply_union_pw_qpolynomial_fold(
3022 __isl_take isl_union_set *uset,
3023 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3025 __isl_give isl_union_pw_qpolynomial_fold *
3026 isl_union_map_apply_union_pw_qpolynomial_fold(
3027 __isl_take isl_union_map *umap,
3028 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3031 The functions taking a map
3032 compose the given map with the given piecewise quasipolynomial reduction.
3033 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3034 over all elements in the intersection of the range of the map
3035 and the domain of the piecewise quasipolynomial reduction
3036 as a function of an element in the domain of the map.
3037 The functions taking a set compute a bound over all elements in the
3038 intersection of the set and the domain of the
3039 piecewise quasipolynomial reduction.
3041 =head2 Dependence Analysis
3043 C<isl> contains specialized functionality for performing
3044 array dataflow analysis. That is, given a I<sink> access relation
3045 and a collection of possible I<source> access relations,
3046 C<isl> can compute relations that describe
3047 for each iteration of the sink access, which iteration
3048 of which of the source access relations was the last
3049 to access the same data element before the given iteration
3051 To compute standard flow dependences, the sink should be
3052 a read, while the sources should be writes.
3053 If any of the source accesses are marked as being I<may>
3054 accesses, then there will be a dependence to the last
3055 I<must> access B<and> to any I<may> access that follows
3056 this last I<must> access.
3057 In particular, if I<all> sources are I<may> accesses,
3058 then memory based dependence analysis is performed.
3059 If, on the other hand, all sources are I<must> accesses,
3060 then value based dependence analysis is performed.
3062 #include <isl/flow.h>
3064 typedef int (*isl_access_level_before)(void *first, void *second);
3066 __isl_give isl_access_info *isl_access_info_alloc(
3067 __isl_take isl_map *sink,
3068 void *sink_user, isl_access_level_before fn,
3070 __isl_give isl_access_info *isl_access_info_add_source(
3071 __isl_take isl_access_info *acc,
3072 __isl_take isl_map *source, int must,
3074 void isl_access_info_free(__isl_take isl_access_info *acc);
3076 __isl_give isl_flow *isl_access_info_compute_flow(
3077 __isl_take isl_access_info *acc);
3079 int isl_flow_foreach(__isl_keep isl_flow *deps,
3080 int (*fn)(__isl_take isl_map *dep, int must,
3081 void *dep_user, void *user),
3083 __isl_give isl_map *isl_flow_get_no_source(
3084 __isl_keep isl_flow *deps, int must);
3085 void isl_flow_free(__isl_take isl_flow *deps);
3087 The function C<isl_access_info_compute_flow> performs the actual
3088 dependence analysis. The other functions are used to construct
3089 the input for this function or to read off the output.
3091 The input is collected in an C<isl_access_info>, which can
3092 be created through a call to C<isl_access_info_alloc>.
3093 The arguments to this functions are the sink access relation
3094 C<sink>, a token C<sink_user> used to identify the sink
3095 access to the user, a callback function for specifying the
3096 relative order of source and sink accesses, and the number
3097 of source access relations that will be added.
3098 The callback function has type C<int (*)(void *first, void *second)>.
3099 The function is called with two user supplied tokens identifying
3100 either a source or the sink and it should return the shared nesting
3101 level and the relative order of the two accesses.
3102 In particular, let I<n> be the number of loops shared by
3103 the two accesses. If C<first> precedes C<second> textually,
3104 then the function should return I<2 * n + 1>; otherwise,
3105 it should return I<2 * n>.
3106 The sources can be added to the C<isl_access_info> by performing
3107 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3108 C<must> indicates whether the source is a I<must> access
3109 or a I<may> access. Note that a multi-valued access relation
3110 should only be marked I<must> if every iteration in the domain
3111 of the relation accesses I<all> elements in its image.
3112 The C<source_user> token is again used to identify
3113 the source access. The range of the source access relation
3114 C<source> should have the same dimension as the range
3115 of the sink access relation.
3116 The C<isl_access_info_free> function should usually not be
3117 called explicitly, because it is called implicitly by
3118 C<isl_access_info_compute_flow>.
3120 The result of the dependence analysis is collected in an
3121 C<isl_flow>. There may be elements of
3122 the sink access for which no preceding source access could be
3123 found or for which all preceding sources are I<may> accesses.
3124 The relations containing these elements can be obtained through
3125 calls to C<isl_flow_get_no_source>, the first with C<must> set
3126 and the second with C<must> unset.
3127 In the case of standard flow dependence analysis,
3128 with the sink a read and the sources I<must> writes,
3129 the first relation corresponds to the reads from uninitialized
3130 array elements and the second relation is empty.
3131 The actual flow dependences can be extracted using
3132 C<isl_flow_foreach>. This function will call the user-specified
3133 callback function C<fn> for each B<non-empty> dependence between
3134 a source and the sink. The callback function is called
3135 with four arguments, the actual flow dependence relation
3136 mapping source iterations to sink iterations, a boolean that
3137 indicates whether it is a I<must> or I<may> dependence, a token
3138 identifying the source and an additional C<void *> with value
3139 equal to the third argument of the C<isl_flow_foreach> call.
3140 A dependence is marked I<must> if it originates from a I<must>
3141 source and if it is not followed by any I<may> sources.
3143 After finishing with an C<isl_flow>, the user should call
3144 C<isl_flow_free> to free all associated memory.
3146 A higher-level interface to dependence analysis is provided
3147 by the following function.
3149 #include <isl/flow.h>
3151 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3152 __isl_take isl_union_map *must_source,
3153 __isl_take isl_union_map *may_source,
3154 __isl_take isl_union_map *schedule,
3155 __isl_give isl_union_map **must_dep,
3156 __isl_give isl_union_map **may_dep,
3157 __isl_give isl_union_map **must_no_source,
3158 __isl_give isl_union_map **may_no_source);
3160 The arrays are identified by the tuple names of the ranges
3161 of the accesses. The iteration domains by the tuple names
3162 of the domains of the accesses and of the schedule.
3163 The relative order of the iteration domains is given by the
3164 schedule. The relations returned through C<must_no_source>
3165 and C<may_no_source> are subsets of C<sink>.
3166 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3167 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3168 any of the other arguments is treated as an error.
3172 B<The functionality described in this section is fairly new
3173 and may be subject to change.>
3175 The following function can be used to compute a schedule
3176 for a union of domains. The generated schedule respects
3177 all C<validity> dependences. That is, all dependence distances
3178 over these dependences in the scheduled space are lexicographically
3179 positive. The generated schedule schedule also tries to minimize
3180 the dependence distances over C<proximity> dependences.
3181 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3182 for groups of domains where the dependence distances have only
3183 non-negative values.
3184 The algorithm used to construct the schedule is similar to that
3187 #include <isl/schedule.h>
3188 __isl_give isl_schedule *isl_union_set_compute_schedule(
3189 __isl_take isl_union_set *domain,
3190 __isl_take isl_union_map *validity,
3191 __isl_take isl_union_map *proximity);
3192 void *isl_schedule_free(__isl_take isl_schedule *sched);
3194 A mapping from the domains to the scheduled space can be obtained
3195 from an C<isl_schedule> using the following function.
3197 __isl_give isl_union_map *isl_schedule_get_map(
3198 __isl_keep isl_schedule *sched);
3200 A representation of the schedule can be printed using
3202 __isl_give isl_printer *isl_printer_print_schedule(
3203 __isl_take isl_printer *p,
3204 __isl_keep isl_schedule *schedule);
3206 A representation of the schedule as a forest of bands can be obtained
3207 using the following function.
3209 __isl_give isl_band_list *isl_schedule_get_band_forest(
3210 __isl_keep isl_schedule *schedule);
3212 The list can be manipulated as explained in L<"Lists">.
3213 The bands inside the list can be copied and freed using the following
3216 #include <isl/band.h>
3217 __isl_give isl_band *isl_band_copy(
3218 __isl_keep isl_band *band);
3219 void *isl_band_free(__isl_take isl_band *band);
3221 Each band contains zero or more scheduling dimensions.
3222 These are referred to as the members of the band.
3223 The section of the schedule that corresponds to the band is
3224 referred to as the partial schedule of the band.
3225 For those nodes that participate in a band, the outer scheduling
3226 dimensions form the prefix schedule, while the inner scheduling
3227 dimensions form the suffix schedule.
3228 That is, if we take a cut of the band forest, then the union of
3229 the concatenations of the prefix, partial and suffix schedules of
3230 each band in the cut is equal to the entire schedule (modulo
3231 some possible padding at the end with zero scheduling dimensions).
3232 The properties of a band can be inspected using the following functions.
3234 #include <isl/band.h>
3235 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3237 int isl_band_has_children(__isl_keep isl_band *band);
3238 __isl_give isl_band_list *isl_band_get_children(
3239 __isl_keep isl_band *band);
3241 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3242 __isl_keep isl_band *band);
3243 __isl_give isl_union_map *isl_band_get_partial_schedule(
3244 __isl_keep isl_band *band);
3245 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3246 __isl_keep isl_band *band);
3248 int isl_band_n_member(__isl_keep isl_band *band);
3249 int isl_band_member_is_zero_distance(
3250 __isl_keep isl_band *band, int pos);
3252 Note that a scheduling dimension is considered to be ``zero
3253 distance'' if it does not carry any proximity dependences
3255 That is, if the dependence distances of the proximity
3256 dependences are all zero in that direction (for fixed
3257 iterations of outer bands).
3259 A representation of the band can be printed using
3261 #include <isl/band.h>
3262 __isl_give isl_printer *isl_printer_print_band(
3263 __isl_take isl_printer *p,
3264 __isl_keep isl_band *band);
3266 =head2 Parametric Vertex Enumeration
3268 The parametric vertex enumeration described in this section
3269 is mainly intended to be used internally and by the C<barvinok>
3272 #include <isl/vertices.h>
3273 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3274 __isl_keep isl_basic_set *bset);
3276 The function C<isl_basic_set_compute_vertices> performs the
3277 actual computation of the parametric vertices and the chamber
3278 decomposition and store the result in an C<isl_vertices> object.
3279 This information can be queried by either iterating over all
3280 the vertices or iterating over all the chambers or cells
3281 and then iterating over all vertices that are active on the chamber.
3283 int isl_vertices_foreach_vertex(
3284 __isl_keep isl_vertices *vertices,
3285 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3288 int isl_vertices_foreach_cell(
3289 __isl_keep isl_vertices *vertices,
3290 int (*fn)(__isl_take isl_cell *cell, void *user),
3292 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3293 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3296 Other operations that can be performed on an C<isl_vertices> object are
3299 isl_ctx *isl_vertices_get_ctx(
3300 __isl_keep isl_vertices *vertices);
3301 int isl_vertices_get_n_vertices(
3302 __isl_keep isl_vertices *vertices);
3303 void isl_vertices_free(__isl_take isl_vertices *vertices);
3305 Vertices can be inspected and destroyed using the following functions.
3307 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3308 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3309 __isl_give isl_basic_set *isl_vertex_get_domain(
3310 __isl_keep isl_vertex *vertex);
3311 __isl_give isl_basic_set *isl_vertex_get_expr(
3312 __isl_keep isl_vertex *vertex);
3313 void isl_vertex_free(__isl_take isl_vertex *vertex);
3315 C<isl_vertex_get_expr> returns a singleton parametric set describing
3316 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3318 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3319 B<rational> basic sets, so they should mainly be used for inspection
3320 and should not be mixed with integer sets.
3322 Chambers can be inspected and destroyed using the following functions.
3324 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3325 __isl_give isl_basic_set *isl_cell_get_domain(
3326 __isl_keep isl_cell *cell);
3327 void isl_cell_free(__isl_take isl_cell *cell);
3331 Although C<isl> is mainly meant to be used as a library,
3332 it also contains some basic applications that use some
3333 of the functionality of C<isl>.
3334 The input may be specified in either the L<isl format>
3335 or the L<PolyLib format>.
3337 =head2 C<isl_polyhedron_sample>
3339 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3340 an integer element of the polyhedron, if there is any.
3341 The first column in the output is the denominator and is always
3342 equal to 1. If the polyhedron contains no integer points,
3343 then a vector of length zero is printed.
3347 C<isl_pip> takes the same input as the C<example> program
3348 from the C<piplib> distribution, i.e., a set of constraints
3349 on the parameters, a line containing only -1 and finally a set
3350 of constraints on a parametric polyhedron.
3351 The coefficients of the parameters appear in the last columns
3352 (but before the final constant column).
3353 The output is the lexicographic minimum of the parametric polyhedron.
3354 As C<isl> currently does not have its own output format, the output
3355 is just a dump of the internal state.
3357 =head2 C<isl_polyhedron_minimize>
3359 C<isl_polyhedron_minimize> computes the minimum of some linear
3360 or affine objective function over the integer points in a polyhedron.
3361 If an affine objective function
3362 is given, then the constant should appear in the last column.
3364 =head2 C<isl_polytope_scan>
3366 Given a polytope, C<isl_polytope_scan> prints
3367 all integer points in the polytope.