3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
90 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
91 Some of the old names have been kept for backward compatibility,
92 but they will be removed in the future.
98 The source of C<isl> can be obtained either as a tarball
99 or from the git repository. Both are available from
100 L<http://freshmeat.net/projects/isl/>.
101 The installation process depends on how you obtained
104 =head2 Installation from the git repository
108 =item 1 Clone or update the repository
110 The first time the source is obtained, you need to clone
113 git clone git://repo.or.cz/isl.git
115 To obtain updates, you need to pull in the latest changes
119 =item 2 Generate C<configure>
125 After performing the above steps, continue
126 with the L<Common installation instructions>.
128 =head2 Common installation instructions
132 =item 1 Obtain C<GMP>
134 Building C<isl> requires C<GMP>, including its headers files.
135 Your distribution may not provide these header files by default
136 and you may need to install a package called C<gmp-devel> or something
137 similar. Alternatively, C<GMP> can be built from
138 source, available from L<http://gmplib.org/>.
142 C<isl> uses the standard C<autoconf> C<configure> script.
147 optionally followed by some configure options.
148 A complete list of options can be obtained by running
152 Below we discuss some of the more common options.
154 C<isl> can optionally use C<piplib>, but no
155 C<piplib> functionality is currently used by default.
156 The C<--with-piplib> option can
157 be used to specify which C<piplib>
158 library to use, either an installed version (C<system>),
159 an externally built version (C<build>)
160 or no version (C<no>). The option C<build> is mostly useful
161 in C<configure> scripts of larger projects that bundle both C<isl>
168 Installation prefix for C<isl>
170 =item C<--with-gmp-prefix>
172 Installation prefix for C<GMP> (architecture-independent files).
174 =item C<--with-gmp-exec-prefix>
176 Installation prefix for C<GMP> (architecture-dependent files).
178 =item C<--with-piplib>
180 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
182 =item C<--with-piplib-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-independent files).
186 =item C<--with-piplib-exec-prefix>
188 Installation prefix for C<system> C<piplib> (architecture-dependent files).
190 =item C<--with-piplib-builddir>
192 Location where C<build> C<piplib> was built.
200 =item 4 Install (optional)
208 =head2 Initialization
210 All manipulations of integer sets and relations occur within
211 the context of an C<isl_ctx>.
212 A given C<isl_ctx> can only be used within a single thread.
213 All arguments of a function are required to have been allocated
214 within the same context.
215 There are currently no functions available for moving an object
216 from one C<isl_ctx> to another C<isl_ctx>. This means that
217 there is currently no way of safely moving an object from one
218 thread to another, unless the whole C<isl_ctx> is moved.
220 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
221 freed using C<isl_ctx_free>.
222 All objects allocated within an C<isl_ctx> should be freed
223 before the C<isl_ctx> itself is freed.
225 isl_ctx *isl_ctx_alloc();
226 void isl_ctx_free(isl_ctx *ctx);
230 All operations on integers, mainly the coefficients
231 of the constraints describing the sets and relations,
232 are performed in exact integer arithmetic using C<GMP>.
233 However, to allow future versions of C<isl> to optionally
234 support fixed integer arithmetic, all calls to C<GMP>
235 are wrapped inside C<isl> specific macros.
236 The basic type is C<isl_int> and the operations below
237 are available on this type.
238 The meanings of these operations are essentially the same
239 as their C<GMP> C<mpz_> counterparts.
240 As always with C<GMP> types, C<isl_int>s need to be
241 initialized with C<isl_int_init> before they can be used
242 and they need to be released with C<isl_int_clear>
244 The user should not assume that an C<isl_int> is represented
245 as a C<mpz_t>, but should instead explicitly convert between
246 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
247 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
251 =item isl_int_init(i)
253 =item isl_int_clear(i)
255 =item isl_int_set(r,i)
257 =item isl_int_set_si(r,i)
259 =item isl_int_set_gmp(r,g)
261 =item isl_int_get_gmp(i,g)
263 =item isl_int_abs(r,i)
265 =item isl_int_neg(r,i)
267 =item isl_int_swap(i,j)
269 =item isl_int_swap_or_set(i,j)
271 =item isl_int_add_ui(r,i,j)
273 =item isl_int_sub_ui(r,i,j)
275 =item isl_int_add(r,i,j)
277 =item isl_int_sub(r,i,j)
279 =item isl_int_mul(r,i,j)
281 =item isl_int_mul_ui(r,i,j)
283 =item isl_int_addmul(r,i,j)
285 =item isl_int_submul(r,i,j)
287 =item isl_int_gcd(r,i,j)
289 =item isl_int_lcm(r,i,j)
291 =item isl_int_divexact(r,i,j)
293 =item isl_int_cdiv_q(r,i,j)
295 =item isl_int_fdiv_q(r,i,j)
297 =item isl_int_fdiv_r(r,i,j)
299 =item isl_int_fdiv_q_ui(r,i,j)
301 =item isl_int_read(r,s)
303 =item isl_int_print(out,i,width)
307 =item isl_int_cmp(i,j)
309 =item isl_int_cmp_si(i,si)
311 =item isl_int_eq(i,j)
313 =item isl_int_ne(i,j)
315 =item isl_int_lt(i,j)
317 =item isl_int_le(i,j)
319 =item isl_int_gt(i,j)
321 =item isl_int_ge(i,j)
323 =item isl_int_abs_eq(i,j)
325 =item isl_int_abs_ne(i,j)
327 =item isl_int_abs_lt(i,j)
329 =item isl_int_abs_gt(i,j)
331 =item isl_int_abs_ge(i,j)
333 =item isl_int_is_zero(i)
335 =item isl_int_is_one(i)
337 =item isl_int_is_negone(i)
339 =item isl_int_is_pos(i)
341 =item isl_int_is_neg(i)
343 =item isl_int_is_nonpos(i)
345 =item isl_int_is_nonneg(i)
347 =item isl_int_is_divisible_by(i,j)
351 =head2 Sets and Relations
353 C<isl> uses six types of objects for representing sets and relations,
354 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
355 C<isl_union_set> and C<isl_union_map>.
356 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
357 can be described as a conjunction of affine constraints, while
358 C<isl_set> and C<isl_map> represent unions of
359 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
360 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
361 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
362 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
363 where dimensions with different space names
364 (see L<Dimension Specifications>) are considered different as well.
365 The difference between sets and relations (maps) is that sets have
366 one set of variables, while relations have two sets of variables,
367 input variables and output variables.
369 =head2 Memory Management
371 Since a high-level operation on sets and/or relations usually involves
372 several substeps and since the user is usually not interested in
373 the intermediate results, most functions that return a new object
374 will also release all the objects passed as arguments.
375 If the user still wants to use one or more of these arguments
376 after the function call, she should pass along a copy of the
377 object rather than the object itself.
378 The user is then responsible for making sure that the original
379 object gets used somewhere else or is explicitly freed.
381 The arguments and return values of all documents functions are
382 annotated to make clear which arguments are released and which
383 arguments are preserved. In particular, the following annotations
390 C<__isl_give> means that a new object is returned.
391 The user should make sure that the returned pointer is
392 used exactly once as a value for an C<__isl_take> argument.
393 In between, it can be used as a value for as many
394 C<__isl_keep> arguments as the user likes.
395 There is one exception, and that is the case where the
396 pointer returned is C<NULL>. Is this case, the user
397 is free to use it as an C<__isl_take> argument or not.
401 C<__isl_take> means that the object the argument points to
402 is taken over by the function and may no longer be used
403 by the user as an argument to any other function.
404 The pointer value must be one returned by a function
405 returning an C<__isl_give> pointer.
406 If the user passes in a C<NULL> value, then this will
407 be treated as an error in the sense that the function will
408 not perform its usual operation. However, it will still
409 make sure that all the the other C<__isl_take> arguments
414 C<__isl_keep> means that the function will only use the object
415 temporarily. After the function has finished, the user
416 can still use it as an argument to other functions.
417 A C<NULL> value will be treated in the same way as
418 a C<NULL> value for an C<__isl_take> argument.
422 =head2 Dimension Specifications
424 Whenever a new set or relation is created from scratch,
425 its dimension needs to be specified using an C<isl_dim>.
428 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
429 unsigned nparam, unsigned n_in, unsigned n_out);
430 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
431 unsigned nparam, unsigned dim);
432 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
433 void isl_dim_free(__isl_take isl_dim *dim);
434 unsigned isl_dim_size(__isl_keep isl_dim *dim,
435 enum isl_dim_type type);
437 The dimension specification used for creating a set
438 needs to be created using C<isl_dim_set_alloc>, while
439 that for creating a relation
440 needs to be created using C<isl_dim_alloc>.
441 C<isl_dim_size> can be used
442 to find out the number of dimensions of each type in
443 a dimension specification, where type may be
444 C<isl_dim_param>, C<isl_dim_in> (only for relations),
445 C<isl_dim_out> (only for relations), C<isl_dim_set>
446 (only for sets) or C<isl_dim_all>.
448 It is often useful to create objects that live in the
449 same space as some other object. This can be accomplished
450 by creating the new objects
451 (see L<Creating New Sets and Relations> or
452 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
453 specification of the original object.
456 __isl_give isl_dim *isl_basic_set_get_dim(
457 __isl_keep isl_basic_set *bset);
458 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
460 #include <isl/union_set.h>
461 __isl_give isl_dim *isl_union_set_get_dim(
462 __isl_keep isl_union_set *uset);
465 __isl_give isl_dim *isl_basic_map_get_dim(
466 __isl_keep isl_basic_map *bmap);
467 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
469 #include <isl/union_map.h>
470 __isl_give isl_dim *isl_union_map_get_dim(
471 __isl_keep isl_union_map *umap);
473 #include <isl/constraint.h>
474 __isl_give isl_dim *isl_constraint_get_dim(
475 __isl_keep isl_constraint *constraint);
477 #include <isl/polynomial.h>
478 __isl_give isl_dim *isl_qpolynomial_get_dim(
479 __isl_keep isl_qpolynomial *qp);
480 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
481 __isl_keep isl_qpolynomial_fold *fold);
482 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
483 __isl_keep isl_pw_qpolynomial *pwqp);
484 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
485 __isl_keep isl_union_pw_qpolynomial *upwqp);
486 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
487 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
490 __isl_give isl_dim *isl_aff_get_dim(
491 __isl_keep isl_aff *aff);
492 __isl_give isl_dim *isl_pw_aff_get_dim(
493 __isl_keep isl_pw_aff *pwaff);
495 #include <isl/point.h>
496 __isl_give isl_dim *isl_point_get_dim(
497 __isl_keep isl_point *pnt);
499 The names of the individual dimensions may be set or read off
500 using the following functions.
503 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
504 enum isl_dim_type type, unsigned pos,
505 __isl_keep const char *name);
506 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
507 enum isl_dim_type type, unsigned pos);
509 Note that C<isl_dim_get_name> returns a pointer to some internal
510 data structure, so the result can only be used while the
511 corresponding C<isl_dim> is alive.
512 Also note that every function that operates on two sets or relations
513 requires that both arguments have the same parameters. This also
514 means that if one of the arguments has named parameters, then the
515 other needs to have named parameters too and the names need to match.
516 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
517 have different parameters (as long as they are named), in which case
518 the result will have as parameters the union of the parameters of
521 The names of entire spaces may be set or read off
522 using the following functions.
525 __isl_give isl_dim *isl_dim_set_tuple_name(
526 __isl_take isl_dim *dim,
527 enum isl_dim_type type, const char *s);
528 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
529 enum isl_dim_type type);
531 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
532 or C<isl_dim_set>. As with C<isl_dim_get_name>,
533 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
535 Binary operations require the corresponding spaces of their arguments
536 to have the same name.
538 Spaces can be nested. In particular, the domain of a set or
539 the domain or range of a relation can be a nested relation.
540 The following functions can be used to construct and deconstruct
541 such nested dimension specifications.
544 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
545 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
546 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
548 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
549 be the dimension specification of a set, while that of
550 C<isl_dim_wrap> should be the dimension specification of a relation.
551 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
552 of a relation, while that of C<isl_dim_wrap> is the dimension specification
555 Dimension specifications can be created from other dimension
556 specifications using the following functions.
558 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
559 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
560 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
561 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
562 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
563 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
564 __isl_take isl_dim *right);
565 __isl_give isl_dim *isl_dim_align_params(
566 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
567 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
568 enum isl_dim_type type, unsigned pos, unsigned n);
569 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
570 enum isl_dim_type type, unsigned n);
571 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
572 enum isl_dim_type type, unsigned first, unsigned n);
573 __isl_give isl_dim *isl_dim_map_from_set(
574 __isl_take isl_dim *dim);
575 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
577 Note that if dimensions are added or removed from a space, then
578 the name and the internal structure are lost.
582 A local space is essentially a dimension specification with
583 zero or more existentially quantified variables.
584 The local space of a basic set or relation can be obtained
585 using the following functions.
588 __isl_give isl_local_space *isl_basic_set_get_local_space(
589 __isl_keep isl_basic_set *bset);
592 __isl_give isl_local_space *isl_basic_map_get_local_space(
593 __isl_keep isl_basic_map *bmap);
595 A new local space can be created from a dimension specification using
597 #include <isl/local_space.h>
598 __isl_give isl_local_space *isl_local_space_from_dim(
599 __isl_take isl_dim *dim);
601 They can be inspected, copied and freed using the following functions.
603 #include <isl/local_space.h>
604 isl_ctx *isl_local_space_get_ctx(
605 __isl_keep isl_local_space *ls);
606 int isl_local_space_dim(__isl_keep isl_local_space *ls,
607 enum isl_dim_type type);
608 const char *isl_local_space_get_dim_name(
609 __isl_keep isl_local_space *ls,
610 enum isl_dim_type type, unsigned pos);
611 __isl_give isl_local_space *isl_local_space_set_dim_name(
612 __isl_take isl_local_space *ls,
613 enum isl_dim_type type, unsigned pos, const char *s);
614 __isl_give isl_dim *isl_local_space_get_dim(
615 __isl_keep isl_local_space *ls);
616 __isl_give isl_div *isl_local_space_get_div(
617 __isl_keep isl_local_space *ls, int pos);
618 __isl_give isl_local_space *isl_local_space_copy(
619 __isl_keep isl_local_space *ls);
620 void *isl_local_space_free(__isl_take isl_local_space *ls);
622 Two local spaces can be compared using
624 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
625 __isl_keep isl_local_space *ls2);
627 Local spaces can be created from other local spaces
628 using the following functions.
630 __isl_give isl_local_space *isl_local_space_from_domain(
631 __isl_take isl_local_space *ls);
632 __isl_give isl_local_space *isl_local_space_add_dims(
633 __isl_take isl_local_space *ls,
634 enum isl_dim_type type, unsigned n);
635 __isl_give isl_local_space *isl_local_space_insert_dims(
636 __isl_take isl_local_space *ls,
637 enum isl_dim_type type, unsigned first, unsigned n);
638 __isl_give isl_local_space *isl_local_space_drop_dims(
639 __isl_take isl_local_space *ls,
640 enum isl_dim_type type, unsigned first, unsigned n);
642 =head2 Input and Output
644 C<isl> supports its own input/output format, which is similar
645 to the C<Omega> format, but also supports the C<PolyLib> format
650 The C<isl> format is similar to that of C<Omega>, but has a different
651 syntax for describing the parameters and allows for the definition
652 of an existentially quantified variable as the integer division
653 of an affine expression.
654 For example, the set of integers C<i> between C<0> and C<n>
655 such that C<i % 10 <= 6> can be described as
657 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
660 A set or relation can have several disjuncts, separated
661 by the keyword C<or>. Each disjunct is either a conjunction
662 of constraints or a projection (C<exists>) of a conjunction
663 of constraints. The constraints are separated by the keyword
666 =head3 C<PolyLib> format
668 If the represented set is a union, then the first line
669 contains a single number representing the number of disjuncts.
670 Otherwise, a line containing the number C<1> is optional.
672 Each disjunct is represented by a matrix of constraints.
673 The first line contains two numbers representing
674 the number of rows and columns,
675 where the number of rows is equal to the number of constraints
676 and the number of columns is equal to two plus the number of variables.
677 The following lines contain the actual rows of the constraint matrix.
678 In each row, the first column indicates whether the constraint
679 is an equality (C<0>) or inequality (C<1>). The final column
680 corresponds to the constant term.
682 If the set is parametric, then the coefficients of the parameters
683 appear in the last columns before the constant column.
684 The coefficients of any existentially quantified variables appear
685 between those of the set variables and those of the parameters.
687 =head3 Extended C<PolyLib> format
689 The extended C<PolyLib> format is nearly identical to the
690 C<PolyLib> format. The only difference is that the line
691 containing the number of rows and columns of a constraint matrix
692 also contains four additional numbers:
693 the number of output dimensions, the number of input dimensions,
694 the number of local dimensions (i.e., the number of existentially
695 quantified variables) and the number of parameters.
696 For sets, the number of ``output'' dimensions is equal
697 to the number of set dimensions, while the number of ``input''
703 __isl_give isl_basic_set *isl_basic_set_read_from_file(
704 isl_ctx *ctx, FILE *input, int nparam);
705 __isl_give isl_basic_set *isl_basic_set_read_from_str(
706 isl_ctx *ctx, const char *str, int nparam);
707 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
708 FILE *input, int nparam);
709 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
710 const char *str, int nparam);
713 __isl_give isl_basic_map *isl_basic_map_read_from_file(
714 isl_ctx *ctx, FILE *input, int nparam);
715 __isl_give isl_basic_map *isl_basic_map_read_from_str(
716 isl_ctx *ctx, const char *str, int nparam);
717 __isl_give isl_map *isl_map_read_from_file(
718 struct isl_ctx *ctx, FILE *input, int nparam);
719 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
720 const char *str, int nparam);
722 #include <isl/union_set.h>
723 __isl_give isl_union_set *isl_union_set_read_from_file(
724 isl_ctx *ctx, FILE *input);
725 __isl_give isl_union_set *isl_union_set_read_from_str(
726 struct isl_ctx *ctx, const char *str);
728 #include <isl/union_map.h>
729 __isl_give isl_union_map *isl_union_map_read_from_file(
730 isl_ctx *ctx, FILE *input);
731 __isl_give isl_union_map *isl_union_map_read_from_str(
732 struct isl_ctx *ctx, const char *str);
734 The input format is autodetected and may be either the C<PolyLib> format
735 or the C<isl> format.
736 C<nparam> specifies how many of the final columns in
737 the C<PolyLib> format correspond to parameters.
738 If input is given in the C<isl> format, then the number
739 of parameters needs to be equal to C<nparam>.
740 If C<nparam> is negative, then any number of parameters
741 is accepted in the C<isl> format and zero parameters
742 are assumed in the C<PolyLib> format.
746 Before anything can be printed, an C<isl_printer> needs to
749 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
751 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
752 void isl_printer_free(__isl_take isl_printer *printer);
753 __isl_give char *isl_printer_get_str(
754 __isl_keep isl_printer *printer);
756 The behavior of the printer can be modified in various ways
758 __isl_give isl_printer *isl_printer_set_output_format(
759 __isl_take isl_printer *p, int output_format);
760 __isl_give isl_printer *isl_printer_set_indent(
761 __isl_take isl_printer *p, int indent);
762 __isl_give isl_printer *isl_printer_indent(
763 __isl_take isl_printer *p, int indent);
764 __isl_give isl_printer *isl_printer_set_prefix(
765 __isl_take isl_printer *p, const char *prefix);
766 __isl_give isl_printer *isl_printer_set_suffix(
767 __isl_take isl_printer *p, const char *suffix);
769 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
770 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
771 and defaults to C<ISL_FORMAT_ISL>.
772 Each line in the output is indented by C<indent> (set by
773 C<isl_printer_set_indent>) spaces
774 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
775 In the C<PolyLib> format output,
776 the coefficients of the existentially quantified variables
777 appear between those of the set variables and those
779 The function C<isl_printer_indent> increases the indentation
780 by the specified amount (which may be negative).
782 To actually print something, use
785 __isl_give isl_printer *isl_printer_print_basic_set(
786 __isl_take isl_printer *printer,
787 __isl_keep isl_basic_set *bset);
788 __isl_give isl_printer *isl_printer_print_set(
789 __isl_take isl_printer *printer,
790 __isl_keep isl_set *set);
793 __isl_give isl_printer *isl_printer_print_basic_map(
794 __isl_take isl_printer *printer,
795 __isl_keep isl_basic_map *bmap);
796 __isl_give isl_printer *isl_printer_print_map(
797 __isl_take isl_printer *printer,
798 __isl_keep isl_map *map);
800 #include <isl/union_set.h>
801 __isl_give isl_printer *isl_printer_print_union_set(
802 __isl_take isl_printer *p,
803 __isl_keep isl_union_set *uset);
805 #include <isl/union_map.h>
806 __isl_give isl_printer *isl_printer_print_union_map(
807 __isl_take isl_printer *p,
808 __isl_keep isl_union_map *umap);
810 When called on a file printer, the following function flushes
811 the file. When called on a string printer, the buffer is cleared.
813 __isl_give isl_printer *isl_printer_flush(
814 __isl_take isl_printer *p);
816 =head2 Creating New Sets and Relations
818 C<isl> has functions for creating some standard sets and relations.
822 =item * Empty sets and relations
824 __isl_give isl_basic_set *isl_basic_set_empty(
825 __isl_take isl_dim *dim);
826 __isl_give isl_basic_map *isl_basic_map_empty(
827 __isl_take isl_dim *dim);
828 __isl_give isl_set *isl_set_empty(
829 __isl_take isl_dim *dim);
830 __isl_give isl_map *isl_map_empty(
831 __isl_take isl_dim *dim);
832 __isl_give isl_union_set *isl_union_set_empty(
833 __isl_take isl_dim *dim);
834 __isl_give isl_union_map *isl_union_map_empty(
835 __isl_take isl_dim *dim);
837 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
838 is only used to specify the parameters.
840 =item * Universe sets and relations
842 __isl_give isl_basic_set *isl_basic_set_universe(
843 __isl_take isl_dim *dim);
844 __isl_give isl_basic_map *isl_basic_map_universe(
845 __isl_take isl_dim *dim);
846 __isl_give isl_set *isl_set_universe(
847 __isl_take isl_dim *dim);
848 __isl_give isl_map *isl_map_universe(
849 __isl_take isl_dim *dim);
850 __isl_give isl_union_set *isl_union_set_universe(
851 __isl_take isl_union_set *uset);
852 __isl_give isl_union_map *isl_union_map_universe(
853 __isl_take isl_union_map *umap);
855 The sets and relations constructed by the functions above
856 contain all integer values, while those constructed by the
857 functions below only contain non-negative values.
859 __isl_give isl_basic_set *isl_basic_set_nat_universe(
860 __isl_take isl_dim *dim);
861 __isl_give isl_basic_map *isl_basic_map_nat_universe(
862 __isl_take isl_dim *dim);
863 __isl_give isl_set *isl_set_nat_universe(
864 __isl_take isl_dim *dim);
865 __isl_give isl_map *isl_map_nat_universe(
866 __isl_take isl_dim *dim);
868 =item * Identity relations
870 __isl_give isl_basic_map *isl_basic_map_identity(
871 __isl_take isl_dim *dim);
872 __isl_give isl_map *isl_map_identity(
873 __isl_take isl_dim *dim);
875 The number of input and output dimensions in C<dim> needs
878 =item * Lexicographic order
880 __isl_give isl_map *isl_map_lex_lt(
881 __isl_take isl_dim *set_dim);
882 __isl_give isl_map *isl_map_lex_le(
883 __isl_take isl_dim *set_dim);
884 __isl_give isl_map *isl_map_lex_gt(
885 __isl_take isl_dim *set_dim);
886 __isl_give isl_map *isl_map_lex_ge(
887 __isl_take isl_dim *set_dim);
888 __isl_give isl_map *isl_map_lex_lt_first(
889 __isl_take isl_dim *dim, unsigned n);
890 __isl_give isl_map *isl_map_lex_le_first(
891 __isl_take isl_dim *dim, unsigned n);
892 __isl_give isl_map *isl_map_lex_gt_first(
893 __isl_take isl_dim *dim, unsigned n);
894 __isl_give isl_map *isl_map_lex_ge_first(
895 __isl_take isl_dim *dim, unsigned n);
897 The first four functions take a dimension specification for a B<set>
898 and return relations that express that the elements in the domain
899 are lexicographically less
900 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
901 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
902 than the elements in the range.
903 The last four functions take a dimension specification for a map
904 and return relations that express that the first C<n> dimensions
905 in the domain are lexicographically less
906 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
907 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
908 than the first C<n> dimensions in the range.
912 A basic set or relation can be converted to a set or relation
913 using the following functions.
915 __isl_give isl_set *isl_set_from_basic_set(
916 __isl_take isl_basic_set *bset);
917 __isl_give isl_map *isl_map_from_basic_map(
918 __isl_take isl_basic_map *bmap);
920 Sets and relations can be converted to union sets and relations
921 using the following functions.
923 __isl_give isl_union_map *isl_union_map_from_map(
924 __isl_take isl_map *map);
925 __isl_give isl_union_set *isl_union_set_from_set(
926 __isl_take isl_set *set);
928 The inverse conversions below can only be used if the input
929 union set or relation is known to contain elements in exactly one
932 __isl_give isl_set *isl_set_from_union_set(
933 __isl_take isl_union_set *uset);
934 __isl_give isl_map *isl_map_from_union_map(
935 __isl_take isl_union_map *umap);
937 Sets and relations can be copied and freed again using the following
940 __isl_give isl_basic_set *isl_basic_set_copy(
941 __isl_keep isl_basic_set *bset);
942 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
943 __isl_give isl_union_set *isl_union_set_copy(
944 __isl_keep isl_union_set *uset);
945 __isl_give isl_basic_map *isl_basic_map_copy(
946 __isl_keep isl_basic_map *bmap);
947 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
948 __isl_give isl_union_map *isl_union_map_copy(
949 __isl_keep isl_union_map *umap);
950 void isl_basic_set_free(__isl_take isl_basic_set *bset);
951 void isl_set_free(__isl_take isl_set *set);
952 void *isl_union_set_free(__isl_take isl_union_set *uset);
953 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
954 void isl_map_free(__isl_take isl_map *map);
955 void *isl_union_map_free(__isl_take isl_union_map *umap);
957 Other sets and relations can be constructed by starting
958 from a universe set or relation, adding equality and/or
959 inequality constraints and then projecting out the
960 existentially quantified variables, if any.
961 Constraints can be constructed, manipulated and
962 added to (or removed from) (basic) sets and relations
963 using the following functions.
965 #include <isl/constraint.h>
966 __isl_give isl_constraint *isl_equality_alloc(
967 __isl_take isl_dim *dim);
968 __isl_give isl_constraint *isl_inequality_alloc(
969 __isl_take isl_dim *dim);
970 void isl_constraint_set_constant(
971 __isl_keep isl_constraint *constraint, isl_int v);
972 void isl_constraint_set_coefficient(
973 __isl_keep isl_constraint *constraint,
974 enum isl_dim_type type, int pos, isl_int v);
975 __isl_give isl_basic_map *isl_basic_map_add_constraint(
976 __isl_take isl_basic_map *bmap,
977 __isl_take isl_constraint *constraint);
978 __isl_give isl_basic_set *isl_basic_set_add_constraint(
979 __isl_take isl_basic_set *bset,
980 __isl_take isl_constraint *constraint);
981 __isl_give isl_map *isl_map_add_constraint(
982 __isl_take isl_map *map,
983 __isl_take isl_constraint *constraint);
984 __isl_give isl_set *isl_set_add_constraint(
985 __isl_take isl_set *set,
986 __isl_take isl_constraint *constraint);
987 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
988 __isl_take isl_basic_set *bset,
989 __isl_take isl_constraint *constraint);
991 For example, to create a set containing the even integers
992 between 10 and 42, you would use the following code.
996 struct isl_constraint *c;
997 struct isl_basic_set *bset;
1000 dim = isl_dim_set_alloc(ctx, 0, 2);
1001 bset = isl_basic_set_universe(isl_dim_copy(dim));
1003 c = isl_equality_alloc(isl_dim_copy(dim));
1004 isl_int_set_si(v, -1);
1005 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1006 isl_int_set_si(v, 2);
1007 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1008 bset = isl_basic_set_add_constraint(bset, c);
1010 c = isl_inequality_alloc(isl_dim_copy(dim));
1011 isl_int_set_si(v, -10);
1012 isl_constraint_set_constant(c, v);
1013 isl_int_set_si(v, 1);
1014 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1015 bset = isl_basic_set_add_constraint(bset, c);
1017 c = isl_inequality_alloc(dim);
1018 isl_int_set_si(v, 42);
1019 isl_constraint_set_constant(c, v);
1020 isl_int_set_si(v, -1);
1021 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1022 bset = isl_basic_set_add_constraint(bset, c);
1024 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1030 struct isl_basic_set *bset;
1031 bset = isl_basic_set_read_from_str(ctx,
1032 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1034 A basic set or relation can also be constructed from two matrices
1035 describing the equalities and the inequalities.
1037 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1038 __isl_take isl_dim *dim,
1039 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1040 enum isl_dim_type c1,
1041 enum isl_dim_type c2, enum isl_dim_type c3,
1042 enum isl_dim_type c4);
1043 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1044 __isl_take isl_dim *dim,
1045 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1046 enum isl_dim_type c1,
1047 enum isl_dim_type c2, enum isl_dim_type c3,
1048 enum isl_dim_type c4, enum isl_dim_type c5);
1050 The C<isl_dim_type> arguments indicate the order in which
1051 different kinds of variables appear in the input matrices
1052 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1053 C<isl_dim_set> and C<isl_dim_div> for sets and
1054 of C<isl_dim_cst>, C<isl_dim_param>,
1055 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1057 A (basic) relation can also be constructed from a (piecewise) affine expression
1058 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1060 __isl_give isl_basic_map *isl_basic_map_from_aff(
1061 __isl_take isl_aff *aff);
1062 __isl_give isl_map *isl_map_from_pw_aff(
1063 __isl_take isl_pw_aff *pwaff);
1064 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1065 __isl_take isl_dim *domain_dim,
1066 __isl_take isl_aff_list *list);
1068 The C<domain_dim> argument describes the domain of the resulting
1069 basic relation. It is required because the C<list> may consist
1070 of zero affine expressions.
1072 =head2 Inspecting Sets and Relations
1074 Usually, the user should not have to care about the actual constraints
1075 of the sets and maps, but should instead apply the abstract operations
1076 explained in the following sections.
1077 Occasionally, however, it may be required to inspect the individual
1078 coefficients of the constraints. This section explains how to do so.
1079 In these cases, it may also be useful to have C<isl> compute
1080 an explicit representation of the existentially quantified variables.
1082 __isl_give isl_set *isl_set_compute_divs(
1083 __isl_take isl_set *set);
1084 __isl_give isl_map *isl_map_compute_divs(
1085 __isl_take isl_map *map);
1086 __isl_give isl_union_set *isl_union_set_compute_divs(
1087 __isl_take isl_union_set *uset);
1088 __isl_give isl_union_map *isl_union_map_compute_divs(
1089 __isl_take isl_union_map *umap);
1091 This explicit representation defines the existentially quantified
1092 variables as integer divisions of the other variables, possibly
1093 including earlier existentially quantified variables.
1094 An explicitly represented existentially quantified variable therefore
1095 has a unique value when the values of the other variables are known.
1096 If, furthermore, the same existentials, i.e., existentials
1097 with the same explicit representations, should appear in the
1098 same order in each of the disjuncts of a set or map, then the user should call
1099 either of the following functions.
1101 __isl_give isl_set *isl_set_align_divs(
1102 __isl_take isl_set *set);
1103 __isl_give isl_map *isl_map_align_divs(
1104 __isl_take isl_map *map);
1106 Alternatively, the existentially quantified variables can be removed
1107 using the following functions, which compute an overapproximation.
1109 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1110 __isl_take isl_basic_set *bset);
1111 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1112 __isl_take isl_basic_map *bmap);
1113 __isl_give isl_set *isl_set_remove_divs(
1114 __isl_take isl_set *set);
1115 __isl_give isl_map *isl_map_remove_divs(
1116 __isl_take isl_map *map);
1118 To iterate over all the sets or maps in a union set or map, use
1120 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1121 int (*fn)(__isl_take isl_set *set, void *user),
1123 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1124 int (*fn)(__isl_take isl_map *map, void *user),
1127 The number of sets or maps in a union set or map can be obtained
1130 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1131 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1133 To extract the set or map from a union with a given dimension
1136 __isl_give isl_set *isl_union_set_extract_set(
1137 __isl_keep isl_union_set *uset,
1138 __isl_take isl_dim *dim);
1139 __isl_give isl_map *isl_union_map_extract_map(
1140 __isl_keep isl_union_map *umap,
1141 __isl_take isl_dim *dim);
1143 To iterate over all the basic sets or maps in a set or map, use
1145 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1146 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1148 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1149 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1152 The callback function C<fn> should return 0 if successful and
1153 -1 if an error occurs. In the latter case, or if any other error
1154 occurs, the above functions will return -1.
1156 It should be noted that C<isl> does not guarantee that
1157 the basic sets or maps passed to C<fn> are disjoint.
1158 If this is required, then the user should call one of
1159 the following functions first.
1161 __isl_give isl_set *isl_set_make_disjoint(
1162 __isl_take isl_set *set);
1163 __isl_give isl_map *isl_map_make_disjoint(
1164 __isl_take isl_map *map);
1166 The number of basic sets in a set can be obtained
1169 int isl_set_n_basic_set(__isl_keep isl_set *set);
1171 To iterate over the constraints of a basic set or map, use
1173 #include <isl/constraint.h>
1175 int isl_basic_map_foreach_constraint(
1176 __isl_keep isl_basic_map *bmap,
1177 int (*fn)(__isl_take isl_constraint *c, void *user),
1179 void isl_constraint_free(struct isl_constraint *c);
1181 Again, the callback function C<fn> should return 0 if successful and
1182 -1 if an error occurs. In the latter case, or if any other error
1183 occurs, the above functions will return -1.
1184 The constraint C<c> represents either an equality or an inequality.
1185 Use the following function to find out whether a constraint
1186 represents an equality. If not, it represents an inequality.
1188 int isl_constraint_is_equality(
1189 __isl_keep isl_constraint *constraint);
1191 The coefficients of the constraints can be inspected using
1192 the following functions.
1194 void isl_constraint_get_constant(
1195 __isl_keep isl_constraint *constraint, isl_int *v);
1196 void isl_constraint_get_coefficient(
1197 __isl_keep isl_constraint *constraint,
1198 enum isl_dim_type type, int pos, isl_int *v);
1199 int isl_constraint_involves_dims(
1200 __isl_keep isl_constraint *constraint,
1201 enum isl_dim_type type, unsigned first, unsigned n);
1203 The explicit representations of the existentially quantified
1204 variables can be inspected using the following functions.
1205 Note that the user is only allowed to use these functions
1206 if the inspected set or map is the result of a call
1207 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1209 __isl_give isl_div *isl_constraint_div(
1210 __isl_keep isl_constraint *constraint, int pos);
1211 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1212 void isl_div_get_constant(__isl_keep isl_div *div,
1214 void isl_div_get_denominator(__isl_keep isl_div *div,
1216 void isl_div_get_coefficient(__isl_keep isl_div *div,
1217 enum isl_dim_type type, int pos, isl_int *v);
1219 To obtain the constraints of a basic set or map in matrix
1220 form, use the following functions.
1222 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1223 __isl_keep isl_basic_set *bset,
1224 enum isl_dim_type c1, enum isl_dim_type c2,
1225 enum isl_dim_type c3, enum isl_dim_type c4);
1226 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1227 __isl_keep isl_basic_set *bset,
1228 enum isl_dim_type c1, enum isl_dim_type c2,
1229 enum isl_dim_type c3, enum isl_dim_type c4);
1230 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1231 __isl_keep isl_basic_map *bmap,
1232 enum isl_dim_type c1,
1233 enum isl_dim_type c2, enum isl_dim_type c3,
1234 enum isl_dim_type c4, enum isl_dim_type c5);
1235 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1236 __isl_keep isl_basic_map *bmap,
1237 enum isl_dim_type c1,
1238 enum isl_dim_type c2, enum isl_dim_type c3,
1239 enum isl_dim_type c4, enum isl_dim_type c5);
1241 The C<isl_dim_type> arguments dictate the order in which
1242 different kinds of variables appear in the resulting matrix
1243 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1244 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1246 To check whether the description of a set or relation depends
1247 on one or more given dimensions, it is not necessary to iterate over all
1248 constraints. Instead the following functions can be used.
1250 int isl_basic_set_involves_dims(
1251 __isl_keep isl_basic_set *bset,
1252 enum isl_dim_type type, unsigned first, unsigned n);
1253 int isl_set_involves_dims(__isl_keep isl_set *set,
1254 enum isl_dim_type type, unsigned first, unsigned n);
1255 int isl_basic_map_involves_dims(
1256 __isl_keep isl_basic_map *bmap,
1257 enum isl_dim_type type, unsigned first, unsigned n);
1258 int isl_map_involves_dims(__isl_keep isl_map *map,
1259 enum isl_dim_type type, unsigned first, unsigned n);
1261 The names of the domain and range spaces of a set or relation can be
1262 read off or set using the following functions.
1264 const char *isl_basic_set_get_tuple_name(
1265 __isl_keep isl_basic_set *bset);
1266 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1267 __isl_take isl_basic_set *set, const char *s);
1268 const char *isl_set_get_tuple_name(
1269 __isl_keep isl_set *set);
1270 const char *isl_basic_map_get_tuple_name(
1271 __isl_keep isl_basic_map *bmap,
1272 enum isl_dim_type type);
1273 const char *isl_map_get_tuple_name(
1274 __isl_keep isl_map *map,
1275 enum isl_dim_type type);
1277 As with C<isl_dim_get_tuple_name>, the value returned points to
1278 an internal data structure.
1279 The names of individual dimensions can be read off using
1280 the following functions.
1282 const char *isl_constraint_get_dim_name(
1283 __isl_keep isl_constraint *constraint,
1284 enum isl_dim_type type, unsigned pos);
1285 const char *isl_basic_set_get_dim_name(
1286 __isl_keep isl_basic_set *bset,
1287 enum isl_dim_type type, unsigned pos);
1288 const char *isl_set_get_dim_name(
1289 __isl_keep isl_set *set,
1290 enum isl_dim_type type, unsigned pos);
1291 const char *isl_basic_map_get_dim_name(
1292 __isl_keep isl_basic_map *bmap,
1293 enum isl_dim_type type, unsigned pos);
1294 const char *isl_map_get_dim_name(
1295 __isl_keep isl_map *map,
1296 enum isl_dim_type type, unsigned pos);
1298 These functions are mostly useful to obtain the names
1303 =head3 Unary Properties
1309 The following functions test whether the given set or relation
1310 contains any integer points. The ``plain'' variants do not perform
1311 any computations, but simply check if the given set or relation
1312 is already known to be empty.
1314 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1315 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1316 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1317 int isl_set_is_empty(__isl_keep isl_set *set);
1318 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1319 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1320 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1321 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1322 int isl_map_is_empty(__isl_keep isl_map *map);
1323 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1325 =item * Universality
1327 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1328 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1329 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1331 =item * Single-valuedness
1333 int isl_map_is_single_valued(__isl_keep isl_map *map);
1334 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1338 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1339 int isl_map_is_injective(__isl_keep isl_map *map);
1340 int isl_union_map_plain_is_injective(
1341 __isl_keep isl_union_map *umap);
1342 int isl_union_map_is_injective(
1343 __isl_keep isl_union_map *umap);
1347 int isl_map_is_bijective(__isl_keep isl_map *map);
1348 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1352 The following functions check whether the domain of the given
1353 (basic) set is a wrapped relation.
1355 int isl_basic_set_is_wrapping(
1356 __isl_keep isl_basic_set *bset);
1357 int isl_set_is_wrapping(__isl_keep isl_set *set);
1359 =item * Internal Product
1361 int isl_basic_map_can_zip(
1362 __isl_keep isl_basic_map *bmap);
1363 int isl_map_can_zip(__isl_keep isl_map *map);
1365 Check whether the product of domain and range of the given relation
1367 i.e., whether both domain and range are nested relations.
1371 =head3 Binary Properties
1377 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1378 __isl_keep isl_set *set2);
1379 int isl_set_is_equal(__isl_keep isl_set *set1,
1380 __isl_keep isl_set *set2);
1381 int isl_union_set_is_equal(
1382 __isl_keep isl_union_set *uset1,
1383 __isl_keep isl_union_set *uset2);
1384 int isl_basic_map_is_equal(
1385 __isl_keep isl_basic_map *bmap1,
1386 __isl_keep isl_basic_map *bmap2);
1387 int isl_map_is_equal(__isl_keep isl_map *map1,
1388 __isl_keep isl_map *map2);
1389 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1390 __isl_keep isl_map *map2);
1391 int isl_union_map_is_equal(
1392 __isl_keep isl_union_map *umap1,
1393 __isl_keep isl_union_map *umap2);
1395 =item * Disjointness
1397 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1398 __isl_keep isl_set *set2);
1402 int isl_set_is_subset(__isl_keep isl_set *set1,
1403 __isl_keep isl_set *set2);
1404 int isl_set_is_strict_subset(
1405 __isl_keep isl_set *set1,
1406 __isl_keep isl_set *set2);
1407 int isl_union_set_is_subset(
1408 __isl_keep isl_union_set *uset1,
1409 __isl_keep isl_union_set *uset2);
1410 int isl_union_set_is_strict_subset(
1411 __isl_keep isl_union_set *uset1,
1412 __isl_keep isl_union_set *uset2);
1413 int isl_basic_map_is_subset(
1414 __isl_keep isl_basic_map *bmap1,
1415 __isl_keep isl_basic_map *bmap2);
1416 int isl_basic_map_is_strict_subset(
1417 __isl_keep isl_basic_map *bmap1,
1418 __isl_keep isl_basic_map *bmap2);
1419 int isl_map_is_subset(
1420 __isl_keep isl_map *map1,
1421 __isl_keep isl_map *map2);
1422 int isl_map_is_strict_subset(
1423 __isl_keep isl_map *map1,
1424 __isl_keep isl_map *map2);
1425 int isl_union_map_is_subset(
1426 __isl_keep isl_union_map *umap1,
1427 __isl_keep isl_union_map *umap2);
1428 int isl_union_map_is_strict_subset(
1429 __isl_keep isl_union_map *umap1,
1430 __isl_keep isl_union_map *umap2);
1434 =head2 Unary Operations
1440 __isl_give isl_set *isl_set_complement(
1441 __isl_take isl_set *set);
1445 __isl_give isl_basic_map *isl_basic_map_reverse(
1446 __isl_take isl_basic_map *bmap);
1447 __isl_give isl_map *isl_map_reverse(
1448 __isl_take isl_map *map);
1449 __isl_give isl_union_map *isl_union_map_reverse(
1450 __isl_take isl_union_map *umap);
1454 __isl_give isl_basic_set *isl_basic_set_project_out(
1455 __isl_take isl_basic_set *bset,
1456 enum isl_dim_type type, unsigned first, unsigned n);
1457 __isl_give isl_basic_map *isl_basic_map_project_out(
1458 __isl_take isl_basic_map *bmap,
1459 enum isl_dim_type type, unsigned first, unsigned n);
1460 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1461 enum isl_dim_type type, unsigned first, unsigned n);
1462 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1463 enum isl_dim_type type, unsigned first, unsigned n);
1464 __isl_give isl_basic_set *isl_basic_map_domain(
1465 __isl_take isl_basic_map *bmap);
1466 __isl_give isl_basic_set *isl_basic_map_range(
1467 __isl_take isl_basic_map *bmap);
1468 __isl_give isl_set *isl_map_domain(
1469 __isl_take isl_map *bmap);
1470 __isl_give isl_set *isl_map_range(
1471 __isl_take isl_map *map);
1472 __isl_give isl_union_set *isl_union_map_domain(
1473 __isl_take isl_union_map *umap);
1474 __isl_give isl_union_set *isl_union_map_range(
1475 __isl_take isl_union_map *umap);
1477 __isl_give isl_basic_map *isl_basic_map_domain_map(
1478 __isl_take isl_basic_map *bmap);
1479 __isl_give isl_basic_map *isl_basic_map_range_map(
1480 __isl_take isl_basic_map *bmap);
1481 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1482 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1483 __isl_give isl_union_map *isl_union_map_domain_map(
1484 __isl_take isl_union_map *umap);
1485 __isl_give isl_union_map *isl_union_map_range_map(
1486 __isl_take isl_union_map *umap);
1488 The functions above construct a (basic, regular or union) relation
1489 that maps (a wrapped version of) the input relation to its domain or range.
1493 __isl_give isl_set *isl_set_eliminate(
1494 __isl_take isl_set *set, enum isl_dim_type type,
1495 unsigned first, unsigned n);
1497 Eliminate the coefficients for the given dimensions from the constraints,
1498 without removing the dimensions.
1502 __isl_give isl_basic_set *isl_basic_set_fix(
1503 __isl_take isl_basic_set *bset,
1504 enum isl_dim_type type, unsigned pos,
1506 __isl_give isl_basic_set *isl_basic_set_fix_si(
1507 __isl_take isl_basic_set *bset,
1508 enum isl_dim_type type, unsigned pos, int value);
1509 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1510 enum isl_dim_type type, unsigned pos,
1512 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1513 enum isl_dim_type type, unsigned pos, int value);
1514 __isl_give isl_basic_map *isl_basic_map_fix_si(
1515 __isl_take isl_basic_map *bmap,
1516 enum isl_dim_type type, unsigned pos, int value);
1517 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1518 enum isl_dim_type type, unsigned pos, int value);
1520 Intersect the set or relation with the hyperplane where the given
1521 dimension has the fixed given value.
1523 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1524 enum isl_dim_type type1, int pos1,
1525 enum isl_dim_type type2, int pos2);
1526 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1527 enum isl_dim_type type1, int pos1,
1528 enum isl_dim_type type2, int pos2);
1530 Intersect the set or relation with the hyperplane where the given
1531 dimensions are equal to each other.
1535 __isl_give isl_map *isl_set_identity(
1536 __isl_take isl_set *set);
1537 __isl_give isl_union_map *isl_union_set_identity(
1538 __isl_take isl_union_set *uset);
1540 Construct an identity relation on the given (union) set.
1544 __isl_give isl_basic_set *isl_basic_map_deltas(
1545 __isl_take isl_basic_map *bmap);
1546 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1547 __isl_give isl_union_set *isl_union_map_deltas(
1548 __isl_take isl_union_map *umap);
1550 These functions return a (basic) set containing the differences
1551 between image elements and corresponding domain elements in the input.
1553 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1554 __isl_take isl_basic_map *bmap);
1555 __isl_give isl_map *isl_map_deltas_map(
1556 __isl_take isl_map *map);
1557 __isl_give isl_union_map *isl_union_map_deltas_map(
1558 __isl_take isl_union_map *umap);
1560 The functions above construct a (basic, regular or union) relation
1561 that maps (a wrapped version of) the input relation to its delta set.
1565 Simplify the representation of a set or relation by trying
1566 to combine pairs of basic sets or relations into a single
1567 basic set or relation.
1569 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1570 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1571 __isl_give isl_union_set *isl_union_set_coalesce(
1572 __isl_take isl_union_set *uset);
1573 __isl_give isl_union_map *isl_union_map_coalesce(
1574 __isl_take isl_union_map *umap);
1576 =item * Detecting equalities
1578 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1579 __isl_take isl_basic_set *bset);
1580 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1581 __isl_take isl_basic_map *bmap);
1582 __isl_give isl_set *isl_set_detect_equalities(
1583 __isl_take isl_set *set);
1584 __isl_give isl_map *isl_map_detect_equalities(
1585 __isl_take isl_map *map);
1586 __isl_give isl_union_set *isl_union_set_detect_equalities(
1587 __isl_take isl_union_set *uset);
1588 __isl_give isl_union_map *isl_union_map_detect_equalities(
1589 __isl_take isl_union_map *umap);
1591 Simplify the representation of a set or relation by detecting implicit
1594 =item * Removing redundant constraints
1596 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1597 __isl_take isl_basic_set *bset);
1598 __isl_give isl_set *isl_set_remove_redundancies(
1599 __isl_take isl_set *set);
1600 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1601 __isl_take isl_basic_map *bmap);
1602 __isl_give isl_map *isl_map_remove_redundancies(
1603 __isl_take isl_map *map);
1607 __isl_give isl_basic_set *isl_set_convex_hull(
1608 __isl_take isl_set *set);
1609 __isl_give isl_basic_map *isl_map_convex_hull(
1610 __isl_take isl_map *map);
1612 If the input set or relation has any existentially quantified
1613 variables, then the result of these operations is currently undefined.
1617 __isl_give isl_basic_set *isl_set_simple_hull(
1618 __isl_take isl_set *set);
1619 __isl_give isl_basic_map *isl_map_simple_hull(
1620 __isl_take isl_map *map);
1621 __isl_give isl_union_map *isl_union_map_simple_hull(
1622 __isl_take isl_union_map *umap);
1624 These functions compute a single basic set or relation
1625 that contains the whole input set or relation.
1626 In particular, the output is described by translates
1627 of the constraints describing the basic sets or relations in the input.
1631 (See \autoref{s:simple hull}.)
1637 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1638 __isl_take isl_basic_set *bset);
1639 __isl_give isl_basic_set *isl_set_affine_hull(
1640 __isl_take isl_set *set);
1641 __isl_give isl_union_set *isl_union_set_affine_hull(
1642 __isl_take isl_union_set *uset);
1643 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1644 __isl_take isl_basic_map *bmap);
1645 __isl_give isl_basic_map *isl_map_affine_hull(
1646 __isl_take isl_map *map);
1647 __isl_give isl_union_map *isl_union_map_affine_hull(
1648 __isl_take isl_union_map *umap);
1650 In case of union sets and relations, the affine hull is computed
1653 =item * Polyhedral hull
1655 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1656 __isl_take isl_set *set);
1657 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1658 __isl_take isl_map *map);
1659 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1660 __isl_take isl_union_set *uset);
1661 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1662 __isl_take isl_union_map *umap);
1664 These functions compute a single basic set or relation
1665 not involving any existentially quantified variables
1666 that contains the whole input set or relation.
1667 In case of union sets and relations, the polyhedral hull is computed
1670 =item * Optimization
1672 #include <isl/ilp.h>
1673 enum isl_lp_result isl_basic_set_max(
1674 __isl_keep isl_basic_set *bset,
1675 __isl_keep isl_aff *obj, isl_int *opt)
1676 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1677 __isl_keep isl_aff *obj, isl_int *opt);
1678 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1679 __isl_keep isl_aff *obj, isl_int *opt);
1681 Compute the minimum or maximum of the integer affine expression C<obj>
1682 over the points in C<set>, returning the result in C<opt>.
1683 The return value may be one of C<isl_lp_error>,
1684 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1686 =item * Parametric optimization
1688 __isl_give isl_pw_aff *isl_set_dim_max(
1689 __isl_take isl_set *set, int pos);
1691 Compute the maximum of the given set dimension as a function of the
1692 parameters, but independently of the other set dimensions.
1693 For lexicographic optimization, see L<"Lexicographic Optimization">.
1697 The following functions compute either the set of (rational) coefficient
1698 values of valid constraints for the given set or the set of (rational)
1699 values satisfying the constraints with coefficients from the given set.
1700 Internally, these two sets of functions perform essentially the
1701 same operations, except that the set of coefficients is assumed to
1702 be a cone, while the set of values may be any polyhedron.
1703 The current implementation is based on the Farkas lemma and
1704 Fourier-Motzkin elimination, but this may change or be made optional
1705 in future. In particular, future implementations may use different
1706 dualization algorithms or skip the elimination step.
1708 __isl_give isl_basic_set *isl_basic_set_coefficients(
1709 __isl_take isl_basic_set *bset);
1710 __isl_give isl_basic_set *isl_set_coefficients(
1711 __isl_take isl_set *set);
1712 __isl_give isl_union_set *isl_union_set_coefficients(
1713 __isl_take isl_union_set *bset);
1714 __isl_give isl_basic_set *isl_basic_set_solutions(
1715 __isl_take isl_basic_set *bset);
1716 __isl_give isl_basic_set *isl_set_solutions(
1717 __isl_take isl_set *set);
1718 __isl_give isl_union_set *isl_union_set_solutions(
1719 __isl_take isl_union_set *bset);
1723 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1725 __isl_give isl_union_map *isl_union_map_power(
1726 __isl_take isl_union_map *umap, int *exact);
1728 Compute a parametric representation for all positive powers I<k> of C<map>.
1729 The result maps I<k> to a nested relation corresponding to the
1730 I<k>th power of C<map>.
1731 The result may be an overapproximation. If the result is known to be exact,
1732 then C<*exact> is set to C<1>.
1734 =item * Transitive closure
1736 __isl_give isl_map *isl_map_transitive_closure(
1737 __isl_take isl_map *map, int *exact);
1738 __isl_give isl_union_map *isl_union_map_transitive_closure(
1739 __isl_take isl_union_map *umap, int *exact);
1741 Compute the transitive closure of C<map>.
1742 The result may be an overapproximation. If the result is known to be exact,
1743 then C<*exact> is set to C<1>.
1745 =item * Reaching path lengths
1747 __isl_give isl_map *isl_map_reaching_path_lengths(
1748 __isl_take isl_map *map, int *exact);
1750 Compute a relation that maps each element in the range of C<map>
1751 to the lengths of all paths composed of edges in C<map> that
1752 end up in the given element.
1753 The result may be an overapproximation. If the result is known to be exact,
1754 then C<*exact> is set to C<1>.
1755 To compute the I<maximal> path length, the resulting relation
1756 should be postprocessed by C<isl_map_lexmax>.
1757 In particular, if the input relation is a dependence relation
1758 (mapping sources to sinks), then the maximal path length corresponds
1759 to the free schedule.
1760 Note, however, that C<isl_map_lexmax> expects the maximum to be
1761 finite, so if the path lengths are unbounded (possibly due to
1762 the overapproximation), then you will get an error message.
1766 __isl_give isl_basic_set *isl_basic_map_wrap(
1767 __isl_take isl_basic_map *bmap);
1768 __isl_give isl_set *isl_map_wrap(
1769 __isl_take isl_map *map);
1770 __isl_give isl_union_set *isl_union_map_wrap(
1771 __isl_take isl_union_map *umap);
1772 __isl_give isl_basic_map *isl_basic_set_unwrap(
1773 __isl_take isl_basic_set *bset);
1774 __isl_give isl_map *isl_set_unwrap(
1775 __isl_take isl_set *set);
1776 __isl_give isl_union_map *isl_union_set_unwrap(
1777 __isl_take isl_union_set *uset);
1781 Remove any internal structure of domain (and range) of the given
1782 set or relation. If there is any such internal structure in the input,
1783 then the name of the space is also removed.
1785 __isl_give isl_basic_set *isl_basic_set_flatten(
1786 __isl_take isl_basic_set *bset);
1787 __isl_give isl_set *isl_set_flatten(
1788 __isl_take isl_set *set);
1789 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1790 __isl_take isl_basic_map *bmap);
1791 __isl_give isl_map *isl_map_flatten_range(
1792 __isl_take isl_map *map);
1793 __isl_give isl_basic_map *isl_basic_map_flatten(
1794 __isl_take isl_basic_map *bmap);
1795 __isl_give isl_map *isl_map_flatten(
1796 __isl_take isl_map *map);
1798 __isl_give isl_map *isl_set_flatten_map(
1799 __isl_take isl_set *set);
1801 The function above constructs a relation
1802 that maps the input set to a flattened version of the set.
1806 Lift the input set to a space with extra dimensions corresponding
1807 to the existentially quantified variables in the input.
1808 In particular, the result lives in a wrapped map where the domain
1809 is the original space and the range corresponds to the original
1810 existentially quantified variables.
1812 __isl_give isl_basic_set *isl_basic_set_lift(
1813 __isl_take isl_basic_set *bset);
1814 __isl_give isl_set *isl_set_lift(
1815 __isl_take isl_set *set);
1816 __isl_give isl_union_set *isl_union_set_lift(
1817 __isl_take isl_union_set *uset);
1819 =item * Internal Product
1821 __isl_give isl_basic_map *isl_basic_map_zip(
1822 __isl_take isl_basic_map *bmap);
1823 __isl_give isl_map *isl_map_zip(
1824 __isl_take isl_map *map);
1825 __isl_give isl_union_map *isl_union_map_zip(
1826 __isl_take isl_union_map *umap);
1828 Given a relation with nested relations for domain and range,
1829 interchange the range of the domain with the domain of the range.
1831 =item * Aligning parameters
1833 __isl_give isl_set *isl_set_align_params(
1834 __isl_take isl_set *set,
1835 __isl_take isl_dim *model);
1836 __isl_give isl_map *isl_map_align_params(
1837 __isl_take isl_map *map,
1838 __isl_take isl_dim *model);
1840 Change the order of the parameters of the given set or relation
1841 such that the first parameters match those of C<model>.
1842 This may involve the introduction of extra parameters.
1843 All parameters need to be named.
1845 =item * Dimension manipulation
1847 __isl_give isl_set *isl_set_add_dims(
1848 __isl_take isl_set *set,
1849 enum isl_dim_type type, unsigned n);
1850 __isl_give isl_map *isl_map_add_dims(
1851 __isl_take isl_map *map,
1852 enum isl_dim_type type, unsigned n);
1854 It is usually not advisable to directly change the (input or output)
1855 space of a set or a relation as this removes the name and the internal
1856 structure of the space. However, the above functions can be useful
1857 to add new parameters, assuming
1858 C<isl_set_align_params> and C<isl_map_align_params>
1863 =head2 Binary Operations
1865 The two arguments of a binary operation not only need to live
1866 in the same C<isl_ctx>, they currently also need to have
1867 the same (number of) parameters.
1869 =head3 Basic Operations
1873 =item * Intersection
1875 __isl_give isl_basic_set *isl_basic_set_intersect(
1876 __isl_take isl_basic_set *bset1,
1877 __isl_take isl_basic_set *bset2);
1878 __isl_give isl_set *isl_set_intersect_params(
1879 __isl_take isl_set *set,
1880 __isl_take isl_set *params);
1881 __isl_give isl_set *isl_set_intersect(
1882 __isl_take isl_set *set1,
1883 __isl_take isl_set *set2);
1884 __isl_give isl_union_set *isl_union_set_intersect(
1885 __isl_take isl_union_set *uset1,
1886 __isl_take isl_union_set *uset2);
1887 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1888 __isl_take isl_basic_map *bmap,
1889 __isl_take isl_basic_set *bset);
1890 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1891 __isl_take isl_basic_map *bmap,
1892 __isl_take isl_basic_set *bset);
1893 __isl_give isl_basic_map *isl_basic_map_intersect(
1894 __isl_take isl_basic_map *bmap1,
1895 __isl_take isl_basic_map *bmap2);
1896 __isl_give isl_map *isl_map_intersect_params(
1897 __isl_take isl_map *map,
1898 __isl_take isl_set *params);
1899 __isl_give isl_map *isl_map_intersect_domain(
1900 __isl_take isl_map *map,
1901 __isl_take isl_set *set);
1902 __isl_give isl_map *isl_map_intersect_range(
1903 __isl_take isl_map *map,
1904 __isl_take isl_set *set);
1905 __isl_give isl_map *isl_map_intersect(
1906 __isl_take isl_map *map1,
1907 __isl_take isl_map *map2);
1908 __isl_give isl_union_map *isl_union_map_intersect_domain(
1909 __isl_take isl_union_map *umap,
1910 __isl_take isl_union_set *uset);
1911 __isl_give isl_union_map *isl_union_map_intersect_range(
1912 __isl_take isl_union_map *umap,
1913 __isl_take isl_union_set *uset);
1914 __isl_give isl_union_map *isl_union_map_intersect(
1915 __isl_take isl_union_map *umap1,
1916 __isl_take isl_union_map *umap2);
1920 __isl_give isl_set *isl_basic_set_union(
1921 __isl_take isl_basic_set *bset1,
1922 __isl_take isl_basic_set *bset2);
1923 __isl_give isl_map *isl_basic_map_union(
1924 __isl_take isl_basic_map *bmap1,
1925 __isl_take isl_basic_map *bmap2);
1926 __isl_give isl_set *isl_set_union(
1927 __isl_take isl_set *set1,
1928 __isl_take isl_set *set2);
1929 __isl_give isl_map *isl_map_union(
1930 __isl_take isl_map *map1,
1931 __isl_take isl_map *map2);
1932 __isl_give isl_union_set *isl_union_set_union(
1933 __isl_take isl_union_set *uset1,
1934 __isl_take isl_union_set *uset2);
1935 __isl_give isl_union_map *isl_union_map_union(
1936 __isl_take isl_union_map *umap1,
1937 __isl_take isl_union_map *umap2);
1939 =item * Set difference
1941 __isl_give isl_set *isl_set_subtract(
1942 __isl_take isl_set *set1,
1943 __isl_take isl_set *set2);
1944 __isl_give isl_map *isl_map_subtract(
1945 __isl_take isl_map *map1,
1946 __isl_take isl_map *map2);
1947 __isl_give isl_union_set *isl_union_set_subtract(
1948 __isl_take isl_union_set *uset1,
1949 __isl_take isl_union_set *uset2);
1950 __isl_give isl_union_map *isl_union_map_subtract(
1951 __isl_take isl_union_map *umap1,
1952 __isl_take isl_union_map *umap2);
1956 __isl_give isl_basic_set *isl_basic_set_apply(
1957 __isl_take isl_basic_set *bset,
1958 __isl_take isl_basic_map *bmap);
1959 __isl_give isl_set *isl_set_apply(
1960 __isl_take isl_set *set,
1961 __isl_take isl_map *map);
1962 __isl_give isl_union_set *isl_union_set_apply(
1963 __isl_take isl_union_set *uset,
1964 __isl_take isl_union_map *umap);
1965 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1966 __isl_take isl_basic_map *bmap1,
1967 __isl_take isl_basic_map *bmap2);
1968 __isl_give isl_basic_map *isl_basic_map_apply_range(
1969 __isl_take isl_basic_map *bmap1,
1970 __isl_take isl_basic_map *bmap2);
1971 __isl_give isl_map *isl_map_apply_domain(
1972 __isl_take isl_map *map1,
1973 __isl_take isl_map *map2);
1974 __isl_give isl_union_map *isl_union_map_apply_domain(
1975 __isl_take isl_union_map *umap1,
1976 __isl_take isl_union_map *umap2);
1977 __isl_give isl_map *isl_map_apply_range(
1978 __isl_take isl_map *map1,
1979 __isl_take isl_map *map2);
1980 __isl_give isl_union_map *isl_union_map_apply_range(
1981 __isl_take isl_union_map *umap1,
1982 __isl_take isl_union_map *umap2);
1984 =item * Cartesian Product
1986 __isl_give isl_set *isl_set_product(
1987 __isl_take isl_set *set1,
1988 __isl_take isl_set *set2);
1989 __isl_give isl_union_set *isl_union_set_product(
1990 __isl_take isl_union_set *uset1,
1991 __isl_take isl_union_set *uset2);
1992 __isl_give isl_basic_map *isl_basic_map_range_product(
1993 __isl_take isl_basic_map *bmap1,
1994 __isl_take isl_basic_map *bmap2);
1995 __isl_give isl_map *isl_map_range_product(
1996 __isl_take isl_map *map1,
1997 __isl_take isl_map *map2);
1998 __isl_give isl_union_map *isl_union_map_range_product(
1999 __isl_take isl_union_map *umap1,
2000 __isl_take isl_union_map *umap2);
2001 __isl_give isl_map *isl_map_product(
2002 __isl_take isl_map *map1,
2003 __isl_take isl_map *map2);
2004 __isl_give isl_union_map *isl_union_map_product(
2005 __isl_take isl_union_map *umap1,
2006 __isl_take isl_union_map *umap2);
2008 The above functions compute the cross product of the given
2009 sets or relations. The domains and ranges of the results
2010 are wrapped maps between domains and ranges of the inputs.
2011 To obtain a ``flat'' product, use the following functions
2014 __isl_give isl_basic_set *isl_basic_set_flat_product(
2015 __isl_take isl_basic_set *bset1,
2016 __isl_take isl_basic_set *bset2);
2017 __isl_give isl_set *isl_set_flat_product(
2018 __isl_take isl_set *set1,
2019 __isl_take isl_set *set2);
2020 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2021 __isl_take isl_basic_map *bmap1,
2022 __isl_take isl_basic_map *bmap2);
2023 __isl_give isl_map *isl_map_flat_range_product(
2024 __isl_take isl_map *map1,
2025 __isl_take isl_map *map2);
2026 __isl_give isl_union_map *isl_union_map_flat_range_product(
2027 __isl_take isl_union_map *umap1,
2028 __isl_take isl_union_map *umap2);
2029 __isl_give isl_basic_map *isl_basic_map_flat_product(
2030 __isl_take isl_basic_map *bmap1,
2031 __isl_take isl_basic_map *bmap2);
2032 __isl_give isl_map *isl_map_flat_product(
2033 __isl_take isl_map *map1,
2034 __isl_take isl_map *map2);
2036 =item * Simplification
2038 __isl_give isl_basic_set *isl_basic_set_gist(
2039 __isl_take isl_basic_set *bset,
2040 __isl_take isl_basic_set *context);
2041 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2042 __isl_take isl_set *context);
2043 __isl_give isl_union_set *isl_union_set_gist(
2044 __isl_take isl_union_set *uset,
2045 __isl_take isl_union_set *context);
2046 __isl_give isl_basic_map *isl_basic_map_gist(
2047 __isl_take isl_basic_map *bmap,
2048 __isl_take isl_basic_map *context);
2049 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2050 __isl_take isl_map *context);
2051 __isl_give isl_union_map *isl_union_map_gist(
2052 __isl_take isl_union_map *umap,
2053 __isl_take isl_union_map *context);
2055 The gist operation returns a set or relation that has the
2056 same intersection with the context as the input set or relation.
2057 Any implicit equality in the intersection is made explicit in the result,
2058 while all inequalities that are redundant with respect to the intersection
2060 In case of union sets and relations, the gist operation is performed
2065 =head3 Lexicographic Optimization
2067 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2068 the following functions
2069 compute a set that contains the lexicographic minimum or maximum
2070 of the elements in C<set> (or C<bset>) for those values of the parameters
2071 that satisfy C<dom>.
2072 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2073 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2075 In other words, the union of the parameter values
2076 for which the result is non-empty and of C<*empty>
2079 __isl_give isl_set *isl_basic_set_partial_lexmin(
2080 __isl_take isl_basic_set *bset,
2081 __isl_take isl_basic_set *dom,
2082 __isl_give isl_set **empty);
2083 __isl_give isl_set *isl_basic_set_partial_lexmax(
2084 __isl_take isl_basic_set *bset,
2085 __isl_take isl_basic_set *dom,
2086 __isl_give isl_set **empty);
2087 __isl_give isl_set *isl_set_partial_lexmin(
2088 __isl_take isl_set *set, __isl_take isl_set *dom,
2089 __isl_give isl_set **empty);
2090 __isl_give isl_set *isl_set_partial_lexmax(
2091 __isl_take isl_set *set, __isl_take isl_set *dom,
2092 __isl_give isl_set **empty);
2094 Given a (basic) set C<set> (or C<bset>), the following functions simply
2095 return a set containing the lexicographic minimum or maximum
2096 of the elements in C<set> (or C<bset>).
2097 In case of union sets, the optimum is computed per space.
2099 __isl_give isl_set *isl_basic_set_lexmin(
2100 __isl_take isl_basic_set *bset);
2101 __isl_give isl_set *isl_basic_set_lexmax(
2102 __isl_take isl_basic_set *bset);
2103 __isl_give isl_set *isl_set_lexmin(
2104 __isl_take isl_set *set);
2105 __isl_give isl_set *isl_set_lexmax(
2106 __isl_take isl_set *set);
2107 __isl_give isl_union_set *isl_union_set_lexmin(
2108 __isl_take isl_union_set *uset);
2109 __isl_give isl_union_set *isl_union_set_lexmax(
2110 __isl_take isl_union_set *uset);
2112 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2113 the following functions
2114 compute a relation that maps each element of C<dom>
2115 to the single lexicographic minimum or maximum
2116 of the elements that are associated to that same
2117 element in C<map> (or C<bmap>).
2118 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2119 that contains the elements in C<dom> that do not map
2120 to any elements in C<map> (or C<bmap>).
2121 In other words, the union of the domain of the result and of C<*empty>
2124 __isl_give isl_map *isl_basic_map_partial_lexmax(
2125 __isl_take isl_basic_map *bmap,
2126 __isl_take isl_basic_set *dom,
2127 __isl_give isl_set **empty);
2128 __isl_give isl_map *isl_basic_map_partial_lexmin(
2129 __isl_take isl_basic_map *bmap,
2130 __isl_take isl_basic_set *dom,
2131 __isl_give isl_set **empty);
2132 __isl_give isl_map *isl_map_partial_lexmax(
2133 __isl_take isl_map *map, __isl_take isl_set *dom,
2134 __isl_give isl_set **empty);
2135 __isl_give isl_map *isl_map_partial_lexmin(
2136 __isl_take isl_map *map, __isl_take isl_set *dom,
2137 __isl_give isl_set **empty);
2139 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2140 return a map mapping each element in the domain of
2141 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2142 of all elements associated to that element.
2143 In case of union relations, the optimum is computed per space.
2145 __isl_give isl_map *isl_basic_map_lexmin(
2146 __isl_take isl_basic_map *bmap);
2147 __isl_give isl_map *isl_basic_map_lexmax(
2148 __isl_take isl_basic_map *bmap);
2149 __isl_give isl_map *isl_map_lexmin(
2150 __isl_take isl_map *map);
2151 __isl_give isl_map *isl_map_lexmax(
2152 __isl_take isl_map *map);
2153 __isl_give isl_union_map *isl_union_map_lexmin(
2154 __isl_take isl_union_map *umap);
2155 __isl_give isl_union_map *isl_union_map_lexmax(
2156 __isl_take isl_union_map *umap);
2160 Lists are defined over several element types, including
2161 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2162 Here we take lists of C<isl_set>s as an example.
2163 Lists can be created, copied and freed using the following functions.
2165 #include <isl/list.h>
2166 __isl_give isl_set_list *isl_set_list_alloc(
2167 isl_ctx *ctx, int n);
2168 __isl_give isl_set_list *isl_set_list_copy(
2169 __isl_keep isl_set_list *list);
2170 __isl_give isl_set_list *isl_set_list_add(
2171 __isl_take isl_set_list *list,
2172 __isl_take isl_set *el);
2173 void isl_set_list_free(__isl_take isl_set_list *list);
2175 C<isl_set_list_alloc> creates an empty list with a capacity for
2178 Lists can be inspected using the following functions.
2180 #include <isl/list.h>
2181 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2182 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2183 __isl_give struct isl_set *isl_set_list_get_set(
2184 __isl_keep isl_set_list *list, int index);
2185 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2186 int (*fn)(__isl_take struct isl_set *el, void *user),
2189 Lists can be printed using
2191 #include <isl/list.h>
2192 __isl_give isl_printer *isl_printer_print_set_list(
2193 __isl_take isl_printer *p,
2194 __isl_keep isl_set_list *list);
2198 Matrices can be created, copied and freed using the following functions.
2200 #include <isl/mat.h>
2201 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2202 unsigned n_row, unsigned n_col);
2203 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2204 void isl_mat_free(__isl_take isl_mat *mat);
2206 Note that the elements of a newly created matrix may have arbitrary values.
2207 The elements can be changed and inspected using the following functions.
2209 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2210 int isl_mat_rows(__isl_keep isl_mat *mat);
2211 int isl_mat_cols(__isl_keep isl_mat *mat);
2212 int isl_mat_get_element(__isl_keep isl_mat *mat,
2213 int row, int col, isl_int *v);
2214 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2215 int row, int col, isl_int v);
2216 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2217 int row, int col, int v);
2219 C<isl_mat_get_element> will return a negative value if anything went wrong.
2220 In that case, the value of C<*v> is undefined.
2222 The following function can be used to compute the (right) inverse
2223 of a matrix, i.e., a matrix such that the product of the original
2224 and the inverse (in that order) is a multiple of the identity matrix.
2225 The input matrix is assumed to be of full row-rank.
2227 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2229 The following function can be used to compute the (right) kernel
2230 (or null space) of a matrix, i.e., a matrix such that the product of
2231 the original and the kernel (in that order) is the zero matrix.
2233 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2235 =head2 Piecewise Quasi Affine Expressions
2237 The zero quasi affine expression can be created using
2239 __isl_give isl_aff *isl_aff_zero(
2240 __isl_take isl_local_space *ls);
2242 A quasi affine expression can also be initialized from an C<isl_div>:
2244 #include <isl/div.h>
2245 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2247 An empty piecewise quasi affine expression (one with no cells)
2248 or a piecewise quasi affine expression with a single cell can
2249 be created using the following functions.
2251 #include <isl/aff.h>
2252 __isl_give isl_pw_aff *isl_pw_aff_empty(
2253 __isl_take isl_dim *dim);
2254 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2255 __isl_take isl_set *set, __isl_take isl_aff *aff);
2257 Quasi affine expressions can be copied and freed using
2259 #include <isl/aff.h>
2260 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2261 void *isl_aff_free(__isl_take isl_aff *aff);
2263 __isl_give isl_pw_aff *isl_pw_aff_copy(
2264 __isl_keep isl_pw_aff *pwaff);
2265 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2267 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2268 using the following function. The constraint is required to have
2269 a non-zero coefficient for the specified dimension.
2271 #include <isl/constraint.h>
2272 __isl_give isl_aff *isl_constraint_get_bound(
2273 __isl_keep isl_constraint *constraint,
2274 enum isl_dim_type type, int pos);
2276 The entire affine expression of the constraint can also be extracted
2277 using the following function.
2279 #include <isl/constraint.h>
2280 __isl_give isl_aff *isl_constraint_get_aff(
2281 __isl_keep isl_constraint *constraint);
2283 Conversely, an equality constraint equating
2284 the affine expression to zero or an inequality constraint enforcing
2285 the affine expression to be non-negative, can be constructed using
2287 __isl_give isl_constraint *isl_equality_from_aff(
2288 __isl_take isl_aff *aff);
2289 __isl_give isl_constraint *isl_inequality_from_aff(
2290 __isl_take isl_aff *aff);
2292 The expression can be inspected using
2294 #include <isl/aff.h>
2295 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2296 int isl_aff_dim(__isl_keep isl_aff *aff,
2297 enum isl_dim_type type);
2298 __isl_give isl_local_space *isl_aff_get_local_space(
2299 __isl_keep isl_aff *aff);
2300 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2301 enum isl_dim_type type, unsigned pos);
2302 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2304 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2305 enum isl_dim_type type, int pos, isl_int *v);
2306 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2308 __isl_give isl_div *isl_aff_get_div(
2309 __isl_keep isl_aff *aff, int pos);
2311 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2312 enum isl_dim_type type, unsigned first, unsigned n);
2313 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2314 enum isl_dim_type type, unsigned first, unsigned n);
2316 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2317 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2318 enum isl_dim_type type);
2319 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2321 It can be modified using
2323 #include <isl/aff.h>
2324 __isl_give isl_aff *isl_aff_set_dim_name(
2325 __isl_take isl_aff *aff, enum isl_dim_type type,
2326 unsigned pos, const char *s);
2327 __isl_give isl_aff *isl_aff_set_constant(
2328 __isl_take isl_aff *aff, isl_int v);
2329 __isl_give isl_aff *isl_aff_set_constant_si(
2330 __isl_take isl_aff *aff, int v);
2331 __isl_give isl_aff *isl_aff_set_coefficient(
2332 __isl_take isl_aff *aff,
2333 enum isl_dim_type type, int pos, isl_int v);
2334 __isl_give isl_aff *isl_aff_set_coefficient_si(
2335 __isl_take isl_aff *aff,
2336 enum isl_dim_type type, int pos, int v);
2337 __isl_give isl_aff *isl_aff_set_denominator(
2338 __isl_take isl_aff *aff, isl_int v);
2340 __isl_give isl_aff *isl_aff_add_constant(
2341 __isl_take isl_aff *aff, isl_int v);
2342 __isl_give isl_aff *isl_aff_add_constant_si(
2343 __isl_take isl_aff *aff, int v);
2344 __isl_give isl_aff *isl_aff_add_coefficient(
2345 __isl_take isl_aff *aff,
2346 enum isl_dim_type type, int pos, isl_int v);
2347 __isl_give isl_aff *isl_aff_add_coefficient_si(
2348 __isl_take isl_aff *aff,
2349 enum isl_dim_type type, int pos, int v);
2351 __isl_give isl_aff *isl_aff_insert_dims(
2352 __isl_take isl_aff *aff,
2353 enum isl_dim_type type, unsigned first, unsigned n);
2354 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2355 __isl_take isl_pw_aff *pwaff,
2356 enum isl_dim_type type, unsigned first, unsigned n);
2357 __isl_give isl_aff *isl_aff_add_dims(
2358 __isl_take isl_aff *aff,
2359 enum isl_dim_type type, unsigned n);
2360 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2361 __isl_take isl_pw_aff *pwaff,
2362 enum isl_dim_type type, unsigned n);
2363 __isl_give isl_aff *isl_aff_drop_dims(
2364 __isl_take isl_aff *aff,
2365 enum isl_dim_type type, unsigned first, unsigned n);
2366 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2367 __isl_take isl_pw_aff *pwaff,
2368 enum isl_dim_type type, unsigned first, unsigned n);
2370 Note that the C<set_constant> and C<set_coefficient> functions
2371 set the I<numerator> of the constant or coefficient, while
2372 C<add_constant> and C<add_coefficient> add an integer value to
2373 the possibly rational constant or coefficient.
2375 To check whether an affine expressions is obviously zero
2376 or obviously equal to some other affine expression, use
2378 #include <isl/aff.h>
2379 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2380 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2381 __isl_keep isl_aff *aff2);
2385 #include <isl/aff.h>
2386 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2387 __isl_take isl_aff *aff2);
2388 __isl_give isl_pw_aff *isl_pw_aff_add(
2389 __isl_take isl_pw_aff *pwaff1,
2390 __isl_take isl_pw_aff *pwaff2);
2391 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2392 __isl_take isl_aff *aff2);
2393 __isl_give isl_pw_aff *isl_pw_aff_sub(
2394 __isl_take isl_pw_aff *pwaff1,
2395 __isl_take isl_pw_aff *pwaff2);
2396 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2397 __isl_give isl_pw_aff *isl_pw_aff_neg(
2398 __isl_take isl_pw_aff *pwaff);
2399 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2400 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2401 __isl_take isl_pw_aff *pwaff);
2402 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2403 __isl_give isl_pw_aff *isl_pw_aff_floor(
2404 __isl_take isl_pw_aff *pwaff);
2405 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2407 __isl_give isl_pw_aff *isl_pw_aff_scale(
2408 __isl_take isl_pw_aff *pwaff, isl_int f);
2409 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2411 __isl_give isl_aff *isl_aff_scale_down_ui(
2412 __isl_take isl_aff *aff, unsigned f);
2413 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2414 __isl_take isl_pw_aff *pwaff, isl_int f);
2416 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2417 __isl_take isl_pw_aff *pwqp);
2419 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2420 __isl_take isl_pw_aff *pwaff,
2421 __isl_take isl_dim *model);
2423 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2424 __isl_take isl_set *context);
2425 __isl_give isl_pw_aff *isl_pw_aff_gist(
2426 __isl_take isl_pw_aff *pwaff,
2427 __isl_take isl_set *context);
2429 __isl_give isl_set *isl_pw_aff_domain(
2430 __isl_take isl_pw_aff *pwaff);
2432 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2433 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2434 __isl_give isl_set *isl_pw_aff_eq_set(
2435 __isl_take isl_pw_aff *pwaff1,
2436 __isl_take isl_pw_aff *pwaff2);
2437 __isl_give isl_set *isl_pw_aff_le_set(
2438 __isl_take isl_pw_aff *pwaff1,
2439 __isl_take isl_pw_aff *pwaff2);
2440 __isl_give isl_set *isl_pw_aff_lt_set(
2441 __isl_take isl_pw_aff *pwaff1,
2442 __isl_take isl_pw_aff *pwaff2);
2443 __isl_give isl_set *isl_pw_aff_ge_set(
2444 __isl_take isl_pw_aff *pwaff1,
2445 __isl_take isl_pw_aff *pwaff2);
2446 __isl_give isl_set *isl_pw_aff_gt_set(
2447 __isl_take isl_pw_aff *pwaff1,
2448 __isl_take isl_pw_aff *pwaff2);
2450 The function C<isl_aff_ge_basic_set> returns a basic set
2451 containing those elements in the shared space
2452 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2453 The function C<isl_aff_ge_set> returns a set
2454 containing those elements in the shared domain
2455 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2457 #include <isl/aff.h>
2458 __isl_give isl_set *isl_pw_aff_nonneg_set(
2459 __isl_take isl_pw_aff *pwaff);
2461 The function C<isl_pw_aff_nonneg_set> returns a set
2462 containing those elements in the domain
2463 of C<pwaff> where C<pwaff> is non-negative.
2465 #include <isl/aff.h>
2466 __isl_give isl_pw_aff *isl_pw_aff_cond(
2467 __isl_take isl_set *cond,
2468 __isl_take isl_pw_aff *pwaff_true,
2469 __isl_take isl_pw_aff *pwaff_false);
2471 The function C<isl_pw_aff_cond> performs a conditional operator
2472 and returns an expression that is equal to C<pwaff_true>
2473 for elements in C<cond> and equal to C<pwaff_false> for elements
2476 #include <isl/aff.h>
2477 __isl_give isl_pw_aff *isl_pw_aff_max(
2478 __isl_take isl_pw_aff *pwaff1,
2479 __isl_take isl_pw_aff *pwaff2);
2481 The function C<isl_pw_aff_max> computes a piecewise quasi-affine
2482 expression with a domain that is the union of those of C<pwaff1> and
2483 C<pwaff2> and such that on each cell, the quasi-affine expression is
2484 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2485 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2486 associated expression is the defined one.
2488 An expression can be printed using
2490 #include <isl/aff.h>
2491 __isl_give isl_printer *isl_printer_print_aff(
2492 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2494 __isl_give isl_printer *isl_printer_print_pw_aff(
2495 __isl_take isl_printer *p,
2496 __isl_keep isl_pw_aff *pwaff);
2500 Points are elements of a set. They can be used to construct
2501 simple sets (boxes) or they can be used to represent the
2502 individual elements of a set.
2503 The zero point (the origin) can be created using
2505 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2507 The coordinates of a point can be inspected, set and changed
2510 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2511 enum isl_dim_type type, int pos, isl_int *v);
2512 __isl_give isl_point *isl_point_set_coordinate(
2513 __isl_take isl_point *pnt,
2514 enum isl_dim_type type, int pos, isl_int v);
2516 __isl_give isl_point *isl_point_add_ui(
2517 __isl_take isl_point *pnt,
2518 enum isl_dim_type type, int pos, unsigned val);
2519 __isl_give isl_point *isl_point_sub_ui(
2520 __isl_take isl_point *pnt,
2521 enum isl_dim_type type, int pos, unsigned val);
2523 Other properties can be obtained using
2525 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2527 Points can be copied or freed using
2529 __isl_give isl_point *isl_point_copy(
2530 __isl_keep isl_point *pnt);
2531 void isl_point_free(__isl_take isl_point *pnt);
2533 A singleton set can be created from a point using
2535 __isl_give isl_basic_set *isl_basic_set_from_point(
2536 __isl_take isl_point *pnt);
2537 __isl_give isl_set *isl_set_from_point(
2538 __isl_take isl_point *pnt);
2540 and a box can be created from two opposite extremal points using
2542 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2543 __isl_take isl_point *pnt1,
2544 __isl_take isl_point *pnt2);
2545 __isl_give isl_set *isl_set_box_from_points(
2546 __isl_take isl_point *pnt1,
2547 __isl_take isl_point *pnt2);
2549 All elements of a B<bounded> (union) set can be enumerated using
2550 the following functions.
2552 int isl_set_foreach_point(__isl_keep isl_set *set,
2553 int (*fn)(__isl_take isl_point *pnt, void *user),
2555 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2556 int (*fn)(__isl_take isl_point *pnt, void *user),
2559 The function C<fn> is called for each integer point in
2560 C<set> with as second argument the last argument of
2561 the C<isl_set_foreach_point> call. The function C<fn>
2562 should return C<0> on success and C<-1> on failure.
2563 In the latter case, C<isl_set_foreach_point> will stop
2564 enumerating and return C<-1> as well.
2565 If the enumeration is performed successfully and to completion,
2566 then C<isl_set_foreach_point> returns C<0>.
2568 To obtain a single point of a (basic) set, use
2570 __isl_give isl_point *isl_basic_set_sample_point(
2571 __isl_take isl_basic_set *bset);
2572 __isl_give isl_point *isl_set_sample_point(
2573 __isl_take isl_set *set);
2575 If C<set> does not contain any (integer) points, then the
2576 resulting point will be ``void'', a property that can be
2579 int isl_point_is_void(__isl_keep isl_point *pnt);
2581 =head2 Piecewise Quasipolynomials
2583 A piecewise quasipolynomial is a particular kind of function that maps
2584 a parametric point to a rational value.
2585 More specifically, a quasipolynomial is a polynomial expression in greatest
2586 integer parts of affine expressions of parameters and variables.
2587 A piecewise quasipolynomial is a subdivision of a given parametric
2588 domain into disjoint cells with a quasipolynomial associated to
2589 each cell. The value of the piecewise quasipolynomial at a given
2590 point is the value of the quasipolynomial associated to the cell
2591 that contains the point. Outside of the union of cells,
2592 the value is assumed to be zero.
2593 For example, the piecewise quasipolynomial
2595 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2597 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2598 A given piecewise quasipolynomial has a fixed domain dimension.
2599 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2600 defined over different domains.
2601 Piecewise quasipolynomials are mainly used by the C<barvinok>
2602 library for representing the number of elements in a parametric set or map.
2603 For example, the piecewise quasipolynomial above represents
2604 the number of points in the map
2606 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2608 =head3 Printing (Piecewise) Quasipolynomials
2610 Quasipolynomials and piecewise quasipolynomials can be printed
2611 using the following functions.
2613 __isl_give isl_printer *isl_printer_print_qpolynomial(
2614 __isl_take isl_printer *p,
2615 __isl_keep isl_qpolynomial *qp);
2617 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2618 __isl_take isl_printer *p,
2619 __isl_keep isl_pw_qpolynomial *pwqp);
2621 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2622 __isl_take isl_printer *p,
2623 __isl_keep isl_union_pw_qpolynomial *upwqp);
2625 The output format of the printer
2626 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2627 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2629 In case of printing in C<ISL_FORMAT_C>, the user may want
2630 to set the names of all dimensions
2632 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2633 __isl_take isl_qpolynomial *qp,
2634 enum isl_dim_type type, unsigned pos,
2636 __isl_give isl_pw_qpolynomial *
2637 isl_pw_qpolynomial_set_dim_name(
2638 __isl_take isl_pw_qpolynomial *pwqp,
2639 enum isl_dim_type type, unsigned pos,
2642 =head3 Creating New (Piecewise) Quasipolynomials
2644 Some simple quasipolynomials can be created using the following functions.
2645 More complicated quasipolynomials can be created by applying
2646 operations such as addition and multiplication
2647 on the resulting quasipolynomials
2649 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2650 __isl_take isl_dim *dim);
2651 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2652 __isl_take isl_dim *dim);
2653 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2654 __isl_take isl_dim *dim);
2655 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2656 __isl_take isl_dim *dim);
2657 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2658 __isl_take isl_dim *dim);
2659 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2660 __isl_take isl_dim *dim,
2661 const isl_int n, const isl_int d);
2662 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2663 __isl_take isl_div *div);
2664 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2665 __isl_take isl_dim *dim,
2666 enum isl_dim_type type, unsigned pos);
2667 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2668 __isl_take isl_aff *aff);
2670 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2671 with a single cell can be created using the following functions.
2672 Multiple of these single cell piecewise quasipolynomials can
2673 be combined to create more complicated piecewise quasipolynomials.
2675 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2676 __isl_take isl_dim *dim);
2677 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2678 __isl_take isl_set *set,
2679 __isl_take isl_qpolynomial *qp);
2681 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2682 __isl_take isl_dim *dim);
2683 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2684 __isl_take isl_pw_qpolynomial *pwqp);
2685 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2686 __isl_take isl_union_pw_qpolynomial *upwqp,
2687 __isl_take isl_pw_qpolynomial *pwqp);
2689 Quasipolynomials can be copied and freed again using the following
2692 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2693 __isl_keep isl_qpolynomial *qp);
2694 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2696 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2697 __isl_keep isl_pw_qpolynomial *pwqp);
2698 void *isl_pw_qpolynomial_free(
2699 __isl_take isl_pw_qpolynomial *pwqp);
2701 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2702 __isl_keep isl_union_pw_qpolynomial *upwqp);
2703 void isl_union_pw_qpolynomial_free(
2704 __isl_take isl_union_pw_qpolynomial *upwqp);
2706 =head3 Inspecting (Piecewise) Quasipolynomials
2708 To iterate over all piecewise quasipolynomials in a union
2709 piecewise quasipolynomial, use the following function
2711 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2712 __isl_keep isl_union_pw_qpolynomial *upwqp,
2713 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2716 To extract the piecewise quasipolynomial from a union with a given dimension
2719 __isl_give isl_pw_qpolynomial *
2720 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2721 __isl_keep isl_union_pw_qpolynomial *upwqp,
2722 __isl_take isl_dim *dim);
2724 To iterate over the cells in a piecewise quasipolynomial,
2725 use either of the following two functions
2727 int isl_pw_qpolynomial_foreach_piece(
2728 __isl_keep isl_pw_qpolynomial *pwqp,
2729 int (*fn)(__isl_take isl_set *set,
2730 __isl_take isl_qpolynomial *qp,
2731 void *user), void *user);
2732 int isl_pw_qpolynomial_foreach_lifted_piece(
2733 __isl_keep isl_pw_qpolynomial *pwqp,
2734 int (*fn)(__isl_take isl_set *set,
2735 __isl_take isl_qpolynomial *qp,
2736 void *user), void *user);
2738 As usual, the function C<fn> should return C<0> on success
2739 and C<-1> on failure. The difference between
2740 C<isl_pw_qpolynomial_foreach_piece> and
2741 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2742 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2743 compute unique representations for all existentially quantified
2744 variables and then turn these existentially quantified variables
2745 into extra set variables, adapting the associated quasipolynomial
2746 accordingly. This means that the C<set> passed to C<fn>
2747 will not have any existentially quantified variables, but that
2748 the dimensions of the sets may be different for different
2749 invocations of C<fn>.
2751 To iterate over all terms in a quasipolynomial,
2754 int isl_qpolynomial_foreach_term(
2755 __isl_keep isl_qpolynomial *qp,
2756 int (*fn)(__isl_take isl_term *term,
2757 void *user), void *user);
2759 The terms themselves can be inspected and freed using
2762 unsigned isl_term_dim(__isl_keep isl_term *term,
2763 enum isl_dim_type type);
2764 void isl_term_get_num(__isl_keep isl_term *term,
2766 void isl_term_get_den(__isl_keep isl_term *term,
2768 int isl_term_get_exp(__isl_keep isl_term *term,
2769 enum isl_dim_type type, unsigned pos);
2770 __isl_give isl_div *isl_term_get_div(
2771 __isl_keep isl_term *term, unsigned pos);
2772 void isl_term_free(__isl_take isl_term *term);
2774 Each term is a product of parameters, set variables and
2775 integer divisions. The function C<isl_term_get_exp>
2776 returns the exponent of a given dimensions in the given term.
2777 The C<isl_int>s in the arguments of C<isl_term_get_num>
2778 and C<isl_term_get_den> need to have been initialized
2779 using C<isl_int_init> before calling these functions.
2781 =head3 Properties of (Piecewise) Quasipolynomials
2783 To check whether a quasipolynomial is actually a constant,
2784 use the following function.
2786 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2787 isl_int *n, isl_int *d);
2789 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2790 then the numerator and denominator of the constant
2791 are returned in C<*n> and C<*d>, respectively.
2793 =head3 Operations on (Piecewise) Quasipolynomials
2795 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2796 __isl_take isl_qpolynomial *qp, isl_int v);
2797 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2798 __isl_take isl_qpolynomial *qp);
2799 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2800 __isl_take isl_qpolynomial *qp1,
2801 __isl_take isl_qpolynomial *qp2);
2802 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2803 __isl_take isl_qpolynomial *qp1,
2804 __isl_take isl_qpolynomial *qp2);
2805 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2806 __isl_take isl_qpolynomial *qp1,
2807 __isl_take isl_qpolynomial *qp2);
2808 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2809 __isl_take isl_qpolynomial *qp, unsigned exponent);
2811 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2812 __isl_take isl_pw_qpolynomial *pwqp1,
2813 __isl_take isl_pw_qpolynomial *pwqp2);
2814 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2815 __isl_take isl_pw_qpolynomial *pwqp1,
2816 __isl_take isl_pw_qpolynomial *pwqp2);
2817 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2818 __isl_take isl_pw_qpolynomial *pwqp1,
2819 __isl_take isl_pw_qpolynomial *pwqp2);
2820 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2821 __isl_take isl_pw_qpolynomial *pwqp);
2822 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2823 __isl_take isl_pw_qpolynomial *pwqp1,
2824 __isl_take isl_pw_qpolynomial *pwqp2);
2826 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2827 __isl_take isl_union_pw_qpolynomial *upwqp1,
2828 __isl_take isl_union_pw_qpolynomial *upwqp2);
2829 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2830 __isl_take isl_union_pw_qpolynomial *upwqp1,
2831 __isl_take isl_union_pw_qpolynomial *upwqp2);
2832 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2833 __isl_take isl_union_pw_qpolynomial *upwqp1,
2834 __isl_take isl_union_pw_qpolynomial *upwqp2);
2836 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2837 __isl_take isl_pw_qpolynomial *pwqp,
2838 __isl_take isl_point *pnt);
2840 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2841 __isl_take isl_union_pw_qpolynomial *upwqp,
2842 __isl_take isl_point *pnt);
2844 __isl_give isl_set *isl_pw_qpolynomial_domain(
2845 __isl_take isl_pw_qpolynomial *pwqp);
2846 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2847 __isl_take isl_pw_qpolynomial *pwpq,
2848 __isl_take isl_set *set);
2850 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2851 __isl_take isl_union_pw_qpolynomial *upwqp);
2852 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2853 __isl_take isl_union_pw_qpolynomial *upwpq,
2854 __isl_take isl_union_set *uset);
2856 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2857 __isl_take isl_qpolynomial *qp,
2858 __isl_take isl_dim *model);
2860 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2861 __isl_take isl_union_pw_qpolynomial *upwqp);
2863 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2864 __isl_take isl_qpolynomial *qp,
2865 __isl_take isl_set *context);
2867 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2868 __isl_take isl_pw_qpolynomial *pwqp,
2869 __isl_take isl_set *context);
2871 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2872 __isl_take isl_union_pw_qpolynomial *upwqp,
2873 __isl_take isl_union_set *context);
2875 The gist operation applies the gist operation to each of
2876 the cells in the domain of the input piecewise quasipolynomial.
2877 The context is also exploited
2878 to simplify the quasipolynomials associated to each cell.
2880 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2881 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2882 __isl_give isl_union_pw_qpolynomial *
2883 isl_union_pw_qpolynomial_to_polynomial(
2884 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2886 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2887 the polynomial will be an overapproximation. If C<sign> is negative,
2888 it will be an underapproximation. If C<sign> is zero, the approximation
2889 will lie somewhere in between.
2891 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2893 A piecewise quasipolynomial reduction is a piecewise
2894 reduction (or fold) of quasipolynomials.
2895 In particular, the reduction can be maximum or a minimum.
2896 The objects are mainly used to represent the result of
2897 an upper or lower bound on a quasipolynomial over its domain,
2898 i.e., as the result of the following function.
2900 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2901 __isl_take isl_pw_qpolynomial *pwqp,
2902 enum isl_fold type, int *tight);
2904 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2905 __isl_take isl_union_pw_qpolynomial *upwqp,
2906 enum isl_fold type, int *tight);
2908 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2909 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2910 is the returned bound is known be tight, i.e., for each value
2911 of the parameters there is at least
2912 one element in the domain that reaches the bound.
2913 If the domain of C<pwqp> is not wrapping, then the bound is computed
2914 over all elements in that domain and the result has a purely parametric
2915 domain. If the domain of C<pwqp> is wrapping, then the bound is
2916 computed over the range of the wrapped relation. The domain of the
2917 wrapped relation becomes the domain of the result.
2919 A (piecewise) quasipolynomial reduction can be copied or freed using the
2920 following functions.
2922 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2923 __isl_keep isl_qpolynomial_fold *fold);
2924 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2925 __isl_keep isl_pw_qpolynomial_fold *pwf);
2926 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2927 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2928 void isl_qpolynomial_fold_free(
2929 __isl_take isl_qpolynomial_fold *fold);
2930 void *isl_pw_qpolynomial_fold_free(
2931 __isl_take isl_pw_qpolynomial_fold *pwf);
2932 void isl_union_pw_qpolynomial_fold_free(
2933 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2935 =head3 Printing Piecewise Quasipolynomial Reductions
2937 Piecewise quasipolynomial reductions can be printed
2938 using the following function.
2940 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2941 __isl_take isl_printer *p,
2942 __isl_keep isl_pw_qpolynomial_fold *pwf);
2943 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2944 __isl_take isl_printer *p,
2945 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2947 For C<isl_printer_print_pw_qpolynomial_fold>,
2948 output format of the printer
2949 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2950 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2951 output format of the printer
2952 needs to be set to C<ISL_FORMAT_ISL>.
2953 In case of printing in C<ISL_FORMAT_C>, the user may want
2954 to set the names of all dimensions
2956 __isl_give isl_pw_qpolynomial_fold *
2957 isl_pw_qpolynomial_fold_set_dim_name(
2958 __isl_take isl_pw_qpolynomial_fold *pwf,
2959 enum isl_dim_type type, unsigned pos,
2962 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2964 To iterate over all piecewise quasipolynomial reductions in a union
2965 piecewise quasipolynomial reduction, use the following function
2967 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2968 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2969 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2970 void *user), void *user);
2972 To iterate over the cells in a piecewise quasipolynomial reduction,
2973 use either of the following two functions
2975 int isl_pw_qpolynomial_fold_foreach_piece(
2976 __isl_keep isl_pw_qpolynomial_fold *pwf,
2977 int (*fn)(__isl_take isl_set *set,
2978 __isl_take isl_qpolynomial_fold *fold,
2979 void *user), void *user);
2980 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2981 __isl_keep isl_pw_qpolynomial_fold *pwf,
2982 int (*fn)(__isl_take isl_set *set,
2983 __isl_take isl_qpolynomial_fold *fold,
2984 void *user), void *user);
2986 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2987 of the difference between these two functions.
2989 To iterate over all quasipolynomials in a reduction, use
2991 int isl_qpolynomial_fold_foreach_qpolynomial(
2992 __isl_keep isl_qpolynomial_fold *fold,
2993 int (*fn)(__isl_take isl_qpolynomial *qp,
2994 void *user), void *user);
2996 =head3 Operations on Piecewise Quasipolynomial Reductions
2998 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
2999 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3001 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3002 __isl_take isl_pw_qpolynomial_fold *pwf1,
3003 __isl_take isl_pw_qpolynomial_fold *pwf2);
3005 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3006 __isl_take isl_pw_qpolynomial_fold *pwf1,
3007 __isl_take isl_pw_qpolynomial_fold *pwf2);
3009 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3010 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3011 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3013 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3014 __isl_take isl_pw_qpolynomial_fold *pwf,
3015 __isl_take isl_point *pnt);
3017 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3018 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3019 __isl_take isl_point *pnt);
3021 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3022 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3023 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3024 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3025 __isl_take isl_union_set *uset);
3027 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3028 __isl_take isl_pw_qpolynomial_fold *pwf);
3030 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3031 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3033 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3034 __isl_take isl_pw_qpolynomial_fold *pwf,
3035 __isl_take isl_set *context);
3037 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3038 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3039 __isl_take isl_union_set *context);
3041 The gist operation applies the gist operation to each of
3042 the cells in the domain of the input piecewise quasipolynomial reduction.
3043 In future, the operation will also exploit the context
3044 to simplify the quasipolynomial reductions associated to each cell.
3046 __isl_give isl_pw_qpolynomial_fold *
3047 isl_set_apply_pw_qpolynomial_fold(
3048 __isl_take isl_set *set,
3049 __isl_take isl_pw_qpolynomial_fold *pwf,
3051 __isl_give isl_pw_qpolynomial_fold *
3052 isl_map_apply_pw_qpolynomial_fold(
3053 __isl_take isl_map *map,
3054 __isl_take isl_pw_qpolynomial_fold *pwf,
3056 __isl_give isl_union_pw_qpolynomial_fold *
3057 isl_union_set_apply_union_pw_qpolynomial_fold(
3058 __isl_take isl_union_set *uset,
3059 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3061 __isl_give isl_union_pw_qpolynomial_fold *
3062 isl_union_map_apply_union_pw_qpolynomial_fold(
3063 __isl_take isl_union_map *umap,
3064 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3067 The functions taking a map
3068 compose the given map with the given piecewise quasipolynomial reduction.
3069 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3070 over all elements in the intersection of the range of the map
3071 and the domain of the piecewise quasipolynomial reduction
3072 as a function of an element in the domain of the map.
3073 The functions taking a set compute a bound over all elements in the
3074 intersection of the set and the domain of the
3075 piecewise quasipolynomial reduction.
3077 =head2 Dependence Analysis
3079 C<isl> contains specialized functionality for performing
3080 array dataflow analysis. That is, given a I<sink> access relation
3081 and a collection of possible I<source> access relations,
3082 C<isl> can compute relations that describe
3083 for each iteration of the sink access, which iteration
3084 of which of the source access relations was the last
3085 to access the same data element before the given iteration
3087 To compute standard flow dependences, the sink should be
3088 a read, while the sources should be writes.
3089 If any of the source accesses are marked as being I<may>
3090 accesses, then there will be a dependence to the last
3091 I<must> access B<and> to any I<may> access that follows
3092 this last I<must> access.
3093 In particular, if I<all> sources are I<may> accesses,
3094 then memory based dependence analysis is performed.
3095 If, on the other hand, all sources are I<must> accesses,
3096 then value based dependence analysis is performed.
3098 #include <isl/flow.h>
3100 typedef int (*isl_access_level_before)(void *first, void *second);
3102 __isl_give isl_access_info *isl_access_info_alloc(
3103 __isl_take isl_map *sink,
3104 void *sink_user, isl_access_level_before fn,
3106 __isl_give isl_access_info *isl_access_info_add_source(
3107 __isl_take isl_access_info *acc,
3108 __isl_take isl_map *source, int must,
3110 void isl_access_info_free(__isl_take isl_access_info *acc);
3112 __isl_give isl_flow *isl_access_info_compute_flow(
3113 __isl_take isl_access_info *acc);
3115 int isl_flow_foreach(__isl_keep isl_flow *deps,
3116 int (*fn)(__isl_take isl_map *dep, int must,
3117 void *dep_user, void *user),
3119 __isl_give isl_map *isl_flow_get_no_source(
3120 __isl_keep isl_flow *deps, int must);
3121 void isl_flow_free(__isl_take isl_flow *deps);
3123 The function C<isl_access_info_compute_flow> performs the actual
3124 dependence analysis. The other functions are used to construct
3125 the input for this function or to read off the output.
3127 The input is collected in an C<isl_access_info>, which can
3128 be created through a call to C<isl_access_info_alloc>.
3129 The arguments to this functions are the sink access relation
3130 C<sink>, a token C<sink_user> used to identify the sink
3131 access to the user, a callback function for specifying the
3132 relative order of source and sink accesses, and the number
3133 of source access relations that will be added.
3134 The callback function has type C<int (*)(void *first, void *second)>.
3135 The function is called with two user supplied tokens identifying
3136 either a source or the sink and it should return the shared nesting
3137 level and the relative order of the two accesses.
3138 In particular, let I<n> be the number of loops shared by
3139 the two accesses. If C<first> precedes C<second> textually,
3140 then the function should return I<2 * n + 1>; otherwise,
3141 it should return I<2 * n>.
3142 The sources can be added to the C<isl_access_info> by performing
3143 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3144 C<must> indicates whether the source is a I<must> access
3145 or a I<may> access. Note that a multi-valued access relation
3146 should only be marked I<must> if every iteration in the domain
3147 of the relation accesses I<all> elements in its image.
3148 The C<source_user> token is again used to identify
3149 the source access. The range of the source access relation
3150 C<source> should have the same dimension as the range
3151 of the sink access relation.
3152 The C<isl_access_info_free> function should usually not be
3153 called explicitly, because it is called implicitly by
3154 C<isl_access_info_compute_flow>.
3156 The result of the dependence analysis is collected in an
3157 C<isl_flow>. There may be elements of
3158 the sink access for which no preceding source access could be
3159 found or for which all preceding sources are I<may> accesses.
3160 The relations containing these elements can be obtained through
3161 calls to C<isl_flow_get_no_source>, the first with C<must> set
3162 and the second with C<must> unset.
3163 In the case of standard flow dependence analysis,
3164 with the sink a read and the sources I<must> writes,
3165 the first relation corresponds to the reads from uninitialized
3166 array elements and the second relation is empty.
3167 The actual flow dependences can be extracted using
3168 C<isl_flow_foreach>. This function will call the user-specified
3169 callback function C<fn> for each B<non-empty> dependence between
3170 a source and the sink. The callback function is called
3171 with four arguments, the actual flow dependence relation
3172 mapping source iterations to sink iterations, a boolean that
3173 indicates whether it is a I<must> or I<may> dependence, a token
3174 identifying the source and an additional C<void *> with value
3175 equal to the third argument of the C<isl_flow_foreach> call.
3176 A dependence is marked I<must> if it originates from a I<must>
3177 source and if it is not followed by any I<may> sources.
3179 After finishing with an C<isl_flow>, the user should call
3180 C<isl_flow_free> to free all associated memory.
3182 A higher-level interface to dependence analysis is provided
3183 by the following function.
3185 #include <isl/flow.h>
3187 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3188 __isl_take isl_union_map *must_source,
3189 __isl_take isl_union_map *may_source,
3190 __isl_take isl_union_map *schedule,
3191 __isl_give isl_union_map **must_dep,
3192 __isl_give isl_union_map **may_dep,
3193 __isl_give isl_union_map **must_no_source,
3194 __isl_give isl_union_map **may_no_source);
3196 The arrays are identified by the tuple names of the ranges
3197 of the accesses. The iteration domains by the tuple names
3198 of the domains of the accesses and of the schedule.
3199 The relative order of the iteration domains is given by the
3200 schedule. The relations returned through C<must_no_source>
3201 and C<may_no_source> are subsets of C<sink>.
3202 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3203 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3204 any of the other arguments is treated as an error.
3208 B<The functionality described in this section is fairly new
3209 and may be subject to change.>
3211 The following function can be used to compute a schedule
3212 for a union of domains. The generated schedule respects
3213 all C<validity> dependences. That is, all dependence distances
3214 over these dependences in the scheduled space are lexicographically
3215 positive. The generated schedule schedule also tries to minimize
3216 the dependence distances over C<proximity> dependences.
3217 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3218 for groups of domains where the dependence distances have only
3219 non-negative values.
3220 The algorithm used to construct the schedule is similar to that
3223 #include <isl/schedule.h>
3224 __isl_give isl_schedule *isl_union_set_compute_schedule(
3225 __isl_take isl_union_set *domain,
3226 __isl_take isl_union_map *validity,
3227 __isl_take isl_union_map *proximity);
3228 void *isl_schedule_free(__isl_take isl_schedule *sched);
3230 A mapping from the domains to the scheduled space can be obtained
3231 from an C<isl_schedule> using the following function.
3233 __isl_give isl_union_map *isl_schedule_get_map(
3234 __isl_keep isl_schedule *sched);
3236 A representation of the schedule can be printed using
3238 __isl_give isl_printer *isl_printer_print_schedule(
3239 __isl_take isl_printer *p,
3240 __isl_keep isl_schedule *schedule);
3242 A representation of the schedule as a forest of bands can be obtained
3243 using the following function.
3245 __isl_give isl_band_list *isl_schedule_get_band_forest(
3246 __isl_keep isl_schedule *schedule);
3248 The list can be manipulated as explained in L<"Lists">.
3249 The bands inside the list can be copied and freed using the following
3252 #include <isl/band.h>
3253 __isl_give isl_band *isl_band_copy(
3254 __isl_keep isl_band *band);
3255 void *isl_band_free(__isl_take isl_band *band);
3257 Each band contains zero or more scheduling dimensions.
3258 These are referred to as the members of the band.
3259 The section of the schedule that corresponds to the band is
3260 referred to as the partial schedule of the band.
3261 For those nodes that participate in a band, the outer scheduling
3262 dimensions form the prefix schedule, while the inner scheduling
3263 dimensions form the suffix schedule.
3264 That is, if we take a cut of the band forest, then the union of
3265 the concatenations of the prefix, partial and suffix schedules of
3266 each band in the cut is equal to the entire schedule (modulo
3267 some possible padding at the end with zero scheduling dimensions).
3268 The properties of a band can be inspected using the following functions.
3270 #include <isl/band.h>
3271 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3273 int isl_band_has_children(__isl_keep isl_band *band);
3274 __isl_give isl_band_list *isl_band_get_children(
3275 __isl_keep isl_band *band);
3277 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3278 __isl_keep isl_band *band);
3279 __isl_give isl_union_map *isl_band_get_partial_schedule(
3280 __isl_keep isl_band *band);
3281 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3282 __isl_keep isl_band *band);
3284 int isl_band_n_member(__isl_keep isl_band *band);
3285 int isl_band_member_is_zero_distance(
3286 __isl_keep isl_band *band, int pos);
3288 Note that a scheduling dimension is considered to be ``zero
3289 distance'' if it does not carry any proximity dependences
3291 That is, if the dependence distances of the proximity
3292 dependences are all zero in that direction (for fixed
3293 iterations of outer bands).
3295 A representation of the band can be printed using
3297 #include <isl/band.h>
3298 __isl_give isl_printer *isl_printer_print_band(
3299 __isl_take isl_printer *p,
3300 __isl_keep isl_band *band);
3302 =head2 Parametric Vertex Enumeration
3304 The parametric vertex enumeration described in this section
3305 is mainly intended to be used internally and by the C<barvinok>
3308 #include <isl/vertices.h>
3309 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3310 __isl_keep isl_basic_set *bset);
3312 The function C<isl_basic_set_compute_vertices> performs the
3313 actual computation of the parametric vertices and the chamber
3314 decomposition and store the result in an C<isl_vertices> object.
3315 This information can be queried by either iterating over all
3316 the vertices or iterating over all the chambers or cells
3317 and then iterating over all vertices that are active on the chamber.
3319 int isl_vertices_foreach_vertex(
3320 __isl_keep isl_vertices *vertices,
3321 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3324 int isl_vertices_foreach_cell(
3325 __isl_keep isl_vertices *vertices,
3326 int (*fn)(__isl_take isl_cell *cell, void *user),
3328 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3329 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3332 Other operations that can be performed on an C<isl_vertices> object are
3335 isl_ctx *isl_vertices_get_ctx(
3336 __isl_keep isl_vertices *vertices);
3337 int isl_vertices_get_n_vertices(
3338 __isl_keep isl_vertices *vertices);
3339 void isl_vertices_free(__isl_take isl_vertices *vertices);
3341 Vertices can be inspected and destroyed using the following functions.
3343 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3344 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3345 __isl_give isl_basic_set *isl_vertex_get_domain(
3346 __isl_keep isl_vertex *vertex);
3347 __isl_give isl_basic_set *isl_vertex_get_expr(
3348 __isl_keep isl_vertex *vertex);
3349 void isl_vertex_free(__isl_take isl_vertex *vertex);
3351 C<isl_vertex_get_expr> returns a singleton parametric set describing
3352 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3354 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3355 B<rational> basic sets, so they should mainly be used for inspection
3356 and should not be mixed with integer sets.
3358 Chambers can be inspected and destroyed using the following functions.
3360 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3361 __isl_give isl_basic_set *isl_cell_get_domain(
3362 __isl_keep isl_cell *cell);
3363 void isl_cell_free(__isl_take isl_cell *cell);
3367 Although C<isl> is mainly meant to be used as a library,
3368 it also contains some basic applications that use some
3369 of the functionality of C<isl>.
3370 The input may be specified in either the L<isl format>
3371 or the L<PolyLib format>.
3373 =head2 C<isl_polyhedron_sample>
3375 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3376 an integer element of the polyhedron, if there is any.
3377 The first column in the output is the denominator and is always
3378 equal to 1. If the polyhedron contains no integer points,
3379 then a vector of length zero is printed.
3383 C<isl_pip> takes the same input as the C<example> program
3384 from the C<piplib> distribution, i.e., a set of constraints
3385 on the parameters, a line containing only -1 and finally a set
3386 of constraints on a parametric polyhedron.
3387 The coefficients of the parameters appear in the last columns
3388 (but before the final constant column).
3389 The output is the lexicographic minimum of the parametric polyhedron.
3390 As C<isl> currently does not have its own output format, the output
3391 is just a dump of the internal state.
3393 =head2 C<isl_polyhedron_minimize>
3395 C<isl_polyhedron_minimize> computes the minimum of some linear
3396 or affine objective function over the integer points in a polyhedron.
3397 If an affine objective function
3398 is given, then the constant should appear in the last column.
3400 =head2 C<isl_polytope_scan>
3402 Given a polytope, C<isl_polytope_scan> prints
3403 all integer points in the polytope.