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.
96 =head3 Changes since isl-0.07
100 =item * The function C<isl_pw_aff_max> has been renamed to
101 C<isl_pw_aff_union_max>.
107 The source of C<isl> can be obtained either as a tarball
108 or from the git repository. Both are available from
109 L<http://freshmeat.net/projects/isl/>.
110 The installation process depends on how you obtained
113 =head2 Installation from the git repository
117 =item 1 Clone or update the repository
119 The first time the source is obtained, you need to clone
122 git clone git://repo.or.cz/isl.git
124 To obtain updates, you need to pull in the latest changes
128 =item 2 Generate C<configure>
134 After performing the above steps, continue
135 with the L<Common installation instructions>.
137 =head2 Common installation instructions
141 =item 1 Obtain C<GMP>
143 Building C<isl> requires C<GMP>, including its headers files.
144 Your distribution may not provide these header files by default
145 and you may need to install a package called C<gmp-devel> or something
146 similar. Alternatively, C<GMP> can be built from
147 source, available from L<http://gmplib.org/>.
151 C<isl> uses the standard C<autoconf> C<configure> script.
156 optionally followed by some configure options.
157 A complete list of options can be obtained by running
161 Below we discuss some of the more common options.
163 C<isl> can optionally use C<piplib>, but no
164 C<piplib> functionality is currently used by default.
165 The C<--with-piplib> option can
166 be used to specify which C<piplib>
167 library to use, either an installed version (C<system>),
168 an externally built version (C<build>)
169 or no version (C<no>). The option C<build> is mostly useful
170 in C<configure> scripts of larger projects that bundle both C<isl>
177 Installation prefix for C<isl>
179 =item C<--with-gmp-prefix>
181 Installation prefix for C<GMP> (architecture-independent files).
183 =item C<--with-gmp-exec-prefix>
185 Installation prefix for C<GMP> (architecture-dependent files).
187 =item C<--with-piplib>
189 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
191 =item C<--with-piplib-prefix>
193 Installation prefix for C<system> C<piplib> (architecture-independent files).
195 =item C<--with-piplib-exec-prefix>
197 Installation prefix for C<system> C<piplib> (architecture-dependent files).
199 =item C<--with-piplib-builddir>
201 Location where C<build> C<piplib> was built.
209 =item 4 Install (optional)
217 =head2 Initialization
219 All manipulations of integer sets and relations occur within
220 the context of an C<isl_ctx>.
221 A given C<isl_ctx> can only be used within a single thread.
222 All arguments of a function are required to have been allocated
223 within the same context.
224 There are currently no functions available for moving an object
225 from one C<isl_ctx> to another C<isl_ctx>. This means that
226 there is currently no way of safely moving an object from one
227 thread to another, unless the whole C<isl_ctx> is moved.
229 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
230 freed using C<isl_ctx_free>.
231 All objects allocated within an C<isl_ctx> should be freed
232 before the C<isl_ctx> itself is freed.
234 isl_ctx *isl_ctx_alloc();
235 void isl_ctx_free(isl_ctx *ctx);
239 All operations on integers, mainly the coefficients
240 of the constraints describing the sets and relations,
241 are performed in exact integer arithmetic using C<GMP>.
242 However, to allow future versions of C<isl> to optionally
243 support fixed integer arithmetic, all calls to C<GMP>
244 are wrapped inside C<isl> specific macros.
245 The basic type is C<isl_int> and the operations below
246 are available on this type.
247 The meanings of these operations are essentially the same
248 as their C<GMP> C<mpz_> counterparts.
249 As always with C<GMP> types, C<isl_int>s need to be
250 initialized with C<isl_int_init> before they can be used
251 and they need to be released with C<isl_int_clear>
253 The user should not assume that an C<isl_int> is represented
254 as a C<mpz_t>, but should instead explicitly convert between
255 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
256 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
260 =item isl_int_init(i)
262 =item isl_int_clear(i)
264 =item isl_int_set(r,i)
266 =item isl_int_set_si(r,i)
268 =item isl_int_set_gmp(r,g)
270 =item isl_int_get_gmp(i,g)
272 =item isl_int_abs(r,i)
274 =item isl_int_neg(r,i)
276 =item isl_int_swap(i,j)
278 =item isl_int_swap_or_set(i,j)
280 =item isl_int_add_ui(r,i,j)
282 =item isl_int_sub_ui(r,i,j)
284 =item isl_int_add(r,i,j)
286 =item isl_int_sub(r,i,j)
288 =item isl_int_mul(r,i,j)
290 =item isl_int_mul_ui(r,i,j)
292 =item isl_int_addmul(r,i,j)
294 =item isl_int_submul(r,i,j)
296 =item isl_int_gcd(r,i,j)
298 =item isl_int_lcm(r,i,j)
300 =item isl_int_divexact(r,i,j)
302 =item isl_int_cdiv_q(r,i,j)
304 =item isl_int_fdiv_q(r,i,j)
306 =item isl_int_fdiv_r(r,i,j)
308 =item isl_int_fdiv_q_ui(r,i,j)
310 =item isl_int_read(r,s)
312 =item isl_int_print(out,i,width)
316 =item isl_int_cmp(i,j)
318 =item isl_int_cmp_si(i,si)
320 =item isl_int_eq(i,j)
322 =item isl_int_ne(i,j)
324 =item isl_int_lt(i,j)
326 =item isl_int_le(i,j)
328 =item isl_int_gt(i,j)
330 =item isl_int_ge(i,j)
332 =item isl_int_abs_eq(i,j)
334 =item isl_int_abs_ne(i,j)
336 =item isl_int_abs_lt(i,j)
338 =item isl_int_abs_gt(i,j)
340 =item isl_int_abs_ge(i,j)
342 =item isl_int_is_zero(i)
344 =item isl_int_is_one(i)
346 =item isl_int_is_negone(i)
348 =item isl_int_is_pos(i)
350 =item isl_int_is_neg(i)
352 =item isl_int_is_nonpos(i)
354 =item isl_int_is_nonneg(i)
356 =item isl_int_is_divisible_by(i,j)
360 =head2 Sets and Relations
362 C<isl> uses six types of objects for representing sets and relations,
363 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
364 C<isl_union_set> and C<isl_union_map>.
365 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
366 can be described as a conjunction of affine constraints, while
367 C<isl_set> and C<isl_map> represent unions of
368 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
369 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
370 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
371 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
372 where dimensions with different space names
373 (see L<Dimension Specifications>) are considered different as well.
374 The difference between sets and relations (maps) is that sets have
375 one set of variables, while relations have two sets of variables,
376 input variables and output variables.
378 =head2 Memory Management
380 Since a high-level operation on sets and/or relations usually involves
381 several substeps and since the user is usually not interested in
382 the intermediate results, most functions that return a new object
383 will also release all the objects passed as arguments.
384 If the user still wants to use one or more of these arguments
385 after the function call, she should pass along a copy of the
386 object rather than the object itself.
387 The user is then responsible for making sure that the original
388 object gets used somewhere else or is explicitly freed.
390 The arguments and return values of all documents functions are
391 annotated to make clear which arguments are released and which
392 arguments are preserved. In particular, the following annotations
399 C<__isl_give> means that a new object is returned.
400 The user should make sure that the returned pointer is
401 used exactly once as a value for an C<__isl_take> argument.
402 In between, it can be used as a value for as many
403 C<__isl_keep> arguments as the user likes.
404 There is one exception, and that is the case where the
405 pointer returned is C<NULL>. Is this case, the user
406 is free to use it as an C<__isl_take> argument or not.
410 C<__isl_take> means that the object the argument points to
411 is taken over by the function and may no longer be used
412 by the user as an argument to any other function.
413 The pointer value must be one returned by a function
414 returning an C<__isl_give> pointer.
415 If the user passes in a C<NULL> value, then this will
416 be treated as an error in the sense that the function will
417 not perform its usual operation. However, it will still
418 make sure that all the the other C<__isl_take> arguments
423 C<__isl_keep> means that the function will only use the object
424 temporarily. After the function has finished, the user
425 can still use it as an argument to other functions.
426 A C<NULL> value will be treated in the same way as
427 a C<NULL> value for an C<__isl_take> argument.
431 =head2 Dimension Specifications
433 Whenever a new set or relation is created from scratch,
434 its dimension needs to be specified using an C<isl_dim>.
437 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
438 unsigned nparam, unsigned n_in, unsigned n_out);
439 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
440 unsigned nparam, unsigned dim);
441 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
442 void isl_dim_free(__isl_take isl_dim *dim);
443 unsigned isl_dim_size(__isl_keep isl_dim *dim,
444 enum isl_dim_type type);
446 The dimension specification used for creating a set
447 needs to be created using C<isl_dim_set_alloc>, while
448 that for creating a relation
449 needs to be created using C<isl_dim_alloc>.
450 C<isl_dim_size> can be used
451 to find out the number of dimensions of each type in
452 a dimension specification, where type may be
453 C<isl_dim_param>, C<isl_dim_in> (only for relations),
454 C<isl_dim_out> (only for relations), C<isl_dim_set>
455 (only for sets) or C<isl_dim_all>.
457 It is often useful to create objects that live in the
458 same space as some other object. This can be accomplished
459 by creating the new objects
460 (see L<Creating New Sets and Relations> or
461 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
462 specification of the original object.
465 __isl_give isl_dim *isl_basic_set_get_dim(
466 __isl_keep isl_basic_set *bset);
467 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
469 #include <isl/union_set.h>
470 __isl_give isl_dim *isl_union_set_get_dim(
471 __isl_keep isl_union_set *uset);
474 __isl_give isl_dim *isl_basic_map_get_dim(
475 __isl_keep isl_basic_map *bmap);
476 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
478 #include <isl/union_map.h>
479 __isl_give isl_dim *isl_union_map_get_dim(
480 __isl_keep isl_union_map *umap);
482 #include <isl/constraint.h>
483 __isl_give isl_dim *isl_constraint_get_dim(
484 __isl_keep isl_constraint *constraint);
486 #include <isl/polynomial.h>
487 __isl_give isl_dim *isl_qpolynomial_get_dim(
488 __isl_keep isl_qpolynomial *qp);
489 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
490 __isl_keep isl_qpolynomial_fold *fold);
491 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
492 __isl_keep isl_pw_qpolynomial *pwqp);
493 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
494 __isl_keep isl_union_pw_qpolynomial *upwqp);
495 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
496 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
499 __isl_give isl_dim *isl_aff_get_dim(
500 __isl_keep isl_aff *aff);
501 __isl_give isl_dim *isl_pw_aff_get_dim(
502 __isl_keep isl_pw_aff *pwaff);
504 #include <isl/point.h>
505 __isl_give isl_dim *isl_point_get_dim(
506 __isl_keep isl_point *pnt);
508 The names of the individual dimensions may be set or read off
509 using the following functions.
512 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
513 enum isl_dim_type type, unsigned pos,
514 __isl_keep const char *name);
515 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
516 enum isl_dim_type type, unsigned pos);
518 Note that C<isl_dim_get_name> returns a pointer to some internal
519 data structure, so the result can only be used while the
520 corresponding C<isl_dim> is alive.
521 Also note that every function that operates on two sets or relations
522 requires that both arguments have the same parameters. This also
523 means that if one of the arguments has named parameters, then the
524 other needs to have named parameters too and the names need to match.
525 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
526 have different parameters (as long as they are named), in which case
527 the result will have as parameters the union of the parameters of
530 The names of entire spaces may be set or read off
531 using the following functions.
534 __isl_give isl_dim *isl_dim_set_tuple_name(
535 __isl_take isl_dim *dim,
536 enum isl_dim_type type, const char *s);
537 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
538 enum isl_dim_type type);
540 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
541 or C<isl_dim_set>. As with C<isl_dim_get_name>,
542 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
544 Binary operations require the corresponding spaces of their arguments
545 to have the same name.
547 Spaces can be nested. In particular, the domain of a set or
548 the domain or range of a relation can be a nested relation.
549 The following functions can be used to construct and deconstruct
550 such nested dimension specifications.
553 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
554 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
555 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
557 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
558 be the dimension specification of a set, while that of
559 C<isl_dim_wrap> should be the dimension specification of a relation.
560 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
561 of a relation, while that of C<isl_dim_wrap> is the dimension specification
564 Dimension specifications can be created from other dimension
565 specifications using the following functions.
567 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
568 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
569 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
570 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
571 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
572 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
573 __isl_take isl_dim *right);
574 __isl_give isl_dim *isl_dim_align_params(
575 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
576 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
577 enum isl_dim_type type, unsigned pos, unsigned n);
578 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
579 enum isl_dim_type type, unsigned n);
580 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
581 enum isl_dim_type type, unsigned first, unsigned n);
582 __isl_give isl_dim *isl_dim_map_from_set(
583 __isl_take isl_dim *dim);
584 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
586 Note that if dimensions are added or removed from a space, then
587 the name and the internal structure are lost.
591 A local space is essentially a dimension specification with
592 zero or more existentially quantified variables.
593 The local space of a basic set or relation can be obtained
594 using the following functions.
597 __isl_give isl_local_space *isl_basic_set_get_local_space(
598 __isl_keep isl_basic_set *bset);
601 __isl_give isl_local_space *isl_basic_map_get_local_space(
602 __isl_keep isl_basic_map *bmap);
604 A new local space can be created from a dimension specification using
606 #include <isl/local_space.h>
607 __isl_give isl_local_space *isl_local_space_from_dim(
608 __isl_take isl_dim *dim);
610 They can be inspected, copied and freed using the following functions.
612 #include <isl/local_space.h>
613 isl_ctx *isl_local_space_get_ctx(
614 __isl_keep isl_local_space *ls);
615 int isl_local_space_dim(__isl_keep isl_local_space *ls,
616 enum isl_dim_type type);
617 const char *isl_local_space_get_dim_name(
618 __isl_keep isl_local_space *ls,
619 enum isl_dim_type type, unsigned pos);
620 __isl_give isl_local_space *isl_local_space_set_dim_name(
621 __isl_take isl_local_space *ls,
622 enum isl_dim_type type, unsigned pos, const char *s);
623 __isl_give isl_dim *isl_local_space_get_dim(
624 __isl_keep isl_local_space *ls);
625 __isl_give isl_div *isl_local_space_get_div(
626 __isl_keep isl_local_space *ls, int pos);
627 __isl_give isl_local_space *isl_local_space_copy(
628 __isl_keep isl_local_space *ls);
629 void *isl_local_space_free(__isl_take isl_local_space *ls);
631 Two local spaces can be compared using
633 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
634 __isl_keep isl_local_space *ls2);
636 Local spaces can be created from other local spaces
637 using the following functions.
639 __isl_give isl_local_space *isl_local_space_from_domain(
640 __isl_take isl_local_space *ls);
641 __isl_give isl_local_space *isl_local_space_add_dims(
642 __isl_take isl_local_space *ls,
643 enum isl_dim_type type, unsigned n);
644 __isl_give isl_local_space *isl_local_space_insert_dims(
645 __isl_take isl_local_space *ls,
646 enum isl_dim_type type, unsigned first, unsigned n);
647 __isl_give isl_local_space *isl_local_space_drop_dims(
648 __isl_take isl_local_space *ls,
649 enum isl_dim_type type, unsigned first, unsigned n);
651 =head2 Input and Output
653 C<isl> supports its own input/output format, which is similar
654 to the C<Omega> format, but also supports the C<PolyLib> format
659 The C<isl> format is similar to that of C<Omega>, but has a different
660 syntax for describing the parameters and allows for the definition
661 of an existentially quantified variable as the integer division
662 of an affine expression.
663 For example, the set of integers C<i> between C<0> and C<n>
664 such that C<i % 10 <= 6> can be described as
666 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
669 A set or relation can have several disjuncts, separated
670 by the keyword C<or>. Each disjunct is either a conjunction
671 of constraints or a projection (C<exists>) of a conjunction
672 of constraints. The constraints are separated by the keyword
675 =head3 C<PolyLib> format
677 If the represented set is a union, then the first line
678 contains a single number representing the number of disjuncts.
679 Otherwise, a line containing the number C<1> is optional.
681 Each disjunct is represented by a matrix of constraints.
682 The first line contains two numbers representing
683 the number of rows and columns,
684 where the number of rows is equal to the number of constraints
685 and the number of columns is equal to two plus the number of variables.
686 The following lines contain the actual rows of the constraint matrix.
687 In each row, the first column indicates whether the constraint
688 is an equality (C<0>) or inequality (C<1>). The final column
689 corresponds to the constant term.
691 If the set is parametric, then the coefficients of the parameters
692 appear in the last columns before the constant column.
693 The coefficients of any existentially quantified variables appear
694 between those of the set variables and those of the parameters.
696 =head3 Extended C<PolyLib> format
698 The extended C<PolyLib> format is nearly identical to the
699 C<PolyLib> format. The only difference is that the line
700 containing the number of rows and columns of a constraint matrix
701 also contains four additional numbers:
702 the number of output dimensions, the number of input dimensions,
703 the number of local dimensions (i.e., the number of existentially
704 quantified variables) and the number of parameters.
705 For sets, the number of ``output'' dimensions is equal
706 to the number of set dimensions, while the number of ``input''
712 __isl_give isl_basic_set *isl_basic_set_read_from_file(
713 isl_ctx *ctx, FILE *input, int nparam);
714 __isl_give isl_basic_set *isl_basic_set_read_from_str(
715 isl_ctx *ctx, const char *str, int nparam);
716 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
717 FILE *input, int nparam);
718 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
719 const char *str, int nparam);
722 __isl_give isl_basic_map *isl_basic_map_read_from_file(
723 isl_ctx *ctx, FILE *input, int nparam);
724 __isl_give isl_basic_map *isl_basic_map_read_from_str(
725 isl_ctx *ctx, const char *str, int nparam);
726 __isl_give isl_map *isl_map_read_from_file(
727 struct isl_ctx *ctx, FILE *input, int nparam);
728 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
729 const char *str, int nparam);
731 #include <isl/union_set.h>
732 __isl_give isl_union_set *isl_union_set_read_from_file(
733 isl_ctx *ctx, FILE *input);
734 __isl_give isl_union_set *isl_union_set_read_from_str(
735 struct isl_ctx *ctx, const char *str);
737 #include <isl/union_map.h>
738 __isl_give isl_union_map *isl_union_map_read_from_file(
739 isl_ctx *ctx, FILE *input);
740 __isl_give isl_union_map *isl_union_map_read_from_str(
741 struct isl_ctx *ctx, const char *str);
743 The input format is autodetected and may be either the C<PolyLib> format
744 or the C<isl> format.
745 C<nparam> specifies how many of the final columns in
746 the C<PolyLib> format correspond to parameters.
747 If input is given in the C<isl> format, then the number
748 of parameters needs to be equal to C<nparam>.
749 If C<nparam> is negative, then any number of parameters
750 is accepted in the C<isl> format and zero parameters
751 are assumed in the C<PolyLib> format.
755 Before anything can be printed, an C<isl_printer> needs to
758 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
760 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
761 void isl_printer_free(__isl_take isl_printer *printer);
762 __isl_give char *isl_printer_get_str(
763 __isl_keep isl_printer *printer);
765 The behavior of the printer can be modified in various ways
767 __isl_give isl_printer *isl_printer_set_output_format(
768 __isl_take isl_printer *p, int output_format);
769 __isl_give isl_printer *isl_printer_set_indent(
770 __isl_take isl_printer *p, int indent);
771 __isl_give isl_printer *isl_printer_indent(
772 __isl_take isl_printer *p, int indent);
773 __isl_give isl_printer *isl_printer_set_prefix(
774 __isl_take isl_printer *p, const char *prefix);
775 __isl_give isl_printer *isl_printer_set_suffix(
776 __isl_take isl_printer *p, const char *suffix);
778 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
779 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
780 and defaults to C<ISL_FORMAT_ISL>.
781 Each line in the output is indented by C<indent> (set by
782 C<isl_printer_set_indent>) spaces
783 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
784 In the C<PolyLib> format output,
785 the coefficients of the existentially quantified variables
786 appear between those of the set variables and those
788 The function C<isl_printer_indent> increases the indentation
789 by the specified amount (which may be negative).
791 To actually print something, use
794 __isl_give isl_printer *isl_printer_print_basic_set(
795 __isl_take isl_printer *printer,
796 __isl_keep isl_basic_set *bset);
797 __isl_give isl_printer *isl_printer_print_set(
798 __isl_take isl_printer *printer,
799 __isl_keep isl_set *set);
802 __isl_give isl_printer *isl_printer_print_basic_map(
803 __isl_take isl_printer *printer,
804 __isl_keep isl_basic_map *bmap);
805 __isl_give isl_printer *isl_printer_print_map(
806 __isl_take isl_printer *printer,
807 __isl_keep isl_map *map);
809 #include <isl/union_set.h>
810 __isl_give isl_printer *isl_printer_print_union_set(
811 __isl_take isl_printer *p,
812 __isl_keep isl_union_set *uset);
814 #include <isl/union_map.h>
815 __isl_give isl_printer *isl_printer_print_union_map(
816 __isl_take isl_printer *p,
817 __isl_keep isl_union_map *umap);
819 When called on a file printer, the following function flushes
820 the file. When called on a string printer, the buffer is cleared.
822 __isl_give isl_printer *isl_printer_flush(
823 __isl_take isl_printer *p);
825 =head2 Creating New Sets and Relations
827 C<isl> has functions for creating some standard sets and relations.
831 =item * Empty sets and relations
833 __isl_give isl_basic_set *isl_basic_set_empty(
834 __isl_take isl_dim *dim);
835 __isl_give isl_basic_map *isl_basic_map_empty(
836 __isl_take isl_dim *dim);
837 __isl_give isl_set *isl_set_empty(
838 __isl_take isl_dim *dim);
839 __isl_give isl_map *isl_map_empty(
840 __isl_take isl_dim *dim);
841 __isl_give isl_union_set *isl_union_set_empty(
842 __isl_take isl_dim *dim);
843 __isl_give isl_union_map *isl_union_map_empty(
844 __isl_take isl_dim *dim);
846 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
847 is only used to specify the parameters.
849 =item * Universe sets and relations
851 __isl_give isl_basic_set *isl_basic_set_universe(
852 __isl_take isl_dim *dim);
853 __isl_give isl_basic_map *isl_basic_map_universe(
854 __isl_take isl_dim *dim);
855 __isl_give isl_set *isl_set_universe(
856 __isl_take isl_dim *dim);
857 __isl_give isl_map *isl_map_universe(
858 __isl_take isl_dim *dim);
859 __isl_give isl_union_set *isl_union_set_universe(
860 __isl_take isl_union_set *uset);
861 __isl_give isl_union_map *isl_union_map_universe(
862 __isl_take isl_union_map *umap);
864 The sets and relations constructed by the functions above
865 contain all integer values, while those constructed by the
866 functions below only contain non-negative values.
868 __isl_give isl_basic_set *isl_basic_set_nat_universe(
869 __isl_take isl_dim *dim);
870 __isl_give isl_basic_map *isl_basic_map_nat_universe(
871 __isl_take isl_dim *dim);
872 __isl_give isl_set *isl_set_nat_universe(
873 __isl_take isl_dim *dim);
874 __isl_give isl_map *isl_map_nat_universe(
875 __isl_take isl_dim *dim);
877 =item * Identity relations
879 __isl_give isl_basic_map *isl_basic_map_identity(
880 __isl_take isl_dim *dim);
881 __isl_give isl_map *isl_map_identity(
882 __isl_take isl_dim *dim);
884 The number of input and output dimensions in C<dim> needs
887 =item * Lexicographic order
889 __isl_give isl_map *isl_map_lex_lt(
890 __isl_take isl_dim *set_dim);
891 __isl_give isl_map *isl_map_lex_le(
892 __isl_take isl_dim *set_dim);
893 __isl_give isl_map *isl_map_lex_gt(
894 __isl_take isl_dim *set_dim);
895 __isl_give isl_map *isl_map_lex_ge(
896 __isl_take isl_dim *set_dim);
897 __isl_give isl_map *isl_map_lex_lt_first(
898 __isl_take isl_dim *dim, unsigned n);
899 __isl_give isl_map *isl_map_lex_le_first(
900 __isl_take isl_dim *dim, unsigned n);
901 __isl_give isl_map *isl_map_lex_gt_first(
902 __isl_take isl_dim *dim, unsigned n);
903 __isl_give isl_map *isl_map_lex_ge_first(
904 __isl_take isl_dim *dim, unsigned n);
906 The first four functions take a dimension specification for a B<set>
907 and return relations that express that the elements in the domain
908 are lexicographically less
909 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
910 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
911 than the elements in the range.
912 The last four functions take a dimension specification for a map
913 and return relations that express that the first C<n> dimensions
914 in the domain are lexicographically less
915 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
916 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
917 than the first C<n> dimensions in the range.
921 A basic set or relation can be converted to a set or relation
922 using the following functions.
924 __isl_give isl_set *isl_set_from_basic_set(
925 __isl_take isl_basic_set *bset);
926 __isl_give isl_map *isl_map_from_basic_map(
927 __isl_take isl_basic_map *bmap);
929 Sets and relations can be converted to union sets and relations
930 using the following functions.
932 __isl_give isl_union_map *isl_union_map_from_map(
933 __isl_take isl_map *map);
934 __isl_give isl_union_set *isl_union_set_from_set(
935 __isl_take isl_set *set);
937 The inverse conversions below can only be used if the input
938 union set or relation is known to contain elements in exactly one
941 __isl_give isl_set *isl_set_from_union_set(
942 __isl_take isl_union_set *uset);
943 __isl_give isl_map *isl_map_from_union_map(
944 __isl_take isl_union_map *umap);
946 Sets and relations can be copied and freed again using the following
949 __isl_give isl_basic_set *isl_basic_set_copy(
950 __isl_keep isl_basic_set *bset);
951 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
952 __isl_give isl_union_set *isl_union_set_copy(
953 __isl_keep isl_union_set *uset);
954 __isl_give isl_basic_map *isl_basic_map_copy(
955 __isl_keep isl_basic_map *bmap);
956 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
957 __isl_give isl_union_map *isl_union_map_copy(
958 __isl_keep isl_union_map *umap);
959 void isl_basic_set_free(__isl_take isl_basic_set *bset);
960 void isl_set_free(__isl_take isl_set *set);
961 void *isl_union_set_free(__isl_take isl_union_set *uset);
962 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
963 void isl_map_free(__isl_take isl_map *map);
964 void *isl_union_map_free(__isl_take isl_union_map *umap);
966 Other sets and relations can be constructed by starting
967 from a universe set or relation, adding equality and/or
968 inequality constraints and then projecting out the
969 existentially quantified variables, if any.
970 Constraints can be constructed, manipulated and
971 added to (or removed from) (basic) sets and relations
972 using the following functions.
974 #include <isl/constraint.h>
975 __isl_give isl_constraint *isl_equality_alloc(
976 __isl_take isl_dim *dim);
977 __isl_give isl_constraint *isl_inequality_alloc(
978 __isl_take isl_dim *dim);
979 void isl_constraint_set_constant(
980 __isl_keep isl_constraint *constraint, isl_int v);
981 void isl_constraint_set_coefficient(
982 __isl_keep isl_constraint *constraint,
983 enum isl_dim_type type, int pos, isl_int v);
984 __isl_give isl_basic_map *isl_basic_map_add_constraint(
985 __isl_take isl_basic_map *bmap,
986 __isl_take isl_constraint *constraint);
987 __isl_give isl_basic_set *isl_basic_set_add_constraint(
988 __isl_take isl_basic_set *bset,
989 __isl_take isl_constraint *constraint);
990 __isl_give isl_map *isl_map_add_constraint(
991 __isl_take isl_map *map,
992 __isl_take isl_constraint *constraint);
993 __isl_give isl_set *isl_set_add_constraint(
994 __isl_take isl_set *set,
995 __isl_take isl_constraint *constraint);
996 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
997 __isl_take isl_basic_set *bset,
998 __isl_take isl_constraint *constraint);
1000 For example, to create a set containing the even integers
1001 between 10 and 42, you would use the following code.
1004 struct isl_dim *dim;
1005 struct isl_constraint *c;
1006 struct isl_basic_set *bset;
1009 dim = isl_dim_set_alloc(ctx, 0, 2);
1010 bset = isl_basic_set_universe(isl_dim_copy(dim));
1012 c = isl_equality_alloc(isl_dim_copy(dim));
1013 isl_int_set_si(v, -1);
1014 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1015 isl_int_set_si(v, 2);
1016 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
1017 bset = isl_basic_set_add_constraint(bset, c);
1019 c = isl_inequality_alloc(isl_dim_copy(dim));
1020 isl_int_set_si(v, -10);
1021 isl_constraint_set_constant(c, v);
1022 isl_int_set_si(v, 1);
1023 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1024 bset = isl_basic_set_add_constraint(bset, c);
1026 c = isl_inequality_alloc(dim);
1027 isl_int_set_si(v, 42);
1028 isl_constraint_set_constant(c, v);
1029 isl_int_set_si(v, -1);
1030 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1031 bset = isl_basic_set_add_constraint(bset, c);
1033 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1039 struct isl_basic_set *bset;
1040 bset = isl_basic_set_read_from_str(ctx,
1041 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1043 A basic set or relation can also be constructed from two matrices
1044 describing the equalities and the inequalities.
1046 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1047 __isl_take isl_dim *dim,
1048 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1049 enum isl_dim_type c1,
1050 enum isl_dim_type c2, enum isl_dim_type c3,
1051 enum isl_dim_type c4);
1052 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1053 __isl_take isl_dim *dim,
1054 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1055 enum isl_dim_type c1,
1056 enum isl_dim_type c2, enum isl_dim_type c3,
1057 enum isl_dim_type c4, enum isl_dim_type c5);
1059 The C<isl_dim_type> arguments indicate the order in which
1060 different kinds of variables appear in the input matrices
1061 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1062 C<isl_dim_set> and C<isl_dim_div> for sets and
1063 of C<isl_dim_cst>, C<isl_dim_param>,
1064 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1066 A (basic) relation can also be constructed from a (piecewise) affine expression
1067 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1069 __isl_give isl_basic_map *isl_basic_map_from_aff(
1070 __isl_take isl_aff *aff);
1071 __isl_give isl_map *isl_map_from_pw_aff(
1072 __isl_take isl_pw_aff *pwaff);
1073 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1074 __isl_take isl_dim *domain_dim,
1075 __isl_take isl_aff_list *list);
1077 The C<domain_dim> argument describes the domain of the resulting
1078 basic relation. It is required because the C<list> may consist
1079 of zero affine expressions.
1081 =head2 Inspecting Sets and Relations
1083 Usually, the user should not have to care about the actual constraints
1084 of the sets and maps, but should instead apply the abstract operations
1085 explained in the following sections.
1086 Occasionally, however, it may be required to inspect the individual
1087 coefficients of the constraints. This section explains how to do so.
1088 In these cases, it may also be useful to have C<isl> compute
1089 an explicit representation of the existentially quantified variables.
1091 __isl_give isl_set *isl_set_compute_divs(
1092 __isl_take isl_set *set);
1093 __isl_give isl_map *isl_map_compute_divs(
1094 __isl_take isl_map *map);
1095 __isl_give isl_union_set *isl_union_set_compute_divs(
1096 __isl_take isl_union_set *uset);
1097 __isl_give isl_union_map *isl_union_map_compute_divs(
1098 __isl_take isl_union_map *umap);
1100 This explicit representation defines the existentially quantified
1101 variables as integer divisions of the other variables, possibly
1102 including earlier existentially quantified variables.
1103 An explicitly represented existentially quantified variable therefore
1104 has a unique value when the values of the other variables are known.
1105 If, furthermore, the same existentials, i.e., existentials
1106 with the same explicit representations, should appear in the
1107 same order in each of the disjuncts of a set or map, then the user should call
1108 either of the following functions.
1110 __isl_give isl_set *isl_set_align_divs(
1111 __isl_take isl_set *set);
1112 __isl_give isl_map *isl_map_align_divs(
1113 __isl_take isl_map *map);
1115 Alternatively, the existentially quantified variables can be removed
1116 using the following functions, which compute an overapproximation.
1118 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1119 __isl_take isl_basic_set *bset);
1120 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1121 __isl_take isl_basic_map *bmap);
1122 __isl_give isl_set *isl_set_remove_divs(
1123 __isl_take isl_set *set);
1124 __isl_give isl_map *isl_map_remove_divs(
1125 __isl_take isl_map *map);
1127 To iterate over all the sets or maps in a union set or map, use
1129 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1130 int (*fn)(__isl_take isl_set *set, void *user),
1132 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1133 int (*fn)(__isl_take isl_map *map, void *user),
1136 The number of sets or maps in a union set or map can be obtained
1139 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1140 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1142 To extract the set or map from a union with a given dimension
1145 __isl_give isl_set *isl_union_set_extract_set(
1146 __isl_keep isl_union_set *uset,
1147 __isl_take isl_dim *dim);
1148 __isl_give isl_map *isl_union_map_extract_map(
1149 __isl_keep isl_union_map *umap,
1150 __isl_take isl_dim *dim);
1152 To iterate over all the basic sets or maps in a set or map, use
1154 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1155 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1157 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1158 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1161 The callback function C<fn> should return 0 if successful and
1162 -1 if an error occurs. In the latter case, or if any other error
1163 occurs, the above functions will return -1.
1165 It should be noted that C<isl> does not guarantee that
1166 the basic sets or maps passed to C<fn> are disjoint.
1167 If this is required, then the user should call one of
1168 the following functions first.
1170 __isl_give isl_set *isl_set_make_disjoint(
1171 __isl_take isl_set *set);
1172 __isl_give isl_map *isl_map_make_disjoint(
1173 __isl_take isl_map *map);
1175 The number of basic sets in a set can be obtained
1178 int isl_set_n_basic_set(__isl_keep isl_set *set);
1180 To iterate over the constraints of a basic set or map, use
1182 #include <isl/constraint.h>
1184 int isl_basic_map_foreach_constraint(
1185 __isl_keep isl_basic_map *bmap,
1186 int (*fn)(__isl_take isl_constraint *c, void *user),
1188 void isl_constraint_free(struct isl_constraint *c);
1190 Again, the callback function C<fn> should return 0 if successful and
1191 -1 if an error occurs. In the latter case, or if any other error
1192 occurs, the above functions will return -1.
1193 The constraint C<c> represents either an equality or an inequality.
1194 Use the following function to find out whether a constraint
1195 represents an equality. If not, it represents an inequality.
1197 int isl_constraint_is_equality(
1198 __isl_keep isl_constraint *constraint);
1200 The coefficients of the constraints can be inspected using
1201 the following functions.
1203 void isl_constraint_get_constant(
1204 __isl_keep isl_constraint *constraint, isl_int *v);
1205 void isl_constraint_get_coefficient(
1206 __isl_keep isl_constraint *constraint,
1207 enum isl_dim_type type, int pos, isl_int *v);
1208 int isl_constraint_involves_dims(
1209 __isl_keep isl_constraint *constraint,
1210 enum isl_dim_type type, unsigned first, unsigned n);
1212 The explicit representations of the existentially quantified
1213 variables can be inspected using the following functions.
1214 Note that the user is only allowed to use these functions
1215 if the inspected set or map is the result of a call
1216 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1218 __isl_give isl_div *isl_constraint_div(
1219 __isl_keep isl_constraint *constraint, int pos);
1220 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1221 void isl_div_get_constant(__isl_keep isl_div *div,
1223 void isl_div_get_denominator(__isl_keep isl_div *div,
1225 void isl_div_get_coefficient(__isl_keep isl_div *div,
1226 enum isl_dim_type type, int pos, isl_int *v);
1228 To obtain the constraints of a basic set or map in matrix
1229 form, use the following functions.
1231 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1232 __isl_keep isl_basic_set *bset,
1233 enum isl_dim_type c1, enum isl_dim_type c2,
1234 enum isl_dim_type c3, enum isl_dim_type c4);
1235 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1236 __isl_keep isl_basic_set *bset,
1237 enum isl_dim_type c1, enum isl_dim_type c2,
1238 enum isl_dim_type c3, enum isl_dim_type c4);
1239 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1240 __isl_keep isl_basic_map *bmap,
1241 enum isl_dim_type c1,
1242 enum isl_dim_type c2, enum isl_dim_type c3,
1243 enum isl_dim_type c4, enum isl_dim_type c5);
1244 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1245 __isl_keep isl_basic_map *bmap,
1246 enum isl_dim_type c1,
1247 enum isl_dim_type c2, enum isl_dim_type c3,
1248 enum isl_dim_type c4, enum isl_dim_type c5);
1250 The C<isl_dim_type> arguments dictate the order in which
1251 different kinds of variables appear in the resulting matrix
1252 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1253 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1255 To check whether the description of a set or relation depends
1256 on one or more given dimensions, it is not necessary to iterate over all
1257 constraints. Instead the following functions can be used.
1259 int isl_basic_set_involves_dims(
1260 __isl_keep isl_basic_set *bset,
1261 enum isl_dim_type type, unsigned first, unsigned n);
1262 int isl_set_involves_dims(__isl_keep isl_set *set,
1263 enum isl_dim_type type, unsigned first, unsigned n);
1264 int isl_basic_map_involves_dims(
1265 __isl_keep isl_basic_map *bmap,
1266 enum isl_dim_type type, unsigned first, unsigned n);
1267 int isl_map_involves_dims(__isl_keep isl_map *map,
1268 enum isl_dim_type type, unsigned first, unsigned n);
1270 The names of the domain and range spaces of a set or relation can be
1271 read off or set using the following functions.
1273 const char *isl_basic_set_get_tuple_name(
1274 __isl_keep isl_basic_set *bset);
1275 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1276 __isl_take isl_basic_set *set, const char *s);
1277 const char *isl_set_get_tuple_name(
1278 __isl_keep isl_set *set);
1279 const char *isl_basic_map_get_tuple_name(
1280 __isl_keep isl_basic_map *bmap,
1281 enum isl_dim_type type);
1282 const char *isl_map_get_tuple_name(
1283 __isl_keep isl_map *map,
1284 enum isl_dim_type type);
1286 As with C<isl_dim_get_tuple_name>, the value returned points to
1287 an internal data structure.
1288 The names of individual dimensions can be read off using
1289 the following functions.
1291 const char *isl_constraint_get_dim_name(
1292 __isl_keep isl_constraint *constraint,
1293 enum isl_dim_type type, unsigned pos);
1294 const char *isl_basic_set_get_dim_name(
1295 __isl_keep isl_basic_set *bset,
1296 enum isl_dim_type type, unsigned pos);
1297 const char *isl_set_get_dim_name(
1298 __isl_keep isl_set *set,
1299 enum isl_dim_type type, unsigned pos);
1300 const char *isl_basic_map_get_dim_name(
1301 __isl_keep isl_basic_map *bmap,
1302 enum isl_dim_type type, unsigned pos);
1303 const char *isl_map_get_dim_name(
1304 __isl_keep isl_map *map,
1305 enum isl_dim_type type, unsigned pos);
1307 These functions are mostly useful to obtain the names
1312 =head3 Unary Properties
1318 The following functions test whether the given set or relation
1319 contains any integer points. The ``plain'' variants do not perform
1320 any computations, but simply check if the given set or relation
1321 is already known to be empty.
1323 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1324 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1325 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1326 int isl_set_is_empty(__isl_keep isl_set *set);
1327 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1328 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1329 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1330 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1331 int isl_map_is_empty(__isl_keep isl_map *map);
1332 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1334 =item * Universality
1336 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1337 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1338 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1340 =item * Single-valuedness
1342 int isl_map_is_single_valued(__isl_keep isl_map *map);
1343 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1347 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1348 int isl_map_is_injective(__isl_keep isl_map *map);
1349 int isl_union_map_plain_is_injective(
1350 __isl_keep isl_union_map *umap);
1351 int isl_union_map_is_injective(
1352 __isl_keep isl_union_map *umap);
1356 int isl_map_is_bijective(__isl_keep isl_map *map);
1357 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1361 The following functions check whether the domain of the given
1362 (basic) set is a wrapped relation.
1364 int isl_basic_set_is_wrapping(
1365 __isl_keep isl_basic_set *bset);
1366 int isl_set_is_wrapping(__isl_keep isl_set *set);
1368 =item * Internal Product
1370 int isl_basic_map_can_zip(
1371 __isl_keep isl_basic_map *bmap);
1372 int isl_map_can_zip(__isl_keep isl_map *map);
1374 Check whether the product of domain and range of the given relation
1376 i.e., whether both domain and range are nested relations.
1380 =head3 Binary Properties
1386 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1387 __isl_keep isl_set *set2);
1388 int isl_set_is_equal(__isl_keep isl_set *set1,
1389 __isl_keep isl_set *set2);
1390 int isl_union_set_is_equal(
1391 __isl_keep isl_union_set *uset1,
1392 __isl_keep isl_union_set *uset2);
1393 int isl_basic_map_is_equal(
1394 __isl_keep isl_basic_map *bmap1,
1395 __isl_keep isl_basic_map *bmap2);
1396 int isl_map_is_equal(__isl_keep isl_map *map1,
1397 __isl_keep isl_map *map2);
1398 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1399 __isl_keep isl_map *map2);
1400 int isl_union_map_is_equal(
1401 __isl_keep isl_union_map *umap1,
1402 __isl_keep isl_union_map *umap2);
1404 =item * Disjointness
1406 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1407 __isl_keep isl_set *set2);
1411 int isl_set_is_subset(__isl_keep isl_set *set1,
1412 __isl_keep isl_set *set2);
1413 int isl_set_is_strict_subset(
1414 __isl_keep isl_set *set1,
1415 __isl_keep isl_set *set2);
1416 int isl_union_set_is_subset(
1417 __isl_keep isl_union_set *uset1,
1418 __isl_keep isl_union_set *uset2);
1419 int isl_union_set_is_strict_subset(
1420 __isl_keep isl_union_set *uset1,
1421 __isl_keep isl_union_set *uset2);
1422 int isl_basic_map_is_subset(
1423 __isl_keep isl_basic_map *bmap1,
1424 __isl_keep isl_basic_map *bmap2);
1425 int isl_basic_map_is_strict_subset(
1426 __isl_keep isl_basic_map *bmap1,
1427 __isl_keep isl_basic_map *bmap2);
1428 int isl_map_is_subset(
1429 __isl_keep isl_map *map1,
1430 __isl_keep isl_map *map2);
1431 int isl_map_is_strict_subset(
1432 __isl_keep isl_map *map1,
1433 __isl_keep isl_map *map2);
1434 int isl_union_map_is_subset(
1435 __isl_keep isl_union_map *umap1,
1436 __isl_keep isl_union_map *umap2);
1437 int isl_union_map_is_strict_subset(
1438 __isl_keep isl_union_map *umap1,
1439 __isl_keep isl_union_map *umap2);
1443 =head2 Unary Operations
1449 __isl_give isl_set *isl_set_complement(
1450 __isl_take isl_set *set);
1454 __isl_give isl_basic_map *isl_basic_map_reverse(
1455 __isl_take isl_basic_map *bmap);
1456 __isl_give isl_map *isl_map_reverse(
1457 __isl_take isl_map *map);
1458 __isl_give isl_union_map *isl_union_map_reverse(
1459 __isl_take isl_union_map *umap);
1463 __isl_give isl_basic_set *isl_basic_set_project_out(
1464 __isl_take isl_basic_set *bset,
1465 enum isl_dim_type type, unsigned first, unsigned n);
1466 __isl_give isl_basic_map *isl_basic_map_project_out(
1467 __isl_take isl_basic_map *bmap,
1468 enum isl_dim_type type, unsigned first, unsigned n);
1469 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1470 enum isl_dim_type type, unsigned first, unsigned n);
1471 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1472 enum isl_dim_type type, unsigned first, unsigned n);
1473 __isl_give isl_basic_set *isl_basic_map_domain(
1474 __isl_take isl_basic_map *bmap);
1475 __isl_give isl_basic_set *isl_basic_map_range(
1476 __isl_take isl_basic_map *bmap);
1477 __isl_give isl_set *isl_map_domain(
1478 __isl_take isl_map *bmap);
1479 __isl_give isl_set *isl_map_range(
1480 __isl_take isl_map *map);
1481 __isl_give isl_union_set *isl_union_map_domain(
1482 __isl_take isl_union_map *umap);
1483 __isl_give isl_union_set *isl_union_map_range(
1484 __isl_take isl_union_map *umap);
1486 __isl_give isl_basic_map *isl_basic_map_domain_map(
1487 __isl_take isl_basic_map *bmap);
1488 __isl_give isl_basic_map *isl_basic_map_range_map(
1489 __isl_take isl_basic_map *bmap);
1490 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1491 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1492 __isl_give isl_union_map *isl_union_map_domain_map(
1493 __isl_take isl_union_map *umap);
1494 __isl_give isl_union_map *isl_union_map_range_map(
1495 __isl_take isl_union_map *umap);
1497 The functions above construct a (basic, regular or union) relation
1498 that maps (a wrapped version of) the input relation to its domain or range.
1502 __isl_give isl_set *isl_set_eliminate(
1503 __isl_take isl_set *set, enum isl_dim_type type,
1504 unsigned first, unsigned n);
1506 Eliminate the coefficients for the given dimensions from the constraints,
1507 without removing the dimensions.
1511 __isl_give isl_basic_set *isl_basic_set_fix(
1512 __isl_take isl_basic_set *bset,
1513 enum isl_dim_type type, unsigned pos,
1515 __isl_give isl_basic_set *isl_basic_set_fix_si(
1516 __isl_take isl_basic_set *bset,
1517 enum isl_dim_type type, unsigned pos, int value);
1518 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1519 enum isl_dim_type type, unsigned pos,
1521 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1522 enum isl_dim_type type, unsigned pos, int value);
1523 __isl_give isl_basic_map *isl_basic_map_fix_si(
1524 __isl_take isl_basic_map *bmap,
1525 enum isl_dim_type type, unsigned pos, int value);
1526 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1527 enum isl_dim_type type, unsigned pos, int value);
1529 Intersect the set or relation with the hyperplane where the given
1530 dimension has the fixed given value.
1532 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1533 enum isl_dim_type type1, int pos1,
1534 enum isl_dim_type type2, int pos2);
1535 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1536 enum isl_dim_type type1, int pos1,
1537 enum isl_dim_type type2, int pos2);
1539 Intersect the set or relation with the hyperplane where the given
1540 dimensions are equal to each other.
1542 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1543 enum isl_dim_type type1, int pos1,
1544 enum isl_dim_type type2, int pos2);
1546 Intersect the relation with the hyperplane where the given
1547 dimensions have opposite values.
1551 __isl_give isl_map *isl_set_identity(
1552 __isl_take isl_set *set);
1553 __isl_give isl_union_map *isl_union_set_identity(
1554 __isl_take isl_union_set *uset);
1556 Construct an identity relation on the given (union) set.
1560 __isl_give isl_basic_set *isl_basic_map_deltas(
1561 __isl_take isl_basic_map *bmap);
1562 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1563 __isl_give isl_union_set *isl_union_map_deltas(
1564 __isl_take isl_union_map *umap);
1566 These functions return a (basic) set containing the differences
1567 between image elements and corresponding domain elements in the input.
1569 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1570 __isl_take isl_basic_map *bmap);
1571 __isl_give isl_map *isl_map_deltas_map(
1572 __isl_take isl_map *map);
1573 __isl_give isl_union_map *isl_union_map_deltas_map(
1574 __isl_take isl_union_map *umap);
1576 The functions above construct a (basic, regular or union) relation
1577 that maps (a wrapped version of) the input relation to its delta set.
1581 Simplify the representation of a set or relation by trying
1582 to combine pairs of basic sets or relations into a single
1583 basic set or relation.
1585 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1586 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1587 __isl_give isl_union_set *isl_union_set_coalesce(
1588 __isl_take isl_union_set *uset);
1589 __isl_give isl_union_map *isl_union_map_coalesce(
1590 __isl_take isl_union_map *umap);
1592 =item * Detecting equalities
1594 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1595 __isl_take isl_basic_set *bset);
1596 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1597 __isl_take isl_basic_map *bmap);
1598 __isl_give isl_set *isl_set_detect_equalities(
1599 __isl_take isl_set *set);
1600 __isl_give isl_map *isl_map_detect_equalities(
1601 __isl_take isl_map *map);
1602 __isl_give isl_union_set *isl_union_set_detect_equalities(
1603 __isl_take isl_union_set *uset);
1604 __isl_give isl_union_map *isl_union_map_detect_equalities(
1605 __isl_take isl_union_map *umap);
1607 Simplify the representation of a set or relation by detecting implicit
1610 =item * Removing redundant constraints
1612 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1613 __isl_take isl_basic_set *bset);
1614 __isl_give isl_set *isl_set_remove_redundancies(
1615 __isl_take isl_set *set);
1616 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1617 __isl_take isl_basic_map *bmap);
1618 __isl_give isl_map *isl_map_remove_redundancies(
1619 __isl_take isl_map *map);
1623 __isl_give isl_basic_set *isl_set_convex_hull(
1624 __isl_take isl_set *set);
1625 __isl_give isl_basic_map *isl_map_convex_hull(
1626 __isl_take isl_map *map);
1628 If the input set or relation has any existentially quantified
1629 variables, then the result of these operations is currently undefined.
1633 __isl_give isl_basic_set *isl_set_simple_hull(
1634 __isl_take isl_set *set);
1635 __isl_give isl_basic_map *isl_map_simple_hull(
1636 __isl_take isl_map *map);
1637 __isl_give isl_union_map *isl_union_map_simple_hull(
1638 __isl_take isl_union_map *umap);
1640 These functions compute a single basic set or relation
1641 that contains the whole input set or relation.
1642 In particular, the output is described by translates
1643 of the constraints describing the basic sets or relations in the input.
1647 (See \autoref{s:simple hull}.)
1653 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1654 __isl_take isl_basic_set *bset);
1655 __isl_give isl_basic_set *isl_set_affine_hull(
1656 __isl_take isl_set *set);
1657 __isl_give isl_union_set *isl_union_set_affine_hull(
1658 __isl_take isl_union_set *uset);
1659 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1660 __isl_take isl_basic_map *bmap);
1661 __isl_give isl_basic_map *isl_map_affine_hull(
1662 __isl_take isl_map *map);
1663 __isl_give isl_union_map *isl_union_map_affine_hull(
1664 __isl_take isl_union_map *umap);
1666 In case of union sets and relations, the affine hull is computed
1669 =item * Polyhedral hull
1671 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1672 __isl_take isl_set *set);
1673 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1674 __isl_take isl_map *map);
1675 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1676 __isl_take isl_union_set *uset);
1677 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1678 __isl_take isl_union_map *umap);
1680 These functions compute a single basic set or relation
1681 not involving any existentially quantified variables
1682 that contains the whole input set or relation.
1683 In case of union sets and relations, the polyhedral hull is computed
1686 =item * Optimization
1688 #include <isl/ilp.h>
1689 enum isl_lp_result isl_basic_set_max(
1690 __isl_keep isl_basic_set *bset,
1691 __isl_keep isl_aff *obj, isl_int *opt)
1692 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
1693 __isl_keep isl_aff *obj, isl_int *opt);
1694 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1695 __isl_keep isl_aff *obj, isl_int *opt);
1697 Compute the minimum or maximum of the integer affine expression C<obj>
1698 over the points in C<set>, returning the result in C<opt>.
1699 The return value may be one of C<isl_lp_error>,
1700 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1702 =item * Parametric optimization
1704 __isl_give isl_pw_aff *isl_set_dim_max(
1705 __isl_take isl_set *set, int pos);
1707 Compute the maximum of the given set dimension as a function of the
1708 parameters, but independently of the other set dimensions.
1709 For lexicographic optimization, see L<"Lexicographic Optimization">.
1713 The following functions compute either the set of (rational) coefficient
1714 values of valid constraints for the given set or the set of (rational)
1715 values satisfying the constraints with coefficients from the given set.
1716 Internally, these two sets of functions perform essentially the
1717 same operations, except that the set of coefficients is assumed to
1718 be a cone, while the set of values may be any polyhedron.
1719 The current implementation is based on the Farkas lemma and
1720 Fourier-Motzkin elimination, but this may change or be made optional
1721 in future. In particular, future implementations may use different
1722 dualization algorithms or skip the elimination step.
1724 __isl_give isl_basic_set *isl_basic_set_coefficients(
1725 __isl_take isl_basic_set *bset);
1726 __isl_give isl_basic_set *isl_set_coefficients(
1727 __isl_take isl_set *set);
1728 __isl_give isl_union_set *isl_union_set_coefficients(
1729 __isl_take isl_union_set *bset);
1730 __isl_give isl_basic_set *isl_basic_set_solutions(
1731 __isl_take isl_basic_set *bset);
1732 __isl_give isl_basic_set *isl_set_solutions(
1733 __isl_take isl_set *set);
1734 __isl_give isl_union_set *isl_union_set_solutions(
1735 __isl_take isl_union_set *bset);
1739 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1741 __isl_give isl_union_map *isl_union_map_power(
1742 __isl_take isl_union_map *umap, int *exact);
1744 Compute a parametric representation for all positive powers I<k> of C<map>.
1745 The result maps I<k> to a nested relation corresponding to the
1746 I<k>th power of C<map>.
1747 The result may be an overapproximation. If the result is known to be exact,
1748 then C<*exact> is set to C<1>.
1750 =item * Transitive closure
1752 __isl_give isl_map *isl_map_transitive_closure(
1753 __isl_take isl_map *map, int *exact);
1754 __isl_give isl_union_map *isl_union_map_transitive_closure(
1755 __isl_take isl_union_map *umap, int *exact);
1757 Compute the transitive closure of C<map>.
1758 The result may be an overapproximation. If the result is known to be exact,
1759 then C<*exact> is set to C<1>.
1761 =item * Reaching path lengths
1763 __isl_give isl_map *isl_map_reaching_path_lengths(
1764 __isl_take isl_map *map, int *exact);
1766 Compute a relation that maps each element in the range of C<map>
1767 to the lengths of all paths composed of edges in C<map> that
1768 end up in the given element.
1769 The result may be an overapproximation. If the result is known to be exact,
1770 then C<*exact> is set to C<1>.
1771 To compute the I<maximal> path length, the resulting relation
1772 should be postprocessed by C<isl_map_lexmax>.
1773 In particular, if the input relation is a dependence relation
1774 (mapping sources to sinks), then the maximal path length corresponds
1775 to the free schedule.
1776 Note, however, that C<isl_map_lexmax> expects the maximum to be
1777 finite, so if the path lengths are unbounded (possibly due to
1778 the overapproximation), then you will get an error message.
1782 __isl_give isl_basic_set *isl_basic_map_wrap(
1783 __isl_take isl_basic_map *bmap);
1784 __isl_give isl_set *isl_map_wrap(
1785 __isl_take isl_map *map);
1786 __isl_give isl_union_set *isl_union_map_wrap(
1787 __isl_take isl_union_map *umap);
1788 __isl_give isl_basic_map *isl_basic_set_unwrap(
1789 __isl_take isl_basic_set *bset);
1790 __isl_give isl_map *isl_set_unwrap(
1791 __isl_take isl_set *set);
1792 __isl_give isl_union_map *isl_union_set_unwrap(
1793 __isl_take isl_union_set *uset);
1797 Remove any internal structure of domain (and range) of the given
1798 set or relation. If there is any such internal structure in the input,
1799 then the name of the space is also removed.
1801 __isl_give isl_basic_set *isl_basic_set_flatten(
1802 __isl_take isl_basic_set *bset);
1803 __isl_give isl_set *isl_set_flatten(
1804 __isl_take isl_set *set);
1805 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1806 __isl_take isl_basic_map *bmap);
1807 __isl_give isl_map *isl_map_flatten_range(
1808 __isl_take isl_map *map);
1809 __isl_give isl_basic_map *isl_basic_map_flatten(
1810 __isl_take isl_basic_map *bmap);
1811 __isl_give isl_map *isl_map_flatten(
1812 __isl_take isl_map *map);
1814 __isl_give isl_map *isl_set_flatten_map(
1815 __isl_take isl_set *set);
1817 The function above constructs a relation
1818 that maps the input set to a flattened version of the set.
1822 Lift the input set to a space with extra dimensions corresponding
1823 to the existentially quantified variables in the input.
1824 In particular, the result lives in a wrapped map where the domain
1825 is the original space and the range corresponds to the original
1826 existentially quantified variables.
1828 __isl_give isl_basic_set *isl_basic_set_lift(
1829 __isl_take isl_basic_set *bset);
1830 __isl_give isl_set *isl_set_lift(
1831 __isl_take isl_set *set);
1832 __isl_give isl_union_set *isl_union_set_lift(
1833 __isl_take isl_union_set *uset);
1835 =item * Internal Product
1837 __isl_give isl_basic_map *isl_basic_map_zip(
1838 __isl_take isl_basic_map *bmap);
1839 __isl_give isl_map *isl_map_zip(
1840 __isl_take isl_map *map);
1841 __isl_give isl_union_map *isl_union_map_zip(
1842 __isl_take isl_union_map *umap);
1844 Given a relation with nested relations for domain and range,
1845 interchange the range of the domain with the domain of the range.
1847 =item * Aligning parameters
1849 __isl_give isl_set *isl_set_align_params(
1850 __isl_take isl_set *set,
1851 __isl_take isl_dim *model);
1852 __isl_give isl_map *isl_map_align_params(
1853 __isl_take isl_map *map,
1854 __isl_take isl_dim *model);
1856 Change the order of the parameters of the given set or relation
1857 such that the first parameters match those of C<model>.
1858 This may involve the introduction of extra parameters.
1859 All parameters need to be named.
1861 =item * Dimension manipulation
1863 __isl_give isl_set *isl_set_add_dims(
1864 __isl_take isl_set *set,
1865 enum isl_dim_type type, unsigned n);
1866 __isl_give isl_map *isl_map_add_dims(
1867 __isl_take isl_map *map,
1868 enum isl_dim_type type, unsigned n);
1870 It is usually not advisable to directly change the (input or output)
1871 space of a set or a relation as this removes the name and the internal
1872 structure of the space. However, the above functions can be useful
1873 to add new parameters, assuming
1874 C<isl_set_align_params> and C<isl_map_align_params>
1879 =head2 Binary Operations
1881 The two arguments of a binary operation not only need to live
1882 in the same C<isl_ctx>, they currently also need to have
1883 the same (number of) parameters.
1885 =head3 Basic Operations
1889 =item * Intersection
1891 __isl_give isl_basic_set *isl_basic_set_intersect(
1892 __isl_take isl_basic_set *bset1,
1893 __isl_take isl_basic_set *bset2);
1894 __isl_give isl_set *isl_set_intersect_params(
1895 __isl_take isl_set *set,
1896 __isl_take isl_set *params);
1897 __isl_give isl_set *isl_set_intersect(
1898 __isl_take isl_set *set1,
1899 __isl_take isl_set *set2);
1900 __isl_give isl_union_set *isl_union_set_intersect(
1901 __isl_take isl_union_set *uset1,
1902 __isl_take isl_union_set *uset2);
1903 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1904 __isl_take isl_basic_map *bmap,
1905 __isl_take isl_basic_set *bset);
1906 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1907 __isl_take isl_basic_map *bmap,
1908 __isl_take isl_basic_set *bset);
1909 __isl_give isl_basic_map *isl_basic_map_intersect(
1910 __isl_take isl_basic_map *bmap1,
1911 __isl_take isl_basic_map *bmap2);
1912 __isl_give isl_map *isl_map_intersect_params(
1913 __isl_take isl_map *map,
1914 __isl_take isl_set *params);
1915 __isl_give isl_map *isl_map_intersect_domain(
1916 __isl_take isl_map *map,
1917 __isl_take isl_set *set);
1918 __isl_give isl_map *isl_map_intersect_range(
1919 __isl_take isl_map *map,
1920 __isl_take isl_set *set);
1921 __isl_give isl_map *isl_map_intersect(
1922 __isl_take isl_map *map1,
1923 __isl_take isl_map *map2);
1924 __isl_give isl_union_map *isl_union_map_intersect_domain(
1925 __isl_take isl_union_map *umap,
1926 __isl_take isl_union_set *uset);
1927 __isl_give isl_union_map *isl_union_map_intersect_range(
1928 __isl_take isl_union_map *umap,
1929 __isl_take isl_union_set *uset);
1930 __isl_give isl_union_map *isl_union_map_intersect(
1931 __isl_take isl_union_map *umap1,
1932 __isl_take isl_union_map *umap2);
1936 __isl_give isl_set *isl_basic_set_union(
1937 __isl_take isl_basic_set *bset1,
1938 __isl_take isl_basic_set *bset2);
1939 __isl_give isl_map *isl_basic_map_union(
1940 __isl_take isl_basic_map *bmap1,
1941 __isl_take isl_basic_map *bmap2);
1942 __isl_give isl_set *isl_set_union(
1943 __isl_take isl_set *set1,
1944 __isl_take isl_set *set2);
1945 __isl_give isl_map *isl_map_union(
1946 __isl_take isl_map *map1,
1947 __isl_take isl_map *map2);
1948 __isl_give isl_union_set *isl_union_set_union(
1949 __isl_take isl_union_set *uset1,
1950 __isl_take isl_union_set *uset2);
1951 __isl_give isl_union_map *isl_union_map_union(
1952 __isl_take isl_union_map *umap1,
1953 __isl_take isl_union_map *umap2);
1955 =item * Set difference
1957 __isl_give isl_set *isl_set_subtract(
1958 __isl_take isl_set *set1,
1959 __isl_take isl_set *set2);
1960 __isl_give isl_map *isl_map_subtract(
1961 __isl_take isl_map *map1,
1962 __isl_take isl_map *map2);
1963 __isl_give isl_union_set *isl_union_set_subtract(
1964 __isl_take isl_union_set *uset1,
1965 __isl_take isl_union_set *uset2);
1966 __isl_give isl_union_map *isl_union_map_subtract(
1967 __isl_take isl_union_map *umap1,
1968 __isl_take isl_union_map *umap2);
1972 __isl_give isl_basic_set *isl_basic_set_apply(
1973 __isl_take isl_basic_set *bset,
1974 __isl_take isl_basic_map *bmap);
1975 __isl_give isl_set *isl_set_apply(
1976 __isl_take isl_set *set,
1977 __isl_take isl_map *map);
1978 __isl_give isl_union_set *isl_union_set_apply(
1979 __isl_take isl_union_set *uset,
1980 __isl_take isl_union_map *umap);
1981 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1982 __isl_take isl_basic_map *bmap1,
1983 __isl_take isl_basic_map *bmap2);
1984 __isl_give isl_basic_map *isl_basic_map_apply_range(
1985 __isl_take isl_basic_map *bmap1,
1986 __isl_take isl_basic_map *bmap2);
1987 __isl_give isl_map *isl_map_apply_domain(
1988 __isl_take isl_map *map1,
1989 __isl_take isl_map *map2);
1990 __isl_give isl_union_map *isl_union_map_apply_domain(
1991 __isl_take isl_union_map *umap1,
1992 __isl_take isl_union_map *umap2);
1993 __isl_give isl_map *isl_map_apply_range(
1994 __isl_take isl_map *map1,
1995 __isl_take isl_map *map2);
1996 __isl_give isl_union_map *isl_union_map_apply_range(
1997 __isl_take isl_union_map *umap1,
1998 __isl_take isl_union_map *umap2);
2000 =item * Cartesian Product
2002 __isl_give isl_set *isl_set_product(
2003 __isl_take isl_set *set1,
2004 __isl_take isl_set *set2);
2005 __isl_give isl_union_set *isl_union_set_product(
2006 __isl_take isl_union_set *uset1,
2007 __isl_take isl_union_set *uset2);
2008 __isl_give isl_basic_map *isl_basic_map_range_product(
2009 __isl_take isl_basic_map *bmap1,
2010 __isl_take isl_basic_map *bmap2);
2011 __isl_give isl_map *isl_map_range_product(
2012 __isl_take isl_map *map1,
2013 __isl_take isl_map *map2);
2014 __isl_give isl_union_map *isl_union_map_range_product(
2015 __isl_take isl_union_map *umap1,
2016 __isl_take isl_union_map *umap2);
2017 __isl_give isl_map *isl_map_product(
2018 __isl_take isl_map *map1,
2019 __isl_take isl_map *map2);
2020 __isl_give isl_union_map *isl_union_map_product(
2021 __isl_take isl_union_map *umap1,
2022 __isl_take isl_union_map *umap2);
2024 The above functions compute the cross product of the given
2025 sets or relations. The domains and ranges of the results
2026 are wrapped maps between domains and ranges of the inputs.
2027 To obtain a ``flat'' product, use the following functions
2030 __isl_give isl_basic_set *isl_basic_set_flat_product(
2031 __isl_take isl_basic_set *bset1,
2032 __isl_take isl_basic_set *bset2);
2033 __isl_give isl_set *isl_set_flat_product(
2034 __isl_take isl_set *set1,
2035 __isl_take isl_set *set2);
2036 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2037 __isl_take isl_basic_map *bmap1,
2038 __isl_take isl_basic_map *bmap2);
2039 __isl_give isl_map *isl_map_flat_range_product(
2040 __isl_take isl_map *map1,
2041 __isl_take isl_map *map2);
2042 __isl_give isl_union_map *isl_union_map_flat_range_product(
2043 __isl_take isl_union_map *umap1,
2044 __isl_take isl_union_map *umap2);
2045 __isl_give isl_basic_map *isl_basic_map_flat_product(
2046 __isl_take isl_basic_map *bmap1,
2047 __isl_take isl_basic_map *bmap2);
2048 __isl_give isl_map *isl_map_flat_product(
2049 __isl_take isl_map *map1,
2050 __isl_take isl_map *map2);
2052 =item * Simplification
2054 __isl_give isl_basic_set *isl_basic_set_gist(
2055 __isl_take isl_basic_set *bset,
2056 __isl_take isl_basic_set *context);
2057 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2058 __isl_take isl_set *context);
2059 __isl_give isl_union_set *isl_union_set_gist(
2060 __isl_take isl_union_set *uset,
2061 __isl_take isl_union_set *context);
2062 __isl_give isl_basic_map *isl_basic_map_gist(
2063 __isl_take isl_basic_map *bmap,
2064 __isl_take isl_basic_map *context);
2065 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2066 __isl_take isl_map *context);
2067 __isl_give isl_union_map *isl_union_map_gist(
2068 __isl_take isl_union_map *umap,
2069 __isl_take isl_union_map *context);
2071 The gist operation returns a set or relation that has the
2072 same intersection with the context as the input set or relation.
2073 Any implicit equality in the intersection is made explicit in the result,
2074 while all inequalities that are redundant with respect to the intersection
2076 In case of union sets and relations, the gist operation is performed
2081 =head3 Lexicographic Optimization
2083 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2084 the following functions
2085 compute a set that contains the lexicographic minimum or maximum
2086 of the elements in C<set> (or C<bset>) for those values of the parameters
2087 that satisfy C<dom>.
2088 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2089 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2091 In other words, the union of the parameter values
2092 for which the result is non-empty and of C<*empty>
2095 __isl_give isl_set *isl_basic_set_partial_lexmin(
2096 __isl_take isl_basic_set *bset,
2097 __isl_take isl_basic_set *dom,
2098 __isl_give isl_set **empty);
2099 __isl_give isl_set *isl_basic_set_partial_lexmax(
2100 __isl_take isl_basic_set *bset,
2101 __isl_take isl_basic_set *dom,
2102 __isl_give isl_set **empty);
2103 __isl_give isl_set *isl_set_partial_lexmin(
2104 __isl_take isl_set *set, __isl_take isl_set *dom,
2105 __isl_give isl_set **empty);
2106 __isl_give isl_set *isl_set_partial_lexmax(
2107 __isl_take isl_set *set, __isl_take isl_set *dom,
2108 __isl_give isl_set **empty);
2110 Given a (basic) set C<set> (or C<bset>), the following functions simply
2111 return a set containing the lexicographic minimum or maximum
2112 of the elements in C<set> (or C<bset>).
2113 In case of union sets, the optimum is computed per space.
2115 __isl_give isl_set *isl_basic_set_lexmin(
2116 __isl_take isl_basic_set *bset);
2117 __isl_give isl_set *isl_basic_set_lexmax(
2118 __isl_take isl_basic_set *bset);
2119 __isl_give isl_set *isl_set_lexmin(
2120 __isl_take isl_set *set);
2121 __isl_give isl_set *isl_set_lexmax(
2122 __isl_take isl_set *set);
2123 __isl_give isl_union_set *isl_union_set_lexmin(
2124 __isl_take isl_union_set *uset);
2125 __isl_give isl_union_set *isl_union_set_lexmax(
2126 __isl_take isl_union_set *uset);
2128 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2129 the following functions
2130 compute a relation that maps each element of C<dom>
2131 to the single lexicographic minimum or maximum
2132 of the elements that are associated to that same
2133 element in C<map> (or C<bmap>).
2134 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2135 that contains the elements in C<dom> that do not map
2136 to any elements in C<map> (or C<bmap>).
2137 In other words, the union of the domain of the result and of C<*empty>
2140 __isl_give isl_map *isl_basic_map_partial_lexmax(
2141 __isl_take isl_basic_map *bmap,
2142 __isl_take isl_basic_set *dom,
2143 __isl_give isl_set **empty);
2144 __isl_give isl_map *isl_basic_map_partial_lexmin(
2145 __isl_take isl_basic_map *bmap,
2146 __isl_take isl_basic_set *dom,
2147 __isl_give isl_set **empty);
2148 __isl_give isl_map *isl_map_partial_lexmax(
2149 __isl_take isl_map *map, __isl_take isl_set *dom,
2150 __isl_give isl_set **empty);
2151 __isl_give isl_map *isl_map_partial_lexmin(
2152 __isl_take isl_map *map, __isl_take isl_set *dom,
2153 __isl_give isl_set **empty);
2155 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2156 return a map mapping each element in the domain of
2157 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2158 of all elements associated to that element.
2159 In case of union relations, the optimum is computed per space.
2161 __isl_give isl_map *isl_basic_map_lexmin(
2162 __isl_take isl_basic_map *bmap);
2163 __isl_give isl_map *isl_basic_map_lexmax(
2164 __isl_take isl_basic_map *bmap);
2165 __isl_give isl_map *isl_map_lexmin(
2166 __isl_take isl_map *map);
2167 __isl_give isl_map *isl_map_lexmax(
2168 __isl_take isl_map *map);
2169 __isl_give isl_union_map *isl_union_map_lexmin(
2170 __isl_take isl_union_map *umap);
2171 __isl_give isl_union_map *isl_union_map_lexmax(
2172 __isl_take isl_union_map *umap);
2176 Lists are defined over several element types, including
2177 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2178 Here we take lists of C<isl_set>s as an example.
2179 Lists can be created, copied and freed using the following functions.
2181 #include <isl/list.h>
2182 __isl_give isl_set_list *isl_set_list_alloc(
2183 isl_ctx *ctx, int n);
2184 __isl_give isl_set_list *isl_set_list_copy(
2185 __isl_keep isl_set_list *list);
2186 __isl_give isl_set_list *isl_set_list_add(
2187 __isl_take isl_set_list *list,
2188 __isl_take isl_set *el);
2189 void isl_set_list_free(__isl_take isl_set_list *list);
2191 C<isl_set_list_alloc> creates an empty list with a capacity for
2194 Lists can be inspected using the following functions.
2196 #include <isl/list.h>
2197 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2198 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2199 __isl_give struct isl_set *isl_set_list_get_set(
2200 __isl_keep isl_set_list *list, int index);
2201 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2202 int (*fn)(__isl_take struct isl_set *el, void *user),
2205 Lists can be printed using
2207 #include <isl/list.h>
2208 __isl_give isl_printer *isl_printer_print_set_list(
2209 __isl_take isl_printer *p,
2210 __isl_keep isl_set_list *list);
2214 Matrices can be created, copied and freed using the following functions.
2216 #include <isl/mat.h>
2217 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2218 unsigned n_row, unsigned n_col);
2219 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2220 void isl_mat_free(__isl_take isl_mat *mat);
2222 Note that the elements of a newly created matrix may have arbitrary values.
2223 The elements can be changed and inspected using the following functions.
2225 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2226 int isl_mat_rows(__isl_keep isl_mat *mat);
2227 int isl_mat_cols(__isl_keep isl_mat *mat);
2228 int isl_mat_get_element(__isl_keep isl_mat *mat,
2229 int row, int col, isl_int *v);
2230 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2231 int row, int col, isl_int v);
2232 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2233 int row, int col, int v);
2235 C<isl_mat_get_element> will return a negative value if anything went wrong.
2236 In that case, the value of C<*v> is undefined.
2238 The following function can be used to compute the (right) inverse
2239 of a matrix, i.e., a matrix such that the product of the original
2240 and the inverse (in that order) is a multiple of the identity matrix.
2241 The input matrix is assumed to be of full row-rank.
2243 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2245 The following function can be used to compute the (right) kernel
2246 (or null space) of a matrix, i.e., a matrix such that the product of
2247 the original and the kernel (in that order) is the zero matrix.
2249 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2251 =head2 Piecewise Quasi Affine Expressions
2253 The zero quasi affine expression can be created using
2255 __isl_give isl_aff *isl_aff_zero(
2256 __isl_take isl_local_space *ls);
2258 A quasi affine expression can also be initialized from an C<isl_div>:
2260 #include <isl/div.h>
2261 __isl_give isl_aff *isl_aff_from_div(__isl_take isl_div *div);
2263 An empty piecewise quasi affine expression (one with no cells)
2264 or a piecewise quasi affine expression with a single cell can
2265 be created using the following functions.
2267 #include <isl/aff.h>
2268 __isl_give isl_pw_aff *isl_pw_aff_empty(
2269 __isl_take isl_dim *dim);
2270 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2271 __isl_take isl_set *set, __isl_take isl_aff *aff);
2273 Quasi affine expressions can be copied and freed using
2275 #include <isl/aff.h>
2276 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2277 void *isl_aff_free(__isl_take isl_aff *aff);
2279 __isl_give isl_pw_aff *isl_pw_aff_copy(
2280 __isl_keep isl_pw_aff *pwaff);
2281 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2283 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2284 using the following function. The constraint is required to have
2285 a non-zero coefficient for the specified dimension.
2287 #include <isl/constraint.h>
2288 __isl_give isl_aff *isl_constraint_get_bound(
2289 __isl_keep isl_constraint *constraint,
2290 enum isl_dim_type type, int pos);
2292 The entire affine expression of the constraint can also be extracted
2293 using the following function.
2295 #include <isl/constraint.h>
2296 __isl_give isl_aff *isl_constraint_get_aff(
2297 __isl_keep isl_constraint *constraint);
2299 Conversely, an equality constraint equating
2300 the affine expression to zero or an inequality constraint enforcing
2301 the affine expression to be non-negative, can be constructed using
2303 __isl_give isl_constraint *isl_equality_from_aff(
2304 __isl_take isl_aff *aff);
2305 __isl_give isl_constraint *isl_inequality_from_aff(
2306 __isl_take isl_aff *aff);
2308 The expression can be inspected using
2310 #include <isl/aff.h>
2311 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2312 int isl_aff_dim(__isl_keep isl_aff *aff,
2313 enum isl_dim_type type);
2314 __isl_give isl_local_space *isl_aff_get_local_space(
2315 __isl_keep isl_aff *aff);
2316 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2317 enum isl_dim_type type, unsigned pos);
2318 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2320 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2321 enum isl_dim_type type, int pos, isl_int *v);
2322 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2324 __isl_give isl_div *isl_aff_get_div(
2325 __isl_keep isl_aff *aff, int pos);
2327 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2328 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2330 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2331 enum isl_dim_type type, unsigned first, unsigned n);
2332 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2333 enum isl_dim_type type, unsigned first, unsigned n);
2335 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2336 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2337 enum isl_dim_type type);
2338 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2340 It can be modified using
2342 #include <isl/aff.h>
2343 __isl_give isl_aff *isl_aff_set_dim_name(
2344 __isl_take isl_aff *aff, enum isl_dim_type type,
2345 unsigned pos, const char *s);
2346 __isl_give isl_aff *isl_aff_set_constant(
2347 __isl_take isl_aff *aff, isl_int v);
2348 __isl_give isl_aff *isl_aff_set_constant_si(
2349 __isl_take isl_aff *aff, int v);
2350 __isl_give isl_aff *isl_aff_set_coefficient(
2351 __isl_take isl_aff *aff,
2352 enum isl_dim_type type, int pos, isl_int v);
2353 __isl_give isl_aff *isl_aff_set_coefficient_si(
2354 __isl_take isl_aff *aff,
2355 enum isl_dim_type type, int pos, int v);
2356 __isl_give isl_aff *isl_aff_set_denominator(
2357 __isl_take isl_aff *aff, isl_int v);
2359 __isl_give isl_aff *isl_aff_add_constant(
2360 __isl_take isl_aff *aff, isl_int v);
2361 __isl_give isl_aff *isl_aff_add_constant_si(
2362 __isl_take isl_aff *aff, int v);
2363 __isl_give isl_aff *isl_aff_add_coefficient(
2364 __isl_take isl_aff *aff,
2365 enum isl_dim_type type, int pos, isl_int v);
2366 __isl_give isl_aff *isl_aff_add_coefficient_si(
2367 __isl_take isl_aff *aff,
2368 enum isl_dim_type type, int pos, int v);
2370 __isl_give isl_aff *isl_aff_insert_dims(
2371 __isl_take isl_aff *aff,
2372 enum isl_dim_type type, unsigned first, unsigned n);
2373 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2374 __isl_take isl_pw_aff *pwaff,
2375 enum isl_dim_type type, unsigned first, unsigned n);
2376 __isl_give isl_aff *isl_aff_add_dims(
2377 __isl_take isl_aff *aff,
2378 enum isl_dim_type type, unsigned n);
2379 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2380 __isl_take isl_pw_aff *pwaff,
2381 enum isl_dim_type type, unsigned n);
2382 __isl_give isl_aff *isl_aff_drop_dims(
2383 __isl_take isl_aff *aff,
2384 enum isl_dim_type type, unsigned first, unsigned n);
2385 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2386 __isl_take isl_pw_aff *pwaff,
2387 enum isl_dim_type type, unsigned first, unsigned n);
2389 Note that the C<set_constant> and C<set_coefficient> functions
2390 set the I<numerator> of the constant or coefficient, while
2391 C<add_constant> and C<add_coefficient> add an integer value to
2392 the possibly rational constant or coefficient.
2394 To check whether an affine expressions is obviously zero
2395 or obviously equal to some other affine expression, use
2397 #include <isl/aff.h>
2398 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2399 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2400 __isl_keep isl_aff *aff2);
2404 #include <isl/aff.h>
2405 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2406 __isl_take isl_aff *aff2);
2407 __isl_give isl_pw_aff *isl_pw_aff_add(
2408 __isl_take isl_pw_aff *pwaff1,
2409 __isl_take isl_pw_aff *pwaff2);
2410 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2411 __isl_take isl_aff *aff2);
2412 __isl_give isl_pw_aff *isl_pw_aff_sub(
2413 __isl_take isl_pw_aff *pwaff1,
2414 __isl_take isl_pw_aff *pwaff2);
2415 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2416 __isl_give isl_pw_aff *isl_pw_aff_neg(
2417 __isl_take isl_pw_aff *pwaff);
2418 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2419 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2420 __isl_take isl_pw_aff *pwaff);
2421 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2422 __isl_give isl_pw_aff *isl_pw_aff_floor(
2423 __isl_take isl_pw_aff *pwaff);
2424 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2426 __isl_give isl_pw_aff *isl_pw_aff_scale(
2427 __isl_take isl_pw_aff *pwaff, isl_int f);
2428 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2430 __isl_give isl_aff *isl_aff_scale_down_ui(
2431 __isl_take isl_aff *aff, unsigned f);
2432 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2433 __isl_take isl_pw_aff *pwaff, isl_int f);
2435 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2436 __isl_take isl_pw_aff *pwqp);
2438 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2439 __isl_take isl_pw_aff *pwaff,
2440 __isl_take isl_dim *model);
2442 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2443 __isl_take isl_set *context);
2444 __isl_give isl_pw_aff *isl_pw_aff_gist(
2445 __isl_take isl_pw_aff *pwaff,
2446 __isl_take isl_set *context);
2448 __isl_give isl_set *isl_pw_aff_domain(
2449 __isl_take isl_pw_aff *pwaff);
2451 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2452 __isl_take isl_aff *aff2);
2453 __isl_give isl_pw_aff *isl_pw_aff_mul(
2454 __isl_take isl_pw_aff *pwaff1,
2455 __isl_take isl_pw_aff *pwaff2);
2457 When multiplying two affine expressions, at least one of the two needs
2460 #include <isl/aff.h>
2461 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2462 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2463 __isl_give isl_set *isl_pw_aff_eq_set(
2464 __isl_take isl_pw_aff *pwaff1,
2465 __isl_take isl_pw_aff *pwaff2);
2466 __isl_give isl_set *isl_pw_aff_ne_set(
2467 __isl_take isl_pw_aff *pwaff1,
2468 __isl_take isl_pw_aff *pwaff2);
2469 __isl_give isl_set *isl_pw_aff_le_set(
2470 __isl_take isl_pw_aff *pwaff1,
2471 __isl_take isl_pw_aff *pwaff2);
2472 __isl_give isl_set *isl_pw_aff_lt_set(
2473 __isl_take isl_pw_aff *pwaff1,
2474 __isl_take isl_pw_aff *pwaff2);
2475 __isl_give isl_set *isl_pw_aff_ge_set(
2476 __isl_take isl_pw_aff *pwaff1,
2477 __isl_take isl_pw_aff *pwaff2);
2478 __isl_give isl_set *isl_pw_aff_gt_set(
2479 __isl_take isl_pw_aff *pwaff1,
2480 __isl_take isl_pw_aff *pwaff2);
2482 The function C<isl_aff_ge_basic_set> returns a basic set
2483 containing those elements in the shared space
2484 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2485 The function C<isl_aff_ge_set> returns a set
2486 containing those elements in the shared domain
2487 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
2489 #include <isl/aff.h>
2490 __isl_give isl_set *isl_pw_aff_nonneg_set(
2491 __isl_take isl_pw_aff *pwaff);
2493 The function C<isl_pw_aff_nonneg_set> returns a set
2494 containing those elements in the domain
2495 of C<pwaff> where C<pwaff> is non-negative.
2497 #include <isl/aff.h>
2498 __isl_give isl_pw_aff *isl_pw_aff_cond(
2499 __isl_take isl_set *cond,
2500 __isl_take isl_pw_aff *pwaff_true,
2501 __isl_take isl_pw_aff *pwaff_false);
2503 The function C<isl_pw_aff_cond> performs a conditional operator
2504 and returns an expression that is equal to C<pwaff_true>
2505 for elements in C<cond> and equal to C<pwaff_false> for elements
2508 #include <isl/aff.h>
2509 __isl_give isl_pw_aff *isl_pw_aff_union_max(
2510 __isl_take isl_pw_aff *pwaff1,
2511 __isl_take isl_pw_aff *pwaff2);
2513 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
2514 expression with a domain that is the union of those of C<pwaff1> and
2515 C<pwaff2> and such that on each cell, the quasi-affine expression is
2516 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2517 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2518 associated expression is the defined one.
2520 An expression can be printed using
2522 #include <isl/aff.h>
2523 __isl_give isl_printer *isl_printer_print_aff(
2524 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2526 __isl_give isl_printer *isl_printer_print_pw_aff(
2527 __isl_take isl_printer *p,
2528 __isl_keep isl_pw_aff *pwaff);
2532 Points are elements of a set. They can be used to construct
2533 simple sets (boxes) or they can be used to represent the
2534 individual elements of a set.
2535 The zero point (the origin) can be created using
2537 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2539 The coordinates of a point can be inspected, set and changed
2542 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2543 enum isl_dim_type type, int pos, isl_int *v);
2544 __isl_give isl_point *isl_point_set_coordinate(
2545 __isl_take isl_point *pnt,
2546 enum isl_dim_type type, int pos, isl_int v);
2548 __isl_give isl_point *isl_point_add_ui(
2549 __isl_take isl_point *pnt,
2550 enum isl_dim_type type, int pos, unsigned val);
2551 __isl_give isl_point *isl_point_sub_ui(
2552 __isl_take isl_point *pnt,
2553 enum isl_dim_type type, int pos, unsigned val);
2555 Other properties can be obtained using
2557 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2559 Points can be copied or freed using
2561 __isl_give isl_point *isl_point_copy(
2562 __isl_keep isl_point *pnt);
2563 void isl_point_free(__isl_take isl_point *pnt);
2565 A singleton set can be created from a point using
2567 __isl_give isl_basic_set *isl_basic_set_from_point(
2568 __isl_take isl_point *pnt);
2569 __isl_give isl_set *isl_set_from_point(
2570 __isl_take isl_point *pnt);
2572 and a box can be created from two opposite extremal points using
2574 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2575 __isl_take isl_point *pnt1,
2576 __isl_take isl_point *pnt2);
2577 __isl_give isl_set *isl_set_box_from_points(
2578 __isl_take isl_point *pnt1,
2579 __isl_take isl_point *pnt2);
2581 All elements of a B<bounded> (union) set can be enumerated using
2582 the following functions.
2584 int isl_set_foreach_point(__isl_keep isl_set *set,
2585 int (*fn)(__isl_take isl_point *pnt, void *user),
2587 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2588 int (*fn)(__isl_take isl_point *pnt, void *user),
2591 The function C<fn> is called for each integer point in
2592 C<set> with as second argument the last argument of
2593 the C<isl_set_foreach_point> call. The function C<fn>
2594 should return C<0> on success and C<-1> on failure.
2595 In the latter case, C<isl_set_foreach_point> will stop
2596 enumerating and return C<-1> as well.
2597 If the enumeration is performed successfully and to completion,
2598 then C<isl_set_foreach_point> returns C<0>.
2600 To obtain a single point of a (basic) set, use
2602 __isl_give isl_point *isl_basic_set_sample_point(
2603 __isl_take isl_basic_set *bset);
2604 __isl_give isl_point *isl_set_sample_point(
2605 __isl_take isl_set *set);
2607 If C<set> does not contain any (integer) points, then the
2608 resulting point will be ``void'', a property that can be
2611 int isl_point_is_void(__isl_keep isl_point *pnt);
2613 =head2 Piecewise Quasipolynomials
2615 A piecewise quasipolynomial is a particular kind of function that maps
2616 a parametric point to a rational value.
2617 More specifically, a quasipolynomial is a polynomial expression in greatest
2618 integer parts of affine expressions of parameters and variables.
2619 A piecewise quasipolynomial is a subdivision of a given parametric
2620 domain into disjoint cells with a quasipolynomial associated to
2621 each cell. The value of the piecewise quasipolynomial at a given
2622 point is the value of the quasipolynomial associated to the cell
2623 that contains the point. Outside of the union of cells,
2624 the value is assumed to be zero.
2625 For example, the piecewise quasipolynomial
2627 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2629 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2630 A given piecewise quasipolynomial has a fixed domain dimension.
2631 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2632 defined over different domains.
2633 Piecewise quasipolynomials are mainly used by the C<barvinok>
2634 library for representing the number of elements in a parametric set or map.
2635 For example, the piecewise quasipolynomial above represents
2636 the number of points in the map
2638 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2640 =head3 Printing (Piecewise) Quasipolynomials
2642 Quasipolynomials and piecewise quasipolynomials can be printed
2643 using the following functions.
2645 __isl_give isl_printer *isl_printer_print_qpolynomial(
2646 __isl_take isl_printer *p,
2647 __isl_keep isl_qpolynomial *qp);
2649 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2650 __isl_take isl_printer *p,
2651 __isl_keep isl_pw_qpolynomial *pwqp);
2653 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2654 __isl_take isl_printer *p,
2655 __isl_keep isl_union_pw_qpolynomial *upwqp);
2657 The output format of the printer
2658 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2659 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2661 In case of printing in C<ISL_FORMAT_C>, the user may want
2662 to set the names of all dimensions
2664 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2665 __isl_take isl_qpolynomial *qp,
2666 enum isl_dim_type type, unsigned pos,
2668 __isl_give isl_pw_qpolynomial *
2669 isl_pw_qpolynomial_set_dim_name(
2670 __isl_take isl_pw_qpolynomial *pwqp,
2671 enum isl_dim_type type, unsigned pos,
2674 =head3 Creating New (Piecewise) Quasipolynomials
2676 Some simple quasipolynomials can be created using the following functions.
2677 More complicated quasipolynomials can be created by applying
2678 operations such as addition and multiplication
2679 on the resulting quasipolynomials
2681 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2682 __isl_take isl_dim *dim);
2683 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2684 __isl_take isl_dim *dim);
2685 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2686 __isl_take isl_dim *dim);
2687 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2688 __isl_take isl_dim *dim);
2689 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2690 __isl_take isl_dim *dim);
2691 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2692 __isl_take isl_dim *dim,
2693 const isl_int n, const isl_int d);
2694 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2695 __isl_take isl_div *div);
2696 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2697 __isl_take isl_dim *dim,
2698 enum isl_dim_type type, unsigned pos);
2699 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2700 __isl_take isl_aff *aff);
2702 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2703 with a single cell can be created using the following functions.
2704 Multiple of these single cell piecewise quasipolynomials can
2705 be combined to create more complicated piecewise quasipolynomials.
2707 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2708 __isl_take isl_dim *dim);
2709 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2710 __isl_take isl_set *set,
2711 __isl_take isl_qpolynomial *qp);
2713 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2714 __isl_take isl_dim *dim);
2715 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2716 __isl_take isl_pw_qpolynomial *pwqp);
2717 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2718 __isl_take isl_union_pw_qpolynomial *upwqp,
2719 __isl_take isl_pw_qpolynomial *pwqp);
2721 Quasipolynomials can be copied and freed again using the following
2724 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2725 __isl_keep isl_qpolynomial *qp);
2726 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2728 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2729 __isl_keep isl_pw_qpolynomial *pwqp);
2730 void *isl_pw_qpolynomial_free(
2731 __isl_take isl_pw_qpolynomial *pwqp);
2733 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2734 __isl_keep isl_union_pw_qpolynomial *upwqp);
2735 void isl_union_pw_qpolynomial_free(
2736 __isl_take isl_union_pw_qpolynomial *upwqp);
2738 =head3 Inspecting (Piecewise) Quasipolynomials
2740 To iterate over all piecewise quasipolynomials in a union
2741 piecewise quasipolynomial, use the following function
2743 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2744 __isl_keep isl_union_pw_qpolynomial *upwqp,
2745 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2748 To extract the piecewise quasipolynomial from a union with a given dimension
2751 __isl_give isl_pw_qpolynomial *
2752 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2753 __isl_keep isl_union_pw_qpolynomial *upwqp,
2754 __isl_take isl_dim *dim);
2756 To iterate over the cells in a piecewise quasipolynomial,
2757 use either of the following two functions
2759 int isl_pw_qpolynomial_foreach_piece(
2760 __isl_keep isl_pw_qpolynomial *pwqp,
2761 int (*fn)(__isl_take isl_set *set,
2762 __isl_take isl_qpolynomial *qp,
2763 void *user), void *user);
2764 int isl_pw_qpolynomial_foreach_lifted_piece(
2765 __isl_keep isl_pw_qpolynomial *pwqp,
2766 int (*fn)(__isl_take isl_set *set,
2767 __isl_take isl_qpolynomial *qp,
2768 void *user), void *user);
2770 As usual, the function C<fn> should return C<0> on success
2771 and C<-1> on failure. The difference between
2772 C<isl_pw_qpolynomial_foreach_piece> and
2773 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2774 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2775 compute unique representations for all existentially quantified
2776 variables and then turn these existentially quantified variables
2777 into extra set variables, adapting the associated quasipolynomial
2778 accordingly. This means that the C<set> passed to C<fn>
2779 will not have any existentially quantified variables, but that
2780 the dimensions of the sets may be different for different
2781 invocations of C<fn>.
2783 To iterate over all terms in a quasipolynomial,
2786 int isl_qpolynomial_foreach_term(
2787 __isl_keep isl_qpolynomial *qp,
2788 int (*fn)(__isl_take isl_term *term,
2789 void *user), void *user);
2791 The terms themselves can be inspected and freed using
2794 unsigned isl_term_dim(__isl_keep isl_term *term,
2795 enum isl_dim_type type);
2796 void isl_term_get_num(__isl_keep isl_term *term,
2798 void isl_term_get_den(__isl_keep isl_term *term,
2800 int isl_term_get_exp(__isl_keep isl_term *term,
2801 enum isl_dim_type type, unsigned pos);
2802 __isl_give isl_div *isl_term_get_div(
2803 __isl_keep isl_term *term, unsigned pos);
2804 void isl_term_free(__isl_take isl_term *term);
2806 Each term is a product of parameters, set variables and
2807 integer divisions. The function C<isl_term_get_exp>
2808 returns the exponent of a given dimensions in the given term.
2809 The C<isl_int>s in the arguments of C<isl_term_get_num>
2810 and C<isl_term_get_den> need to have been initialized
2811 using C<isl_int_init> before calling these functions.
2813 =head3 Properties of (Piecewise) Quasipolynomials
2815 To check whether a quasipolynomial is actually a constant,
2816 use the following function.
2818 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2819 isl_int *n, isl_int *d);
2821 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2822 then the numerator and denominator of the constant
2823 are returned in C<*n> and C<*d>, respectively.
2825 =head3 Operations on (Piecewise) Quasipolynomials
2827 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2828 __isl_take isl_qpolynomial *qp, isl_int v);
2829 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2830 __isl_take isl_qpolynomial *qp);
2831 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2832 __isl_take isl_qpolynomial *qp1,
2833 __isl_take isl_qpolynomial *qp2);
2834 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2835 __isl_take isl_qpolynomial *qp1,
2836 __isl_take isl_qpolynomial *qp2);
2837 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2838 __isl_take isl_qpolynomial *qp1,
2839 __isl_take isl_qpolynomial *qp2);
2840 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2841 __isl_take isl_qpolynomial *qp, unsigned exponent);
2843 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2844 __isl_take isl_pw_qpolynomial *pwqp1,
2845 __isl_take isl_pw_qpolynomial *pwqp2);
2846 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2847 __isl_take isl_pw_qpolynomial *pwqp1,
2848 __isl_take isl_pw_qpolynomial *pwqp2);
2849 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2850 __isl_take isl_pw_qpolynomial *pwqp1,
2851 __isl_take isl_pw_qpolynomial *pwqp2);
2852 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2853 __isl_take isl_pw_qpolynomial *pwqp);
2854 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2855 __isl_take isl_pw_qpolynomial *pwqp1,
2856 __isl_take isl_pw_qpolynomial *pwqp2);
2858 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2859 __isl_take isl_union_pw_qpolynomial *upwqp1,
2860 __isl_take isl_union_pw_qpolynomial *upwqp2);
2861 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2862 __isl_take isl_union_pw_qpolynomial *upwqp1,
2863 __isl_take isl_union_pw_qpolynomial *upwqp2);
2864 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2865 __isl_take isl_union_pw_qpolynomial *upwqp1,
2866 __isl_take isl_union_pw_qpolynomial *upwqp2);
2868 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2869 __isl_take isl_pw_qpolynomial *pwqp,
2870 __isl_take isl_point *pnt);
2872 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2873 __isl_take isl_union_pw_qpolynomial *upwqp,
2874 __isl_take isl_point *pnt);
2876 __isl_give isl_set *isl_pw_qpolynomial_domain(
2877 __isl_take isl_pw_qpolynomial *pwqp);
2878 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2879 __isl_take isl_pw_qpolynomial *pwpq,
2880 __isl_take isl_set *set);
2882 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2883 __isl_take isl_union_pw_qpolynomial *upwqp);
2884 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2885 __isl_take isl_union_pw_qpolynomial *upwpq,
2886 __isl_take isl_union_set *uset);
2888 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2889 __isl_take isl_qpolynomial *qp,
2890 __isl_take isl_dim *model);
2892 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2893 __isl_take isl_union_pw_qpolynomial *upwqp);
2895 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2896 __isl_take isl_qpolynomial *qp,
2897 __isl_take isl_set *context);
2899 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2900 __isl_take isl_pw_qpolynomial *pwqp,
2901 __isl_take isl_set *context);
2903 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2904 __isl_take isl_union_pw_qpolynomial *upwqp,
2905 __isl_take isl_union_set *context);
2907 The gist operation applies the gist operation to each of
2908 the cells in the domain of the input piecewise quasipolynomial.
2909 The context is also exploited
2910 to simplify the quasipolynomials associated to each cell.
2912 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2913 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2914 __isl_give isl_union_pw_qpolynomial *
2915 isl_union_pw_qpolynomial_to_polynomial(
2916 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2918 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2919 the polynomial will be an overapproximation. If C<sign> is negative,
2920 it will be an underapproximation. If C<sign> is zero, the approximation
2921 will lie somewhere in between.
2923 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2925 A piecewise quasipolynomial reduction is a piecewise
2926 reduction (or fold) of quasipolynomials.
2927 In particular, the reduction can be maximum or a minimum.
2928 The objects are mainly used to represent the result of
2929 an upper or lower bound on a quasipolynomial over its domain,
2930 i.e., as the result of the following function.
2932 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2933 __isl_take isl_pw_qpolynomial *pwqp,
2934 enum isl_fold type, int *tight);
2936 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2937 __isl_take isl_union_pw_qpolynomial *upwqp,
2938 enum isl_fold type, int *tight);
2940 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2941 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2942 is the returned bound is known be tight, i.e., for each value
2943 of the parameters there is at least
2944 one element in the domain that reaches the bound.
2945 If the domain of C<pwqp> is not wrapping, then the bound is computed
2946 over all elements in that domain and the result has a purely parametric
2947 domain. If the domain of C<pwqp> is wrapping, then the bound is
2948 computed over the range of the wrapped relation. The domain of the
2949 wrapped relation becomes the domain of the result.
2951 A (piecewise) quasipolynomial reduction can be copied or freed using the
2952 following functions.
2954 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2955 __isl_keep isl_qpolynomial_fold *fold);
2956 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2957 __isl_keep isl_pw_qpolynomial_fold *pwf);
2958 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2959 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2960 void isl_qpolynomial_fold_free(
2961 __isl_take isl_qpolynomial_fold *fold);
2962 void *isl_pw_qpolynomial_fold_free(
2963 __isl_take isl_pw_qpolynomial_fold *pwf);
2964 void isl_union_pw_qpolynomial_fold_free(
2965 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2967 =head3 Printing Piecewise Quasipolynomial Reductions
2969 Piecewise quasipolynomial reductions can be printed
2970 using the following function.
2972 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2973 __isl_take isl_printer *p,
2974 __isl_keep isl_pw_qpolynomial_fold *pwf);
2975 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2976 __isl_take isl_printer *p,
2977 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2979 For C<isl_printer_print_pw_qpolynomial_fold>,
2980 output format of the printer
2981 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2982 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2983 output format of the printer
2984 needs to be set to C<ISL_FORMAT_ISL>.
2985 In case of printing in C<ISL_FORMAT_C>, the user may want
2986 to set the names of all dimensions
2988 __isl_give isl_pw_qpolynomial_fold *
2989 isl_pw_qpolynomial_fold_set_dim_name(
2990 __isl_take isl_pw_qpolynomial_fold *pwf,
2991 enum isl_dim_type type, unsigned pos,
2994 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2996 To iterate over all piecewise quasipolynomial reductions in a union
2997 piecewise quasipolynomial reduction, use the following function
2999 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3000 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3001 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3002 void *user), void *user);
3004 To iterate over the cells in a piecewise quasipolynomial reduction,
3005 use either of the following two functions
3007 int isl_pw_qpolynomial_fold_foreach_piece(
3008 __isl_keep isl_pw_qpolynomial_fold *pwf,
3009 int (*fn)(__isl_take isl_set *set,
3010 __isl_take isl_qpolynomial_fold *fold,
3011 void *user), void *user);
3012 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3013 __isl_keep isl_pw_qpolynomial_fold *pwf,
3014 int (*fn)(__isl_take isl_set *set,
3015 __isl_take isl_qpolynomial_fold *fold,
3016 void *user), void *user);
3018 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3019 of the difference between these two functions.
3021 To iterate over all quasipolynomials in a reduction, use
3023 int isl_qpolynomial_fold_foreach_qpolynomial(
3024 __isl_keep isl_qpolynomial_fold *fold,
3025 int (*fn)(__isl_take isl_qpolynomial *qp,
3026 void *user), void *user);
3028 =head3 Operations on Piecewise Quasipolynomial Reductions
3030 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3031 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3033 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3034 __isl_take isl_pw_qpolynomial_fold *pwf1,
3035 __isl_take isl_pw_qpolynomial_fold *pwf2);
3037 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3038 __isl_take isl_pw_qpolynomial_fold *pwf1,
3039 __isl_take isl_pw_qpolynomial_fold *pwf2);
3041 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3042 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3043 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3045 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3046 __isl_take isl_pw_qpolynomial_fold *pwf,
3047 __isl_take isl_point *pnt);
3049 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3050 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3051 __isl_take isl_point *pnt);
3053 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3054 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3055 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3056 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3057 __isl_take isl_union_set *uset);
3059 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3060 __isl_take isl_pw_qpolynomial_fold *pwf);
3062 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3063 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3065 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3066 __isl_take isl_pw_qpolynomial_fold *pwf,
3067 __isl_take isl_set *context);
3069 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3070 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3071 __isl_take isl_union_set *context);
3073 The gist operation applies the gist operation to each of
3074 the cells in the domain of the input piecewise quasipolynomial reduction.
3075 In future, the operation will also exploit the context
3076 to simplify the quasipolynomial reductions associated to each cell.
3078 __isl_give isl_pw_qpolynomial_fold *
3079 isl_set_apply_pw_qpolynomial_fold(
3080 __isl_take isl_set *set,
3081 __isl_take isl_pw_qpolynomial_fold *pwf,
3083 __isl_give isl_pw_qpolynomial_fold *
3084 isl_map_apply_pw_qpolynomial_fold(
3085 __isl_take isl_map *map,
3086 __isl_take isl_pw_qpolynomial_fold *pwf,
3088 __isl_give isl_union_pw_qpolynomial_fold *
3089 isl_union_set_apply_union_pw_qpolynomial_fold(
3090 __isl_take isl_union_set *uset,
3091 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3093 __isl_give isl_union_pw_qpolynomial_fold *
3094 isl_union_map_apply_union_pw_qpolynomial_fold(
3095 __isl_take isl_union_map *umap,
3096 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3099 The functions taking a map
3100 compose the given map with the given piecewise quasipolynomial reduction.
3101 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3102 over all elements in the intersection of the range of the map
3103 and the domain of the piecewise quasipolynomial reduction
3104 as a function of an element in the domain of the map.
3105 The functions taking a set compute a bound over all elements in the
3106 intersection of the set and the domain of the
3107 piecewise quasipolynomial reduction.
3109 =head2 Dependence Analysis
3111 C<isl> contains specialized functionality for performing
3112 array dataflow analysis. That is, given a I<sink> access relation
3113 and a collection of possible I<source> access relations,
3114 C<isl> can compute relations that describe
3115 for each iteration of the sink access, which iteration
3116 of which of the source access relations was the last
3117 to access the same data element before the given iteration
3119 To compute standard flow dependences, the sink should be
3120 a read, while the sources should be writes.
3121 If any of the source accesses are marked as being I<may>
3122 accesses, then there will be a dependence to the last
3123 I<must> access B<and> to any I<may> access that follows
3124 this last I<must> access.
3125 In particular, if I<all> sources are I<may> accesses,
3126 then memory based dependence analysis is performed.
3127 If, on the other hand, all sources are I<must> accesses,
3128 then value based dependence analysis is performed.
3130 #include <isl/flow.h>
3132 typedef int (*isl_access_level_before)(void *first, void *second);
3134 __isl_give isl_access_info *isl_access_info_alloc(
3135 __isl_take isl_map *sink,
3136 void *sink_user, isl_access_level_before fn,
3138 __isl_give isl_access_info *isl_access_info_add_source(
3139 __isl_take isl_access_info *acc,
3140 __isl_take isl_map *source, int must,
3142 void isl_access_info_free(__isl_take isl_access_info *acc);
3144 __isl_give isl_flow *isl_access_info_compute_flow(
3145 __isl_take isl_access_info *acc);
3147 int isl_flow_foreach(__isl_keep isl_flow *deps,
3148 int (*fn)(__isl_take isl_map *dep, int must,
3149 void *dep_user, void *user),
3151 __isl_give isl_map *isl_flow_get_no_source(
3152 __isl_keep isl_flow *deps, int must);
3153 void isl_flow_free(__isl_take isl_flow *deps);
3155 The function C<isl_access_info_compute_flow> performs the actual
3156 dependence analysis. The other functions are used to construct
3157 the input for this function or to read off the output.
3159 The input is collected in an C<isl_access_info>, which can
3160 be created through a call to C<isl_access_info_alloc>.
3161 The arguments to this functions are the sink access relation
3162 C<sink>, a token C<sink_user> used to identify the sink
3163 access to the user, a callback function for specifying the
3164 relative order of source and sink accesses, and the number
3165 of source access relations that will be added.
3166 The callback function has type C<int (*)(void *first, void *second)>.
3167 The function is called with two user supplied tokens identifying
3168 either a source or the sink and it should return the shared nesting
3169 level and the relative order of the two accesses.
3170 In particular, let I<n> be the number of loops shared by
3171 the two accesses. If C<first> precedes C<second> textually,
3172 then the function should return I<2 * n + 1>; otherwise,
3173 it should return I<2 * n>.
3174 The sources can be added to the C<isl_access_info> by performing
3175 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3176 C<must> indicates whether the source is a I<must> access
3177 or a I<may> access. Note that a multi-valued access relation
3178 should only be marked I<must> if every iteration in the domain
3179 of the relation accesses I<all> elements in its image.
3180 The C<source_user> token is again used to identify
3181 the source access. The range of the source access relation
3182 C<source> should have the same dimension as the range
3183 of the sink access relation.
3184 The C<isl_access_info_free> function should usually not be
3185 called explicitly, because it is called implicitly by
3186 C<isl_access_info_compute_flow>.
3188 The result of the dependence analysis is collected in an
3189 C<isl_flow>. There may be elements of
3190 the sink access for which no preceding source access could be
3191 found or for which all preceding sources are I<may> accesses.
3192 The relations containing these elements can be obtained through
3193 calls to C<isl_flow_get_no_source>, the first with C<must> set
3194 and the second with C<must> unset.
3195 In the case of standard flow dependence analysis,
3196 with the sink a read and the sources I<must> writes,
3197 the first relation corresponds to the reads from uninitialized
3198 array elements and the second relation is empty.
3199 The actual flow dependences can be extracted using
3200 C<isl_flow_foreach>. This function will call the user-specified
3201 callback function C<fn> for each B<non-empty> dependence between
3202 a source and the sink. The callback function is called
3203 with four arguments, the actual flow dependence relation
3204 mapping source iterations to sink iterations, a boolean that
3205 indicates whether it is a I<must> or I<may> dependence, a token
3206 identifying the source and an additional C<void *> with value
3207 equal to the third argument of the C<isl_flow_foreach> call.
3208 A dependence is marked I<must> if it originates from a I<must>
3209 source and if it is not followed by any I<may> sources.
3211 After finishing with an C<isl_flow>, the user should call
3212 C<isl_flow_free> to free all associated memory.
3214 A higher-level interface to dependence analysis is provided
3215 by the following function.
3217 #include <isl/flow.h>
3219 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3220 __isl_take isl_union_map *must_source,
3221 __isl_take isl_union_map *may_source,
3222 __isl_take isl_union_map *schedule,
3223 __isl_give isl_union_map **must_dep,
3224 __isl_give isl_union_map **may_dep,
3225 __isl_give isl_union_map **must_no_source,
3226 __isl_give isl_union_map **may_no_source);
3228 The arrays are identified by the tuple names of the ranges
3229 of the accesses. The iteration domains by the tuple names
3230 of the domains of the accesses and of the schedule.
3231 The relative order of the iteration domains is given by the
3232 schedule. The relations returned through C<must_no_source>
3233 and C<may_no_source> are subsets of C<sink>.
3234 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3235 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3236 any of the other arguments is treated as an error.
3240 B<The functionality described in this section is fairly new
3241 and may be subject to change.>
3243 The following function can be used to compute a schedule
3244 for a union of domains. The generated schedule respects
3245 all C<validity> dependences. That is, all dependence distances
3246 over these dependences in the scheduled space are lexicographically
3247 positive. The generated schedule schedule also tries to minimize
3248 the dependence distances over C<proximity> dependences.
3249 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3250 for groups of domains where the dependence distances have only
3251 non-negative values.
3252 The algorithm used to construct the schedule is similar to that
3255 #include <isl/schedule.h>
3256 __isl_give isl_schedule *isl_union_set_compute_schedule(
3257 __isl_take isl_union_set *domain,
3258 __isl_take isl_union_map *validity,
3259 __isl_take isl_union_map *proximity);
3260 void *isl_schedule_free(__isl_take isl_schedule *sched);
3262 A mapping from the domains to the scheduled space can be obtained
3263 from an C<isl_schedule> using the following function.
3265 __isl_give isl_union_map *isl_schedule_get_map(
3266 __isl_keep isl_schedule *sched);
3268 A representation of the schedule can be printed using
3270 __isl_give isl_printer *isl_printer_print_schedule(
3271 __isl_take isl_printer *p,
3272 __isl_keep isl_schedule *schedule);
3274 A representation of the schedule as a forest of bands can be obtained
3275 using the following function.
3277 __isl_give isl_band_list *isl_schedule_get_band_forest(
3278 __isl_keep isl_schedule *schedule);
3280 The list can be manipulated as explained in L<"Lists">.
3281 The bands inside the list can be copied and freed using the following
3284 #include <isl/band.h>
3285 __isl_give isl_band *isl_band_copy(
3286 __isl_keep isl_band *band);
3287 void *isl_band_free(__isl_take isl_band *band);
3289 Each band contains zero or more scheduling dimensions.
3290 These are referred to as the members of the band.
3291 The section of the schedule that corresponds to the band is
3292 referred to as the partial schedule of the band.
3293 For those nodes that participate in a band, the outer scheduling
3294 dimensions form the prefix schedule, while the inner scheduling
3295 dimensions form the suffix schedule.
3296 That is, if we take a cut of the band forest, then the union of
3297 the concatenations of the prefix, partial and suffix schedules of
3298 each band in the cut is equal to the entire schedule (modulo
3299 some possible padding at the end with zero scheduling dimensions).
3300 The properties of a band can be inspected using the following functions.
3302 #include <isl/band.h>
3303 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3305 int isl_band_has_children(__isl_keep isl_band *band);
3306 __isl_give isl_band_list *isl_band_get_children(
3307 __isl_keep isl_band *band);
3309 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3310 __isl_keep isl_band *band);
3311 __isl_give isl_union_map *isl_band_get_partial_schedule(
3312 __isl_keep isl_band *band);
3313 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3314 __isl_keep isl_band *band);
3316 int isl_band_n_member(__isl_keep isl_band *band);
3317 int isl_band_member_is_zero_distance(
3318 __isl_keep isl_band *band, int pos);
3320 Note that a scheduling dimension is considered to be ``zero
3321 distance'' if it does not carry any proximity dependences
3323 That is, if the dependence distances of the proximity
3324 dependences are all zero in that direction (for fixed
3325 iterations of outer bands).
3327 A representation of the band can be printed using
3329 #include <isl/band.h>
3330 __isl_give isl_printer *isl_printer_print_band(
3331 __isl_take isl_printer *p,
3332 __isl_keep isl_band *band);
3334 =head2 Parametric Vertex Enumeration
3336 The parametric vertex enumeration described in this section
3337 is mainly intended to be used internally and by the C<barvinok>
3340 #include <isl/vertices.h>
3341 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3342 __isl_keep isl_basic_set *bset);
3344 The function C<isl_basic_set_compute_vertices> performs the
3345 actual computation of the parametric vertices and the chamber
3346 decomposition and store the result in an C<isl_vertices> object.
3347 This information can be queried by either iterating over all
3348 the vertices or iterating over all the chambers or cells
3349 and then iterating over all vertices that are active on the chamber.
3351 int isl_vertices_foreach_vertex(
3352 __isl_keep isl_vertices *vertices,
3353 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3356 int isl_vertices_foreach_cell(
3357 __isl_keep isl_vertices *vertices,
3358 int (*fn)(__isl_take isl_cell *cell, void *user),
3360 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3361 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3364 Other operations that can be performed on an C<isl_vertices> object are
3367 isl_ctx *isl_vertices_get_ctx(
3368 __isl_keep isl_vertices *vertices);
3369 int isl_vertices_get_n_vertices(
3370 __isl_keep isl_vertices *vertices);
3371 void isl_vertices_free(__isl_take isl_vertices *vertices);
3373 Vertices can be inspected and destroyed using the following functions.
3375 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3376 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3377 __isl_give isl_basic_set *isl_vertex_get_domain(
3378 __isl_keep isl_vertex *vertex);
3379 __isl_give isl_basic_set *isl_vertex_get_expr(
3380 __isl_keep isl_vertex *vertex);
3381 void isl_vertex_free(__isl_take isl_vertex *vertex);
3383 C<isl_vertex_get_expr> returns a singleton parametric set describing
3384 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3386 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3387 B<rational> basic sets, so they should mainly be used for inspection
3388 and should not be mixed with integer sets.
3390 Chambers can be inspected and destroyed using the following functions.
3392 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3393 __isl_give isl_basic_set *isl_cell_get_domain(
3394 __isl_keep isl_cell *cell);
3395 void isl_cell_free(__isl_take isl_cell *cell);
3399 Although C<isl> is mainly meant to be used as a library,
3400 it also contains some basic applications that use some
3401 of the functionality of C<isl>.
3402 The input may be specified in either the L<isl format>
3403 or the L<PolyLib format>.
3405 =head2 C<isl_polyhedron_sample>
3407 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3408 an integer element of the polyhedron, if there is any.
3409 The first column in the output is the denominator and is always
3410 equal to 1. If the polyhedron contains no integer points,
3411 then a vector of length zero is printed.
3415 C<isl_pip> takes the same input as the C<example> program
3416 from the C<piplib> distribution, i.e., a set of constraints
3417 on the parameters, a line containing only -1 and finally a set
3418 of constraints on a parametric polyhedron.
3419 The coefficients of the parameters appear in the last columns
3420 (but before the final constant column).
3421 The output is the lexicographic minimum of the parametric polyhedron.
3422 As C<isl> currently does not have its own output format, the output
3423 is just a dump of the internal state.
3425 =head2 C<isl_polyhedron_minimize>
3427 C<isl_polyhedron_minimize> computes the minimum of some linear
3428 or affine objective function over the integer points in a polyhedron.
3429 If an affine objective function
3430 is given, then the constant should appear in the last column.
3432 =head2 C<isl_polytope_scan>
3434 Given a polytope, C<isl_polytope_scan> prints
3435 all integer points in the polytope.