3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
477 __isl_keep isl_pw_qpolynomial *pwqp);
478 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
479 __isl_keep isl_union_pw_qpolynomial *upwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
481 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
483 The names of the individual dimensions may be set or read off
484 using the following functions.
487 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
488 enum isl_dim_type type, unsigned pos,
489 __isl_keep const char *name);
490 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
491 enum isl_dim_type type, unsigned pos);
493 Note that C<isl_dim_get_name> returns a pointer to some internal
494 data structure, so the result can only be used while the
495 corresponding C<isl_dim> is alive.
496 Also note that every function that operates on two sets or relations
497 requires that both arguments have the same parameters. This also
498 means that if one of the arguments has named parameters, then the
499 other needs to have named parameters too and the names need to match.
500 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
501 have different parameters (as long as they are named), in which case
502 the result will have as parameters the union of the parameters of
505 The names of entire spaces may be set or read off
506 using the following functions.
509 __isl_give isl_dim *isl_dim_set_tuple_name(
510 __isl_take isl_dim *dim,
511 enum isl_dim_type type, const char *s);
512 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
513 enum isl_dim_type type);
515 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
516 or C<isl_dim_set>. As with C<isl_dim_get_name>,
517 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
519 Binary operations require the corresponding spaces of their arguments
520 to have the same name.
522 Spaces can be nested. In particular, the domain of a set or
523 the domain or range of a relation can be a nested relation.
524 The following functions can be used to construct and deconstruct
525 such nested dimension specifications.
528 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
529 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
530 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
532 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
533 be the dimension specification of a set, while that of
534 C<isl_dim_wrap> should be the dimension specification of a relation.
535 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
536 of a relation, while that of C<isl_dim_wrap> is the dimension specification
539 Dimension specifications can be created from other dimension
540 specifications using the following functions.
542 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
543 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
544 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
545 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
546 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
547 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
548 __isl_take isl_dim *right);
549 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
550 enum isl_dim_type type, unsigned pos, unsigned n);
551 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
552 enum isl_dim_type type, unsigned n);
553 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
554 enum isl_dim_type type, unsigned first, unsigned n);
555 __isl_give isl_dim *isl_dim_map_from_set(
556 __isl_take isl_dim *dim);
557 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
559 Note that if dimensions are added or removed from a space, then
560 the name and the internal structure are lost.
564 A local space is essentially a dimension specification with
565 zero or more existentially quantified variables.
566 The local space of a basic set or relation can be obtained
567 using the following functions.
570 __isl_give isl_local_space *isl_basic_set_get_local_space(
571 __isl_keep isl_basic_set *bset);
574 __isl_give isl_local_space *isl_basic_map_get_local_space(
575 __isl_keep isl_basic_map *bmap);
577 A new local space can be created from a dimension specification using
579 #include <isl/local_space.h>
580 __isl_give isl_local_space *isl_local_space_from_dim(
581 __isl_take isl_dim *dim);
583 They can be inspected, copied and freed using the following functions.
585 #include <isl/local_space.h>
586 isl_ctx *isl_local_space_get_ctx(
587 __isl_keep isl_local_space *ls);
588 int isl_local_space_dim(__isl_keep isl_local_space *ls,
589 enum isl_dim_type type);
590 const char *isl_local_space_get_dim_name(
591 __isl_keep isl_local_space *ls,
592 enum isl_dim_type type, unsigned pos);
593 __isl_give isl_dim *isl_local_space_get_dim(
594 __isl_keep isl_local_space *ls);
595 __isl_give isl_div *isl_local_space_get_div(
596 __isl_keep isl_local_space *ls, int pos);
597 __isl_give isl_local_space *isl_local_space_copy(
598 __isl_keep isl_local_space *ls);
599 void *isl_local_space_free(__isl_take isl_local_space *ls);
601 =head2 Input and Output
603 C<isl> supports its own input/output format, which is similar
604 to the C<Omega> format, but also supports the C<PolyLib> format
609 The C<isl> format is similar to that of C<Omega>, but has a different
610 syntax for describing the parameters and allows for the definition
611 of an existentially quantified variable as the integer division
612 of an affine expression.
613 For example, the set of integers C<i> between C<0> and C<n>
614 such that C<i % 10 <= 6> can be described as
616 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
619 A set or relation can have several disjuncts, separated
620 by the keyword C<or>. Each disjunct is either a conjunction
621 of constraints or a projection (C<exists>) of a conjunction
622 of constraints. The constraints are separated by the keyword
625 =head3 C<PolyLib> format
627 If the represented set is a union, then the first line
628 contains a single number representing the number of disjuncts.
629 Otherwise, a line containing the number C<1> is optional.
631 Each disjunct is represented by a matrix of constraints.
632 The first line contains two numbers representing
633 the number of rows and columns,
634 where the number of rows is equal to the number of constraints
635 and the number of columns is equal to two plus the number of variables.
636 The following lines contain the actual rows of the constraint matrix.
637 In each row, the first column indicates whether the constraint
638 is an equality (C<0>) or inequality (C<1>). The final column
639 corresponds to the constant term.
641 If the set is parametric, then the coefficients of the parameters
642 appear in the last columns before the constant column.
643 The coefficients of any existentially quantified variables appear
644 between those of the set variables and those of the parameters.
646 =head3 Extended C<PolyLib> format
648 The extended C<PolyLib> format is nearly identical to the
649 C<PolyLib> format. The only difference is that the line
650 containing the number of rows and columns of a constraint matrix
651 also contains four additional numbers:
652 the number of output dimensions, the number of input dimensions,
653 the number of local dimensions (i.e., the number of existentially
654 quantified variables) and the number of parameters.
655 For sets, the number of ``output'' dimensions is equal
656 to the number of set dimensions, while the number of ``input''
662 __isl_give isl_basic_set *isl_basic_set_read_from_file(
663 isl_ctx *ctx, FILE *input, int nparam);
664 __isl_give isl_basic_set *isl_basic_set_read_from_str(
665 isl_ctx *ctx, const char *str, int nparam);
666 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
667 FILE *input, int nparam);
668 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
669 const char *str, int nparam);
672 __isl_give isl_basic_map *isl_basic_map_read_from_file(
673 isl_ctx *ctx, FILE *input, int nparam);
674 __isl_give isl_basic_map *isl_basic_map_read_from_str(
675 isl_ctx *ctx, const char *str, int nparam);
676 __isl_give isl_map *isl_map_read_from_file(
677 struct isl_ctx *ctx, FILE *input, int nparam);
678 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
679 const char *str, int nparam);
681 #include <isl/union_set.h>
682 __isl_give isl_union_set *isl_union_set_read_from_file(
683 isl_ctx *ctx, FILE *input);
684 __isl_give isl_union_set *isl_union_set_read_from_str(
685 struct isl_ctx *ctx, const char *str);
687 #include <isl/union_map.h>
688 __isl_give isl_union_map *isl_union_map_read_from_file(
689 isl_ctx *ctx, FILE *input);
690 __isl_give isl_union_map *isl_union_map_read_from_str(
691 struct isl_ctx *ctx, const char *str);
693 The input format is autodetected and may be either the C<PolyLib> format
694 or the C<isl> format.
695 C<nparam> specifies how many of the final columns in
696 the C<PolyLib> format correspond to parameters.
697 If input is given in the C<isl> format, then the number
698 of parameters needs to be equal to C<nparam>.
699 If C<nparam> is negative, then any number of parameters
700 is accepted in the C<isl> format and zero parameters
701 are assumed in the C<PolyLib> format.
705 Before anything can be printed, an C<isl_printer> needs to
708 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
710 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
711 void isl_printer_free(__isl_take isl_printer *printer);
712 __isl_give char *isl_printer_get_str(
713 __isl_keep isl_printer *printer);
715 The behavior of the printer can be modified in various ways
717 __isl_give isl_printer *isl_printer_set_output_format(
718 __isl_take isl_printer *p, int output_format);
719 __isl_give isl_printer *isl_printer_set_indent(
720 __isl_take isl_printer *p, int indent);
721 __isl_give isl_printer *isl_printer_set_prefix(
722 __isl_take isl_printer *p, const char *prefix);
723 __isl_give isl_printer *isl_printer_set_suffix(
724 __isl_take isl_printer *p, const char *suffix);
726 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
727 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
728 and defaults to C<ISL_FORMAT_ISL>.
729 Each line in the output is indented by C<indent> spaces
730 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
731 In the C<PolyLib> format output,
732 the coefficients of the existentially quantified variables
733 appear between those of the set variables and those
736 To actually print something, use
739 __isl_give isl_printer *isl_printer_print_basic_set(
740 __isl_take isl_printer *printer,
741 __isl_keep isl_basic_set *bset);
742 __isl_give isl_printer *isl_printer_print_set(
743 __isl_take isl_printer *printer,
744 __isl_keep isl_set *set);
747 __isl_give isl_printer *isl_printer_print_basic_map(
748 __isl_take isl_printer *printer,
749 __isl_keep isl_basic_map *bmap);
750 __isl_give isl_printer *isl_printer_print_map(
751 __isl_take isl_printer *printer,
752 __isl_keep isl_map *map);
754 #include <isl/union_set.h>
755 __isl_give isl_printer *isl_printer_print_union_set(
756 __isl_take isl_printer *p,
757 __isl_keep isl_union_set *uset);
759 #include <isl/union_map.h>
760 __isl_give isl_printer *isl_printer_print_union_map(
761 __isl_take isl_printer *p,
762 __isl_keep isl_union_map *umap);
764 When called on a file printer, the following function flushes
765 the file. When called on a string printer, the buffer is cleared.
767 __isl_give isl_printer *isl_printer_flush(
768 __isl_take isl_printer *p);
770 =head2 Creating New Sets and Relations
772 C<isl> has functions for creating some standard sets and relations.
776 =item * Empty sets and relations
778 __isl_give isl_basic_set *isl_basic_set_empty(
779 __isl_take isl_dim *dim);
780 __isl_give isl_basic_map *isl_basic_map_empty(
781 __isl_take isl_dim *dim);
782 __isl_give isl_set *isl_set_empty(
783 __isl_take isl_dim *dim);
784 __isl_give isl_map *isl_map_empty(
785 __isl_take isl_dim *dim);
786 __isl_give isl_union_set *isl_union_set_empty(
787 __isl_take isl_dim *dim);
788 __isl_give isl_union_map *isl_union_map_empty(
789 __isl_take isl_dim *dim);
791 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
792 is only used to specify the parameters.
794 =item * Universe sets and relations
796 __isl_give isl_basic_set *isl_basic_set_universe(
797 __isl_take isl_dim *dim);
798 __isl_give isl_basic_map *isl_basic_map_universe(
799 __isl_take isl_dim *dim);
800 __isl_give isl_set *isl_set_universe(
801 __isl_take isl_dim *dim);
802 __isl_give isl_map *isl_map_universe(
803 __isl_take isl_dim *dim);
804 __isl_give isl_union_set *isl_union_set_universe(
805 __isl_take isl_union_set *uset);
806 __isl_give isl_union_map *isl_union_map_universe(
807 __isl_take isl_union_map *umap);
809 The sets and relations constructed by the functions above
810 contain all integer values, while those constructed by the
811 functions below only contain non-negative values.
813 __isl_give isl_basic_set *isl_basic_set_nat_universe(
814 __isl_take isl_dim *dim);
815 __isl_give isl_basic_map *isl_basic_map_nat_universe(
816 __isl_take isl_dim *dim);
817 __isl_give isl_set *isl_set_nat_universe(
818 __isl_take isl_dim *dim);
819 __isl_give isl_map *isl_map_nat_universe(
820 __isl_take isl_dim *dim);
822 =item * Identity relations
824 __isl_give isl_basic_map *isl_basic_map_identity(
825 __isl_take isl_dim *dim);
826 __isl_give isl_map *isl_map_identity(
827 __isl_take isl_dim *dim);
829 The number of input and output dimensions in C<dim> needs
832 =item * Lexicographic order
834 __isl_give isl_map *isl_map_lex_lt(
835 __isl_take isl_dim *set_dim);
836 __isl_give isl_map *isl_map_lex_le(
837 __isl_take isl_dim *set_dim);
838 __isl_give isl_map *isl_map_lex_gt(
839 __isl_take isl_dim *set_dim);
840 __isl_give isl_map *isl_map_lex_ge(
841 __isl_take isl_dim *set_dim);
842 __isl_give isl_map *isl_map_lex_lt_first(
843 __isl_take isl_dim *dim, unsigned n);
844 __isl_give isl_map *isl_map_lex_le_first(
845 __isl_take isl_dim *dim, unsigned n);
846 __isl_give isl_map *isl_map_lex_gt_first(
847 __isl_take isl_dim *dim, unsigned n);
848 __isl_give isl_map *isl_map_lex_ge_first(
849 __isl_take isl_dim *dim, unsigned n);
851 The first four functions take a dimension specification for a B<set>
852 and return relations that express that the elements in the domain
853 are lexicographically less
854 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
855 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
856 than the elements in the range.
857 The last four functions take a dimension specification for a map
858 and return relations that express that the first C<n> dimensions
859 in the domain are lexicographically less
860 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
861 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
862 than the first C<n> dimensions in the range.
866 A basic set or relation can be converted to a set or relation
867 using the following functions.
869 __isl_give isl_set *isl_set_from_basic_set(
870 __isl_take isl_basic_set *bset);
871 __isl_give isl_map *isl_map_from_basic_map(
872 __isl_take isl_basic_map *bmap);
874 Sets and relations can be converted to union sets and relations
875 using the following functions.
877 __isl_give isl_union_map *isl_union_map_from_map(
878 __isl_take isl_map *map);
879 __isl_give isl_union_set *isl_union_set_from_set(
880 __isl_take isl_set *set);
882 Sets and relations can be copied and freed again using the following
885 __isl_give isl_basic_set *isl_basic_set_copy(
886 __isl_keep isl_basic_set *bset);
887 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
888 __isl_give isl_union_set *isl_union_set_copy(
889 __isl_keep isl_union_set *uset);
890 __isl_give isl_basic_map *isl_basic_map_copy(
891 __isl_keep isl_basic_map *bmap);
892 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
893 __isl_give isl_union_map *isl_union_map_copy(
894 __isl_keep isl_union_map *umap);
895 void isl_basic_set_free(__isl_take isl_basic_set *bset);
896 void isl_set_free(__isl_take isl_set *set);
897 void isl_union_set_free(__isl_take isl_union_set *uset);
898 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
899 void isl_map_free(__isl_take isl_map *map);
900 void isl_union_map_free(__isl_take isl_union_map *umap);
902 Other sets and relations can be constructed by starting
903 from a universe set or relation, adding equality and/or
904 inequality constraints and then projecting out the
905 existentially quantified variables, if any.
906 Constraints can be constructed, manipulated and
907 added to (basic) sets and relations using the following functions.
909 #include <isl/constraint.h>
910 __isl_give isl_constraint *isl_equality_alloc(
911 __isl_take isl_dim *dim);
912 __isl_give isl_constraint *isl_inequality_alloc(
913 __isl_take isl_dim *dim);
914 void isl_constraint_set_constant(
915 __isl_keep isl_constraint *constraint, isl_int v);
916 void isl_constraint_set_coefficient(
917 __isl_keep isl_constraint *constraint,
918 enum isl_dim_type type, int pos, isl_int v);
919 __isl_give isl_basic_map *isl_basic_map_add_constraint(
920 __isl_take isl_basic_map *bmap,
921 __isl_take isl_constraint *constraint);
922 __isl_give isl_basic_set *isl_basic_set_add_constraint(
923 __isl_take isl_basic_set *bset,
924 __isl_take isl_constraint *constraint);
925 __isl_give isl_map *isl_map_add_constraint(
926 __isl_take isl_map *map,
927 __isl_take isl_constraint *constraint);
928 __isl_give isl_set *isl_set_add_constraint(
929 __isl_take isl_set *set,
930 __isl_take isl_constraint *constraint);
932 For example, to create a set containing the even integers
933 between 10 and 42, you would use the following code.
937 struct isl_constraint *c;
938 struct isl_basic_set *bset;
941 dim = isl_dim_set_alloc(ctx, 0, 2);
942 bset = isl_basic_set_universe(isl_dim_copy(dim));
944 c = isl_equality_alloc(isl_dim_copy(dim));
945 isl_int_set_si(v, -1);
946 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
947 isl_int_set_si(v, 2);
948 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
949 bset = isl_basic_set_add_constraint(bset, c);
951 c = isl_inequality_alloc(isl_dim_copy(dim));
952 isl_int_set_si(v, -10);
953 isl_constraint_set_constant(c, v);
954 isl_int_set_si(v, 1);
955 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
956 bset = isl_basic_set_add_constraint(bset, c);
958 c = isl_inequality_alloc(dim);
959 isl_int_set_si(v, 42);
960 isl_constraint_set_constant(c, v);
961 isl_int_set_si(v, -1);
962 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
963 bset = isl_basic_set_add_constraint(bset, c);
965 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
971 struct isl_basic_set *bset;
972 bset = isl_basic_set_read_from_str(ctx,
973 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
975 A basic set or relation can also be constructed from two matrices
976 describing the equalities and the inequalities.
978 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
979 __isl_take isl_dim *dim,
980 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
981 enum isl_dim_type c1,
982 enum isl_dim_type c2, enum isl_dim_type c3,
983 enum isl_dim_type c4);
984 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
985 __isl_take isl_dim *dim,
986 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
987 enum isl_dim_type c1,
988 enum isl_dim_type c2, enum isl_dim_type c3,
989 enum isl_dim_type c4, enum isl_dim_type c5);
991 The C<isl_dim_type> arguments indicate the order in which
992 different kinds of variables appear in the input matrices
993 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
994 C<isl_dim_set> and C<isl_dim_div> for sets and
995 of C<isl_dim_cst>, C<isl_dim_param>,
996 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
998 =head2 Inspecting Sets and Relations
1000 Usually, the user should not have to care about the actual constraints
1001 of the sets and maps, but should instead apply the abstract operations
1002 explained in the following sections.
1003 Occasionally, however, it may be required to inspect the individual
1004 coefficients of the constraints. This section explains how to do so.
1005 In these cases, it may also be useful to have C<isl> compute
1006 an explicit representation of the existentially quantified variables.
1008 __isl_give isl_set *isl_set_compute_divs(
1009 __isl_take isl_set *set);
1010 __isl_give isl_map *isl_map_compute_divs(
1011 __isl_take isl_map *map);
1012 __isl_give isl_union_set *isl_union_set_compute_divs(
1013 __isl_take isl_union_set *uset);
1014 __isl_give isl_union_map *isl_union_map_compute_divs(
1015 __isl_take isl_union_map *umap);
1017 This explicit representation defines the existentially quantified
1018 variables as integer divisions of the other variables, possibly
1019 including earlier existentially quantified variables.
1020 An explicitly represented existentially quantified variable therefore
1021 has a unique value when the values of the other variables are known.
1022 If, furthermore, the same existentials, i.e., existentials
1023 with the same explicit representations, should appear in the
1024 same order in each of the disjuncts of a set or map, then the user should call
1025 either of the following functions.
1027 __isl_give isl_set *isl_set_align_divs(
1028 __isl_take isl_set *set);
1029 __isl_give isl_map *isl_map_align_divs(
1030 __isl_take isl_map *map);
1032 Alternatively, the existentially quantified variables can be removed
1033 using the following functions, which compute an overapproximation.
1035 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1036 __isl_take isl_basic_set *bset);
1037 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1038 __isl_take isl_basic_map *bmap);
1039 __isl_give isl_set *isl_set_remove_divs(
1040 __isl_take isl_set *set);
1041 __isl_give isl_map *isl_map_remove_divs(
1042 __isl_take isl_map *map);
1044 To iterate over all the sets or maps in a union set or map, use
1046 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1047 int (*fn)(__isl_take isl_set *set, void *user),
1049 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1050 int (*fn)(__isl_take isl_map *map, void *user),
1053 The number of sets or maps in a union set or map can be obtained
1056 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1057 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1059 To extract the set or map from a union with a given dimension
1062 __isl_give isl_set *isl_union_set_extract_set(
1063 __isl_keep isl_union_set *uset,
1064 __isl_take isl_dim *dim);
1065 __isl_give isl_map *isl_union_map_extract_map(
1066 __isl_keep isl_union_map *umap,
1067 __isl_take isl_dim *dim);
1069 To iterate over all the basic sets or maps in a set or map, use
1071 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1072 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1074 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1075 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1078 The callback function C<fn> should return 0 if successful and
1079 -1 if an error occurs. In the latter case, or if any other error
1080 occurs, the above functions will return -1.
1082 It should be noted that C<isl> does not guarantee that
1083 the basic sets or maps passed to C<fn> are disjoint.
1084 If this is required, then the user should call one of
1085 the following functions first.
1087 __isl_give isl_set *isl_set_make_disjoint(
1088 __isl_take isl_set *set);
1089 __isl_give isl_map *isl_map_make_disjoint(
1090 __isl_take isl_map *map);
1092 The number of basic sets in a set can be obtained
1095 int isl_set_n_basic_set(__isl_keep isl_set *set);
1097 To iterate over the constraints of a basic set or map, use
1099 #include <isl/constraint.h>
1101 int isl_basic_map_foreach_constraint(
1102 __isl_keep isl_basic_map *bmap,
1103 int (*fn)(__isl_take isl_constraint *c, void *user),
1105 void isl_constraint_free(struct isl_constraint *c);
1107 Again, the callback function C<fn> should return 0 if successful and
1108 -1 if an error occurs. In the latter case, or if any other error
1109 occurs, the above functions will return -1.
1110 The constraint C<c> represents either an equality or an inequality.
1111 Use the following function to find out whether a constraint
1112 represents an equality. If not, it represents an inequality.
1114 int isl_constraint_is_equality(
1115 __isl_keep isl_constraint *constraint);
1117 The coefficients of the constraints can be inspected using
1118 the following functions.
1120 void isl_constraint_get_constant(
1121 __isl_keep isl_constraint *constraint, isl_int *v);
1122 void isl_constraint_get_coefficient(
1123 __isl_keep isl_constraint *constraint,
1124 enum isl_dim_type type, int pos, isl_int *v);
1125 int isl_constraint_involves_dims(
1126 __isl_keep isl_constraint *constraint,
1127 enum isl_dim_type type, unsigned first, unsigned n);
1129 The explicit representations of the existentially quantified
1130 variables can be inspected using the following functions.
1131 Note that the user is only allowed to use these functions
1132 if the inspected set or map is the result of a call
1133 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1135 __isl_give isl_div *isl_constraint_div(
1136 __isl_keep isl_constraint *constraint, int pos);
1137 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1138 void isl_div_get_constant(__isl_keep isl_div *div,
1140 void isl_div_get_denominator(__isl_keep isl_div *div,
1142 void isl_div_get_coefficient(__isl_keep isl_div *div,
1143 enum isl_dim_type type, int pos, isl_int *v);
1145 To obtain the constraints of a basic set or map in matrix
1146 form, use the following functions.
1148 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1149 __isl_keep isl_basic_set *bset,
1150 enum isl_dim_type c1, enum isl_dim_type c2,
1151 enum isl_dim_type c3, enum isl_dim_type c4);
1152 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1153 __isl_keep isl_basic_set *bset,
1154 enum isl_dim_type c1, enum isl_dim_type c2,
1155 enum isl_dim_type c3, enum isl_dim_type c4);
1156 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1157 __isl_keep isl_basic_map *bmap,
1158 enum isl_dim_type c1,
1159 enum isl_dim_type c2, enum isl_dim_type c3,
1160 enum isl_dim_type c4, enum isl_dim_type c5);
1161 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1162 __isl_keep isl_basic_map *bmap,
1163 enum isl_dim_type c1,
1164 enum isl_dim_type c2, enum isl_dim_type c3,
1165 enum isl_dim_type c4, enum isl_dim_type c5);
1167 The C<isl_dim_type> arguments dictate the order in which
1168 different kinds of variables appear in the resulting matrix
1169 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1170 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1172 The names of the domain and range spaces of a set or relation can be
1173 read off using the following functions.
1175 const char *isl_basic_set_get_tuple_name(
1176 __isl_keep isl_basic_set *bset);
1177 const char *isl_set_get_tuple_name(
1178 __isl_keep isl_set *set);
1179 const char *isl_basic_map_get_tuple_name(
1180 __isl_keep isl_basic_map *bmap,
1181 enum isl_dim_type type);
1182 const char *isl_map_get_tuple_name(
1183 __isl_keep isl_map *map,
1184 enum isl_dim_type type);
1186 As with C<isl_dim_get_tuple_name>, the value returned points to
1187 an internal data structure.
1188 The names of individual dimensions can be read off using
1189 the following functions.
1191 const char *isl_constraint_get_dim_name(
1192 __isl_keep isl_constraint *constraint,
1193 enum isl_dim_type type, unsigned pos);
1194 const char *isl_basic_set_get_dim_name(
1195 __isl_keep isl_basic_set *bset,
1196 enum isl_dim_type type, unsigned pos);
1197 const char *isl_set_get_dim_name(
1198 __isl_keep isl_set *set,
1199 enum isl_dim_type type, unsigned pos);
1200 const char *isl_basic_map_get_dim_name(
1201 __isl_keep isl_basic_map *bmap,
1202 enum isl_dim_type type, unsigned pos);
1203 const char *isl_map_get_dim_name(
1204 __isl_keep isl_map *map,
1205 enum isl_dim_type type, unsigned pos);
1207 These functions are mostly useful to obtain the names
1212 =head3 Unary Properties
1218 The following functions test whether the given set or relation
1219 contains any integer points. The ``plain'' variants do not perform
1220 any computations, but simply check if the given set or relation
1221 is already known to be empty.
1223 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1224 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1225 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1226 int isl_set_is_empty(__isl_keep isl_set *set);
1227 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1228 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1229 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1230 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1231 int isl_map_is_empty(__isl_keep isl_map *map);
1232 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1234 =item * Universality
1236 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1237 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1238 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1240 =item * Single-valuedness
1242 int isl_map_is_single_valued(__isl_keep isl_map *map);
1243 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1247 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1248 int isl_map_is_injective(__isl_keep isl_map *map);
1249 int isl_union_map_plain_is_injective(
1250 __isl_keep isl_union_map *umap);
1251 int isl_union_map_is_injective(
1252 __isl_keep isl_union_map *umap);
1256 int isl_map_is_bijective(__isl_keep isl_map *map);
1257 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1261 The following functions check whether the domain of the given
1262 (basic) set is a wrapped relation.
1264 int isl_basic_set_is_wrapping(
1265 __isl_keep isl_basic_set *bset);
1266 int isl_set_is_wrapping(__isl_keep isl_set *set);
1268 =item * Internal Product
1270 int isl_basic_map_can_zip(
1271 __isl_keep isl_basic_map *bmap);
1272 int isl_map_can_zip(__isl_keep isl_map *map);
1274 Check whether the product of domain and range of the given relation
1276 i.e., whether both domain and range are nested relations.
1280 =head3 Binary Properties
1286 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1287 __isl_keep isl_set *set2);
1288 int isl_set_is_equal(__isl_keep isl_set *set1,
1289 __isl_keep isl_set *set2);
1290 int isl_union_set_is_equal(
1291 __isl_keep isl_union_set *uset1,
1292 __isl_keep isl_union_set *uset2);
1293 int isl_basic_map_is_equal(
1294 __isl_keep isl_basic_map *bmap1,
1295 __isl_keep isl_basic_map *bmap2);
1296 int isl_map_is_equal(__isl_keep isl_map *map1,
1297 __isl_keep isl_map *map2);
1298 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1299 __isl_keep isl_map *map2);
1300 int isl_union_map_is_equal(
1301 __isl_keep isl_union_map *umap1,
1302 __isl_keep isl_union_map *umap2);
1304 =item * Disjointness
1306 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1307 __isl_keep isl_set *set2);
1311 int isl_set_is_subset(__isl_keep isl_set *set1,
1312 __isl_keep isl_set *set2);
1313 int isl_set_is_strict_subset(
1314 __isl_keep isl_set *set1,
1315 __isl_keep isl_set *set2);
1316 int isl_union_set_is_subset(
1317 __isl_keep isl_union_set *uset1,
1318 __isl_keep isl_union_set *uset2);
1319 int isl_union_set_is_strict_subset(
1320 __isl_keep isl_union_set *uset1,
1321 __isl_keep isl_union_set *uset2);
1322 int isl_basic_map_is_subset(
1323 __isl_keep isl_basic_map *bmap1,
1324 __isl_keep isl_basic_map *bmap2);
1325 int isl_basic_map_is_strict_subset(
1326 __isl_keep isl_basic_map *bmap1,
1327 __isl_keep isl_basic_map *bmap2);
1328 int isl_map_is_subset(
1329 __isl_keep isl_map *map1,
1330 __isl_keep isl_map *map2);
1331 int isl_map_is_strict_subset(
1332 __isl_keep isl_map *map1,
1333 __isl_keep isl_map *map2);
1334 int isl_union_map_is_subset(
1335 __isl_keep isl_union_map *umap1,
1336 __isl_keep isl_union_map *umap2);
1337 int isl_union_map_is_strict_subset(
1338 __isl_keep isl_union_map *umap1,
1339 __isl_keep isl_union_map *umap2);
1343 =head2 Unary Operations
1349 __isl_give isl_set *isl_set_complement(
1350 __isl_take isl_set *set);
1354 __isl_give isl_basic_map *isl_basic_map_reverse(
1355 __isl_take isl_basic_map *bmap);
1356 __isl_give isl_map *isl_map_reverse(
1357 __isl_take isl_map *map);
1358 __isl_give isl_union_map *isl_union_map_reverse(
1359 __isl_take isl_union_map *umap);
1363 __isl_give isl_basic_set *isl_basic_set_project_out(
1364 __isl_take isl_basic_set *bset,
1365 enum isl_dim_type type, unsigned first, unsigned n);
1366 __isl_give isl_basic_map *isl_basic_map_project_out(
1367 __isl_take isl_basic_map *bmap,
1368 enum isl_dim_type type, unsigned first, unsigned n);
1369 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1370 enum isl_dim_type type, unsigned first, unsigned n);
1371 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1372 enum isl_dim_type type, unsigned first, unsigned n);
1373 __isl_give isl_basic_set *isl_basic_map_domain(
1374 __isl_take isl_basic_map *bmap);
1375 __isl_give isl_basic_set *isl_basic_map_range(
1376 __isl_take isl_basic_map *bmap);
1377 __isl_give isl_set *isl_map_domain(
1378 __isl_take isl_map *bmap);
1379 __isl_give isl_set *isl_map_range(
1380 __isl_take isl_map *map);
1381 __isl_give isl_union_set *isl_union_map_domain(
1382 __isl_take isl_union_map *umap);
1383 __isl_give isl_union_set *isl_union_map_range(
1384 __isl_take isl_union_map *umap);
1386 __isl_give isl_basic_map *isl_basic_map_domain_map(
1387 __isl_take isl_basic_map *bmap);
1388 __isl_give isl_basic_map *isl_basic_map_range_map(
1389 __isl_take isl_basic_map *bmap);
1390 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1391 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1392 __isl_give isl_union_map *isl_union_map_domain_map(
1393 __isl_take isl_union_map *umap);
1394 __isl_give isl_union_map *isl_union_map_range_map(
1395 __isl_take isl_union_map *umap);
1397 The functions above construct a (basic, regular or union) relation
1398 that maps (a wrapped version of) the input relation to its domain or range.
1402 __isl_give isl_set *isl_set_eliminate(
1403 __isl_take isl_set *set, enum isl_dim_type type,
1404 unsigned first, unsigned n);
1406 Eliminate the coefficients for the given dimensions from the constraints,
1407 without removing the dimensions.
1411 __isl_give isl_map *isl_set_identity(
1412 __isl_take isl_set *set);
1413 __isl_give isl_union_map *isl_union_set_identity(
1414 __isl_take isl_union_set *uset);
1416 Construct an identity relation on the given (union) set.
1420 __isl_give isl_basic_set *isl_basic_map_deltas(
1421 __isl_take isl_basic_map *bmap);
1422 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1423 __isl_give isl_union_set *isl_union_map_deltas(
1424 __isl_take isl_union_map *umap);
1426 These functions return a (basic) set containing the differences
1427 between image elements and corresponding domain elements in the input.
1429 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1430 __isl_take isl_basic_map *bmap);
1431 __isl_give isl_map *isl_map_deltas_map(
1432 __isl_take isl_map *map);
1433 __isl_give isl_union_map *isl_union_map_deltas_map(
1434 __isl_take isl_union_map *umap);
1436 The functions above construct a (basic, regular or union) relation
1437 that maps (a wrapped version of) the input relation to its delta set.
1441 Simplify the representation of a set or relation by trying
1442 to combine pairs of basic sets or relations into a single
1443 basic set or relation.
1445 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1446 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1447 __isl_give isl_union_set *isl_union_set_coalesce(
1448 __isl_take isl_union_set *uset);
1449 __isl_give isl_union_map *isl_union_map_coalesce(
1450 __isl_take isl_union_map *umap);
1452 =item * Detecting equalities
1454 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1455 __isl_take isl_basic_set *bset);
1456 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1457 __isl_take isl_basic_map *bmap);
1458 __isl_give isl_set *isl_set_detect_equalities(
1459 __isl_take isl_set *set);
1460 __isl_give isl_map *isl_map_detect_equalities(
1461 __isl_take isl_map *map);
1462 __isl_give isl_union_set *isl_union_set_detect_equalities(
1463 __isl_take isl_union_set *uset);
1464 __isl_give isl_union_map *isl_union_map_detect_equalities(
1465 __isl_take isl_union_map *umap);
1467 Simplify the representation of a set or relation by detecting implicit
1470 =item * Removing redundant constraints
1472 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1473 __isl_take isl_basic_set *bset);
1474 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1475 __isl_take isl_basic_map *bmap);
1479 __isl_give isl_basic_set *isl_set_convex_hull(
1480 __isl_take isl_set *set);
1481 __isl_give isl_basic_map *isl_map_convex_hull(
1482 __isl_take isl_map *map);
1484 If the input set or relation has any existentially quantified
1485 variables, then the result of these operations is currently undefined.
1489 __isl_give isl_basic_set *isl_set_simple_hull(
1490 __isl_take isl_set *set);
1491 __isl_give isl_basic_map *isl_map_simple_hull(
1492 __isl_take isl_map *map);
1493 __isl_give isl_union_map *isl_union_map_simple_hull(
1494 __isl_take isl_union_map *umap);
1496 These functions compute a single basic set or relation
1497 that contains the whole input set or relation.
1498 In particular, the output is described by translates
1499 of the constraints describing the basic sets or relations in the input.
1503 (See \autoref{s:simple hull}.)
1509 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1510 __isl_take isl_basic_set *bset);
1511 __isl_give isl_basic_set *isl_set_affine_hull(
1512 __isl_take isl_set *set);
1513 __isl_give isl_union_set *isl_union_set_affine_hull(
1514 __isl_take isl_union_set *uset);
1515 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1516 __isl_take isl_basic_map *bmap);
1517 __isl_give isl_basic_map *isl_map_affine_hull(
1518 __isl_take isl_map *map);
1519 __isl_give isl_union_map *isl_union_map_affine_hull(
1520 __isl_take isl_union_map *umap);
1522 In case of union sets and relations, the affine hull is computed
1525 =item * Polyhedral hull
1527 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1528 __isl_take isl_set *set);
1529 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1530 __isl_take isl_map *map);
1531 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1532 __isl_take isl_union_set *uset);
1533 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1534 __isl_take isl_union_map *umap);
1536 These functions compute a single basic set or relation
1537 not involving any existentially quantified variables
1538 that contains the whole input set or relation.
1539 In case of union sets and relations, the polyhedral hull is computed
1542 =item * Optimization
1544 #include <isl/ilp.h>
1545 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1546 __isl_keep isl_aff *obj, isl_int *opt);
1548 Compute the maximum of the integer affine expression C<obj>
1549 over the points in C<set>, returning the result in C<opt>.
1550 The return value may be one of C<isl_lp_error>,
1551 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1555 The following functions compute either the set of (rational) coefficient
1556 values of valid constraints for the given set or the set of (rational)
1557 values satisfying the constraints with coefficients from the given set.
1558 Internally, these two sets of functions perform essentially the
1559 same operations, except that the set of coefficients is assumed to
1560 be a cone, while the set of values may be any polyhedron.
1561 The current implementation is based on the Farkas lemma and
1562 Fourier-Motzkin elimination, but this may change or be made optional
1563 in future. In particular, future implementations may use different
1564 dualization algorithms or skip the elimination step.
1566 __isl_give isl_basic_set *isl_basic_set_coefficients(
1567 __isl_take isl_basic_set *bset);
1568 __isl_give isl_basic_set *isl_set_coefficients(
1569 __isl_take isl_set *set);
1570 __isl_give isl_union_set *isl_union_set_coefficients(
1571 __isl_take isl_union_set *bset);
1572 __isl_give isl_basic_set *isl_basic_set_solutions(
1573 __isl_take isl_basic_set *bset);
1574 __isl_give isl_basic_set *isl_set_solutions(
1575 __isl_take isl_set *set);
1576 __isl_give isl_union_set *isl_union_set_solutions(
1577 __isl_take isl_union_set *bset);
1581 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1583 __isl_give isl_union_map *isl_union_map_power(
1584 __isl_take isl_union_map *umap, int *exact);
1586 Compute a parametric representation for all positive powers I<k> of C<map>.
1587 The result maps I<k> to a nested relation corresponding to the
1588 I<k>th power of C<map>.
1589 The result may be an overapproximation. If the result is known to be exact,
1590 then C<*exact> is set to C<1>.
1592 =item * Transitive closure
1594 __isl_give isl_map *isl_map_transitive_closure(
1595 __isl_take isl_map *map, int *exact);
1596 __isl_give isl_union_map *isl_union_map_transitive_closure(
1597 __isl_take isl_union_map *umap, int *exact);
1599 Compute the transitive closure of C<map>.
1600 The result may be an overapproximation. If the result is known to be exact,
1601 then C<*exact> is set to C<1>.
1603 =item * Reaching path lengths
1605 __isl_give isl_map *isl_map_reaching_path_lengths(
1606 __isl_take isl_map *map, int *exact);
1608 Compute a relation that maps each element in the range of C<map>
1609 to the lengths of all paths composed of edges in C<map> that
1610 end up in the given element.
1611 The result may be an overapproximation. If the result is known to be exact,
1612 then C<*exact> is set to C<1>.
1613 To compute the I<maximal> path length, the resulting relation
1614 should be postprocessed by C<isl_map_lexmax>.
1615 In particular, if the input relation is a dependence relation
1616 (mapping sources to sinks), then the maximal path length corresponds
1617 to the free schedule.
1618 Note, however, that C<isl_map_lexmax> expects the maximum to be
1619 finite, so if the path lengths are unbounded (possibly due to
1620 the overapproximation), then you will get an error message.
1624 __isl_give isl_basic_set *isl_basic_map_wrap(
1625 __isl_take isl_basic_map *bmap);
1626 __isl_give isl_set *isl_map_wrap(
1627 __isl_take isl_map *map);
1628 __isl_give isl_union_set *isl_union_map_wrap(
1629 __isl_take isl_union_map *umap);
1630 __isl_give isl_basic_map *isl_basic_set_unwrap(
1631 __isl_take isl_basic_set *bset);
1632 __isl_give isl_map *isl_set_unwrap(
1633 __isl_take isl_set *set);
1634 __isl_give isl_union_map *isl_union_set_unwrap(
1635 __isl_take isl_union_set *uset);
1639 Remove any internal structure of domain (and range) of the given
1640 set or relation. If there is any such internal structure in the input,
1641 then the name of the space is also removed.
1643 __isl_give isl_basic_set *isl_basic_set_flatten(
1644 __isl_take isl_basic_set *bset);
1645 __isl_give isl_set *isl_set_flatten(
1646 __isl_take isl_set *set);
1647 __isl_give isl_basic_map *isl_basic_map_flatten(
1648 __isl_take isl_basic_map *bmap);
1649 __isl_give isl_map *isl_map_flatten(
1650 __isl_take isl_map *map);
1652 __isl_give isl_map *isl_set_flatten_map(
1653 __isl_take isl_set *set);
1655 The function above constructs a relation
1656 that maps the input set to a flattened version of the set.
1660 Lift the input set to a space with extra dimensions corresponding
1661 to the existentially quantified variables in the input.
1662 In particular, the result lives in a wrapped map where the domain
1663 is the original space and the range corresponds to the original
1664 existentially quantified variables.
1666 __isl_give isl_basic_set *isl_basic_set_lift(
1667 __isl_take isl_basic_set *bset);
1668 __isl_give isl_set *isl_set_lift(
1669 __isl_take isl_set *set);
1670 __isl_give isl_union_set *isl_union_set_lift(
1671 __isl_take isl_union_set *uset);
1673 =item * Internal Product
1675 __isl_give isl_basic_map *isl_basic_map_zip(
1676 __isl_take isl_basic_map *bmap);
1677 __isl_give isl_map *isl_map_zip(
1678 __isl_take isl_map *map);
1679 __isl_give isl_union_map *isl_union_map_zip(
1680 __isl_take isl_union_map *umap);
1682 Given a relation with nested relations for domain and range,
1683 interchange the range of the domain with the domain of the range.
1685 =item * Aligning parameters
1687 __isl_give isl_set *isl_set_align_params(
1688 __isl_take isl_set *set,
1689 __isl_take isl_dim *model);
1690 __isl_give isl_map *isl_map_align_params(
1691 __isl_take isl_map *map,
1692 __isl_take isl_dim *model);
1694 Change the order of the parameters of the given set or relation
1695 such that the first parameters match those of C<model>.
1696 This may involve the introduction of extra parameters.
1697 All parameters need to be named.
1699 =item * Dimension manipulation
1701 __isl_give isl_set *isl_set_add_dims(
1702 __isl_take isl_set *set,
1703 enum isl_dim_type type, unsigned n);
1704 __isl_give isl_map *isl_map_add_dims(
1705 __isl_take isl_map *map,
1706 enum isl_dim_type type, unsigned n);
1708 It is usually not advisable to directly change the (input or output)
1709 space of a set or a relation as this removes the name and the internal
1710 structure of the space. However, the above functions can be useful
1711 to add new parameters, assuming
1712 C<isl_set_align_params> and C<isl_map_align_params>
1717 =head2 Binary Operations
1719 The two arguments of a binary operation not only need to live
1720 in the same C<isl_ctx>, they currently also need to have
1721 the same (number of) parameters.
1723 =head3 Basic Operations
1727 =item * Intersection
1729 __isl_give isl_basic_set *isl_basic_set_intersect(
1730 __isl_take isl_basic_set *bset1,
1731 __isl_take isl_basic_set *bset2);
1732 __isl_give isl_set *isl_set_intersect(
1733 __isl_take isl_set *set1,
1734 __isl_take isl_set *set2);
1735 __isl_give isl_union_set *isl_union_set_intersect(
1736 __isl_take isl_union_set *uset1,
1737 __isl_take isl_union_set *uset2);
1738 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1739 __isl_take isl_basic_map *bmap,
1740 __isl_take isl_basic_set *bset);
1741 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1742 __isl_take isl_basic_map *bmap,
1743 __isl_take isl_basic_set *bset);
1744 __isl_give isl_basic_map *isl_basic_map_intersect(
1745 __isl_take isl_basic_map *bmap1,
1746 __isl_take isl_basic_map *bmap2);
1747 __isl_give isl_map *isl_map_intersect_domain(
1748 __isl_take isl_map *map,
1749 __isl_take isl_set *set);
1750 __isl_give isl_map *isl_map_intersect_range(
1751 __isl_take isl_map *map,
1752 __isl_take isl_set *set);
1753 __isl_give isl_map *isl_map_intersect(
1754 __isl_take isl_map *map1,
1755 __isl_take isl_map *map2);
1756 __isl_give isl_union_map *isl_union_map_intersect_domain(
1757 __isl_take isl_union_map *umap,
1758 __isl_take isl_union_set *uset);
1759 __isl_give isl_union_map *isl_union_map_intersect_range(
1760 __isl_take isl_union_map *umap,
1761 __isl_take isl_union_set *uset);
1762 __isl_give isl_union_map *isl_union_map_intersect(
1763 __isl_take isl_union_map *umap1,
1764 __isl_take isl_union_map *umap2);
1768 __isl_give isl_set *isl_basic_set_union(
1769 __isl_take isl_basic_set *bset1,
1770 __isl_take isl_basic_set *bset2);
1771 __isl_give isl_map *isl_basic_map_union(
1772 __isl_take isl_basic_map *bmap1,
1773 __isl_take isl_basic_map *bmap2);
1774 __isl_give isl_set *isl_set_union(
1775 __isl_take isl_set *set1,
1776 __isl_take isl_set *set2);
1777 __isl_give isl_map *isl_map_union(
1778 __isl_take isl_map *map1,
1779 __isl_take isl_map *map2);
1780 __isl_give isl_union_set *isl_union_set_union(
1781 __isl_take isl_union_set *uset1,
1782 __isl_take isl_union_set *uset2);
1783 __isl_give isl_union_map *isl_union_map_union(
1784 __isl_take isl_union_map *umap1,
1785 __isl_take isl_union_map *umap2);
1787 =item * Set difference
1789 __isl_give isl_set *isl_set_subtract(
1790 __isl_take isl_set *set1,
1791 __isl_take isl_set *set2);
1792 __isl_give isl_map *isl_map_subtract(
1793 __isl_take isl_map *map1,
1794 __isl_take isl_map *map2);
1795 __isl_give isl_union_set *isl_union_set_subtract(
1796 __isl_take isl_union_set *uset1,
1797 __isl_take isl_union_set *uset2);
1798 __isl_give isl_union_map *isl_union_map_subtract(
1799 __isl_take isl_union_map *umap1,
1800 __isl_take isl_union_map *umap2);
1804 __isl_give isl_basic_set *isl_basic_set_apply(
1805 __isl_take isl_basic_set *bset,
1806 __isl_take isl_basic_map *bmap);
1807 __isl_give isl_set *isl_set_apply(
1808 __isl_take isl_set *set,
1809 __isl_take isl_map *map);
1810 __isl_give isl_union_set *isl_union_set_apply(
1811 __isl_take isl_union_set *uset,
1812 __isl_take isl_union_map *umap);
1813 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1814 __isl_take isl_basic_map *bmap1,
1815 __isl_take isl_basic_map *bmap2);
1816 __isl_give isl_basic_map *isl_basic_map_apply_range(
1817 __isl_take isl_basic_map *bmap1,
1818 __isl_take isl_basic_map *bmap2);
1819 __isl_give isl_map *isl_map_apply_domain(
1820 __isl_take isl_map *map1,
1821 __isl_take isl_map *map2);
1822 __isl_give isl_union_map *isl_union_map_apply_domain(
1823 __isl_take isl_union_map *umap1,
1824 __isl_take isl_union_map *umap2);
1825 __isl_give isl_map *isl_map_apply_range(
1826 __isl_take isl_map *map1,
1827 __isl_take isl_map *map2);
1828 __isl_give isl_union_map *isl_union_map_apply_range(
1829 __isl_take isl_union_map *umap1,
1830 __isl_take isl_union_map *umap2);
1832 =item * Cartesian Product
1834 __isl_give isl_set *isl_set_product(
1835 __isl_take isl_set *set1,
1836 __isl_take isl_set *set2);
1837 __isl_give isl_union_set *isl_union_set_product(
1838 __isl_take isl_union_set *uset1,
1839 __isl_take isl_union_set *uset2);
1840 __isl_give isl_basic_map *isl_basic_map_range_product(
1841 __isl_take isl_basic_map *bmap1,
1842 __isl_take isl_basic_map *bmap2);
1843 __isl_give isl_map *isl_map_range_product(
1844 __isl_take isl_map *map1,
1845 __isl_take isl_map *map2);
1846 __isl_give isl_union_map *isl_union_map_range_product(
1847 __isl_take isl_union_map *umap1,
1848 __isl_take isl_union_map *umap2);
1849 __isl_give isl_map *isl_map_product(
1850 __isl_take isl_map *map1,
1851 __isl_take isl_map *map2);
1852 __isl_give isl_union_map *isl_union_map_product(
1853 __isl_take isl_union_map *umap1,
1854 __isl_take isl_union_map *umap2);
1856 The above functions compute the cross product of the given
1857 sets or relations. The domains and ranges of the results
1858 are wrapped maps between domains and ranges of the inputs.
1859 To obtain a ``flat'' product, use the following functions
1862 __isl_give isl_basic_set *isl_basic_set_flat_product(
1863 __isl_take isl_basic_set *bset1,
1864 __isl_take isl_basic_set *bset2);
1865 __isl_give isl_set *isl_set_flat_product(
1866 __isl_take isl_set *set1,
1867 __isl_take isl_set *set2);
1868 __isl_give isl_basic_map *isl_basic_map_flat_product(
1869 __isl_take isl_basic_map *bmap1,
1870 __isl_take isl_basic_map *bmap2);
1871 __isl_give isl_map *isl_map_flat_product(
1872 __isl_take isl_map *map1,
1873 __isl_take isl_map *map2);
1875 =item * Simplification
1877 __isl_give isl_basic_set *isl_basic_set_gist(
1878 __isl_take isl_basic_set *bset,
1879 __isl_take isl_basic_set *context);
1880 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1881 __isl_take isl_set *context);
1882 __isl_give isl_union_set *isl_union_set_gist(
1883 __isl_take isl_union_set *uset,
1884 __isl_take isl_union_set *context);
1885 __isl_give isl_basic_map *isl_basic_map_gist(
1886 __isl_take isl_basic_map *bmap,
1887 __isl_take isl_basic_map *context);
1888 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1889 __isl_take isl_map *context);
1890 __isl_give isl_union_map *isl_union_map_gist(
1891 __isl_take isl_union_map *umap,
1892 __isl_take isl_union_map *context);
1894 The gist operation returns a set or relation that has the
1895 same intersection with the context as the input set or relation.
1896 Any implicit equality in the intersection is made explicit in the result,
1897 while all inequalities that are redundant with respect to the intersection
1899 In case of union sets and relations, the gist operation is performed
1904 =head3 Lexicographic Optimization
1906 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1907 the following functions
1908 compute a set that contains the lexicographic minimum or maximum
1909 of the elements in C<set> (or C<bset>) for those values of the parameters
1910 that satisfy C<dom>.
1911 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1912 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1914 In other words, the union of the parameter values
1915 for which the result is non-empty and of C<*empty>
1918 __isl_give isl_set *isl_basic_set_partial_lexmin(
1919 __isl_take isl_basic_set *bset,
1920 __isl_take isl_basic_set *dom,
1921 __isl_give isl_set **empty);
1922 __isl_give isl_set *isl_basic_set_partial_lexmax(
1923 __isl_take isl_basic_set *bset,
1924 __isl_take isl_basic_set *dom,
1925 __isl_give isl_set **empty);
1926 __isl_give isl_set *isl_set_partial_lexmin(
1927 __isl_take isl_set *set, __isl_take isl_set *dom,
1928 __isl_give isl_set **empty);
1929 __isl_give isl_set *isl_set_partial_lexmax(
1930 __isl_take isl_set *set, __isl_take isl_set *dom,
1931 __isl_give isl_set **empty);
1933 Given a (basic) set C<set> (or C<bset>), the following functions simply
1934 return a set containing the lexicographic minimum or maximum
1935 of the elements in C<set> (or C<bset>).
1936 In case of union sets, the optimum is computed per space.
1938 __isl_give isl_set *isl_basic_set_lexmin(
1939 __isl_take isl_basic_set *bset);
1940 __isl_give isl_set *isl_basic_set_lexmax(
1941 __isl_take isl_basic_set *bset);
1942 __isl_give isl_set *isl_set_lexmin(
1943 __isl_take isl_set *set);
1944 __isl_give isl_set *isl_set_lexmax(
1945 __isl_take isl_set *set);
1946 __isl_give isl_union_set *isl_union_set_lexmin(
1947 __isl_take isl_union_set *uset);
1948 __isl_give isl_union_set *isl_union_set_lexmax(
1949 __isl_take isl_union_set *uset);
1951 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1952 the following functions
1953 compute a relation that maps each element of C<dom>
1954 to the single lexicographic minimum or maximum
1955 of the elements that are associated to that same
1956 element in C<map> (or C<bmap>).
1957 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1958 that contains the elements in C<dom> that do not map
1959 to any elements in C<map> (or C<bmap>).
1960 In other words, the union of the domain of the result and of C<*empty>
1963 __isl_give isl_map *isl_basic_map_partial_lexmax(
1964 __isl_take isl_basic_map *bmap,
1965 __isl_take isl_basic_set *dom,
1966 __isl_give isl_set **empty);
1967 __isl_give isl_map *isl_basic_map_partial_lexmin(
1968 __isl_take isl_basic_map *bmap,
1969 __isl_take isl_basic_set *dom,
1970 __isl_give isl_set **empty);
1971 __isl_give isl_map *isl_map_partial_lexmax(
1972 __isl_take isl_map *map, __isl_take isl_set *dom,
1973 __isl_give isl_set **empty);
1974 __isl_give isl_map *isl_map_partial_lexmin(
1975 __isl_take isl_map *map, __isl_take isl_set *dom,
1976 __isl_give isl_set **empty);
1978 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1979 return a map mapping each element in the domain of
1980 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1981 of all elements associated to that element.
1982 In case of union relations, the optimum is computed per space.
1984 __isl_give isl_map *isl_basic_map_lexmin(
1985 __isl_take isl_basic_map *bmap);
1986 __isl_give isl_map *isl_basic_map_lexmax(
1987 __isl_take isl_basic_map *bmap);
1988 __isl_give isl_map *isl_map_lexmin(
1989 __isl_take isl_map *map);
1990 __isl_give isl_map *isl_map_lexmax(
1991 __isl_take isl_map *map);
1992 __isl_give isl_union_map *isl_union_map_lexmin(
1993 __isl_take isl_union_map *umap);
1994 __isl_give isl_union_map *isl_union_map_lexmax(
1995 __isl_take isl_union_map *umap);
1999 Matrices can be created, copied and freed using the following functions.
2001 #include <isl/mat.h>
2002 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2003 unsigned n_row, unsigned n_col);
2004 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2005 void isl_mat_free(__isl_take isl_mat *mat);
2007 Note that the elements of a newly created matrix may have arbitrary values.
2008 The elements can be changed and inspected using the following functions.
2010 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2011 int isl_mat_rows(__isl_keep isl_mat *mat);
2012 int isl_mat_cols(__isl_keep isl_mat *mat);
2013 int isl_mat_get_element(__isl_keep isl_mat *mat,
2014 int row, int col, isl_int *v);
2015 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2016 int row, int col, isl_int v);
2017 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2018 int row, int col, int v);
2020 C<isl_mat_get_element> will return a negative value if anything went wrong.
2021 In that case, the value of C<*v> is undefined.
2023 The following function can be used to compute the (right) inverse
2024 of a matrix, i.e., a matrix such that the product of the original
2025 and the inverse (in that order) is a multiple of the identity matrix.
2026 The input matrix is assumed to be of full row-rank.
2028 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2030 The following function can be used to compute the (right) kernel
2031 (or null space) of a matrix, i.e., a matrix such that the product of
2032 the original and the kernel (in that order) is the zero matrix.
2034 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2036 =head2 Quasi Affine Expressions
2038 The zero quasi affine expression can be created using
2040 __isl_give isl_aff *isl_aff_zero(
2041 __isl_take isl_local_space *ls);
2043 Quasi affine expressions can be copied and free using
2045 #include <isl/aff.h>
2046 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2047 void *isl_aff_free(__isl_take isl_aff *aff);
2049 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2050 using the following function. The constraint is required to have
2051 a non-zero coefficient for the specified dimension.
2053 #include <isl/constraint.h>
2054 __isl_give isl_aff *isl_constraint_get_bound(
2055 __isl_keep isl_constraint *constraint,
2056 enum isl_dim_type type, int pos);
2058 Conversely, an equality constraint can be constructed, equating
2059 the affine expression to zero, using
2061 __isl_give isl_constraint *isl_equality_from_aff(
2062 __isl_take isl_aff *aff);
2064 The expression can be inspected using
2066 #include <isl/aff.h>
2067 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2068 int isl_aff_dim(__isl_keep isl_aff *aff,
2069 enum isl_dim_type type);
2070 __isl_give isl_local_space *isl_aff_get_local_space(
2071 __isl_keep isl_aff *aff);
2072 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2073 enum isl_dim_type type, unsigned pos);
2074 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2076 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2077 enum isl_dim_type type, int pos, isl_int *v);
2078 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2080 __isl_give isl_div *isl_aff_get_div(
2081 __isl_keep isl_aff *aff, int pos);
2083 It can be modified using
2085 #include <isl/aff.h>
2086 __isl_give isl_aff *isl_aff_set_constant(
2087 __isl_take isl_aff *aff, isl_int v);
2088 __isl_give isl_aff *isl_aff_set_constant_si(
2089 __isl_take isl_aff *aff, int v);
2090 __isl_give isl_aff *isl_aff_set_coefficient(
2091 __isl_take isl_aff *aff,
2092 enum isl_dim_type type, int pos, isl_int v);
2093 __isl_give isl_aff *isl_aff_set_coefficient_si(
2094 __isl_take isl_aff *aff,
2095 enum isl_dim_type type, int pos, int v);
2096 __isl_give isl_aff *isl_aff_set_denominator(
2097 __isl_take isl_aff *aff, isl_int v);
2099 __isl_give isl_aff *isl_aff_add_constant(
2100 __isl_take isl_aff *aff, isl_int v);
2101 __isl_give isl_aff *isl_aff_add_coefficient_si(
2102 __isl_take isl_aff *aff,
2103 enum isl_dim_type type, int pos, int v);
2105 Note that the C<set_constant> and C<set_coefficient> functions
2106 set the I<numerator> of the constant or coefficient, while
2107 C<add_constant> and C<add_coefficient> add an integer value to
2108 the possibly rational constant or coefficient.
2112 #include <isl/aff.h>
2113 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2114 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2116 An expression can be printed using
2118 #include <isl/aff.h>
2119 __isl_give isl_printer *isl_printer_print_aff(
2120 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2124 Points are elements of a set. They can be used to construct
2125 simple sets (boxes) or they can be used to represent the
2126 individual elements of a set.
2127 The zero point (the origin) can be created using
2129 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2131 The coordinates of a point can be inspected, set and changed
2134 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2135 enum isl_dim_type type, int pos, isl_int *v);
2136 __isl_give isl_point *isl_point_set_coordinate(
2137 __isl_take isl_point *pnt,
2138 enum isl_dim_type type, int pos, isl_int v);
2140 __isl_give isl_point *isl_point_add_ui(
2141 __isl_take isl_point *pnt,
2142 enum isl_dim_type type, int pos, unsigned val);
2143 __isl_give isl_point *isl_point_sub_ui(
2144 __isl_take isl_point *pnt,
2145 enum isl_dim_type type, int pos, unsigned val);
2147 Points can be copied or freed using
2149 __isl_give isl_point *isl_point_copy(
2150 __isl_keep isl_point *pnt);
2151 void isl_point_free(__isl_take isl_point *pnt);
2153 A singleton set can be created from a point using
2155 __isl_give isl_basic_set *isl_basic_set_from_point(
2156 __isl_take isl_point *pnt);
2157 __isl_give isl_set *isl_set_from_point(
2158 __isl_take isl_point *pnt);
2160 and a box can be created from two opposite extremal points using
2162 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2163 __isl_take isl_point *pnt1,
2164 __isl_take isl_point *pnt2);
2165 __isl_give isl_set *isl_set_box_from_points(
2166 __isl_take isl_point *pnt1,
2167 __isl_take isl_point *pnt2);
2169 All elements of a B<bounded> (union) set can be enumerated using
2170 the following functions.
2172 int isl_set_foreach_point(__isl_keep isl_set *set,
2173 int (*fn)(__isl_take isl_point *pnt, void *user),
2175 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2176 int (*fn)(__isl_take isl_point *pnt, void *user),
2179 The function C<fn> is called for each integer point in
2180 C<set> with as second argument the last argument of
2181 the C<isl_set_foreach_point> call. The function C<fn>
2182 should return C<0> on success and C<-1> on failure.
2183 In the latter case, C<isl_set_foreach_point> will stop
2184 enumerating and return C<-1> as well.
2185 If the enumeration is performed successfully and to completion,
2186 then C<isl_set_foreach_point> returns C<0>.
2188 To obtain a single point of a (basic) set, use
2190 __isl_give isl_point *isl_basic_set_sample_point(
2191 __isl_take isl_basic_set *bset);
2192 __isl_give isl_point *isl_set_sample_point(
2193 __isl_take isl_set *set);
2195 If C<set> does not contain any (integer) points, then the
2196 resulting point will be ``void'', a property that can be
2199 int isl_point_is_void(__isl_keep isl_point *pnt);
2201 =head2 Piecewise Quasipolynomials
2203 A piecewise quasipolynomial is a particular kind of function that maps
2204 a parametric point to a rational value.
2205 More specifically, a quasipolynomial is a polynomial expression in greatest
2206 integer parts of affine expressions of parameters and variables.
2207 A piecewise quasipolynomial is a subdivision of a given parametric
2208 domain into disjoint cells with a quasipolynomial associated to
2209 each cell. The value of the piecewise quasipolynomial at a given
2210 point is the value of the quasipolynomial associated to the cell
2211 that contains the point. Outside of the union of cells,
2212 the value is assumed to be zero.
2213 For example, the piecewise quasipolynomial
2215 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2217 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2218 A given piecewise quasipolynomial has a fixed domain dimension.
2219 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2220 defined over different domains.
2221 Piecewise quasipolynomials are mainly used by the C<barvinok>
2222 library for representing the number of elements in a parametric set or map.
2223 For example, the piecewise quasipolynomial above represents
2224 the number of points in the map
2226 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2228 =head3 Printing (Piecewise) Quasipolynomials
2230 Quasipolynomials and piecewise quasipolynomials can be printed
2231 using the following functions.
2233 __isl_give isl_printer *isl_printer_print_qpolynomial(
2234 __isl_take isl_printer *p,
2235 __isl_keep isl_qpolynomial *qp);
2237 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2238 __isl_take isl_printer *p,
2239 __isl_keep isl_pw_qpolynomial *pwqp);
2241 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2242 __isl_take isl_printer *p,
2243 __isl_keep isl_union_pw_qpolynomial *upwqp);
2245 The output format of the printer
2246 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2247 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2249 In case of printing in C<ISL_FORMAT_C>, the user may want
2250 to set the names of all dimensions
2252 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2253 __isl_take isl_qpolynomial *qp,
2254 enum isl_dim_type type, unsigned pos,
2256 __isl_give isl_pw_qpolynomial *
2257 isl_pw_qpolynomial_set_dim_name(
2258 __isl_take isl_pw_qpolynomial *pwqp,
2259 enum isl_dim_type type, unsigned pos,
2262 =head3 Creating New (Piecewise) Quasipolynomials
2264 Some simple quasipolynomials can be created using the following functions.
2265 More complicated quasipolynomials can be created by applying
2266 operations such as addition and multiplication
2267 on the resulting quasipolynomials
2269 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2270 __isl_take isl_dim *dim);
2271 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2272 __isl_take isl_dim *dim);
2273 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2274 __isl_take isl_dim *dim);
2275 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2276 __isl_take isl_dim *dim);
2277 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2278 __isl_take isl_dim *dim);
2279 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2280 __isl_take isl_dim *dim,
2281 const isl_int n, const isl_int d);
2282 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2283 __isl_take isl_div *div);
2284 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2285 __isl_take isl_dim *dim,
2286 enum isl_dim_type type, unsigned pos);
2288 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2289 with a single cell can be created using the following functions.
2290 Multiple of these single cell piecewise quasipolynomials can
2291 be combined to create more complicated piecewise quasipolynomials.
2293 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2294 __isl_take isl_dim *dim);
2295 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2296 __isl_take isl_set *set,
2297 __isl_take isl_qpolynomial *qp);
2299 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2300 __isl_take isl_dim *dim);
2301 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2302 __isl_take isl_pw_qpolynomial *pwqp);
2303 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2304 __isl_take isl_union_pw_qpolynomial *upwqp,
2305 __isl_take isl_pw_qpolynomial *pwqp);
2307 Quasipolynomials can be copied and freed again using the following
2310 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2311 __isl_keep isl_qpolynomial *qp);
2312 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2314 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2315 __isl_keep isl_pw_qpolynomial *pwqp);
2316 void isl_pw_qpolynomial_free(
2317 __isl_take isl_pw_qpolynomial *pwqp);
2319 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2320 __isl_keep isl_union_pw_qpolynomial *upwqp);
2321 void isl_union_pw_qpolynomial_free(
2322 __isl_take isl_union_pw_qpolynomial *upwqp);
2324 =head3 Inspecting (Piecewise) Quasipolynomials
2326 To iterate over all piecewise quasipolynomials in a union
2327 piecewise quasipolynomial, use the following function
2329 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2330 __isl_keep isl_union_pw_qpolynomial *upwqp,
2331 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2334 To extract the piecewise quasipolynomial from a union with a given dimension
2337 __isl_give isl_pw_qpolynomial *
2338 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2339 __isl_keep isl_union_pw_qpolynomial *upwqp,
2340 __isl_take isl_dim *dim);
2342 To iterate over the cells in a piecewise quasipolynomial,
2343 use either of the following two functions
2345 int isl_pw_qpolynomial_foreach_piece(
2346 __isl_keep isl_pw_qpolynomial *pwqp,
2347 int (*fn)(__isl_take isl_set *set,
2348 __isl_take isl_qpolynomial *qp,
2349 void *user), void *user);
2350 int isl_pw_qpolynomial_foreach_lifted_piece(
2351 __isl_keep isl_pw_qpolynomial *pwqp,
2352 int (*fn)(__isl_take isl_set *set,
2353 __isl_take isl_qpolynomial *qp,
2354 void *user), void *user);
2356 As usual, the function C<fn> should return C<0> on success
2357 and C<-1> on failure. The difference between
2358 C<isl_pw_qpolynomial_foreach_piece> and
2359 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2360 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2361 compute unique representations for all existentially quantified
2362 variables and then turn these existentially quantified variables
2363 into extra set variables, adapting the associated quasipolynomial
2364 accordingly. This means that the C<set> passed to C<fn>
2365 will not have any existentially quantified variables, but that
2366 the dimensions of the sets may be different for different
2367 invocations of C<fn>.
2369 To iterate over all terms in a quasipolynomial,
2372 int isl_qpolynomial_foreach_term(
2373 __isl_keep isl_qpolynomial *qp,
2374 int (*fn)(__isl_take isl_term *term,
2375 void *user), void *user);
2377 The terms themselves can be inspected and freed using
2380 unsigned isl_term_dim(__isl_keep isl_term *term,
2381 enum isl_dim_type type);
2382 void isl_term_get_num(__isl_keep isl_term *term,
2384 void isl_term_get_den(__isl_keep isl_term *term,
2386 int isl_term_get_exp(__isl_keep isl_term *term,
2387 enum isl_dim_type type, unsigned pos);
2388 __isl_give isl_div *isl_term_get_div(
2389 __isl_keep isl_term *term, unsigned pos);
2390 void isl_term_free(__isl_take isl_term *term);
2392 Each term is a product of parameters, set variables and
2393 integer divisions. The function C<isl_term_get_exp>
2394 returns the exponent of a given dimensions in the given term.
2395 The C<isl_int>s in the arguments of C<isl_term_get_num>
2396 and C<isl_term_get_den> need to have been initialized
2397 using C<isl_int_init> before calling these functions.
2399 =head3 Properties of (Piecewise) Quasipolynomials
2401 To check whether a quasipolynomial is actually a constant,
2402 use the following function.
2404 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2405 isl_int *n, isl_int *d);
2407 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2408 then the numerator and denominator of the constant
2409 are returned in C<*n> and C<*d>, respectively.
2411 =head3 Operations on (Piecewise) Quasipolynomials
2413 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2414 __isl_take isl_qpolynomial *qp);
2415 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2416 __isl_take isl_qpolynomial *qp1,
2417 __isl_take isl_qpolynomial *qp2);
2418 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2419 __isl_take isl_qpolynomial *qp1,
2420 __isl_take isl_qpolynomial *qp2);
2421 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2422 __isl_take isl_qpolynomial *qp1,
2423 __isl_take isl_qpolynomial *qp2);
2424 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2425 __isl_take isl_qpolynomial *qp, unsigned exponent);
2427 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2428 __isl_take isl_pw_qpolynomial *pwqp1,
2429 __isl_take isl_pw_qpolynomial *pwqp2);
2430 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2431 __isl_take isl_pw_qpolynomial *pwqp1,
2432 __isl_take isl_pw_qpolynomial *pwqp2);
2433 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2434 __isl_take isl_pw_qpolynomial *pwqp1,
2435 __isl_take isl_pw_qpolynomial *pwqp2);
2436 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2437 __isl_take isl_pw_qpolynomial *pwqp);
2438 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2439 __isl_take isl_pw_qpolynomial *pwqp1,
2440 __isl_take isl_pw_qpolynomial *pwqp2);
2442 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2443 __isl_take isl_union_pw_qpolynomial *upwqp1,
2444 __isl_take isl_union_pw_qpolynomial *upwqp2);
2445 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2446 __isl_take isl_union_pw_qpolynomial *upwqp1,
2447 __isl_take isl_union_pw_qpolynomial *upwqp2);
2448 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2449 __isl_take isl_union_pw_qpolynomial *upwqp1,
2450 __isl_take isl_union_pw_qpolynomial *upwqp2);
2452 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2453 __isl_take isl_pw_qpolynomial *pwqp,
2454 __isl_take isl_point *pnt);
2456 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2457 __isl_take isl_union_pw_qpolynomial *upwqp,
2458 __isl_take isl_point *pnt);
2460 __isl_give isl_set *isl_pw_qpolynomial_domain(
2461 __isl_take isl_pw_qpolynomial *pwqp);
2462 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2463 __isl_take isl_pw_qpolynomial *pwpq,
2464 __isl_take isl_set *set);
2466 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2467 __isl_take isl_union_pw_qpolynomial *upwqp);
2468 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2469 __isl_take isl_union_pw_qpolynomial *upwpq,
2470 __isl_take isl_union_set *uset);
2472 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2473 __isl_take isl_qpolynomial *qp,
2474 __isl_take isl_dim *model);
2476 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2477 __isl_take isl_union_pw_qpolynomial *upwqp);
2479 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2480 __isl_take isl_qpolynomial *qp,
2481 __isl_take isl_set *context);
2483 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2484 __isl_take isl_pw_qpolynomial *pwqp,
2485 __isl_take isl_set *context);
2487 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2488 __isl_take isl_union_pw_qpolynomial *upwqp,
2489 __isl_take isl_union_set *context);
2491 The gist operation applies the gist operation to each of
2492 the cells in the domain of the input piecewise quasipolynomial.
2493 The context is also exploited
2494 to simplify the quasipolynomials associated to each cell.
2496 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2497 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2498 __isl_give isl_union_pw_qpolynomial *
2499 isl_union_pw_qpolynomial_to_polynomial(
2500 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2502 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2503 the polynomial will be an overapproximation. If C<sign> is negative,
2504 it will be an underapproximation. If C<sign> is zero, the approximation
2505 will lie somewhere in between.
2507 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2509 A piecewise quasipolynomial reduction is a piecewise
2510 reduction (or fold) of quasipolynomials.
2511 In particular, the reduction can be maximum or a minimum.
2512 The objects are mainly used to represent the result of
2513 an upper or lower bound on a quasipolynomial over its domain,
2514 i.e., as the result of the following function.
2516 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2517 __isl_take isl_pw_qpolynomial *pwqp,
2518 enum isl_fold type, int *tight);
2520 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2521 __isl_take isl_union_pw_qpolynomial *upwqp,
2522 enum isl_fold type, int *tight);
2524 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2525 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2526 is the returned bound is known be tight, i.e., for each value
2527 of the parameters there is at least
2528 one element in the domain that reaches the bound.
2529 If the domain of C<pwqp> is not wrapping, then the bound is computed
2530 over all elements in that domain and the result has a purely parametric
2531 domain. If the domain of C<pwqp> is wrapping, then the bound is
2532 computed over the range of the wrapped relation. The domain of the
2533 wrapped relation becomes the domain of the result.
2535 A (piecewise) quasipolynomial reduction can be copied or freed using the
2536 following functions.
2538 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2539 __isl_keep isl_qpolynomial_fold *fold);
2540 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2541 __isl_keep isl_pw_qpolynomial_fold *pwf);
2542 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2543 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2544 void isl_qpolynomial_fold_free(
2545 __isl_take isl_qpolynomial_fold *fold);
2546 void isl_pw_qpolynomial_fold_free(
2547 __isl_take isl_pw_qpolynomial_fold *pwf);
2548 void isl_union_pw_qpolynomial_fold_free(
2549 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2551 =head3 Printing Piecewise Quasipolynomial Reductions
2553 Piecewise quasipolynomial reductions can be printed
2554 using the following function.
2556 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2557 __isl_take isl_printer *p,
2558 __isl_keep isl_pw_qpolynomial_fold *pwf);
2559 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2560 __isl_take isl_printer *p,
2561 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2563 For C<isl_printer_print_pw_qpolynomial_fold>,
2564 output format of the printer
2565 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2566 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2567 output format of the printer
2568 needs to be set to C<ISL_FORMAT_ISL>.
2569 In case of printing in C<ISL_FORMAT_C>, the user may want
2570 to set the names of all dimensions
2572 __isl_give isl_pw_qpolynomial_fold *
2573 isl_pw_qpolynomial_fold_set_dim_name(
2574 __isl_take isl_pw_qpolynomial_fold *pwf,
2575 enum isl_dim_type type, unsigned pos,
2578 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2580 To iterate over all piecewise quasipolynomial reductions in a union
2581 piecewise quasipolynomial reduction, use the following function
2583 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2584 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2585 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2586 void *user), void *user);
2588 To iterate over the cells in a piecewise quasipolynomial reduction,
2589 use either of the following two functions
2591 int isl_pw_qpolynomial_fold_foreach_piece(
2592 __isl_keep isl_pw_qpolynomial_fold *pwf,
2593 int (*fn)(__isl_take isl_set *set,
2594 __isl_take isl_qpolynomial_fold *fold,
2595 void *user), void *user);
2596 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2597 __isl_keep isl_pw_qpolynomial_fold *pwf,
2598 int (*fn)(__isl_take isl_set *set,
2599 __isl_take isl_qpolynomial_fold *fold,
2600 void *user), void *user);
2602 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2603 of the difference between these two functions.
2605 To iterate over all quasipolynomials in a reduction, use
2607 int isl_qpolynomial_fold_foreach_qpolynomial(
2608 __isl_keep isl_qpolynomial_fold *fold,
2609 int (*fn)(__isl_take isl_qpolynomial *qp,
2610 void *user), void *user);
2612 =head3 Operations on Piecewise Quasipolynomial Reductions
2614 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2615 __isl_take isl_pw_qpolynomial_fold *pwf1,
2616 __isl_take isl_pw_qpolynomial_fold *pwf2);
2618 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2619 __isl_take isl_pw_qpolynomial_fold *pwf1,
2620 __isl_take isl_pw_qpolynomial_fold *pwf2);
2622 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2623 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2624 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2626 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2627 __isl_take isl_pw_qpolynomial_fold *pwf,
2628 __isl_take isl_point *pnt);
2630 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2631 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2632 __isl_take isl_point *pnt);
2634 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2635 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2636 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2637 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2638 __isl_take isl_union_set *uset);
2640 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2641 __isl_take isl_pw_qpolynomial_fold *pwf);
2643 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2644 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2646 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2647 __isl_take isl_pw_qpolynomial_fold *pwf,
2648 __isl_take isl_set *context);
2650 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2651 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2652 __isl_take isl_union_set *context);
2654 The gist operation applies the gist operation to each of
2655 the cells in the domain of the input piecewise quasipolynomial reduction.
2656 In future, the operation will also exploit the context
2657 to simplify the quasipolynomial reductions associated to each cell.
2659 __isl_give isl_pw_qpolynomial_fold *
2660 isl_set_apply_pw_qpolynomial_fold(
2661 __isl_take isl_set *set,
2662 __isl_take isl_pw_qpolynomial_fold *pwf,
2664 __isl_give isl_pw_qpolynomial_fold *
2665 isl_map_apply_pw_qpolynomial_fold(
2666 __isl_take isl_map *map,
2667 __isl_take isl_pw_qpolynomial_fold *pwf,
2669 __isl_give isl_union_pw_qpolynomial_fold *
2670 isl_union_set_apply_union_pw_qpolynomial_fold(
2671 __isl_take isl_union_set *uset,
2672 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2674 __isl_give isl_union_pw_qpolynomial_fold *
2675 isl_union_map_apply_union_pw_qpolynomial_fold(
2676 __isl_take isl_union_map *umap,
2677 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2680 The functions taking a map
2681 compose the given map with the given piecewise quasipolynomial reduction.
2682 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2683 over all elements in the intersection of the range of the map
2684 and the domain of the piecewise quasipolynomial reduction
2685 as a function of an element in the domain of the map.
2686 The functions taking a set compute a bound over all elements in the
2687 intersection of the set and the domain of the
2688 piecewise quasipolynomial reduction.
2690 =head2 Dependence Analysis
2692 C<isl> contains specialized functionality for performing
2693 array dataflow analysis. That is, given a I<sink> access relation
2694 and a collection of possible I<source> access relations,
2695 C<isl> can compute relations that describe
2696 for each iteration of the sink access, which iteration
2697 of which of the source access relations was the last
2698 to access the same data element before the given iteration
2700 To compute standard flow dependences, the sink should be
2701 a read, while the sources should be writes.
2702 If any of the source accesses are marked as being I<may>
2703 accesses, then there will be a dependence to the last
2704 I<must> access B<and> to any I<may> access that follows
2705 this last I<must> access.
2706 In particular, if I<all> sources are I<may> accesses,
2707 then memory based dependence analysis is performed.
2708 If, on the other hand, all sources are I<must> accesses,
2709 then value based dependence analysis is performed.
2711 #include <isl/flow.h>
2713 typedef int (*isl_access_level_before)(void *first, void *second);
2715 __isl_give isl_access_info *isl_access_info_alloc(
2716 __isl_take isl_map *sink,
2717 void *sink_user, isl_access_level_before fn,
2719 __isl_give isl_access_info *isl_access_info_add_source(
2720 __isl_take isl_access_info *acc,
2721 __isl_take isl_map *source, int must,
2723 void isl_access_info_free(__isl_take isl_access_info *acc);
2725 __isl_give isl_flow *isl_access_info_compute_flow(
2726 __isl_take isl_access_info *acc);
2728 int isl_flow_foreach(__isl_keep isl_flow *deps,
2729 int (*fn)(__isl_take isl_map *dep, int must,
2730 void *dep_user, void *user),
2732 __isl_give isl_map *isl_flow_get_no_source(
2733 __isl_keep isl_flow *deps, int must);
2734 void isl_flow_free(__isl_take isl_flow *deps);
2736 The function C<isl_access_info_compute_flow> performs the actual
2737 dependence analysis. The other functions are used to construct
2738 the input for this function or to read off the output.
2740 The input is collected in an C<isl_access_info>, which can
2741 be created through a call to C<isl_access_info_alloc>.
2742 The arguments to this functions are the sink access relation
2743 C<sink>, a token C<sink_user> used to identify the sink
2744 access to the user, a callback function for specifying the
2745 relative order of source and sink accesses, and the number
2746 of source access relations that will be added.
2747 The callback function has type C<int (*)(void *first, void *second)>.
2748 The function is called with two user supplied tokens identifying
2749 either a source or the sink and it should return the shared nesting
2750 level and the relative order of the two accesses.
2751 In particular, let I<n> be the number of loops shared by
2752 the two accesses. If C<first> precedes C<second> textually,
2753 then the function should return I<2 * n + 1>; otherwise,
2754 it should return I<2 * n>.
2755 The sources can be added to the C<isl_access_info> by performing
2756 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2757 C<must> indicates whether the source is a I<must> access
2758 or a I<may> access. Note that a multi-valued access relation
2759 should only be marked I<must> if every iteration in the domain
2760 of the relation accesses I<all> elements in its image.
2761 The C<source_user> token is again used to identify
2762 the source access. The range of the source access relation
2763 C<source> should have the same dimension as the range
2764 of the sink access relation.
2765 The C<isl_access_info_free> function should usually not be
2766 called explicitly, because it is called implicitly by
2767 C<isl_access_info_compute_flow>.
2769 The result of the dependence analysis is collected in an
2770 C<isl_flow>. There may be elements of
2771 the sink access for which no preceding source access could be
2772 found or for which all preceding sources are I<may> accesses.
2773 The relations containing these elements can be obtained through
2774 calls to C<isl_flow_get_no_source>, the first with C<must> set
2775 and the second with C<must> unset.
2776 In the case of standard flow dependence analysis,
2777 with the sink a read and the sources I<must> writes,
2778 the first relation corresponds to the reads from uninitialized
2779 array elements and the second relation is empty.
2780 The actual flow dependences can be extracted using
2781 C<isl_flow_foreach>. This function will call the user-specified
2782 callback function C<fn> for each B<non-empty> dependence between
2783 a source and the sink. The callback function is called
2784 with four arguments, the actual flow dependence relation
2785 mapping source iterations to sink iterations, a boolean that
2786 indicates whether it is a I<must> or I<may> dependence, a token
2787 identifying the source and an additional C<void *> with value
2788 equal to the third argument of the C<isl_flow_foreach> call.
2789 A dependence is marked I<must> if it originates from a I<must>
2790 source and if it is not followed by any I<may> sources.
2792 After finishing with an C<isl_flow>, the user should call
2793 C<isl_flow_free> to free all associated memory.
2795 A higher-level interface to dependence analysis is provided
2796 by the following function.
2798 #include <isl/flow.h>
2800 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2801 __isl_take isl_union_map *must_source,
2802 __isl_take isl_union_map *may_source,
2803 __isl_take isl_union_map *schedule,
2804 __isl_give isl_union_map **must_dep,
2805 __isl_give isl_union_map **may_dep,
2806 __isl_give isl_union_map **must_no_source,
2807 __isl_give isl_union_map **may_no_source);
2809 The arrays are identified by the tuple names of the ranges
2810 of the accesses. The iteration domains by the tuple names
2811 of the domains of the accesses and of the schedule.
2812 The relative order of the iteration domains is given by the
2813 schedule. The relations returned through C<must_no_source>
2814 and C<may_no_source> are subsets of C<sink>.
2815 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2816 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2817 any of the other arguments is treated as an error.
2821 B<The functionality described in this section is fairly new
2822 and may be subject to change.>
2824 The following function can be used to compute a schedule
2825 for a union of domains. The generated schedule respects
2826 all C<validity> dependences. That is, all dependence distances
2827 over these dependences in the scheduled space are lexicographically
2828 positive. The generated schedule schedule also tries to minimize
2829 the dependence distances over C<proximity> dependences.
2830 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2831 for groups of domains where the dependence distances have only
2832 non-negative values.
2833 The algorithm used to construct the schedule is similar to that
2836 #include <isl/schedule.h>
2837 __isl_give isl_schedule *isl_union_set_compute_schedule(
2838 __isl_take isl_union_set *domain,
2839 __isl_take isl_union_map *validity,
2840 __isl_take isl_union_map *proximity);
2841 void *isl_schedule_free(__isl_take isl_schedule *sched);
2843 A mapping from the domains to the scheduled space can be obtained
2844 from an C<isl_schedule> using the following function.
2846 __isl_give isl_union_map *isl_schedule_get_map(
2847 __isl_keep isl_schedule *sched);
2849 This mapping can also be obtained in pieces using the following functions.
2851 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
2852 __isl_give isl_union_map *isl_schedule_get_band(
2853 __isl_keep isl_schedule *sched, unsigned band);
2855 C<isl_schedule_n_band> returns the maximal number of bands.
2856 C<isl_schedule_get_band> returns a union of mappings from a domain to
2857 the band of consecutive schedule dimensions with the given sequence
2858 number for that domain. Bands with the same sequence number but for
2859 different domains may be completely unrelated.
2860 Within a band, the corresponding coordinates of the distance vectors
2861 are all non-negative, assuming that the coordinates for all previous
2864 =head2 Parametric Vertex Enumeration
2866 The parametric vertex enumeration described in this section
2867 is mainly intended to be used internally and by the C<barvinok>
2870 #include <isl/vertices.h>
2871 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2872 __isl_keep isl_basic_set *bset);
2874 The function C<isl_basic_set_compute_vertices> performs the
2875 actual computation of the parametric vertices and the chamber
2876 decomposition and store the result in an C<isl_vertices> object.
2877 This information can be queried by either iterating over all
2878 the vertices or iterating over all the chambers or cells
2879 and then iterating over all vertices that are active on the chamber.
2881 int isl_vertices_foreach_vertex(
2882 __isl_keep isl_vertices *vertices,
2883 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2886 int isl_vertices_foreach_cell(
2887 __isl_keep isl_vertices *vertices,
2888 int (*fn)(__isl_take isl_cell *cell, void *user),
2890 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2891 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2894 Other operations that can be performed on an C<isl_vertices> object are
2897 isl_ctx *isl_vertices_get_ctx(
2898 __isl_keep isl_vertices *vertices);
2899 int isl_vertices_get_n_vertices(
2900 __isl_keep isl_vertices *vertices);
2901 void isl_vertices_free(__isl_take isl_vertices *vertices);
2903 Vertices can be inspected and destroyed using the following functions.
2905 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2906 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2907 __isl_give isl_basic_set *isl_vertex_get_domain(
2908 __isl_keep isl_vertex *vertex);
2909 __isl_give isl_basic_set *isl_vertex_get_expr(
2910 __isl_keep isl_vertex *vertex);
2911 void isl_vertex_free(__isl_take isl_vertex *vertex);
2913 C<isl_vertex_get_expr> returns a singleton parametric set describing
2914 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2916 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2917 B<rational> basic sets, so they should mainly be used for inspection
2918 and should not be mixed with integer sets.
2920 Chambers can be inspected and destroyed using the following functions.
2922 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2923 __isl_give isl_basic_set *isl_cell_get_domain(
2924 __isl_keep isl_cell *cell);
2925 void isl_cell_free(__isl_take isl_cell *cell);
2929 Although C<isl> is mainly meant to be used as a library,
2930 it also contains some basic applications that use some
2931 of the functionality of C<isl>.
2932 The input may be specified in either the L<isl format>
2933 or the L<PolyLib format>.
2935 =head2 C<isl_polyhedron_sample>
2937 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2938 an integer element of the polyhedron, if there is any.
2939 The first column in the output is the denominator and is always
2940 equal to 1. If the polyhedron contains no integer points,
2941 then a vector of length zero is printed.
2945 C<isl_pip> takes the same input as the C<example> program
2946 from the C<piplib> distribution, i.e., a set of constraints
2947 on the parameters, a line containing only -1 and finally a set
2948 of constraints on a parametric polyhedron.
2949 The coefficients of the parameters appear in the last columns
2950 (but before the final constant column).
2951 The output is the lexicographic minimum of the parametric polyhedron.
2952 As C<isl> currently does not have its own output format, the output
2953 is just a dump of the internal state.
2955 =head2 C<isl_polyhedron_minimize>
2957 C<isl_polyhedron_minimize> computes the minimum of some linear
2958 or affine objective function over the integer points in a polyhedron.
2959 If an affine objective function
2960 is given, then the constant should appear in the last column.
2962 =head2 C<isl_polytope_scan>
2964 Given a polytope, C<isl_polytope_scan> prints
2965 all integer points in the polytope.