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);
484 __isl_give isl_dim *isl_aff_get_dim(
485 __isl_keep isl_aff *aff);
487 The names of the individual dimensions may be set or read off
488 using the following functions.
491 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
492 enum isl_dim_type type, unsigned pos,
493 __isl_keep const char *name);
494 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
495 enum isl_dim_type type, unsigned pos);
497 Note that C<isl_dim_get_name> returns a pointer to some internal
498 data structure, so the result can only be used while the
499 corresponding C<isl_dim> is alive.
500 Also note that every function that operates on two sets or relations
501 requires that both arguments have the same parameters. This also
502 means that if one of the arguments has named parameters, then the
503 other needs to have named parameters too and the names need to match.
504 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
505 have different parameters (as long as they are named), in which case
506 the result will have as parameters the union of the parameters of
509 The names of entire spaces may be set or read off
510 using the following functions.
513 __isl_give isl_dim *isl_dim_set_tuple_name(
514 __isl_take isl_dim *dim,
515 enum isl_dim_type type, const char *s);
516 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
517 enum isl_dim_type type);
519 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
520 or C<isl_dim_set>. As with C<isl_dim_get_name>,
521 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
523 Binary operations require the corresponding spaces of their arguments
524 to have the same name.
526 Spaces can be nested. In particular, the domain of a set or
527 the domain or range of a relation can be a nested relation.
528 The following functions can be used to construct and deconstruct
529 such nested dimension specifications.
532 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
533 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
534 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
536 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
537 be the dimension specification of a set, while that of
538 C<isl_dim_wrap> should be the dimension specification of a relation.
539 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
540 of a relation, while that of C<isl_dim_wrap> is the dimension specification
543 Dimension specifications can be created from other dimension
544 specifications using the following functions.
546 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
547 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
548 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
549 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
550 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
551 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
552 __isl_take isl_dim *right);
553 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
554 enum isl_dim_type type, unsigned pos, unsigned n);
555 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
556 enum isl_dim_type type, unsigned n);
557 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
558 enum isl_dim_type type, unsigned first, unsigned n);
559 __isl_give isl_dim *isl_dim_map_from_set(
560 __isl_take isl_dim *dim);
561 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
563 Note that if dimensions are added or removed from a space, then
564 the name and the internal structure are lost.
568 A local space is essentially a dimension specification with
569 zero or more existentially quantified variables.
570 The local space of a basic set or relation can be obtained
571 using the following functions.
574 __isl_give isl_local_space *isl_basic_set_get_local_space(
575 __isl_keep isl_basic_set *bset);
578 __isl_give isl_local_space *isl_basic_map_get_local_space(
579 __isl_keep isl_basic_map *bmap);
581 A new local space can be created from a dimension specification using
583 #include <isl/local_space.h>
584 __isl_give isl_local_space *isl_local_space_from_dim(
585 __isl_take isl_dim *dim);
587 They can be inspected, copied and freed using the following functions.
589 #include <isl/local_space.h>
590 isl_ctx *isl_local_space_get_ctx(
591 __isl_keep isl_local_space *ls);
592 int isl_local_space_dim(__isl_keep isl_local_space *ls,
593 enum isl_dim_type type);
594 const char *isl_local_space_get_dim_name(
595 __isl_keep isl_local_space *ls,
596 enum isl_dim_type type, unsigned pos);
597 __isl_give isl_dim *isl_local_space_get_dim(
598 __isl_keep isl_local_space *ls);
599 __isl_give isl_div *isl_local_space_get_div(
600 __isl_keep isl_local_space *ls, int pos);
601 __isl_give isl_local_space *isl_local_space_copy(
602 __isl_keep isl_local_space *ls);
603 void *isl_local_space_free(__isl_take isl_local_space *ls);
605 =head2 Input and Output
607 C<isl> supports its own input/output format, which is similar
608 to the C<Omega> format, but also supports the C<PolyLib> format
613 The C<isl> format is similar to that of C<Omega>, but has a different
614 syntax for describing the parameters and allows for the definition
615 of an existentially quantified variable as the integer division
616 of an affine expression.
617 For example, the set of integers C<i> between C<0> and C<n>
618 such that C<i % 10 <= 6> can be described as
620 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
623 A set or relation can have several disjuncts, separated
624 by the keyword C<or>. Each disjunct is either a conjunction
625 of constraints or a projection (C<exists>) of a conjunction
626 of constraints. The constraints are separated by the keyword
629 =head3 C<PolyLib> format
631 If the represented set is a union, then the first line
632 contains a single number representing the number of disjuncts.
633 Otherwise, a line containing the number C<1> is optional.
635 Each disjunct is represented by a matrix of constraints.
636 The first line contains two numbers representing
637 the number of rows and columns,
638 where the number of rows is equal to the number of constraints
639 and the number of columns is equal to two plus the number of variables.
640 The following lines contain the actual rows of the constraint matrix.
641 In each row, the first column indicates whether the constraint
642 is an equality (C<0>) or inequality (C<1>). The final column
643 corresponds to the constant term.
645 If the set is parametric, then the coefficients of the parameters
646 appear in the last columns before the constant column.
647 The coefficients of any existentially quantified variables appear
648 between those of the set variables and those of the parameters.
650 =head3 Extended C<PolyLib> format
652 The extended C<PolyLib> format is nearly identical to the
653 C<PolyLib> format. The only difference is that the line
654 containing the number of rows and columns of a constraint matrix
655 also contains four additional numbers:
656 the number of output dimensions, the number of input dimensions,
657 the number of local dimensions (i.e., the number of existentially
658 quantified variables) and the number of parameters.
659 For sets, the number of ``output'' dimensions is equal
660 to the number of set dimensions, while the number of ``input''
666 __isl_give isl_basic_set *isl_basic_set_read_from_file(
667 isl_ctx *ctx, FILE *input, int nparam);
668 __isl_give isl_basic_set *isl_basic_set_read_from_str(
669 isl_ctx *ctx, const char *str, int nparam);
670 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
671 FILE *input, int nparam);
672 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
673 const char *str, int nparam);
676 __isl_give isl_basic_map *isl_basic_map_read_from_file(
677 isl_ctx *ctx, FILE *input, int nparam);
678 __isl_give isl_basic_map *isl_basic_map_read_from_str(
679 isl_ctx *ctx, const char *str, int nparam);
680 __isl_give isl_map *isl_map_read_from_file(
681 struct isl_ctx *ctx, FILE *input, int nparam);
682 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
683 const char *str, int nparam);
685 #include <isl/union_set.h>
686 __isl_give isl_union_set *isl_union_set_read_from_file(
687 isl_ctx *ctx, FILE *input);
688 __isl_give isl_union_set *isl_union_set_read_from_str(
689 struct isl_ctx *ctx, const char *str);
691 #include <isl/union_map.h>
692 __isl_give isl_union_map *isl_union_map_read_from_file(
693 isl_ctx *ctx, FILE *input);
694 __isl_give isl_union_map *isl_union_map_read_from_str(
695 struct isl_ctx *ctx, const char *str);
697 The input format is autodetected and may be either the C<PolyLib> format
698 or the C<isl> format.
699 C<nparam> specifies how many of the final columns in
700 the C<PolyLib> format correspond to parameters.
701 If input is given in the C<isl> format, then the number
702 of parameters needs to be equal to C<nparam>.
703 If C<nparam> is negative, then any number of parameters
704 is accepted in the C<isl> format and zero parameters
705 are assumed in the C<PolyLib> format.
709 Before anything can be printed, an C<isl_printer> needs to
712 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
714 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
715 void isl_printer_free(__isl_take isl_printer *printer);
716 __isl_give char *isl_printer_get_str(
717 __isl_keep isl_printer *printer);
719 The behavior of the printer can be modified in various ways
721 __isl_give isl_printer *isl_printer_set_output_format(
722 __isl_take isl_printer *p, int output_format);
723 __isl_give isl_printer *isl_printer_set_indent(
724 __isl_take isl_printer *p, int indent);
725 __isl_give isl_printer *isl_printer_set_prefix(
726 __isl_take isl_printer *p, const char *prefix);
727 __isl_give isl_printer *isl_printer_set_suffix(
728 __isl_take isl_printer *p, const char *suffix);
730 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
731 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
732 and defaults to C<ISL_FORMAT_ISL>.
733 Each line in the output is indented by C<indent> spaces
734 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
735 In the C<PolyLib> format output,
736 the coefficients of the existentially quantified variables
737 appear between those of the set variables and those
740 To actually print something, use
743 __isl_give isl_printer *isl_printer_print_basic_set(
744 __isl_take isl_printer *printer,
745 __isl_keep isl_basic_set *bset);
746 __isl_give isl_printer *isl_printer_print_set(
747 __isl_take isl_printer *printer,
748 __isl_keep isl_set *set);
751 __isl_give isl_printer *isl_printer_print_basic_map(
752 __isl_take isl_printer *printer,
753 __isl_keep isl_basic_map *bmap);
754 __isl_give isl_printer *isl_printer_print_map(
755 __isl_take isl_printer *printer,
756 __isl_keep isl_map *map);
758 #include <isl/union_set.h>
759 __isl_give isl_printer *isl_printer_print_union_set(
760 __isl_take isl_printer *p,
761 __isl_keep isl_union_set *uset);
763 #include <isl/union_map.h>
764 __isl_give isl_printer *isl_printer_print_union_map(
765 __isl_take isl_printer *p,
766 __isl_keep isl_union_map *umap);
768 When called on a file printer, the following function flushes
769 the file. When called on a string printer, the buffer is cleared.
771 __isl_give isl_printer *isl_printer_flush(
772 __isl_take isl_printer *p);
774 =head2 Creating New Sets and Relations
776 C<isl> has functions for creating some standard sets and relations.
780 =item * Empty sets and relations
782 __isl_give isl_basic_set *isl_basic_set_empty(
783 __isl_take isl_dim *dim);
784 __isl_give isl_basic_map *isl_basic_map_empty(
785 __isl_take isl_dim *dim);
786 __isl_give isl_set *isl_set_empty(
787 __isl_take isl_dim *dim);
788 __isl_give isl_map *isl_map_empty(
789 __isl_take isl_dim *dim);
790 __isl_give isl_union_set *isl_union_set_empty(
791 __isl_take isl_dim *dim);
792 __isl_give isl_union_map *isl_union_map_empty(
793 __isl_take isl_dim *dim);
795 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
796 is only used to specify the parameters.
798 =item * Universe sets and relations
800 __isl_give isl_basic_set *isl_basic_set_universe(
801 __isl_take isl_dim *dim);
802 __isl_give isl_basic_map *isl_basic_map_universe(
803 __isl_take isl_dim *dim);
804 __isl_give isl_set *isl_set_universe(
805 __isl_take isl_dim *dim);
806 __isl_give isl_map *isl_map_universe(
807 __isl_take isl_dim *dim);
808 __isl_give isl_union_set *isl_union_set_universe(
809 __isl_take isl_union_set *uset);
810 __isl_give isl_union_map *isl_union_map_universe(
811 __isl_take isl_union_map *umap);
813 The sets and relations constructed by the functions above
814 contain all integer values, while those constructed by the
815 functions below only contain non-negative values.
817 __isl_give isl_basic_set *isl_basic_set_nat_universe(
818 __isl_take isl_dim *dim);
819 __isl_give isl_basic_map *isl_basic_map_nat_universe(
820 __isl_take isl_dim *dim);
821 __isl_give isl_set *isl_set_nat_universe(
822 __isl_take isl_dim *dim);
823 __isl_give isl_map *isl_map_nat_universe(
824 __isl_take isl_dim *dim);
826 =item * Identity relations
828 __isl_give isl_basic_map *isl_basic_map_identity(
829 __isl_take isl_dim *dim);
830 __isl_give isl_map *isl_map_identity(
831 __isl_take isl_dim *dim);
833 The number of input and output dimensions in C<dim> needs
836 =item * Lexicographic order
838 __isl_give isl_map *isl_map_lex_lt(
839 __isl_take isl_dim *set_dim);
840 __isl_give isl_map *isl_map_lex_le(
841 __isl_take isl_dim *set_dim);
842 __isl_give isl_map *isl_map_lex_gt(
843 __isl_take isl_dim *set_dim);
844 __isl_give isl_map *isl_map_lex_ge(
845 __isl_take isl_dim *set_dim);
846 __isl_give isl_map *isl_map_lex_lt_first(
847 __isl_take isl_dim *dim, unsigned n);
848 __isl_give isl_map *isl_map_lex_le_first(
849 __isl_take isl_dim *dim, unsigned n);
850 __isl_give isl_map *isl_map_lex_gt_first(
851 __isl_take isl_dim *dim, unsigned n);
852 __isl_give isl_map *isl_map_lex_ge_first(
853 __isl_take isl_dim *dim, unsigned n);
855 The first four functions take a dimension specification for a B<set>
856 and return relations that express that the elements in the domain
857 are lexicographically less
858 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
859 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
860 than the elements in the range.
861 The last four functions take a dimension specification for a map
862 and return relations that express that the first C<n> dimensions
863 in the domain are lexicographically less
864 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
865 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
866 than the first C<n> dimensions in the range.
870 A basic set or relation can be converted to a set or relation
871 using the following functions.
873 __isl_give isl_set *isl_set_from_basic_set(
874 __isl_take isl_basic_set *bset);
875 __isl_give isl_map *isl_map_from_basic_map(
876 __isl_take isl_basic_map *bmap);
878 Sets and relations can be converted to union sets and relations
879 using the following functions.
881 __isl_give isl_union_map *isl_union_map_from_map(
882 __isl_take isl_map *map);
883 __isl_give isl_union_set *isl_union_set_from_set(
884 __isl_take isl_set *set);
886 Sets and relations can be copied and freed again using the following
889 __isl_give isl_basic_set *isl_basic_set_copy(
890 __isl_keep isl_basic_set *bset);
891 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
892 __isl_give isl_union_set *isl_union_set_copy(
893 __isl_keep isl_union_set *uset);
894 __isl_give isl_basic_map *isl_basic_map_copy(
895 __isl_keep isl_basic_map *bmap);
896 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
897 __isl_give isl_union_map *isl_union_map_copy(
898 __isl_keep isl_union_map *umap);
899 void isl_basic_set_free(__isl_take isl_basic_set *bset);
900 void isl_set_free(__isl_take isl_set *set);
901 void isl_union_set_free(__isl_take isl_union_set *uset);
902 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
903 void isl_map_free(__isl_take isl_map *map);
904 void isl_union_map_free(__isl_take isl_union_map *umap);
906 Other sets and relations can be constructed by starting
907 from a universe set or relation, adding equality and/or
908 inequality constraints and then projecting out the
909 existentially quantified variables, if any.
910 Constraints can be constructed, manipulated and
911 added to (basic) sets and relations using the following functions.
913 #include <isl/constraint.h>
914 __isl_give isl_constraint *isl_equality_alloc(
915 __isl_take isl_dim *dim);
916 __isl_give isl_constraint *isl_inequality_alloc(
917 __isl_take isl_dim *dim);
918 void isl_constraint_set_constant(
919 __isl_keep isl_constraint *constraint, isl_int v);
920 void isl_constraint_set_coefficient(
921 __isl_keep isl_constraint *constraint,
922 enum isl_dim_type type, int pos, isl_int v);
923 __isl_give isl_basic_map *isl_basic_map_add_constraint(
924 __isl_take isl_basic_map *bmap,
925 __isl_take isl_constraint *constraint);
926 __isl_give isl_basic_set *isl_basic_set_add_constraint(
927 __isl_take isl_basic_set *bset,
928 __isl_take isl_constraint *constraint);
929 __isl_give isl_map *isl_map_add_constraint(
930 __isl_take isl_map *map,
931 __isl_take isl_constraint *constraint);
932 __isl_give isl_set *isl_set_add_constraint(
933 __isl_take isl_set *set,
934 __isl_take isl_constraint *constraint);
936 For example, to create a set containing the even integers
937 between 10 and 42, you would use the following code.
941 struct isl_constraint *c;
942 struct isl_basic_set *bset;
945 dim = isl_dim_set_alloc(ctx, 0, 2);
946 bset = isl_basic_set_universe(isl_dim_copy(dim));
948 c = isl_equality_alloc(isl_dim_copy(dim));
949 isl_int_set_si(v, -1);
950 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
951 isl_int_set_si(v, 2);
952 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
953 bset = isl_basic_set_add_constraint(bset, c);
955 c = isl_inequality_alloc(isl_dim_copy(dim));
956 isl_int_set_si(v, -10);
957 isl_constraint_set_constant(c, v);
958 isl_int_set_si(v, 1);
959 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
960 bset = isl_basic_set_add_constraint(bset, c);
962 c = isl_inequality_alloc(dim);
963 isl_int_set_si(v, 42);
964 isl_constraint_set_constant(c, v);
965 isl_int_set_si(v, -1);
966 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
967 bset = isl_basic_set_add_constraint(bset, c);
969 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
975 struct isl_basic_set *bset;
976 bset = isl_basic_set_read_from_str(ctx,
977 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
979 A basic set or relation can also be constructed from two matrices
980 describing the equalities and the inequalities.
982 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
983 __isl_take isl_dim *dim,
984 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
985 enum isl_dim_type c1,
986 enum isl_dim_type c2, enum isl_dim_type c3,
987 enum isl_dim_type c4);
988 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
989 __isl_take isl_dim *dim,
990 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
991 enum isl_dim_type c1,
992 enum isl_dim_type c2, enum isl_dim_type c3,
993 enum isl_dim_type c4, enum isl_dim_type c5);
995 The C<isl_dim_type> arguments indicate the order in which
996 different kinds of variables appear in the input matrices
997 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
998 C<isl_dim_set> and C<isl_dim_div> for sets and
999 of C<isl_dim_cst>, C<isl_dim_param>,
1000 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1002 =head2 Inspecting Sets and Relations
1004 Usually, the user should not have to care about the actual constraints
1005 of the sets and maps, but should instead apply the abstract operations
1006 explained in the following sections.
1007 Occasionally, however, it may be required to inspect the individual
1008 coefficients of the constraints. This section explains how to do so.
1009 In these cases, it may also be useful to have C<isl> compute
1010 an explicit representation of the existentially quantified variables.
1012 __isl_give isl_set *isl_set_compute_divs(
1013 __isl_take isl_set *set);
1014 __isl_give isl_map *isl_map_compute_divs(
1015 __isl_take isl_map *map);
1016 __isl_give isl_union_set *isl_union_set_compute_divs(
1017 __isl_take isl_union_set *uset);
1018 __isl_give isl_union_map *isl_union_map_compute_divs(
1019 __isl_take isl_union_map *umap);
1021 This explicit representation defines the existentially quantified
1022 variables as integer divisions of the other variables, possibly
1023 including earlier existentially quantified variables.
1024 An explicitly represented existentially quantified variable therefore
1025 has a unique value when the values of the other variables are known.
1026 If, furthermore, the same existentials, i.e., existentials
1027 with the same explicit representations, should appear in the
1028 same order in each of the disjuncts of a set or map, then the user should call
1029 either of the following functions.
1031 __isl_give isl_set *isl_set_align_divs(
1032 __isl_take isl_set *set);
1033 __isl_give isl_map *isl_map_align_divs(
1034 __isl_take isl_map *map);
1036 Alternatively, the existentially quantified variables can be removed
1037 using the following functions, which compute an overapproximation.
1039 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1040 __isl_take isl_basic_set *bset);
1041 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1042 __isl_take isl_basic_map *bmap);
1043 __isl_give isl_set *isl_set_remove_divs(
1044 __isl_take isl_set *set);
1045 __isl_give isl_map *isl_map_remove_divs(
1046 __isl_take isl_map *map);
1048 To iterate over all the sets or maps in a union set or map, use
1050 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1051 int (*fn)(__isl_take isl_set *set, void *user),
1053 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1054 int (*fn)(__isl_take isl_map *map, void *user),
1057 The number of sets or maps in a union set or map can be obtained
1060 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1061 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1063 To extract the set or map from a union with a given dimension
1066 __isl_give isl_set *isl_union_set_extract_set(
1067 __isl_keep isl_union_set *uset,
1068 __isl_take isl_dim *dim);
1069 __isl_give isl_map *isl_union_map_extract_map(
1070 __isl_keep isl_union_map *umap,
1071 __isl_take isl_dim *dim);
1073 To iterate over all the basic sets or maps in a set or map, use
1075 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1076 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1078 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1079 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1082 The callback function C<fn> should return 0 if successful and
1083 -1 if an error occurs. In the latter case, or if any other error
1084 occurs, the above functions will return -1.
1086 It should be noted that C<isl> does not guarantee that
1087 the basic sets or maps passed to C<fn> are disjoint.
1088 If this is required, then the user should call one of
1089 the following functions first.
1091 __isl_give isl_set *isl_set_make_disjoint(
1092 __isl_take isl_set *set);
1093 __isl_give isl_map *isl_map_make_disjoint(
1094 __isl_take isl_map *map);
1096 The number of basic sets in a set can be obtained
1099 int isl_set_n_basic_set(__isl_keep isl_set *set);
1101 To iterate over the constraints of a basic set or map, use
1103 #include <isl/constraint.h>
1105 int isl_basic_map_foreach_constraint(
1106 __isl_keep isl_basic_map *bmap,
1107 int (*fn)(__isl_take isl_constraint *c, void *user),
1109 void isl_constraint_free(struct isl_constraint *c);
1111 Again, the callback function C<fn> should return 0 if successful and
1112 -1 if an error occurs. In the latter case, or if any other error
1113 occurs, the above functions will return -1.
1114 The constraint C<c> represents either an equality or an inequality.
1115 Use the following function to find out whether a constraint
1116 represents an equality. If not, it represents an inequality.
1118 int isl_constraint_is_equality(
1119 __isl_keep isl_constraint *constraint);
1121 The coefficients of the constraints can be inspected using
1122 the following functions.
1124 void isl_constraint_get_constant(
1125 __isl_keep isl_constraint *constraint, isl_int *v);
1126 void isl_constraint_get_coefficient(
1127 __isl_keep isl_constraint *constraint,
1128 enum isl_dim_type type, int pos, isl_int *v);
1129 int isl_constraint_involves_dims(
1130 __isl_keep isl_constraint *constraint,
1131 enum isl_dim_type type, unsigned first, unsigned n);
1133 The explicit representations of the existentially quantified
1134 variables can be inspected using the following functions.
1135 Note that the user is only allowed to use these functions
1136 if the inspected set or map is the result of a call
1137 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1139 __isl_give isl_div *isl_constraint_div(
1140 __isl_keep isl_constraint *constraint, int pos);
1141 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1142 void isl_div_get_constant(__isl_keep isl_div *div,
1144 void isl_div_get_denominator(__isl_keep isl_div *div,
1146 void isl_div_get_coefficient(__isl_keep isl_div *div,
1147 enum isl_dim_type type, int pos, isl_int *v);
1149 To obtain the constraints of a basic set or map in matrix
1150 form, use the following functions.
1152 __isl_give isl_mat *isl_basic_set_equalities_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_set_inequalities_matrix(
1157 __isl_keep isl_basic_set *bset,
1158 enum isl_dim_type c1, enum isl_dim_type c2,
1159 enum isl_dim_type c3, enum isl_dim_type c4);
1160 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1161 __isl_keep isl_basic_map *bmap,
1162 enum isl_dim_type c1,
1163 enum isl_dim_type c2, enum isl_dim_type c3,
1164 enum isl_dim_type c4, enum isl_dim_type c5);
1165 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1166 __isl_keep isl_basic_map *bmap,
1167 enum isl_dim_type c1,
1168 enum isl_dim_type c2, enum isl_dim_type c3,
1169 enum isl_dim_type c4, enum isl_dim_type c5);
1171 The C<isl_dim_type> arguments dictate the order in which
1172 different kinds of variables appear in the resulting matrix
1173 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1174 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1176 The names of the domain and range spaces of a set or relation can be
1177 read off using the following functions.
1179 const char *isl_basic_set_get_tuple_name(
1180 __isl_keep isl_basic_set *bset);
1181 const char *isl_set_get_tuple_name(
1182 __isl_keep isl_set *set);
1183 const char *isl_basic_map_get_tuple_name(
1184 __isl_keep isl_basic_map *bmap,
1185 enum isl_dim_type type);
1186 const char *isl_map_get_tuple_name(
1187 __isl_keep isl_map *map,
1188 enum isl_dim_type type);
1190 As with C<isl_dim_get_tuple_name>, the value returned points to
1191 an internal data structure.
1192 The names of individual dimensions can be read off using
1193 the following functions.
1195 const char *isl_constraint_get_dim_name(
1196 __isl_keep isl_constraint *constraint,
1197 enum isl_dim_type type, unsigned pos);
1198 const char *isl_basic_set_get_dim_name(
1199 __isl_keep isl_basic_set *bset,
1200 enum isl_dim_type type, unsigned pos);
1201 const char *isl_set_get_dim_name(
1202 __isl_keep isl_set *set,
1203 enum isl_dim_type type, unsigned pos);
1204 const char *isl_basic_map_get_dim_name(
1205 __isl_keep isl_basic_map *bmap,
1206 enum isl_dim_type type, unsigned pos);
1207 const char *isl_map_get_dim_name(
1208 __isl_keep isl_map *map,
1209 enum isl_dim_type type, unsigned pos);
1211 These functions are mostly useful to obtain the names
1216 =head3 Unary Properties
1222 The following functions test whether the given set or relation
1223 contains any integer points. The ``plain'' variants do not perform
1224 any computations, but simply check if the given set or relation
1225 is already known to be empty.
1227 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1228 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1229 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1230 int isl_set_is_empty(__isl_keep isl_set *set);
1231 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1232 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1233 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1234 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1235 int isl_map_is_empty(__isl_keep isl_map *map);
1236 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1238 =item * Universality
1240 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1241 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1242 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1244 =item * Single-valuedness
1246 int isl_map_is_single_valued(__isl_keep isl_map *map);
1247 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1251 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1252 int isl_map_is_injective(__isl_keep isl_map *map);
1253 int isl_union_map_plain_is_injective(
1254 __isl_keep isl_union_map *umap);
1255 int isl_union_map_is_injective(
1256 __isl_keep isl_union_map *umap);
1260 int isl_map_is_bijective(__isl_keep isl_map *map);
1261 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1265 The following functions check whether the domain of the given
1266 (basic) set is a wrapped relation.
1268 int isl_basic_set_is_wrapping(
1269 __isl_keep isl_basic_set *bset);
1270 int isl_set_is_wrapping(__isl_keep isl_set *set);
1272 =item * Internal Product
1274 int isl_basic_map_can_zip(
1275 __isl_keep isl_basic_map *bmap);
1276 int isl_map_can_zip(__isl_keep isl_map *map);
1278 Check whether the product of domain and range of the given relation
1280 i.e., whether both domain and range are nested relations.
1284 =head3 Binary Properties
1290 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1291 __isl_keep isl_set *set2);
1292 int isl_set_is_equal(__isl_keep isl_set *set1,
1293 __isl_keep isl_set *set2);
1294 int isl_union_set_is_equal(
1295 __isl_keep isl_union_set *uset1,
1296 __isl_keep isl_union_set *uset2);
1297 int isl_basic_map_is_equal(
1298 __isl_keep isl_basic_map *bmap1,
1299 __isl_keep isl_basic_map *bmap2);
1300 int isl_map_is_equal(__isl_keep isl_map *map1,
1301 __isl_keep isl_map *map2);
1302 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1303 __isl_keep isl_map *map2);
1304 int isl_union_map_is_equal(
1305 __isl_keep isl_union_map *umap1,
1306 __isl_keep isl_union_map *umap2);
1308 =item * Disjointness
1310 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1311 __isl_keep isl_set *set2);
1315 int isl_set_is_subset(__isl_keep isl_set *set1,
1316 __isl_keep isl_set *set2);
1317 int isl_set_is_strict_subset(
1318 __isl_keep isl_set *set1,
1319 __isl_keep isl_set *set2);
1320 int isl_union_set_is_subset(
1321 __isl_keep isl_union_set *uset1,
1322 __isl_keep isl_union_set *uset2);
1323 int isl_union_set_is_strict_subset(
1324 __isl_keep isl_union_set *uset1,
1325 __isl_keep isl_union_set *uset2);
1326 int isl_basic_map_is_subset(
1327 __isl_keep isl_basic_map *bmap1,
1328 __isl_keep isl_basic_map *bmap2);
1329 int isl_basic_map_is_strict_subset(
1330 __isl_keep isl_basic_map *bmap1,
1331 __isl_keep isl_basic_map *bmap2);
1332 int isl_map_is_subset(
1333 __isl_keep isl_map *map1,
1334 __isl_keep isl_map *map2);
1335 int isl_map_is_strict_subset(
1336 __isl_keep isl_map *map1,
1337 __isl_keep isl_map *map2);
1338 int isl_union_map_is_subset(
1339 __isl_keep isl_union_map *umap1,
1340 __isl_keep isl_union_map *umap2);
1341 int isl_union_map_is_strict_subset(
1342 __isl_keep isl_union_map *umap1,
1343 __isl_keep isl_union_map *umap2);
1347 =head2 Unary Operations
1353 __isl_give isl_set *isl_set_complement(
1354 __isl_take isl_set *set);
1358 __isl_give isl_basic_map *isl_basic_map_reverse(
1359 __isl_take isl_basic_map *bmap);
1360 __isl_give isl_map *isl_map_reverse(
1361 __isl_take isl_map *map);
1362 __isl_give isl_union_map *isl_union_map_reverse(
1363 __isl_take isl_union_map *umap);
1367 __isl_give isl_basic_set *isl_basic_set_project_out(
1368 __isl_take isl_basic_set *bset,
1369 enum isl_dim_type type, unsigned first, unsigned n);
1370 __isl_give isl_basic_map *isl_basic_map_project_out(
1371 __isl_take isl_basic_map *bmap,
1372 enum isl_dim_type type, unsigned first, unsigned n);
1373 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1374 enum isl_dim_type type, unsigned first, unsigned n);
1375 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1376 enum isl_dim_type type, unsigned first, unsigned n);
1377 __isl_give isl_basic_set *isl_basic_map_domain(
1378 __isl_take isl_basic_map *bmap);
1379 __isl_give isl_basic_set *isl_basic_map_range(
1380 __isl_take isl_basic_map *bmap);
1381 __isl_give isl_set *isl_map_domain(
1382 __isl_take isl_map *bmap);
1383 __isl_give isl_set *isl_map_range(
1384 __isl_take isl_map *map);
1385 __isl_give isl_union_set *isl_union_map_domain(
1386 __isl_take isl_union_map *umap);
1387 __isl_give isl_union_set *isl_union_map_range(
1388 __isl_take isl_union_map *umap);
1390 __isl_give isl_basic_map *isl_basic_map_domain_map(
1391 __isl_take isl_basic_map *bmap);
1392 __isl_give isl_basic_map *isl_basic_map_range_map(
1393 __isl_take isl_basic_map *bmap);
1394 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1395 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1396 __isl_give isl_union_map *isl_union_map_domain_map(
1397 __isl_take isl_union_map *umap);
1398 __isl_give isl_union_map *isl_union_map_range_map(
1399 __isl_take isl_union_map *umap);
1401 The functions above construct a (basic, regular or union) relation
1402 that maps (a wrapped version of) the input relation to its domain or range.
1406 __isl_give isl_set *isl_set_eliminate(
1407 __isl_take isl_set *set, enum isl_dim_type type,
1408 unsigned first, unsigned n);
1410 Eliminate the coefficients for the given dimensions from the constraints,
1411 without removing the dimensions.
1415 __isl_give isl_map *isl_set_identity(
1416 __isl_take isl_set *set);
1417 __isl_give isl_union_map *isl_union_set_identity(
1418 __isl_take isl_union_set *uset);
1420 Construct an identity relation on the given (union) set.
1424 __isl_give isl_basic_set *isl_basic_map_deltas(
1425 __isl_take isl_basic_map *bmap);
1426 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1427 __isl_give isl_union_set *isl_union_map_deltas(
1428 __isl_take isl_union_map *umap);
1430 These functions return a (basic) set containing the differences
1431 between image elements and corresponding domain elements in the input.
1433 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1434 __isl_take isl_basic_map *bmap);
1435 __isl_give isl_map *isl_map_deltas_map(
1436 __isl_take isl_map *map);
1437 __isl_give isl_union_map *isl_union_map_deltas_map(
1438 __isl_take isl_union_map *umap);
1440 The functions above construct a (basic, regular or union) relation
1441 that maps (a wrapped version of) the input relation to its delta set.
1445 Simplify the representation of a set or relation by trying
1446 to combine pairs of basic sets or relations into a single
1447 basic set or relation.
1449 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1450 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1451 __isl_give isl_union_set *isl_union_set_coalesce(
1452 __isl_take isl_union_set *uset);
1453 __isl_give isl_union_map *isl_union_map_coalesce(
1454 __isl_take isl_union_map *umap);
1456 =item * Detecting equalities
1458 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1459 __isl_take isl_basic_set *bset);
1460 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1461 __isl_take isl_basic_map *bmap);
1462 __isl_give isl_set *isl_set_detect_equalities(
1463 __isl_take isl_set *set);
1464 __isl_give isl_map *isl_map_detect_equalities(
1465 __isl_take isl_map *map);
1466 __isl_give isl_union_set *isl_union_set_detect_equalities(
1467 __isl_take isl_union_set *uset);
1468 __isl_give isl_union_map *isl_union_map_detect_equalities(
1469 __isl_take isl_union_map *umap);
1471 Simplify the representation of a set or relation by detecting implicit
1474 =item * Removing redundant constraints
1476 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1477 __isl_take isl_basic_set *bset);
1478 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1479 __isl_take isl_basic_map *bmap);
1483 __isl_give isl_basic_set *isl_set_convex_hull(
1484 __isl_take isl_set *set);
1485 __isl_give isl_basic_map *isl_map_convex_hull(
1486 __isl_take isl_map *map);
1488 If the input set or relation has any existentially quantified
1489 variables, then the result of these operations is currently undefined.
1493 __isl_give isl_basic_set *isl_set_simple_hull(
1494 __isl_take isl_set *set);
1495 __isl_give isl_basic_map *isl_map_simple_hull(
1496 __isl_take isl_map *map);
1497 __isl_give isl_union_map *isl_union_map_simple_hull(
1498 __isl_take isl_union_map *umap);
1500 These functions compute a single basic set or relation
1501 that contains the whole input set or relation.
1502 In particular, the output is described by translates
1503 of the constraints describing the basic sets or relations in the input.
1507 (See \autoref{s:simple hull}.)
1513 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1514 __isl_take isl_basic_set *bset);
1515 __isl_give isl_basic_set *isl_set_affine_hull(
1516 __isl_take isl_set *set);
1517 __isl_give isl_union_set *isl_union_set_affine_hull(
1518 __isl_take isl_union_set *uset);
1519 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1520 __isl_take isl_basic_map *bmap);
1521 __isl_give isl_basic_map *isl_map_affine_hull(
1522 __isl_take isl_map *map);
1523 __isl_give isl_union_map *isl_union_map_affine_hull(
1524 __isl_take isl_union_map *umap);
1526 In case of union sets and relations, the affine hull is computed
1529 =item * Polyhedral hull
1531 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1532 __isl_take isl_set *set);
1533 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1534 __isl_take isl_map *map);
1535 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1536 __isl_take isl_union_set *uset);
1537 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1538 __isl_take isl_union_map *umap);
1540 These functions compute a single basic set or relation
1541 not involving any existentially quantified variables
1542 that contains the whole input set or relation.
1543 In case of union sets and relations, the polyhedral hull is computed
1546 =item * Optimization
1548 #include <isl/ilp.h>
1549 enum isl_lp_result isl_basic_set_max(
1550 __isl_keep isl_basic_set *bset,
1551 __isl_keep isl_aff *obj, isl_int *opt)
1552 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1553 __isl_keep isl_aff *obj, isl_int *opt);
1555 Compute the maximum of the integer affine expression C<obj>
1556 over the points in C<set>, returning the result in C<opt>.
1557 The return value may be one of C<isl_lp_error>,
1558 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1562 The following functions compute either the set of (rational) coefficient
1563 values of valid constraints for the given set or the set of (rational)
1564 values satisfying the constraints with coefficients from the given set.
1565 Internally, these two sets of functions perform essentially the
1566 same operations, except that the set of coefficients is assumed to
1567 be a cone, while the set of values may be any polyhedron.
1568 The current implementation is based on the Farkas lemma and
1569 Fourier-Motzkin elimination, but this may change or be made optional
1570 in future. In particular, future implementations may use different
1571 dualization algorithms or skip the elimination step.
1573 __isl_give isl_basic_set *isl_basic_set_coefficients(
1574 __isl_take isl_basic_set *bset);
1575 __isl_give isl_basic_set *isl_set_coefficients(
1576 __isl_take isl_set *set);
1577 __isl_give isl_union_set *isl_union_set_coefficients(
1578 __isl_take isl_union_set *bset);
1579 __isl_give isl_basic_set *isl_basic_set_solutions(
1580 __isl_take isl_basic_set *bset);
1581 __isl_give isl_basic_set *isl_set_solutions(
1582 __isl_take isl_set *set);
1583 __isl_give isl_union_set *isl_union_set_solutions(
1584 __isl_take isl_union_set *bset);
1588 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1590 __isl_give isl_union_map *isl_union_map_power(
1591 __isl_take isl_union_map *umap, int *exact);
1593 Compute a parametric representation for all positive powers I<k> of C<map>.
1594 The result maps I<k> to a nested relation corresponding to the
1595 I<k>th power of C<map>.
1596 The result may be an overapproximation. If the result is known to be exact,
1597 then C<*exact> is set to C<1>.
1599 =item * Transitive closure
1601 __isl_give isl_map *isl_map_transitive_closure(
1602 __isl_take isl_map *map, int *exact);
1603 __isl_give isl_union_map *isl_union_map_transitive_closure(
1604 __isl_take isl_union_map *umap, int *exact);
1606 Compute the transitive closure of C<map>.
1607 The result may be an overapproximation. If the result is known to be exact,
1608 then C<*exact> is set to C<1>.
1610 =item * Reaching path lengths
1612 __isl_give isl_map *isl_map_reaching_path_lengths(
1613 __isl_take isl_map *map, int *exact);
1615 Compute a relation that maps each element in the range of C<map>
1616 to the lengths of all paths composed of edges in C<map> that
1617 end up in the given element.
1618 The result may be an overapproximation. If the result is known to be exact,
1619 then C<*exact> is set to C<1>.
1620 To compute the I<maximal> path length, the resulting relation
1621 should be postprocessed by C<isl_map_lexmax>.
1622 In particular, if the input relation is a dependence relation
1623 (mapping sources to sinks), then the maximal path length corresponds
1624 to the free schedule.
1625 Note, however, that C<isl_map_lexmax> expects the maximum to be
1626 finite, so if the path lengths are unbounded (possibly due to
1627 the overapproximation), then you will get an error message.
1631 __isl_give isl_basic_set *isl_basic_map_wrap(
1632 __isl_take isl_basic_map *bmap);
1633 __isl_give isl_set *isl_map_wrap(
1634 __isl_take isl_map *map);
1635 __isl_give isl_union_set *isl_union_map_wrap(
1636 __isl_take isl_union_map *umap);
1637 __isl_give isl_basic_map *isl_basic_set_unwrap(
1638 __isl_take isl_basic_set *bset);
1639 __isl_give isl_map *isl_set_unwrap(
1640 __isl_take isl_set *set);
1641 __isl_give isl_union_map *isl_union_set_unwrap(
1642 __isl_take isl_union_set *uset);
1646 Remove any internal structure of domain (and range) of the given
1647 set or relation. If there is any such internal structure in the input,
1648 then the name of the space is also removed.
1650 __isl_give isl_basic_set *isl_basic_set_flatten(
1651 __isl_take isl_basic_set *bset);
1652 __isl_give isl_set *isl_set_flatten(
1653 __isl_take isl_set *set);
1654 __isl_give isl_basic_map *isl_basic_map_flatten(
1655 __isl_take isl_basic_map *bmap);
1656 __isl_give isl_map *isl_map_flatten(
1657 __isl_take isl_map *map);
1659 __isl_give isl_map *isl_set_flatten_map(
1660 __isl_take isl_set *set);
1662 The function above constructs a relation
1663 that maps the input set to a flattened version of the set.
1667 Lift the input set to a space with extra dimensions corresponding
1668 to the existentially quantified variables in the input.
1669 In particular, the result lives in a wrapped map where the domain
1670 is the original space and the range corresponds to the original
1671 existentially quantified variables.
1673 __isl_give isl_basic_set *isl_basic_set_lift(
1674 __isl_take isl_basic_set *bset);
1675 __isl_give isl_set *isl_set_lift(
1676 __isl_take isl_set *set);
1677 __isl_give isl_union_set *isl_union_set_lift(
1678 __isl_take isl_union_set *uset);
1680 =item * Internal Product
1682 __isl_give isl_basic_map *isl_basic_map_zip(
1683 __isl_take isl_basic_map *bmap);
1684 __isl_give isl_map *isl_map_zip(
1685 __isl_take isl_map *map);
1686 __isl_give isl_union_map *isl_union_map_zip(
1687 __isl_take isl_union_map *umap);
1689 Given a relation with nested relations for domain and range,
1690 interchange the range of the domain with the domain of the range.
1692 =item * Aligning parameters
1694 __isl_give isl_set *isl_set_align_params(
1695 __isl_take isl_set *set,
1696 __isl_take isl_dim *model);
1697 __isl_give isl_map *isl_map_align_params(
1698 __isl_take isl_map *map,
1699 __isl_take isl_dim *model);
1701 Change the order of the parameters of the given set or relation
1702 such that the first parameters match those of C<model>.
1703 This may involve the introduction of extra parameters.
1704 All parameters need to be named.
1706 =item * Dimension manipulation
1708 __isl_give isl_set *isl_set_add_dims(
1709 __isl_take isl_set *set,
1710 enum isl_dim_type type, unsigned n);
1711 __isl_give isl_map *isl_map_add_dims(
1712 __isl_take isl_map *map,
1713 enum isl_dim_type type, unsigned n);
1715 It is usually not advisable to directly change the (input or output)
1716 space of a set or a relation as this removes the name and the internal
1717 structure of the space. However, the above functions can be useful
1718 to add new parameters, assuming
1719 C<isl_set_align_params> and C<isl_map_align_params>
1724 =head2 Binary Operations
1726 The two arguments of a binary operation not only need to live
1727 in the same C<isl_ctx>, they currently also need to have
1728 the same (number of) parameters.
1730 =head3 Basic Operations
1734 =item * Intersection
1736 __isl_give isl_basic_set *isl_basic_set_intersect(
1737 __isl_take isl_basic_set *bset1,
1738 __isl_take isl_basic_set *bset2);
1739 __isl_give isl_set *isl_set_intersect(
1740 __isl_take isl_set *set1,
1741 __isl_take isl_set *set2);
1742 __isl_give isl_union_set *isl_union_set_intersect(
1743 __isl_take isl_union_set *uset1,
1744 __isl_take isl_union_set *uset2);
1745 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1746 __isl_take isl_basic_map *bmap,
1747 __isl_take isl_basic_set *bset);
1748 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1749 __isl_take isl_basic_map *bmap,
1750 __isl_take isl_basic_set *bset);
1751 __isl_give isl_basic_map *isl_basic_map_intersect(
1752 __isl_take isl_basic_map *bmap1,
1753 __isl_take isl_basic_map *bmap2);
1754 __isl_give isl_map *isl_map_intersect_domain(
1755 __isl_take isl_map *map,
1756 __isl_take isl_set *set);
1757 __isl_give isl_map *isl_map_intersect_range(
1758 __isl_take isl_map *map,
1759 __isl_take isl_set *set);
1760 __isl_give isl_map *isl_map_intersect(
1761 __isl_take isl_map *map1,
1762 __isl_take isl_map *map2);
1763 __isl_give isl_union_map *isl_union_map_intersect_domain(
1764 __isl_take isl_union_map *umap,
1765 __isl_take isl_union_set *uset);
1766 __isl_give isl_union_map *isl_union_map_intersect_range(
1767 __isl_take isl_union_map *umap,
1768 __isl_take isl_union_set *uset);
1769 __isl_give isl_union_map *isl_union_map_intersect(
1770 __isl_take isl_union_map *umap1,
1771 __isl_take isl_union_map *umap2);
1775 __isl_give isl_set *isl_basic_set_union(
1776 __isl_take isl_basic_set *bset1,
1777 __isl_take isl_basic_set *bset2);
1778 __isl_give isl_map *isl_basic_map_union(
1779 __isl_take isl_basic_map *bmap1,
1780 __isl_take isl_basic_map *bmap2);
1781 __isl_give isl_set *isl_set_union(
1782 __isl_take isl_set *set1,
1783 __isl_take isl_set *set2);
1784 __isl_give isl_map *isl_map_union(
1785 __isl_take isl_map *map1,
1786 __isl_take isl_map *map2);
1787 __isl_give isl_union_set *isl_union_set_union(
1788 __isl_take isl_union_set *uset1,
1789 __isl_take isl_union_set *uset2);
1790 __isl_give isl_union_map *isl_union_map_union(
1791 __isl_take isl_union_map *umap1,
1792 __isl_take isl_union_map *umap2);
1794 =item * Set difference
1796 __isl_give isl_set *isl_set_subtract(
1797 __isl_take isl_set *set1,
1798 __isl_take isl_set *set2);
1799 __isl_give isl_map *isl_map_subtract(
1800 __isl_take isl_map *map1,
1801 __isl_take isl_map *map2);
1802 __isl_give isl_union_set *isl_union_set_subtract(
1803 __isl_take isl_union_set *uset1,
1804 __isl_take isl_union_set *uset2);
1805 __isl_give isl_union_map *isl_union_map_subtract(
1806 __isl_take isl_union_map *umap1,
1807 __isl_take isl_union_map *umap2);
1811 __isl_give isl_basic_set *isl_basic_set_apply(
1812 __isl_take isl_basic_set *bset,
1813 __isl_take isl_basic_map *bmap);
1814 __isl_give isl_set *isl_set_apply(
1815 __isl_take isl_set *set,
1816 __isl_take isl_map *map);
1817 __isl_give isl_union_set *isl_union_set_apply(
1818 __isl_take isl_union_set *uset,
1819 __isl_take isl_union_map *umap);
1820 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1821 __isl_take isl_basic_map *bmap1,
1822 __isl_take isl_basic_map *bmap2);
1823 __isl_give isl_basic_map *isl_basic_map_apply_range(
1824 __isl_take isl_basic_map *bmap1,
1825 __isl_take isl_basic_map *bmap2);
1826 __isl_give isl_map *isl_map_apply_domain(
1827 __isl_take isl_map *map1,
1828 __isl_take isl_map *map2);
1829 __isl_give isl_union_map *isl_union_map_apply_domain(
1830 __isl_take isl_union_map *umap1,
1831 __isl_take isl_union_map *umap2);
1832 __isl_give isl_map *isl_map_apply_range(
1833 __isl_take isl_map *map1,
1834 __isl_take isl_map *map2);
1835 __isl_give isl_union_map *isl_union_map_apply_range(
1836 __isl_take isl_union_map *umap1,
1837 __isl_take isl_union_map *umap2);
1839 =item * Cartesian Product
1841 __isl_give isl_set *isl_set_product(
1842 __isl_take isl_set *set1,
1843 __isl_take isl_set *set2);
1844 __isl_give isl_union_set *isl_union_set_product(
1845 __isl_take isl_union_set *uset1,
1846 __isl_take isl_union_set *uset2);
1847 __isl_give isl_basic_map *isl_basic_map_range_product(
1848 __isl_take isl_basic_map *bmap1,
1849 __isl_take isl_basic_map *bmap2);
1850 __isl_give isl_map *isl_map_range_product(
1851 __isl_take isl_map *map1,
1852 __isl_take isl_map *map2);
1853 __isl_give isl_union_map *isl_union_map_range_product(
1854 __isl_take isl_union_map *umap1,
1855 __isl_take isl_union_map *umap2);
1856 __isl_give isl_map *isl_map_product(
1857 __isl_take isl_map *map1,
1858 __isl_take isl_map *map2);
1859 __isl_give isl_union_map *isl_union_map_product(
1860 __isl_take isl_union_map *umap1,
1861 __isl_take isl_union_map *umap2);
1863 The above functions compute the cross product of the given
1864 sets or relations. The domains and ranges of the results
1865 are wrapped maps between domains and ranges of the inputs.
1866 To obtain a ``flat'' product, use the following functions
1869 __isl_give isl_basic_set *isl_basic_set_flat_product(
1870 __isl_take isl_basic_set *bset1,
1871 __isl_take isl_basic_set *bset2);
1872 __isl_give isl_set *isl_set_flat_product(
1873 __isl_take isl_set *set1,
1874 __isl_take isl_set *set2);
1875 __isl_give isl_basic_map *isl_basic_map_flat_product(
1876 __isl_take isl_basic_map *bmap1,
1877 __isl_take isl_basic_map *bmap2);
1878 __isl_give isl_map *isl_map_flat_product(
1879 __isl_take isl_map *map1,
1880 __isl_take isl_map *map2);
1882 =item * Simplification
1884 __isl_give isl_basic_set *isl_basic_set_gist(
1885 __isl_take isl_basic_set *bset,
1886 __isl_take isl_basic_set *context);
1887 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1888 __isl_take isl_set *context);
1889 __isl_give isl_union_set *isl_union_set_gist(
1890 __isl_take isl_union_set *uset,
1891 __isl_take isl_union_set *context);
1892 __isl_give isl_basic_map *isl_basic_map_gist(
1893 __isl_take isl_basic_map *bmap,
1894 __isl_take isl_basic_map *context);
1895 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1896 __isl_take isl_map *context);
1897 __isl_give isl_union_map *isl_union_map_gist(
1898 __isl_take isl_union_map *umap,
1899 __isl_take isl_union_map *context);
1901 The gist operation returns a set or relation that has the
1902 same intersection with the context as the input set or relation.
1903 Any implicit equality in the intersection is made explicit in the result,
1904 while all inequalities that are redundant with respect to the intersection
1906 In case of union sets and relations, the gist operation is performed
1911 =head3 Lexicographic Optimization
1913 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1914 the following functions
1915 compute a set that contains the lexicographic minimum or maximum
1916 of the elements in C<set> (or C<bset>) for those values of the parameters
1917 that satisfy C<dom>.
1918 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1919 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1921 In other words, the union of the parameter values
1922 for which the result is non-empty and of C<*empty>
1925 __isl_give isl_set *isl_basic_set_partial_lexmin(
1926 __isl_take isl_basic_set *bset,
1927 __isl_take isl_basic_set *dom,
1928 __isl_give isl_set **empty);
1929 __isl_give isl_set *isl_basic_set_partial_lexmax(
1930 __isl_take isl_basic_set *bset,
1931 __isl_take isl_basic_set *dom,
1932 __isl_give isl_set **empty);
1933 __isl_give isl_set *isl_set_partial_lexmin(
1934 __isl_take isl_set *set, __isl_take isl_set *dom,
1935 __isl_give isl_set **empty);
1936 __isl_give isl_set *isl_set_partial_lexmax(
1937 __isl_take isl_set *set, __isl_take isl_set *dom,
1938 __isl_give isl_set **empty);
1940 Given a (basic) set C<set> (or C<bset>), the following functions simply
1941 return a set containing the lexicographic minimum or maximum
1942 of the elements in C<set> (or C<bset>).
1943 In case of union sets, the optimum is computed per space.
1945 __isl_give isl_set *isl_basic_set_lexmin(
1946 __isl_take isl_basic_set *bset);
1947 __isl_give isl_set *isl_basic_set_lexmax(
1948 __isl_take isl_basic_set *bset);
1949 __isl_give isl_set *isl_set_lexmin(
1950 __isl_take isl_set *set);
1951 __isl_give isl_set *isl_set_lexmax(
1952 __isl_take isl_set *set);
1953 __isl_give isl_union_set *isl_union_set_lexmin(
1954 __isl_take isl_union_set *uset);
1955 __isl_give isl_union_set *isl_union_set_lexmax(
1956 __isl_take isl_union_set *uset);
1958 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1959 the following functions
1960 compute a relation that maps each element of C<dom>
1961 to the single lexicographic minimum or maximum
1962 of the elements that are associated to that same
1963 element in C<map> (or C<bmap>).
1964 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1965 that contains the elements in C<dom> that do not map
1966 to any elements in C<map> (or C<bmap>).
1967 In other words, the union of the domain of the result and of C<*empty>
1970 __isl_give isl_map *isl_basic_map_partial_lexmax(
1971 __isl_take isl_basic_map *bmap,
1972 __isl_take isl_basic_set *dom,
1973 __isl_give isl_set **empty);
1974 __isl_give isl_map *isl_basic_map_partial_lexmin(
1975 __isl_take isl_basic_map *bmap,
1976 __isl_take isl_basic_set *dom,
1977 __isl_give isl_set **empty);
1978 __isl_give isl_map *isl_map_partial_lexmax(
1979 __isl_take isl_map *map, __isl_take isl_set *dom,
1980 __isl_give isl_set **empty);
1981 __isl_give isl_map *isl_map_partial_lexmin(
1982 __isl_take isl_map *map, __isl_take isl_set *dom,
1983 __isl_give isl_set **empty);
1985 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1986 return a map mapping each element in the domain of
1987 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1988 of all elements associated to that element.
1989 In case of union relations, the optimum is computed per space.
1991 __isl_give isl_map *isl_basic_map_lexmin(
1992 __isl_take isl_basic_map *bmap);
1993 __isl_give isl_map *isl_basic_map_lexmax(
1994 __isl_take isl_basic_map *bmap);
1995 __isl_give isl_map *isl_map_lexmin(
1996 __isl_take isl_map *map);
1997 __isl_give isl_map *isl_map_lexmax(
1998 __isl_take isl_map *map);
1999 __isl_give isl_union_map *isl_union_map_lexmin(
2000 __isl_take isl_union_map *umap);
2001 __isl_give isl_union_map *isl_union_map_lexmax(
2002 __isl_take isl_union_map *umap);
2006 Lists are defined over several element types, including
2007 C<isl_basic_set> and C<isl_set>.
2008 Here we take lists of C<isl_set>s as an example.
2010 #include <isl/list.h>
2011 __isl_give isl_set_list *isl_set_list_alloc(
2012 isl_ctx *ctx, int n);
2013 __isl_give isl_set_list *isl_set_list_add(
2014 __isl_take isl_set_list *list,
2015 __isl_take isl_set *el);
2016 void isl_set_list_free(__isl_take isl_set_list *list);
2018 C<isl_set_list_alloc> creates an empty list with a capacity for
2023 Matrices can be created, copied and freed using the following functions.
2025 #include <isl/mat.h>
2026 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2027 unsigned n_row, unsigned n_col);
2028 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2029 void isl_mat_free(__isl_take isl_mat *mat);
2031 Note that the elements of a newly created matrix may have arbitrary values.
2032 The elements can be changed and inspected using the following functions.
2034 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2035 int isl_mat_rows(__isl_keep isl_mat *mat);
2036 int isl_mat_cols(__isl_keep isl_mat *mat);
2037 int isl_mat_get_element(__isl_keep isl_mat *mat,
2038 int row, int col, isl_int *v);
2039 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2040 int row, int col, isl_int v);
2041 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2042 int row, int col, int v);
2044 C<isl_mat_get_element> will return a negative value if anything went wrong.
2045 In that case, the value of C<*v> is undefined.
2047 The following function can be used to compute the (right) inverse
2048 of a matrix, i.e., a matrix such that the product of the original
2049 and the inverse (in that order) is a multiple of the identity matrix.
2050 The input matrix is assumed to be of full row-rank.
2052 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2054 The following function can be used to compute the (right) kernel
2055 (or null space) of a matrix, i.e., a matrix such that the product of
2056 the original and the kernel (in that order) is the zero matrix.
2058 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2060 =head2 Quasi Affine Expressions
2062 The zero quasi affine expression can be created using
2064 __isl_give isl_aff *isl_aff_zero(
2065 __isl_take isl_local_space *ls);
2067 Quasi affine expressions can be copied and free using
2069 #include <isl/aff.h>
2070 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2071 void *isl_aff_free(__isl_take isl_aff *aff);
2073 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2074 using the following function. The constraint is required to have
2075 a non-zero coefficient for the specified dimension.
2077 #include <isl/constraint.h>
2078 __isl_give isl_aff *isl_constraint_get_bound(
2079 __isl_keep isl_constraint *constraint,
2080 enum isl_dim_type type, int pos);
2082 Conversely, an equality constraint equating
2083 the affine expression to zero or an inequality constraint enforcing
2084 the affine expression to be non-negative, can be constructed using
2086 __isl_give isl_constraint *isl_equality_from_aff(
2087 __isl_take isl_aff *aff);
2088 __isl_give isl_constraint *isl_inequality_from_aff(
2089 __isl_take isl_aff *aff);
2091 The expression can be inspected using
2093 #include <isl/aff.h>
2094 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2095 int isl_aff_dim(__isl_keep isl_aff *aff,
2096 enum isl_dim_type type);
2097 __isl_give isl_local_space *isl_aff_get_local_space(
2098 __isl_keep isl_aff *aff);
2099 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2100 enum isl_dim_type type, unsigned pos);
2101 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2103 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2104 enum isl_dim_type type, int pos, isl_int *v);
2105 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2107 __isl_give isl_div *isl_aff_get_div(
2108 __isl_keep isl_aff *aff, int pos);
2110 It can be modified using
2112 #include <isl/aff.h>
2113 __isl_give isl_aff *isl_aff_set_constant(
2114 __isl_take isl_aff *aff, isl_int v);
2115 __isl_give isl_aff *isl_aff_set_constant_si(
2116 __isl_take isl_aff *aff, int v);
2117 __isl_give isl_aff *isl_aff_set_coefficient(
2118 __isl_take isl_aff *aff,
2119 enum isl_dim_type type, int pos, isl_int v);
2120 __isl_give isl_aff *isl_aff_set_coefficient_si(
2121 __isl_take isl_aff *aff,
2122 enum isl_dim_type type, int pos, int v);
2123 __isl_give isl_aff *isl_aff_set_denominator(
2124 __isl_take isl_aff *aff, isl_int v);
2126 __isl_give isl_aff *isl_aff_add_constant(
2127 __isl_take isl_aff *aff, isl_int v);
2128 __isl_give isl_aff *isl_aff_add_coefficient_si(
2129 __isl_take isl_aff *aff,
2130 enum isl_dim_type type, int pos, int v);
2132 Note that the C<set_constant> and C<set_coefficient> functions
2133 set the I<numerator> of the constant or coefficient, while
2134 C<add_constant> and C<add_coefficient> add an integer value to
2135 the possibly rational constant or coefficient.
2139 #include <isl/aff.h>
2140 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2141 __isl_take isl_aff *aff2);
2142 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2143 __isl_take isl_aff *aff2);
2144 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2145 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2146 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2148 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2151 An expression can be printed using
2153 #include <isl/aff.h>
2154 __isl_give isl_printer *isl_printer_print_aff(
2155 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2159 Points are elements of a set. They can be used to construct
2160 simple sets (boxes) or they can be used to represent the
2161 individual elements of a set.
2162 The zero point (the origin) can be created using
2164 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2166 The coordinates of a point can be inspected, set and changed
2169 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2170 enum isl_dim_type type, int pos, isl_int *v);
2171 __isl_give isl_point *isl_point_set_coordinate(
2172 __isl_take isl_point *pnt,
2173 enum isl_dim_type type, int pos, isl_int v);
2175 __isl_give isl_point *isl_point_add_ui(
2176 __isl_take isl_point *pnt,
2177 enum isl_dim_type type, int pos, unsigned val);
2178 __isl_give isl_point *isl_point_sub_ui(
2179 __isl_take isl_point *pnt,
2180 enum isl_dim_type type, int pos, unsigned val);
2182 Points can be copied or freed using
2184 __isl_give isl_point *isl_point_copy(
2185 __isl_keep isl_point *pnt);
2186 void isl_point_free(__isl_take isl_point *pnt);
2188 A singleton set can be created from a point using
2190 __isl_give isl_basic_set *isl_basic_set_from_point(
2191 __isl_take isl_point *pnt);
2192 __isl_give isl_set *isl_set_from_point(
2193 __isl_take isl_point *pnt);
2195 and a box can be created from two opposite extremal points using
2197 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2198 __isl_take isl_point *pnt1,
2199 __isl_take isl_point *pnt2);
2200 __isl_give isl_set *isl_set_box_from_points(
2201 __isl_take isl_point *pnt1,
2202 __isl_take isl_point *pnt2);
2204 All elements of a B<bounded> (union) set can be enumerated using
2205 the following functions.
2207 int isl_set_foreach_point(__isl_keep isl_set *set,
2208 int (*fn)(__isl_take isl_point *pnt, void *user),
2210 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2211 int (*fn)(__isl_take isl_point *pnt, void *user),
2214 The function C<fn> is called for each integer point in
2215 C<set> with as second argument the last argument of
2216 the C<isl_set_foreach_point> call. The function C<fn>
2217 should return C<0> on success and C<-1> on failure.
2218 In the latter case, C<isl_set_foreach_point> will stop
2219 enumerating and return C<-1> as well.
2220 If the enumeration is performed successfully and to completion,
2221 then C<isl_set_foreach_point> returns C<0>.
2223 To obtain a single point of a (basic) set, use
2225 __isl_give isl_point *isl_basic_set_sample_point(
2226 __isl_take isl_basic_set *bset);
2227 __isl_give isl_point *isl_set_sample_point(
2228 __isl_take isl_set *set);
2230 If C<set> does not contain any (integer) points, then the
2231 resulting point will be ``void'', a property that can be
2234 int isl_point_is_void(__isl_keep isl_point *pnt);
2236 =head2 Piecewise Quasipolynomials
2238 A piecewise quasipolynomial is a particular kind of function that maps
2239 a parametric point to a rational value.
2240 More specifically, a quasipolynomial is a polynomial expression in greatest
2241 integer parts of affine expressions of parameters and variables.
2242 A piecewise quasipolynomial is a subdivision of a given parametric
2243 domain into disjoint cells with a quasipolynomial associated to
2244 each cell. The value of the piecewise quasipolynomial at a given
2245 point is the value of the quasipolynomial associated to the cell
2246 that contains the point. Outside of the union of cells,
2247 the value is assumed to be zero.
2248 For example, the piecewise quasipolynomial
2250 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2252 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2253 A given piecewise quasipolynomial has a fixed domain dimension.
2254 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2255 defined over different domains.
2256 Piecewise quasipolynomials are mainly used by the C<barvinok>
2257 library for representing the number of elements in a parametric set or map.
2258 For example, the piecewise quasipolynomial above represents
2259 the number of points in the map
2261 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2263 =head3 Printing (Piecewise) Quasipolynomials
2265 Quasipolynomials and piecewise quasipolynomials can be printed
2266 using the following functions.
2268 __isl_give isl_printer *isl_printer_print_qpolynomial(
2269 __isl_take isl_printer *p,
2270 __isl_keep isl_qpolynomial *qp);
2272 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2273 __isl_take isl_printer *p,
2274 __isl_keep isl_pw_qpolynomial *pwqp);
2276 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2277 __isl_take isl_printer *p,
2278 __isl_keep isl_union_pw_qpolynomial *upwqp);
2280 The output format of the printer
2281 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2282 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2284 In case of printing in C<ISL_FORMAT_C>, the user may want
2285 to set the names of all dimensions
2287 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2288 __isl_take isl_qpolynomial *qp,
2289 enum isl_dim_type type, unsigned pos,
2291 __isl_give isl_pw_qpolynomial *
2292 isl_pw_qpolynomial_set_dim_name(
2293 __isl_take isl_pw_qpolynomial *pwqp,
2294 enum isl_dim_type type, unsigned pos,
2297 =head3 Creating New (Piecewise) Quasipolynomials
2299 Some simple quasipolynomials can be created using the following functions.
2300 More complicated quasipolynomials can be created by applying
2301 operations such as addition and multiplication
2302 on the resulting quasipolynomials
2304 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2305 __isl_take isl_dim *dim);
2306 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2307 __isl_take isl_dim *dim);
2308 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2309 __isl_take isl_dim *dim);
2310 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2311 __isl_take isl_dim *dim);
2312 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2313 __isl_take isl_dim *dim);
2314 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2315 __isl_take isl_dim *dim,
2316 const isl_int n, const isl_int d);
2317 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2318 __isl_take isl_div *div);
2319 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2320 __isl_take isl_dim *dim,
2321 enum isl_dim_type type, unsigned pos);
2322 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2323 __isl_take isl_aff *aff);
2325 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2326 with a single cell can be created using the following functions.
2327 Multiple of these single cell piecewise quasipolynomials can
2328 be combined to create more complicated piecewise quasipolynomials.
2330 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2331 __isl_take isl_dim *dim);
2332 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2333 __isl_take isl_set *set,
2334 __isl_take isl_qpolynomial *qp);
2336 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2337 __isl_take isl_dim *dim);
2338 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2339 __isl_take isl_pw_qpolynomial *pwqp);
2340 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2341 __isl_take isl_union_pw_qpolynomial *upwqp,
2342 __isl_take isl_pw_qpolynomial *pwqp);
2344 Quasipolynomials can be copied and freed again using the following
2347 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2348 __isl_keep isl_qpolynomial *qp);
2349 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2351 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2352 __isl_keep isl_pw_qpolynomial *pwqp);
2353 void isl_pw_qpolynomial_free(
2354 __isl_take isl_pw_qpolynomial *pwqp);
2356 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2357 __isl_keep isl_union_pw_qpolynomial *upwqp);
2358 void isl_union_pw_qpolynomial_free(
2359 __isl_take isl_union_pw_qpolynomial *upwqp);
2361 =head3 Inspecting (Piecewise) Quasipolynomials
2363 To iterate over all piecewise quasipolynomials in a union
2364 piecewise quasipolynomial, use the following function
2366 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2367 __isl_keep isl_union_pw_qpolynomial *upwqp,
2368 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2371 To extract the piecewise quasipolynomial from a union with a given dimension
2374 __isl_give isl_pw_qpolynomial *
2375 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2376 __isl_keep isl_union_pw_qpolynomial *upwqp,
2377 __isl_take isl_dim *dim);
2379 To iterate over the cells in a piecewise quasipolynomial,
2380 use either of the following two functions
2382 int isl_pw_qpolynomial_foreach_piece(
2383 __isl_keep isl_pw_qpolynomial *pwqp,
2384 int (*fn)(__isl_take isl_set *set,
2385 __isl_take isl_qpolynomial *qp,
2386 void *user), void *user);
2387 int isl_pw_qpolynomial_foreach_lifted_piece(
2388 __isl_keep isl_pw_qpolynomial *pwqp,
2389 int (*fn)(__isl_take isl_set *set,
2390 __isl_take isl_qpolynomial *qp,
2391 void *user), void *user);
2393 As usual, the function C<fn> should return C<0> on success
2394 and C<-1> on failure. The difference between
2395 C<isl_pw_qpolynomial_foreach_piece> and
2396 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2397 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2398 compute unique representations for all existentially quantified
2399 variables and then turn these existentially quantified variables
2400 into extra set variables, adapting the associated quasipolynomial
2401 accordingly. This means that the C<set> passed to C<fn>
2402 will not have any existentially quantified variables, but that
2403 the dimensions of the sets may be different for different
2404 invocations of C<fn>.
2406 To iterate over all terms in a quasipolynomial,
2409 int isl_qpolynomial_foreach_term(
2410 __isl_keep isl_qpolynomial *qp,
2411 int (*fn)(__isl_take isl_term *term,
2412 void *user), void *user);
2414 The terms themselves can be inspected and freed using
2417 unsigned isl_term_dim(__isl_keep isl_term *term,
2418 enum isl_dim_type type);
2419 void isl_term_get_num(__isl_keep isl_term *term,
2421 void isl_term_get_den(__isl_keep isl_term *term,
2423 int isl_term_get_exp(__isl_keep isl_term *term,
2424 enum isl_dim_type type, unsigned pos);
2425 __isl_give isl_div *isl_term_get_div(
2426 __isl_keep isl_term *term, unsigned pos);
2427 void isl_term_free(__isl_take isl_term *term);
2429 Each term is a product of parameters, set variables and
2430 integer divisions. The function C<isl_term_get_exp>
2431 returns the exponent of a given dimensions in the given term.
2432 The C<isl_int>s in the arguments of C<isl_term_get_num>
2433 and C<isl_term_get_den> need to have been initialized
2434 using C<isl_int_init> before calling these functions.
2436 =head3 Properties of (Piecewise) Quasipolynomials
2438 To check whether a quasipolynomial is actually a constant,
2439 use the following function.
2441 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2442 isl_int *n, isl_int *d);
2444 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2445 then the numerator and denominator of the constant
2446 are returned in C<*n> and C<*d>, respectively.
2448 =head3 Operations on (Piecewise) Quasipolynomials
2450 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2451 __isl_take isl_qpolynomial *qp);
2452 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2453 __isl_take isl_qpolynomial *qp1,
2454 __isl_take isl_qpolynomial *qp2);
2455 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2456 __isl_take isl_qpolynomial *qp1,
2457 __isl_take isl_qpolynomial *qp2);
2458 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2459 __isl_take isl_qpolynomial *qp1,
2460 __isl_take isl_qpolynomial *qp2);
2461 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2462 __isl_take isl_qpolynomial *qp, unsigned exponent);
2464 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2465 __isl_take isl_pw_qpolynomial *pwqp1,
2466 __isl_take isl_pw_qpolynomial *pwqp2);
2467 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2468 __isl_take isl_pw_qpolynomial *pwqp1,
2469 __isl_take isl_pw_qpolynomial *pwqp2);
2470 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2471 __isl_take isl_pw_qpolynomial *pwqp1,
2472 __isl_take isl_pw_qpolynomial *pwqp2);
2473 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2474 __isl_take isl_pw_qpolynomial *pwqp);
2475 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2476 __isl_take isl_pw_qpolynomial *pwqp1,
2477 __isl_take isl_pw_qpolynomial *pwqp2);
2479 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2480 __isl_take isl_union_pw_qpolynomial *upwqp1,
2481 __isl_take isl_union_pw_qpolynomial *upwqp2);
2482 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2483 __isl_take isl_union_pw_qpolynomial *upwqp1,
2484 __isl_take isl_union_pw_qpolynomial *upwqp2);
2485 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2486 __isl_take isl_union_pw_qpolynomial *upwqp1,
2487 __isl_take isl_union_pw_qpolynomial *upwqp2);
2489 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2490 __isl_take isl_pw_qpolynomial *pwqp,
2491 __isl_take isl_point *pnt);
2493 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2494 __isl_take isl_union_pw_qpolynomial *upwqp,
2495 __isl_take isl_point *pnt);
2497 __isl_give isl_set *isl_pw_qpolynomial_domain(
2498 __isl_take isl_pw_qpolynomial *pwqp);
2499 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2500 __isl_take isl_pw_qpolynomial *pwpq,
2501 __isl_take isl_set *set);
2503 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2504 __isl_take isl_union_pw_qpolynomial *upwqp);
2505 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2506 __isl_take isl_union_pw_qpolynomial *upwpq,
2507 __isl_take isl_union_set *uset);
2509 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2510 __isl_take isl_qpolynomial *qp,
2511 __isl_take isl_dim *model);
2513 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2514 __isl_take isl_union_pw_qpolynomial *upwqp);
2516 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2517 __isl_take isl_qpolynomial *qp,
2518 __isl_take isl_set *context);
2520 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2521 __isl_take isl_pw_qpolynomial *pwqp,
2522 __isl_take isl_set *context);
2524 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2525 __isl_take isl_union_pw_qpolynomial *upwqp,
2526 __isl_take isl_union_set *context);
2528 The gist operation applies the gist operation to each of
2529 the cells in the domain of the input piecewise quasipolynomial.
2530 The context is also exploited
2531 to simplify the quasipolynomials associated to each cell.
2533 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2534 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2535 __isl_give isl_union_pw_qpolynomial *
2536 isl_union_pw_qpolynomial_to_polynomial(
2537 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2539 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2540 the polynomial will be an overapproximation. If C<sign> is negative,
2541 it will be an underapproximation. If C<sign> is zero, the approximation
2542 will lie somewhere in between.
2544 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2546 A piecewise quasipolynomial reduction is a piecewise
2547 reduction (or fold) of quasipolynomials.
2548 In particular, the reduction can be maximum or a minimum.
2549 The objects are mainly used to represent the result of
2550 an upper or lower bound on a quasipolynomial over its domain,
2551 i.e., as the result of the following function.
2553 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2554 __isl_take isl_pw_qpolynomial *pwqp,
2555 enum isl_fold type, int *tight);
2557 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2558 __isl_take isl_union_pw_qpolynomial *upwqp,
2559 enum isl_fold type, int *tight);
2561 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2562 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2563 is the returned bound is known be tight, i.e., for each value
2564 of the parameters there is at least
2565 one element in the domain that reaches the bound.
2566 If the domain of C<pwqp> is not wrapping, then the bound is computed
2567 over all elements in that domain and the result has a purely parametric
2568 domain. If the domain of C<pwqp> is wrapping, then the bound is
2569 computed over the range of the wrapped relation. The domain of the
2570 wrapped relation becomes the domain of the result.
2572 A (piecewise) quasipolynomial reduction can be copied or freed using the
2573 following functions.
2575 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2576 __isl_keep isl_qpolynomial_fold *fold);
2577 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2578 __isl_keep isl_pw_qpolynomial_fold *pwf);
2579 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2580 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2581 void isl_qpolynomial_fold_free(
2582 __isl_take isl_qpolynomial_fold *fold);
2583 void isl_pw_qpolynomial_fold_free(
2584 __isl_take isl_pw_qpolynomial_fold *pwf);
2585 void isl_union_pw_qpolynomial_fold_free(
2586 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2588 =head3 Printing Piecewise Quasipolynomial Reductions
2590 Piecewise quasipolynomial reductions can be printed
2591 using the following function.
2593 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2594 __isl_take isl_printer *p,
2595 __isl_keep isl_pw_qpolynomial_fold *pwf);
2596 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2597 __isl_take isl_printer *p,
2598 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2600 For C<isl_printer_print_pw_qpolynomial_fold>,
2601 output format of the printer
2602 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2603 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2604 output format of the printer
2605 needs to be set to C<ISL_FORMAT_ISL>.
2606 In case of printing in C<ISL_FORMAT_C>, the user may want
2607 to set the names of all dimensions
2609 __isl_give isl_pw_qpolynomial_fold *
2610 isl_pw_qpolynomial_fold_set_dim_name(
2611 __isl_take isl_pw_qpolynomial_fold *pwf,
2612 enum isl_dim_type type, unsigned pos,
2615 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2617 To iterate over all piecewise quasipolynomial reductions in a union
2618 piecewise quasipolynomial reduction, use the following function
2620 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2621 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2622 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2623 void *user), void *user);
2625 To iterate over the cells in a piecewise quasipolynomial reduction,
2626 use either of the following two functions
2628 int isl_pw_qpolynomial_fold_foreach_piece(
2629 __isl_keep isl_pw_qpolynomial_fold *pwf,
2630 int (*fn)(__isl_take isl_set *set,
2631 __isl_take isl_qpolynomial_fold *fold,
2632 void *user), void *user);
2633 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2634 __isl_keep isl_pw_qpolynomial_fold *pwf,
2635 int (*fn)(__isl_take isl_set *set,
2636 __isl_take isl_qpolynomial_fold *fold,
2637 void *user), void *user);
2639 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2640 of the difference between these two functions.
2642 To iterate over all quasipolynomials in a reduction, use
2644 int isl_qpolynomial_fold_foreach_qpolynomial(
2645 __isl_keep isl_qpolynomial_fold *fold,
2646 int (*fn)(__isl_take isl_qpolynomial *qp,
2647 void *user), void *user);
2649 =head3 Operations on Piecewise Quasipolynomial Reductions
2651 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2652 __isl_take isl_pw_qpolynomial_fold *pwf1,
2653 __isl_take isl_pw_qpolynomial_fold *pwf2);
2655 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2656 __isl_take isl_pw_qpolynomial_fold *pwf1,
2657 __isl_take isl_pw_qpolynomial_fold *pwf2);
2659 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2660 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2661 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2663 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2664 __isl_take isl_pw_qpolynomial_fold *pwf,
2665 __isl_take isl_point *pnt);
2667 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2668 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2669 __isl_take isl_point *pnt);
2671 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2672 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2673 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2674 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2675 __isl_take isl_union_set *uset);
2677 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2678 __isl_take isl_pw_qpolynomial_fold *pwf);
2680 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2681 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2683 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2684 __isl_take isl_pw_qpolynomial_fold *pwf,
2685 __isl_take isl_set *context);
2687 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2688 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2689 __isl_take isl_union_set *context);
2691 The gist operation applies the gist operation to each of
2692 the cells in the domain of the input piecewise quasipolynomial reduction.
2693 In future, the operation will also exploit the context
2694 to simplify the quasipolynomial reductions associated to each cell.
2696 __isl_give isl_pw_qpolynomial_fold *
2697 isl_set_apply_pw_qpolynomial_fold(
2698 __isl_take isl_set *set,
2699 __isl_take isl_pw_qpolynomial_fold *pwf,
2701 __isl_give isl_pw_qpolynomial_fold *
2702 isl_map_apply_pw_qpolynomial_fold(
2703 __isl_take isl_map *map,
2704 __isl_take isl_pw_qpolynomial_fold *pwf,
2706 __isl_give isl_union_pw_qpolynomial_fold *
2707 isl_union_set_apply_union_pw_qpolynomial_fold(
2708 __isl_take isl_union_set *uset,
2709 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2711 __isl_give isl_union_pw_qpolynomial_fold *
2712 isl_union_map_apply_union_pw_qpolynomial_fold(
2713 __isl_take isl_union_map *umap,
2714 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2717 The functions taking a map
2718 compose the given map with the given piecewise quasipolynomial reduction.
2719 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2720 over all elements in the intersection of the range of the map
2721 and the domain of the piecewise quasipolynomial reduction
2722 as a function of an element in the domain of the map.
2723 The functions taking a set compute a bound over all elements in the
2724 intersection of the set and the domain of the
2725 piecewise quasipolynomial reduction.
2727 =head2 Dependence Analysis
2729 C<isl> contains specialized functionality for performing
2730 array dataflow analysis. That is, given a I<sink> access relation
2731 and a collection of possible I<source> access relations,
2732 C<isl> can compute relations that describe
2733 for each iteration of the sink access, which iteration
2734 of which of the source access relations was the last
2735 to access the same data element before the given iteration
2737 To compute standard flow dependences, the sink should be
2738 a read, while the sources should be writes.
2739 If any of the source accesses are marked as being I<may>
2740 accesses, then there will be a dependence to the last
2741 I<must> access B<and> to any I<may> access that follows
2742 this last I<must> access.
2743 In particular, if I<all> sources are I<may> accesses,
2744 then memory based dependence analysis is performed.
2745 If, on the other hand, all sources are I<must> accesses,
2746 then value based dependence analysis is performed.
2748 #include <isl/flow.h>
2750 typedef int (*isl_access_level_before)(void *first, void *second);
2752 __isl_give isl_access_info *isl_access_info_alloc(
2753 __isl_take isl_map *sink,
2754 void *sink_user, isl_access_level_before fn,
2756 __isl_give isl_access_info *isl_access_info_add_source(
2757 __isl_take isl_access_info *acc,
2758 __isl_take isl_map *source, int must,
2760 void isl_access_info_free(__isl_take isl_access_info *acc);
2762 __isl_give isl_flow *isl_access_info_compute_flow(
2763 __isl_take isl_access_info *acc);
2765 int isl_flow_foreach(__isl_keep isl_flow *deps,
2766 int (*fn)(__isl_take isl_map *dep, int must,
2767 void *dep_user, void *user),
2769 __isl_give isl_map *isl_flow_get_no_source(
2770 __isl_keep isl_flow *deps, int must);
2771 void isl_flow_free(__isl_take isl_flow *deps);
2773 The function C<isl_access_info_compute_flow> performs the actual
2774 dependence analysis. The other functions are used to construct
2775 the input for this function or to read off the output.
2777 The input is collected in an C<isl_access_info>, which can
2778 be created through a call to C<isl_access_info_alloc>.
2779 The arguments to this functions are the sink access relation
2780 C<sink>, a token C<sink_user> used to identify the sink
2781 access to the user, a callback function for specifying the
2782 relative order of source and sink accesses, and the number
2783 of source access relations that will be added.
2784 The callback function has type C<int (*)(void *first, void *second)>.
2785 The function is called with two user supplied tokens identifying
2786 either a source or the sink and it should return the shared nesting
2787 level and the relative order of the two accesses.
2788 In particular, let I<n> be the number of loops shared by
2789 the two accesses. If C<first> precedes C<second> textually,
2790 then the function should return I<2 * n + 1>; otherwise,
2791 it should return I<2 * n>.
2792 The sources can be added to the C<isl_access_info> by performing
2793 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2794 C<must> indicates whether the source is a I<must> access
2795 or a I<may> access. Note that a multi-valued access relation
2796 should only be marked I<must> if every iteration in the domain
2797 of the relation accesses I<all> elements in its image.
2798 The C<source_user> token is again used to identify
2799 the source access. The range of the source access relation
2800 C<source> should have the same dimension as the range
2801 of the sink access relation.
2802 The C<isl_access_info_free> function should usually not be
2803 called explicitly, because it is called implicitly by
2804 C<isl_access_info_compute_flow>.
2806 The result of the dependence analysis is collected in an
2807 C<isl_flow>. There may be elements of
2808 the sink access for which no preceding source access could be
2809 found or for which all preceding sources are I<may> accesses.
2810 The relations containing these elements can be obtained through
2811 calls to C<isl_flow_get_no_source>, the first with C<must> set
2812 and the second with C<must> unset.
2813 In the case of standard flow dependence analysis,
2814 with the sink a read and the sources I<must> writes,
2815 the first relation corresponds to the reads from uninitialized
2816 array elements and the second relation is empty.
2817 The actual flow dependences can be extracted using
2818 C<isl_flow_foreach>. This function will call the user-specified
2819 callback function C<fn> for each B<non-empty> dependence between
2820 a source and the sink. The callback function is called
2821 with four arguments, the actual flow dependence relation
2822 mapping source iterations to sink iterations, a boolean that
2823 indicates whether it is a I<must> or I<may> dependence, a token
2824 identifying the source and an additional C<void *> with value
2825 equal to the third argument of the C<isl_flow_foreach> call.
2826 A dependence is marked I<must> if it originates from a I<must>
2827 source and if it is not followed by any I<may> sources.
2829 After finishing with an C<isl_flow>, the user should call
2830 C<isl_flow_free> to free all associated memory.
2832 A higher-level interface to dependence analysis is provided
2833 by the following function.
2835 #include <isl/flow.h>
2837 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2838 __isl_take isl_union_map *must_source,
2839 __isl_take isl_union_map *may_source,
2840 __isl_take isl_union_map *schedule,
2841 __isl_give isl_union_map **must_dep,
2842 __isl_give isl_union_map **may_dep,
2843 __isl_give isl_union_map **must_no_source,
2844 __isl_give isl_union_map **may_no_source);
2846 The arrays are identified by the tuple names of the ranges
2847 of the accesses. The iteration domains by the tuple names
2848 of the domains of the accesses and of the schedule.
2849 The relative order of the iteration domains is given by the
2850 schedule. The relations returned through C<must_no_source>
2851 and C<may_no_source> are subsets of C<sink>.
2852 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2853 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2854 any of the other arguments is treated as an error.
2858 B<The functionality described in this section is fairly new
2859 and may be subject to change.>
2861 The following function can be used to compute a schedule
2862 for a union of domains. The generated schedule respects
2863 all C<validity> dependences. That is, all dependence distances
2864 over these dependences in the scheduled space are lexicographically
2865 positive. The generated schedule schedule also tries to minimize
2866 the dependence distances over C<proximity> dependences.
2867 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2868 for groups of domains where the dependence distances have only
2869 non-negative values.
2870 The algorithm used to construct the schedule is similar to that
2873 #include <isl/schedule.h>
2874 __isl_give isl_schedule *isl_union_set_compute_schedule(
2875 __isl_take isl_union_set *domain,
2876 __isl_take isl_union_map *validity,
2877 __isl_take isl_union_map *proximity);
2878 void *isl_schedule_free(__isl_take isl_schedule *sched);
2880 A mapping from the domains to the scheduled space can be obtained
2881 from an C<isl_schedule> using the following function.
2883 __isl_give isl_union_map *isl_schedule_get_map(
2884 __isl_keep isl_schedule *sched);
2886 This mapping can also be obtained in pieces using the following functions.
2888 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
2889 __isl_give isl_union_map *isl_schedule_get_band(
2890 __isl_keep isl_schedule *sched, unsigned band);
2892 C<isl_schedule_n_band> returns the maximal number of bands.
2893 C<isl_schedule_get_band> returns a union of mappings from a domain to
2894 the band of consecutive schedule dimensions with the given sequence
2895 number for that domain. Bands with the same sequence number but for
2896 different domains may be completely unrelated.
2897 Within a band, the corresponding coordinates of the distance vectors
2898 are all non-negative, assuming that the coordinates for all previous
2901 =head2 Parametric Vertex Enumeration
2903 The parametric vertex enumeration described in this section
2904 is mainly intended to be used internally and by the C<barvinok>
2907 #include <isl/vertices.h>
2908 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2909 __isl_keep isl_basic_set *bset);
2911 The function C<isl_basic_set_compute_vertices> performs the
2912 actual computation of the parametric vertices and the chamber
2913 decomposition and store the result in an C<isl_vertices> object.
2914 This information can be queried by either iterating over all
2915 the vertices or iterating over all the chambers or cells
2916 and then iterating over all vertices that are active on the chamber.
2918 int isl_vertices_foreach_vertex(
2919 __isl_keep isl_vertices *vertices,
2920 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2923 int isl_vertices_foreach_cell(
2924 __isl_keep isl_vertices *vertices,
2925 int (*fn)(__isl_take isl_cell *cell, void *user),
2927 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2928 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2931 Other operations that can be performed on an C<isl_vertices> object are
2934 isl_ctx *isl_vertices_get_ctx(
2935 __isl_keep isl_vertices *vertices);
2936 int isl_vertices_get_n_vertices(
2937 __isl_keep isl_vertices *vertices);
2938 void isl_vertices_free(__isl_take isl_vertices *vertices);
2940 Vertices can be inspected and destroyed using the following functions.
2942 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2943 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2944 __isl_give isl_basic_set *isl_vertex_get_domain(
2945 __isl_keep isl_vertex *vertex);
2946 __isl_give isl_basic_set *isl_vertex_get_expr(
2947 __isl_keep isl_vertex *vertex);
2948 void isl_vertex_free(__isl_take isl_vertex *vertex);
2950 C<isl_vertex_get_expr> returns a singleton parametric set describing
2951 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2953 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2954 B<rational> basic sets, so they should mainly be used for inspection
2955 and should not be mixed with integer sets.
2957 Chambers can be inspected and destroyed using the following functions.
2959 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2960 __isl_give isl_basic_set *isl_cell_get_domain(
2961 __isl_keep isl_cell *cell);
2962 void isl_cell_free(__isl_take isl_cell *cell);
2966 Although C<isl> is mainly meant to be used as a library,
2967 it also contains some basic applications that use some
2968 of the functionality of C<isl>.
2969 The input may be specified in either the L<isl format>
2970 or the L<PolyLib format>.
2972 =head2 C<isl_polyhedron_sample>
2974 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2975 an integer element of the polyhedron, if there is any.
2976 The first column in the output is the denominator and is always
2977 equal to 1. If the polyhedron contains no integer points,
2978 then a vector of length zero is printed.
2982 C<isl_pip> takes the same input as the C<example> program
2983 from the C<piplib> distribution, i.e., a set of constraints
2984 on the parameters, a line containing only -1 and finally a set
2985 of constraints on a parametric polyhedron.
2986 The coefficients of the parameters appear in the last columns
2987 (but before the final constant column).
2988 The output is the lexicographic minimum of the parametric polyhedron.
2989 As C<isl> currently does not have its own output format, the output
2990 is just a dump of the internal state.
2992 =head2 C<isl_polyhedron_minimize>
2994 C<isl_polyhedron_minimize> computes the minimum of some linear
2995 or affine objective function over the integer points in a polyhedron.
2996 If an affine objective function
2997 is given, then the constant should appear in the last column.
2999 =head2 C<isl_polytope_scan>
3001 Given a polytope, C<isl_polytope_scan> prints
3002 all integer points in the polytope.