3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
477 __isl_keep isl_pw_qpolynomial *pwqp);
478 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
479 __isl_keep isl_union_pw_qpolynomial *upwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
481 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
483 The names of the individual dimensions may be set or read off
484 using the following functions.
487 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
488 enum isl_dim_type type, unsigned pos,
489 __isl_keep const char *name);
490 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
491 enum isl_dim_type type, unsigned pos);
493 Note that C<isl_dim_get_name> returns a pointer to some internal
494 data structure, so the result can only be used while the
495 corresponding C<isl_dim> is alive.
496 Also note that every function that operates on two sets or relations
497 requires that both arguments have the same parameters. This also
498 means that if one of the arguments has named parameters, then the
499 other needs to have named parameters too and the names need to match.
500 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
501 have different parameters (as long as they are named), in which case
502 the result will have as parameters the union of the parameters of
505 The names of entire spaces may be set or read off
506 using the following functions.
509 __isl_give isl_dim *isl_dim_set_tuple_name(
510 __isl_take isl_dim *dim,
511 enum isl_dim_type type, const char *s);
512 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
513 enum isl_dim_type type);
515 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
516 or C<isl_dim_set>. As with C<isl_dim_get_name>,
517 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
519 Binary operations require the corresponding spaces of their arguments
520 to have the same name.
522 Spaces can be nested. In particular, the domain of a set or
523 the domain or range of a relation can be a nested relation.
524 The following functions can be used to construct and deconstruct
525 such nested dimension specifications.
528 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
529 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
530 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
532 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
533 be the dimension specification of a set, while that of
534 C<isl_dim_wrap> should be the dimension specification of a relation.
535 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
536 of a relation, while that of C<isl_dim_wrap> is the dimension specification
539 Dimension specifications can be created from other dimension
540 specifications using the following functions.
542 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
543 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
544 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
545 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
546 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
547 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
548 __isl_take isl_dim *right);
549 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
550 enum isl_dim_type type, unsigned pos, unsigned n);
551 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
552 enum isl_dim_type type, unsigned n);
553 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
554 enum isl_dim_type type, unsigned first, unsigned n);
555 __isl_give isl_dim *isl_dim_map_from_set(
556 __isl_take isl_dim *dim);
557 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
559 Note that if dimensions are added or removed from a space, then
560 the name and the internal structure are lost.
564 A local space is essentially a dimension specification with
565 zero or more existentially quantified variables.
566 The local space of a basic set or relation can be obtained
567 using the following functions.
570 __isl_give isl_local_space *isl_basic_set_get_local_space(
571 __isl_keep isl_basic_set *bset);
574 __isl_give isl_local_space *isl_basic_map_get_local_space(
575 __isl_keep isl_basic_map *bmap);
577 A new local space can be created from a dimension specification using
579 #include <isl/local_space.h>
580 __isl_give isl_local_space *isl_local_space_from_dim(
581 __isl_take isl_dim *dim);
583 They can be inspected, copied and freed using the following functions.
585 #include <isl/local_space.h>
586 isl_ctx *isl_local_space_get_ctx(
587 __isl_keep isl_local_space *ls);
588 int isl_local_space_dim(__isl_keep isl_local_space *ls,
589 enum isl_dim_type type);
590 const char *isl_local_space_get_dim_name(
591 __isl_keep isl_local_space *ls,
592 enum isl_dim_type type, unsigned pos);
593 __isl_give isl_dim *isl_local_space_get_dim(
594 __isl_keep isl_local_space *ls);
595 __isl_give isl_div *isl_local_space_get_div(
596 __isl_keep isl_local_space *ls, int pos);
597 __isl_give isl_local_space *isl_local_space_copy(
598 __isl_keep isl_local_space *ls);
599 void *isl_local_space_free(__isl_take isl_local_space *ls);
601 =head2 Input and Output
603 C<isl> supports its own input/output format, which is similar
604 to the C<Omega> format, but also supports the C<PolyLib> format
609 The C<isl> format is similar to that of C<Omega>, but has a different
610 syntax for describing the parameters and allows for the definition
611 of an existentially quantified variable as the integer division
612 of an affine expression.
613 For example, the set of integers C<i> between C<0> and C<n>
614 such that C<i % 10 <= 6> can be described as
616 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
619 A set or relation can have several disjuncts, separated
620 by the keyword C<or>. Each disjunct is either a conjunction
621 of constraints or a projection (C<exists>) of a conjunction
622 of constraints. The constraints are separated by the keyword
625 =head3 C<PolyLib> format
627 If the represented set is a union, then the first line
628 contains a single number representing the number of disjuncts.
629 Otherwise, a line containing the number C<1> is optional.
631 Each disjunct is represented by a matrix of constraints.
632 The first line contains two numbers representing
633 the number of rows and columns,
634 where the number of rows is equal to the number of constraints
635 and the number of columns is equal to two plus the number of variables.
636 The following lines contain the actual rows of the constraint matrix.
637 In each row, the first column indicates whether the constraint
638 is an equality (C<0>) or inequality (C<1>). The final column
639 corresponds to the constant term.
641 If the set is parametric, then the coefficients of the parameters
642 appear in the last columns before the constant column.
643 The coefficients of any existentially quantified variables appear
644 between those of the set variables and those of the parameters.
646 =head3 Extended C<PolyLib> format
648 The extended C<PolyLib> format is nearly identical to the
649 C<PolyLib> format. The only difference is that the line
650 containing the number of rows and columns of a constraint matrix
651 also contains four additional numbers:
652 the number of output dimensions, the number of input dimensions,
653 the number of local dimensions (i.e., the number of existentially
654 quantified variables) and the number of parameters.
655 For sets, the number of ``output'' dimensions is equal
656 to the number of set dimensions, while the number of ``input''
662 __isl_give isl_basic_set *isl_basic_set_read_from_file(
663 isl_ctx *ctx, FILE *input, int nparam);
664 __isl_give isl_basic_set *isl_basic_set_read_from_str(
665 isl_ctx *ctx, const char *str, int nparam);
666 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
667 FILE *input, int nparam);
668 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
669 const char *str, int nparam);
672 __isl_give isl_basic_map *isl_basic_map_read_from_file(
673 isl_ctx *ctx, FILE *input, int nparam);
674 __isl_give isl_basic_map *isl_basic_map_read_from_str(
675 isl_ctx *ctx, const char *str, int nparam);
676 __isl_give isl_map *isl_map_read_from_file(
677 struct isl_ctx *ctx, FILE *input, int nparam);
678 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
679 const char *str, int nparam);
681 #include <isl/union_set.h>
682 __isl_give isl_union_set *isl_union_set_read_from_file(
683 isl_ctx *ctx, FILE *input);
684 __isl_give isl_union_set *isl_union_set_read_from_str(
685 struct isl_ctx *ctx, const char *str);
687 #include <isl/union_map.h>
688 __isl_give isl_union_map *isl_union_map_read_from_file(
689 isl_ctx *ctx, FILE *input);
690 __isl_give isl_union_map *isl_union_map_read_from_str(
691 struct isl_ctx *ctx, const char *str);
693 The input format is autodetected and may be either the C<PolyLib> format
694 or the C<isl> format.
695 C<nparam> specifies how many of the final columns in
696 the C<PolyLib> format correspond to parameters.
697 If input is given in the C<isl> format, then the number
698 of parameters needs to be equal to C<nparam>.
699 If C<nparam> is negative, then any number of parameters
700 is accepted in the C<isl> format and zero parameters
701 are assumed in the C<PolyLib> format.
705 Before anything can be printed, an C<isl_printer> needs to
708 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
710 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
711 void isl_printer_free(__isl_take isl_printer *printer);
712 __isl_give char *isl_printer_get_str(
713 __isl_keep isl_printer *printer);
715 The behavior of the printer can be modified in various ways
717 __isl_give isl_printer *isl_printer_set_output_format(
718 __isl_take isl_printer *p, int output_format);
719 __isl_give isl_printer *isl_printer_set_indent(
720 __isl_take isl_printer *p, int indent);
721 __isl_give isl_printer *isl_printer_set_prefix(
722 __isl_take isl_printer *p, const char *prefix);
723 __isl_give isl_printer *isl_printer_set_suffix(
724 __isl_take isl_printer *p, const char *suffix);
726 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
727 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
728 and defaults to C<ISL_FORMAT_ISL>.
729 Each line in the output is indented by C<indent> spaces
730 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
731 In the C<PolyLib> format output,
732 the coefficients of the existentially quantified variables
733 appear between those of the set variables and those
736 To actually print something, use
739 __isl_give isl_printer *isl_printer_print_basic_set(
740 __isl_take isl_printer *printer,
741 __isl_keep isl_basic_set *bset);
742 __isl_give isl_printer *isl_printer_print_set(
743 __isl_take isl_printer *printer,
744 __isl_keep isl_set *set);
747 __isl_give isl_printer *isl_printer_print_basic_map(
748 __isl_take isl_printer *printer,
749 __isl_keep isl_basic_map *bmap);
750 __isl_give isl_printer *isl_printer_print_map(
751 __isl_take isl_printer *printer,
752 __isl_keep isl_map *map);
754 #include <isl/union_set.h>
755 __isl_give isl_printer *isl_printer_print_union_set(
756 __isl_take isl_printer *p,
757 __isl_keep isl_union_set *uset);
759 #include <isl/union_map.h>
760 __isl_give isl_printer *isl_printer_print_union_map(
761 __isl_take isl_printer *p,
762 __isl_keep isl_union_map *umap);
764 When called on a file printer, the following function flushes
765 the file. When called on a string printer, the buffer is cleared.
767 __isl_give isl_printer *isl_printer_flush(
768 __isl_take isl_printer *p);
770 =head2 Creating New Sets and Relations
772 C<isl> has functions for creating some standard sets and relations.
776 =item * Empty sets and relations
778 __isl_give isl_basic_set *isl_basic_set_empty(
779 __isl_take isl_dim *dim);
780 __isl_give isl_basic_map *isl_basic_map_empty(
781 __isl_take isl_dim *dim);
782 __isl_give isl_set *isl_set_empty(
783 __isl_take isl_dim *dim);
784 __isl_give isl_map *isl_map_empty(
785 __isl_take isl_dim *dim);
786 __isl_give isl_union_set *isl_union_set_empty(
787 __isl_take isl_dim *dim);
788 __isl_give isl_union_map *isl_union_map_empty(
789 __isl_take isl_dim *dim);
791 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
792 is only used to specify the parameters.
794 =item * Universe sets and relations
796 __isl_give isl_basic_set *isl_basic_set_universe(
797 __isl_take isl_dim *dim);
798 __isl_give isl_basic_map *isl_basic_map_universe(
799 __isl_take isl_dim *dim);
800 __isl_give isl_set *isl_set_universe(
801 __isl_take isl_dim *dim);
802 __isl_give isl_map *isl_map_universe(
803 __isl_take isl_dim *dim);
804 __isl_give isl_union_set *isl_union_set_universe(
805 __isl_take isl_union_set *uset);
806 __isl_give isl_union_map *isl_union_map_universe(
807 __isl_take isl_union_map *umap);
809 The sets and relations constructed by the functions above
810 contain all integer values, while those constructed by the
811 functions below only contain non-negative values.
813 __isl_give isl_basic_set *isl_basic_set_nat_universe(
814 __isl_take isl_dim *dim);
815 __isl_give isl_basic_map *isl_basic_map_nat_universe(
816 __isl_take isl_dim *dim);
817 __isl_give isl_set *isl_set_nat_universe(
818 __isl_take isl_dim *dim);
819 __isl_give isl_map *isl_map_nat_universe(
820 __isl_take isl_dim *dim);
822 =item * Identity relations
824 __isl_give isl_basic_map *isl_basic_map_identity(
825 __isl_take isl_dim *dim);
826 __isl_give isl_map *isl_map_identity(
827 __isl_take isl_dim *dim);
829 The number of input and output dimensions in C<dim> needs
832 =item * Lexicographic order
834 __isl_give isl_map *isl_map_lex_lt(
835 __isl_take isl_dim *set_dim);
836 __isl_give isl_map *isl_map_lex_le(
837 __isl_take isl_dim *set_dim);
838 __isl_give isl_map *isl_map_lex_gt(
839 __isl_take isl_dim *set_dim);
840 __isl_give isl_map *isl_map_lex_ge(
841 __isl_take isl_dim *set_dim);
842 __isl_give isl_map *isl_map_lex_lt_first(
843 __isl_take isl_dim *dim, unsigned n);
844 __isl_give isl_map *isl_map_lex_le_first(
845 __isl_take isl_dim *dim, unsigned n);
846 __isl_give isl_map *isl_map_lex_gt_first(
847 __isl_take isl_dim *dim, unsigned n);
848 __isl_give isl_map *isl_map_lex_ge_first(
849 __isl_take isl_dim *dim, unsigned n);
851 The first four functions take a dimension specification for a B<set>
852 and return relations that express that the elements in the domain
853 are lexicographically less
854 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
855 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
856 than the elements in the range.
857 The last four functions take a dimension specification for a map
858 and return relations that express that the first C<n> dimensions
859 in the domain are lexicographically less
860 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
861 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
862 than the first C<n> dimensions in the range.
866 A basic set or relation can be converted to a set or relation
867 using the following functions.
869 __isl_give isl_set *isl_set_from_basic_set(
870 __isl_take isl_basic_set *bset);
871 __isl_give isl_map *isl_map_from_basic_map(
872 __isl_take isl_basic_map *bmap);
874 Sets and relations can be converted to union sets and relations
875 using the following functions.
877 __isl_give isl_union_map *isl_union_map_from_map(
878 __isl_take isl_map *map);
879 __isl_give isl_union_set *isl_union_set_from_set(
880 __isl_take isl_set *set);
882 Sets and relations can be copied and freed again using the following
885 __isl_give isl_basic_set *isl_basic_set_copy(
886 __isl_keep isl_basic_set *bset);
887 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
888 __isl_give isl_union_set *isl_union_set_copy(
889 __isl_keep isl_union_set *uset);
890 __isl_give isl_basic_map *isl_basic_map_copy(
891 __isl_keep isl_basic_map *bmap);
892 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
893 __isl_give isl_union_map *isl_union_map_copy(
894 __isl_keep isl_union_map *umap);
895 void isl_basic_set_free(__isl_take isl_basic_set *bset);
896 void isl_set_free(__isl_take isl_set *set);
897 void isl_union_set_free(__isl_take isl_union_set *uset);
898 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
899 void isl_map_free(__isl_take isl_map *map);
900 void isl_union_map_free(__isl_take isl_union_map *umap);
902 Other sets and relations can be constructed by starting
903 from a universe set or relation, adding equality and/or
904 inequality constraints and then projecting out the
905 existentially quantified variables, if any.
906 Constraints can be constructed, manipulated and
907 added to basic sets and relations using the following functions.
909 #include <isl/constraint.h>
910 __isl_give isl_constraint *isl_equality_alloc(
911 __isl_take isl_dim *dim);
912 __isl_give isl_constraint *isl_inequality_alloc(
913 __isl_take isl_dim *dim);
914 void isl_constraint_set_constant(
915 __isl_keep isl_constraint *constraint, isl_int v);
916 void isl_constraint_set_coefficient(
917 __isl_keep isl_constraint *constraint,
918 enum isl_dim_type type, int pos, isl_int v);
919 __isl_give isl_basic_map *isl_basic_map_add_constraint(
920 __isl_take isl_basic_map *bmap,
921 __isl_take isl_constraint *constraint);
922 __isl_give isl_basic_set *isl_basic_set_add_constraint(
923 __isl_take isl_basic_set *bset,
924 __isl_take isl_constraint *constraint);
926 For example, to create a set containing the even integers
927 between 10 and 42, you would use the following code.
931 struct isl_constraint *c;
932 struct isl_basic_set *bset;
935 dim = isl_dim_set_alloc(ctx, 0, 2);
936 bset = isl_basic_set_universe(isl_dim_copy(dim));
938 c = isl_equality_alloc(isl_dim_copy(dim));
939 isl_int_set_si(v, -1);
940 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
941 isl_int_set_si(v, 2);
942 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
943 bset = isl_basic_set_add_constraint(bset, c);
945 c = isl_inequality_alloc(isl_dim_copy(dim));
946 isl_int_set_si(v, -10);
947 isl_constraint_set_constant(c, v);
948 isl_int_set_si(v, 1);
949 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
950 bset = isl_basic_set_add_constraint(bset, c);
952 c = isl_inequality_alloc(dim);
953 isl_int_set_si(v, 42);
954 isl_constraint_set_constant(c, v);
955 isl_int_set_si(v, -1);
956 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
957 bset = isl_basic_set_add_constraint(bset, c);
959 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
965 struct isl_basic_set *bset;
966 bset = isl_basic_set_read_from_str(ctx,
967 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
969 A basic set or relation can also be constructed from two matrices
970 describing the equalities and the inequalities.
972 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
973 __isl_take isl_dim *dim,
974 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
975 enum isl_dim_type c1,
976 enum isl_dim_type c2, enum isl_dim_type c3,
977 enum isl_dim_type c4);
978 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
979 __isl_take isl_dim *dim,
980 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
981 enum isl_dim_type c1,
982 enum isl_dim_type c2, enum isl_dim_type c3,
983 enum isl_dim_type c4, enum isl_dim_type c5);
985 The C<isl_dim_type> arguments indicate the order in which
986 different kinds of variables appear in the input matrices
987 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
988 C<isl_dim_set> and C<isl_dim_div> for sets and
989 of C<isl_dim_cst>, C<isl_dim_param>,
990 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
992 =head2 Inspecting Sets and Relations
994 Usually, the user should not have to care about the actual constraints
995 of the sets and maps, but should instead apply the abstract operations
996 explained in the following sections.
997 Occasionally, however, it may be required to inspect the individual
998 coefficients of the constraints. This section explains how to do so.
999 In these cases, it may also be useful to have C<isl> compute
1000 an explicit representation of the existentially quantified variables.
1002 __isl_give isl_set *isl_set_compute_divs(
1003 __isl_take isl_set *set);
1004 __isl_give isl_map *isl_map_compute_divs(
1005 __isl_take isl_map *map);
1006 __isl_give isl_union_set *isl_union_set_compute_divs(
1007 __isl_take isl_union_set *uset);
1008 __isl_give isl_union_map *isl_union_map_compute_divs(
1009 __isl_take isl_union_map *umap);
1011 This explicit representation defines the existentially quantified
1012 variables as integer divisions of the other variables, possibly
1013 including earlier existentially quantified variables.
1014 An explicitly represented existentially quantified variable therefore
1015 has a unique value when the values of the other variables are known.
1016 If, furthermore, the same existentials, i.e., existentials
1017 with the same explicit representations, should appear in the
1018 same order in each of the disjuncts of a set or map, then the user should call
1019 either of the following functions.
1021 __isl_give isl_set *isl_set_align_divs(
1022 __isl_take isl_set *set);
1023 __isl_give isl_map *isl_map_align_divs(
1024 __isl_take isl_map *map);
1026 Alternatively, the existentially quantified variables can be removed
1027 using the following functions, which compute an overapproximation.
1029 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1030 __isl_take isl_basic_set *bset);
1031 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1032 __isl_take isl_basic_map *bmap);
1033 __isl_give isl_set *isl_set_remove_divs(
1034 __isl_take isl_set *set);
1035 __isl_give isl_map *isl_map_remove_divs(
1036 __isl_take isl_map *map);
1038 To iterate over all the sets or maps in a union set or map, use
1040 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1041 int (*fn)(__isl_take isl_set *set, void *user),
1043 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1044 int (*fn)(__isl_take isl_map *map, void *user),
1047 The number of sets or maps in a union set or map can be obtained
1050 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1051 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1053 To extract the set or map from a union with a given dimension
1056 __isl_give isl_set *isl_union_set_extract_set(
1057 __isl_keep isl_union_set *uset,
1058 __isl_take isl_dim *dim);
1059 __isl_give isl_map *isl_union_map_extract_map(
1060 __isl_keep isl_union_map *umap,
1061 __isl_take isl_dim *dim);
1063 To iterate over all the basic sets or maps in a set or map, use
1065 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1066 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1068 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1069 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1072 The callback function C<fn> should return 0 if successful and
1073 -1 if an error occurs. In the latter case, or if any other error
1074 occurs, the above functions will return -1.
1076 It should be noted that C<isl> does not guarantee that
1077 the basic sets or maps passed to C<fn> are disjoint.
1078 If this is required, then the user should call one of
1079 the following functions first.
1081 __isl_give isl_set *isl_set_make_disjoint(
1082 __isl_take isl_set *set);
1083 __isl_give isl_map *isl_map_make_disjoint(
1084 __isl_take isl_map *map);
1086 The number of basic sets in a set can be obtained
1089 int isl_set_n_basic_set(__isl_keep isl_set *set);
1091 To iterate over the constraints of a basic set or map, use
1093 #include <isl/constraint.h>
1095 int isl_basic_map_foreach_constraint(
1096 __isl_keep isl_basic_map *bmap,
1097 int (*fn)(__isl_take isl_constraint *c, void *user),
1099 void isl_constraint_free(struct isl_constraint *c);
1101 Again, the callback function C<fn> should return 0 if successful and
1102 -1 if an error occurs. In the latter case, or if any other error
1103 occurs, the above functions will return -1.
1104 The constraint C<c> represents either an equality or an inequality.
1105 Use the following function to find out whether a constraint
1106 represents an equality. If not, it represents an inequality.
1108 int isl_constraint_is_equality(
1109 __isl_keep isl_constraint *constraint);
1111 The coefficients of the constraints can be inspected using
1112 the following functions.
1114 void isl_constraint_get_constant(
1115 __isl_keep isl_constraint *constraint, isl_int *v);
1116 void isl_constraint_get_coefficient(
1117 __isl_keep isl_constraint *constraint,
1118 enum isl_dim_type type, int pos, isl_int *v);
1119 int isl_constraint_involves_dims(
1120 __isl_keep isl_constraint *constraint,
1121 enum isl_dim_type type, unsigned first, unsigned n);
1123 The explicit representations of the existentially quantified
1124 variables can be inspected using the following functions.
1125 Note that the user is only allowed to use these functions
1126 if the inspected set or map is the result of a call
1127 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1129 __isl_give isl_div *isl_constraint_div(
1130 __isl_keep isl_constraint *constraint, int pos);
1131 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1132 void isl_div_get_constant(__isl_keep isl_div *div,
1134 void isl_div_get_denominator(__isl_keep isl_div *div,
1136 void isl_div_get_coefficient(__isl_keep isl_div *div,
1137 enum isl_dim_type type, int pos, isl_int *v);
1139 To obtain the constraints of a basic set or map in matrix
1140 form, use the following functions.
1142 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1143 __isl_keep isl_basic_set *bset,
1144 enum isl_dim_type c1, enum isl_dim_type c2,
1145 enum isl_dim_type c3, enum isl_dim_type c4);
1146 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1147 __isl_keep isl_basic_set *bset,
1148 enum isl_dim_type c1, enum isl_dim_type c2,
1149 enum isl_dim_type c3, enum isl_dim_type c4);
1150 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1151 __isl_keep isl_basic_map *bmap,
1152 enum isl_dim_type c1,
1153 enum isl_dim_type c2, enum isl_dim_type c3,
1154 enum isl_dim_type c4, enum isl_dim_type c5);
1155 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1156 __isl_keep isl_basic_map *bmap,
1157 enum isl_dim_type c1,
1158 enum isl_dim_type c2, enum isl_dim_type c3,
1159 enum isl_dim_type c4, enum isl_dim_type c5);
1161 The C<isl_dim_type> arguments dictate the order in which
1162 different kinds of variables appear in the resulting matrix
1163 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1164 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1166 The names of the domain and range spaces of a set or relation can be
1167 read off using the following functions.
1169 const char *isl_basic_set_get_tuple_name(
1170 __isl_keep isl_basic_set *bset);
1171 const char *isl_set_get_tuple_name(
1172 __isl_keep isl_set *set);
1173 const char *isl_basic_map_get_tuple_name(
1174 __isl_keep isl_basic_map *bmap,
1175 enum isl_dim_type type);
1176 const char *isl_map_get_tuple_name(
1177 __isl_keep isl_map *map,
1178 enum isl_dim_type type);
1180 As with C<isl_dim_get_tuple_name>, the value returned points to
1181 an internal data structure.
1182 The names of individual dimensions can be read off using
1183 the following functions.
1185 const char *isl_constraint_get_dim_name(
1186 __isl_keep isl_constraint *constraint,
1187 enum isl_dim_type type, unsigned pos);
1188 const char *isl_basic_set_get_dim_name(
1189 __isl_keep isl_basic_set *bset,
1190 enum isl_dim_type type, unsigned pos);
1191 const char *isl_set_get_dim_name(
1192 __isl_keep isl_set *set,
1193 enum isl_dim_type type, unsigned pos);
1194 const char *isl_basic_map_get_dim_name(
1195 __isl_keep isl_basic_map *bmap,
1196 enum isl_dim_type type, unsigned pos);
1197 const char *isl_map_get_dim_name(
1198 __isl_keep isl_map *map,
1199 enum isl_dim_type type, unsigned pos);
1201 These functions are mostly useful to obtain the names
1206 =head3 Unary Properties
1212 The following functions test whether the given set or relation
1213 contains any integer points. The ``plain'' variants do not perform
1214 any computations, but simply check if the given set or relation
1215 is already known to be empty.
1217 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1218 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1219 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1220 int isl_set_is_empty(__isl_keep isl_set *set);
1221 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1222 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1223 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1224 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1225 int isl_map_is_empty(__isl_keep isl_map *map);
1226 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1228 =item * Universality
1230 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1231 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1232 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1234 =item * Single-valuedness
1236 int isl_map_is_single_valued(__isl_keep isl_map *map);
1237 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1241 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1242 int isl_map_is_injective(__isl_keep isl_map *map);
1243 int isl_union_map_plain_is_injective(
1244 __isl_keep isl_union_map *umap);
1245 int isl_union_map_is_injective(
1246 __isl_keep isl_union_map *umap);
1250 int isl_map_is_bijective(__isl_keep isl_map *map);
1251 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1255 The following functions check whether the domain of the given
1256 (basic) set is a wrapped relation.
1258 int isl_basic_set_is_wrapping(
1259 __isl_keep isl_basic_set *bset);
1260 int isl_set_is_wrapping(__isl_keep isl_set *set);
1262 =item * Internal Product
1264 int isl_basic_map_can_zip(
1265 __isl_keep isl_basic_map *bmap);
1266 int isl_map_can_zip(__isl_keep isl_map *map);
1268 Check whether the product of domain and range of the given relation
1270 i.e., whether both domain and range are nested relations.
1274 =head3 Binary Properties
1280 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1281 __isl_keep isl_set *set2);
1282 int isl_set_is_equal(__isl_keep isl_set *set1,
1283 __isl_keep isl_set *set2);
1284 int isl_union_set_is_equal(
1285 __isl_keep isl_union_set *uset1,
1286 __isl_keep isl_union_set *uset2);
1287 int isl_basic_map_is_equal(
1288 __isl_keep isl_basic_map *bmap1,
1289 __isl_keep isl_basic_map *bmap2);
1290 int isl_map_is_equal(__isl_keep isl_map *map1,
1291 __isl_keep isl_map *map2);
1292 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1293 __isl_keep isl_map *map2);
1294 int isl_union_map_is_equal(
1295 __isl_keep isl_union_map *umap1,
1296 __isl_keep isl_union_map *umap2);
1298 =item * Disjointness
1300 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1301 __isl_keep isl_set *set2);
1305 int isl_set_is_subset(__isl_keep isl_set *set1,
1306 __isl_keep isl_set *set2);
1307 int isl_set_is_strict_subset(
1308 __isl_keep isl_set *set1,
1309 __isl_keep isl_set *set2);
1310 int isl_union_set_is_subset(
1311 __isl_keep isl_union_set *uset1,
1312 __isl_keep isl_union_set *uset2);
1313 int isl_union_set_is_strict_subset(
1314 __isl_keep isl_union_set *uset1,
1315 __isl_keep isl_union_set *uset2);
1316 int isl_basic_map_is_subset(
1317 __isl_keep isl_basic_map *bmap1,
1318 __isl_keep isl_basic_map *bmap2);
1319 int isl_basic_map_is_strict_subset(
1320 __isl_keep isl_basic_map *bmap1,
1321 __isl_keep isl_basic_map *bmap2);
1322 int isl_map_is_subset(
1323 __isl_keep isl_map *map1,
1324 __isl_keep isl_map *map2);
1325 int isl_map_is_strict_subset(
1326 __isl_keep isl_map *map1,
1327 __isl_keep isl_map *map2);
1328 int isl_union_map_is_subset(
1329 __isl_keep isl_union_map *umap1,
1330 __isl_keep isl_union_map *umap2);
1331 int isl_union_map_is_strict_subset(
1332 __isl_keep isl_union_map *umap1,
1333 __isl_keep isl_union_map *umap2);
1337 =head2 Unary Operations
1343 __isl_give isl_set *isl_set_complement(
1344 __isl_take isl_set *set);
1348 __isl_give isl_basic_map *isl_basic_map_reverse(
1349 __isl_take isl_basic_map *bmap);
1350 __isl_give isl_map *isl_map_reverse(
1351 __isl_take isl_map *map);
1352 __isl_give isl_union_map *isl_union_map_reverse(
1353 __isl_take isl_union_map *umap);
1357 __isl_give isl_basic_set *isl_basic_set_project_out(
1358 __isl_take isl_basic_set *bset,
1359 enum isl_dim_type type, unsigned first, unsigned n);
1360 __isl_give isl_basic_map *isl_basic_map_project_out(
1361 __isl_take isl_basic_map *bmap,
1362 enum isl_dim_type type, unsigned first, unsigned n);
1363 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1364 enum isl_dim_type type, unsigned first, unsigned n);
1365 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1366 enum isl_dim_type type, unsigned first, unsigned n);
1367 __isl_give isl_basic_set *isl_basic_map_domain(
1368 __isl_take isl_basic_map *bmap);
1369 __isl_give isl_basic_set *isl_basic_map_range(
1370 __isl_take isl_basic_map *bmap);
1371 __isl_give isl_set *isl_map_domain(
1372 __isl_take isl_map *bmap);
1373 __isl_give isl_set *isl_map_range(
1374 __isl_take isl_map *map);
1375 __isl_give isl_union_set *isl_union_map_domain(
1376 __isl_take isl_union_map *umap);
1377 __isl_give isl_union_set *isl_union_map_range(
1378 __isl_take isl_union_map *umap);
1380 __isl_give isl_basic_map *isl_basic_map_domain_map(
1381 __isl_take isl_basic_map *bmap);
1382 __isl_give isl_basic_map *isl_basic_map_range_map(
1383 __isl_take isl_basic_map *bmap);
1384 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1385 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1386 __isl_give isl_union_map *isl_union_map_domain_map(
1387 __isl_take isl_union_map *umap);
1388 __isl_give isl_union_map *isl_union_map_range_map(
1389 __isl_take isl_union_map *umap);
1391 The functions above construct a (basic, regular or union) relation
1392 that maps (a wrapped version of) the input relation to its domain or range.
1396 __isl_give isl_set *isl_set_eliminate(
1397 __isl_take isl_set *set, enum isl_dim_type type,
1398 unsigned first, unsigned n);
1400 Eliminate the coefficients for the given dimensions from the constraints,
1401 without removing the dimensions.
1405 __isl_give isl_map *isl_set_identity(
1406 __isl_take isl_set *set);
1407 __isl_give isl_union_map *isl_union_set_identity(
1408 __isl_take isl_union_set *uset);
1410 Construct an identity relation on the given (union) set.
1414 __isl_give isl_basic_set *isl_basic_map_deltas(
1415 __isl_take isl_basic_map *bmap);
1416 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1417 __isl_give isl_union_set *isl_union_map_deltas(
1418 __isl_take isl_union_map *umap);
1420 These functions return a (basic) set containing the differences
1421 between image elements and corresponding domain elements in the input.
1423 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1424 __isl_take isl_basic_map *bmap);
1425 __isl_give isl_map *isl_map_deltas_map(
1426 __isl_take isl_map *map);
1427 __isl_give isl_union_map *isl_union_map_deltas_map(
1428 __isl_take isl_union_map *umap);
1430 The functions above construct a (basic, regular or union) relation
1431 that maps (a wrapped version of) the input relation to its delta set.
1435 Simplify the representation of a set or relation by trying
1436 to combine pairs of basic sets or relations into a single
1437 basic set or relation.
1439 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1440 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1441 __isl_give isl_union_set *isl_union_set_coalesce(
1442 __isl_take isl_union_set *uset);
1443 __isl_give isl_union_map *isl_union_map_coalesce(
1444 __isl_take isl_union_map *umap);
1446 =item * Detecting equalities
1448 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1449 __isl_take isl_basic_set *bset);
1450 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1451 __isl_take isl_basic_map *bmap);
1452 __isl_give isl_set *isl_set_detect_equalities(
1453 __isl_take isl_set *set);
1454 __isl_give isl_map *isl_map_detect_equalities(
1455 __isl_take isl_map *map);
1456 __isl_give isl_union_set *isl_union_set_detect_equalities(
1457 __isl_take isl_union_set *uset);
1458 __isl_give isl_union_map *isl_union_map_detect_equalities(
1459 __isl_take isl_union_map *umap);
1461 Simplify the representation of a set or relation by detecting implicit
1464 =item * Removing redundant constraints
1466 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1467 __isl_take isl_basic_set *bset);
1468 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1469 __isl_take isl_basic_map *bmap);
1473 __isl_give isl_basic_set *isl_set_convex_hull(
1474 __isl_take isl_set *set);
1475 __isl_give isl_basic_map *isl_map_convex_hull(
1476 __isl_take isl_map *map);
1478 If the input set or relation has any existentially quantified
1479 variables, then the result of these operations is currently undefined.
1483 __isl_give isl_basic_set *isl_set_simple_hull(
1484 __isl_take isl_set *set);
1485 __isl_give isl_basic_map *isl_map_simple_hull(
1486 __isl_take isl_map *map);
1487 __isl_give isl_union_map *isl_union_map_simple_hull(
1488 __isl_take isl_union_map *umap);
1490 These functions compute a single basic set or relation
1491 that contains the whole input set or relation.
1492 In particular, the output is described by translates
1493 of the constraints describing the basic sets or relations in the input.
1497 (See \autoref{s:simple hull}.)
1503 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1504 __isl_take isl_basic_set *bset);
1505 __isl_give isl_basic_set *isl_set_affine_hull(
1506 __isl_take isl_set *set);
1507 __isl_give isl_union_set *isl_union_set_affine_hull(
1508 __isl_take isl_union_set *uset);
1509 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1510 __isl_take isl_basic_map *bmap);
1511 __isl_give isl_basic_map *isl_map_affine_hull(
1512 __isl_take isl_map *map);
1513 __isl_give isl_union_map *isl_union_map_affine_hull(
1514 __isl_take isl_union_map *umap);
1516 In case of union sets and relations, the affine hull is computed
1519 =item * Polyhedral hull
1521 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1522 __isl_take isl_set *set);
1523 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1524 __isl_take isl_map *map);
1525 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1526 __isl_take isl_union_set *uset);
1527 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1528 __isl_take isl_union_map *umap);
1530 These functions compute a single basic set or relation
1531 not involving any existentially quantified variables
1532 that contains the whole input set or relation.
1533 In case of union sets and relations, the polyhedral hull is computed
1538 The following functions compute either the set of (rational) coefficient
1539 values of valid constraints for the given set or the set of (rational)
1540 values satisfying the constraints with coefficients from the given set.
1541 Internally, these two sets of functions perform essentially the
1542 same operations, except that the set of coefficients is assumed to
1543 be a cone, while the set of values may be any polyhedron.
1544 The current implementation is based on the Farkas lemma and
1545 Fourier-Motzkin elimination, but this may change or be made optional
1546 in future. In particular, future implementations may use different
1547 dualization algorithms or skip the elimination step.
1549 __isl_give isl_basic_set *isl_basic_set_coefficients(
1550 __isl_take isl_basic_set *bset);
1551 __isl_give isl_basic_set *isl_set_coefficients(
1552 __isl_take isl_set *set);
1553 __isl_give isl_union_set *isl_union_set_coefficients(
1554 __isl_take isl_union_set *bset);
1555 __isl_give isl_basic_set *isl_basic_set_solutions(
1556 __isl_take isl_basic_set *bset);
1557 __isl_give isl_basic_set *isl_set_solutions(
1558 __isl_take isl_set *set);
1559 __isl_give isl_union_set *isl_union_set_solutions(
1560 __isl_take isl_union_set *bset);
1564 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1566 __isl_give isl_union_map *isl_union_map_power(
1567 __isl_take isl_union_map *umap, int *exact);
1569 Compute a parametric representation for all positive powers I<k> of C<map>.
1570 The result maps I<k> to a nested relation corresponding to the
1571 I<k>th power of C<map>.
1572 The result may be an overapproximation. If the result is known to be exact,
1573 then C<*exact> is set to C<1>.
1575 =item * Transitive closure
1577 __isl_give isl_map *isl_map_transitive_closure(
1578 __isl_take isl_map *map, int *exact);
1579 __isl_give isl_union_map *isl_union_map_transitive_closure(
1580 __isl_take isl_union_map *umap, int *exact);
1582 Compute the transitive closure of C<map>.
1583 The result may be an overapproximation. If the result is known to be exact,
1584 then C<*exact> is set to C<1>.
1586 =item * Reaching path lengths
1588 __isl_give isl_map *isl_map_reaching_path_lengths(
1589 __isl_take isl_map *map, int *exact);
1591 Compute a relation that maps each element in the range of C<map>
1592 to the lengths of all paths composed of edges in C<map> that
1593 end up in the given element.
1594 The result may be an overapproximation. If the result is known to be exact,
1595 then C<*exact> is set to C<1>.
1596 To compute the I<maximal> path length, the resulting relation
1597 should be postprocessed by C<isl_map_lexmax>.
1598 In particular, if the input relation is a dependence relation
1599 (mapping sources to sinks), then the maximal path length corresponds
1600 to the free schedule.
1601 Note, however, that C<isl_map_lexmax> expects the maximum to be
1602 finite, so if the path lengths are unbounded (possibly due to
1603 the overapproximation), then you will get an error message.
1607 __isl_give isl_basic_set *isl_basic_map_wrap(
1608 __isl_take isl_basic_map *bmap);
1609 __isl_give isl_set *isl_map_wrap(
1610 __isl_take isl_map *map);
1611 __isl_give isl_union_set *isl_union_map_wrap(
1612 __isl_take isl_union_map *umap);
1613 __isl_give isl_basic_map *isl_basic_set_unwrap(
1614 __isl_take isl_basic_set *bset);
1615 __isl_give isl_map *isl_set_unwrap(
1616 __isl_take isl_set *set);
1617 __isl_give isl_union_map *isl_union_set_unwrap(
1618 __isl_take isl_union_set *uset);
1622 Remove any internal structure of domain (and range) of the given
1623 set or relation. If there is any such internal structure in the input,
1624 then the name of the space is also removed.
1626 __isl_give isl_basic_set *isl_basic_set_flatten(
1627 __isl_take isl_basic_set *bset);
1628 __isl_give isl_set *isl_set_flatten(
1629 __isl_take isl_set *set);
1630 __isl_give isl_basic_map *isl_basic_map_flatten(
1631 __isl_take isl_basic_map *bmap);
1632 __isl_give isl_map *isl_map_flatten(
1633 __isl_take isl_map *map);
1635 __isl_give isl_map *isl_set_flatten_map(
1636 __isl_take isl_set *set);
1638 The function above constructs a relation
1639 that maps the input set to a flattened version of the set.
1643 Lift the input set to a space with extra dimensions corresponding
1644 to the existentially quantified variables in the input.
1645 In particular, the result lives in a wrapped map where the domain
1646 is the original space and the range corresponds to the original
1647 existentially quantified variables.
1649 __isl_give isl_basic_set *isl_basic_set_lift(
1650 __isl_take isl_basic_set *bset);
1651 __isl_give isl_set *isl_set_lift(
1652 __isl_take isl_set *set);
1653 __isl_give isl_union_set *isl_union_set_lift(
1654 __isl_take isl_union_set *uset);
1656 =item * Internal Product
1658 __isl_give isl_basic_map *isl_basic_map_zip(
1659 __isl_take isl_basic_map *bmap);
1660 __isl_give isl_map *isl_map_zip(
1661 __isl_take isl_map *map);
1662 __isl_give isl_union_map *isl_union_map_zip(
1663 __isl_take isl_union_map *umap);
1665 Given a relation with nested relations for domain and range,
1666 interchange the range of the domain with the domain of the range.
1668 =item * Aligning parameters
1670 __isl_give isl_set *isl_set_align_params(
1671 __isl_take isl_set *set,
1672 __isl_take isl_dim *model);
1673 __isl_give isl_map *isl_map_align_params(
1674 __isl_take isl_map *map,
1675 __isl_take isl_dim *model);
1677 Change the order of the parameters of the given set or relation
1678 such that the first parameters match those of C<model>.
1679 This may involve the introduction of extra parameters.
1680 All parameters need to be named.
1682 =item * Dimension manipulation
1684 __isl_give isl_set *isl_set_add_dims(
1685 __isl_take isl_set *set,
1686 enum isl_dim_type type, unsigned n);
1687 __isl_give isl_map *isl_map_add_dims(
1688 __isl_take isl_map *map,
1689 enum isl_dim_type type, unsigned n);
1691 It is usually not advisable to directly change the (input or output)
1692 space of a set or a relation as this removes the name and the internal
1693 structure of the space. However, the above functions can be useful
1694 to add new parameters, assuming
1695 C<isl_set_align_params> and C<isl_map_align_params>
1700 =head2 Binary Operations
1702 The two arguments of a binary operation not only need to live
1703 in the same C<isl_ctx>, they currently also need to have
1704 the same (number of) parameters.
1706 =head3 Basic Operations
1710 =item * Intersection
1712 __isl_give isl_basic_set *isl_basic_set_intersect(
1713 __isl_take isl_basic_set *bset1,
1714 __isl_take isl_basic_set *bset2);
1715 __isl_give isl_set *isl_set_intersect(
1716 __isl_take isl_set *set1,
1717 __isl_take isl_set *set2);
1718 __isl_give isl_union_set *isl_union_set_intersect(
1719 __isl_take isl_union_set *uset1,
1720 __isl_take isl_union_set *uset2);
1721 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1722 __isl_take isl_basic_map *bmap,
1723 __isl_take isl_basic_set *bset);
1724 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1725 __isl_take isl_basic_map *bmap,
1726 __isl_take isl_basic_set *bset);
1727 __isl_give isl_basic_map *isl_basic_map_intersect(
1728 __isl_take isl_basic_map *bmap1,
1729 __isl_take isl_basic_map *bmap2);
1730 __isl_give isl_map *isl_map_intersect_domain(
1731 __isl_take isl_map *map,
1732 __isl_take isl_set *set);
1733 __isl_give isl_map *isl_map_intersect_range(
1734 __isl_take isl_map *map,
1735 __isl_take isl_set *set);
1736 __isl_give isl_map *isl_map_intersect(
1737 __isl_take isl_map *map1,
1738 __isl_take isl_map *map2);
1739 __isl_give isl_union_map *isl_union_map_intersect_domain(
1740 __isl_take isl_union_map *umap,
1741 __isl_take isl_union_set *uset);
1742 __isl_give isl_union_map *isl_union_map_intersect_range(
1743 __isl_take isl_union_map *umap,
1744 __isl_take isl_union_set *uset);
1745 __isl_give isl_union_map *isl_union_map_intersect(
1746 __isl_take isl_union_map *umap1,
1747 __isl_take isl_union_map *umap2);
1751 __isl_give isl_set *isl_basic_set_union(
1752 __isl_take isl_basic_set *bset1,
1753 __isl_take isl_basic_set *bset2);
1754 __isl_give isl_map *isl_basic_map_union(
1755 __isl_take isl_basic_map *bmap1,
1756 __isl_take isl_basic_map *bmap2);
1757 __isl_give isl_set *isl_set_union(
1758 __isl_take isl_set *set1,
1759 __isl_take isl_set *set2);
1760 __isl_give isl_map *isl_map_union(
1761 __isl_take isl_map *map1,
1762 __isl_take isl_map *map2);
1763 __isl_give isl_union_set *isl_union_set_union(
1764 __isl_take isl_union_set *uset1,
1765 __isl_take isl_union_set *uset2);
1766 __isl_give isl_union_map *isl_union_map_union(
1767 __isl_take isl_union_map *umap1,
1768 __isl_take isl_union_map *umap2);
1770 =item * Set difference
1772 __isl_give isl_set *isl_set_subtract(
1773 __isl_take isl_set *set1,
1774 __isl_take isl_set *set2);
1775 __isl_give isl_map *isl_map_subtract(
1776 __isl_take isl_map *map1,
1777 __isl_take isl_map *map2);
1778 __isl_give isl_union_set *isl_union_set_subtract(
1779 __isl_take isl_union_set *uset1,
1780 __isl_take isl_union_set *uset2);
1781 __isl_give isl_union_map *isl_union_map_subtract(
1782 __isl_take isl_union_map *umap1,
1783 __isl_take isl_union_map *umap2);
1787 __isl_give isl_basic_set *isl_basic_set_apply(
1788 __isl_take isl_basic_set *bset,
1789 __isl_take isl_basic_map *bmap);
1790 __isl_give isl_set *isl_set_apply(
1791 __isl_take isl_set *set,
1792 __isl_take isl_map *map);
1793 __isl_give isl_union_set *isl_union_set_apply(
1794 __isl_take isl_union_set *uset,
1795 __isl_take isl_union_map *umap);
1796 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1797 __isl_take isl_basic_map *bmap1,
1798 __isl_take isl_basic_map *bmap2);
1799 __isl_give isl_basic_map *isl_basic_map_apply_range(
1800 __isl_take isl_basic_map *bmap1,
1801 __isl_take isl_basic_map *bmap2);
1802 __isl_give isl_map *isl_map_apply_domain(
1803 __isl_take isl_map *map1,
1804 __isl_take isl_map *map2);
1805 __isl_give isl_union_map *isl_union_map_apply_domain(
1806 __isl_take isl_union_map *umap1,
1807 __isl_take isl_union_map *umap2);
1808 __isl_give isl_map *isl_map_apply_range(
1809 __isl_take isl_map *map1,
1810 __isl_take isl_map *map2);
1811 __isl_give isl_union_map *isl_union_map_apply_range(
1812 __isl_take isl_union_map *umap1,
1813 __isl_take isl_union_map *umap2);
1815 =item * Cartesian Product
1817 __isl_give isl_set *isl_set_product(
1818 __isl_take isl_set *set1,
1819 __isl_take isl_set *set2);
1820 __isl_give isl_union_set *isl_union_set_product(
1821 __isl_take isl_union_set *uset1,
1822 __isl_take isl_union_set *uset2);
1823 __isl_give isl_basic_map *isl_basic_map_range_product(
1824 __isl_take isl_basic_map *bmap1,
1825 __isl_take isl_basic_map *bmap2);
1826 __isl_give isl_map *isl_map_range_product(
1827 __isl_take isl_map *map1,
1828 __isl_take isl_map *map2);
1829 __isl_give isl_union_map *isl_union_map_range_product(
1830 __isl_take isl_union_map *umap1,
1831 __isl_take isl_union_map *umap2);
1832 __isl_give isl_map *isl_map_product(
1833 __isl_take isl_map *map1,
1834 __isl_take isl_map *map2);
1835 __isl_give isl_union_map *isl_union_map_product(
1836 __isl_take isl_union_map *umap1,
1837 __isl_take isl_union_map *umap2);
1839 The above functions compute the cross product of the given
1840 sets or relations. The domains and ranges of the results
1841 are wrapped maps between domains and ranges of the inputs.
1842 To obtain a ``flat'' product, use the following functions
1845 __isl_give isl_basic_set *isl_basic_set_flat_product(
1846 __isl_take isl_basic_set *bset1,
1847 __isl_take isl_basic_set *bset2);
1848 __isl_give isl_set *isl_set_flat_product(
1849 __isl_take isl_set *set1,
1850 __isl_take isl_set *set2);
1851 __isl_give isl_basic_map *isl_basic_map_flat_product(
1852 __isl_take isl_basic_map *bmap1,
1853 __isl_take isl_basic_map *bmap2);
1854 __isl_give isl_map *isl_map_flat_product(
1855 __isl_take isl_map *map1,
1856 __isl_take isl_map *map2);
1858 =item * Simplification
1860 __isl_give isl_basic_set *isl_basic_set_gist(
1861 __isl_take isl_basic_set *bset,
1862 __isl_take isl_basic_set *context);
1863 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1864 __isl_take isl_set *context);
1865 __isl_give isl_union_set *isl_union_set_gist(
1866 __isl_take isl_union_set *uset,
1867 __isl_take isl_union_set *context);
1868 __isl_give isl_basic_map *isl_basic_map_gist(
1869 __isl_take isl_basic_map *bmap,
1870 __isl_take isl_basic_map *context);
1871 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1872 __isl_take isl_map *context);
1873 __isl_give isl_union_map *isl_union_map_gist(
1874 __isl_take isl_union_map *umap,
1875 __isl_take isl_union_map *context);
1877 The gist operation returns a set or relation that has the
1878 same intersection with the context as the input set or relation.
1879 Any implicit equality in the intersection is made explicit in the result,
1880 while all inequalities that are redundant with respect to the intersection
1882 In case of union sets and relations, the gist operation is performed
1887 =head3 Lexicographic Optimization
1889 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1890 the following functions
1891 compute a set that contains the lexicographic minimum or maximum
1892 of the elements in C<set> (or C<bset>) for those values of the parameters
1893 that satisfy C<dom>.
1894 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1895 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1897 In other words, the union of the parameter values
1898 for which the result is non-empty and of C<*empty>
1901 __isl_give isl_set *isl_basic_set_partial_lexmin(
1902 __isl_take isl_basic_set *bset,
1903 __isl_take isl_basic_set *dom,
1904 __isl_give isl_set **empty);
1905 __isl_give isl_set *isl_basic_set_partial_lexmax(
1906 __isl_take isl_basic_set *bset,
1907 __isl_take isl_basic_set *dom,
1908 __isl_give isl_set **empty);
1909 __isl_give isl_set *isl_set_partial_lexmin(
1910 __isl_take isl_set *set, __isl_take isl_set *dom,
1911 __isl_give isl_set **empty);
1912 __isl_give isl_set *isl_set_partial_lexmax(
1913 __isl_take isl_set *set, __isl_take isl_set *dom,
1914 __isl_give isl_set **empty);
1916 Given a (basic) set C<set> (or C<bset>), the following functions simply
1917 return a set containing the lexicographic minimum or maximum
1918 of the elements in C<set> (or C<bset>).
1919 In case of union sets, the optimum is computed per space.
1921 __isl_give isl_set *isl_basic_set_lexmin(
1922 __isl_take isl_basic_set *bset);
1923 __isl_give isl_set *isl_basic_set_lexmax(
1924 __isl_take isl_basic_set *bset);
1925 __isl_give isl_set *isl_set_lexmin(
1926 __isl_take isl_set *set);
1927 __isl_give isl_set *isl_set_lexmax(
1928 __isl_take isl_set *set);
1929 __isl_give isl_union_set *isl_union_set_lexmin(
1930 __isl_take isl_union_set *uset);
1931 __isl_give isl_union_set *isl_union_set_lexmax(
1932 __isl_take isl_union_set *uset);
1934 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1935 the following functions
1936 compute a relation that maps each element of C<dom>
1937 to the single lexicographic minimum or maximum
1938 of the elements that are associated to that same
1939 element in C<map> (or C<bmap>).
1940 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1941 that contains the elements in C<dom> that do not map
1942 to any elements in C<map> (or C<bmap>).
1943 In other words, the union of the domain of the result and of C<*empty>
1946 __isl_give isl_map *isl_basic_map_partial_lexmax(
1947 __isl_take isl_basic_map *bmap,
1948 __isl_take isl_basic_set *dom,
1949 __isl_give isl_set **empty);
1950 __isl_give isl_map *isl_basic_map_partial_lexmin(
1951 __isl_take isl_basic_map *bmap,
1952 __isl_take isl_basic_set *dom,
1953 __isl_give isl_set **empty);
1954 __isl_give isl_map *isl_map_partial_lexmax(
1955 __isl_take isl_map *map, __isl_take isl_set *dom,
1956 __isl_give isl_set **empty);
1957 __isl_give isl_map *isl_map_partial_lexmin(
1958 __isl_take isl_map *map, __isl_take isl_set *dom,
1959 __isl_give isl_set **empty);
1961 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1962 return a map mapping each element in the domain of
1963 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1964 of all elements associated to that element.
1965 In case of union relations, the optimum is computed per space.
1967 __isl_give isl_map *isl_basic_map_lexmin(
1968 __isl_take isl_basic_map *bmap);
1969 __isl_give isl_map *isl_basic_map_lexmax(
1970 __isl_take isl_basic_map *bmap);
1971 __isl_give isl_map *isl_map_lexmin(
1972 __isl_take isl_map *map);
1973 __isl_give isl_map *isl_map_lexmax(
1974 __isl_take isl_map *map);
1975 __isl_give isl_union_map *isl_union_map_lexmin(
1976 __isl_take isl_union_map *umap);
1977 __isl_give isl_union_map *isl_union_map_lexmax(
1978 __isl_take isl_union_map *umap);
1982 Matrices can be created, copied and freed using the following functions.
1984 #include <isl/mat.h>
1985 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1986 unsigned n_row, unsigned n_col);
1987 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1988 void isl_mat_free(__isl_take isl_mat *mat);
1990 Note that the elements of a newly created matrix may have arbitrary values.
1991 The elements can be changed and inspected using the following functions.
1993 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
1994 int isl_mat_rows(__isl_keep isl_mat *mat);
1995 int isl_mat_cols(__isl_keep isl_mat *mat);
1996 int isl_mat_get_element(__isl_keep isl_mat *mat,
1997 int row, int col, isl_int *v);
1998 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1999 int row, int col, isl_int v);
2000 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2001 int row, int col, int v);
2003 C<isl_mat_get_element> will return a negative value if anything went wrong.
2004 In that case, the value of C<*v> is undefined.
2006 The following function can be used to compute the (right) inverse
2007 of a matrix, i.e., a matrix such that the product of the original
2008 and the inverse (in that order) is a multiple of the identity matrix.
2009 The input matrix is assumed to be of full row-rank.
2011 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2013 The following function can be used to compute the (right) kernel
2014 (or null space) of a matrix, i.e., a matrix such that the product of
2015 the original and the kernel (in that order) is the zero matrix.
2017 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2019 =head2 Quasi Affine Expressions
2021 The zero quasi affine expression can be created using
2023 __isl_give isl_aff *isl_aff_zero(
2024 __isl_take isl_local_space *ls);
2026 Quasi affine expressions can be copied and free using
2028 #include <isl/aff.h>
2029 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2030 void *isl_aff_free(__isl_take isl_aff *aff);
2032 The expression can be inspected using
2034 #include <isl/aff.h>
2035 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2036 int isl_aff_dim(__isl_keep isl_aff *aff,
2037 enum isl_dim_type type);
2038 __isl_give isl_local_space *isl_aff_get_local_space(
2039 __isl_keep isl_aff *aff);
2040 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2041 enum isl_dim_type type, unsigned pos);
2042 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2044 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2045 enum isl_dim_type type, int pos, isl_int *v);
2046 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2048 __isl_give isl_div *isl_aff_get_div(
2049 __isl_keep isl_aff *aff, int pos);
2051 It can be modified using
2053 #include <isl/aff.h>
2054 __isl_give isl_aff *isl_aff_set_constant(
2055 __isl_take isl_aff *aff, isl_int v);
2056 __isl_give isl_aff *isl_aff_set_constant_si(
2057 __isl_take isl_aff *aff, int v);
2058 __isl_give isl_aff *isl_aff_set_coefficient(
2059 __isl_take isl_aff *aff,
2060 enum isl_dim_type type, int pos, isl_int v);
2061 __isl_give isl_aff *isl_aff_set_coefficient_si(
2062 __isl_take isl_aff *aff,
2063 enum isl_dim_type type, int pos, int v);
2064 __isl_give isl_aff *isl_aff_set_denominator(
2065 __isl_take isl_aff *aff, isl_int v);
2067 __isl_give isl_aff *isl_aff_add_constant(
2068 __isl_take isl_aff *aff, isl_int v);
2069 __isl_give isl_aff *isl_aff_add_coefficient_si(
2070 __isl_take isl_aff *aff,
2071 enum isl_dim_type type, int pos, int v);
2073 Note that the C<set_constant> and C<set_coefficient> functions
2074 set the I<numerator> of the constant or coefficient, while
2075 C<add_constant> and C<add_coefficient> add an integer value to
2076 the possibly rational constant or coefficient.
2080 #include <isl/aff.h>
2081 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2082 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2084 An expression can be printed using
2086 #include <isl/aff.h>
2087 __isl_give isl_printer *isl_printer_print_aff(
2088 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2092 Points are elements of a set. They can be used to construct
2093 simple sets (boxes) or they can be used to represent the
2094 individual elements of a set.
2095 The zero point (the origin) can be created using
2097 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2099 The coordinates of a point can be inspected, set and changed
2102 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2103 enum isl_dim_type type, int pos, isl_int *v);
2104 __isl_give isl_point *isl_point_set_coordinate(
2105 __isl_take isl_point *pnt,
2106 enum isl_dim_type type, int pos, isl_int v);
2108 __isl_give isl_point *isl_point_add_ui(
2109 __isl_take isl_point *pnt,
2110 enum isl_dim_type type, int pos, unsigned val);
2111 __isl_give isl_point *isl_point_sub_ui(
2112 __isl_take isl_point *pnt,
2113 enum isl_dim_type type, int pos, unsigned val);
2115 Points can be copied or freed using
2117 __isl_give isl_point *isl_point_copy(
2118 __isl_keep isl_point *pnt);
2119 void isl_point_free(__isl_take isl_point *pnt);
2121 A singleton set can be created from a point using
2123 __isl_give isl_basic_set *isl_basic_set_from_point(
2124 __isl_take isl_point *pnt);
2125 __isl_give isl_set *isl_set_from_point(
2126 __isl_take isl_point *pnt);
2128 and a box can be created from two opposite extremal points using
2130 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2131 __isl_take isl_point *pnt1,
2132 __isl_take isl_point *pnt2);
2133 __isl_give isl_set *isl_set_box_from_points(
2134 __isl_take isl_point *pnt1,
2135 __isl_take isl_point *pnt2);
2137 All elements of a B<bounded> (union) set can be enumerated using
2138 the following functions.
2140 int isl_set_foreach_point(__isl_keep isl_set *set,
2141 int (*fn)(__isl_take isl_point *pnt, void *user),
2143 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2144 int (*fn)(__isl_take isl_point *pnt, void *user),
2147 The function C<fn> is called for each integer point in
2148 C<set> with as second argument the last argument of
2149 the C<isl_set_foreach_point> call. The function C<fn>
2150 should return C<0> on success and C<-1> on failure.
2151 In the latter case, C<isl_set_foreach_point> will stop
2152 enumerating and return C<-1> as well.
2153 If the enumeration is performed successfully and to completion,
2154 then C<isl_set_foreach_point> returns C<0>.
2156 To obtain a single point of a (basic) set, use
2158 __isl_give isl_point *isl_basic_set_sample_point(
2159 __isl_take isl_basic_set *bset);
2160 __isl_give isl_point *isl_set_sample_point(
2161 __isl_take isl_set *set);
2163 If C<set> does not contain any (integer) points, then the
2164 resulting point will be ``void'', a property that can be
2167 int isl_point_is_void(__isl_keep isl_point *pnt);
2169 =head2 Piecewise Quasipolynomials
2171 A piecewise quasipolynomial is a particular kind of function that maps
2172 a parametric point to a rational value.
2173 More specifically, a quasipolynomial is a polynomial expression in greatest
2174 integer parts of affine expressions of parameters and variables.
2175 A piecewise quasipolynomial is a subdivision of a given parametric
2176 domain into disjoint cells with a quasipolynomial associated to
2177 each cell. The value of the piecewise quasipolynomial at a given
2178 point is the value of the quasipolynomial associated to the cell
2179 that contains the point. Outside of the union of cells,
2180 the value is assumed to be zero.
2181 For example, the piecewise quasipolynomial
2183 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2185 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2186 A given piecewise quasipolynomial has a fixed domain dimension.
2187 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2188 defined over different domains.
2189 Piecewise quasipolynomials are mainly used by the C<barvinok>
2190 library for representing the number of elements in a parametric set or map.
2191 For example, the piecewise quasipolynomial above represents
2192 the number of points in the map
2194 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2196 =head3 Printing (Piecewise) Quasipolynomials
2198 Quasipolynomials and piecewise quasipolynomials can be printed
2199 using the following functions.
2201 __isl_give isl_printer *isl_printer_print_qpolynomial(
2202 __isl_take isl_printer *p,
2203 __isl_keep isl_qpolynomial *qp);
2205 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2206 __isl_take isl_printer *p,
2207 __isl_keep isl_pw_qpolynomial *pwqp);
2209 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2210 __isl_take isl_printer *p,
2211 __isl_keep isl_union_pw_qpolynomial *upwqp);
2213 The output format of the printer
2214 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2215 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2217 In case of printing in C<ISL_FORMAT_C>, the user may want
2218 to set the names of all dimensions
2220 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2221 __isl_take isl_qpolynomial *qp,
2222 enum isl_dim_type type, unsigned pos,
2224 __isl_give isl_pw_qpolynomial *
2225 isl_pw_qpolynomial_set_dim_name(
2226 __isl_take isl_pw_qpolynomial *pwqp,
2227 enum isl_dim_type type, unsigned pos,
2230 =head3 Creating New (Piecewise) Quasipolynomials
2232 Some simple quasipolynomials can be created using the following functions.
2233 More complicated quasipolynomials can be created by applying
2234 operations such as addition and multiplication
2235 on the resulting quasipolynomials
2237 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2238 __isl_take isl_dim *dim);
2239 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2240 __isl_take isl_dim *dim);
2241 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2242 __isl_take isl_dim *dim);
2243 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2244 __isl_take isl_dim *dim);
2245 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2246 __isl_take isl_dim *dim);
2247 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2248 __isl_take isl_dim *dim,
2249 const isl_int n, const isl_int d);
2250 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2251 __isl_take isl_div *div);
2252 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2253 __isl_take isl_dim *dim,
2254 enum isl_dim_type type, unsigned pos);
2256 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2257 with a single cell can be created using the following functions.
2258 Multiple of these single cell piecewise quasipolynomials can
2259 be combined to create more complicated piecewise quasipolynomials.
2261 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2262 __isl_take isl_dim *dim);
2263 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2264 __isl_take isl_set *set,
2265 __isl_take isl_qpolynomial *qp);
2267 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2268 __isl_take isl_dim *dim);
2269 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2270 __isl_take isl_pw_qpolynomial *pwqp);
2271 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2272 __isl_take isl_union_pw_qpolynomial *upwqp,
2273 __isl_take isl_pw_qpolynomial *pwqp);
2275 Quasipolynomials can be copied and freed again using the following
2278 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2279 __isl_keep isl_qpolynomial *qp);
2280 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2282 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2283 __isl_keep isl_pw_qpolynomial *pwqp);
2284 void isl_pw_qpolynomial_free(
2285 __isl_take isl_pw_qpolynomial *pwqp);
2287 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2288 __isl_keep isl_union_pw_qpolynomial *upwqp);
2289 void isl_union_pw_qpolynomial_free(
2290 __isl_take isl_union_pw_qpolynomial *upwqp);
2292 =head3 Inspecting (Piecewise) Quasipolynomials
2294 To iterate over all piecewise quasipolynomials in a union
2295 piecewise quasipolynomial, use the following function
2297 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2298 __isl_keep isl_union_pw_qpolynomial *upwqp,
2299 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2302 To extract the piecewise quasipolynomial from a union with a given dimension
2305 __isl_give isl_pw_qpolynomial *
2306 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2307 __isl_keep isl_union_pw_qpolynomial *upwqp,
2308 __isl_take isl_dim *dim);
2310 To iterate over the cells in a piecewise quasipolynomial,
2311 use either of the following two functions
2313 int isl_pw_qpolynomial_foreach_piece(
2314 __isl_keep isl_pw_qpolynomial *pwqp,
2315 int (*fn)(__isl_take isl_set *set,
2316 __isl_take isl_qpolynomial *qp,
2317 void *user), void *user);
2318 int isl_pw_qpolynomial_foreach_lifted_piece(
2319 __isl_keep isl_pw_qpolynomial *pwqp,
2320 int (*fn)(__isl_take isl_set *set,
2321 __isl_take isl_qpolynomial *qp,
2322 void *user), void *user);
2324 As usual, the function C<fn> should return C<0> on success
2325 and C<-1> on failure. The difference between
2326 C<isl_pw_qpolynomial_foreach_piece> and
2327 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2328 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2329 compute unique representations for all existentially quantified
2330 variables and then turn these existentially quantified variables
2331 into extra set variables, adapting the associated quasipolynomial
2332 accordingly. This means that the C<set> passed to C<fn>
2333 will not have any existentially quantified variables, but that
2334 the dimensions of the sets may be different for different
2335 invocations of C<fn>.
2337 To iterate over all terms in a quasipolynomial,
2340 int isl_qpolynomial_foreach_term(
2341 __isl_keep isl_qpolynomial *qp,
2342 int (*fn)(__isl_take isl_term *term,
2343 void *user), void *user);
2345 The terms themselves can be inspected and freed using
2348 unsigned isl_term_dim(__isl_keep isl_term *term,
2349 enum isl_dim_type type);
2350 void isl_term_get_num(__isl_keep isl_term *term,
2352 void isl_term_get_den(__isl_keep isl_term *term,
2354 int isl_term_get_exp(__isl_keep isl_term *term,
2355 enum isl_dim_type type, unsigned pos);
2356 __isl_give isl_div *isl_term_get_div(
2357 __isl_keep isl_term *term, unsigned pos);
2358 void isl_term_free(__isl_take isl_term *term);
2360 Each term is a product of parameters, set variables and
2361 integer divisions. The function C<isl_term_get_exp>
2362 returns the exponent of a given dimensions in the given term.
2363 The C<isl_int>s in the arguments of C<isl_term_get_num>
2364 and C<isl_term_get_den> need to have been initialized
2365 using C<isl_int_init> before calling these functions.
2367 =head3 Properties of (Piecewise) Quasipolynomials
2369 To check whether a quasipolynomial is actually a constant,
2370 use the following function.
2372 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2373 isl_int *n, isl_int *d);
2375 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2376 then the numerator and denominator of the constant
2377 are returned in C<*n> and C<*d>, respectively.
2379 =head3 Operations on (Piecewise) Quasipolynomials
2381 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2382 __isl_take isl_qpolynomial *qp);
2383 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2384 __isl_take isl_qpolynomial *qp1,
2385 __isl_take isl_qpolynomial *qp2);
2386 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2387 __isl_take isl_qpolynomial *qp1,
2388 __isl_take isl_qpolynomial *qp2);
2389 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2390 __isl_take isl_qpolynomial *qp1,
2391 __isl_take isl_qpolynomial *qp2);
2392 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2393 __isl_take isl_qpolynomial *qp, unsigned exponent);
2395 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2396 __isl_take isl_pw_qpolynomial *pwqp1,
2397 __isl_take isl_pw_qpolynomial *pwqp2);
2398 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2399 __isl_take isl_pw_qpolynomial *pwqp1,
2400 __isl_take isl_pw_qpolynomial *pwqp2);
2401 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2402 __isl_take isl_pw_qpolynomial *pwqp1,
2403 __isl_take isl_pw_qpolynomial *pwqp2);
2404 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2405 __isl_take isl_pw_qpolynomial *pwqp);
2406 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2407 __isl_take isl_pw_qpolynomial *pwqp1,
2408 __isl_take isl_pw_qpolynomial *pwqp2);
2410 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2411 __isl_take isl_union_pw_qpolynomial *upwqp1,
2412 __isl_take isl_union_pw_qpolynomial *upwqp2);
2413 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2414 __isl_take isl_union_pw_qpolynomial *upwqp1,
2415 __isl_take isl_union_pw_qpolynomial *upwqp2);
2416 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2417 __isl_take isl_union_pw_qpolynomial *upwqp1,
2418 __isl_take isl_union_pw_qpolynomial *upwqp2);
2420 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2421 __isl_take isl_pw_qpolynomial *pwqp,
2422 __isl_take isl_point *pnt);
2424 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2425 __isl_take isl_union_pw_qpolynomial *upwqp,
2426 __isl_take isl_point *pnt);
2428 __isl_give isl_set *isl_pw_qpolynomial_domain(
2429 __isl_take isl_pw_qpolynomial *pwqp);
2430 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2431 __isl_take isl_pw_qpolynomial *pwpq,
2432 __isl_take isl_set *set);
2434 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2435 __isl_take isl_union_pw_qpolynomial *upwqp);
2436 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2437 __isl_take isl_union_pw_qpolynomial *upwpq,
2438 __isl_take isl_union_set *uset);
2440 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2441 __isl_take isl_qpolynomial *qp,
2442 __isl_take isl_dim *model);
2444 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2445 __isl_take isl_union_pw_qpolynomial *upwqp);
2447 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2448 __isl_take isl_qpolynomial *qp,
2449 __isl_take isl_set *context);
2451 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2452 __isl_take isl_pw_qpolynomial *pwqp,
2453 __isl_take isl_set *context);
2455 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2456 __isl_take isl_union_pw_qpolynomial *upwqp,
2457 __isl_take isl_union_set *context);
2459 The gist operation applies the gist operation to each of
2460 the cells in the domain of the input piecewise quasipolynomial.
2461 The context is also exploited
2462 to simplify the quasipolynomials associated to each cell.
2464 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2465 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2466 __isl_give isl_union_pw_qpolynomial *
2467 isl_union_pw_qpolynomial_to_polynomial(
2468 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2470 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2471 the polynomial will be an overapproximation. If C<sign> is negative,
2472 it will be an underapproximation. If C<sign> is zero, the approximation
2473 will lie somewhere in between.
2475 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2477 A piecewise quasipolynomial reduction is a piecewise
2478 reduction (or fold) of quasipolynomials.
2479 In particular, the reduction can be maximum or a minimum.
2480 The objects are mainly used to represent the result of
2481 an upper or lower bound on a quasipolynomial over its domain,
2482 i.e., as the result of the following function.
2484 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2485 __isl_take isl_pw_qpolynomial *pwqp,
2486 enum isl_fold type, int *tight);
2488 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2489 __isl_take isl_union_pw_qpolynomial *upwqp,
2490 enum isl_fold type, int *tight);
2492 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2493 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2494 is the returned bound is known be tight, i.e., for each value
2495 of the parameters there is at least
2496 one element in the domain that reaches the bound.
2497 If the domain of C<pwqp> is not wrapping, then the bound is computed
2498 over all elements in that domain and the result has a purely parametric
2499 domain. If the domain of C<pwqp> is wrapping, then the bound is
2500 computed over the range of the wrapped relation. The domain of the
2501 wrapped relation becomes the domain of the result.
2503 A (piecewise) quasipolynomial reduction can be copied or freed using the
2504 following functions.
2506 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2507 __isl_keep isl_qpolynomial_fold *fold);
2508 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2509 __isl_keep isl_pw_qpolynomial_fold *pwf);
2510 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2511 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2512 void isl_qpolynomial_fold_free(
2513 __isl_take isl_qpolynomial_fold *fold);
2514 void isl_pw_qpolynomial_fold_free(
2515 __isl_take isl_pw_qpolynomial_fold *pwf);
2516 void isl_union_pw_qpolynomial_fold_free(
2517 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2519 =head3 Printing Piecewise Quasipolynomial Reductions
2521 Piecewise quasipolynomial reductions can be printed
2522 using the following function.
2524 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2525 __isl_take isl_printer *p,
2526 __isl_keep isl_pw_qpolynomial_fold *pwf);
2527 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2528 __isl_take isl_printer *p,
2529 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2531 For C<isl_printer_print_pw_qpolynomial_fold>,
2532 output format of the printer
2533 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2534 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2535 output format of the printer
2536 needs to be set to C<ISL_FORMAT_ISL>.
2537 In case of printing in C<ISL_FORMAT_C>, the user may want
2538 to set the names of all dimensions
2540 __isl_give isl_pw_qpolynomial_fold *
2541 isl_pw_qpolynomial_fold_set_dim_name(
2542 __isl_take isl_pw_qpolynomial_fold *pwf,
2543 enum isl_dim_type type, unsigned pos,
2546 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2548 To iterate over all piecewise quasipolynomial reductions in a union
2549 piecewise quasipolynomial reduction, use the following function
2551 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2552 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2553 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2554 void *user), void *user);
2556 To iterate over the cells in a piecewise quasipolynomial reduction,
2557 use either of the following two functions
2559 int isl_pw_qpolynomial_fold_foreach_piece(
2560 __isl_keep isl_pw_qpolynomial_fold *pwf,
2561 int (*fn)(__isl_take isl_set *set,
2562 __isl_take isl_qpolynomial_fold *fold,
2563 void *user), void *user);
2564 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2565 __isl_keep isl_pw_qpolynomial_fold *pwf,
2566 int (*fn)(__isl_take isl_set *set,
2567 __isl_take isl_qpolynomial_fold *fold,
2568 void *user), void *user);
2570 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2571 of the difference between these two functions.
2573 To iterate over all quasipolynomials in a reduction, use
2575 int isl_qpolynomial_fold_foreach_qpolynomial(
2576 __isl_keep isl_qpolynomial_fold *fold,
2577 int (*fn)(__isl_take isl_qpolynomial *qp,
2578 void *user), void *user);
2580 =head3 Operations on Piecewise Quasipolynomial Reductions
2582 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2583 __isl_take isl_pw_qpolynomial_fold *pwf1,
2584 __isl_take isl_pw_qpolynomial_fold *pwf2);
2586 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2587 __isl_take isl_pw_qpolynomial_fold *pwf1,
2588 __isl_take isl_pw_qpolynomial_fold *pwf2);
2590 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2591 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2592 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2594 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2595 __isl_take isl_pw_qpolynomial_fold *pwf,
2596 __isl_take isl_point *pnt);
2598 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2599 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2600 __isl_take isl_point *pnt);
2602 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2603 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2604 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2605 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2606 __isl_take isl_union_set *uset);
2608 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2609 __isl_take isl_pw_qpolynomial_fold *pwf);
2611 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2612 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2614 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2615 __isl_take isl_pw_qpolynomial_fold *pwf,
2616 __isl_take isl_set *context);
2618 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2619 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2620 __isl_take isl_union_set *context);
2622 The gist operation applies the gist operation to each of
2623 the cells in the domain of the input piecewise quasipolynomial reduction.
2624 In future, the operation will also exploit the context
2625 to simplify the quasipolynomial reductions associated to each cell.
2627 __isl_give isl_pw_qpolynomial_fold *
2628 isl_set_apply_pw_qpolynomial_fold(
2629 __isl_take isl_set *set,
2630 __isl_take isl_pw_qpolynomial_fold *pwf,
2632 __isl_give isl_pw_qpolynomial_fold *
2633 isl_map_apply_pw_qpolynomial_fold(
2634 __isl_take isl_map *map,
2635 __isl_take isl_pw_qpolynomial_fold *pwf,
2637 __isl_give isl_union_pw_qpolynomial_fold *
2638 isl_union_set_apply_union_pw_qpolynomial_fold(
2639 __isl_take isl_union_set *uset,
2640 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2642 __isl_give isl_union_pw_qpolynomial_fold *
2643 isl_union_map_apply_union_pw_qpolynomial_fold(
2644 __isl_take isl_union_map *umap,
2645 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2648 The functions taking a map
2649 compose the given map with the given piecewise quasipolynomial reduction.
2650 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2651 over all elements in the intersection of the range of the map
2652 and the domain of the piecewise quasipolynomial reduction
2653 as a function of an element in the domain of the map.
2654 The functions taking a set compute a bound over all elements in the
2655 intersection of the set and the domain of the
2656 piecewise quasipolynomial reduction.
2658 =head2 Dependence Analysis
2660 C<isl> contains specialized functionality for performing
2661 array dataflow analysis. That is, given a I<sink> access relation
2662 and a collection of possible I<source> access relations,
2663 C<isl> can compute relations that describe
2664 for each iteration of the sink access, which iteration
2665 of which of the source access relations was the last
2666 to access the same data element before the given iteration
2668 To compute standard flow dependences, the sink should be
2669 a read, while the sources should be writes.
2670 If any of the source accesses are marked as being I<may>
2671 accesses, then there will be a dependence to the last
2672 I<must> access B<and> to any I<may> access that follows
2673 this last I<must> access.
2674 In particular, if I<all> sources are I<may> accesses,
2675 then memory based dependence analysis is performed.
2676 If, on the other hand, all sources are I<must> accesses,
2677 then value based dependence analysis is performed.
2679 #include <isl/flow.h>
2681 typedef int (*isl_access_level_before)(void *first, void *second);
2683 __isl_give isl_access_info *isl_access_info_alloc(
2684 __isl_take isl_map *sink,
2685 void *sink_user, isl_access_level_before fn,
2687 __isl_give isl_access_info *isl_access_info_add_source(
2688 __isl_take isl_access_info *acc,
2689 __isl_take isl_map *source, int must,
2691 void isl_access_info_free(__isl_take isl_access_info *acc);
2693 __isl_give isl_flow *isl_access_info_compute_flow(
2694 __isl_take isl_access_info *acc);
2696 int isl_flow_foreach(__isl_keep isl_flow *deps,
2697 int (*fn)(__isl_take isl_map *dep, int must,
2698 void *dep_user, void *user),
2700 __isl_give isl_map *isl_flow_get_no_source(
2701 __isl_keep isl_flow *deps, int must);
2702 void isl_flow_free(__isl_take isl_flow *deps);
2704 The function C<isl_access_info_compute_flow> performs the actual
2705 dependence analysis. The other functions are used to construct
2706 the input for this function or to read off the output.
2708 The input is collected in an C<isl_access_info>, which can
2709 be created through a call to C<isl_access_info_alloc>.
2710 The arguments to this functions are the sink access relation
2711 C<sink>, a token C<sink_user> used to identify the sink
2712 access to the user, a callback function for specifying the
2713 relative order of source and sink accesses, and the number
2714 of source access relations that will be added.
2715 The callback function has type C<int (*)(void *first, void *second)>.
2716 The function is called with two user supplied tokens identifying
2717 either a source or the sink and it should return the shared nesting
2718 level and the relative order of the two accesses.
2719 In particular, let I<n> be the number of loops shared by
2720 the two accesses. If C<first> precedes C<second> textually,
2721 then the function should return I<2 * n + 1>; otherwise,
2722 it should return I<2 * n>.
2723 The sources can be added to the C<isl_access_info> by performing
2724 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2725 C<must> indicates whether the source is a I<must> access
2726 or a I<may> access. Note that a multi-valued access relation
2727 should only be marked I<must> if every iteration in the domain
2728 of the relation accesses I<all> elements in its image.
2729 The C<source_user> token is again used to identify
2730 the source access. The range of the source access relation
2731 C<source> should have the same dimension as the range
2732 of the sink access relation.
2733 The C<isl_access_info_free> function should usually not be
2734 called explicitly, because it is called implicitly by
2735 C<isl_access_info_compute_flow>.
2737 The result of the dependence analysis is collected in an
2738 C<isl_flow>. There may be elements of
2739 the sink access for which no preceding source access could be
2740 found or for which all preceding sources are I<may> accesses.
2741 The relations containing these elements can be obtained through
2742 calls to C<isl_flow_get_no_source>, the first with C<must> set
2743 and the second with C<must> unset.
2744 In the case of standard flow dependence analysis,
2745 with the sink a read and the sources I<must> writes,
2746 the first relation corresponds to the reads from uninitialized
2747 array elements and the second relation is empty.
2748 The actual flow dependences can be extracted using
2749 C<isl_flow_foreach>. This function will call the user-specified
2750 callback function C<fn> for each B<non-empty> dependence between
2751 a source and the sink. The callback function is called
2752 with four arguments, the actual flow dependence relation
2753 mapping source iterations to sink iterations, a boolean that
2754 indicates whether it is a I<must> or I<may> dependence, a token
2755 identifying the source and an additional C<void *> with value
2756 equal to the third argument of the C<isl_flow_foreach> call.
2757 A dependence is marked I<must> if it originates from a I<must>
2758 source and if it is not followed by any I<may> sources.
2760 After finishing with an C<isl_flow>, the user should call
2761 C<isl_flow_free> to free all associated memory.
2763 A higher-level interface to dependence analysis is provided
2764 by the following function.
2766 #include <isl/flow.h>
2768 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2769 __isl_take isl_union_map *must_source,
2770 __isl_take isl_union_map *may_source,
2771 __isl_take isl_union_map *schedule,
2772 __isl_give isl_union_map **must_dep,
2773 __isl_give isl_union_map **may_dep,
2774 __isl_give isl_union_map **must_no_source,
2775 __isl_give isl_union_map **may_no_source);
2777 The arrays are identified by the tuple names of the ranges
2778 of the accesses. The iteration domains by the tuple names
2779 of the domains of the accesses and of the schedule.
2780 The relative order of the iteration domains is given by the
2781 schedule. The relations returned through C<must_no_source>
2782 and C<may_no_source> are subsets of C<sink>.
2783 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2784 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2785 any of the other arguments is treated as an error.
2789 B<The functionality described in this section is fairly new
2790 and may be subject to change.>
2792 The following function can be used to compute a schedule
2793 for a union of domains. The generated schedule respects
2794 all C<validity> dependences. That is, all dependence distances
2795 over these dependences in the scheduled space are lexicographically
2796 positive. The generated schedule schedule also tries to minimize
2797 the dependence distances over C<proximity> dependences.
2798 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2799 for groups of domains where the dependence distances have only
2800 non-negative values.
2801 The algorithm used to construct the schedule is similar to that
2804 #include <isl/schedule.h>
2805 __isl_give isl_schedule *isl_union_set_compute_schedule(
2806 __isl_take isl_union_set *domain,
2807 __isl_take isl_union_map *validity,
2808 __isl_take isl_union_map *proximity);
2809 void *isl_schedule_free(__isl_take isl_schedule *sched);
2811 A mapping from the domains to the scheduled space can be obtained
2812 from an C<isl_schedule> using the following function.
2814 __isl_give isl_union_map *isl_schedule_get_map(
2815 __isl_keep isl_schedule *sched);
2817 This mapping can also be obtained in pieces using the following functions.
2819 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
2820 __isl_give isl_union_map *isl_schedule_get_band(
2821 __isl_keep isl_schedule *sched, unsigned band);
2823 C<isl_schedule_n_band> returns the maximal number of bands.
2824 C<isl_schedule_get_band> returns a union of mappings from a domain to
2825 the band of consecutive schedule dimensions with the given sequence
2826 number for that domain. Bands with the same sequence number but for
2827 different domains may be completely unrelated.
2828 Within a band, the corresponding coordinates of the distance vectors
2829 are all non-negative, assuming that the coordinates for all previous
2832 =head2 Parametric Vertex Enumeration
2834 The parametric vertex enumeration described in this section
2835 is mainly intended to be used internally and by the C<barvinok>
2838 #include <isl/vertices.h>
2839 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2840 __isl_keep isl_basic_set *bset);
2842 The function C<isl_basic_set_compute_vertices> performs the
2843 actual computation of the parametric vertices and the chamber
2844 decomposition and store the result in an C<isl_vertices> object.
2845 This information can be queried by either iterating over all
2846 the vertices or iterating over all the chambers or cells
2847 and then iterating over all vertices that are active on the chamber.
2849 int isl_vertices_foreach_vertex(
2850 __isl_keep isl_vertices *vertices,
2851 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2854 int isl_vertices_foreach_cell(
2855 __isl_keep isl_vertices *vertices,
2856 int (*fn)(__isl_take isl_cell *cell, void *user),
2858 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2859 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2862 Other operations that can be performed on an C<isl_vertices> object are
2865 isl_ctx *isl_vertices_get_ctx(
2866 __isl_keep isl_vertices *vertices);
2867 int isl_vertices_get_n_vertices(
2868 __isl_keep isl_vertices *vertices);
2869 void isl_vertices_free(__isl_take isl_vertices *vertices);
2871 Vertices can be inspected and destroyed using the following functions.
2873 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2874 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2875 __isl_give isl_basic_set *isl_vertex_get_domain(
2876 __isl_keep isl_vertex *vertex);
2877 __isl_give isl_basic_set *isl_vertex_get_expr(
2878 __isl_keep isl_vertex *vertex);
2879 void isl_vertex_free(__isl_take isl_vertex *vertex);
2881 C<isl_vertex_get_expr> returns a singleton parametric set describing
2882 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2884 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2885 B<rational> basic sets, so they should mainly be used for inspection
2886 and should not be mixed with integer sets.
2888 Chambers can be inspected and destroyed using the following functions.
2890 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2891 __isl_give isl_basic_set *isl_cell_get_domain(
2892 __isl_keep isl_cell *cell);
2893 void isl_cell_free(__isl_take isl_cell *cell);
2897 Although C<isl> is mainly meant to be used as a library,
2898 it also contains some basic applications that use some
2899 of the functionality of C<isl>.
2900 The input may be specified in either the L<isl format>
2901 or the L<PolyLib format>.
2903 =head2 C<isl_polyhedron_sample>
2905 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2906 an integer element of the polyhedron, if there is any.
2907 The first column in the output is the denominator and is always
2908 equal to 1. If the polyhedron contains no integer points,
2909 then a vector of length zero is printed.
2913 C<isl_pip> takes the same input as the C<example> program
2914 from the C<piplib> distribution, i.e., a set of constraints
2915 on the parameters, a line containing only -1 and finally a set
2916 of constraints on a parametric polyhedron.
2917 The coefficients of the parameters appear in the last columns
2918 (but before the final constant column).
2919 The output is the lexicographic minimum of the parametric polyhedron.
2920 As C<isl> currently does not have its own output format, the output
2921 is just a dump of the internal state.
2923 =head2 C<isl_polyhedron_minimize>
2925 C<isl_polyhedron_minimize> computes the minimum of some linear
2926 or affine objective function over the integer points in a polyhedron.
2927 If an affine objective function
2928 is given, then the constant should appear in the last column.
2930 =head2 C<isl_polytope_scan>
2932 Given a polytope, C<isl_polytope_scan> prints
2933 all integer points in the polytope.