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_qpolynomial_fold_get_dim(
477 __isl_keep isl_qpolynomial_fold *fold);
478 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
479 __isl_keep isl_pw_qpolynomial *pwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
481 __isl_keep isl_union_pw_qpolynomial *upwqp);
482 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
483 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
486 __isl_give isl_dim *isl_aff_get_dim(
487 __isl_keep isl_aff *aff);
488 __isl_give isl_dim *isl_pw_aff_get_dim(
489 __isl_keep isl_pw_aff *pwaff);
491 #include <isl/point.h>
492 __isl_give isl_dim *isl_point_get_dim(
493 __isl_keep isl_point *pnt);
495 The names of the individual dimensions may be set or read off
496 using the following functions.
499 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
500 enum isl_dim_type type, unsigned pos,
501 __isl_keep const char *name);
502 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
503 enum isl_dim_type type, unsigned pos);
505 Note that C<isl_dim_get_name> returns a pointer to some internal
506 data structure, so the result can only be used while the
507 corresponding C<isl_dim> is alive.
508 Also note that every function that operates on two sets or relations
509 requires that both arguments have the same parameters. This also
510 means that if one of the arguments has named parameters, then the
511 other needs to have named parameters too and the names need to match.
512 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
513 have different parameters (as long as they are named), in which case
514 the result will have as parameters the union of the parameters of
517 The names of entire spaces may be set or read off
518 using the following functions.
521 __isl_give isl_dim *isl_dim_set_tuple_name(
522 __isl_take isl_dim *dim,
523 enum isl_dim_type type, const char *s);
524 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
525 enum isl_dim_type type);
527 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
528 or C<isl_dim_set>. As with C<isl_dim_get_name>,
529 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
531 Binary operations require the corresponding spaces of their arguments
532 to have the same name.
534 Spaces can be nested. In particular, the domain of a set or
535 the domain or range of a relation can be a nested relation.
536 The following functions can be used to construct and deconstruct
537 such nested dimension specifications.
540 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
541 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
542 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
544 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
545 be the dimension specification of a set, while that of
546 C<isl_dim_wrap> should be the dimension specification of a relation.
547 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
548 of a relation, while that of C<isl_dim_wrap> is the dimension specification
551 Dimension specifications can be created from other dimension
552 specifications using the following functions.
554 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
555 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
556 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
557 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
558 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
559 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
560 __isl_take isl_dim *right);
561 __isl_give isl_dim *isl_dim_align_params(
562 __isl_take isl_dim *dim1, __isl_take isl_dim *dim2)
563 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
564 enum isl_dim_type type, unsigned pos, unsigned n);
565 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
566 enum isl_dim_type type, unsigned n);
567 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
568 enum isl_dim_type type, unsigned first, unsigned n);
569 __isl_give isl_dim *isl_dim_map_from_set(
570 __isl_take isl_dim *dim);
571 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
573 Note that if dimensions are added or removed from a space, then
574 the name and the internal structure are lost.
578 A local space is essentially a dimension specification with
579 zero or more existentially quantified variables.
580 The local space of a basic set or relation can be obtained
581 using the following functions.
584 __isl_give isl_local_space *isl_basic_set_get_local_space(
585 __isl_keep isl_basic_set *bset);
588 __isl_give isl_local_space *isl_basic_map_get_local_space(
589 __isl_keep isl_basic_map *bmap);
591 A new local space can be created from a dimension specification using
593 #include <isl/local_space.h>
594 __isl_give isl_local_space *isl_local_space_from_dim(
595 __isl_take isl_dim *dim);
597 They can be inspected, copied and freed using the following functions.
599 #include <isl/local_space.h>
600 isl_ctx *isl_local_space_get_ctx(
601 __isl_keep isl_local_space *ls);
602 int isl_local_space_dim(__isl_keep isl_local_space *ls,
603 enum isl_dim_type type);
604 const char *isl_local_space_get_dim_name(
605 __isl_keep isl_local_space *ls,
606 enum isl_dim_type type, unsigned pos);
607 __isl_give isl_local_space *isl_local_space_set_dim_name(
608 __isl_take isl_local_space *ls,
609 enum isl_dim_type type, unsigned pos, const char *s);
610 __isl_give isl_dim *isl_local_space_get_dim(
611 __isl_keep isl_local_space *ls);
612 __isl_give isl_div *isl_local_space_get_div(
613 __isl_keep isl_local_space *ls, int pos);
614 __isl_give isl_local_space *isl_local_space_copy(
615 __isl_keep isl_local_space *ls);
616 void *isl_local_space_free(__isl_take isl_local_space *ls);
618 Two local spaces can be compared using
620 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
621 __isl_keep isl_local_space *ls2);
623 Local spaces can be created from other local spaces
624 using the following functions.
626 __isl_give isl_local_space *isl_local_space_from_domain(
627 __isl_take isl_local_space *ls);
628 __isl_give isl_local_space *isl_local_space_add_dims(
629 __isl_take isl_local_space *ls,
630 enum isl_dim_type type, unsigned n);
631 __isl_give isl_local_space *isl_local_space_insert_dims(
632 __isl_take isl_local_space *ls,
633 enum isl_dim_type type, unsigned first, unsigned n);
634 __isl_give isl_local_space *isl_local_space_drop_dims(
635 __isl_take isl_local_space *ls,
636 enum isl_dim_type type, unsigned first, unsigned n);
638 =head2 Input and Output
640 C<isl> supports its own input/output format, which is similar
641 to the C<Omega> format, but also supports the C<PolyLib> format
646 The C<isl> format is similar to that of C<Omega>, but has a different
647 syntax for describing the parameters and allows for the definition
648 of an existentially quantified variable as the integer division
649 of an affine expression.
650 For example, the set of integers C<i> between C<0> and C<n>
651 such that C<i % 10 <= 6> can be described as
653 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
656 A set or relation can have several disjuncts, separated
657 by the keyword C<or>. Each disjunct is either a conjunction
658 of constraints or a projection (C<exists>) of a conjunction
659 of constraints. The constraints are separated by the keyword
662 =head3 C<PolyLib> format
664 If the represented set is a union, then the first line
665 contains a single number representing the number of disjuncts.
666 Otherwise, a line containing the number C<1> is optional.
668 Each disjunct is represented by a matrix of constraints.
669 The first line contains two numbers representing
670 the number of rows and columns,
671 where the number of rows is equal to the number of constraints
672 and the number of columns is equal to two plus the number of variables.
673 The following lines contain the actual rows of the constraint matrix.
674 In each row, the first column indicates whether the constraint
675 is an equality (C<0>) or inequality (C<1>). The final column
676 corresponds to the constant term.
678 If the set is parametric, then the coefficients of the parameters
679 appear in the last columns before the constant column.
680 The coefficients of any existentially quantified variables appear
681 between those of the set variables and those of the parameters.
683 =head3 Extended C<PolyLib> format
685 The extended C<PolyLib> format is nearly identical to the
686 C<PolyLib> format. The only difference is that the line
687 containing the number of rows and columns of a constraint matrix
688 also contains four additional numbers:
689 the number of output dimensions, the number of input dimensions,
690 the number of local dimensions (i.e., the number of existentially
691 quantified variables) and the number of parameters.
692 For sets, the number of ``output'' dimensions is equal
693 to the number of set dimensions, while the number of ``input''
699 __isl_give isl_basic_set *isl_basic_set_read_from_file(
700 isl_ctx *ctx, FILE *input, int nparam);
701 __isl_give isl_basic_set *isl_basic_set_read_from_str(
702 isl_ctx *ctx, const char *str, int nparam);
703 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
704 FILE *input, int nparam);
705 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
706 const char *str, int nparam);
709 __isl_give isl_basic_map *isl_basic_map_read_from_file(
710 isl_ctx *ctx, FILE *input, int nparam);
711 __isl_give isl_basic_map *isl_basic_map_read_from_str(
712 isl_ctx *ctx, const char *str, int nparam);
713 __isl_give isl_map *isl_map_read_from_file(
714 struct isl_ctx *ctx, FILE *input, int nparam);
715 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
716 const char *str, int nparam);
718 #include <isl/union_set.h>
719 __isl_give isl_union_set *isl_union_set_read_from_file(
720 isl_ctx *ctx, FILE *input);
721 __isl_give isl_union_set *isl_union_set_read_from_str(
722 struct isl_ctx *ctx, const char *str);
724 #include <isl/union_map.h>
725 __isl_give isl_union_map *isl_union_map_read_from_file(
726 isl_ctx *ctx, FILE *input);
727 __isl_give isl_union_map *isl_union_map_read_from_str(
728 struct isl_ctx *ctx, const char *str);
730 The input format is autodetected and may be either the C<PolyLib> format
731 or the C<isl> format.
732 C<nparam> specifies how many of the final columns in
733 the C<PolyLib> format correspond to parameters.
734 If input is given in the C<isl> format, then the number
735 of parameters needs to be equal to C<nparam>.
736 If C<nparam> is negative, then any number of parameters
737 is accepted in the C<isl> format and zero parameters
738 are assumed in the C<PolyLib> format.
742 Before anything can be printed, an C<isl_printer> needs to
745 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
747 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
748 void isl_printer_free(__isl_take isl_printer *printer);
749 __isl_give char *isl_printer_get_str(
750 __isl_keep isl_printer *printer);
752 The behavior of the printer can be modified in various ways
754 __isl_give isl_printer *isl_printer_set_output_format(
755 __isl_take isl_printer *p, int output_format);
756 __isl_give isl_printer *isl_printer_set_indent(
757 __isl_take isl_printer *p, int indent);
758 __isl_give isl_printer *isl_printer_indent(
759 __isl_take isl_printer *p, int indent);
760 __isl_give isl_printer *isl_printer_set_prefix(
761 __isl_take isl_printer *p, const char *prefix);
762 __isl_give isl_printer *isl_printer_set_suffix(
763 __isl_take isl_printer *p, const char *suffix);
765 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
766 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
767 and defaults to C<ISL_FORMAT_ISL>.
768 Each line in the output is indented by C<indent> (set by
769 C<isl_printer_set_indent>) spaces
770 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
771 In the C<PolyLib> format output,
772 the coefficients of the existentially quantified variables
773 appear between those of the set variables and those
775 The function C<isl_printer_indent> increases the indentation
776 by the specified amount (which may be negative).
778 To actually print something, use
781 __isl_give isl_printer *isl_printer_print_basic_set(
782 __isl_take isl_printer *printer,
783 __isl_keep isl_basic_set *bset);
784 __isl_give isl_printer *isl_printer_print_set(
785 __isl_take isl_printer *printer,
786 __isl_keep isl_set *set);
789 __isl_give isl_printer *isl_printer_print_basic_map(
790 __isl_take isl_printer *printer,
791 __isl_keep isl_basic_map *bmap);
792 __isl_give isl_printer *isl_printer_print_map(
793 __isl_take isl_printer *printer,
794 __isl_keep isl_map *map);
796 #include <isl/union_set.h>
797 __isl_give isl_printer *isl_printer_print_union_set(
798 __isl_take isl_printer *p,
799 __isl_keep isl_union_set *uset);
801 #include <isl/union_map.h>
802 __isl_give isl_printer *isl_printer_print_union_map(
803 __isl_take isl_printer *p,
804 __isl_keep isl_union_map *umap);
806 When called on a file printer, the following function flushes
807 the file. When called on a string printer, the buffer is cleared.
809 __isl_give isl_printer *isl_printer_flush(
810 __isl_take isl_printer *p);
812 =head2 Creating New Sets and Relations
814 C<isl> has functions for creating some standard sets and relations.
818 =item * Empty sets and relations
820 __isl_give isl_basic_set *isl_basic_set_empty(
821 __isl_take isl_dim *dim);
822 __isl_give isl_basic_map *isl_basic_map_empty(
823 __isl_take isl_dim *dim);
824 __isl_give isl_set *isl_set_empty(
825 __isl_take isl_dim *dim);
826 __isl_give isl_map *isl_map_empty(
827 __isl_take isl_dim *dim);
828 __isl_give isl_union_set *isl_union_set_empty(
829 __isl_take isl_dim *dim);
830 __isl_give isl_union_map *isl_union_map_empty(
831 __isl_take isl_dim *dim);
833 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
834 is only used to specify the parameters.
836 =item * Universe sets and relations
838 __isl_give isl_basic_set *isl_basic_set_universe(
839 __isl_take isl_dim *dim);
840 __isl_give isl_basic_map *isl_basic_map_universe(
841 __isl_take isl_dim *dim);
842 __isl_give isl_set *isl_set_universe(
843 __isl_take isl_dim *dim);
844 __isl_give isl_map *isl_map_universe(
845 __isl_take isl_dim *dim);
846 __isl_give isl_union_set *isl_union_set_universe(
847 __isl_take isl_union_set *uset);
848 __isl_give isl_union_map *isl_union_map_universe(
849 __isl_take isl_union_map *umap);
851 The sets and relations constructed by the functions above
852 contain all integer values, while those constructed by the
853 functions below only contain non-negative values.
855 __isl_give isl_basic_set *isl_basic_set_nat_universe(
856 __isl_take isl_dim *dim);
857 __isl_give isl_basic_map *isl_basic_map_nat_universe(
858 __isl_take isl_dim *dim);
859 __isl_give isl_set *isl_set_nat_universe(
860 __isl_take isl_dim *dim);
861 __isl_give isl_map *isl_map_nat_universe(
862 __isl_take isl_dim *dim);
864 =item * Identity relations
866 __isl_give isl_basic_map *isl_basic_map_identity(
867 __isl_take isl_dim *dim);
868 __isl_give isl_map *isl_map_identity(
869 __isl_take isl_dim *dim);
871 The number of input and output dimensions in C<dim> needs
874 =item * Lexicographic order
876 __isl_give isl_map *isl_map_lex_lt(
877 __isl_take isl_dim *set_dim);
878 __isl_give isl_map *isl_map_lex_le(
879 __isl_take isl_dim *set_dim);
880 __isl_give isl_map *isl_map_lex_gt(
881 __isl_take isl_dim *set_dim);
882 __isl_give isl_map *isl_map_lex_ge(
883 __isl_take isl_dim *set_dim);
884 __isl_give isl_map *isl_map_lex_lt_first(
885 __isl_take isl_dim *dim, unsigned n);
886 __isl_give isl_map *isl_map_lex_le_first(
887 __isl_take isl_dim *dim, unsigned n);
888 __isl_give isl_map *isl_map_lex_gt_first(
889 __isl_take isl_dim *dim, unsigned n);
890 __isl_give isl_map *isl_map_lex_ge_first(
891 __isl_take isl_dim *dim, unsigned n);
893 The first four functions take a dimension specification for a B<set>
894 and return relations that express that the elements in the domain
895 are lexicographically less
896 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
897 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
898 than the elements in the range.
899 The last four functions take a dimension specification for a map
900 and return relations that express that the first C<n> dimensions
901 in the domain are lexicographically less
902 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
903 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
904 than the first C<n> dimensions in the range.
908 A basic set or relation can be converted to a set or relation
909 using the following functions.
911 __isl_give isl_set *isl_set_from_basic_set(
912 __isl_take isl_basic_set *bset);
913 __isl_give isl_map *isl_map_from_basic_map(
914 __isl_take isl_basic_map *bmap);
916 Sets and relations can be converted to union sets and relations
917 using the following functions.
919 __isl_give isl_union_map *isl_union_map_from_map(
920 __isl_take isl_map *map);
921 __isl_give isl_union_set *isl_union_set_from_set(
922 __isl_take isl_set *set);
924 Sets and relations can be copied and freed again using the following
927 __isl_give isl_basic_set *isl_basic_set_copy(
928 __isl_keep isl_basic_set *bset);
929 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
930 __isl_give isl_union_set *isl_union_set_copy(
931 __isl_keep isl_union_set *uset);
932 __isl_give isl_basic_map *isl_basic_map_copy(
933 __isl_keep isl_basic_map *bmap);
934 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
935 __isl_give isl_union_map *isl_union_map_copy(
936 __isl_keep isl_union_map *umap);
937 void isl_basic_set_free(__isl_take isl_basic_set *bset);
938 void isl_set_free(__isl_take isl_set *set);
939 void isl_union_set_free(__isl_take isl_union_set *uset);
940 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
941 void isl_map_free(__isl_take isl_map *map);
942 void isl_union_map_free(__isl_take isl_union_map *umap);
944 Other sets and relations can be constructed by starting
945 from a universe set or relation, adding equality and/or
946 inequality constraints and then projecting out the
947 existentially quantified variables, if any.
948 Constraints can be constructed, manipulated and
949 added to (basic) sets and relations using the following functions.
951 #include <isl/constraint.h>
952 __isl_give isl_constraint *isl_equality_alloc(
953 __isl_take isl_dim *dim);
954 __isl_give isl_constraint *isl_inequality_alloc(
955 __isl_take isl_dim *dim);
956 void isl_constraint_set_constant(
957 __isl_keep isl_constraint *constraint, isl_int v);
958 void isl_constraint_set_coefficient(
959 __isl_keep isl_constraint *constraint,
960 enum isl_dim_type type, int pos, isl_int v);
961 __isl_give isl_basic_map *isl_basic_map_add_constraint(
962 __isl_take isl_basic_map *bmap,
963 __isl_take isl_constraint *constraint);
964 __isl_give isl_basic_set *isl_basic_set_add_constraint(
965 __isl_take isl_basic_set *bset,
966 __isl_take isl_constraint *constraint);
967 __isl_give isl_map *isl_map_add_constraint(
968 __isl_take isl_map *map,
969 __isl_take isl_constraint *constraint);
970 __isl_give isl_set *isl_set_add_constraint(
971 __isl_take isl_set *set,
972 __isl_take isl_constraint *constraint);
974 For example, to create a set containing the even integers
975 between 10 and 42, you would use the following code.
979 struct isl_constraint *c;
980 struct isl_basic_set *bset;
983 dim = isl_dim_set_alloc(ctx, 0, 2);
984 bset = isl_basic_set_universe(isl_dim_copy(dim));
986 c = isl_equality_alloc(isl_dim_copy(dim));
987 isl_int_set_si(v, -1);
988 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
989 isl_int_set_si(v, 2);
990 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
991 bset = isl_basic_set_add_constraint(bset, c);
993 c = isl_inequality_alloc(isl_dim_copy(dim));
994 isl_int_set_si(v, -10);
995 isl_constraint_set_constant(c, v);
996 isl_int_set_si(v, 1);
997 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
998 bset = isl_basic_set_add_constraint(bset, c);
1000 c = isl_inequality_alloc(dim);
1001 isl_int_set_si(v, 42);
1002 isl_constraint_set_constant(c, v);
1003 isl_int_set_si(v, -1);
1004 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
1005 bset = isl_basic_set_add_constraint(bset, c);
1007 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1013 struct isl_basic_set *bset;
1014 bset = isl_basic_set_read_from_str(ctx,
1015 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
1017 A basic set or relation can also be constructed from two matrices
1018 describing the equalities and the inequalities.
1020 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1021 __isl_take isl_dim *dim,
1022 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1023 enum isl_dim_type c1,
1024 enum isl_dim_type c2, enum isl_dim_type c3,
1025 enum isl_dim_type c4);
1026 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1027 __isl_take isl_dim *dim,
1028 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1029 enum isl_dim_type c1,
1030 enum isl_dim_type c2, enum isl_dim_type c3,
1031 enum isl_dim_type c4, enum isl_dim_type c5);
1033 The C<isl_dim_type> arguments indicate the order in which
1034 different kinds of variables appear in the input matrices
1035 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1036 C<isl_dim_set> and C<isl_dim_div> for sets and
1037 of C<isl_dim_cst>, C<isl_dim_param>,
1038 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1040 A (basic) relation can also be constructed from a (piecewise) affine expression
1041 or a list of affine expressions (See L<"Piecewise Quasi Affine Expressions">).
1043 __isl_give isl_basic_map *isl_basic_map_from_aff(
1044 __isl_take isl_aff *aff);
1045 __isl_give isl_map *isl_map_from_pw_aff(
1046 __isl_take isl_pw_aff *pwaff);
1047 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1048 __isl_take isl_dim *domain_dim,
1049 __isl_take isl_aff_list *list);
1051 The C<domain_dim> argument describes the domain of the resulting
1052 basic relation. It is required because the C<list> may consist
1053 of zero affine expressions.
1055 =head2 Inspecting Sets and Relations
1057 Usually, the user should not have to care about the actual constraints
1058 of the sets and maps, but should instead apply the abstract operations
1059 explained in the following sections.
1060 Occasionally, however, it may be required to inspect the individual
1061 coefficients of the constraints. This section explains how to do so.
1062 In these cases, it may also be useful to have C<isl> compute
1063 an explicit representation of the existentially quantified variables.
1065 __isl_give isl_set *isl_set_compute_divs(
1066 __isl_take isl_set *set);
1067 __isl_give isl_map *isl_map_compute_divs(
1068 __isl_take isl_map *map);
1069 __isl_give isl_union_set *isl_union_set_compute_divs(
1070 __isl_take isl_union_set *uset);
1071 __isl_give isl_union_map *isl_union_map_compute_divs(
1072 __isl_take isl_union_map *umap);
1074 This explicit representation defines the existentially quantified
1075 variables as integer divisions of the other variables, possibly
1076 including earlier existentially quantified variables.
1077 An explicitly represented existentially quantified variable therefore
1078 has a unique value when the values of the other variables are known.
1079 If, furthermore, the same existentials, i.e., existentials
1080 with the same explicit representations, should appear in the
1081 same order in each of the disjuncts of a set or map, then the user should call
1082 either of the following functions.
1084 __isl_give isl_set *isl_set_align_divs(
1085 __isl_take isl_set *set);
1086 __isl_give isl_map *isl_map_align_divs(
1087 __isl_take isl_map *map);
1089 Alternatively, the existentially quantified variables can be removed
1090 using the following functions, which compute an overapproximation.
1092 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1093 __isl_take isl_basic_set *bset);
1094 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1095 __isl_take isl_basic_map *bmap);
1096 __isl_give isl_set *isl_set_remove_divs(
1097 __isl_take isl_set *set);
1098 __isl_give isl_map *isl_map_remove_divs(
1099 __isl_take isl_map *map);
1101 To iterate over all the sets or maps in a union set or map, use
1103 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1104 int (*fn)(__isl_take isl_set *set, void *user),
1106 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1107 int (*fn)(__isl_take isl_map *map, void *user),
1110 The number of sets or maps in a union set or map can be obtained
1113 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1114 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1116 To extract the set or map from a union with a given dimension
1119 __isl_give isl_set *isl_union_set_extract_set(
1120 __isl_keep isl_union_set *uset,
1121 __isl_take isl_dim *dim);
1122 __isl_give isl_map *isl_union_map_extract_map(
1123 __isl_keep isl_union_map *umap,
1124 __isl_take isl_dim *dim);
1126 To iterate over all the basic sets or maps in a set or map, use
1128 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1129 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1131 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1132 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1135 The callback function C<fn> should return 0 if successful and
1136 -1 if an error occurs. In the latter case, or if any other error
1137 occurs, the above functions will return -1.
1139 It should be noted that C<isl> does not guarantee that
1140 the basic sets or maps passed to C<fn> are disjoint.
1141 If this is required, then the user should call one of
1142 the following functions first.
1144 __isl_give isl_set *isl_set_make_disjoint(
1145 __isl_take isl_set *set);
1146 __isl_give isl_map *isl_map_make_disjoint(
1147 __isl_take isl_map *map);
1149 The number of basic sets in a set can be obtained
1152 int isl_set_n_basic_set(__isl_keep isl_set *set);
1154 To iterate over the constraints of a basic set or map, use
1156 #include <isl/constraint.h>
1158 int isl_basic_map_foreach_constraint(
1159 __isl_keep isl_basic_map *bmap,
1160 int (*fn)(__isl_take isl_constraint *c, void *user),
1162 void isl_constraint_free(struct isl_constraint *c);
1164 Again, the callback function C<fn> should return 0 if successful and
1165 -1 if an error occurs. In the latter case, or if any other error
1166 occurs, the above functions will return -1.
1167 The constraint C<c> represents either an equality or an inequality.
1168 Use the following function to find out whether a constraint
1169 represents an equality. If not, it represents an inequality.
1171 int isl_constraint_is_equality(
1172 __isl_keep isl_constraint *constraint);
1174 The coefficients of the constraints can be inspected using
1175 the following functions.
1177 void isl_constraint_get_constant(
1178 __isl_keep isl_constraint *constraint, isl_int *v);
1179 void isl_constraint_get_coefficient(
1180 __isl_keep isl_constraint *constraint,
1181 enum isl_dim_type type, int pos, isl_int *v);
1182 int isl_constraint_involves_dims(
1183 __isl_keep isl_constraint *constraint,
1184 enum isl_dim_type type, unsigned first, unsigned n);
1186 The explicit representations of the existentially quantified
1187 variables can be inspected using the following functions.
1188 Note that the user is only allowed to use these functions
1189 if the inspected set or map is the result of a call
1190 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1192 __isl_give isl_div *isl_constraint_div(
1193 __isl_keep isl_constraint *constraint, int pos);
1194 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1195 void isl_div_get_constant(__isl_keep isl_div *div,
1197 void isl_div_get_denominator(__isl_keep isl_div *div,
1199 void isl_div_get_coefficient(__isl_keep isl_div *div,
1200 enum isl_dim_type type, int pos, isl_int *v);
1202 To obtain the constraints of a basic set or map in matrix
1203 form, use the following functions.
1205 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1206 __isl_keep isl_basic_set *bset,
1207 enum isl_dim_type c1, enum isl_dim_type c2,
1208 enum isl_dim_type c3, enum isl_dim_type c4);
1209 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1210 __isl_keep isl_basic_set *bset,
1211 enum isl_dim_type c1, enum isl_dim_type c2,
1212 enum isl_dim_type c3, enum isl_dim_type c4);
1213 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1214 __isl_keep isl_basic_map *bmap,
1215 enum isl_dim_type c1,
1216 enum isl_dim_type c2, enum isl_dim_type c3,
1217 enum isl_dim_type c4, enum isl_dim_type c5);
1218 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1219 __isl_keep isl_basic_map *bmap,
1220 enum isl_dim_type c1,
1221 enum isl_dim_type c2, enum isl_dim_type c3,
1222 enum isl_dim_type c4, enum isl_dim_type c5);
1224 The C<isl_dim_type> arguments dictate the order in which
1225 different kinds of variables appear in the resulting matrix
1226 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1227 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1229 The names of the domain and range spaces of a set or relation can be
1230 read off or set using the following functions.
1232 const char *isl_basic_set_get_tuple_name(
1233 __isl_keep isl_basic_set *bset);
1234 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1235 __isl_take isl_basic_set *set, const char *s);
1236 const char *isl_set_get_tuple_name(
1237 __isl_keep isl_set *set);
1238 const char *isl_basic_map_get_tuple_name(
1239 __isl_keep isl_basic_map *bmap,
1240 enum isl_dim_type type);
1241 const char *isl_map_get_tuple_name(
1242 __isl_keep isl_map *map,
1243 enum isl_dim_type type);
1245 As with C<isl_dim_get_tuple_name>, the value returned points to
1246 an internal data structure.
1247 The names of individual dimensions can be read off using
1248 the following functions.
1250 const char *isl_constraint_get_dim_name(
1251 __isl_keep isl_constraint *constraint,
1252 enum isl_dim_type type, unsigned pos);
1253 const char *isl_basic_set_get_dim_name(
1254 __isl_keep isl_basic_set *bset,
1255 enum isl_dim_type type, unsigned pos);
1256 const char *isl_set_get_dim_name(
1257 __isl_keep isl_set *set,
1258 enum isl_dim_type type, unsigned pos);
1259 const char *isl_basic_map_get_dim_name(
1260 __isl_keep isl_basic_map *bmap,
1261 enum isl_dim_type type, unsigned pos);
1262 const char *isl_map_get_dim_name(
1263 __isl_keep isl_map *map,
1264 enum isl_dim_type type, unsigned pos);
1266 These functions are mostly useful to obtain the names
1271 =head3 Unary Properties
1277 The following functions test whether the given set or relation
1278 contains any integer points. The ``plain'' variants do not perform
1279 any computations, but simply check if the given set or relation
1280 is already known to be empty.
1282 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1283 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1284 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1285 int isl_set_is_empty(__isl_keep isl_set *set);
1286 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1287 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1288 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1289 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1290 int isl_map_is_empty(__isl_keep isl_map *map);
1291 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1293 =item * Universality
1295 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1296 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1297 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1299 =item * Single-valuedness
1301 int isl_map_is_single_valued(__isl_keep isl_map *map);
1302 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1306 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1307 int isl_map_is_injective(__isl_keep isl_map *map);
1308 int isl_union_map_plain_is_injective(
1309 __isl_keep isl_union_map *umap);
1310 int isl_union_map_is_injective(
1311 __isl_keep isl_union_map *umap);
1315 int isl_map_is_bijective(__isl_keep isl_map *map);
1316 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1320 The following functions check whether the domain of the given
1321 (basic) set is a wrapped relation.
1323 int isl_basic_set_is_wrapping(
1324 __isl_keep isl_basic_set *bset);
1325 int isl_set_is_wrapping(__isl_keep isl_set *set);
1327 =item * Internal Product
1329 int isl_basic_map_can_zip(
1330 __isl_keep isl_basic_map *bmap);
1331 int isl_map_can_zip(__isl_keep isl_map *map);
1333 Check whether the product of domain and range of the given relation
1335 i.e., whether both domain and range are nested relations.
1339 =head3 Binary Properties
1345 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1346 __isl_keep isl_set *set2);
1347 int isl_set_is_equal(__isl_keep isl_set *set1,
1348 __isl_keep isl_set *set2);
1349 int isl_union_set_is_equal(
1350 __isl_keep isl_union_set *uset1,
1351 __isl_keep isl_union_set *uset2);
1352 int isl_basic_map_is_equal(
1353 __isl_keep isl_basic_map *bmap1,
1354 __isl_keep isl_basic_map *bmap2);
1355 int isl_map_is_equal(__isl_keep isl_map *map1,
1356 __isl_keep isl_map *map2);
1357 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1358 __isl_keep isl_map *map2);
1359 int isl_union_map_is_equal(
1360 __isl_keep isl_union_map *umap1,
1361 __isl_keep isl_union_map *umap2);
1363 =item * Disjointness
1365 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1366 __isl_keep isl_set *set2);
1370 int isl_set_is_subset(__isl_keep isl_set *set1,
1371 __isl_keep isl_set *set2);
1372 int isl_set_is_strict_subset(
1373 __isl_keep isl_set *set1,
1374 __isl_keep isl_set *set2);
1375 int isl_union_set_is_subset(
1376 __isl_keep isl_union_set *uset1,
1377 __isl_keep isl_union_set *uset2);
1378 int isl_union_set_is_strict_subset(
1379 __isl_keep isl_union_set *uset1,
1380 __isl_keep isl_union_set *uset2);
1381 int isl_basic_map_is_subset(
1382 __isl_keep isl_basic_map *bmap1,
1383 __isl_keep isl_basic_map *bmap2);
1384 int isl_basic_map_is_strict_subset(
1385 __isl_keep isl_basic_map *bmap1,
1386 __isl_keep isl_basic_map *bmap2);
1387 int isl_map_is_subset(
1388 __isl_keep isl_map *map1,
1389 __isl_keep isl_map *map2);
1390 int isl_map_is_strict_subset(
1391 __isl_keep isl_map *map1,
1392 __isl_keep isl_map *map2);
1393 int isl_union_map_is_subset(
1394 __isl_keep isl_union_map *umap1,
1395 __isl_keep isl_union_map *umap2);
1396 int isl_union_map_is_strict_subset(
1397 __isl_keep isl_union_map *umap1,
1398 __isl_keep isl_union_map *umap2);
1402 =head2 Unary Operations
1408 __isl_give isl_set *isl_set_complement(
1409 __isl_take isl_set *set);
1413 __isl_give isl_basic_map *isl_basic_map_reverse(
1414 __isl_take isl_basic_map *bmap);
1415 __isl_give isl_map *isl_map_reverse(
1416 __isl_take isl_map *map);
1417 __isl_give isl_union_map *isl_union_map_reverse(
1418 __isl_take isl_union_map *umap);
1422 __isl_give isl_basic_set *isl_basic_set_project_out(
1423 __isl_take isl_basic_set *bset,
1424 enum isl_dim_type type, unsigned first, unsigned n);
1425 __isl_give isl_basic_map *isl_basic_map_project_out(
1426 __isl_take isl_basic_map *bmap,
1427 enum isl_dim_type type, unsigned first, unsigned n);
1428 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1429 enum isl_dim_type type, unsigned first, unsigned n);
1430 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1431 enum isl_dim_type type, unsigned first, unsigned n);
1432 __isl_give isl_basic_set *isl_basic_map_domain(
1433 __isl_take isl_basic_map *bmap);
1434 __isl_give isl_basic_set *isl_basic_map_range(
1435 __isl_take isl_basic_map *bmap);
1436 __isl_give isl_set *isl_map_domain(
1437 __isl_take isl_map *bmap);
1438 __isl_give isl_set *isl_map_range(
1439 __isl_take isl_map *map);
1440 __isl_give isl_union_set *isl_union_map_domain(
1441 __isl_take isl_union_map *umap);
1442 __isl_give isl_union_set *isl_union_map_range(
1443 __isl_take isl_union_map *umap);
1445 __isl_give isl_basic_map *isl_basic_map_domain_map(
1446 __isl_take isl_basic_map *bmap);
1447 __isl_give isl_basic_map *isl_basic_map_range_map(
1448 __isl_take isl_basic_map *bmap);
1449 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1450 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1451 __isl_give isl_union_map *isl_union_map_domain_map(
1452 __isl_take isl_union_map *umap);
1453 __isl_give isl_union_map *isl_union_map_range_map(
1454 __isl_take isl_union_map *umap);
1456 The functions above construct a (basic, regular or union) relation
1457 that maps (a wrapped version of) the input relation to its domain or range.
1461 __isl_give isl_set *isl_set_eliminate(
1462 __isl_take isl_set *set, enum isl_dim_type type,
1463 unsigned first, unsigned n);
1465 Eliminate the coefficients for the given dimensions from the constraints,
1466 without removing the dimensions.
1470 __isl_give isl_basic_set *isl_basic_set_fix(
1471 __isl_take isl_basic_set *bset,
1472 enum isl_dim_type type, unsigned pos,
1474 __isl_give isl_basic_set *isl_basic_set_fix_si(
1475 __isl_take isl_basic_set *bset,
1476 enum isl_dim_type type, unsigned pos, int value);
1477 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1478 enum isl_dim_type type, unsigned pos,
1480 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1481 enum isl_dim_type type, unsigned pos, int value);
1482 __isl_give isl_basic_map *isl_basic_map_fix_si(
1483 __isl_take isl_basic_map *bmap,
1484 enum isl_dim_type type, unsigned pos, int value);
1485 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1486 enum isl_dim_type type, unsigned pos, int value);
1488 Intersect the set or relation with the hyperplane where the given
1489 dimension has the fixed given value.
1493 __isl_give isl_map *isl_set_identity(
1494 __isl_take isl_set *set);
1495 __isl_give isl_union_map *isl_union_set_identity(
1496 __isl_take isl_union_set *uset);
1498 Construct an identity relation on the given (union) set.
1502 __isl_give isl_basic_set *isl_basic_map_deltas(
1503 __isl_take isl_basic_map *bmap);
1504 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1505 __isl_give isl_union_set *isl_union_map_deltas(
1506 __isl_take isl_union_map *umap);
1508 These functions return a (basic) set containing the differences
1509 between image elements and corresponding domain elements in the input.
1511 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1512 __isl_take isl_basic_map *bmap);
1513 __isl_give isl_map *isl_map_deltas_map(
1514 __isl_take isl_map *map);
1515 __isl_give isl_union_map *isl_union_map_deltas_map(
1516 __isl_take isl_union_map *umap);
1518 The functions above construct a (basic, regular or union) relation
1519 that maps (a wrapped version of) the input relation to its delta set.
1523 Simplify the representation of a set or relation by trying
1524 to combine pairs of basic sets or relations into a single
1525 basic set or relation.
1527 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1528 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1529 __isl_give isl_union_set *isl_union_set_coalesce(
1530 __isl_take isl_union_set *uset);
1531 __isl_give isl_union_map *isl_union_map_coalesce(
1532 __isl_take isl_union_map *umap);
1534 =item * Detecting equalities
1536 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1537 __isl_take isl_basic_set *bset);
1538 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1539 __isl_take isl_basic_map *bmap);
1540 __isl_give isl_set *isl_set_detect_equalities(
1541 __isl_take isl_set *set);
1542 __isl_give isl_map *isl_map_detect_equalities(
1543 __isl_take isl_map *map);
1544 __isl_give isl_union_set *isl_union_set_detect_equalities(
1545 __isl_take isl_union_set *uset);
1546 __isl_give isl_union_map *isl_union_map_detect_equalities(
1547 __isl_take isl_union_map *umap);
1549 Simplify the representation of a set or relation by detecting implicit
1552 =item * Removing redundant constraints
1554 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1555 __isl_take isl_basic_set *bset);
1556 __isl_give isl_set *isl_set_remove_redundancies(
1557 __isl_take isl_set *set);
1558 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1559 __isl_take isl_basic_map *bmap);
1560 __isl_give isl_map *isl_map_remove_redundancies(
1561 __isl_take isl_map *map);
1565 __isl_give isl_basic_set *isl_set_convex_hull(
1566 __isl_take isl_set *set);
1567 __isl_give isl_basic_map *isl_map_convex_hull(
1568 __isl_take isl_map *map);
1570 If the input set or relation has any existentially quantified
1571 variables, then the result of these operations is currently undefined.
1575 __isl_give isl_basic_set *isl_set_simple_hull(
1576 __isl_take isl_set *set);
1577 __isl_give isl_basic_map *isl_map_simple_hull(
1578 __isl_take isl_map *map);
1579 __isl_give isl_union_map *isl_union_map_simple_hull(
1580 __isl_take isl_union_map *umap);
1582 These functions compute a single basic set or relation
1583 that contains the whole input set or relation.
1584 In particular, the output is described by translates
1585 of the constraints describing the basic sets or relations in the input.
1589 (See \autoref{s:simple hull}.)
1595 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1596 __isl_take isl_basic_set *bset);
1597 __isl_give isl_basic_set *isl_set_affine_hull(
1598 __isl_take isl_set *set);
1599 __isl_give isl_union_set *isl_union_set_affine_hull(
1600 __isl_take isl_union_set *uset);
1601 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1602 __isl_take isl_basic_map *bmap);
1603 __isl_give isl_basic_map *isl_map_affine_hull(
1604 __isl_take isl_map *map);
1605 __isl_give isl_union_map *isl_union_map_affine_hull(
1606 __isl_take isl_union_map *umap);
1608 In case of union sets and relations, the affine hull is computed
1611 =item * Polyhedral hull
1613 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1614 __isl_take isl_set *set);
1615 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1616 __isl_take isl_map *map);
1617 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1618 __isl_take isl_union_set *uset);
1619 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1620 __isl_take isl_union_map *umap);
1622 These functions compute a single basic set or relation
1623 not involving any existentially quantified variables
1624 that contains the whole input set or relation.
1625 In case of union sets and relations, the polyhedral hull is computed
1628 =item * Optimization
1630 #include <isl/ilp.h>
1631 enum isl_lp_result isl_basic_set_max(
1632 __isl_keep isl_basic_set *bset,
1633 __isl_keep isl_aff *obj, isl_int *opt)
1634 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
1635 __isl_keep isl_aff *obj, isl_int *opt);
1637 Compute the maximum of the integer affine expression C<obj>
1638 over the points in C<set>, returning the result in C<opt>.
1639 The return value may be one of C<isl_lp_error>,
1640 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
1642 =item * Parametric optimization
1644 __isl_give isl_pw_aff *isl_set_dim_max(
1645 __isl_take isl_set *set, int pos);
1647 Compute the maximum of the given set dimension as a function of the
1648 parameters, but independently of the other set dimensions.
1649 For lexicographic optimization, see L<"Lexicographic Optimization">.
1653 The following functions compute either the set of (rational) coefficient
1654 values of valid constraints for the given set or the set of (rational)
1655 values satisfying the constraints with coefficients from the given set.
1656 Internally, these two sets of functions perform essentially the
1657 same operations, except that the set of coefficients is assumed to
1658 be a cone, while the set of values may be any polyhedron.
1659 The current implementation is based on the Farkas lemma and
1660 Fourier-Motzkin elimination, but this may change or be made optional
1661 in future. In particular, future implementations may use different
1662 dualization algorithms or skip the elimination step.
1664 __isl_give isl_basic_set *isl_basic_set_coefficients(
1665 __isl_take isl_basic_set *bset);
1666 __isl_give isl_basic_set *isl_set_coefficients(
1667 __isl_take isl_set *set);
1668 __isl_give isl_union_set *isl_union_set_coefficients(
1669 __isl_take isl_union_set *bset);
1670 __isl_give isl_basic_set *isl_basic_set_solutions(
1671 __isl_take isl_basic_set *bset);
1672 __isl_give isl_basic_set *isl_set_solutions(
1673 __isl_take isl_set *set);
1674 __isl_give isl_union_set *isl_union_set_solutions(
1675 __isl_take isl_union_set *bset);
1679 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1681 __isl_give isl_union_map *isl_union_map_power(
1682 __isl_take isl_union_map *umap, int *exact);
1684 Compute a parametric representation for all positive powers I<k> of C<map>.
1685 The result maps I<k> to a nested relation corresponding to the
1686 I<k>th power of C<map>.
1687 The result may be an overapproximation. If the result is known to be exact,
1688 then C<*exact> is set to C<1>.
1690 =item * Transitive closure
1692 __isl_give isl_map *isl_map_transitive_closure(
1693 __isl_take isl_map *map, int *exact);
1694 __isl_give isl_union_map *isl_union_map_transitive_closure(
1695 __isl_take isl_union_map *umap, int *exact);
1697 Compute the transitive closure of C<map>.
1698 The result may be an overapproximation. If the result is known to be exact,
1699 then C<*exact> is set to C<1>.
1701 =item * Reaching path lengths
1703 __isl_give isl_map *isl_map_reaching_path_lengths(
1704 __isl_take isl_map *map, int *exact);
1706 Compute a relation that maps each element in the range of C<map>
1707 to the lengths of all paths composed of edges in C<map> that
1708 end up in the given element.
1709 The result may be an overapproximation. If the result is known to be exact,
1710 then C<*exact> is set to C<1>.
1711 To compute the I<maximal> path length, the resulting relation
1712 should be postprocessed by C<isl_map_lexmax>.
1713 In particular, if the input relation is a dependence relation
1714 (mapping sources to sinks), then the maximal path length corresponds
1715 to the free schedule.
1716 Note, however, that C<isl_map_lexmax> expects the maximum to be
1717 finite, so if the path lengths are unbounded (possibly due to
1718 the overapproximation), then you will get an error message.
1722 __isl_give isl_basic_set *isl_basic_map_wrap(
1723 __isl_take isl_basic_map *bmap);
1724 __isl_give isl_set *isl_map_wrap(
1725 __isl_take isl_map *map);
1726 __isl_give isl_union_set *isl_union_map_wrap(
1727 __isl_take isl_union_map *umap);
1728 __isl_give isl_basic_map *isl_basic_set_unwrap(
1729 __isl_take isl_basic_set *bset);
1730 __isl_give isl_map *isl_set_unwrap(
1731 __isl_take isl_set *set);
1732 __isl_give isl_union_map *isl_union_set_unwrap(
1733 __isl_take isl_union_set *uset);
1737 Remove any internal structure of domain (and range) of the given
1738 set or relation. If there is any such internal structure in the input,
1739 then the name of the space is also removed.
1741 __isl_give isl_basic_set *isl_basic_set_flatten(
1742 __isl_take isl_basic_set *bset);
1743 __isl_give isl_set *isl_set_flatten(
1744 __isl_take isl_set *set);
1745 __isl_give isl_basic_map *isl_basic_map_flatten_range(
1746 __isl_take isl_basic_map *bmap);
1747 __isl_give isl_map *isl_map_flatten_range(
1748 __isl_take isl_map *map);
1749 __isl_give isl_basic_map *isl_basic_map_flatten(
1750 __isl_take isl_basic_map *bmap);
1751 __isl_give isl_map *isl_map_flatten(
1752 __isl_take isl_map *map);
1754 __isl_give isl_map *isl_set_flatten_map(
1755 __isl_take isl_set *set);
1757 The function above constructs a relation
1758 that maps the input set to a flattened version of the set.
1762 Lift the input set to a space with extra dimensions corresponding
1763 to the existentially quantified variables in the input.
1764 In particular, the result lives in a wrapped map where the domain
1765 is the original space and the range corresponds to the original
1766 existentially quantified variables.
1768 __isl_give isl_basic_set *isl_basic_set_lift(
1769 __isl_take isl_basic_set *bset);
1770 __isl_give isl_set *isl_set_lift(
1771 __isl_take isl_set *set);
1772 __isl_give isl_union_set *isl_union_set_lift(
1773 __isl_take isl_union_set *uset);
1775 =item * Internal Product
1777 __isl_give isl_basic_map *isl_basic_map_zip(
1778 __isl_take isl_basic_map *bmap);
1779 __isl_give isl_map *isl_map_zip(
1780 __isl_take isl_map *map);
1781 __isl_give isl_union_map *isl_union_map_zip(
1782 __isl_take isl_union_map *umap);
1784 Given a relation with nested relations for domain and range,
1785 interchange the range of the domain with the domain of the range.
1787 =item * Aligning parameters
1789 __isl_give isl_set *isl_set_align_params(
1790 __isl_take isl_set *set,
1791 __isl_take isl_dim *model);
1792 __isl_give isl_map *isl_map_align_params(
1793 __isl_take isl_map *map,
1794 __isl_take isl_dim *model);
1796 Change the order of the parameters of the given set or relation
1797 such that the first parameters match those of C<model>.
1798 This may involve the introduction of extra parameters.
1799 All parameters need to be named.
1801 =item * Dimension manipulation
1803 __isl_give isl_set *isl_set_add_dims(
1804 __isl_take isl_set *set,
1805 enum isl_dim_type type, unsigned n);
1806 __isl_give isl_map *isl_map_add_dims(
1807 __isl_take isl_map *map,
1808 enum isl_dim_type type, unsigned n);
1810 It is usually not advisable to directly change the (input or output)
1811 space of a set or a relation as this removes the name and the internal
1812 structure of the space. However, the above functions can be useful
1813 to add new parameters, assuming
1814 C<isl_set_align_params> and C<isl_map_align_params>
1819 =head2 Binary Operations
1821 The two arguments of a binary operation not only need to live
1822 in the same C<isl_ctx>, they currently also need to have
1823 the same (number of) parameters.
1825 =head3 Basic Operations
1829 =item * Intersection
1831 __isl_give isl_basic_set *isl_basic_set_intersect(
1832 __isl_take isl_basic_set *bset1,
1833 __isl_take isl_basic_set *bset2);
1834 __isl_give isl_set *isl_set_intersect(
1835 __isl_take isl_set *set1,
1836 __isl_take isl_set *set2);
1837 __isl_give isl_union_set *isl_union_set_intersect(
1838 __isl_take isl_union_set *uset1,
1839 __isl_take isl_union_set *uset2);
1840 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1841 __isl_take isl_basic_map *bmap,
1842 __isl_take isl_basic_set *bset);
1843 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1844 __isl_take isl_basic_map *bmap,
1845 __isl_take isl_basic_set *bset);
1846 __isl_give isl_basic_map *isl_basic_map_intersect(
1847 __isl_take isl_basic_map *bmap1,
1848 __isl_take isl_basic_map *bmap2);
1849 __isl_give isl_map *isl_map_intersect_domain(
1850 __isl_take isl_map *map,
1851 __isl_take isl_set *set);
1852 __isl_give isl_map *isl_map_intersect_range(
1853 __isl_take isl_map *map,
1854 __isl_take isl_set *set);
1855 __isl_give isl_map *isl_map_intersect(
1856 __isl_take isl_map *map1,
1857 __isl_take isl_map *map2);
1858 __isl_give isl_union_map *isl_union_map_intersect_domain(
1859 __isl_take isl_union_map *umap,
1860 __isl_take isl_union_set *uset);
1861 __isl_give isl_union_map *isl_union_map_intersect_range(
1862 __isl_take isl_union_map *umap,
1863 __isl_take isl_union_set *uset);
1864 __isl_give isl_union_map *isl_union_map_intersect(
1865 __isl_take isl_union_map *umap1,
1866 __isl_take isl_union_map *umap2);
1870 __isl_give isl_set *isl_basic_set_union(
1871 __isl_take isl_basic_set *bset1,
1872 __isl_take isl_basic_set *bset2);
1873 __isl_give isl_map *isl_basic_map_union(
1874 __isl_take isl_basic_map *bmap1,
1875 __isl_take isl_basic_map *bmap2);
1876 __isl_give isl_set *isl_set_union(
1877 __isl_take isl_set *set1,
1878 __isl_take isl_set *set2);
1879 __isl_give isl_map *isl_map_union(
1880 __isl_take isl_map *map1,
1881 __isl_take isl_map *map2);
1882 __isl_give isl_union_set *isl_union_set_union(
1883 __isl_take isl_union_set *uset1,
1884 __isl_take isl_union_set *uset2);
1885 __isl_give isl_union_map *isl_union_map_union(
1886 __isl_take isl_union_map *umap1,
1887 __isl_take isl_union_map *umap2);
1889 =item * Set difference
1891 __isl_give isl_set *isl_set_subtract(
1892 __isl_take isl_set *set1,
1893 __isl_take isl_set *set2);
1894 __isl_give isl_map *isl_map_subtract(
1895 __isl_take isl_map *map1,
1896 __isl_take isl_map *map2);
1897 __isl_give isl_union_set *isl_union_set_subtract(
1898 __isl_take isl_union_set *uset1,
1899 __isl_take isl_union_set *uset2);
1900 __isl_give isl_union_map *isl_union_map_subtract(
1901 __isl_take isl_union_map *umap1,
1902 __isl_take isl_union_map *umap2);
1906 __isl_give isl_basic_set *isl_basic_set_apply(
1907 __isl_take isl_basic_set *bset,
1908 __isl_take isl_basic_map *bmap);
1909 __isl_give isl_set *isl_set_apply(
1910 __isl_take isl_set *set,
1911 __isl_take isl_map *map);
1912 __isl_give isl_union_set *isl_union_set_apply(
1913 __isl_take isl_union_set *uset,
1914 __isl_take isl_union_map *umap);
1915 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1916 __isl_take isl_basic_map *bmap1,
1917 __isl_take isl_basic_map *bmap2);
1918 __isl_give isl_basic_map *isl_basic_map_apply_range(
1919 __isl_take isl_basic_map *bmap1,
1920 __isl_take isl_basic_map *bmap2);
1921 __isl_give isl_map *isl_map_apply_domain(
1922 __isl_take isl_map *map1,
1923 __isl_take isl_map *map2);
1924 __isl_give isl_union_map *isl_union_map_apply_domain(
1925 __isl_take isl_union_map *umap1,
1926 __isl_take isl_union_map *umap2);
1927 __isl_give isl_map *isl_map_apply_range(
1928 __isl_take isl_map *map1,
1929 __isl_take isl_map *map2);
1930 __isl_give isl_union_map *isl_union_map_apply_range(
1931 __isl_take isl_union_map *umap1,
1932 __isl_take isl_union_map *umap2);
1934 =item * Cartesian Product
1936 __isl_give isl_set *isl_set_product(
1937 __isl_take isl_set *set1,
1938 __isl_take isl_set *set2);
1939 __isl_give isl_union_set *isl_union_set_product(
1940 __isl_take isl_union_set *uset1,
1941 __isl_take isl_union_set *uset2);
1942 __isl_give isl_basic_map *isl_basic_map_range_product(
1943 __isl_take isl_basic_map *bmap1,
1944 __isl_take isl_basic_map *bmap2);
1945 __isl_give isl_map *isl_map_range_product(
1946 __isl_take isl_map *map1,
1947 __isl_take isl_map *map2);
1948 __isl_give isl_union_map *isl_union_map_range_product(
1949 __isl_take isl_union_map *umap1,
1950 __isl_take isl_union_map *umap2);
1951 __isl_give isl_map *isl_map_product(
1952 __isl_take isl_map *map1,
1953 __isl_take isl_map *map2);
1954 __isl_give isl_union_map *isl_union_map_product(
1955 __isl_take isl_union_map *umap1,
1956 __isl_take isl_union_map *umap2);
1958 The above functions compute the cross product of the given
1959 sets or relations. The domains and ranges of the results
1960 are wrapped maps between domains and ranges of the inputs.
1961 To obtain a ``flat'' product, use the following functions
1964 __isl_give isl_basic_set *isl_basic_set_flat_product(
1965 __isl_take isl_basic_set *bset1,
1966 __isl_take isl_basic_set *bset2);
1967 __isl_give isl_set *isl_set_flat_product(
1968 __isl_take isl_set *set1,
1969 __isl_take isl_set *set2);
1970 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
1971 __isl_take isl_basic_map *bmap1,
1972 __isl_take isl_basic_map *bmap2);
1973 __isl_give isl_map *isl_map_flat_range_product(
1974 __isl_take isl_map *map1,
1975 __isl_take isl_map *map2);
1976 __isl_give isl_union_map *isl_union_map_flat_range_product(
1977 __isl_take isl_union_map *umap1,
1978 __isl_take isl_union_map *umap2);
1979 __isl_give isl_basic_map *isl_basic_map_flat_product(
1980 __isl_take isl_basic_map *bmap1,
1981 __isl_take isl_basic_map *bmap2);
1982 __isl_give isl_map *isl_map_flat_product(
1983 __isl_take isl_map *map1,
1984 __isl_take isl_map *map2);
1986 =item * Simplification
1988 __isl_give isl_basic_set *isl_basic_set_gist(
1989 __isl_take isl_basic_set *bset,
1990 __isl_take isl_basic_set *context);
1991 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1992 __isl_take isl_set *context);
1993 __isl_give isl_union_set *isl_union_set_gist(
1994 __isl_take isl_union_set *uset,
1995 __isl_take isl_union_set *context);
1996 __isl_give isl_basic_map *isl_basic_map_gist(
1997 __isl_take isl_basic_map *bmap,
1998 __isl_take isl_basic_map *context);
1999 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2000 __isl_take isl_map *context);
2001 __isl_give isl_union_map *isl_union_map_gist(
2002 __isl_take isl_union_map *umap,
2003 __isl_take isl_union_map *context);
2005 The gist operation returns a set or relation that has the
2006 same intersection with the context as the input set or relation.
2007 Any implicit equality in the intersection is made explicit in the result,
2008 while all inequalities that are redundant with respect to the intersection
2010 In case of union sets and relations, the gist operation is performed
2015 =head3 Lexicographic Optimization
2017 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2018 the following functions
2019 compute a set that contains the lexicographic minimum or maximum
2020 of the elements in C<set> (or C<bset>) for those values of the parameters
2021 that satisfy C<dom>.
2022 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2023 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2025 In other words, the union of the parameter values
2026 for which the result is non-empty and of C<*empty>
2029 __isl_give isl_set *isl_basic_set_partial_lexmin(
2030 __isl_take isl_basic_set *bset,
2031 __isl_take isl_basic_set *dom,
2032 __isl_give isl_set **empty);
2033 __isl_give isl_set *isl_basic_set_partial_lexmax(
2034 __isl_take isl_basic_set *bset,
2035 __isl_take isl_basic_set *dom,
2036 __isl_give isl_set **empty);
2037 __isl_give isl_set *isl_set_partial_lexmin(
2038 __isl_take isl_set *set, __isl_take isl_set *dom,
2039 __isl_give isl_set **empty);
2040 __isl_give isl_set *isl_set_partial_lexmax(
2041 __isl_take isl_set *set, __isl_take isl_set *dom,
2042 __isl_give isl_set **empty);
2044 Given a (basic) set C<set> (or C<bset>), the following functions simply
2045 return a set containing the lexicographic minimum or maximum
2046 of the elements in C<set> (or C<bset>).
2047 In case of union sets, the optimum is computed per space.
2049 __isl_give isl_set *isl_basic_set_lexmin(
2050 __isl_take isl_basic_set *bset);
2051 __isl_give isl_set *isl_basic_set_lexmax(
2052 __isl_take isl_basic_set *bset);
2053 __isl_give isl_set *isl_set_lexmin(
2054 __isl_take isl_set *set);
2055 __isl_give isl_set *isl_set_lexmax(
2056 __isl_take isl_set *set);
2057 __isl_give isl_union_set *isl_union_set_lexmin(
2058 __isl_take isl_union_set *uset);
2059 __isl_give isl_union_set *isl_union_set_lexmax(
2060 __isl_take isl_union_set *uset);
2062 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2063 the following functions
2064 compute a relation that maps each element of C<dom>
2065 to the single lexicographic minimum or maximum
2066 of the elements that are associated to that same
2067 element in C<map> (or C<bmap>).
2068 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2069 that contains the elements in C<dom> that do not map
2070 to any elements in C<map> (or C<bmap>).
2071 In other words, the union of the domain of the result and of C<*empty>
2074 __isl_give isl_map *isl_basic_map_partial_lexmax(
2075 __isl_take isl_basic_map *bmap,
2076 __isl_take isl_basic_set *dom,
2077 __isl_give isl_set **empty);
2078 __isl_give isl_map *isl_basic_map_partial_lexmin(
2079 __isl_take isl_basic_map *bmap,
2080 __isl_take isl_basic_set *dom,
2081 __isl_give isl_set **empty);
2082 __isl_give isl_map *isl_map_partial_lexmax(
2083 __isl_take isl_map *map, __isl_take isl_set *dom,
2084 __isl_give isl_set **empty);
2085 __isl_give isl_map *isl_map_partial_lexmin(
2086 __isl_take isl_map *map, __isl_take isl_set *dom,
2087 __isl_give isl_set **empty);
2089 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2090 return a map mapping each element in the domain of
2091 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2092 of all elements associated to that element.
2093 In case of union relations, the optimum is computed per space.
2095 __isl_give isl_map *isl_basic_map_lexmin(
2096 __isl_take isl_basic_map *bmap);
2097 __isl_give isl_map *isl_basic_map_lexmax(
2098 __isl_take isl_basic_map *bmap);
2099 __isl_give isl_map *isl_map_lexmin(
2100 __isl_take isl_map *map);
2101 __isl_give isl_map *isl_map_lexmax(
2102 __isl_take isl_map *map);
2103 __isl_give isl_union_map *isl_union_map_lexmin(
2104 __isl_take isl_union_map *umap);
2105 __isl_give isl_union_map *isl_union_map_lexmax(
2106 __isl_take isl_union_map *umap);
2110 Lists are defined over several element types, including
2111 C<isl_aff>, C<isl_basic_set> and C<isl_set>.
2112 Here we take lists of C<isl_set>s as an example.
2113 Lists can be created, copied and freed using the following functions.
2115 #include <isl/list.h>
2116 __isl_give isl_set_list *isl_set_list_alloc(
2117 isl_ctx *ctx, int n);
2118 __isl_give isl_set_list *isl_set_list_copy(
2119 __isl_keep isl_set_list *list);
2120 __isl_give isl_set_list *isl_set_list_add(
2121 __isl_take isl_set_list *list,
2122 __isl_take isl_set *el);
2123 void isl_set_list_free(__isl_take isl_set_list *list);
2125 C<isl_set_list_alloc> creates an empty list with a capacity for
2128 Lists can be inspected using the following functions.
2130 #include <isl/list.h>
2131 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2132 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2133 __isl_give struct isl_set *isl_set_list_get_set(
2134 __isl_keep isl_set_list *list, int index);
2135 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2136 int (*fn)(__isl_take struct isl_set *el, void *user),
2139 Lists can be printed using
2141 #include <isl/list.h>
2142 __isl_give isl_printer *isl_printer_print_set_list(
2143 __isl_take isl_printer *p,
2144 __isl_keep isl_set_list *list);
2148 Matrices can be created, copied and freed using the following functions.
2150 #include <isl/mat.h>
2151 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
2152 unsigned n_row, unsigned n_col);
2153 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2154 void isl_mat_free(__isl_take isl_mat *mat);
2156 Note that the elements of a newly created matrix may have arbitrary values.
2157 The elements can be changed and inspected using the following functions.
2159 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2160 int isl_mat_rows(__isl_keep isl_mat *mat);
2161 int isl_mat_cols(__isl_keep isl_mat *mat);
2162 int isl_mat_get_element(__isl_keep isl_mat *mat,
2163 int row, int col, isl_int *v);
2164 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2165 int row, int col, isl_int v);
2166 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2167 int row, int col, int v);
2169 C<isl_mat_get_element> will return a negative value if anything went wrong.
2170 In that case, the value of C<*v> is undefined.
2172 The following function can be used to compute the (right) inverse
2173 of a matrix, i.e., a matrix such that the product of the original
2174 and the inverse (in that order) is a multiple of the identity matrix.
2175 The input matrix is assumed to be of full row-rank.
2177 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2179 The following function can be used to compute the (right) kernel
2180 (or null space) of a matrix, i.e., a matrix such that the product of
2181 the original and the kernel (in that order) is the zero matrix.
2183 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2185 =head2 Piecewise Quasi Affine Expressions
2187 The zero quasi affine expression can be created using
2189 __isl_give isl_aff *isl_aff_zero(
2190 __isl_take isl_local_space *ls);
2192 An empty piecewise quasi affine expression (one with no cells)
2193 or a piecewise quasi affine expression with a single cell can
2194 be created using the following functions.
2196 #include <isl/aff.h>
2197 __isl_give isl_pw_aff *isl_pw_aff_empty(
2198 __isl_take isl_dim *dim);
2199 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2200 __isl_take isl_set *set, __isl_take isl_aff *aff);
2202 Quasi affine expressions can be copied and free using
2204 #include <isl/aff.h>
2205 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2206 void *isl_aff_free(__isl_take isl_aff *aff);
2208 __isl_give isl_pw_aff *isl_pw_aff_copy(
2209 __isl_keep isl_pw_aff *pwaff);
2210 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2212 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2213 using the following function. The constraint is required to have
2214 a non-zero coefficient for the specified dimension.
2216 #include <isl/constraint.h>
2217 __isl_give isl_aff *isl_constraint_get_bound(
2218 __isl_keep isl_constraint *constraint,
2219 enum isl_dim_type type, int pos);
2221 Conversely, an equality constraint equating
2222 the affine expression to zero or an inequality constraint enforcing
2223 the affine expression to be non-negative, can be constructed using
2225 __isl_give isl_constraint *isl_equality_from_aff(
2226 __isl_take isl_aff *aff);
2227 __isl_give isl_constraint *isl_inequality_from_aff(
2228 __isl_take isl_aff *aff);
2230 The expression can be inspected using
2232 #include <isl/aff.h>
2233 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2234 int isl_aff_dim(__isl_keep isl_aff *aff,
2235 enum isl_dim_type type);
2236 __isl_give isl_local_space *isl_aff_get_local_space(
2237 __isl_keep isl_aff *aff);
2238 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2239 enum isl_dim_type type, unsigned pos);
2240 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2242 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2243 enum isl_dim_type type, int pos, isl_int *v);
2244 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2246 __isl_give isl_div *isl_aff_get_div(
2247 __isl_keep isl_aff *aff, int pos);
2249 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2250 enum isl_dim_type type, unsigned first, unsigned n);
2251 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2252 enum isl_dim_type type, unsigned first, unsigned n);
2254 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2255 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2256 enum isl_dim_type type);
2257 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2259 It can be modified using
2261 #include <isl/aff.h>
2262 __isl_give isl_aff *isl_aff_set_dim_name(
2263 __isl_take isl_aff *aff, enum isl_dim_type type,
2264 unsigned pos, const char *s);
2265 __isl_give isl_aff *isl_aff_set_constant(
2266 __isl_take isl_aff *aff, isl_int v);
2267 __isl_give isl_aff *isl_aff_set_constant_si(
2268 __isl_take isl_aff *aff, int v);
2269 __isl_give isl_aff *isl_aff_set_coefficient(
2270 __isl_take isl_aff *aff,
2271 enum isl_dim_type type, int pos, isl_int v);
2272 __isl_give isl_aff *isl_aff_set_coefficient_si(
2273 __isl_take isl_aff *aff,
2274 enum isl_dim_type type, int pos, int v);
2275 __isl_give isl_aff *isl_aff_set_denominator(
2276 __isl_take isl_aff *aff, isl_int v);
2278 __isl_give isl_aff *isl_aff_add_constant(
2279 __isl_take isl_aff *aff, isl_int v);
2280 __isl_give isl_aff *isl_aff_add_constant_si(
2281 __isl_take isl_aff *aff, int v);
2282 __isl_give isl_aff *isl_aff_add_coefficient(
2283 __isl_take isl_aff *aff,
2284 enum isl_dim_type type, int pos, isl_int v);
2285 __isl_give isl_aff *isl_aff_add_coefficient_si(
2286 __isl_take isl_aff *aff,
2287 enum isl_dim_type type, int pos, int v);
2289 __isl_give isl_aff *isl_aff_insert_dims(
2290 __isl_take isl_aff *aff,
2291 enum isl_dim_type type, unsigned first, unsigned n);
2292 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2293 __isl_take isl_pw_aff *pwaff,
2294 enum isl_dim_type type, unsigned first, unsigned n);
2295 __isl_give isl_aff *isl_aff_add_dims(
2296 __isl_take isl_aff *aff,
2297 enum isl_dim_type type, unsigned n);
2298 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2299 __isl_take isl_pw_aff *pwaff,
2300 enum isl_dim_type type, unsigned n);
2301 __isl_give isl_aff *isl_aff_drop_dims(
2302 __isl_take isl_aff *aff,
2303 enum isl_dim_type type, unsigned first, unsigned n);
2304 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2305 __isl_take isl_pw_aff *pwaff,
2306 enum isl_dim_type type, unsigned first, unsigned n);
2308 Note that the C<set_constant> and C<set_coefficient> functions
2309 set the I<numerator> of the constant or coefficient, while
2310 C<add_constant> and C<add_coefficient> add an integer value to
2311 the possibly rational constant or coefficient.
2313 To check whether an affine expressions is obviously zero
2314 or obviously equal to some other affine expression, use
2316 #include <isl/aff.h>
2317 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2318 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2319 __isl_keep isl_aff *aff2);
2323 #include <isl/aff.h>
2324 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2325 __isl_take isl_aff *aff2);
2326 __isl_give isl_pw_aff *isl_pw_aff_add(
2327 __isl_take isl_pw_aff *pwaff1,
2328 __isl_take isl_pw_aff *pwaff2);
2329 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2330 __isl_take isl_aff *aff2);
2331 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2332 __isl_give isl_pw_aff *isl_pw_aff_neg(
2333 __isl_take isl_pw_aff *pwaff);
2334 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2335 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2336 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2338 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2340 __isl_give isl_aff *isl_aff_scale_down_ui(
2341 __isl_take isl_aff *aff, unsigned f);
2343 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2344 __isl_take isl_pw_aff *pwqp);
2346 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2347 __isl_take isl_set *context);
2348 __isl_give isl_pw_aff *isl_pw_aff_gist(
2349 __isl_take isl_pw_aff *pwaff,
2350 __isl_take isl_set *context);
2352 __isl_give isl_set *isl_pw_aff_domain(
2353 __isl_take isl_pw_aff *pwaff);
2355 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2356 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2358 The function C<isl_aff_ge_basic_set> returns a basic set
2359 containing those elements in the shared space
2360 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
2362 #include <isl/aff.h>
2363 __isl_give isl_pw_aff *isl_pw_aff_max(
2364 __isl_take isl_pw_aff *pwaff1,
2365 __isl_take isl_pw_aff *pwaff2);
2367 The function C<isl_pw_aff_max> computes a piecewise quasi-affine
2368 expression with a domain that is the union of those of C<pwaff1> and
2369 C<pwaff2> and such that on each cell, the quasi-affine expression is
2370 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
2371 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
2372 associated expression is the defined one.
2374 An expression can be printed using
2376 #include <isl/aff.h>
2377 __isl_give isl_printer *isl_printer_print_aff(
2378 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
2380 __isl_give isl_printer *isl_printer_print_pw_aff(
2381 __isl_take isl_printer *p,
2382 __isl_keep isl_pw_aff *pwaff);
2386 Points are elements of a set. They can be used to construct
2387 simple sets (boxes) or they can be used to represent the
2388 individual elements of a set.
2389 The zero point (the origin) can be created using
2391 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
2393 The coordinates of a point can be inspected, set and changed
2396 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
2397 enum isl_dim_type type, int pos, isl_int *v);
2398 __isl_give isl_point *isl_point_set_coordinate(
2399 __isl_take isl_point *pnt,
2400 enum isl_dim_type type, int pos, isl_int v);
2402 __isl_give isl_point *isl_point_add_ui(
2403 __isl_take isl_point *pnt,
2404 enum isl_dim_type type, int pos, unsigned val);
2405 __isl_give isl_point *isl_point_sub_ui(
2406 __isl_take isl_point *pnt,
2407 enum isl_dim_type type, int pos, unsigned val);
2409 Other properties can be obtained using
2411 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
2413 Points can be copied or freed using
2415 __isl_give isl_point *isl_point_copy(
2416 __isl_keep isl_point *pnt);
2417 void isl_point_free(__isl_take isl_point *pnt);
2419 A singleton set can be created from a point using
2421 __isl_give isl_basic_set *isl_basic_set_from_point(
2422 __isl_take isl_point *pnt);
2423 __isl_give isl_set *isl_set_from_point(
2424 __isl_take isl_point *pnt);
2426 and a box can be created from two opposite extremal points using
2428 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2429 __isl_take isl_point *pnt1,
2430 __isl_take isl_point *pnt2);
2431 __isl_give isl_set *isl_set_box_from_points(
2432 __isl_take isl_point *pnt1,
2433 __isl_take isl_point *pnt2);
2435 All elements of a B<bounded> (union) set can be enumerated using
2436 the following functions.
2438 int isl_set_foreach_point(__isl_keep isl_set *set,
2439 int (*fn)(__isl_take isl_point *pnt, void *user),
2441 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2442 int (*fn)(__isl_take isl_point *pnt, void *user),
2445 The function C<fn> is called for each integer point in
2446 C<set> with as second argument the last argument of
2447 the C<isl_set_foreach_point> call. The function C<fn>
2448 should return C<0> on success and C<-1> on failure.
2449 In the latter case, C<isl_set_foreach_point> will stop
2450 enumerating and return C<-1> as well.
2451 If the enumeration is performed successfully and to completion,
2452 then C<isl_set_foreach_point> returns C<0>.
2454 To obtain a single point of a (basic) set, use
2456 __isl_give isl_point *isl_basic_set_sample_point(
2457 __isl_take isl_basic_set *bset);
2458 __isl_give isl_point *isl_set_sample_point(
2459 __isl_take isl_set *set);
2461 If C<set> does not contain any (integer) points, then the
2462 resulting point will be ``void'', a property that can be
2465 int isl_point_is_void(__isl_keep isl_point *pnt);
2467 =head2 Piecewise Quasipolynomials
2469 A piecewise quasipolynomial is a particular kind of function that maps
2470 a parametric point to a rational value.
2471 More specifically, a quasipolynomial is a polynomial expression in greatest
2472 integer parts of affine expressions of parameters and variables.
2473 A piecewise quasipolynomial is a subdivision of a given parametric
2474 domain into disjoint cells with a quasipolynomial associated to
2475 each cell. The value of the piecewise quasipolynomial at a given
2476 point is the value of the quasipolynomial associated to the cell
2477 that contains the point. Outside of the union of cells,
2478 the value is assumed to be zero.
2479 For example, the piecewise quasipolynomial
2481 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2483 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2484 A given piecewise quasipolynomial has a fixed domain dimension.
2485 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2486 defined over different domains.
2487 Piecewise quasipolynomials are mainly used by the C<barvinok>
2488 library for representing the number of elements in a parametric set or map.
2489 For example, the piecewise quasipolynomial above represents
2490 the number of points in the map
2492 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2494 =head3 Printing (Piecewise) Quasipolynomials
2496 Quasipolynomials and piecewise quasipolynomials can be printed
2497 using the following functions.
2499 __isl_give isl_printer *isl_printer_print_qpolynomial(
2500 __isl_take isl_printer *p,
2501 __isl_keep isl_qpolynomial *qp);
2503 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2504 __isl_take isl_printer *p,
2505 __isl_keep isl_pw_qpolynomial *pwqp);
2507 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2508 __isl_take isl_printer *p,
2509 __isl_keep isl_union_pw_qpolynomial *upwqp);
2511 The output format of the printer
2512 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2513 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2515 In case of printing in C<ISL_FORMAT_C>, the user may want
2516 to set the names of all dimensions
2518 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2519 __isl_take isl_qpolynomial *qp,
2520 enum isl_dim_type type, unsigned pos,
2522 __isl_give isl_pw_qpolynomial *
2523 isl_pw_qpolynomial_set_dim_name(
2524 __isl_take isl_pw_qpolynomial *pwqp,
2525 enum isl_dim_type type, unsigned pos,
2528 =head3 Creating New (Piecewise) Quasipolynomials
2530 Some simple quasipolynomials can be created using the following functions.
2531 More complicated quasipolynomials can be created by applying
2532 operations such as addition and multiplication
2533 on the resulting quasipolynomials
2535 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2536 __isl_take isl_dim *dim);
2537 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2538 __isl_take isl_dim *dim);
2539 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2540 __isl_take isl_dim *dim);
2541 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2542 __isl_take isl_dim *dim);
2543 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2544 __isl_take isl_dim *dim);
2545 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2546 __isl_take isl_dim *dim,
2547 const isl_int n, const isl_int d);
2548 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2549 __isl_take isl_div *div);
2550 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2551 __isl_take isl_dim *dim,
2552 enum isl_dim_type type, unsigned pos);
2553 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2554 __isl_take isl_aff *aff);
2556 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2557 with a single cell can be created using the following functions.
2558 Multiple of these single cell piecewise quasipolynomials can
2559 be combined to create more complicated piecewise quasipolynomials.
2561 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2562 __isl_take isl_dim *dim);
2563 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2564 __isl_take isl_set *set,
2565 __isl_take isl_qpolynomial *qp);
2567 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2568 __isl_take isl_dim *dim);
2569 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2570 __isl_take isl_pw_qpolynomial *pwqp);
2571 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2572 __isl_take isl_union_pw_qpolynomial *upwqp,
2573 __isl_take isl_pw_qpolynomial *pwqp);
2575 Quasipolynomials can be copied and freed again using the following
2578 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2579 __isl_keep isl_qpolynomial *qp);
2580 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2582 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2583 __isl_keep isl_pw_qpolynomial *pwqp);
2584 void *isl_pw_qpolynomial_free(
2585 __isl_take isl_pw_qpolynomial *pwqp);
2587 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2588 __isl_keep isl_union_pw_qpolynomial *upwqp);
2589 void isl_union_pw_qpolynomial_free(
2590 __isl_take isl_union_pw_qpolynomial *upwqp);
2592 =head3 Inspecting (Piecewise) Quasipolynomials
2594 To iterate over all piecewise quasipolynomials in a union
2595 piecewise quasipolynomial, use the following function
2597 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2598 __isl_keep isl_union_pw_qpolynomial *upwqp,
2599 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2602 To extract the piecewise quasipolynomial from a union with a given dimension
2605 __isl_give isl_pw_qpolynomial *
2606 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2607 __isl_keep isl_union_pw_qpolynomial *upwqp,
2608 __isl_take isl_dim *dim);
2610 To iterate over the cells in a piecewise quasipolynomial,
2611 use either of the following two functions
2613 int isl_pw_qpolynomial_foreach_piece(
2614 __isl_keep isl_pw_qpolynomial *pwqp,
2615 int (*fn)(__isl_take isl_set *set,
2616 __isl_take isl_qpolynomial *qp,
2617 void *user), void *user);
2618 int isl_pw_qpolynomial_foreach_lifted_piece(
2619 __isl_keep isl_pw_qpolynomial *pwqp,
2620 int (*fn)(__isl_take isl_set *set,
2621 __isl_take isl_qpolynomial *qp,
2622 void *user), void *user);
2624 As usual, the function C<fn> should return C<0> on success
2625 and C<-1> on failure. The difference between
2626 C<isl_pw_qpolynomial_foreach_piece> and
2627 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2628 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2629 compute unique representations for all existentially quantified
2630 variables and then turn these existentially quantified variables
2631 into extra set variables, adapting the associated quasipolynomial
2632 accordingly. This means that the C<set> passed to C<fn>
2633 will not have any existentially quantified variables, but that
2634 the dimensions of the sets may be different for different
2635 invocations of C<fn>.
2637 To iterate over all terms in a quasipolynomial,
2640 int isl_qpolynomial_foreach_term(
2641 __isl_keep isl_qpolynomial *qp,
2642 int (*fn)(__isl_take isl_term *term,
2643 void *user), void *user);
2645 The terms themselves can be inspected and freed using
2648 unsigned isl_term_dim(__isl_keep isl_term *term,
2649 enum isl_dim_type type);
2650 void isl_term_get_num(__isl_keep isl_term *term,
2652 void isl_term_get_den(__isl_keep isl_term *term,
2654 int isl_term_get_exp(__isl_keep isl_term *term,
2655 enum isl_dim_type type, unsigned pos);
2656 __isl_give isl_div *isl_term_get_div(
2657 __isl_keep isl_term *term, unsigned pos);
2658 void isl_term_free(__isl_take isl_term *term);
2660 Each term is a product of parameters, set variables and
2661 integer divisions. The function C<isl_term_get_exp>
2662 returns the exponent of a given dimensions in the given term.
2663 The C<isl_int>s in the arguments of C<isl_term_get_num>
2664 and C<isl_term_get_den> need to have been initialized
2665 using C<isl_int_init> before calling these functions.
2667 =head3 Properties of (Piecewise) Quasipolynomials
2669 To check whether a quasipolynomial is actually a constant,
2670 use the following function.
2672 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2673 isl_int *n, isl_int *d);
2675 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2676 then the numerator and denominator of the constant
2677 are returned in C<*n> and C<*d>, respectively.
2679 =head3 Operations on (Piecewise) Quasipolynomials
2681 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
2682 __isl_take isl_qpolynomial *qp, isl_int v);
2683 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2684 __isl_take isl_qpolynomial *qp);
2685 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2686 __isl_take isl_qpolynomial *qp1,
2687 __isl_take isl_qpolynomial *qp2);
2688 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2689 __isl_take isl_qpolynomial *qp1,
2690 __isl_take isl_qpolynomial *qp2);
2691 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2692 __isl_take isl_qpolynomial *qp1,
2693 __isl_take isl_qpolynomial *qp2);
2694 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2695 __isl_take isl_qpolynomial *qp, unsigned exponent);
2697 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2698 __isl_take isl_pw_qpolynomial *pwqp1,
2699 __isl_take isl_pw_qpolynomial *pwqp2);
2700 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2701 __isl_take isl_pw_qpolynomial *pwqp1,
2702 __isl_take isl_pw_qpolynomial *pwqp2);
2703 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2704 __isl_take isl_pw_qpolynomial *pwqp1,
2705 __isl_take isl_pw_qpolynomial *pwqp2);
2706 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2707 __isl_take isl_pw_qpolynomial *pwqp);
2708 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2709 __isl_take isl_pw_qpolynomial *pwqp1,
2710 __isl_take isl_pw_qpolynomial *pwqp2);
2712 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2713 __isl_take isl_union_pw_qpolynomial *upwqp1,
2714 __isl_take isl_union_pw_qpolynomial *upwqp2);
2715 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2716 __isl_take isl_union_pw_qpolynomial *upwqp1,
2717 __isl_take isl_union_pw_qpolynomial *upwqp2);
2718 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2719 __isl_take isl_union_pw_qpolynomial *upwqp1,
2720 __isl_take isl_union_pw_qpolynomial *upwqp2);
2722 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2723 __isl_take isl_pw_qpolynomial *pwqp,
2724 __isl_take isl_point *pnt);
2726 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2727 __isl_take isl_union_pw_qpolynomial *upwqp,
2728 __isl_take isl_point *pnt);
2730 __isl_give isl_set *isl_pw_qpolynomial_domain(
2731 __isl_take isl_pw_qpolynomial *pwqp);
2732 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2733 __isl_take isl_pw_qpolynomial *pwpq,
2734 __isl_take isl_set *set);
2736 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2737 __isl_take isl_union_pw_qpolynomial *upwqp);
2738 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2739 __isl_take isl_union_pw_qpolynomial *upwpq,
2740 __isl_take isl_union_set *uset);
2742 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2743 __isl_take isl_qpolynomial *qp,
2744 __isl_take isl_dim *model);
2746 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2747 __isl_take isl_union_pw_qpolynomial *upwqp);
2749 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2750 __isl_take isl_qpolynomial *qp,
2751 __isl_take isl_set *context);
2753 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2754 __isl_take isl_pw_qpolynomial *pwqp,
2755 __isl_take isl_set *context);
2757 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2758 __isl_take isl_union_pw_qpolynomial *upwqp,
2759 __isl_take isl_union_set *context);
2761 The gist operation applies the gist operation to each of
2762 the cells in the domain of the input piecewise quasipolynomial.
2763 The context is also exploited
2764 to simplify the quasipolynomials associated to each cell.
2766 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2767 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2768 __isl_give isl_union_pw_qpolynomial *
2769 isl_union_pw_qpolynomial_to_polynomial(
2770 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2772 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2773 the polynomial will be an overapproximation. If C<sign> is negative,
2774 it will be an underapproximation. If C<sign> is zero, the approximation
2775 will lie somewhere in between.
2777 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2779 A piecewise quasipolynomial reduction is a piecewise
2780 reduction (or fold) of quasipolynomials.
2781 In particular, the reduction can be maximum or a minimum.
2782 The objects are mainly used to represent the result of
2783 an upper or lower bound on a quasipolynomial over its domain,
2784 i.e., as the result of the following function.
2786 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2787 __isl_take isl_pw_qpolynomial *pwqp,
2788 enum isl_fold type, int *tight);
2790 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2791 __isl_take isl_union_pw_qpolynomial *upwqp,
2792 enum isl_fold type, int *tight);
2794 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2795 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2796 is the returned bound is known be tight, i.e., for each value
2797 of the parameters there is at least
2798 one element in the domain that reaches the bound.
2799 If the domain of C<pwqp> is not wrapping, then the bound is computed
2800 over all elements in that domain and the result has a purely parametric
2801 domain. If the domain of C<pwqp> is wrapping, then the bound is
2802 computed over the range of the wrapped relation. The domain of the
2803 wrapped relation becomes the domain of the result.
2805 A (piecewise) quasipolynomial reduction can be copied or freed using the
2806 following functions.
2808 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2809 __isl_keep isl_qpolynomial_fold *fold);
2810 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2811 __isl_keep isl_pw_qpolynomial_fold *pwf);
2812 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2813 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2814 void isl_qpolynomial_fold_free(
2815 __isl_take isl_qpolynomial_fold *fold);
2816 void *isl_pw_qpolynomial_fold_free(
2817 __isl_take isl_pw_qpolynomial_fold *pwf);
2818 void isl_union_pw_qpolynomial_fold_free(
2819 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2821 =head3 Printing Piecewise Quasipolynomial Reductions
2823 Piecewise quasipolynomial reductions can be printed
2824 using the following function.
2826 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2827 __isl_take isl_printer *p,
2828 __isl_keep isl_pw_qpolynomial_fold *pwf);
2829 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2830 __isl_take isl_printer *p,
2831 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2833 For C<isl_printer_print_pw_qpolynomial_fold>,
2834 output format of the printer
2835 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2836 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2837 output format of the printer
2838 needs to be set to C<ISL_FORMAT_ISL>.
2839 In case of printing in C<ISL_FORMAT_C>, the user may want
2840 to set the names of all dimensions
2842 __isl_give isl_pw_qpolynomial_fold *
2843 isl_pw_qpolynomial_fold_set_dim_name(
2844 __isl_take isl_pw_qpolynomial_fold *pwf,
2845 enum isl_dim_type type, unsigned pos,
2848 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2850 To iterate over all piecewise quasipolynomial reductions in a union
2851 piecewise quasipolynomial reduction, use the following function
2853 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2854 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2855 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2856 void *user), void *user);
2858 To iterate over the cells in a piecewise quasipolynomial reduction,
2859 use either of the following two functions
2861 int isl_pw_qpolynomial_fold_foreach_piece(
2862 __isl_keep isl_pw_qpolynomial_fold *pwf,
2863 int (*fn)(__isl_take isl_set *set,
2864 __isl_take isl_qpolynomial_fold *fold,
2865 void *user), void *user);
2866 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2867 __isl_keep isl_pw_qpolynomial_fold *pwf,
2868 int (*fn)(__isl_take isl_set *set,
2869 __isl_take isl_qpolynomial_fold *fold,
2870 void *user), void *user);
2872 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2873 of the difference between these two functions.
2875 To iterate over all quasipolynomials in a reduction, use
2877 int isl_qpolynomial_fold_foreach_qpolynomial(
2878 __isl_keep isl_qpolynomial_fold *fold,
2879 int (*fn)(__isl_take isl_qpolynomial *qp,
2880 void *user), void *user);
2882 =head3 Operations on Piecewise Quasipolynomial Reductions
2884 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
2885 __isl_take isl_qpolynomial_fold *fold, isl_int v);
2887 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2888 __isl_take isl_pw_qpolynomial_fold *pwf1,
2889 __isl_take isl_pw_qpolynomial_fold *pwf2);
2891 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2892 __isl_take isl_pw_qpolynomial_fold *pwf1,
2893 __isl_take isl_pw_qpolynomial_fold *pwf2);
2895 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2896 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2897 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2899 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2900 __isl_take isl_pw_qpolynomial_fold *pwf,
2901 __isl_take isl_point *pnt);
2903 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2904 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2905 __isl_take isl_point *pnt);
2907 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2908 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2909 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2910 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2911 __isl_take isl_union_set *uset);
2913 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2914 __isl_take isl_pw_qpolynomial_fold *pwf);
2916 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2917 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2919 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2920 __isl_take isl_pw_qpolynomial_fold *pwf,
2921 __isl_take isl_set *context);
2923 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2924 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2925 __isl_take isl_union_set *context);
2927 The gist operation applies the gist operation to each of
2928 the cells in the domain of the input piecewise quasipolynomial reduction.
2929 In future, the operation will also exploit the context
2930 to simplify the quasipolynomial reductions associated to each cell.
2932 __isl_give isl_pw_qpolynomial_fold *
2933 isl_set_apply_pw_qpolynomial_fold(
2934 __isl_take isl_set *set,
2935 __isl_take isl_pw_qpolynomial_fold *pwf,
2937 __isl_give isl_pw_qpolynomial_fold *
2938 isl_map_apply_pw_qpolynomial_fold(
2939 __isl_take isl_map *map,
2940 __isl_take isl_pw_qpolynomial_fold *pwf,
2942 __isl_give isl_union_pw_qpolynomial_fold *
2943 isl_union_set_apply_union_pw_qpolynomial_fold(
2944 __isl_take isl_union_set *uset,
2945 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2947 __isl_give isl_union_pw_qpolynomial_fold *
2948 isl_union_map_apply_union_pw_qpolynomial_fold(
2949 __isl_take isl_union_map *umap,
2950 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2953 The functions taking a map
2954 compose the given map with the given piecewise quasipolynomial reduction.
2955 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2956 over all elements in the intersection of the range of the map
2957 and the domain of the piecewise quasipolynomial reduction
2958 as a function of an element in the domain of the map.
2959 The functions taking a set compute a bound over all elements in the
2960 intersection of the set and the domain of the
2961 piecewise quasipolynomial reduction.
2963 =head2 Dependence Analysis
2965 C<isl> contains specialized functionality for performing
2966 array dataflow analysis. That is, given a I<sink> access relation
2967 and a collection of possible I<source> access relations,
2968 C<isl> can compute relations that describe
2969 for each iteration of the sink access, which iteration
2970 of which of the source access relations was the last
2971 to access the same data element before the given iteration
2973 To compute standard flow dependences, the sink should be
2974 a read, while the sources should be writes.
2975 If any of the source accesses are marked as being I<may>
2976 accesses, then there will be a dependence to the last
2977 I<must> access B<and> to any I<may> access that follows
2978 this last I<must> access.
2979 In particular, if I<all> sources are I<may> accesses,
2980 then memory based dependence analysis is performed.
2981 If, on the other hand, all sources are I<must> accesses,
2982 then value based dependence analysis is performed.
2984 #include <isl/flow.h>
2986 typedef int (*isl_access_level_before)(void *first, void *second);
2988 __isl_give isl_access_info *isl_access_info_alloc(
2989 __isl_take isl_map *sink,
2990 void *sink_user, isl_access_level_before fn,
2992 __isl_give isl_access_info *isl_access_info_add_source(
2993 __isl_take isl_access_info *acc,
2994 __isl_take isl_map *source, int must,
2996 void isl_access_info_free(__isl_take isl_access_info *acc);
2998 __isl_give isl_flow *isl_access_info_compute_flow(
2999 __isl_take isl_access_info *acc);
3001 int isl_flow_foreach(__isl_keep isl_flow *deps,
3002 int (*fn)(__isl_take isl_map *dep, int must,
3003 void *dep_user, void *user),
3005 __isl_give isl_map *isl_flow_get_no_source(
3006 __isl_keep isl_flow *deps, int must);
3007 void isl_flow_free(__isl_take isl_flow *deps);
3009 The function C<isl_access_info_compute_flow> performs the actual
3010 dependence analysis. The other functions are used to construct
3011 the input for this function or to read off the output.
3013 The input is collected in an C<isl_access_info>, which can
3014 be created through a call to C<isl_access_info_alloc>.
3015 The arguments to this functions are the sink access relation
3016 C<sink>, a token C<sink_user> used to identify the sink
3017 access to the user, a callback function for specifying the
3018 relative order of source and sink accesses, and the number
3019 of source access relations that will be added.
3020 The callback function has type C<int (*)(void *first, void *second)>.
3021 The function is called with two user supplied tokens identifying
3022 either a source or the sink and it should return the shared nesting
3023 level and the relative order of the two accesses.
3024 In particular, let I<n> be the number of loops shared by
3025 the two accesses. If C<first> precedes C<second> textually,
3026 then the function should return I<2 * n + 1>; otherwise,
3027 it should return I<2 * n>.
3028 The sources can be added to the C<isl_access_info> by performing
3029 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3030 C<must> indicates whether the source is a I<must> access
3031 or a I<may> access. Note that a multi-valued access relation
3032 should only be marked I<must> if every iteration in the domain
3033 of the relation accesses I<all> elements in its image.
3034 The C<source_user> token is again used to identify
3035 the source access. The range of the source access relation
3036 C<source> should have the same dimension as the range
3037 of the sink access relation.
3038 The C<isl_access_info_free> function should usually not be
3039 called explicitly, because it is called implicitly by
3040 C<isl_access_info_compute_flow>.
3042 The result of the dependence analysis is collected in an
3043 C<isl_flow>. There may be elements of
3044 the sink access for which no preceding source access could be
3045 found or for which all preceding sources are I<may> accesses.
3046 The relations containing these elements can be obtained through
3047 calls to C<isl_flow_get_no_source>, the first with C<must> set
3048 and the second with C<must> unset.
3049 In the case of standard flow dependence analysis,
3050 with the sink a read and the sources I<must> writes,
3051 the first relation corresponds to the reads from uninitialized
3052 array elements and the second relation is empty.
3053 The actual flow dependences can be extracted using
3054 C<isl_flow_foreach>. This function will call the user-specified
3055 callback function C<fn> for each B<non-empty> dependence between
3056 a source and the sink. The callback function is called
3057 with four arguments, the actual flow dependence relation
3058 mapping source iterations to sink iterations, a boolean that
3059 indicates whether it is a I<must> or I<may> dependence, a token
3060 identifying the source and an additional C<void *> with value
3061 equal to the third argument of the C<isl_flow_foreach> call.
3062 A dependence is marked I<must> if it originates from a I<must>
3063 source and if it is not followed by any I<may> sources.
3065 After finishing with an C<isl_flow>, the user should call
3066 C<isl_flow_free> to free all associated memory.
3068 A higher-level interface to dependence analysis is provided
3069 by the following function.
3071 #include <isl/flow.h>
3073 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
3074 __isl_take isl_union_map *must_source,
3075 __isl_take isl_union_map *may_source,
3076 __isl_take isl_union_map *schedule,
3077 __isl_give isl_union_map **must_dep,
3078 __isl_give isl_union_map **may_dep,
3079 __isl_give isl_union_map **must_no_source,
3080 __isl_give isl_union_map **may_no_source);
3082 The arrays are identified by the tuple names of the ranges
3083 of the accesses. The iteration domains by the tuple names
3084 of the domains of the accesses and of the schedule.
3085 The relative order of the iteration domains is given by the
3086 schedule. The relations returned through C<must_no_source>
3087 and C<may_no_source> are subsets of C<sink>.
3088 Any of C<must_dep>, C<may_dep>, C<must_no_source>
3089 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
3090 any of the other arguments is treated as an error.
3094 B<The functionality described in this section is fairly new
3095 and may be subject to change.>
3097 The following function can be used to compute a schedule
3098 for a union of domains. The generated schedule respects
3099 all C<validity> dependences. That is, all dependence distances
3100 over these dependences in the scheduled space are lexicographically
3101 positive. The generated schedule schedule also tries to minimize
3102 the dependence distances over C<proximity> dependences.
3103 Moreover, it tries to obtain sequences (bands) of schedule dimensions
3104 for groups of domains where the dependence distances have only
3105 non-negative values.
3106 The algorithm used to construct the schedule is similar to that
3109 #include <isl/schedule.h>
3110 __isl_give isl_schedule *isl_union_set_compute_schedule(
3111 __isl_take isl_union_set *domain,
3112 __isl_take isl_union_map *validity,
3113 __isl_take isl_union_map *proximity);
3114 void *isl_schedule_free(__isl_take isl_schedule *sched);
3116 A mapping from the domains to the scheduled space can be obtained
3117 from an C<isl_schedule> using the following function.
3119 __isl_give isl_union_map *isl_schedule_get_map(
3120 __isl_keep isl_schedule *sched);
3122 A representation of the schedule can be printed using
3124 __isl_give isl_printer *isl_printer_print_schedule(
3125 __isl_take isl_printer *p,
3126 __isl_keep isl_schedule *schedule);
3128 A representation of the schedule as a forest of bands can be obtained
3129 using the following function.
3131 __isl_give isl_band_list *isl_schedule_get_band_forest(
3132 __isl_keep isl_schedule *schedule);
3134 The list can be manipulated as explained in L<"Lists">.
3135 The bands inside the list can be copied and freed using the following
3138 #include <isl/band.h>
3139 __isl_give isl_band *isl_band_copy(
3140 __isl_keep isl_band *band);
3141 void *isl_band_free(__isl_take isl_band *band);
3143 Each band contains zero or more scheduling dimensions.
3144 These are referred to as the members of the band.
3145 The section of the schedule that corresponds to the band is
3146 referred to as the partial schedule of the band.
3147 For those nodes that participate in a band, the outer scheduling
3148 dimensions form the prefix schedule, while the inner scheduling
3149 dimensions form the suffix schedule.
3150 That is, if we take a cut of the band forest, then the union of
3151 the concatenations of the prefix, partial and suffix schedules of
3152 each band in the cut is equal to the entire schedule (modulo
3153 some possible padding at the end with zero scheduling dimensions).
3154 The properties of a band can be inspected using the following functions.
3156 #include <isl/band.h>
3157 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
3159 int isl_band_has_children(__isl_keep isl_band *band);
3160 __isl_give isl_band_list *isl_band_get_children(
3161 __isl_keep isl_band *band);
3163 __isl_give isl_union_map *isl_band_get_prefix_schedule(
3164 __isl_keep isl_band *band);
3165 __isl_give isl_union_map *isl_band_get_partial_schedule(
3166 __isl_keep isl_band *band);
3167 __isl_give isl_union_map *isl_band_get_suffix_schedule(
3168 __isl_keep isl_band *band);
3170 int isl_band_n_member(__isl_keep isl_band *band);
3171 int isl_band_member_is_zero_distance(
3172 __isl_keep isl_band *band, int pos);
3174 Note that a scheduling dimension is considered to be ``zero
3175 distance'' if it does not carry any proximity dependences
3177 That is, if the dependence distances of the proximity
3178 dependences are all zero in that direction (for fixed
3179 iterations of outer bands).
3181 A representation of the band can be printed using
3183 #include <isl/band.h>
3184 __isl_give isl_printer *isl_printer_print_band(
3185 __isl_take isl_printer *p,
3186 __isl_keep isl_band *band);
3188 Alternatively, the schedule mapping
3189 can also be obtained in pieces using the following functions.
3191 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
3192 __isl_give isl_union_map *isl_schedule_get_band(
3193 __isl_keep isl_schedule *sched, unsigned band);
3195 C<isl_schedule_n_band> returns the maximal number of bands.
3196 C<isl_schedule_get_band> returns a union of mappings from a domain to
3197 the band of consecutive schedule dimensions with the given sequence
3198 number for that domain. Bands with the same sequence number but for
3199 different domains may be completely unrelated.
3200 Within a band, the corresponding coordinates of the distance vectors
3201 are all non-negative, assuming that the coordinates for all previous
3204 =head2 Parametric Vertex Enumeration
3206 The parametric vertex enumeration described in this section
3207 is mainly intended to be used internally and by the C<barvinok>
3210 #include <isl/vertices.h>
3211 __isl_give isl_vertices *isl_basic_set_compute_vertices(
3212 __isl_keep isl_basic_set *bset);
3214 The function C<isl_basic_set_compute_vertices> performs the
3215 actual computation of the parametric vertices and the chamber
3216 decomposition and store the result in an C<isl_vertices> object.
3217 This information can be queried by either iterating over all
3218 the vertices or iterating over all the chambers or cells
3219 and then iterating over all vertices that are active on the chamber.
3221 int isl_vertices_foreach_vertex(
3222 __isl_keep isl_vertices *vertices,
3223 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3226 int isl_vertices_foreach_cell(
3227 __isl_keep isl_vertices *vertices,
3228 int (*fn)(__isl_take isl_cell *cell, void *user),
3230 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
3231 int (*fn)(__isl_take isl_vertex *vertex, void *user),
3234 Other operations that can be performed on an C<isl_vertices> object are
3237 isl_ctx *isl_vertices_get_ctx(
3238 __isl_keep isl_vertices *vertices);
3239 int isl_vertices_get_n_vertices(
3240 __isl_keep isl_vertices *vertices);
3241 void isl_vertices_free(__isl_take isl_vertices *vertices);
3243 Vertices can be inspected and destroyed using the following functions.
3245 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
3246 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
3247 __isl_give isl_basic_set *isl_vertex_get_domain(
3248 __isl_keep isl_vertex *vertex);
3249 __isl_give isl_basic_set *isl_vertex_get_expr(
3250 __isl_keep isl_vertex *vertex);
3251 void isl_vertex_free(__isl_take isl_vertex *vertex);
3253 C<isl_vertex_get_expr> returns a singleton parametric set describing
3254 the vertex, while C<isl_vertex_get_domain> returns the activity domain
3256 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
3257 B<rational> basic sets, so they should mainly be used for inspection
3258 and should not be mixed with integer sets.
3260 Chambers can be inspected and destroyed using the following functions.
3262 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
3263 __isl_give isl_basic_set *isl_cell_get_domain(
3264 __isl_keep isl_cell *cell);
3265 void isl_cell_free(__isl_take isl_cell *cell);
3269 Although C<isl> is mainly meant to be used as a library,
3270 it also contains some basic applications that use some
3271 of the functionality of C<isl>.
3272 The input may be specified in either the L<isl format>
3273 or the L<PolyLib format>.
3275 =head2 C<isl_polyhedron_sample>
3277 C<isl_polyhedron_sample> takes a polyhedron as input and prints
3278 an integer element of the polyhedron, if there is any.
3279 The first column in the output is the denominator and is always
3280 equal to 1. If the polyhedron contains no integer points,
3281 then a vector of length zero is printed.
3285 C<isl_pip> takes the same input as the C<example> program
3286 from the C<piplib> distribution, i.e., a set of constraints
3287 on the parameters, a line containing only -1 and finally a set
3288 of constraints on a parametric polyhedron.
3289 The coefficients of the parameters appear in the last columns
3290 (but before the final constant column).
3291 The output is the lexicographic minimum of the parametric polyhedron.
3292 As C<isl> currently does not have its own output format, the output
3293 is just a dump of the internal state.
3295 =head2 C<isl_polyhedron_minimize>
3297 C<isl_polyhedron_minimize> computes the minimum of some linear
3298 or affine objective function over the integer points in a polyhedron.
3299 If an affine objective function
3300 is given, then the constant should appear in the last column.
3302 =head2 C<isl_polytope_scan>
3304 Given a polytope, C<isl_polytope_scan> prints
3305 all integer points in the polytope.