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 a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
158 The source of C<isl> can be obtained either as a tarball
159 or from the git repository. Both are available from
160 L<http://freshmeat.net/projects/isl/>.
161 The installation process depends on how you obtained
164 =head2 Installation from the git repository
168 =item 1 Clone or update the repository
170 The first time the source is obtained, you need to clone
173 git clone git://repo.or.cz/isl.git
175 To obtain updates, you need to pull in the latest changes
179 =item 2 Generate C<configure>
185 After performing the above steps, continue
186 with the L<Common installation instructions>.
188 =head2 Common installation instructions
192 =item 1 Obtain C<GMP>
194 Building C<isl> requires C<GMP>, including its headers files.
195 Your distribution may not provide these header files by default
196 and you may need to install a package called C<gmp-devel> or something
197 similar. Alternatively, C<GMP> can be built from
198 source, available from L<http://gmplib.org/>.
202 C<isl> uses the standard C<autoconf> C<configure> script.
207 optionally followed by some configure options.
208 A complete list of options can be obtained by running
212 Below we discuss some of the more common options.
214 C<isl> can optionally use C<piplib>, but no
215 C<piplib> functionality is currently used by default.
216 The C<--with-piplib> option can
217 be used to specify which C<piplib>
218 library to use, either an installed version (C<system>),
219 an externally built version (C<build>)
220 or no version (C<no>). The option C<build> is mostly useful
221 in C<configure> scripts of larger projects that bundle both C<isl>
228 Installation prefix for C<isl>
230 =item C<--with-gmp-prefix>
232 Installation prefix for C<GMP> (architecture-independent files).
234 =item C<--with-gmp-exec-prefix>
236 Installation prefix for C<GMP> (architecture-dependent files).
238 =item C<--with-piplib>
240 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
242 =item C<--with-piplib-prefix>
244 Installation prefix for C<system> C<piplib> (architecture-independent files).
246 =item C<--with-piplib-exec-prefix>
248 Installation prefix for C<system> C<piplib> (architecture-dependent files).
250 =item C<--with-piplib-builddir>
252 Location where C<build> C<piplib> was built.
260 =item 4 Install (optional)
268 =head2 Initialization
270 All manipulations of integer sets and relations occur within
271 the context of an C<isl_ctx>.
272 A given C<isl_ctx> can only be used within a single thread.
273 All arguments of a function are required to have been allocated
274 within the same context.
275 There are currently no functions available for moving an object
276 from one C<isl_ctx> to another C<isl_ctx>. This means that
277 there is currently no way of safely moving an object from one
278 thread to another, unless the whole C<isl_ctx> is moved.
280 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
281 freed using C<isl_ctx_free>.
282 All objects allocated within an C<isl_ctx> should be freed
283 before the C<isl_ctx> itself is freed.
285 isl_ctx *isl_ctx_alloc();
286 void isl_ctx_free(isl_ctx *ctx);
290 All operations on integers, mainly the coefficients
291 of the constraints describing the sets and relations,
292 are performed in exact integer arithmetic using C<GMP>.
293 However, to allow future versions of C<isl> to optionally
294 support fixed integer arithmetic, all calls to C<GMP>
295 are wrapped inside C<isl> specific macros.
296 The basic type is C<isl_int> and the operations below
297 are available on this type.
298 The meanings of these operations are essentially the same
299 as their C<GMP> C<mpz_> counterparts.
300 As always with C<GMP> types, C<isl_int>s need to be
301 initialized with C<isl_int_init> before they can be used
302 and they need to be released with C<isl_int_clear>
304 The user should not assume that an C<isl_int> is represented
305 as a C<mpz_t>, but should instead explicitly convert between
306 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
307 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
311 =item isl_int_init(i)
313 =item isl_int_clear(i)
315 =item isl_int_set(r,i)
317 =item isl_int_set_si(r,i)
319 =item isl_int_set_gmp(r,g)
321 =item isl_int_get_gmp(i,g)
323 =item isl_int_abs(r,i)
325 =item isl_int_neg(r,i)
327 =item isl_int_swap(i,j)
329 =item isl_int_swap_or_set(i,j)
331 =item isl_int_add_ui(r,i,j)
333 =item isl_int_sub_ui(r,i,j)
335 =item isl_int_add(r,i,j)
337 =item isl_int_sub(r,i,j)
339 =item isl_int_mul(r,i,j)
341 =item isl_int_mul_ui(r,i,j)
343 =item isl_int_addmul(r,i,j)
345 =item isl_int_submul(r,i,j)
347 =item isl_int_gcd(r,i,j)
349 =item isl_int_lcm(r,i,j)
351 =item isl_int_divexact(r,i,j)
353 =item isl_int_cdiv_q(r,i,j)
355 =item isl_int_fdiv_q(r,i,j)
357 =item isl_int_fdiv_r(r,i,j)
359 =item isl_int_fdiv_q_ui(r,i,j)
361 =item isl_int_read(r,s)
363 =item isl_int_print(out,i,width)
367 =item isl_int_cmp(i,j)
369 =item isl_int_cmp_si(i,si)
371 =item isl_int_eq(i,j)
373 =item isl_int_ne(i,j)
375 =item isl_int_lt(i,j)
377 =item isl_int_le(i,j)
379 =item isl_int_gt(i,j)
381 =item isl_int_ge(i,j)
383 =item isl_int_abs_eq(i,j)
385 =item isl_int_abs_ne(i,j)
387 =item isl_int_abs_lt(i,j)
389 =item isl_int_abs_gt(i,j)
391 =item isl_int_abs_ge(i,j)
393 =item isl_int_is_zero(i)
395 =item isl_int_is_one(i)
397 =item isl_int_is_negone(i)
399 =item isl_int_is_pos(i)
401 =item isl_int_is_neg(i)
403 =item isl_int_is_nonpos(i)
405 =item isl_int_is_nonneg(i)
407 =item isl_int_is_divisible_by(i,j)
411 =head2 Sets and Relations
413 C<isl> uses six types of objects for representing sets and relations,
414 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
415 C<isl_union_set> and C<isl_union_map>.
416 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
417 can be described as a conjunction of affine constraints, while
418 C<isl_set> and C<isl_map> represent unions of
419 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
420 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
421 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
422 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
423 where spaces are considered different if they have a different number
424 of dimensions and/or different names (see L<"Spaces">).
425 The difference between sets and relations (maps) is that sets have
426 one set of variables, while relations have two sets of variables,
427 input variables and output variables.
429 =head2 Memory Management
431 Since a high-level operation on sets and/or relations usually involves
432 several substeps and since the user is usually not interested in
433 the intermediate results, most functions that return a new object
434 will also release all the objects passed as arguments.
435 If the user still wants to use one or more of these arguments
436 after the function call, she should pass along a copy of the
437 object rather than the object itself.
438 The user is then responsible for making sure that the original
439 object gets used somewhere else or is explicitly freed.
441 The arguments and return values of all documented functions are
442 annotated to make clear which arguments are released and which
443 arguments are preserved. In particular, the following annotations
450 C<__isl_give> means that a new object is returned.
451 The user should make sure that the returned pointer is
452 used exactly once as a value for an C<__isl_take> argument.
453 In between, it can be used as a value for as many
454 C<__isl_keep> arguments as the user likes.
455 There is one exception, and that is the case where the
456 pointer returned is C<NULL>. Is this case, the user
457 is free to use it as an C<__isl_take> argument or not.
461 C<__isl_take> means that the object the argument points to
462 is taken over by the function and may no longer be used
463 by the user as an argument to any other function.
464 The pointer value must be one returned by a function
465 returning an C<__isl_give> pointer.
466 If the user passes in a C<NULL> value, then this will
467 be treated as an error in the sense that the function will
468 not perform its usual operation. However, it will still
469 make sure that all the other C<__isl_take> arguments
474 C<__isl_keep> means that the function will only use the object
475 temporarily. After the function has finished, the user
476 can still use it as an argument to other functions.
477 A C<NULL> value will be treated in the same way as
478 a C<NULL> value for an C<__isl_take> argument.
482 =head2 Error Handling
484 C<isl> supports different ways to react in case a runtime error is triggered.
485 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
486 with two maps that have incompatible spaces. There are three possible ways
487 to react on error: to warn, to continue or to abort.
489 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
490 the last error in the corresponding C<isl_ctx> and the function in which the
491 error was triggered returns C<NULL>. An error does not corrupt internal state,
492 such that isl can continue to be used. C<isl> also provides functions to
493 read the last error and to reset the memory that stores the last error. The
494 last error is only stored for information purposes. Its presence does not
495 change the behavior of C<isl>. Hence, resetting an error is not required to
496 continue to use isl, but only to observe new errors.
499 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
500 void isl_ctx_reset_error(isl_ctx *ctx);
502 Another option is to continue on error. This is similar to warn on error mode,
503 except that C<isl> does not print any warning. This allows a program to
504 implement its own error reporting.
506 The last option is to directly abort the execution of the program from within
507 the isl library. This makes it obviously impossible to recover from an error,
508 but it allows to directly spot the error location. By aborting on error,
509 debuggers break at the location the error occurred and can provide a stack
510 trace. Other tools that automatically provide stack traces on abort or that do
511 not want to continue execution after an error was triggered may also prefer to
514 The on error behavior of isl can be specified by calling
515 C<isl_options_set_on_error> or by setting the command line option
516 C<--isl-on-error>. Valid arguments for the function call are
517 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
518 choices for the command line option are C<warn>, C<continue> and C<abort>.
519 It is also possible to query the current error mode.
521 #include <isl/options.h>
522 int isl_options_set_on_error(isl_ctx *ctx, int val);
523 int isl_options_get_on_error(isl_ctx *ctx);
527 Identifiers are used to identify both individual dimensions
528 and tuples of dimensions. They consist of a name and an optional
529 pointer. Identifiers with the same name but different pointer values
530 are considered to be distinct.
531 Identifiers can be constructed, copied, freed, inspected and printed
532 using the following functions.
535 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
536 __isl_keep const char *name, void *user);
537 __isl_give isl_id *isl_id_copy(isl_id *id);
538 void *isl_id_free(__isl_take isl_id *id);
540 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
541 void *isl_id_get_user(__isl_keep isl_id *id);
542 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
544 __isl_give isl_printer *isl_printer_print_id(
545 __isl_take isl_printer *p, __isl_keep isl_id *id);
547 Note that C<isl_id_get_name> returns a pointer to some internal
548 data structure, so the result can only be used while the
549 corresponding C<isl_id> is alive.
553 Whenever a new set or relation is created from scratch,
554 the space in which it lives needs to be specified using an C<isl_space>.
556 #include <isl/space.h>
557 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
558 unsigned nparam, unsigned n_in, unsigned n_out);
559 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
561 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
562 unsigned nparam, unsigned dim);
563 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
564 void isl_space_free(__isl_take isl_space *space);
565 unsigned isl_space_dim(__isl_keep isl_space *space,
566 enum isl_dim_type type);
568 The space used for creating a parameter domain
569 needs to be created using C<isl_space_params_alloc>.
570 For other sets, the space
571 needs to be created using C<isl_space_set_alloc>, while
572 for a relation, the space
573 needs to be created using C<isl_space_alloc>.
574 C<isl_space_dim> can be used
575 to find out the number of dimensions of each type in
576 a space, where type may be
577 C<isl_dim_param>, C<isl_dim_in> (only for relations),
578 C<isl_dim_out> (only for relations), C<isl_dim_set>
579 (only for sets) or C<isl_dim_all>.
581 To check whether a given space is that of a set or a map
582 or whether it is a parameter space, use these functions:
584 #include <isl/space.h>
585 int isl_space_is_params(__isl_keep isl_space *space);
586 int isl_space_is_set(__isl_keep isl_space *space);
588 It is often useful to create objects that live in the
589 same space as some other object. This can be accomplished
590 by creating the new objects
591 (see L<Creating New Sets and Relations> or
592 L<Creating New (Piecewise) Quasipolynomials>) based on the space
593 of the original object.
596 __isl_give isl_space *isl_basic_set_get_space(
597 __isl_keep isl_basic_set *bset);
598 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
600 #include <isl/union_set.h>
601 __isl_give isl_space *isl_union_set_get_space(
602 __isl_keep isl_union_set *uset);
605 __isl_give isl_space *isl_basic_map_get_space(
606 __isl_keep isl_basic_map *bmap);
607 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
609 #include <isl/union_map.h>
610 __isl_give isl_space *isl_union_map_get_space(
611 __isl_keep isl_union_map *umap);
613 #include <isl/constraint.h>
614 __isl_give isl_space *isl_constraint_get_space(
615 __isl_keep isl_constraint *constraint);
617 #include <isl/polynomial.h>
618 __isl_give isl_space *isl_qpolynomial_get_domain_space(
619 __isl_keep isl_qpolynomial *qp);
620 __isl_give isl_space *isl_qpolynomial_get_space(
621 __isl_keep isl_qpolynomial *qp);
622 __isl_give isl_space *isl_qpolynomial_fold_get_space(
623 __isl_keep isl_qpolynomial_fold *fold);
624 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
625 __isl_keep isl_pw_qpolynomial *pwqp);
626 __isl_give isl_space *isl_pw_qpolynomial_get_space(
627 __isl_keep isl_pw_qpolynomial *pwqp);
628 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
629 __isl_keep isl_pw_qpolynomial_fold *pwf);
630 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
631 __isl_keep isl_pw_qpolynomial_fold *pwf);
632 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
633 __isl_keep isl_union_pw_qpolynomial *upwqp);
634 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
635 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
638 __isl_give isl_space *isl_aff_get_domain_space(
639 __isl_keep isl_aff *aff);
640 __isl_give isl_space *isl_aff_get_space(
641 __isl_keep isl_aff *aff);
642 __isl_give isl_space *isl_pw_aff_get_domain_space(
643 __isl_keep isl_pw_aff *pwaff);
644 __isl_give isl_space *isl_pw_aff_get_space(
645 __isl_keep isl_pw_aff *pwaff);
646 __isl_give isl_space *isl_multi_aff_get_space(
647 __isl_keep isl_multi_aff *maff);
648 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
649 __isl_keep isl_pw_multi_aff *pma);
650 __isl_give isl_space *isl_pw_multi_aff_get_space(
651 __isl_keep isl_pw_multi_aff *pma);
653 #include <isl/point.h>
654 __isl_give isl_space *isl_point_get_space(
655 __isl_keep isl_point *pnt);
657 The identifiers or names of the individual dimensions may be set or read off
658 using the following functions.
660 #include <isl/space.h>
661 __isl_give isl_space *isl_space_set_dim_id(
662 __isl_take isl_space *space,
663 enum isl_dim_type type, unsigned pos,
664 __isl_take isl_id *id);
665 int isl_space_has_dim_id(__isl_keep isl_space *space,
666 enum isl_dim_type type, unsigned pos);
667 __isl_give isl_id *isl_space_get_dim_id(
668 __isl_keep isl_space *space,
669 enum isl_dim_type type, unsigned pos);
670 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
671 enum isl_dim_type type, unsigned pos,
672 __isl_keep const char *name);
673 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
674 enum isl_dim_type type, unsigned pos);
676 Note that C<isl_space_get_name> returns a pointer to some internal
677 data structure, so the result can only be used while the
678 corresponding C<isl_space> is alive.
679 Also note that every function that operates on two sets or relations
680 requires that both arguments have the same parameters. This also
681 means that if one of the arguments has named parameters, then the
682 other needs to have named parameters too and the names need to match.
683 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
684 arguments may have different parameters (as long as they are named),
685 in which case the result will have as parameters the union of the parameters of
688 Given the identifier or name of a dimension (typically a parameter),
689 its position can be obtained from the following function.
691 #include <isl/space.h>
692 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
693 enum isl_dim_type type, __isl_keep isl_id *id);
694 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
695 enum isl_dim_type type, const char *name);
697 The identifiers or names of entire spaces may be set or read off
698 using the following functions.
700 #include <isl/space.h>
701 __isl_give isl_space *isl_space_set_tuple_id(
702 __isl_take isl_space *space,
703 enum isl_dim_type type, __isl_take isl_id *id);
704 __isl_give isl_space *isl_space_reset_tuple_id(
705 __isl_take isl_space *space, enum isl_dim_type type);
706 int isl_space_has_tuple_id(__isl_keep isl_space *space,
707 enum isl_dim_type type);
708 __isl_give isl_id *isl_space_get_tuple_id(
709 __isl_keep isl_space *space, enum isl_dim_type type);
710 __isl_give isl_space *isl_space_set_tuple_name(
711 __isl_take isl_space *space,
712 enum isl_dim_type type, const char *s);
713 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
714 enum isl_dim_type type);
716 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
717 or C<isl_dim_set>. As with C<isl_space_get_name>,
718 the C<isl_space_get_tuple_name> function returns a pointer to some internal
720 Binary operations require the corresponding spaces of their arguments
721 to have the same name.
723 Spaces can be nested. In particular, the domain of a set or
724 the domain or range of a relation can be a nested relation.
725 The following functions can be used to construct and deconstruct
728 #include <isl/space.h>
729 int isl_space_is_wrapping(__isl_keep isl_space *space);
730 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
731 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
733 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
734 be the space of a set, while that of
735 C<isl_space_wrap> should be the space of a relation.
736 Conversely, the output of C<isl_space_unwrap> is the space
737 of a relation, while that of C<isl_space_wrap> is the space of a set.
739 Spaces can be created from other spaces
740 using the following functions.
742 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
743 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
744 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
745 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
746 __isl_give isl_space *isl_space_params(
747 __isl_take isl_space *space);
748 __isl_give isl_space *isl_space_set_from_params(
749 __isl_take isl_space *space);
750 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
751 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
752 __isl_take isl_space *right);
753 __isl_give isl_space *isl_space_align_params(
754 __isl_take isl_space *space1, __isl_take isl_space *space2)
755 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
756 enum isl_dim_type type, unsigned pos, unsigned n);
757 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
758 enum isl_dim_type type, unsigned n);
759 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
760 enum isl_dim_type type, unsigned first, unsigned n);
761 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
762 enum isl_dim_type dst_type, unsigned dst_pos,
763 enum isl_dim_type src_type, unsigned src_pos,
765 __isl_give isl_space *isl_space_map_from_set(
766 __isl_take isl_space *space);
767 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
769 Note that if dimensions are added or removed from a space, then
770 the name and the internal structure are lost.
774 A local space is essentially a space with
775 zero or more existentially quantified variables.
776 The local space of a basic set or relation can be obtained
777 using the following functions.
780 __isl_give isl_local_space *isl_basic_set_get_local_space(
781 __isl_keep isl_basic_set *bset);
784 __isl_give isl_local_space *isl_basic_map_get_local_space(
785 __isl_keep isl_basic_map *bmap);
787 A new local space can be created from a space using
789 #include <isl/local_space.h>
790 __isl_give isl_local_space *isl_local_space_from_space(
791 __isl_take isl_space *space);
793 They can be inspected, modified, copied and freed using the following functions.
795 #include <isl/local_space.h>
796 isl_ctx *isl_local_space_get_ctx(
797 __isl_keep isl_local_space *ls);
798 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
799 int isl_local_space_dim(__isl_keep isl_local_space *ls,
800 enum isl_dim_type type);
801 const char *isl_local_space_get_dim_name(
802 __isl_keep isl_local_space *ls,
803 enum isl_dim_type type, unsigned pos);
804 __isl_give isl_local_space *isl_local_space_set_dim_name(
805 __isl_take isl_local_space *ls,
806 enum isl_dim_type type, unsigned pos, const char *s);
807 __isl_give isl_local_space *isl_local_space_set_dim_id(
808 __isl_take isl_local_space *ls,
809 enum isl_dim_type type, unsigned pos,
810 __isl_take isl_id *id);
811 __isl_give isl_space *isl_local_space_get_space(
812 __isl_keep isl_local_space *ls);
813 __isl_give isl_aff *isl_local_space_get_div(
814 __isl_keep isl_local_space *ls, int pos);
815 __isl_give isl_local_space *isl_local_space_copy(
816 __isl_keep isl_local_space *ls);
817 void *isl_local_space_free(__isl_take isl_local_space *ls);
819 Two local spaces can be compared using
821 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
822 __isl_keep isl_local_space *ls2);
824 Local spaces can be created from other local spaces
825 using the following functions.
827 __isl_give isl_local_space *isl_local_space_domain(
828 __isl_take isl_local_space *ls);
829 __isl_give isl_local_space *isl_local_space_range(
830 __isl_take isl_local_space *ls);
831 __isl_give isl_local_space *isl_local_space_from_domain(
832 __isl_take isl_local_space *ls);
833 __isl_give isl_local_space *isl_local_space_intersect(
834 __isl_take isl_local_space *ls1,
835 __isl_take isl_local_space *ls2);
836 __isl_give isl_local_space *isl_local_space_add_dims(
837 __isl_take isl_local_space *ls,
838 enum isl_dim_type type, unsigned n);
839 __isl_give isl_local_space *isl_local_space_insert_dims(
840 __isl_take isl_local_space *ls,
841 enum isl_dim_type type, unsigned first, unsigned n);
842 __isl_give isl_local_space *isl_local_space_drop_dims(
843 __isl_take isl_local_space *ls,
844 enum isl_dim_type type, unsigned first, unsigned n);
846 =head2 Input and Output
848 C<isl> supports its own input/output format, which is similar
849 to the C<Omega> format, but also supports the C<PolyLib> format
854 The C<isl> format is similar to that of C<Omega>, but has a different
855 syntax for describing the parameters and allows for the definition
856 of an existentially quantified variable as the integer division
857 of an affine expression.
858 For example, the set of integers C<i> between C<0> and C<n>
859 such that C<i % 10 <= 6> can be described as
861 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
864 A set or relation can have several disjuncts, separated
865 by the keyword C<or>. Each disjunct is either a conjunction
866 of constraints or a projection (C<exists>) of a conjunction
867 of constraints. The constraints are separated by the keyword
870 =head3 C<PolyLib> format
872 If the represented set is a union, then the first line
873 contains a single number representing the number of disjuncts.
874 Otherwise, a line containing the number C<1> is optional.
876 Each disjunct is represented by a matrix of constraints.
877 The first line contains two numbers representing
878 the number of rows and columns,
879 where the number of rows is equal to the number of constraints
880 and the number of columns is equal to two plus the number of variables.
881 The following lines contain the actual rows of the constraint matrix.
882 In each row, the first column indicates whether the constraint
883 is an equality (C<0>) or inequality (C<1>). The final column
884 corresponds to the constant term.
886 If the set is parametric, then the coefficients of the parameters
887 appear in the last columns before the constant column.
888 The coefficients of any existentially quantified variables appear
889 between those of the set variables and those of the parameters.
891 =head3 Extended C<PolyLib> format
893 The extended C<PolyLib> format is nearly identical to the
894 C<PolyLib> format. The only difference is that the line
895 containing the number of rows and columns of a constraint matrix
896 also contains four additional numbers:
897 the number of output dimensions, the number of input dimensions,
898 the number of local dimensions (i.e., the number of existentially
899 quantified variables) and the number of parameters.
900 For sets, the number of ``output'' dimensions is equal
901 to the number of set dimensions, while the number of ``input''
907 __isl_give isl_basic_set *isl_basic_set_read_from_file(
908 isl_ctx *ctx, FILE *input);
909 __isl_give isl_basic_set *isl_basic_set_read_from_str(
910 isl_ctx *ctx, const char *str);
911 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
913 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
917 __isl_give isl_basic_map *isl_basic_map_read_from_file(
918 isl_ctx *ctx, FILE *input);
919 __isl_give isl_basic_map *isl_basic_map_read_from_str(
920 isl_ctx *ctx, const char *str);
921 __isl_give isl_map *isl_map_read_from_file(
922 isl_ctx *ctx, FILE *input);
923 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
926 #include <isl/union_set.h>
927 __isl_give isl_union_set *isl_union_set_read_from_file(
928 isl_ctx *ctx, FILE *input);
929 __isl_give isl_union_set *isl_union_set_read_from_str(
930 isl_ctx *ctx, const char *str);
932 #include <isl/union_map.h>
933 __isl_give isl_union_map *isl_union_map_read_from_file(
934 isl_ctx *ctx, FILE *input);
935 __isl_give isl_union_map *isl_union_map_read_from_str(
936 isl_ctx *ctx, const char *str);
938 The input format is autodetected and may be either the C<PolyLib> format
939 or the C<isl> format.
943 Before anything can be printed, an C<isl_printer> needs to
946 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
948 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
949 void isl_printer_free(__isl_take isl_printer *printer);
950 __isl_give char *isl_printer_get_str(
951 __isl_keep isl_printer *printer);
953 The behavior of the printer can be modified in various ways
955 __isl_give isl_printer *isl_printer_set_output_format(
956 __isl_take isl_printer *p, int output_format);
957 __isl_give isl_printer *isl_printer_set_indent(
958 __isl_take isl_printer *p, int indent);
959 __isl_give isl_printer *isl_printer_indent(
960 __isl_take isl_printer *p, int indent);
961 __isl_give isl_printer *isl_printer_set_prefix(
962 __isl_take isl_printer *p, const char *prefix);
963 __isl_give isl_printer *isl_printer_set_suffix(
964 __isl_take isl_printer *p, const char *suffix);
966 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
967 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
968 and defaults to C<ISL_FORMAT_ISL>.
969 Each line in the output is indented by C<indent> (set by
970 C<isl_printer_set_indent>) spaces
971 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
972 In the C<PolyLib> format output,
973 the coefficients of the existentially quantified variables
974 appear between those of the set variables and those
976 The function C<isl_printer_indent> increases the indentation
977 by the specified amount (which may be negative).
979 To actually print something, use
982 __isl_give isl_printer *isl_printer_print_basic_set(
983 __isl_take isl_printer *printer,
984 __isl_keep isl_basic_set *bset);
985 __isl_give isl_printer *isl_printer_print_set(
986 __isl_take isl_printer *printer,
987 __isl_keep isl_set *set);
990 __isl_give isl_printer *isl_printer_print_basic_map(
991 __isl_take isl_printer *printer,
992 __isl_keep isl_basic_map *bmap);
993 __isl_give isl_printer *isl_printer_print_map(
994 __isl_take isl_printer *printer,
995 __isl_keep isl_map *map);
997 #include <isl/union_set.h>
998 __isl_give isl_printer *isl_printer_print_union_set(
999 __isl_take isl_printer *p,
1000 __isl_keep isl_union_set *uset);
1002 #include <isl/union_map.h>
1003 __isl_give isl_printer *isl_printer_print_union_map(
1004 __isl_take isl_printer *p,
1005 __isl_keep isl_union_map *umap);
1007 When called on a file printer, the following function flushes
1008 the file. When called on a string printer, the buffer is cleared.
1010 __isl_give isl_printer *isl_printer_flush(
1011 __isl_take isl_printer *p);
1013 =head2 Creating New Sets and Relations
1015 C<isl> has functions for creating some standard sets and relations.
1019 =item * Empty sets and relations
1021 __isl_give isl_basic_set *isl_basic_set_empty(
1022 __isl_take isl_space *space);
1023 __isl_give isl_basic_map *isl_basic_map_empty(
1024 __isl_take isl_space *space);
1025 __isl_give isl_set *isl_set_empty(
1026 __isl_take isl_space *space);
1027 __isl_give isl_map *isl_map_empty(
1028 __isl_take isl_space *space);
1029 __isl_give isl_union_set *isl_union_set_empty(
1030 __isl_take isl_space *space);
1031 __isl_give isl_union_map *isl_union_map_empty(
1032 __isl_take isl_space *space);
1034 For C<isl_union_set>s and C<isl_union_map>s, the space
1035 is only used to specify the parameters.
1037 =item * Universe sets and relations
1039 __isl_give isl_basic_set *isl_basic_set_universe(
1040 __isl_take isl_space *space);
1041 __isl_give isl_basic_map *isl_basic_map_universe(
1042 __isl_take isl_space *space);
1043 __isl_give isl_set *isl_set_universe(
1044 __isl_take isl_space *space);
1045 __isl_give isl_map *isl_map_universe(
1046 __isl_take isl_space *space);
1047 __isl_give isl_union_set *isl_union_set_universe(
1048 __isl_take isl_union_set *uset);
1049 __isl_give isl_union_map *isl_union_map_universe(
1050 __isl_take isl_union_map *umap);
1052 The sets and relations constructed by the functions above
1053 contain all integer values, while those constructed by the
1054 functions below only contain non-negative values.
1056 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1057 __isl_take isl_space *space);
1058 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1059 __isl_take isl_space *space);
1060 __isl_give isl_set *isl_set_nat_universe(
1061 __isl_take isl_space *space);
1062 __isl_give isl_map *isl_map_nat_universe(
1063 __isl_take isl_space *space);
1065 =item * Identity relations
1067 __isl_give isl_basic_map *isl_basic_map_identity(
1068 __isl_take isl_space *space);
1069 __isl_give isl_map *isl_map_identity(
1070 __isl_take isl_space *space);
1072 The number of input and output dimensions in C<space> needs
1075 =item * Lexicographic order
1077 __isl_give isl_map *isl_map_lex_lt(
1078 __isl_take isl_space *set_space);
1079 __isl_give isl_map *isl_map_lex_le(
1080 __isl_take isl_space *set_space);
1081 __isl_give isl_map *isl_map_lex_gt(
1082 __isl_take isl_space *set_space);
1083 __isl_give isl_map *isl_map_lex_ge(
1084 __isl_take isl_space *set_space);
1085 __isl_give isl_map *isl_map_lex_lt_first(
1086 __isl_take isl_space *space, unsigned n);
1087 __isl_give isl_map *isl_map_lex_le_first(
1088 __isl_take isl_space *space, unsigned n);
1089 __isl_give isl_map *isl_map_lex_gt_first(
1090 __isl_take isl_space *space, unsigned n);
1091 __isl_give isl_map *isl_map_lex_ge_first(
1092 __isl_take isl_space *space, unsigned n);
1094 The first four functions take a space for a B<set>
1095 and return relations that express that the elements in the domain
1096 are lexicographically less
1097 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1098 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1099 than the elements in the range.
1100 The last four functions take a space for a map
1101 and return relations that express that the first C<n> dimensions
1102 in the domain are lexicographically less
1103 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1104 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1105 than the first C<n> dimensions in the range.
1109 A basic set or relation can be converted to a set or relation
1110 using the following functions.
1112 __isl_give isl_set *isl_set_from_basic_set(
1113 __isl_take isl_basic_set *bset);
1114 __isl_give isl_map *isl_map_from_basic_map(
1115 __isl_take isl_basic_map *bmap);
1117 Sets and relations can be converted to union sets and relations
1118 using the following functions.
1120 __isl_give isl_union_map *isl_union_map_from_map(
1121 __isl_take isl_map *map);
1122 __isl_give isl_union_set *isl_union_set_from_set(
1123 __isl_take isl_set *set);
1125 The inverse conversions below can only be used if the input
1126 union set or relation is known to contain elements in exactly one
1129 __isl_give isl_set *isl_set_from_union_set(
1130 __isl_take isl_union_set *uset);
1131 __isl_give isl_map *isl_map_from_union_map(
1132 __isl_take isl_union_map *umap);
1134 A zero-dimensional set can be constructed on a given parameter domain
1135 using the following function.
1137 __isl_give isl_set *isl_set_from_params(
1138 __isl_take isl_set *set);
1140 Sets and relations can be copied and freed again using the following
1143 __isl_give isl_basic_set *isl_basic_set_copy(
1144 __isl_keep isl_basic_set *bset);
1145 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1146 __isl_give isl_union_set *isl_union_set_copy(
1147 __isl_keep isl_union_set *uset);
1148 __isl_give isl_basic_map *isl_basic_map_copy(
1149 __isl_keep isl_basic_map *bmap);
1150 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1151 __isl_give isl_union_map *isl_union_map_copy(
1152 __isl_keep isl_union_map *umap);
1153 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1154 void isl_set_free(__isl_take isl_set *set);
1155 void *isl_union_set_free(__isl_take isl_union_set *uset);
1156 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1157 void isl_map_free(__isl_take isl_map *map);
1158 void *isl_union_map_free(__isl_take isl_union_map *umap);
1160 Other sets and relations can be constructed by starting
1161 from a universe set or relation, adding equality and/or
1162 inequality constraints and then projecting out the
1163 existentially quantified variables, if any.
1164 Constraints can be constructed, manipulated and
1165 added to (or removed from) (basic) sets and relations
1166 using the following functions.
1168 #include <isl/constraint.h>
1169 __isl_give isl_constraint *isl_equality_alloc(
1170 __isl_take isl_local_space *ls);
1171 __isl_give isl_constraint *isl_inequality_alloc(
1172 __isl_take isl_local_space *ls);
1173 __isl_give isl_constraint *isl_constraint_set_constant(
1174 __isl_take isl_constraint *constraint, isl_int v);
1175 __isl_give isl_constraint *isl_constraint_set_constant_si(
1176 __isl_take isl_constraint *constraint, int v);
1177 __isl_give isl_constraint *isl_constraint_set_coefficient(
1178 __isl_take isl_constraint *constraint,
1179 enum isl_dim_type type, int pos, isl_int v);
1180 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1181 __isl_take isl_constraint *constraint,
1182 enum isl_dim_type type, int pos, int v);
1183 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1184 __isl_take isl_basic_map *bmap,
1185 __isl_take isl_constraint *constraint);
1186 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1187 __isl_take isl_basic_set *bset,
1188 __isl_take isl_constraint *constraint);
1189 __isl_give isl_map *isl_map_add_constraint(
1190 __isl_take isl_map *map,
1191 __isl_take isl_constraint *constraint);
1192 __isl_give isl_set *isl_set_add_constraint(
1193 __isl_take isl_set *set,
1194 __isl_take isl_constraint *constraint);
1195 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1196 __isl_take isl_basic_set *bset,
1197 __isl_take isl_constraint *constraint);
1199 For example, to create a set containing the even integers
1200 between 10 and 42, you would use the following code.
1203 isl_local_space *ls;
1205 isl_basic_set *bset;
1207 space = isl_space_set_alloc(ctx, 0, 2);
1208 bset = isl_basic_set_universe(isl_space_copy(space));
1209 ls = isl_local_space_from_space(space);
1211 c = isl_equality_alloc(isl_local_space_copy(ls));
1212 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1213 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1214 bset = isl_basic_set_add_constraint(bset, c);
1216 c = isl_inequality_alloc(isl_local_space_copy(ls));
1217 c = isl_constraint_set_constant_si(c, -10);
1218 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1219 bset = isl_basic_set_add_constraint(bset, c);
1221 c = isl_inequality_alloc(ls);
1222 c = isl_constraint_set_constant_si(c, 42);
1223 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1224 bset = isl_basic_set_add_constraint(bset, c);
1226 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1230 isl_basic_set *bset;
1231 bset = isl_basic_set_read_from_str(ctx,
1232 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1234 A basic set or relation can also be constructed from two matrices
1235 describing the equalities and the inequalities.
1237 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1238 __isl_take isl_space *space,
1239 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1240 enum isl_dim_type c1,
1241 enum isl_dim_type c2, enum isl_dim_type c3,
1242 enum isl_dim_type c4);
1243 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1244 __isl_take isl_space *space,
1245 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1246 enum isl_dim_type c1,
1247 enum isl_dim_type c2, enum isl_dim_type c3,
1248 enum isl_dim_type c4, enum isl_dim_type c5);
1250 The C<isl_dim_type> arguments indicate the order in which
1251 different kinds of variables appear in the input matrices
1252 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1253 C<isl_dim_set> and C<isl_dim_div> for sets and
1254 of C<isl_dim_cst>, C<isl_dim_param>,
1255 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1257 A (basic) set or relation can also be constructed from a (piecewise)
1258 (multiple) affine expression
1259 or a list of affine expressions
1260 (See L<"Piecewise Quasi Affine Expressions"> and
1261 L<"Piecewise Multiple Quasi Affine Expressions">).
1263 __isl_give isl_basic_map *isl_basic_map_from_aff(
1264 __isl_take isl_aff *aff);
1265 __isl_give isl_set *isl_set_from_pw_aff(
1266 __isl_take isl_pw_aff *pwaff);
1267 __isl_give isl_map *isl_map_from_pw_aff(
1268 __isl_take isl_pw_aff *pwaff);
1269 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1270 __isl_take isl_space *domain_space,
1271 __isl_take isl_aff_list *list);
1272 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1273 __isl_take isl_multi_aff *maff)
1274 __isl_give isl_set *isl_set_from_pw_multi_aff(
1275 __isl_take isl_pw_multi_aff *pma);
1276 __isl_give isl_map *isl_map_from_pw_multi_aff(
1277 __isl_take isl_pw_multi_aff *pma);
1279 The C<domain_dim> argument describes the domain of the resulting
1280 basic relation. It is required because the C<list> may consist
1281 of zero affine expressions.
1283 =head2 Inspecting Sets and Relations
1285 Usually, the user should not have to care about the actual constraints
1286 of the sets and maps, but should instead apply the abstract operations
1287 explained in the following sections.
1288 Occasionally, however, it may be required to inspect the individual
1289 coefficients of the constraints. This section explains how to do so.
1290 In these cases, it may also be useful to have C<isl> compute
1291 an explicit representation of the existentially quantified variables.
1293 __isl_give isl_set *isl_set_compute_divs(
1294 __isl_take isl_set *set);
1295 __isl_give isl_map *isl_map_compute_divs(
1296 __isl_take isl_map *map);
1297 __isl_give isl_union_set *isl_union_set_compute_divs(
1298 __isl_take isl_union_set *uset);
1299 __isl_give isl_union_map *isl_union_map_compute_divs(
1300 __isl_take isl_union_map *umap);
1302 This explicit representation defines the existentially quantified
1303 variables as integer divisions of the other variables, possibly
1304 including earlier existentially quantified variables.
1305 An explicitly represented existentially quantified variable therefore
1306 has a unique value when the values of the other variables are known.
1307 If, furthermore, the same existentials, i.e., existentials
1308 with the same explicit representations, should appear in the
1309 same order in each of the disjuncts of a set or map, then the user should call
1310 either of the following functions.
1312 __isl_give isl_set *isl_set_align_divs(
1313 __isl_take isl_set *set);
1314 __isl_give isl_map *isl_map_align_divs(
1315 __isl_take isl_map *map);
1317 Alternatively, the existentially quantified variables can be removed
1318 using the following functions, which compute an overapproximation.
1320 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1321 __isl_take isl_basic_set *bset);
1322 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1323 __isl_take isl_basic_map *bmap);
1324 __isl_give isl_set *isl_set_remove_divs(
1325 __isl_take isl_set *set);
1326 __isl_give isl_map *isl_map_remove_divs(
1327 __isl_take isl_map *map);
1329 To iterate over all the sets or maps in a union set or map, use
1331 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1332 int (*fn)(__isl_take isl_set *set, void *user),
1334 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1335 int (*fn)(__isl_take isl_map *map, void *user),
1338 The number of sets or maps in a union set or map can be obtained
1341 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1342 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1344 To extract the set or map in a given space from a union, use
1346 __isl_give isl_set *isl_union_set_extract_set(
1347 __isl_keep isl_union_set *uset,
1348 __isl_take isl_space *space);
1349 __isl_give isl_map *isl_union_map_extract_map(
1350 __isl_keep isl_union_map *umap,
1351 __isl_take isl_space *space);
1353 To iterate over all the basic sets or maps in a set or map, use
1355 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1356 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1358 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1359 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1362 The callback function C<fn> should return 0 if successful and
1363 -1 if an error occurs. In the latter case, or if any other error
1364 occurs, the above functions will return -1.
1366 It should be noted that C<isl> does not guarantee that
1367 the basic sets or maps passed to C<fn> are disjoint.
1368 If this is required, then the user should call one of
1369 the following functions first.
1371 __isl_give isl_set *isl_set_make_disjoint(
1372 __isl_take isl_set *set);
1373 __isl_give isl_map *isl_map_make_disjoint(
1374 __isl_take isl_map *map);
1376 The number of basic sets in a set can be obtained
1379 int isl_set_n_basic_set(__isl_keep isl_set *set);
1381 To iterate over the constraints of a basic set or map, use
1383 #include <isl/constraint.h>
1385 int isl_basic_map_foreach_constraint(
1386 __isl_keep isl_basic_map *bmap,
1387 int (*fn)(__isl_take isl_constraint *c, void *user),
1389 void *isl_constraint_free(__isl_take isl_constraint *c);
1391 Again, the callback function C<fn> should return 0 if successful and
1392 -1 if an error occurs. In the latter case, or if any other error
1393 occurs, the above functions will return -1.
1394 The constraint C<c> represents either an equality or an inequality.
1395 Use the following function to find out whether a constraint
1396 represents an equality. If not, it represents an inequality.
1398 int isl_constraint_is_equality(
1399 __isl_keep isl_constraint *constraint);
1401 The coefficients of the constraints can be inspected using
1402 the following functions.
1404 void isl_constraint_get_constant(
1405 __isl_keep isl_constraint *constraint, isl_int *v);
1406 void isl_constraint_get_coefficient(
1407 __isl_keep isl_constraint *constraint,
1408 enum isl_dim_type type, int pos, isl_int *v);
1409 int isl_constraint_involves_dims(
1410 __isl_keep isl_constraint *constraint,
1411 enum isl_dim_type type, unsigned first, unsigned n);
1413 The explicit representations of the existentially quantified
1414 variables can be inspected using the following function.
1415 Note that the user is only allowed to use this function
1416 if the inspected set or map is the result of a call
1417 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1418 The existentially quantified variable is equal to the floor
1419 of the returned affine expression. The affine expression
1420 itself can be inspected using the functions in
1421 L<"Piecewise Quasi Affine Expressions">.
1423 __isl_give isl_aff *isl_constraint_get_div(
1424 __isl_keep isl_constraint *constraint, int pos);
1426 To obtain the constraints of a basic set or map in matrix
1427 form, use the following functions.
1429 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1430 __isl_keep isl_basic_set *bset,
1431 enum isl_dim_type c1, enum isl_dim_type c2,
1432 enum isl_dim_type c3, enum isl_dim_type c4);
1433 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1434 __isl_keep isl_basic_set *bset,
1435 enum isl_dim_type c1, enum isl_dim_type c2,
1436 enum isl_dim_type c3, enum isl_dim_type c4);
1437 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1438 __isl_keep isl_basic_map *bmap,
1439 enum isl_dim_type c1,
1440 enum isl_dim_type c2, enum isl_dim_type c3,
1441 enum isl_dim_type c4, enum isl_dim_type c5);
1442 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1443 __isl_keep isl_basic_map *bmap,
1444 enum isl_dim_type c1,
1445 enum isl_dim_type c2, enum isl_dim_type c3,
1446 enum isl_dim_type c4, enum isl_dim_type c5);
1448 The C<isl_dim_type> arguments dictate the order in which
1449 different kinds of variables appear in the resulting matrix
1450 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1451 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1453 The number of parameters, input, output or set dimensions can
1454 be obtained using the following functions.
1456 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1457 enum isl_dim_type type);
1458 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1459 enum isl_dim_type type);
1460 unsigned isl_set_dim(__isl_keep isl_set *set,
1461 enum isl_dim_type type);
1462 unsigned isl_map_dim(__isl_keep isl_map *map,
1463 enum isl_dim_type type);
1465 To check whether the description of a set or relation depends
1466 on one or more given dimensions, it is not necessary to iterate over all
1467 constraints. Instead the following functions can be used.
1469 int isl_basic_set_involves_dims(
1470 __isl_keep isl_basic_set *bset,
1471 enum isl_dim_type type, unsigned first, unsigned n);
1472 int isl_set_involves_dims(__isl_keep isl_set *set,
1473 enum isl_dim_type type, unsigned first, unsigned n);
1474 int isl_basic_map_involves_dims(
1475 __isl_keep isl_basic_map *bmap,
1476 enum isl_dim_type type, unsigned first, unsigned n);
1477 int isl_map_involves_dims(__isl_keep isl_map *map,
1478 enum isl_dim_type type, unsigned first, unsigned n);
1480 Similarly, the following functions can be used to check whether
1481 a given dimension is involved in any lower or upper bound.
1483 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1484 enum isl_dim_type type, unsigned pos);
1485 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1486 enum isl_dim_type type, unsigned pos);
1488 The identifiers or names of the domain and range spaces of a set
1489 or relation can be read off or set using the following functions.
1491 __isl_give isl_set *isl_set_set_tuple_id(
1492 __isl_take isl_set *set, __isl_take isl_id *id);
1493 __isl_give isl_set *isl_set_reset_tuple_id(
1494 __isl_take isl_set *set);
1495 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1496 __isl_give isl_id *isl_set_get_tuple_id(
1497 __isl_keep isl_set *set);
1498 __isl_give isl_map *isl_map_set_tuple_id(
1499 __isl_take isl_map *map, enum isl_dim_type type,
1500 __isl_take isl_id *id);
1501 __isl_give isl_map *isl_map_reset_tuple_id(
1502 __isl_take isl_map *map, enum isl_dim_type type);
1503 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1504 enum isl_dim_type type);
1505 __isl_give isl_id *isl_map_get_tuple_id(
1506 __isl_keep isl_map *map, enum isl_dim_type type);
1508 const char *isl_basic_set_get_tuple_name(
1509 __isl_keep isl_basic_set *bset);
1510 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1511 __isl_take isl_basic_set *set, const char *s);
1512 const char *isl_set_get_tuple_name(
1513 __isl_keep isl_set *set);
1514 const char *isl_basic_map_get_tuple_name(
1515 __isl_keep isl_basic_map *bmap,
1516 enum isl_dim_type type);
1517 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1518 __isl_take isl_basic_map *bmap,
1519 enum isl_dim_type type, const char *s);
1520 const char *isl_map_get_tuple_name(
1521 __isl_keep isl_map *map,
1522 enum isl_dim_type type);
1524 As with C<isl_space_get_tuple_name>, the value returned points to
1525 an internal data structure.
1526 The identifiers, positions or names of individual dimensions can be
1527 read off using the following functions.
1529 __isl_give isl_set *isl_set_set_dim_id(
1530 __isl_take isl_set *set, enum isl_dim_type type,
1531 unsigned pos, __isl_take isl_id *id);
1532 int isl_set_has_dim_id(__isl_keep isl_set *set,
1533 enum isl_dim_type type, unsigned pos);
1534 __isl_give isl_id *isl_set_get_dim_id(
1535 __isl_keep isl_set *set, enum isl_dim_type type,
1537 int isl_basic_map_has_dim_id(
1538 __isl_keep isl_basic_map *bmap,
1539 enum isl_dim_type type, unsigned pos);
1540 __isl_give isl_map *isl_map_set_dim_id(
1541 __isl_take isl_map *map, enum isl_dim_type type,
1542 unsigned pos, __isl_take isl_id *id);
1543 int isl_map_has_dim_id(__isl_keep isl_map *map,
1544 enum isl_dim_type type, unsigned pos);
1545 __isl_give isl_id *isl_map_get_dim_id(
1546 __isl_keep isl_map *map, enum isl_dim_type type,
1549 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1550 enum isl_dim_type type, __isl_keep isl_id *id);
1551 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1552 enum isl_dim_type type, __isl_keep isl_id *id);
1553 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1554 enum isl_dim_type type, const char *name);
1555 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1556 enum isl_dim_type type, const char *name);
1558 const char *isl_constraint_get_dim_name(
1559 __isl_keep isl_constraint *constraint,
1560 enum isl_dim_type type, unsigned pos);
1561 const char *isl_basic_set_get_dim_name(
1562 __isl_keep isl_basic_set *bset,
1563 enum isl_dim_type type, unsigned pos);
1564 const char *isl_set_get_dim_name(
1565 __isl_keep isl_set *set,
1566 enum isl_dim_type type, unsigned pos);
1567 const char *isl_basic_map_get_dim_name(
1568 __isl_keep isl_basic_map *bmap,
1569 enum isl_dim_type type, unsigned pos);
1570 const char *isl_map_get_dim_name(
1571 __isl_keep isl_map *map,
1572 enum isl_dim_type type, unsigned pos);
1574 These functions are mostly useful to obtain the identifiers, positions
1575 or names of the parameters. Identifiers of individual dimensions are
1576 essentially only useful for printing. They are ignored by all other
1577 operations and may not be preserved across those operations.
1581 =head3 Unary Properties
1587 The following functions test whether the given set or relation
1588 contains any integer points. The ``plain'' variants do not perform
1589 any computations, but simply check if the given set or relation
1590 is already known to be empty.
1592 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1593 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1594 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1595 int isl_set_is_empty(__isl_keep isl_set *set);
1596 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1597 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1598 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1599 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1600 int isl_map_is_empty(__isl_keep isl_map *map);
1601 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1603 =item * Universality
1605 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1606 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1607 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1609 =item * Single-valuedness
1611 int isl_map_is_single_valued(__isl_keep isl_map *map);
1612 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1616 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1617 int isl_map_is_injective(__isl_keep isl_map *map);
1618 int isl_union_map_plain_is_injective(
1619 __isl_keep isl_union_map *umap);
1620 int isl_union_map_is_injective(
1621 __isl_keep isl_union_map *umap);
1625 int isl_map_is_bijective(__isl_keep isl_map *map);
1626 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1630 int isl_basic_map_plain_is_fixed(
1631 __isl_keep isl_basic_map *bmap,
1632 enum isl_dim_type type, unsigned pos,
1634 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1635 enum isl_dim_type type, unsigned pos,
1637 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1638 enum isl_dim_type type, unsigned pos,
1641 Check if the relation obviously lies on a hyperplane where the given dimension
1642 has a fixed value and if so, return that value in C<*val>.
1646 To check whether a set is a parameter domain, use this function:
1648 int isl_set_is_params(__isl_keep isl_set *set);
1649 int isl_union_set_is_params(
1650 __isl_keep isl_union_set *uset);
1654 The following functions check whether the domain of the given
1655 (basic) set is a wrapped relation.
1657 int isl_basic_set_is_wrapping(
1658 __isl_keep isl_basic_set *bset);
1659 int isl_set_is_wrapping(__isl_keep isl_set *set);
1661 =item * Internal Product
1663 int isl_basic_map_can_zip(
1664 __isl_keep isl_basic_map *bmap);
1665 int isl_map_can_zip(__isl_keep isl_map *map);
1667 Check whether the product of domain and range of the given relation
1669 i.e., whether both domain and range are nested relations.
1673 =head3 Binary Properties
1679 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1680 __isl_keep isl_set *set2);
1681 int isl_set_is_equal(__isl_keep isl_set *set1,
1682 __isl_keep isl_set *set2);
1683 int isl_union_set_is_equal(
1684 __isl_keep isl_union_set *uset1,
1685 __isl_keep isl_union_set *uset2);
1686 int isl_basic_map_is_equal(
1687 __isl_keep isl_basic_map *bmap1,
1688 __isl_keep isl_basic_map *bmap2);
1689 int isl_map_is_equal(__isl_keep isl_map *map1,
1690 __isl_keep isl_map *map2);
1691 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1692 __isl_keep isl_map *map2);
1693 int isl_union_map_is_equal(
1694 __isl_keep isl_union_map *umap1,
1695 __isl_keep isl_union_map *umap2);
1697 =item * Disjointness
1699 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1700 __isl_keep isl_set *set2);
1704 int isl_set_is_subset(__isl_keep isl_set *set1,
1705 __isl_keep isl_set *set2);
1706 int isl_set_is_strict_subset(
1707 __isl_keep isl_set *set1,
1708 __isl_keep isl_set *set2);
1709 int isl_union_set_is_subset(
1710 __isl_keep isl_union_set *uset1,
1711 __isl_keep isl_union_set *uset2);
1712 int isl_union_set_is_strict_subset(
1713 __isl_keep isl_union_set *uset1,
1714 __isl_keep isl_union_set *uset2);
1715 int isl_basic_map_is_subset(
1716 __isl_keep isl_basic_map *bmap1,
1717 __isl_keep isl_basic_map *bmap2);
1718 int isl_basic_map_is_strict_subset(
1719 __isl_keep isl_basic_map *bmap1,
1720 __isl_keep isl_basic_map *bmap2);
1721 int isl_map_is_subset(
1722 __isl_keep isl_map *map1,
1723 __isl_keep isl_map *map2);
1724 int isl_map_is_strict_subset(
1725 __isl_keep isl_map *map1,
1726 __isl_keep isl_map *map2);
1727 int isl_union_map_is_subset(
1728 __isl_keep isl_union_map *umap1,
1729 __isl_keep isl_union_map *umap2);
1730 int isl_union_map_is_strict_subset(
1731 __isl_keep isl_union_map *umap1,
1732 __isl_keep isl_union_map *umap2);
1736 =head2 Unary Operations
1742 __isl_give isl_set *isl_set_complement(
1743 __isl_take isl_set *set);
1747 __isl_give isl_basic_map *isl_basic_map_reverse(
1748 __isl_take isl_basic_map *bmap);
1749 __isl_give isl_map *isl_map_reverse(
1750 __isl_take isl_map *map);
1751 __isl_give isl_union_map *isl_union_map_reverse(
1752 __isl_take isl_union_map *umap);
1756 __isl_give isl_basic_set *isl_basic_set_project_out(
1757 __isl_take isl_basic_set *bset,
1758 enum isl_dim_type type, unsigned first, unsigned n);
1759 __isl_give isl_basic_map *isl_basic_map_project_out(
1760 __isl_take isl_basic_map *bmap,
1761 enum isl_dim_type type, unsigned first, unsigned n);
1762 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1763 enum isl_dim_type type, unsigned first, unsigned n);
1764 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1765 enum isl_dim_type type, unsigned first, unsigned n);
1766 __isl_give isl_basic_set *isl_basic_set_params(
1767 __isl_take isl_basic_set *bset);
1768 __isl_give isl_basic_set *isl_basic_map_domain(
1769 __isl_take isl_basic_map *bmap);
1770 __isl_give isl_basic_set *isl_basic_map_range(
1771 __isl_take isl_basic_map *bmap);
1772 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1773 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1774 __isl_give isl_set *isl_map_domain(
1775 __isl_take isl_map *bmap);
1776 __isl_give isl_set *isl_map_range(
1777 __isl_take isl_map *map);
1778 __isl_give isl_set *isl_union_set_params(
1779 __isl_take isl_union_set *uset);
1780 __isl_give isl_set *isl_union_map_params(
1781 __isl_take isl_union_map *umap);
1782 __isl_give isl_union_set *isl_union_map_domain(
1783 __isl_take isl_union_map *umap);
1784 __isl_give isl_union_set *isl_union_map_range(
1785 __isl_take isl_union_map *umap);
1787 __isl_give isl_basic_map *isl_basic_map_domain_map(
1788 __isl_take isl_basic_map *bmap);
1789 __isl_give isl_basic_map *isl_basic_map_range_map(
1790 __isl_take isl_basic_map *bmap);
1791 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1792 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1793 __isl_give isl_union_map *isl_union_map_domain_map(
1794 __isl_take isl_union_map *umap);
1795 __isl_give isl_union_map *isl_union_map_range_map(
1796 __isl_take isl_union_map *umap);
1798 The functions above construct a (basic, regular or union) relation
1799 that maps (a wrapped version of) the input relation to its domain or range.
1803 __isl_give isl_set *isl_set_eliminate(
1804 __isl_take isl_set *set, enum isl_dim_type type,
1805 unsigned first, unsigned n);
1806 __isl_give isl_basic_map *isl_basic_map_eliminate(
1807 __isl_take isl_basic_map *bmap,
1808 enum isl_dim_type type,
1809 unsigned first, unsigned n);
1810 __isl_give isl_map *isl_map_eliminate(
1811 __isl_take isl_map *map, enum isl_dim_type type,
1812 unsigned first, unsigned n);
1814 Eliminate the coefficients for the given dimensions from the constraints,
1815 without removing the dimensions.
1819 __isl_give isl_basic_set *isl_basic_set_fix(
1820 __isl_take isl_basic_set *bset,
1821 enum isl_dim_type type, unsigned pos,
1823 __isl_give isl_basic_set *isl_basic_set_fix_si(
1824 __isl_take isl_basic_set *bset,
1825 enum isl_dim_type type, unsigned pos, int value);
1826 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1827 enum isl_dim_type type, unsigned pos,
1829 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1830 enum isl_dim_type type, unsigned pos, int value);
1831 __isl_give isl_basic_map *isl_basic_map_fix_si(
1832 __isl_take isl_basic_map *bmap,
1833 enum isl_dim_type type, unsigned pos, int value);
1834 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1835 enum isl_dim_type type, unsigned pos, int value);
1837 Intersect the set or relation with the hyperplane where the given
1838 dimension has the fixed given value.
1840 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1841 __isl_take isl_basic_map *bmap,
1842 enum isl_dim_type type, unsigned pos, int value);
1843 __isl_give isl_set *isl_set_lower_bound_si(
1844 __isl_take isl_set *set,
1845 enum isl_dim_type type, unsigned pos, int value);
1846 __isl_give isl_map *isl_map_lower_bound_si(
1847 __isl_take isl_map *map,
1848 enum isl_dim_type type, unsigned pos, int value);
1849 __isl_give isl_set *isl_set_upper_bound_si(
1850 __isl_take isl_set *set,
1851 enum isl_dim_type type, unsigned pos, int value);
1852 __isl_give isl_map *isl_map_upper_bound_si(
1853 __isl_take isl_map *map,
1854 enum isl_dim_type type, unsigned pos, int value);
1856 Intersect the set or relation with the half-space where the given
1857 dimension has a value bounded the fixed given value.
1859 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1860 enum isl_dim_type type1, int pos1,
1861 enum isl_dim_type type2, int pos2);
1862 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1863 enum isl_dim_type type1, int pos1,
1864 enum isl_dim_type type2, int pos2);
1866 Intersect the set or relation with the hyperplane where the given
1867 dimensions are equal to each other.
1869 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1870 enum isl_dim_type type1, int pos1,
1871 enum isl_dim_type type2, int pos2);
1873 Intersect the relation with the hyperplane where the given
1874 dimensions have opposite values.
1878 __isl_give isl_map *isl_set_identity(
1879 __isl_take isl_set *set);
1880 __isl_give isl_union_map *isl_union_set_identity(
1881 __isl_take isl_union_set *uset);
1883 Construct an identity relation on the given (union) set.
1887 __isl_give isl_basic_set *isl_basic_map_deltas(
1888 __isl_take isl_basic_map *bmap);
1889 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1890 __isl_give isl_union_set *isl_union_map_deltas(
1891 __isl_take isl_union_map *umap);
1893 These functions return a (basic) set containing the differences
1894 between image elements and corresponding domain elements in the input.
1896 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1897 __isl_take isl_basic_map *bmap);
1898 __isl_give isl_map *isl_map_deltas_map(
1899 __isl_take isl_map *map);
1900 __isl_give isl_union_map *isl_union_map_deltas_map(
1901 __isl_take isl_union_map *umap);
1903 The functions above construct a (basic, regular or union) relation
1904 that maps (a wrapped version of) the input relation to its delta set.
1908 Simplify the representation of a set or relation by trying
1909 to combine pairs of basic sets or relations into a single
1910 basic set or relation.
1912 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1913 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1914 __isl_give isl_union_set *isl_union_set_coalesce(
1915 __isl_take isl_union_set *uset);
1916 __isl_give isl_union_map *isl_union_map_coalesce(
1917 __isl_take isl_union_map *umap);
1919 =item * Detecting equalities
1921 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1922 __isl_take isl_basic_set *bset);
1923 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1924 __isl_take isl_basic_map *bmap);
1925 __isl_give isl_set *isl_set_detect_equalities(
1926 __isl_take isl_set *set);
1927 __isl_give isl_map *isl_map_detect_equalities(
1928 __isl_take isl_map *map);
1929 __isl_give isl_union_set *isl_union_set_detect_equalities(
1930 __isl_take isl_union_set *uset);
1931 __isl_give isl_union_map *isl_union_map_detect_equalities(
1932 __isl_take isl_union_map *umap);
1934 Simplify the representation of a set or relation by detecting implicit
1937 =item * Removing redundant constraints
1939 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1940 __isl_take isl_basic_set *bset);
1941 __isl_give isl_set *isl_set_remove_redundancies(
1942 __isl_take isl_set *set);
1943 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1944 __isl_take isl_basic_map *bmap);
1945 __isl_give isl_map *isl_map_remove_redundancies(
1946 __isl_take isl_map *map);
1950 __isl_give isl_basic_set *isl_set_convex_hull(
1951 __isl_take isl_set *set);
1952 __isl_give isl_basic_map *isl_map_convex_hull(
1953 __isl_take isl_map *map);
1955 If the input set or relation has any existentially quantified
1956 variables, then the result of these operations is currently undefined.
1960 __isl_give isl_basic_set *isl_set_simple_hull(
1961 __isl_take isl_set *set);
1962 __isl_give isl_basic_map *isl_map_simple_hull(
1963 __isl_take isl_map *map);
1964 __isl_give isl_union_map *isl_union_map_simple_hull(
1965 __isl_take isl_union_map *umap);
1967 These functions compute a single basic set or relation
1968 that contains the whole input set or relation.
1969 In particular, the output is described by translates
1970 of the constraints describing the basic sets or relations in the input.
1974 (See \autoref{s:simple hull}.)
1980 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1981 __isl_take isl_basic_set *bset);
1982 __isl_give isl_basic_set *isl_set_affine_hull(
1983 __isl_take isl_set *set);
1984 __isl_give isl_union_set *isl_union_set_affine_hull(
1985 __isl_take isl_union_set *uset);
1986 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1987 __isl_take isl_basic_map *bmap);
1988 __isl_give isl_basic_map *isl_map_affine_hull(
1989 __isl_take isl_map *map);
1990 __isl_give isl_union_map *isl_union_map_affine_hull(
1991 __isl_take isl_union_map *umap);
1993 In case of union sets and relations, the affine hull is computed
1996 =item * Polyhedral hull
1998 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1999 __isl_take isl_set *set);
2000 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2001 __isl_take isl_map *map);
2002 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2003 __isl_take isl_union_set *uset);
2004 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2005 __isl_take isl_union_map *umap);
2007 These functions compute a single basic set or relation
2008 not involving any existentially quantified variables
2009 that contains the whole input set or relation.
2010 In case of union sets and relations, the polyhedral hull is computed
2013 =item * Optimization
2015 #include <isl/ilp.h>
2016 enum isl_lp_result isl_basic_set_max(
2017 __isl_keep isl_basic_set *bset,
2018 __isl_keep isl_aff *obj, isl_int *opt)
2019 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2020 __isl_keep isl_aff *obj, isl_int *opt);
2021 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2022 __isl_keep isl_aff *obj, isl_int *opt);
2024 Compute the minimum or maximum of the integer affine expression C<obj>
2025 over the points in C<set>, returning the result in C<opt>.
2026 The return value may be one of C<isl_lp_error>,
2027 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2029 =item * Parametric optimization
2031 __isl_give isl_pw_aff *isl_set_dim_min(
2032 __isl_take isl_set *set, int pos);
2033 __isl_give isl_pw_aff *isl_set_dim_max(
2034 __isl_take isl_set *set, int pos);
2035 __isl_give isl_pw_aff *isl_map_dim_max(
2036 __isl_take isl_map *map, int pos);
2038 Compute the minimum or maximum of the given set or output dimension
2039 as a function of the parameters (and input dimensions), but independently
2040 of the other set or output dimensions.
2041 For lexicographic optimization, see L<"Lexicographic Optimization">.
2045 The following functions compute either the set of (rational) coefficient
2046 values of valid constraints for the given set or the set of (rational)
2047 values satisfying the constraints with coefficients from the given set.
2048 Internally, these two sets of functions perform essentially the
2049 same operations, except that the set of coefficients is assumed to
2050 be a cone, while the set of values may be any polyhedron.
2051 The current implementation is based on the Farkas lemma and
2052 Fourier-Motzkin elimination, but this may change or be made optional
2053 in future. In particular, future implementations may use different
2054 dualization algorithms or skip the elimination step.
2056 __isl_give isl_basic_set *isl_basic_set_coefficients(
2057 __isl_take isl_basic_set *bset);
2058 __isl_give isl_basic_set *isl_set_coefficients(
2059 __isl_take isl_set *set);
2060 __isl_give isl_union_set *isl_union_set_coefficients(
2061 __isl_take isl_union_set *bset);
2062 __isl_give isl_basic_set *isl_basic_set_solutions(
2063 __isl_take isl_basic_set *bset);
2064 __isl_give isl_basic_set *isl_set_solutions(
2065 __isl_take isl_set *set);
2066 __isl_give isl_union_set *isl_union_set_solutions(
2067 __isl_take isl_union_set *bset);
2071 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2073 __isl_give isl_union_map *isl_union_map_power(
2074 __isl_take isl_union_map *umap, int *exact);
2076 Compute a parametric representation for all positive powers I<k> of C<map>.
2077 The result maps I<k> to a nested relation corresponding to the
2078 I<k>th power of C<map>.
2079 The result may be an overapproximation. If the result is known to be exact,
2080 then C<*exact> is set to C<1>.
2082 =item * Transitive closure
2084 __isl_give isl_map *isl_map_transitive_closure(
2085 __isl_take isl_map *map, int *exact);
2086 __isl_give isl_union_map *isl_union_map_transitive_closure(
2087 __isl_take isl_union_map *umap, int *exact);
2089 Compute the transitive closure of C<map>.
2090 The result may be an overapproximation. If the result is known to be exact,
2091 then C<*exact> is set to C<1>.
2093 =item * Reaching path lengths
2095 __isl_give isl_map *isl_map_reaching_path_lengths(
2096 __isl_take isl_map *map, int *exact);
2098 Compute a relation that maps each element in the range of C<map>
2099 to the lengths of all paths composed of edges in C<map> that
2100 end up in the given element.
2101 The result may be an overapproximation. If the result is known to be exact,
2102 then C<*exact> is set to C<1>.
2103 To compute the I<maximal> path length, the resulting relation
2104 should be postprocessed by C<isl_map_lexmax>.
2105 In particular, if the input relation is a dependence relation
2106 (mapping sources to sinks), then the maximal path length corresponds
2107 to the free schedule.
2108 Note, however, that C<isl_map_lexmax> expects the maximum to be
2109 finite, so if the path lengths are unbounded (possibly due to
2110 the overapproximation), then you will get an error message.
2114 __isl_give isl_basic_set *isl_basic_map_wrap(
2115 __isl_take isl_basic_map *bmap);
2116 __isl_give isl_set *isl_map_wrap(
2117 __isl_take isl_map *map);
2118 __isl_give isl_union_set *isl_union_map_wrap(
2119 __isl_take isl_union_map *umap);
2120 __isl_give isl_basic_map *isl_basic_set_unwrap(
2121 __isl_take isl_basic_set *bset);
2122 __isl_give isl_map *isl_set_unwrap(
2123 __isl_take isl_set *set);
2124 __isl_give isl_union_map *isl_union_set_unwrap(
2125 __isl_take isl_union_set *uset);
2129 Remove any internal structure of domain (and range) of the given
2130 set or relation. If there is any such internal structure in the input,
2131 then the name of the space is also removed.
2133 __isl_give isl_basic_set *isl_basic_set_flatten(
2134 __isl_take isl_basic_set *bset);
2135 __isl_give isl_set *isl_set_flatten(
2136 __isl_take isl_set *set);
2137 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2138 __isl_take isl_basic_map *bmap);
2139 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2140 __isl_take isl_basic_map *bmap);
2141 __isl_give isl_map *isl_map_flatten_range(
2142 __isl_take isl_map *map);
2143 __isl_give isl_map *isl_map_flatten_domain(
2144 __isl_take isl_map *map);
2145 __isl_give isl_basic_map *isl_basic_map_flatten(
2146 __isl_take isl_basic_map *bmap);
2147 __isl_give isl_map *isl_map_flatten(
2148 __isl_take isl_map *map);
2150 __isl_give isl_map *isl_set_flatten_map(
2151 __isl_take isl_set *set);
2153 The function above constructs a relation
2154 that maps the input set to a flattened version of the set.
2158 Lift the input set to a space with extra dimensions corresponding
2159 to the existentially quantified variables in the input.
2160 In particular, the result lives in a wrapped map where the domain
2161 is the original space and the range corresponds to the original
2162 existentially quantified variables.
2164 __isl_give isl_basic_set *isl_basic_set_lift(
2165 __isl_take isl_basic_set *bset);
2166 __isl_give isl_set *isl_set_lift(
2167 __isl_take isl_set *set);
2168 __isl_give isl_union_set *isl_union_set_lift(
2169 __isl_take isl_union_set *uset);
2171 Given a local space that contains the existentially quantified
2172 variables of a set, a basic relation that, when applied to
2173 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2174 can be constructed using the following function.
2176 #include <isl/local_space.h>
2177 __isl_give isl_basic_map *isl_local_space_lifting(
2178 __isl_take isl_local_space *ls);
2180 =item * Internal Product
2182 __isl_give isl_basic_map *isl_basic_map_zip(
2183 __isl_take isl_basic_map *bmap);
2184 __isl_give isl_map *isl_map_zip(
2185 __isl_take isl_map *map);
2186 __isl_give isl_union_map *isl_union_map_zip(
2187 __isl_take isl_union_map *umap);
2189 Given a relation with nested relations for domain and range,
2190 interchange the range of the domain with the domain of the range.
2192 =item * Aligning parameters
2194 __isl_give isl_set *isl_set_align_params(
2195 __isl_take isl_set *set,
2196 __isl_take isl_space *model);
2197 __isl_give isl_map *isl_map_align_params(
2198 __isl_take isl_map *map,
2199 __isl_take isl_space *model);
2201 Change the order of the parameters of the given set or relation
2202 such that the first parameters match those of C<model>.
2203 This may involve the introduction of extra parameters.
2204 All parameters need to be named.
2206 =item * Dimension manipulation
2208 __isl_give isl_set *isl_set_add_dims(
2209 __isl_take isl_set *set,
2210 enum isl_dim_type type, unsigned n);
2211 __isl_give isl_map *isl_map_add_dims(
2212 __isl_take isl_map *map,
2213 enum isl_dim_type type, unsigned n);
2214 __isl_give isl_set *isl_set_insert_dims(
2215 __isl_take isl_set *set,
2216 enum isl_dim_type type, unsigned pos, unsigned n);
2217 __isl_give isl_map *isl_map_insert_dims(
2218 __isl_take isl_map *map,
2219 enum isl_dim_type type, unsigned pos, unsigned n);
2220 __isl_give isl_basic_set *isl_basic_set_move_dims(
2221 __isl_take isl_basic_set *bset,
2222 enum isl_dim_type dst_type, unsigned dst_pos,
2223 enum isl_dim_type src_type, unsigned src_pos,
2225 __isl_give isl_basic_map *isl_basic_map_move_dims(
2226 __isl_take isl_basic_map *bmap,
2227 enum isl_dim_type dst_type, unsigned dst_pos,
2228 enum isl_dim_type src_type, unsigned src_pos,
2230 __isl_give isl_set *isl_set_move_dims(
2231 __isl_take isl_set *set,
2232 enum isl_dim_type dst_type, unsigned dst_pos,
2233 enum isl_dim_type src_type, unsigned src_pos,
2235 __isl_give isl_map *isl_map_move_dims(
2236 __isl_take isl_map *map,
2237 enum isl_dim_type dst_type, unsigned dst_pos,
2238 enum isl_dim_type src_type, unsigned src_pos,
2241 It is usually not advisable to directly change the (input or output)
2242 space of a set or a relation as this removes the name and the internal
2243 structure of the space. However, the above functions can be useful
2244 to add new parameters, assuming
2245 C<isl_set_align_params> and C<isl_map_align_params>
2250 =head2 Binary Operations
2252 The two arguments of a binary operation not only need to live
2253 in the same C<isl_ctx>, they currently also need to have
2254 the same (number of) parameters.
2256 =head3 Basic Operations
2260 =item * Intersection
2262 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2263 __isl_take isl_basic_set *bset1,
2264 __isl_take isl_basic_set *bset2);
2265 __isl_give isl_basic_set *isl_basic_set_intersect(
2266 __isl_take isl_basic_set *bset1,
2267 __isl_take isl_basic_set *bset2);
2268 __isl_give isl_set *isl_set_intersect_params(
2269 __isl_take isl_set *set,
2270 __isl_take isl_set *params);
2271 __isl_give isl_set *isl_set_intersect(
2272 __isl_take isl_set *set1,
2273 __isl_take isl_set *set2);
2274 __isl_give isl_union_set *isl_union_set_intersect_params(
2275 __isl_take isl_union_set *uset,
2276 __isl_take isl_set *set);
2277 __isl_give isl_union_map *isl_union_map_intersect_params(
2278 __isl_take isl_union_map *umap,
2279 __isl_take isl_set *set);
2280 __isl_give isl_union_set *isl_union_set_intersect(
2281 __isl_take isl_union_set *uset1,
2282 __isl_take isl_union_set *uset2);
2283 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2284 __isl_take isl_basic_map *bmap,
2285 __isl_take isl_basic_set *bset);
2286 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2287 __isl_take isl_basic_map *bmap,
2288 __isl_take isl_basic_set *bset);
2289 __isl_give isl_basic_map *isl_basic_map_intersect(
2290 __isl_take isl_basic_map *bmap1,
2291 __isl_take isl_basic_map *bmap2);
2292 __isl_give isl_map *isl_map_intersect_params(
2293 __isl_take isl_map *map,
2294 __isl_take isl_set *params);
2295 __isl_give isl_map *isl_map_intersect_domain(
2296 __isl_take isl_map *map,
2297 __isl_take isl_set *set);
2298 __isl_give isl_map *isl_map_intersect_range(
2299 __isl_take isl_map *map,
2300 __isl_take isl_set *set);
2301 __isl_give isl_map *isl_map_intersect(
2302 __isl_take isl_map *map1,
2303 __isl_take isl_map *map2);
2304 __isl_give isl_union_map *isl_union_map_intersect_domain(
2305 __isl_take isl_union_map *umap,
2306 __isl_take isl_union_set *uset);
2307 __isl_give isl_union_map *isl_union_map_intersect_range(
2308 __isl_take isl_union_map *umap,
2309 __isl_take isl_union_set *uset);
2310 __isl_give isl_union_map *isl_union_map_intersect(
2311 __isl_take isl_union_map *umap1,
2312 __isl_take isl_union_map *umap2);
2316 __isl_give isl_set *isl_basic_set_union(
2317 __isl_take isl_basic_set *bset1,
2318 __isl_take isl_basic_set *bset2);
2319 __isl_give isl_map *isl_basic_map_union(
2320 __isl_take isl_basic_map *bmap1,
2321 __isl_take isl_basic_map *bmap2);
2322 __isl_give isl_set *isl_set_union(
2323 __isl_take isl_set *set1,
2324 __isl_take isl_set *set2);
2325 __isl_give isl_map *isl_map_union(
2326 __isl_take isl_map *map1,
2327 __isl_take isl_map *map2);
2328 __isl_give isl_union_set *isl_union_set_union(
2329 __isl_take isl_union_set *uset1,
2330 __isl_take isl_union_set *uset2);
2331 __isl_give isl_union_map *isl_union_map_union(
2332 __isl_take isl_union_map *umap1,
2333 __isl_take isl_union_map *umap2);
2335 =item * Set difference
2337 __isl_give isl_set *isl_set_subtract(
2338 __isl_take isl_set *set1,
2339 __isl_take isl_set *set2);
2340 __isl_give isl_map *isl_map_subtract(
2341 __isl_take isl_map *map1,
2342 __isl_take isl_map *map2);
2343 __isl_give isl_map *isl_map_subtract_domain(
2344 __isl_take isl_map *map,
2345 __isl_take isl_set *dom);
2346 __isl_give isl_map *isl_map_subtract_range(
2347 __isl_take isl_map *map,
2348 __isl_take isl_set *dom);
2349 __isl_give isl_union_set *isl_union_set_subtract(
2350 __isl_take isl_union_set *uset1,
2351 __isl_take isl_union_set *uset2);
2352 __isl_give isl_union_map *isl_union_map_subtract(
2353 __isl_take isl_union_map *umap1,
2354 __isl_take isl_union_map *umap2);
2358 __isl_give isl_basic_set *isl_basic_set_apply(
2359 __isl_take isl_basic_set *bset,
2360 __isl_take isl_basic_map *bmap);
2361 __isl_give isl_set *isl_set_apply(
2362 __isl_take isl_set *set,
2363 __isl_take isl_map *map);
2364 __isl_give isl_union_set *isl_union_set_apply(
2365 __isl_take isl_union_set *uset,
2366 __isl_take isl_union_map *umap);
2367 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2368 __isl_take isl_basic_map *bmap1,
2369 __isl_take isl_basic_map *bmap2);
2370 __isl_give isl_basic_map *isl_basic_map_apply_range(
2371 __isl_take isl_basic_map *bmap1,
2372 __isl_take isl_basic_map *bmap2);
2373 __isl_give isl_map *isl_map_apply_domain(
2374 __isl_take isl_map *map1,
2375 __isl_take isl_map *map2);
2376 __isl_give isl_union_map *isl_union_map_apply_domain(
2377 __isl_take isl_union_map *umap1,
2378 __isl_take isl_union_map *umap2);
2379 __isl_give isl_map *isl_map_apply_range(
2380 __isl_take isl_map *map1,
2381 __isl_take isl_map *map2);
2382 __isl_give isl_union_map *isl_union_map_apply_range(
2383 __isl_take isl_union_map *umap1,
2384 __isl_take isl_union_map *umap2);
2386 =item * Cartesian Product
2388 __isl_give isl_set *isl_set_product(
2389 __isl_take isl_set *set1,
2390 __isl_take isl_set *set2);
2391 __isl_give isl_union_set *isl_union_set_product(
2392 __isl_take isl_union_set *uset1,
2393 __isl_take isl_union_set *uset2);
2394 __isl_give isl_basic_map *isl_basic_map_domain_product(
2395 __isl_take isl_basic_map *bmap1,
2396 __isl_take isl_basic_map *bmap2);
2397 __isl_give isl_basic_map *isl_basic_map_range_product(
2398 __isl_take isl_basic_map *bmap1,
2399 __isl_take isl_basic_map *bmap2);
2400 __isl_give isl_map *isl_map_domain_product(
2401 __isl_take isl_map *map1,
2402 __isl_take isl_map *map2);
2403 __isl_give isl_map *isl_map_range_product(
2404 __isl_take isl_map *map1,
2405 __isl_take isl_map *map2);
2406 __isl_give isl_union_map *isl_union_map_range_product(
2407 __isl_take isl_union_map *umap1,
2408 __isl_take isl_union_map *umap2);
2409 __isl_give isl_map *isl_map_product(
2410 __isl_take isl_map *map1,
2411 __isl_take isl_map *map2);
2412 __isl_give isl_union_map *isl_union_map_product(
2413 __isl_take isl_union_map *umap1,
2414 __isl_take isl_union_map *umap2);
2416 The above functions compute the cross product of the given
2417 sets or relations. The domains and ranges of the results
2418 are wrapped maps between domains and ranges of the inputs.
2419 To obtain a ``flat'' product, use the following functions
2422 __isl_give isl_basic_set *isl_basic_set_flat_product(
2423 __isl_take isl_basic_set *bset1,
2424 __isl_take isl_basic_set *bset2);
2425 __isl_give isl_set *isl_set_flat_product(
2426 __isl_take isl_set *set1,
2427 __isl_take isl_set *set2);
2428 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2429 __isl_take isl_basic_map *bmap1,
2430 __isl_take isl_basic_map *bmap2);
2431 __isl_give isl_map *isl_map_flat_domain_product(
2432 __isl_take isl_map *map1,
2433 __isl_take isl_map *map2);
2434 __isl_give isl_map *isl_map_flat_range_product(
2435 __isl_take isl_map *map1,
2436 __isl_take isl_map *map2);
2437 __isl_give isl_union_map *isl_union_map_flat_range_product(
2438 __isl_take isl_union_map *umap1,
2439 __isl_take isl_union_map *umap2);
2440 __isl_give isl_basic_map *isl_basic_map_flat_product(
2441 __isl_take isl_basic_map *bmap1,
2442 __isl_take isl_basic_map *bmap2);
2443 __isl_give isl_map *isl_map_flat_product(
2444 __isl_take isl_map *map1,
2445 __isl_take isl_map *map2);
2447 =item * Simplification
2449 __isl_give isl_basic_set *isl_basic_set_gist(
2450 __isl_take isl_basic_set *bset,
2451 __isl_take isl_basic_set *context);
2452 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2453 __isl_take isl_set *context);
2454 __isl_give isl_set *isl_set_gist_params(
2455 __isl_take isl_set *set,
2456 __isl_take isl_set *context);
2457 __isl_give isl_union_set *isl_union_set_gist(
2458 __isl_take isl_union_set *uset,
2459 __isl_take isl_union_set *context);
2460 __isl_give isl_union_set *isl_union_set_gist_params(
2461 __isl_take isl_union_set *uset,
2462 __isl_take isl_set *set);
2463 __isl_give isl_basic_map *isl_basic_map_gist(
2464 __isl_take isl_basic_map *bmap,
2465 __isl_take isl_basic_map *context);
2466 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2467 __isl_take isl_map *context);
2468 __isl_give isl_map *isl_map_gist_params(
2469 __isl_take isl_map *map,
2470 __isl_take isl_set *context);
2471 __isl_give isl_map *isl_map_gist_domain(
2472 __isl_take isl_map *map,
2473 __isl_take isl_set *context);
2474 __isl_give isl_map *isl_map_gist_range(
2475 __isl_take isl_map *map,
2476 __isl_take isl_set *context);
2477 __isl_give isl_union_map *isl_union_map_gist(
2478 __isl_take isl_union_map *umap,
2479 __isl_take isl_union_map *context);
2480 __isl_give isl_union_map *isl_union_map_gist_params(
2481 __isl_take isl_union_map *umap,
2482 __isl_take isl_set *set);
2483 __isl_give isl_union_map *isl_union_map_gist_domain(
2484 __isl_take isl_union_map *umap,
2485 __isl_take isl_union_set *uset);
2487 The gist operation returns a set or relation that has the
2488 same intersection with the context as the input set or relation.
2489 Any implicit equality in the intersection is made explicit in the result,
2490 while all inequalities that are redundant with respect to the intersection
2492 In case of union sets and relations, the gist operation is performed
2497 =head3 Lexicographic Optimization
2499 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2500 the following functions
2501 compute a set that contains the lexicographic minimum or maximum
2502 of the elements in C<set> (or C<bset>) for those values of the parameters
2503 that satisfy C<dom>.
2504 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2505 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2507 In other words, the union of the parameter values
2508 for which the result is non-empty and of C<*empty>
2511 __isl_give isl_set *isl_basic_set_partial_lexmin(
2512 __isl_take isl_basic_set *bset,
2513 __isl_take isl_basic_set *dom,
2514 __isl_give isl_set **empty);
2515 __isl_give isl_set *isl_basic_set_partial_lexmax(
2516 __isl_take isl_basic_set *bset,
2517 __isl_take isl_basic_set *dom,
2518 __isl_give isl_set **empty);
2519 __isl_give isl_set *isl_set_partial_lexmin(
2520 __isl_take isl_set *set, __isl_take isl_set *dom,
2521 __isl_give isl_set **empty);
2522 __isl_give isl_set *isl_set_partial_lexmax(
2523 __isl_take isl_set *set, __isl_take isl_set *dom,
2524 __isl_give isl_set **empty);
2526 Given a (basic) set C<set> (or C<bset>), the following functions simply
2527 return a set containing the lexicographic minimum or maximum
2528 of the elements in C<set> (or C<bset>).
2529 In case of union sets, the optimum is computed per space.
2531 __isl_give isl_set *isl_basic_set_lexmin(
2532 __isl_take isl_basic_set *bset);
2533 __isl_give isl_set *isl_basic_set_lexmax(
2534 __isl_take isl_basic_set *bset);
2535 __isl_give isl_set *isl_set_lexmin(
2536 __isl_take isl_set *set);
2537 __isl_give isl_set *isl_set_lexmax(
2538 __isl_take isl_set *set);
2539 __isl_give isl_union_set *isl_union_set_lexmin(
2540 __isl_take isl_union_set *uset);
2541 __isl_give isl_union_set *isl_union_set_lexmax(
2542 __isl_take isl_union_set *uset);
2544 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2545 the following functions
2546 compute a relation that maps each element of C<dom>
2547 to the single lexicographic minimum or maximum
2548 of the elements that are associated to that same
2549 element in C<map> (or C<bmap>).
2550 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2551 that contains the elements in C<dom> that do not map
2552 to any elements in C<map> (or C<bmap>).
2553 In other words, the union of the domain of the result and of C<*empty>
2556 __isl_give isl_map *isl_basic_map_partial_lexmax(
2557 __isl_take isl_basic_map *bmap,
2558 __isl_take isl_basic_set *dom,
2559 __isl_give isl_set **empty);
2560 __isl_give isl_map *isl_basic_map_partial_lexmin(
2561 __isl_take isl_basic_map *bmap,
2562 __isl_take isl_basic_set *dom,
2563 __isl_give isl_set **empty);
2564 __isl_give isl_map *isl_map_partial_lexmax(
2565 __isl_take isl_map *map, __isl_take isl_set *dom,
2566 __isl_give isl_set **empty);
2567 __isl_give isl_map *isl_map_partial_lexmin(
2568 __isl_take isl_map *map, __isl_take isl_set *dom,
2569 __isl_give isl_set **empty);
2571 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2572 return a map mapping each element in the domain of
2573 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2574 of all elements associated to that element.
2575 In case of union relations, the optimum is computed per space.
2577 __isl_give isl_map *isl_basic_map_lexmin(
2578 __isl_take isl_basic_map *bmap);
2579 __isl_give isl_map *isl_basic_map_lexmax(
2580 __isl_take isl_basic_map *bmap);
2581 __isl_give isl_map *isl_map_lexmin(
2582 __isl_take isl_map *map);
2583 __isl_give isl_map *isl_map_lexmax(
2584 __isl_take isl_map *map);
2585 __isl_give isl_union_map *isl_union_map_lexmin(
2586 __isl_take isl_union_map *umap);
2587 __isl_give isl_union_map *isl_union_map_lexmax(
2588 __isl_take isl_union_map *umap);
2590 The following functions return their result in the form of
2591 a piecewise multi-affine expression
2592 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2593 but are otherwise equivalent to the corresponding functions
2594 returning a basic set or relation.
2596 __isl_give isl_pw_multi_aff *
2597 isl_basic_map_lexmin_pw_multi_aff(
2598 __isl_take isl_basic_map *bmap);
2599 __isl_give isl_pw_multi_aff *
2600 isl_basic_set_partial_lexmin_pw_multi_aff(
2601 __isl_take isl_basic_set *bset,
2602 __isl_take isl_basic_set *dom,
2603 __isl_give isl_set **empty);
2604 __isl_give isl_pw_multi_aff *
2605 isl_basic_set_partial_lexmax_pw_multi_aff(
2606 __isl_take isl_basic_set *bset,
2607 __isl_take isl_basic_set *dom,
2608 __isl_give isl_set **empty);
2609 __isl_give isl_pw_multi_aff *
2610 isl_basic_map_partial_lexmin_pw_multi_aff(
2611 __isl_take isl_basic_map *bmap,
2612 __isl_take isl_basic_set *dom,
2613 __isl_give isl_set **empty);
2614 __isl_give isl_pw_multi_aff *
2615 isl_basic_map_partial_lexmax_pw_multi_aff(
2616 __isl_take isl_basic_map *bmap,
2617 __isl_take isl_basic_set *dom,
2618 __isl_give isl_set **empty);
2622 Lists are defined over several element types, including
2623 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2624 Here we take lists of C<isl_set>s as an example.
2625 Lists can be created, copied and freed using the following functions.
2627 #include <isl/list.h>
2628 __isl_give isl_set_list *isl_set_list_from_set(
2629 __isl_take isl_set *el);
2630 __isl_give isl_set_list *isl_set_list_alloc(
2631 isl_ctx *ctx, int n);
2632 __isl_give isl_set_list *isl_set_list_copy(
2633 __isl_keep isl_set_list *list);
2634 __isl_give isl_set_list *isl_set_list_add(
2635 __isl_take isl_set_list *list,
2636 __isl_take isl_set *el);
2637 __isl_give isl_set_list *isl_set_list_concat(
2638 __isl_take isl_set_list *list1,
2639 __isl_take isl_set_list *list2);
2640 void *isl_set_list_free(__isl_take isl_set_list *list);
2642 C<isl_set_list_alloc> creates an empty list with a capacity for
2643 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2646 Lists can be inspected using the following functions.
2648 #include <isl/list.h>
2649 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2650 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2651 __isl_give isl_set *isl_set_list_get_set(
2652 __isl_keep isl_set_list *list, int index);
2653 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2654 int (*fn)(__isl_take isl_set *el, void *user),
2657 Lists can be printed using
2659 #include <isl/list.h>
2660 __isl_give isl_printer *isl_printer_print_set_list(
2661 __isl_take isl_printer *p,
2662 __isl_keep isl_set_list *list);
2666 Matrices can be created, copied and freed using the following functions.
2668 #include <isl/mat.h>
2669 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2670 unsigned n_row, unsigned n_col);
2671 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2672 void isl_mat_free(__isl_take isl_mat *mat);
2674 Note that the elements of a newly created matrix may have arbitrary values.
2675 The elements can be changed and inspected using the following functions.
2677 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2678 int isl_mat_rows(__isl_keep isl_mat *mat);
2679 int isl_mat_cols(__isl_keep isl_mat *mat);
2680 int isl_mat_get_element(__isl_keep isl_mat *mat,
2681 int row, int col, isl_int *v);
2682 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2683 int row, int col, isl_int v);
2684 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2685 int row, int col, int v);
2687 C<isl_mat_get_element> will return a negative value if anything went wrong.
2688 In that case, the value of C<*v> is undefined.
2690 The following function can be used to compute the (right) inverse
2691 of a matrix, i.e., a matrix such that the product of the original
2692 and the inverse (in that order) is a multiple of the identity matrix.
2693 The input matrix is assumed to be of full row-rank.
2695 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2697 The following function can be used to compute the (right) kernel
2698 (or null space) of a matrix, i.e., a matrix such that the product of
2699 the original and the kernel (in that order) is the zero matrix.
2701 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2703 =head2 Piecewise Quasi Affine Expressions
2705 The zero quasi affine expression on a given domain can be created using
2707 __isl_give isl_aff *isl_aff_zero_on_domain(
2708 __isl_take isl_local_space *ls);
2710 Note that the space in which the resulting object lives is a map space
2711 with the given space as domain and a one-dimensional range.
2713 An empty piecewise quasi affine expression (one with no cells)
2714 or a piecewise quasi affine expression with a single cell can
2715 be created using the following functions.
2717 #include <isl/aff.h>
2718 __isl_give isl_pw_aff *isl_pw_aff_empty(
2719 __isl_take isl_space *space);
2720 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2721 __isl_take isl_set *set, __isl_take isl_aff *aff);
2722 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2723 __isl_take isl_aff *aff);
2725 Quasi affine expressions can be copied and freed using
2727 #include <isl/aff.h>
2728 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2729 void *isl_aff_free(__isl_take isl_aff *aff);
2731 __isl_give isl_pw_aff *isl_pw_aff_copy(
2732 __isl_keep isl_pw_aff *pwaff);
2733 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2735 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2736 using the following function. The constraint is required to have
2737 a non-zero coefficient for the specified dimension.
2739 #include <isl/constraint.h>
2740 __isl_give isl_aff *isl_constraint_get_bound(
2741 __isl_keep isl_constraint *constraint,
2742 enum isl_dim_type type, int pos);
2744 The entire affine expression of the constraint can also be extracted
2745 using the following function.
2747 #include <isl/constraint.h>
2748 __isl_give isl_aff *isl_constraint_get_aff(
2749 __isl_keep isl_constraint *constraint);
2751 Conversely, an equality constraint equating
2752 the affine expression to zero or an inequality constraint enforcing
2753 the affine expression to be non-negative, can be constructed using
2755 __isl_give isl_constraint *isl_equality_from_aff(
2756 __isl_take isl_aff *aff);
2757 __isl_give isl_constraint *isl_inequality_from_aff(
2758 __isl_take isl_aff *aff);
2760 The expression can be inspected using
2762 #include <isl/aff.h>
2763 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2764 int isl_aff_dim(__isl_keep isl_aff *aff,
2765 enum isl_dim_type type);
2766 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2767 __isl_keep isl_aff *aff);
2768 __isl_give isl_local_space *isl_aff_get_local_space(
2769 __isl_keep isl_aff *aff);
2770 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2771 enum isl_dim_type type, unsigned pos);
2772 const char *isl_pw_aff_get_dim_name(
2773 __isl_keep isl_pw_aff *pa,
2774 enum isl_dim_type type, unsigned pos);
2775 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2776 enum isl_dim_type type, unsigned pos);
2777 __isl_give isl_id *isl_pw_aff_get_dim_id(
2778 __isl_keep isl_pw_aff *pa,
2779 enum isl_dim_type type, unsigned pos);
2780 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2782 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2783 enum isl_dim_type type, int pos, isl_int *v);
2784 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2786 __isl_give isl_aff *isl_aff_get_div(
2787 __isl_keep isl_aff *aff, int pos);
2789 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2790 int (*fn)(__isl_take isl_set *set,
2791 __isl_take isl_aff *aff,
2792 void *user), void *user);
2794 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2795 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2797 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2798 enum isl_dim_type type, unsigned first, unsigned n);
2799 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2800 enum isl_dim_type type, unsigned first, unsigned n);
2802 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2803 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2804 enum isl_dim_type type);
2805 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2807 It can be modified using
2809 #include <isl/aff.h>
2810 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2811 __isl_take isl_pw_aff *pwaff,
2812 enum isl_dim_type type, __isl_take isl_id *id);
2813 __isl_give isl_aff *isl_aff_set_dim_name(
2814 __isl_take isl_aff *aff, enum isl_dim_type type,
2815 unsigned pos, const char *s);
2816 __isl_give isl_aff *isl_aff_set_dim_id(
2817 __isl_take isl_aff *aff, enum isl_dim_type type,
2818 unsigned pos, __isl_take isl_id *id);
2819 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2820 __isl_take isl_pw_aff *pma,
2821 enum isl_dim_type type, unsigned pos,
2822 __isl_take isl_id *id);
2823 __isl_give isl_aff *isl_aff_set_constant(
2824 __isl_take isl_aff *aff, isl_int v);
2825 __isl_give isl_aff *isl_aff_set_constant_si(
2826 __isl_take isl_aff *aff, int v);
2827 __isl_give isl_aff *isl_aff_set_coefficient(
2828 __isl_take isl_aff *aff,
2829 enum isl_dim_type type, int pos, isl_int v);
2830 __isl_give isl_aff *isl_aff_set_coefficient_si(
2831 __isl_take isl_aff *aff,
2832 enum isl_dim_type type, int pos, int v);
2833 __isl_give isl_aff *isl_aff_set_denominator(
2834 __isl_take isl_aff *aff, isl_int v);
2836 __isl_give isl_aff *isl_aff_add_constant(
2837 __isl_take isl_aff *aff, isl_int v);
2838 __isl_give isl_aff *isl_aff_add_constant_si(
2839 __isl_take isl_aff *aff, int v);
2840 __isl_give isl_aff *isl_aff_add_coefficient(
2841 __isl_take isl_aff *aff,
2842 enum isl_dim_type type, int pos, isl_int v);
2843 __isl_give isl_aff *isl_aff_add_coefficient_si(
2844 __isl_take isl_aff *aff,
2845 enum isl_dim_type type, int pos, int v);
2847 __isl_give isl_aff *isl_aff_insert_dims(
2848 __isl_take isl_aff *aff,
2849 enum isl_dim_type type, unsigned first, unsigned n);
2850 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2851 __isl_take isl_pw_aff *pwaff,
2852 enum isl_dim_type type, unsigned first, unsigned n);
2853 __isl_give isl_aff *isl_aff_add_dims(
2854 __isl_take isl_aff *aff,
2855 enum isl_dim_type type, unsigned n);
2856 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2857 __isl_take isl_pw_aff *pwaff,
2858 enum isl_dim_type type, unsigned n);
2859 __isl_give isl_aff *isl_aff_drop_dims(
2860 __isl_take isl_aff *aff,
2861 enum isl_dim_type type, unsigned first, unsigned n);
2862 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2863 __isl_take isl_pw_aff *pwaff,
2864 enum isl_dim_type type, unsigned first, unsigned n);
2866 Note that the C<set_constant> and C<set_coefficient> functions
2867 set the I<numerator> of the constant or coefficient, while
2868 C<add_constant> and C<add_coefficient> add an integer value to
2869 the possibly rational constant or coefficient.
2871 To check whether an affine expressions is obviously zero
2872 or obviously equal to some other affine expression, use
2874 #include <isl/aff.h>
2875 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2876 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2877 __isl_keep isl_aff *aff2);
2878 int isl_pw_aff_plain_is_equal(
2879 __isl_keep isl_pw_aff *pwaff1,
2880 __isl_keep isl_pw_aff *pwaff2);
2884 #include <isl/aff.h>
2885 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2886 __isl_take isl_aff *aff2);
2887 __isl_give isl_pw_aff *isl_pw_aff_add(
2888 __isl_take isl_pw_aff *pwaff1,
2889 __isl_take isl_pw_aff *pwaff2);
2890 __isl_give isl_pw_aff *isl_pw_aff_min(
2891 __isl_take isl_pw_aff *pwaff1,
2892 __isl_take isl_pw_aff *pwaff2);
2893 __isl_give isl_pw_aff *isl_pw_aff_max(
2894 __isl_take isl_pw_aff *pwaff1,
2895 __isl_take isl_pw_aff *pwaff2);
2896 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2897 __isl_take isl_aff *aff2);
2898 __isl_give isl_pw_aff *isl_pw_aff_sub(
2899 __isl_take isl_pw_aff *pwaff1,
2900 __isl_take isl_pw_aff *pwaff2);
2901 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2902 __isl_give isl_pw_aff *isl_pw_aff_neg(
2903 __isl_take isl_pw_aff *pwaff);
2904 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2905 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2906 __isl_take isl_pw_aff *pwaff);
2907 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2908 __isl_give isl_pw_aff *isl_pw_aff_floor(
2909 __isl_take isl_pw_aff *pwaff);
2910 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2912 __isl_give isl_pw_aff *isl_pw_aff_mod(
2913 __isl_take isl_pw_aff *pwaff, isl_int mod);
2914 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2916 __isl_give isl_pw_aff *isl_pw_aff_scale(
2917 __isl_take isl_pw_aff *pwaff, isl_int f);
2918 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2920 __isl_give isl_aff *isl_aff_scale_down_ui(
2921 __isl_take isl_aff *aff, unsigned f);
2922 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2923 __isl_take isl_pw_aff *pwaff, isl_int f);
2925 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2926 __isl_take isl_pw_aff_list *list);
2927 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2928 __isl_take isl_pw_aff_list *list);
2930 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2931 __isl_take isl_pw_aff *pwqp);
2933 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2934 __isl_take isl_pw_aff *pwaff,
2935 __isl_take isl_space *model);
2937 __isl_give isl_aff *isl_aff_gist_params(
2938 __isl_take isl_aff *aff,
2939 __isl_take isl_set *context);
2940 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2941 __isl_take isl_set *context);
2942 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
2943 __isl_take isl_pw_aff *pwaff,
2944 __isl_take isl_set *context);
2945 __isl_give isl_pw_aff *isl_pw_aff_gist(
2946 __isl_take isl_pw_aff *pwaff,
2947 __isl_take isl_set *context);
2949 __isl_give isl_set *isl_pw_aff_domain(
2950 __isl_take isl_pw_aff *pwaff);
2951 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2952 __isl_take isl_pw_aff *pa,
2953 __isl_take isl_set *set);
2954 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
2955 __isl_take isl_pw_aff *pa,
2956 __isl_take isl_set *set);
2958 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2959 __isl_take isl_aff *aff2);
2960 __isl_give isl_pw_aff *isl_pw_aff_mul(
2961 __isl_take isl_pw_aff *pwaff1,
2962 __isl_take isl_pw_aff *pwaff2);
2964 When multiplying two affine expressions, at least one of the two needs
2967 #include <isl/aff.h>
2968 __isl_give isl_basic_set *isl_aff_le_basic_set(
2969 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2970 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2971 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2972 __isl_give isl_set *isl_pw_aff_eq_set(
2973 __isl_take isl_pw_aff *pwaff1,
2974 __isl_take isl_pw_aff *pwaff2);
2975 __isl_give isl_set *isl_pw_aff_ne_set(
2976 __isl_take isl_pw_aff *pwaff1,
2977 __isl_take isl_pw_aff *pwaff2);
2978 __isl_give isl_set *isl_pw_aff_le_set(
2979 __isl_take isl_pw_aff *pwaff1,
2980 __isl_take isl_pw_aff *pwaff2);
2981 __isl_give isl_set *isl_pw_aff_lt_set(
2982 __isl_take isl_pw_aff *pwaff1,
2983 __isl_take isl_pw_aff *pwaff2);
2984 __isl_give isl_set *isl_pw_aff_ge_set(
2985 __isl_take isl_pw_aff *pwaff1,
2986 __isl_take isl_pw_aff *pwaff2);
2987 __isl_give isl_set *isl_pw_aff_gt_set(
2988 __isl_take isl_pw_aff *pwaff1,
2989 __isl_take isl_pw_aff *pwaff2);
2991 __isl_give isl_set *isl_pw_aff_list_eq_set(
2992 __isl_take isl_pw_aff_list *list1,
2993 __isl_take isl_pw_aff_list *list2);
2994 __isl_give isl_set *isl_pw_aff_list_ne_set(
2995 __isl_take isl_pw_aff_list *list1,
2996 __isl_take isl_pw_aff_list *list2);
2997 __isl_give isl_set *isl_pw_aff_list_le_set(
2998 __isl_take isl_pw_aff_list *list1,
2999 __isl_take isl_pw_aff_list *list2);
3000 __isl_give isl_set *isl_pw_aff_list_lt_set(
3001 __isl_take isl_pw_aff_list *list1,
3002 __isl_take isl_pw_aff_list *list2);
3003 __isl_give isl_set *isl_pw_aff_list_ge_set(
3004 __isl_take isl_pw_aff_list *list1,
3005 __isl_take isl_pw_aff_list *list2);
3006 __isl_give isl_set *isl_pw_aff_list_gt_set(
3007 __isl_take isl_pw_aff_list *list1,
3008 __isl_take isl_pw_aff_list *list2);
3010 The function C<isl_aff_ge_basic_set> returns a basic set
3011 containing those elements in the shared space
3012 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3013 The function C<isl_aff_ge_set> returns a set
3014 containing those elements in the shared domain
3015 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3016 The functions operating on C<isl_pw_aff_list> apply the corresponding
3017 C<isl_pw_aff> function to each pair of elements in the two lists.
3019 #include <isl/aff.h>
3020 __isl_give isl_set *isl_pw_aff_nonneg_set(
3021 __isl_take isl_pw_aff *pwaff);
3022 __isl_give isl_set *isl_pw_aff_zero_set(
3023 __isl_take isl_pw_aff *pwaff);
3024 __isl_give isl_set *isl_pw_aff_non_zero_set(
3025 __isl_take isl_pw_aff *pwaff);
3027 The function C<isl_pw_aff_nonneg_set> returns a set
3028 containing those elements in the domain
3029 of C<pwaff> where C<pwaff> is non-negative.
3031 #include <isl/aff.h>
3032 __isl_give isl_pw_aff *isl_pw_aff_cond(
3033 __isl_take isl_set *cond,
3034 __isl_take isl_pw_aff *pwaff_true,
3035 __isl_take isl_pw_aff *pwaff_false);
3037 The function C<isl_pw_aff_cond> performs a conditional operator
3038 and returns an expression that is equal to C<pwaff_true>
3039 for elements in C<cond> and equal to C<pwaff_false> for elements
3042 #include <isl/aff.h>
3043 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3044 __isl_take isl_pw_aff *pwaff1,
3045 __isl_take isl_pw_aff *pwaff2);
3046 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3047 __isl_take isl_pw_aff *pwaff1,
3048 __isl_take isl_pw_aff *pwaff2);
3049 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3050 __isl_take isl_pw_aff *pwaff1,
3051 __isl_take isl_pw_aff *pwaff2);
3053 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3054 expression with a domain that is the union of those of C<pwaff1> and
3055 C<pwaff2> and such that on each cell, the quasi-affine expression is
3056 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3057 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3058 associated expression is the defined one.
3060 An expression can be read from input using
3062 #include <isl/aff.h>
3063 __isl_give isl_aff *isl_aff_read_from_str(
3064 isl_ctx *ctx, const char *str);
3065 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3066 isl_ctx *ctx, const char *str);
3068 An expression can be printed using
3070 #include <isl/aff.h>
3071 __isl_give isl_printer *isl_printer_print_aff(
3072 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3074 __isl_give isl_printer *isl_printer_print_pw_aff(
3075 __isl_take isl_printer *p,
3076 __isl_keep isl_pw_aff *pwaff);
3078 =head2 Piecewise Multiple Quasi Affine Expressions
3080 An C<isl_multi_aff> object represents a sequence of
3081 zero or more affine expressions, all defined on the same domain space.
3083 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3086 #include <isl/aff.h>
3087 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3088 __isl_take isl_space *space,
3089 __isl_take isl_aff_list *list);
3091 An empty piecewise multiple quasi affine expression (one with no cells) or
3092 a piecewise multiple quasi affine expression with a single cell can
3093 be created using the following functions.
3095 #include <isl/aff.h>
3096 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3097 __isl_take isl_space *space);
3098 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3099 __isl_take isl_set *set,
3100 __isl_take isl_multi_aff *maff);
3102 A piecewise multiple quasi affine expression can also be initialized
3103 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3104 and the C<isl_map> is single-valued.
3106 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3107 __isl_take isl_set *set);
3108 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3109 __isl_take isl_map *map);
3111 Multiple quasi affine expressions can be copied and freed using
3113 #include <isl/aff.h>
3114 __isl_give isl_multi_aff *isl_multi_aff_copy(
3115 __isl_keep isl_multi_aff *maff);
3116 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3118 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3119 __isl_keep isl_pw_multi_aff *pma);
3120 void *isl_pw_multi_aff_free(
3121 __isl_take isl_pw_multi_aff *pma);
3123 The expression can be inspected using
3125 #include <isl/aff.h>
3126 isl_ctx *isl_multi_aff_get_ctx(
3127 __isl_keep isl_multi_aff *maff);
3128 isl_ctx *isl_pw_multi_aff_get_ctx(
3129 __isl_keep isl_pw_multi_aff *pma);
3130 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3131 enum isl_dim_type type);
3132 unsigned isl_pw_multi_aff_dim(
3133 __isl_keep isl_pw_multi_aff *pma,
3134 enum isl_dim_type type);
3135 __isl_give isl_aff *isl_multi_aff_get_aff(
3136 __isl_keep isl_multi_aff *multi, int pos);
3137 const char *isl_pw_multi_aff_get_dim_name(
3138 __isl_keep isl_pw_multi_aff *pma,
3139 enum isl_dim_type type, unsigned pos);
3140 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3141 __isl_keep isl_pw_multi_aff *pma,
3142 enum isl_dim_type type, unsigned pos);
3143 const char *isl_multi_aff_get_tuple_name(
3144 __isl_keep isl_multi_aff *multi,
3145 enum isl_dim_type type);
3146 const char *isl_pw_multi_aff_get_tuple_name(
3147 __isl_keep isl_pw_multi_aff *pma,
3148 enum isl_dim_type type);
3149 int isl_pw_multi_aff_has_tuple_id(
3150 __isl_keep isl_pw_multi_aff *pma,
3151 enum isl_dim_type type);
3152 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3153 __isl_keep isl_pw_multi_aff *pma,
3154 enum isl_dim_type type);
3156 int isl_pw_multi_aff_foreach_piece(
3157 __isl_keep isl_pw_multi_aff *pma,
3158 int (*fn)(__isl_take isl_set *set,
3159 __isl_take isl_multi_aff *maff,
3160 void *user), void *user);
3162 It can be modified using
3164 #include <isl/aff.h>
3165 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3166 __isl_take isl_multi_aff *maff,
3167 enum isl_dim_type type, unsigned pos, const char *s);
3168 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3169 __isl_take isl_pw_multi_aff *pma,
3170 enum isl_dim_type type, __isl_take isl_id *id);
3172 To check whether two multiple affine expressions are
3173 obviously equal to each other, use
3175 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3176 __isl_keep isl_multi_aff *maff2);
3177 int isl_pw_multi_aff_plain_is_equal(
3178 __isl_keep isl_pw_multi_aff *pma1,
3179 __isl_keep isl_pw_multi_aff *pma2);
3183 #include <isl/aff.h>
3184 __isl_give isl_multi_aff *isl_multi_aff_add(
3185 __isl_take isl_multi_aff *maff1,
3186 __isl_take isl_multi_aff *maff2);
3187 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3188 __isl_take isl_pw_multi_aff *pma1,
3189 __isl_take isl_pw_multi_aff *pma2);
3190 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3191 __isl_take isl_pw_multi_aff *pma1,
3192 __isl_take isl_pw_multi_aff *pma2);
3193 __isl_give isl_multi_aff *isl_multi_aff_scale(
3194 __isl_take isl_multi_aff *maff,
3196 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3197 __isl_take isl_pw_multi_aff *pma,
3198 __isl_take isl_set *set);
3199 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3200 __isl_take isl_pw_multi_aff *pma,
3201 __isl_take isl_set *set);
3202 __isl_give isl_multi_aff *isl_multi_aff_lift(
3203 __isl_take isl_multi_aff *maff,
3204 __isl_give isl_local_space **ls);
3205 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3206 __isl_take isl_multi_aff *maff,
3207 __isl_take isl_set *context);
3208 __isl_give isl_multi_aff *isl_multi_aff_gist(
3209 __isl_take isl_multi_aff *maff,
3210 __isl_take isl_set *context);
3211 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3212 __isl_take isl_pw_multi_aff *pma,
3213 __isl_take isl_set *set);
3214 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3215 __isl_take isl_pw_multi_aff *pma,
3216 __isl_take isl_set *set);
3218 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3219 then it is assigned the local space that lies at the basis of
3220 the lifting applied.
3222 An expression can be read from input using
3224 #include <isl/aff.h>
3225 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3226 isl_ctx *ctx, const char *str);
3227 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3228 isl_ctx *ctx, const char *str);
3230 An expression can be printed using
3232 #include <isl/aff.h>
3233 __isl_give isl_printer *isl_printer_print_multi_aff(
3234 __isl_take isl_printer *p,
3235 __isl_keep isl_multi_aff *maff);
3236 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3237 __isl_take isl_printer *p,
3238 __isl_keep isl_pw_multi_aff *pma);
3242 Points are elements of a set. They can be used to construct
3243 simple sets (boxes) or they can be used to represent the
3244 individual elements of a set.
3245 The zero point (the origin) can be created using
3247 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3249 The coordinates of a point can be inspected, set and changed
3252 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3253 enum isl_dim_type type, int pos, isl_int *v);
3254 __isl_give isl_point *isl_point_set_coordinate(
3255 __isl_take isl_point *pnt,
3256 enum isl_dim_type type, int pos, isl_int v);
3258 __isl_give isl_point *isl_point_add_ui(
3259 __isl_take isl_point *pnt,
3260 enum isl_dim_type type, int pos, unsigned val);
3261 __isl_give isl_point *isl_point_sub_ui(
3262 __isl_take isl_point *pnt,
3263 enum isl_dim_type type, int pos, unsigned val);
3265 Other properties can be obtained using
3267 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3269 Points can be copied or freed using
3271 __isl_give isl_point *isl_point_copy(
3272 __isl_keep isl_point *pnt);
3273 void isl_point_free(__isl_take isl_point *pnt);
3275 A singleton set can be created from a point using
3277 __isl_give isl_basic_set *isl_basic_set_from_point(
3278 __isl_take isl_point *pnt);
3279 __isl_give isl_set *isl_set_from_point(
3280 __isl_take isl_point *pnt);
3282 and a box can be created from two opposite extremal points using
3284 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3285 __isl_take isl_point *pnt1,
3286 __isl_take isl_point *pnt2);
3287 __isl_give isl_set *isl_set_box_from_points(
3288 __isl_take isl_point *pnt1,
3289 __isl_take isl_point *pnt2);
3291 All elements of a B<bounded> (union) set can be enumerated using
3292 the following functions.
3294 int isl_set_foreach_point(__isl_keep isl_set *set,
3295 int (*fn)(__isl_take isl_point *pnt, void *user),
3297 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3298 int (*fn)(__isl_take isl_point *pnt, void *user),
3301 The function C<fn> is called for each integer point in
3302 C<set> with as second argument the last argument of
3303 the C<isl_set_foreach_point> call. The function C<fn>
3304 should return C<0> on success and C<-1> on failure.
3305 In the latter case, C<isl_set_foreach_point> will stop
3306 enumerating and return C<-1> as well.
3307 If the enumeration is performed successfully and to completion,
3308 then C<isl_set_foreach_point> returns C<0>.
3310 To obtain a single point of a (basic) set, use
3312 __isl_give isl_point *isl_basic_set_sample_point(
3313 __isl_take isl_basic_set *bset);
3314 __isl_give isl_point *isl_set_sample_point(
3315 __isl_take isl_set *set);
3317 If C<set> does not contain any (integer) points, then the
3318 resulting point will be ``void'', a property that can be
3321 int isl_point_is_void(__isl_keep isl_point *pnt);
3323 =head2 Piecewise Quasipolynomials
3325 A piecewise quasipolynomial is a particular kind of function that maps
3326 a parametric point to a rational value.
3327 More specifically, a quasipolynomial is a polynomial expression in greatest
3328 integer parts of affine expressions of parameters and variables.
3329 A piecewise quasipolynomial is a subdivision of a given parametric
3330 domain into disjoint cells with a quasipolynomial associated to
3331 each cell. The value of the piecewise quasipolynomial at a given
3332 point is the value of the quasipolynomial associated to the cell
3333 that contains the point. Outside of the union of cells,
3334 the value is assumed to be zero.
3335 For example, the piecewise quasipolynomial
3337 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3339 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3340 A given piecewise quasipolynomial has a fixed domain dimension.
3341 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3342 defined over different domains.
3343 Piecewise quasipolynomials are mainly used by the C<barvinok>
3344 library for representing the number of elements in a parametric set or map.
3345 For example, the piecewise quasipolynomial above represents
3346 the number of points in the map
3348 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3350 =head3 Input and Output
3352 Piecewise quasipolynomials can be read from input using
3354 __isl_give isl_union_pw_qpolynomial *
3355 isl_union_pw_qpolynomial_read_from_str(
3356 isl_ctx *ctx, const char *str);
3358 Quasipolynomials and piecewise quasipolynomials can be printed
3359 using the following functions.
3361 __isl_give isl_printer *isl_printer_print_qpolynomial(
3362 __isl_take isl_printer *p,
3363 __isl_keep isl_qpolynomial *qp);
3365 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3366 __isl_take isl_printer *p,
3367 __isl_keep isl_pw_qpolynomial *pwqp);
3369 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3370 __isl_take isl_printer *p,
3371 __isl_keep isl_union_pw_qpolynomial *upwqp);
3373 The output format of the printer
3374 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3375 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3377 In case of printing in C<ISL_FORMAT_C>, the user may want
3378 to set the names of all dimensions
3380 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3381 __isl_take isl_qpolynomial *qp,
3382 enum isl_dim_type type, unsigned pos,
3384 __isl_give isl_pw_qpolynomial *
3385 isl_pw_qpolynomial_set_dim_name(
3386 __isl_take isl_pw_qpolynomial *pwqp,
3387 enum isl_dim_type type, unsigned pos,
3390 =head3 Creating New (Piecewise) Quasipolynomials
3392 Some simple quasipolynomials can be created using the following functions.
3393 More complicated quasipolynomials can be created by applying
3394 operations such as addition and multiplication
3395 on the resulting quasipolynomials
3397 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3398 __isl_take isl_space *domain);
3399 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3400 __isl_take isl_space *domain);
3401 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3402 __isl_take isl_space *domain);
3403 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3404 __isl_take isl_space *domain);
3405 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3406 __isl_take isl_space *domain);
3407 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3408 __isl_take isl_space *domain,
3409 const isl_int n, const isl_int d);
3410 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3411 __isl_take isl_space *domain,
3412 enum isl_dim_type type, unsigned pos);
3413 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3414 __isl_take isl_aff *aff);
3416 Note that the space in which a quasipolynomial lives is a map space
3417 with a one-dimensional range. The C<domain> argument in some of
3418 the functions above corresponds to the domain of this map space.
3420 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3421 with a single cell can be created using the following functions.
3422 Multiple of these single cell piecewise quasipolynomials can
3423 be combined to create more complicated piecewise quasipolynomials.
3425 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3426 __isl_take isl_space *space);
3427 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3428 __isl_take isl_set *set,
3429 __isl_take isl_qpolynomial *qp);
3430 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3431 __isl_take isl_qpolynomial *qp);
3432 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3433 __isl_take isl_pw_aff *pwaff);
3435 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3436 __isl_take isl_space *space);
3437 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3438 __isl_take isl_pw_qpolynomial *pwqp);
3439 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3440 __isl_take isl_union_pw_qpolynomial *upwqp,
3441 __isl_take isl_pw_qpolynomial *pwqp);
3443 Quasipolynomials can be copied and freed again using the following
3446 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3447 __isl_keep isl_qpolynomial *qp);
3448 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3450 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3451 __isl_keep isl_pw_qpolynomial *pwqp);
3452 void *isl_pw_qpolynomial_free(
3453 __isl_take isl_pw_qpolynomial *pwqp);
3455 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3456 __isl_keep isl_union_pw_qpolynomial *upwqp);
3457 void isl_union_pw_qpolynomial_free(
3458 __isl_take isl_union_pw_qpolynomial *upwqp);
3460 =head3 Inspecting (Piecewise) Quasipolynomials
3462 To iterate over all piecewise quasipolynomials in a union
3463 piecewise quasipolynomial, use the following function
3465 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3466 __isl_keep isl_union_pw_qpolynomial *upwqp,
3467 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3470 To extract the piecewise quasipolynomial in a given space from a union, use
3472 __isl_give isl_pw_qpolynomial *
3473 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3474 __isl_keep isl_union_pw_qpolynomial *upwqp,
3475 __isl_take isl_space *space);
3477 To iterate over the cells in a piecewise quasipolynomial,
3478 use either of the following two functions
3480 int isl_pw_qpolynomial_foreach_piece(
3481 __isl_keep isl_pw_qpolynomial *pwqp,
3482 int (*fn)(__isl_take isl_set *set,
3483 __isl_take isl_qpolynomial *qp,
3484 void *user), void *user);
3485 int isl_pw_qpolynomial_foreach_lifted_piece(
3486 __isl_keep isl_pw_qpolynomial *pwqp,
3487 int (*fn)(__isl_take isl_set *set,
3488 __isl_take isl_qpolynomial *qp,
3489 void *user), void *user);
3491 As usual, the function C<fn> should return C<0> on success
3492 and C<-1> on failure. The difference between
3493 C<isl_pw_qpolynomial_foreach_piece> and
3494 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3495 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3496 compute unique representations for all existentially quantified
3497 variables and then turn these existentially quantified variables
3498 into extra set variables, adapting the associated quasipolynomial
3499 accordingly. This means that the C<set> passed to C<fn>
3500 will not have any existentially quantified variables, but that
3501 the dimensions of the sets may be different for different
3502 invocations of C<fn>.
3504 To iterate over all terms in a quasipolynomial,
3507 int isl_qpolynomial_foreach_term(
3508 __isl_keep isl_qpolynomial *qp,
3509 int (*fn)(__isl_take isl_term *term,
3510 void *user), void *user);
3512 The terms themselves can be inspected and freed using
3515 unsigned isl_term_dim(__isl_keep isl_term *term,
3516 enum isl_dim_type type);
3517 void isl_term_get_num(__isl_keep isl_term *term,
3519 void isl_term_get_den(__isl_keep isl_term *term,
3521 int isl_term_get_exp(__isl_keep isl_term *term,
3522 enum isl_dim_type type, unsigned pos);
3523 __isl_give isl_aff *isl_term_get_div(
3524 __isl_keep isl_term *term, unsigned pos);
3525 void isl_term_free(__isl_take isl_term *term);
3527 Each term is a product of parameters, set variables and
3528 integer divisions. The function C<isl_term_get_exp>
3529 returns the exponent of a given dimensions in the given term.
3530 The C<isl_int>s in the arguments of C<isl_term_get_num>
3531 and C<isl_term_get_den> need to have been initialized
3532 using C<isl_int_init> before calling these functions.
3534 =head3 Properties of (Piecewise) Quasipolynomials
3536 To check whether a quasipolynomial is actually a constant,
3537 use the following function.
3539 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3540 isl_int *n, isl_int *d);
3542 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3543 then the numerator and denominator of the constant
3544 are returned in C<*n> and C<*d>, respectively.
3546 To check whether two union piecewise quasipolynomials are
3547 obviously equal, use
3549 int isl_union_pw_qpolynomial_plain_is_equal(
3550 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3551 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3553 =head3 Operations on (Piecewise) Quasipolynomials
3555 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3556 __isl_take isl_qpolynomial *qp, isl_int v);
3557 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3558 __isl_take isl_qpolynomial *qp);
3559 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3560 __isl_take isl_qpolynomial *qp1,
3561 __isl_take isl_qpolynomial *qp2);
3562 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3563 __isl_take isl_qpolynomial *qp1,
3564 __isl_take isl_qpolynomial *qp2);
3565 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3566 __isl_take isl_qpolynomial *qp1,
3567 __isl_take isl_qpolynomial *qp2);
3568 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3569 __isl_take isl_qpolynomial *qp, unsigned exponent);
3571 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3572 __isl_take isl_pw_qpolynomial *pwqp1,
3573 __isl_take isl_pw_qpolynomial *pwqp2);
3574 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3575 __isl_take isl_pw_qpolynomial *pwqp1,
3576 __isl_take isl_pw_qpolynomial *pwqp2);
3577 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3578 __isl_take isl_pw_qpolynomial *pwqp1,
3579 __isl_take isl_pw_qpolynomial *pwqp2);
3580 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3581 __isl_take isl_pw_qpolynomial *pwqp);
3582 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3583 __isl_take isl_pw_qpolynomial *pwqp1,
3584 __isl_take isl_pw_qpolynomial *pwqp2);
3585 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3586 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3588 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3589 __isl_take isl_union_pw_qpolynomial *upwqp1,
3590 __isl_take isl_union_pw_qpolynomial *upwqp2);
3591 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3592 __isl_take isl_union_pw_qpolynomial *upwqp1,
3593 __isl_take isl_union_pw_qpolynomial *upwqp2);
3594 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3595 __isl_take isl_union_pw_qpolynomial *upwqp1,
3596 __isl_take isl_union_pw_qpolynomial *upwqp2);
3598 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3599 __isl_take isl_pw_qpolynomial *pwqp,
3600 __isl_take isl_point *pnt);
3602 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3603 __isl_take isl_union_pw_qpolynomial *upwqp,
3604 __isl_take isl_point *pnt);
3606 __isl_give isl_set *isl_pw_qpolynomial_domain(
3607 __isl_take isl_pw_qpolynomial *pwqp);
3608 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3609 __isl_take isl_pw_qpolynomial *pwpq,
3610 __isl_take isl_set *set);
3611 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3612 __isl_take isl_pw_qpolynomial *pwpq,
3613 __isl_take isl_set *set);
3615 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3616 __isl_take isl_union_pw_qpolynomial *upwqp);
3617 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3618 __isl_take isl_union_pw_qpolynomial *upwpq,
3619 __isl_take isl_union_set *uset);
3620 __isl_give isl_union_pw_qpolynomial *
3621 isl_union_pw_qpolynomial_intersect_params(
3622 __isl_take isl_union_pw_qpolynomial *upwpq,
3623 __isl_take isl_set *set);
3625 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3626 __isl_take isl_qpolynomial *qp,
3627 __isl_take isl_space *model);
3629 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3630 __isl_take isl_qpolynomial *qp);
3631 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3632 __isl_take isl_pw_qpolynomial *pwqp);
3634 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3635 __isl_take isl_union_pw_qpolynomial *upwqp);
3637 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3638 __isl_take isl_qpolynomial *qp,
3639 __isl_take isl_set *context);
3640 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3641 __isl_take isl_qpolynomial *qp,
3642 __isl_take isl_set *context);
3644 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3645 __isl_take isl_pw_qpolynomial *pwqp,
3646 __isl_take isl_set *context);
3647 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3648 __isl_take isl_pw_qpolynomial *pwqp,
3649 __isl_take isl_set *context);
3651 __isl_give isl_union_pw_qpolynomial *
3652 isl_union_pw_qpolynomial_gist_params(
3653 __isl_take isl_union_pw_qpolynomial *upwqp,
3654 __isl_take isl_set *context);
3655 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3656 __isl_take isl_union_pw_qpolynomial *upwqp,
3657 __isl_take isl_union_set *context);
3659 The gist operation applies the gist operation to each of
3660 the cells in the domain of the input piecewise quasipolynomial.
3661 The context is also exploited
3662 to simplify the quasipolynomials associated to each cell.
3664 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3665 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3666 __isl_give isl_union_pw_qpolynomial *
3667 isl_union_pw_qpolynomial_to_polynomial(
3668 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3670 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3671 the polynomial will be an overapproximation. If C<sign> is negative,
3672 it will be an underapproximation. If C<sign> is zero, the approximation
3673 will lie somewhere in between.
3675 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3677 A piecewise quasipolynomial reduction is a piecewise
3678 reduction (or fold) of quasipolynomials.
3679 In particular, the reduction can be maximum or a minimum.
3680 The objects are mainly used to represent the result of
3681 an upper or lower bound on a quasipolynomial over its domain,
3682 i.e., as the result of the following function.
3684 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3685 __isl_take isl_pw_qpolynomial *pwqp,
3686 enum isl_fold type, int *tight);
3688 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3689 __isl_take isl_union_pw_qpolynomial *upwqp,
3690 enum isl_fold type, int *tight);
3692 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3693 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3694 is the returned bound is known be tight, i.e., for each value
3695 of the parameters there is at least
3696 one element in the domain that reaches the bound.
3697 If the domain of C<pwqp> is not wrapping, then the bound is computed
3698 over all elements in that domain and the result has a purely parametric
3699 domain. If the domain of C<pwqp> is wrapping, then the bound is
3700 computed over the range of the wrapped relation. The domain of the
3701 wrapped relation becomes the domain of the result.
3703 A (piecewise) quasipolynomial reduction can be copied or freed using the
3704 following functions.
3706 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3707 __isl_keep isl_qpolynomial_fold *fold);
3708 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3709 __isl_keep isl_pw_qpolynomial_fold *pwf);
3710 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3711 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3712 void isl_qpolynomial_fold_free(
3713 __isl_take isl_qpolynomial_fold *fold);
3714 void *isl_pw_qpolynomial_fold_free(
3715 __isl_take isl_pw_qpolynomial_fold *pwf);
3716 void isl_union_pw_qpolynomial_fold_free(
3717 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3719 =head3 Printing Piecewise Quasipolynomial Reductions
3721 Piecewise quasipolynomial reductions can be printed
3722 using the following function.
3724 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3725 __isl_take isl_printer *p,
3726 __isl_keep isl_pw_qpolynomial_fold *pwf);
3727 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3728 __isl_take isl_printer *p,
3729 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3731 For C<isl_printer_print_pw_qpolynomial_fold>,
3732 output format of the printer
3733 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3734 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3735 output format of the printer
3736 needs to be set to C<ISL_FORMAT_ISL>.
3737 In case of printing in C<ISL_FORMAT_C>, the user may want
3738 to set the names of all dimensions
3740 __isl_give isl_pw_qpolynomial_fold *
3741 isl_pw_qpolynomial_fold_set_dim_name(
3742 __isl_take isl_pw_qpolynomial_fold *pwf,
3743 enum isl_dim_type type, unsigned pos,
3746 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3748 To iterate over all piecewise quasipolynomial reductions in a union
3749 piecewise quasipolynomial reduction, use the following function
3751 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3752 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3753 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3754 void *user), void *user);
3756 To iterate over the cells in a piecewise quasipolynomial reduction,
3757 use either of the following two functions
3759 int isl_pw_qpolynomial_fold_foreach_piece(
3760 __isl_keep isl_pw_qpolynomial_fold *pwf,
3761 int (*fn)(__isl_take isl_set *set,
3762 __isl_take isl_qpolynomial_fold *fold,
3763 void *user), void *user);
3764 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3765 __isl_keep isl_pw_qpolynomial_fold *pwf,
3766 int (*fn)(__isl_take isl_set *set,
3767 __isl_take isl_qpolynomial_fold *fold,
3768 void *user), void *user);
3770 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3771 of the difference between these two functions.
3773 To iterate over all quasipolynomials in a reduction, use
3775 int isl_qpolynomial_fold_foreach_qpolynomial(
3776 __isl_keep isl_qpolynomial_fold *fold,
3777 int (*fn)(__isl_take isl_qpolynomial *qp,
3778 void *user), void *user);
3780 =head3 Properties of Piecewise Quasipolynomial Reductions
3782 To check whether two union piecewise quasipolynomial reductions are
3783 obviously equal, use
3785 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3786 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3787 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3789 =head3 Operations on Piecewise Quasipolynomial Reductions
3791 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3792 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3794 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3795 __isl_take isl_pw_qpolynomial_fold *pwf1,
3796 __isl_take isl_pw_qpolynomial_fold *pwf2);
3798 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3799 __isl_take isl_pw_qpolynomial_fold *pwf1,
3800 __isl_take isl_pw_qpolynomial_fold *pwf2);
3802 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3803 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3804 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3806 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3807 __isl_take isl_pw_qpolynomial_fold *pwf,
3808 __isl_take isl_point *pnt);
3810 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3811 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3812 __isl_take isl_point *pnt);
3814 __isl_give isl_pw_qpolynomial_fold *
3815 sl_pw_qpolynomial_fold_intersect_params(
3816 __isl_take isl_pw_qpolynomial_fold *pwf,
3817 __isl_take isl_set *set);
3819 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3820 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3821 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3822 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3823 __isl_take isl_union_set *uset);
3824 __isl_give isl_union_pw_qpolynomial_fold *
3825 isl_union_pw_qpolynomial_fold_intersect_params(
3826 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3827 __isl_take isl_set *set);
3829 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3830 __isl_take isl_pw_qpolynomial_fold *pwf);
3832 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3833 __isl_take isl_pw_qpolynomial_fold *pwf);
3835 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3836 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3838 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
3839 __isl_take isl_qpolynomial_fold *fold,
3840 __isl_take isl_set *context);
3841 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
3842 __isl_take isl_qpolynomial_fold *fold,
3843 __isl_take isl_set *context);
3845 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3846 __isl_take isl_pw_qpolynomial_fold *pwf,
3847 __isl_take isl_set *context);
3848 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
3849 __isl_take isl_pw_qpolynomial_fold *pwf,
3850 __isl_take isl_set *context);
3852 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3853 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3854 __isl_take isl_union_set *context);
3855 __isl_give isl_union_pw_qpolynomial_fold *
3856 isl_union_pw_qpolynomial_fold_gist_params(
3857 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3858 __isl_take isl_set *context);
3860 The gist operation applies the gist operation to each of
3861 the cells in the domain of the input piecewise quasipolynomial reduction.
3862 In future, the operation will also exploit the context
3863 to simplify the quasipolynomial reductions associated to each cell.
3865 __isl_give isl_pw_qpolynomial_fold *
3866 isl_set_apply_pw_qpolynomial_fold(
3867 __isl_take isl_set *set,
3868 __isl_take isl_pw_qpolynomial_fold *pwf,
3870 __isl_give isl_pw_qpolynomial_fold *
3871 isl_map_apply_pw_qpolynomial_fold(
3872 __isl_take isl_map *map,
3873 __isl_take isl_pw_qpolynomial_fold *pwf,
3875 __isl_give isl_union_pw_qpolynomial_fold *
3876 isl_union_set_apply_union_pw_qpolynomial_fold(
3877 __isl_take isl_union_set *uset,
3878 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3880 __isl_give isl_union_pw_qpolynomial_fold *
3881 isl_union_map_apply_union_pw_qpolynomial_fold(
3882 __isl_take isl_union_map *umap,
3883 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3886 The functions taking a map
3887 compose the given map with the given piecewise quasipolynomial reduction.
3888 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3889 over all elements in the intersection of the range of the map
3890 and the domain of the piecewise quasipolynomial reduction
3891 as a function of an element in the domain of the map.
3892 The functions taking a set compute a bound over all elements in the
3893 intersection of the set and the domain of the
3894 piecewise quasipolynomial reduction.
3896 =head2 Dependence Analysis
3898 C<isl> contains specialized functionality for performing
3899 array dataflow analysis. That is, given a I<sink> access relation
3900 and a collection of possible I<source> access relations,
3901 C<isl> can compute relations that describe
3902 for each iteration of the sink access, which iteration
3903 of which of the source access relations was the last
3904 to access the same data element before the given iteration
3906 The resulting dependence relations map source iterations
3907 to the corresponding sink iterations.
3908 To compute standard flow dependences, the sink should be
3909 a read, while the sources should be writes.
3910 If any of the source accesses are marked as being I<may>
3911 accesses, then there will be a dependence from the last
3912 I<must> access B<and> from any I<may> access that follows
3913 this last I<must> access.
3914 In particular, if I<all> sources are I<may> accesses,
3915 then memory based dependence analysis is performed.
3916 If, on the other hand, all sources are I<must> accesses,
3917 then value based dependence analysis is performed.
3919 #include <isl/flow.h>
3921 typedef int (*isl_access_level_before)(void *first, void *second);
3923 __isl_give isl_access_info *isl_access_info_alloc(
3924 __isl_take isl_map *sink,
3925 void *sink_user, isl_access_level_before fn,
3927 __isl_give isl_access_info *isl_access_info_add_source(
3928 __isl_take isl_access_info *acc,
3929 __isl_take isl_map *source, int must,
3931 void isl_access_info_free(__isl_take isl_access_info *acc);
3933 __isl_give isl_flow *isl_access_info_compute_flow(
3934 __isl_take isl_access_info *acc);
3936 int isl_flow_foreach(__isl_keep isl_flow *deps,
3937 int (*fn)(__isl_take isl_map *dep, int must,
3938 void *dep_user, void *user),
3940 __isl_give isl_map *isl_flow_get_no_source(
3941 __isl_keep isl_flow *deps, int must);
3942 void isl_flow_free(__isl_take isl_flow *deps);
3944 The function C<isl_access_info_compute_flow> performs the actual
3945 dependence analysis. The other functions are used to construct
3946 the input for this function or to read off the output.
3948 The input is collected in an C<isl_access_info>, which can
3949 be created through a call to C<isl_access_info_alloc>.
3950 The arguments to this functions are the sink access relation
3951 C<sink>, a token C<sink_user> used to identify the sink
3952 access to the user, a callback function for specifying the
3953 relative order of source and sink accesses, and the number
3954 of source access relations that will be added.
3955 The callback function has type C<int (*)(void *first, void *second)>.
3956 The function is called with two user supplied tokens identifying
3957 either a source or the sink and it should return the shared nesting
3958 level and the relative order of the two accesses.
3959 In particular, let I<n> be the number of loops shared by
3960 the two accesses. If C<first> precedes C<second> textually,
3961 then the function should return I<2 * n + 1>; otherwise,
3962 it should return I<2 * n>.
3963 The sources can be added to the C<isl_access_info> by performing
3964 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3965 C<must> indicates whether the source is a I<must> access
3966 or a I<may> access. Note that a multi-valued access relation
3967 should only be marked I<must> if every iteration in the domain
3968 of the relation accesses I<all> elements in its image.
3969 The C<source_user> token is again used to identify
3970 the source access. The range of the source access relation
3971 C<source> should have the same dimension as the range
3972 of the sink access relation.
3973 The C<isl_access_info_free> function should usually not be
3974 called explicitly, because it is called implicitly by
3975 C<isl_access_info_compute_flow>.
3977 The result of the dependence analysis is collected in an
3978 C<isl_flow>. There may be elements of
3979 the sink access for which no preceding source access could be
3980 found or for which all preceding sources are I<may> accesses.
3981 The relations containing these elements can be obtained through
3982 calls to C<isl_flow_get_no_source>, the first with C<must> set
3983 and the second with C<must> unset.
3984 In the case of standard flow dependence analysis,
3985 with the sink a read and the sources I<must> writes,
3986 the first relation corresponds to the reads from uninitialized
3987 array elements and the second relation is empty.
3988 The actual flow dependences can be extracted using
3989 C<isl_flow_foreach>. This function will call the user-specified
3990 callback function C<fn> for each B<non-empty> dependence between
3991 a source and the sink. The callback function is called
3992 with four arguments, the actual flow dependence relation
3993 mapping source iterations to sink iterations, a boolean that
3994 indicates whether it is a I<must> or I<may> dependence, a token
3995 identifying the source and an additional C<void *> with value
3996 equal to the third argument of the C<isl_flow_foreach> call.
3997 A dependence is marked I<must> if it originates from a I<must>
3998 source and if it is not followed by any I<may> sources.
4000 After finishing with an C<isl_flow>, the user should call
4001 C<isl_flow_free> to free all associated memory.
4003 A higher-level interface to dependence analysis is provided
4004 by the following function.
4006 #include <isl/flow.h>
4008 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4009 __isl_take isl_union_map *must_source,
4010 __isl_take isl_union_map *may_source,
4011 __isl_take isl_union_map *schedule,
4012 __isl_give isl_union_map **must_dep,
4013 __isl_give isl_union_map **may_dep,
4014 __isl_give isl_union_map **must_no_source,
4015 __isl_give isl_union_map **may_no_source);
4017 The arrays are identified by the tuple names of the ranges
4018 of the accesses. The iteration domains by the tuple names
4019 of the domains of the accesses and of the schedule.
4020 The relative order of the iteration domains is given by the
4021 schedule. The relations returned through C<must_no_source>
4022 and C<may_no_source> are subsets of C<sink>.
4023 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4024 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4025 any of the other arguments is treated as an error.
4029 B<The functionality described in this section is fairly new
4030 and may be subject to change.>
4032 The following function can be used to compute a schedule
4033 for a union of domains. The generated schedule respects
4034 all C<validity> dependences. That is, all dependence distances
4035 over these dependences in the scheduled space are lexicographically
4036 positive. The generated schedule schedule also tries to minimize
4037 the dependence distances over C<proximity> dependences.
4038 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4039 for groups of domains where the dependence distances have only
4040 non-negative values.
4041 The algorithm used to construct the schedule is similar to that
4044 #include <isl/schedule.h>
4045 __isl_give isl_schedule *isl_union_set_compute_schedule(
4046 __isl_take isl_union_set *domain,
4047 __isl_take isl_union_map *validity,
4048 __isl_take isl_union_map *proximity);
4049 void *isl_schedule_free(__isl_take isl_schedule *sched);
4051 A mapping from the domains to the scheduled space can be obtained
4052 from an C<isl_schedule> using the following function.
4054 __isl_give isl_union_map *isl_schedule_get_map(
4055 __isl_keep isl_schedule *sched);
4057 A representation of the schedule can be printed using
4059 __isl_give isl_printer *isl_printer_print_schedule(
4060 __isl_take isl_printer *p,
4061 __isl_keep isl_schedule *schedule);
4063 A representation of the schedule as a forest of bands can be obtained
4064 using the following function.
4066 __isl_give isl_band_list *isl_schedule_get_band_forest(
4067 __isl_keep isl_schedule *schedule);
4069 The list can be manipulated as explained in L<"Lists">.
4070 The bands inside the list can be copied and freed using the following
4073 #include <isl/band.h>
4074 __isl_give isl_band *isl_band_copy(
4075 __isl_keep isl_band *band);
4076 void *isl_band_free(__isl_take isl_band *band);
4078 Each band contains zero or more scheduling dimensions.
4079 These are referred to as the members of the band.
4080 The section of the schedule that corresponds to the band is
4081 referred to as the partial schedule of the band.
4082 For those nodes that participate in a band, the outer scheduling
4083 dimensions form the prefix schedule, while the inner scheduling
4084 dimensions form the suffix schedule.
4085 That is, if we take a cut of the band forest, then the union of
4086 the concatenations of the prefix, partial and suffix schedules of
4087 each band in the cut is equal to the entire schedule (modulo
4088 some possible padding at the end with zero scheduling dimensions).
4089 The properties of a band can be inspected using the following functions.
4091 #include <isl/band.h>
4092 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4094 int isl_band_has_children(__isl_keep isl_band *band);
4095 __isl_give isl_band_list *isl_band_get_children(
4096 __isl_keep isl_band *band);
4098 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4099 __isl_keep isl_band *band);
4100 __isl_give isl_union_map *isl_band_get_partial_schedule(
4101 __isl_keep isl_band *band);
4102 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4103 __isl_keep isl_band *band);
4105 int isl_band_n_member(__isl_keep isl_band *band);
4106 int isl_band_member_is_zero_distance(
4107 __isl_keep isl_band *band, int pos);
4109 Note that a scheduling dimension is considered to be ``zero
4110 distance'' if it does not carry any proximity dependences
4112 That is, if the dependence distances of the proximity
4113 dependences are all zero in that direction (for fixed
4114 iterations of outer bands).
4116 A representation of the band can be printed using
4118 #include <isl/band.h>
4119 __isl_give isl_printer *isl_printer_print_band(
4120 __isl_take isl_printer *p,
4121 __isl_keep isl_band *band);
4125 #include <isl/schedule.h>
4126 int isl_options_set_schedule_outer_zero_distance(
4127 isl_ctx *ctx, int val);
4128 int isl_options_get_schedule_outer_zero_distance(
4133 =item * schedule_outer_zero_distance
4135 It this option is set, then we try to construct schedules
4136 where the outermost scheduling dimension in each band
4137 results in a zero dependence distance over the proximity
4142 =head2 Parametric Vertex Enumeration
4144 The parametric vertex enumeration described in this section
4145 is mainly intended to be used internally and by the C<barvinok>
4148 #include <isl/vertices.h>
4149 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4150 __isl_keep isl_basic_set *bset);
4152 The function C<isl_basic_set_compute_vertices> performs the
4153 actual computation of the parametric vertices and the chamber
4154 decomposition and store the result in an C<isl_vertices> object.
4155 This information can be queried by either iterating over all
4156 the vertices or iterating over all the chambers or cells
4157 and then iterating over all vertices that are active on the chamber.
4159 int isl_vertices_foreach_vertex(
4160 __isl_keep isl_vertices *vertices,
4161 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4164 int isl_vertices_foreach_cell(
4165 __isl_keep isl_vertices *vertices,
4166 int (*fn)(__isl_take isl_cell *cell, void *user),
4168 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4169 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4172 Other operations that can be performed on an C<isl_vertices> object are
4175 isl_ctx *isl_vertices_get_ctx(
4176 __isl_keep isl_vertices *vertices);
4177 int isl_vertices_get_n_vertices(
4178 __isl_keep isl_vertices *vertices);
4179 void isl_vertices_free(__isl_take isl_vertices *vertices);
4181 Vertices can be inspected and destroyed using the following functions.
4183 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4184 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4185 __isl_give isl_basic_set *isl_vertex_get_domain(
4186 __isl_keep isl_vertex *vertex);
4187 __isl_give isl_basic_set *isl_vertex_get_expr(
4188 __isl_keep isl_vertex *vertex);
4189 void isl_vertex_free(__isl_take isl_vertex *vertex);
4191 C<isl_vertex_get_expr> returns a singleton parametric set describing
4192 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4194 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4195 B<rational> basic sets, so they should mainly be used for inspection
4196 and should not be mixed with integer sets.
4198 Chambers can be inspected and destroyed using the following functions.
4200 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4201 __isl_give isl_basic_set *isl_cell_get_domain(
4202 __isl_keep isl_cell *cell);
4203 void isl_cell_free(__isl_take isl_cell *cell);
4207 Although C<isl> is mainly meant to be used as a library,
4208 it also contains some basic applications that use some
4209 of the functionality of C<isl>.
4210 The input may be specified in either the L<isl format>
4211 or the L<PolyLib format>.
4213 =head2 C<isl_polyhedron_sample>
4215 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4216 an integer element of the polyhedron, if there is any.
4217 The first column in the output is the denominator and is always
4218 equal to 1. If the polyhedron contains no integer points,
4219 then a vector of length zero is printed.
4223 C<isl_pip> takes the same input as the C<example> program
4224 from the C<piplib> distribution, i.e., a set of constraints
4225 on the parameters, a line containing only -1 and finally a set
4226 of constraints on a parametric polyhedron.
4227 The coefficients of the parameters appear in the last columns
4228 (but before the final constant column).
4229 The output is the lexicographic minimum of the parametric polyhedron.
4230 As C<isl> currently does not have its own output format, the output
4231 is just a dump of the internal state.
4233 =head2 C<isl_polyhedron_minimize>
4235 C<isl_polyhedron_minimize> computes the minimum of some linear
4236 or affine objective function over the integer points in a polyhedron.
4237 If an affine objective function
4238 is given, then the constant should appear in the last column.
4240 =head2 C<isl_polytope_scan>
4242 Given a polytope, C<isl_polytope_scan> prints
4243 all integer points in the polytope.