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_map_from_domain_and_range(
768 __isl_take isl_space *domain,
769 __isl_take isl_space *range);
770 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
772 Note that if dimensions are added or removed from a space, then
773 the name and the internal structure are lost.
777 A local space is essentially a space with
778 zero or more existentially quantified variables.
779 The local space of a basic set or relation can be obtained
780 using the following functions.
783 __isl_give isl_local_space *isl_basic_set_get_local_space(
784 __isl_keep isl_basic_set *bset);
787 __isl_give isl_local_space *isl_basic_map_get_local_space(
788 __isl_keep isl_basic_map *bmap);
790 A new local space can be created from a space using
792 #include <isl/local_space.h>
793 __isl_give isl_local_space *isl_local_space_from_space(
794 __isl_take isl_space *space);
796 They can be inspected, modified, copied and freed using the following functions.
798 #include <isl/local_space.h>
799 isl_ctx *isl_local_space_get_ctx(
800 __isl_keep isl_local_space *ls);
801 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
802 int isl_local_space_dim(__isl_keep isl_local_space *ls,
803 enum isl_dim_type type);
804 const char *isl_local_space_get_dim_name(
805 __isl_keep isl_local_space *ls,
806 enum isl_dim_type type, unsigned pos);
807 __isl_give isl_local_space *isl_local_space_set_dim_name(
808 __isl_take isl_local_space *ls,
809 enum isl_dim_type type, unsigned pos, const char *s);
810 __isl_give isl_local_space *isl_local_space_set_dim_id(
811 __isl_take isl_local_space *ls,
812 enum isl_dim_type type, unsigned pos,
813 __isl_take isl_id *id);
814 __isl_give isl_space *isl_local_space_get_space(
815 __isl_keep isl_local_space *ls);
816 __isl_give isl_aff *isl_local_space_get_div(
817 __isl_keep isl_local_space *ls, int pos);
818 __isl_give isl_local_space *isl_local_space_copy(
819 __isl_keep isl_local_space *ls);
820 void *isl_local_space_free(__isl_take isl_local_space *ls);
822 Two local spaces can be compared using
824 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
825 __isl_keep isl_local_space *ls2);
827 Local spaces can be created from other local spaces
828 using the following functions.
830 __isl_give isl_local_space *isl_local_space_domain(
831 __isl_take isl_local_space *ls);
832 __isl_give isl_local_space *isl_local_space_range(
833 __isl_take isl_local_space *ls);
834 __isl_give isl_local_space *isl_local_space_from_domain(
835 __isl_take isl_local_space *ls);
836 __isl_give isl_local_space *isl_local_space_intersect(
837 __isl_take isl_local_space *ls1,
838 __isl_take isl_local_space *ls2);
839 __isl_give isl_local_space *isl_local_space_add_dims(
840 __isl_take isl_local_space *ls,
841 enum isl_dim_type type, unsigned n);
842 __isl_give isl_local_space *isl_local_space_insert_dims(
843 __isl_take isl_local_space *ls,
844 enum isl_dim_type type, unsigned first, unsigned n);
845 __isl_give isl_local_space *isl_local_space_drop_dims(
846 __isl_take isl_local_space *ls,
847 enum isl_dim_type type, unsigned first, unsigned n);
849 =head2 Input and Output
851 C<isl> supports its own input/output format, which is similar
852 to the C<Omega> format, but also supports the C<PolyLib> format
857 The C<isl> format is similar to that of C<Omega>, but has a different
858 syntax for describing the parameters and allows for the definition
859 of an existentially quantified variable as the integer division
860 of an affine expression.
861 For example, the set of integers C<i> between C<0> and C<n>
862 such that C<i % 10 <= 6> can be described as
864 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
867 A set or relation can have several disjuncts, separated
868 by the keyword C<or>. Each disjunct is either a conjunction
869 of constraints or a projection (C<exists>) of a conjunction
870 of constraints. The constraints are separated by the keyword
873 =head3 C<PolyLib> format
875 If the represented set is a union, then the first line
876 contains a single number representing the number of disjuncts.
877 Otherwise, a line containing the number C<1> is optional.
879 Each disjunct is represented by a matrix of constraints.
880 The first line contains two numbers representing
881 the number of rows and columns,
882 where the number of rows is equal to the number of constraints
883 and the number of columns is equal to two plus the number of variables.
884 The following lines contain the actual rows of the constraint matrix.
885 In each row, the first column indicates whether the constraint
886 is an equality (C<0>) or inequality (C<1>). The final column
887 corresponds to the constant term.
889 If the set is parametric, then the coefficients of the parameters
890 appear in the last columns before the constant column.
891 The coefficients of any existentially quantified variables appear
892 between those of the set variables and those of the parameters.
894 =head3 Extended C<PolyLib> format
896 The extended C<PolyLib> format is nearly identical to the
897 C<PolyLib> format. The only difference is that the line
898 containing the number of rows and columns of a constraint matrix
899 also contains four additional numbers:
900 the number of output dimensions, the number of input dimensions,
901 the number of local dimensions (i.e., the number of existentially
902 quantified variables) and the number of parameters.
903 For sets, the number of ``output'' dimensions is equal
904 to the number of set dimensions, while the number of ``input''
910 __isl_give isl_basic_set *isl_basic_set_read_from_file(
911 isl_ctx *ctx, FILE *input);
912 __isl_give isl_basic_set *isl_basic_set_read_from_str(
913 isl_ctx *ctx, const char *str);
914 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
916 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
920 __isl_give isl_basic_map *isl_basic_map_read_from_file(
921 isl_ctx *ctx, FILE *input);
922 __isl_give isl_basic_map *isl_basic_map_read_from_str(
923 isl_ctx *ctx, const char *str);
924 __isl_give isl_map *isl_map_read_from_file(
925 isl_ctx *ctx, FILE *input);
926 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
929 #include <isl/union_set.h>
930 __isl_give isl_union_set *isl_union_set_read_from_file(
931 isl_ctx *ctx, FILE *input);
932 __isl_give isl_union_set *isl_union_set_read_from_str(
933 isl_ctx *ctx, const char *str);
935 #include <isl/union_map.h>
936 __isl_give isl_union_map *isl_union_map_read_from_file(
937 isl_ctx *ctx, FILE *input);
938 __isl_give isl_union_map *isl_union_map_read_from_str(
939 isl_ctx *ctx, const char *str);
941 The input format is autodetected and may be either the C<PolyLib> format
942 or the C<isl> format.
946 Before anything can be printed, an C<isl_printer> needs to
949 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
951 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
952 void isl_printer_free(__isl_take isl_printer *printer);
953 __isl_give char *isl_printer_get_str(
954 __isl_keep isl_printer *printer);
956 The behavior of the printer can be modified in various ways
958 __isl_give isl_printer *isl_printer_set_output_format(
959 __isl_take isl_printer *p, int output_format);
960 __isl_give isl_printer *isl_printer_set_indent(
961 __isl_take isl_printer *p, int indent);
962 __isl_give isl_printer *isl_printer_indent(
963 __isl_take isl_printer *p, int indent);
964 __isl_give isl_printer *isl_printer_set_prefix(
965 __isl_take isl_printer *p, const char *prefix);
966 __isl_give isl_printer *isl_printer_set_suffix(
967 __isl_take isl_printer *p, const char *suffix);
969 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
970 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
971 and defaults to C<ISL_FORMAT_ISL>.
972 Each line in the output is indented by C<indent> (set by
973 C<isl_printer_set_indent>) spaces
974 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
975 In the C<PolyLib> format output,
976 the coefficients of the existentially quantified variables
977 appear between those of the set variables and those
979 The function C<isl_printer_indent> increases the indentation
980 by the specified amount (which may be negative).
982 To actually print something, use
985 __isl_give isl_printer *isl_printer_print_basic_set(
986 __isl_take isl_printer *printer,
987 __isl_keep isl_basic_set *bset);
988 __isl_give isl_printer *isl_printer_print_set(
989 __isl_take isl_printer *printer,
990 __isl_keep isl_set *set);
993 __isl_give isl_printer *isl_printer_print_basic_map(
994 __isl_take isl_printer *printer,
995 __isl_keep isl_basic_map *bmap);
996 __isl_give isl_printer *isl_printer_print_map(
997 __isl_take isl_printer *printer,
998 __isl_keep isl_map *map);
1000 #include <isl/union_set.h>
1001 __isl_give isl_printer *isl_printer_print_union_set(
1002 __isl_take isl_printer *p,
1003 __isl_keep isl_union_set *uset);
1005 #include <isl/union_map.h>
1006 __isl_give isl_printer *isl_printer_print_union_map(
1007 __isl_take isl_printer *p,
1008 __isl_keep isl_union_map *umap);
1010 When called on a file printer, the following function flushes
1011 the file. When called on a string printer, the buffer is cleared.
1013 __isl_give isl_printer *isl_printer_flush(
1014 __isl_take isl_printer *p);
1016 =head2 Creating New Sets and Relations
1018 C<isl> has functions for creating some standard sets and relations.
1022 =item * Empty sets and relations
1024 __isl_give isl_basic_set *isl_basic_set_empty(
1025 __isl_take isl_space *space);
1026 __isl_give isl_basic_map *isl_basic_map_empty(
1027 __isl_take isl_space *space);
1028 __isl_give isl_set *isl_set_empty(
1029 __isl_take isl_space *space);
1030 __isl_give isl_map *isl_map_empty(
1031 __isl_take isl_space *space);
1032 __isl_give isl_union_set *isl_union_set_empty(
1033 __isl_take isl_space *space);
1034 __isl_give isl_union_map *isl_union_map_empty(
1035 __isl_take isl_space *space);
1037 For C<isl_union_set>s and C<isl_union_map>s, the space
1038 is only used to specify the parameters.
1040 =item * Universe sets and relations
1042 __isl_give isl_basic_set *isl_basic_set_universe(
1043 __isl_take isl_space *space);
1044 __isl_give isl_basic_map *isl_basic_map_universe(
1045 __isl_take isl_space *space);
1046 __isl_give isl_set *isl_set_universe(
1047 __isl_take isl_space *space);
1048 __isl_give isl_map *isl_map_universe(
1049 __isl_take isl_space *space);
1050 __isl_give isl_union_set *isl_union_set_universe(
1051 __isl_take isl_union_set *uset);
1052 __isl_give isl_union_map *isl_union_map_universe(
1053 __isl_take isl_union_map *umap);
1055 The sets and relations constructed by the functions above
1056 contain all integer values, while those constructed by the
1057 functions below only contain non-negative values.
1059 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1060 __isl_take isl_space *space);
1061 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1062 __isl_take isl_space *space);
1063 __isl_give isl_set *isl_set_nat_universe(
1064 __isl_take isl_space *space);
1065 __isl_give isl_map *isl_map_nat_universe(
1066 __isl_take isl_space *space);
1068 =item * Identity relations
1070 __isl_give isl_basic_map *isl_basic_map_identity(
1071 __isl_take isl_space *space);
1072 __isl_give isl_map *isl_map_identity(
1073 __isl_take isl_space *space);
1075 The number of input and output dimensions in C<space> needs
1078 =item * Lexicographic order
1080 __isl_give isl_map *isl_map_lex_lt(
1081 __isl_take isl_space *set_space);
1082 __isl_give isl_map *isl_map_lex_le(
1083 __isl_take isl_space *set_space);
1084 __isl_give isl_map *isl_map_lex_gt(
1085 __isl_take isl_space *set_space);
1086 __isl_give isl_map *isl_map_lex_ge(
1087 __isl_take isl_space *set_space);
1088 __isl_give isl_map *isl_map_lex_lt_first(
1089 __isl_take isl_space *space, unsigned n);
1090 __isl_give isl_map *isl_map_lex_le_first(
1091 __isl_take isl_space *space, unsigned n);
1092 __isl_give isl_map *isl_map_lex_gt_first(
1093 __isl_take isl_space *space, unsigned n);
1094 __isl_give isl_map *isl_map_lex_ge_first(
1095 __isl_take isl_space *space, unsigned n);
1097 The first four functions take a space for a B<set>
1098 and return relations that express that the elements in the domain
1099 are lexicographically less
1100 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1101 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1102 than the elements in the range.
1103 The last four functions take a space for a map
1104 and return relations that express that the first C<n> dimensions
1105 in the domain are lexicographically less
1106 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1107 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1108 than the first C<n> dimensions in the range.
1112 A basic set or relation can be converted to a set or relation
1113 using the following functions.
1115 __isl_give isl_set *isl_set_from_basic_set(
1116 __isl_take isl_basic_set *bset);
1117 __isl_give isl_map *isl_map_from_basic_map(
1118 __isl_take isl_basic_map *bmap);
1120 Sets and relations can be converted to union sets and relations
1121 using the following functions.
1123 __isl_give isl_union_map *isl_union_map_from_map(
1124 __isl_take isl_map *map);
1125 __isl_give isl_union_set *isl_union_set_from_set(
1126 __isl_take isl_set *set);
1128 The inverse conversions below can only be used if the input
1129 union set or relation is known to contain elements in exactly one
1132 __isl_give isl_set *isl_set_from_union_set(
1133 __isl_take isl_union_set *uset);
1134 __isl_give isl_map *isl_map_from_union_map(
1135 __isl_take isl_union_map *umap);
1137 A zero-dimensional set can be constructed on a given parameter domain
1138 using the following function.
1140 __isl_give isl_set *isl_set_from_params(
1141 __isl_take isl_set *set);
1143 Sets and relations can be copied and freed again using the following
1146 __isl_give isl_basic_set *isl_basic_set_copy(
1147 __isl_keep isl_basic_set *bset);
1148 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1149 __isl_give isl_union_set *isl_union_set_copy(
1150 __isl_keep isl_union_set *uset);
1151 __isl_give isl_basic_map *isl_basic_map_copy(
1152 __isl_keep isl_basic_map *bmap);
1153 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1154 __isl_give isl_union_map *isl_union_map_copy(
1155 __isl_keep isl_union_map *umap);
1156 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1157 void isl_set_free(__isl_take isl_set *set);
1158 void *isl_union_set_free(__isl_take isl_union_set *uset);
1159 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1160 void isl_map_free(__isl_take isl_map *map);
1161 void *isl_union_map_free(__isl_take isl_union_map *umap);
1163 Other sets and relations can be constructed by starting
1164 from a universe set or relation, adding equality and/or
1165 inequality constraints and then projecting out the
1166 existentially quantified variables, if any.
1167 Constraints can be constructed, manipulated and
1168 added to (or removed from) (basic) sets and relations
1169 using the following functions.
1171 #include <isl/constraint.h>
1172 __isl_give isl_constraint *isl_equality_alloc(
1173 __isl_take isl_local_space *ls);
1174 __isl_give isl_constraint *isl_inequality_alloc(
1175 __isl_take isl_local_space *ls);
1176 __isl_give isl_constraint *isl_constraint_set_constant(
1177 __isl_take isl_constraint *constraint, isl_int v);
1178 __isl_give isl_constraint *isl_constraint_set_constant_si(
1179 __isl_take isl_constraint *constraint, int v);
1180 __isl_give isl_constraint *isl_constraint_set_coefficient(
1181 __isl_take isl_constraint *constraint,
1182 enum isl_dim_type type, int pos, isl_int v);
1183 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1184 __isl_take isl_constraint *constraint,
1185 enum isl_dim_type type, int pos, int v);
1186 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1187 __isl_take isl_basic_map *bmap,
1188 __isl_take isl_constraint *constraint);
1189 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1190 __isl_take isl_basic_set *bset,
1191 __isl_take isl_constraint *constraint);
1192 __isl_give isl_map *isl_map_add_constraint(
1193 __isl_take isl_map *map,
1194 __isl_take isl_constraint *constraint);
1195 __isl_give isl_set *isl_set_add_constraint(
1196 __isl_take isl_set *set,
1197 __isl_take isl_constraint *constraint);
1198 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1199 __isl_take isl_basic_set *bset,
1200 __isl_take isl_constraint *constraint);
1202 For example, to create a set containing the even integers
1203 between 10 and 42, you would use the following code.
1206 isl_local_space *ls;
1208 isl_basic_set *bset;
1210 space = isl_space_set_alloc(ctx, 0, 2);
1211 bset = isl_basic_set_universe(isl_space_copy(space));
1212 ls = isl_local_space_from_space(space);
1214 c = isl_equality_alloc(isl_local_space_copy(ls));
1215 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1216 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1217 bset = isl_basic_set_add_constraint(bset, c);
1219 c = isl_inequality_alloc(isl_local_space_copy(ls));
1220 c = isl_constraint_set_constant_si(c, -10);
1221 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1222 bset = isl_basic_set_add_constraint(bset, c);
1224 c = isl_inequality_alloc(ls);
1225 c = isl_constraint_set_constant_si(c, 42);
1226 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1227 bset = isl_basic_set_add_constraint(bset, c);
1229 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1233 isl_basic_set *bset;
1234 bset = isl_basic_set_read_from_str(ctx,
1235 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1237 A basic set or relation can also be constructed from two matrices
1238 describing the equalities and the inequalities.
1240 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1241 __isl_take isl_space *space,
1242 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1243 enum isl_dim_type c1,
1244 enum isl_dim_type c2, enum isl_dim_type c3,
1245 enum isl_dim_type c4);
1246 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1247 __isl_take isl_space *space,
1248 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1249 enum isl_dim_type c1,
1250 enum isl_dim_type c2, enum isl_dim_type c3,
1251 enum isl_dim_type c4, enum isl_dim_type c5);
1253 The C<isl_dim_type> arguments indicate the order in which
1254 different kinds of variables appear in the input matrices
1255 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1256 C<isl_dim_set> and C<isl_dim_div> for sets and
1257 of C<isl_dim_cst>, C<isl_dim_param>,
1258 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1260 A (basic) set or relation can also be constructed from a (piecewise)
1261 (multiple) affine expression
1262 or a list of affine expressions
1263 (See L<"Piecewise Quasi Affine Expressions"> and
1264 L<"Piecewise Multiple Quasi Affine Expressions">).
1266 __isl_give isl_basic_map *isl_basic_map_from_aff(
1267 __isl_take isl_aff *aff);
1268 __isl_give isl_set *isl_set_from_pw_aff(
1269 __isl_take isl_pw_aff *pwaff);
1270 __isl_give isl_map *isl_map_from_pw_aff(
1271 __isl_take isl_pw_aff *pwaff);
1272 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1273 __isl_take isl_space *domain_space,
1274 __isl_take isl_aff_list *list);
1275 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1276 __isl_take isl_multi_aff *maff)
1277 __isl_give isl_set *isl_set_from_pw_multi_aff(
1278 __isl_take isl_pw_multi_aff *pma);
1279 __isl_give isl_map *isl_map_from_pw_multi_aff(
1280 __isl_take isl_pw_multi_aff *pma);
1282 The C<domain_dim> argument describes the domain of the resulting
1283 basic relation. It is required because the C<list> may consist
1284 of zero affine expressions.
1286 =head2 Inspecting Sets and Relations
1288 Usually, the user should not have to care about the actual constraints
1289 of the sets and maps, but should instead apply the abstract operations
1290 explained in the following sections.
1291 Occasionally, however, it may be required to inspect the individual
1292 coefficients of the constraints. This section explains how to do so.
1293 In these cases, it may also be useful to have C<isl> compute
1294 an explicit representation of the existentially quantified variables.
1296 __isl_give isl_set *isl_set_compute_divs(
1297 __isl_take isl_set *set);
1298 __isl_give isl_map *isl_map_compute_divs(
1299 __isl_take isl_map *map);
1300 __isl_give isl_union_set *isl_union_set_compute_divs(
1301 __isl_take isl_union_set *uset);
1302 __isl_give isl_union_map *isl_union_map_compute_divs(
1303 __isl_take isl_union_map *umap);
1305 This explicit representation defines the existentially quantified
1306 variables as integer divisions of the other variables, possibly
1307 including earlier existentially quantified variables.
1308 An explicitly represented existentially quantified variable therefore
1309 has a unique value when the values of the other variables are known.
1310 If, furthermore, the same existentials, i.e., existentials
1311 with the same explicit representations, should appear in the
1312 same order in each of the disjuncts of a set or map, then the user should call
1313 either of the following functions.
1315 __isl_give isl_set *isl_set_align_divs(
1316 __isl_take isl_set *set);
1317 __isl_give isl_map *isl_map_align_divs(
1318 __isl_take isl_map *map);
1320 Alternatively, the existentially quantified variables can be removed
1321 using the following functions, which compute an overapproximation.
1323 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1324 __isl_take isl_basic_set *bset);
1325 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1326 __isl_take isl_basic_map *bmap);
1327 __isl_give isl_set *isl_set_remove_divs(
1328 __isl_take isl_set *set);
1329 __isl_give isl_map *isl_map_remove_divs(
1330 __isl_take isl_map *map);
1332 To iterate over all the sets or maps in a union set or map, use
1334 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1335 int (*fn)(__isl_take isl_set *set, void *user),
1337 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1338 int (*fn)(__isl_take isl_map *map, void *user),
1341 The number of sets or maps in a union set or map can be obtained
1344 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1345 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1347 To extract the set or map in a given space from a union, use
1349 __isl_give isl_set *isl_union_set_extract_set(
1350 __isl_keep isl_union_set *uset,
1351 __isl_take isl_space *space);
1352 __isl_give isl_map *isl_union_map_extract_map(
1353 __isl_keep isl_union_map *umap,
1354 __isl_take isl_space *space);
1356 To iterate over all the basic sets or maps in a set or map, use
1358 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1359 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1361 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1362 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1365 The callback function C<fn> should return 0 if successful and
1366 -1 if an error occurs. In the latter case, or if any other error
1367 occurs, the above functions will return -1.
1369 It should be noted that C<isl> does not guarantee that
1370 the basic sets or maps passed to C<fn> are disjoint.
1371 If this is required, then the user should call one of
1372 the following functions first.
1374 __isl_give isl_set *isl_set_make_disjoint(
1375 __isl_take isl_set *set);
1376 __isl_give isl_map *isl_map_make_disjoint(
1377 __isl_take isl_map *map);
1379 The number of basic sets in a set can be obtained
1382 int isl_set_n_basic_set(__isl_keep isl_set *set);
1384 To iterate over the constraints of a basic set or map, use
1386 #include <isl/constraint.h>
1388 int isl_basic_map_foreach_constraint(
1389 __isl_keep isl_basic_map *bmap,
1390 int (*fn)(__isl_take isl_constraint *c, void *user),
1392 void *isl_constraint_free(__isl_take isl_constraint *c);
1394 Again, the callback function C<fn> should return 0 if successful and
1395 -1 if an error occurs. In the latter case, or if any other error
1396 occurs, the above functions will return -1.
1397 The constraint C<c> represents either an equality or an inequality.
1398 Use the following function to find out whether a constraint
1399 represents an equality. If not, it represents an inequality.
1401 int isl_constraint_is_equality(
1402 __isl_keep isl_constraint *constraint);
1404 The coefficients of the constraints can be inspected using
1405 the following functions.
1407 void isl_constraint_get_constant(
1408 __isl_keep isl_constraint *constraint, isl_int *v);
1409 void isl_constraint_get_coefficient(
1410 __isl_keep isl_constraint *constraint,
1411 enum isl_dim_type type, int pos, isl_int *v);
1412 int isl_constraint_involves_dims(
1413 __isl_keep isl_constraint *constraint,
1414 enum isl_dim_type type, unsigned first, unsigned n);
1416 The explicit representations of the existentially quantified
1417 variables can be inspected using the following function.
1418 Note that the user is only allowed to use this function
1419 if the inspected set or map is the result of a call
1420 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1421 The existentially quantified variable is equal to the floor
1422 of the returned affine expression. The affine expression
1423 itself can be inspected using the functions in
1424 L<"Piecewise Quasi Affine Expressions">.
1426 __isl_give isl_aff *isl_constraint_get_div(
1427 __isl_keep isl_constraint *constraint, int pos);
1429 To obtain the constraints of a basic set or map in matrix
1430 form, use the following functions.
1432 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1433 __isl_keep isl_basic_set *bset,
1434 enum isl_dim_type c1, enum isl_dim_type c2,
1435 enum isl_dim_type c3, enum isl_dim_type c4);
1436 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1437 __isl_keep isl_basic_set *bset,
1438 enum isl_dim_type c1, enum isl_dim_type c2,
1439 enum isl_dim_type c3, enum isl_dim_type c4);
1440 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1441 __isl_keep isl_basic_map *bmap,
1442 enum isl_dim_type c1,
1443 enum isl_dim_type c2, enum isl_dim_type c3,
1444 enum isl_dim_type c4, enum isl_dim_type c5);
1445 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1446 __isl_keep isl_basic_map *bmap,
1447 enum isl_dim_type c1,
1448 enum isl_dim_type c2, enum isl_dim_type c3,
1449 enum isl_dim_type c4, enum isl_dim_type c5);
1451 The C<isl_dim_type> arguments dictate the order in which
1452 different kinds of variables appear in the resulting matrix
1453 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1454 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1456 The number of parameters, input, output or set dimensions can
1457 be obtained using the following functions.
1459 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1460 enum isl_dim_type type);
1461 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1462 enum isl_dim_type type);
1463 unsigned isl_set_dim(__isl_keep isl_set *set,
1464 enum isl_dim_type type);
1465 unsigned isl_map_dim(__isl_keep isl_map *map,
1466 enum isl_dim_type type);
1468 To check whether the description of a set or relation depends
1469 on one or more given dimensions, it is not necessary to iterate over all
1470 constraints. Instead the following functions can be used.
1472 int isl_basic_set_involves_dims(
1473 __isl_keep isl_basic_set *bset,
1474 enum isl_dim_type type, unsigned first, unsigned n);
1475 int isl_set_involves_dims(__isl_keep isl_set *set,
1476 enum isl_dim_type type, unsigned first, unsigned n);
1477 int isl_basic_map_involves_dims(
1478 __isl_keep isl_basic_map *bmap,
1479 enum isl_dim_type type, unsigned first, unsigned n);
1480 int isl_map_involves_dims(__isl_keep isl_map *map,
1481 enum isl_dim_type type, unsigned first, unsigned n);
1483 Similarly, the following functions can be used to check whether
1484 a given dimension is involved in any lower or upper bound.
1486 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1487 enum isl_dim_type type, unsigned pos);
1488 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1489 enum isl_dim_type type, unsigned pos);
1491 The identifiers or names of the domain and range spaces of a set
1492 or relation can be read off or set using the following functions.
1494 __isl_give isl_set *isl_set_set_tuple_id(
1495 __isl_take isl_set *set, __isl_take isl_id *id);
1496 __isl_give isl_set *isl_set_reset_tuple_id(
1497 __isl_take isl_set *set);
1498 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1499 __isl_give isl_id *isl_set_get_tuple_id(
1500 __isl_keep isl_set *set);
1501 __isl_give isl_map *isl_map_set_tuple_id(
1502 __isl_take isl_map *map, enum isl_dim_type type,
1503 __isl_take isl_id *id);
1504 __isl_give isl_map *isl_map_reset_tuple_id(
1505 __isl_take isl_map *map, enum isl_dim_type type);
1506 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1507 enum isl_dim_type type);
1508 __isl_give isl_id *isl_map_get_tuple_id(
1509 __isl_keep isl_map *map, enum isl_dim_type type);
1511 const char *isl_basic_set_get_tuple_name(
1512 __isl_keep isl_basic_set *bset);
1513 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1514 __isl_take isl_basic_set *set, const char *s);
1515 const char *isl_set_get_tuple_name(
1516 __isl_keep isl_set *set);
1517 const char *isl_basic_map_get_tuple_name(
1518 __isl_keep isl_basic_map *bmap,
1519 enum isl_dim_type type);
1520 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1521 __isl_take isl_basic_map *bmap,
1522 enum isl_dim_type type, const char *s);
1523 const char *isl_map_get_tuple_name(
1524 __isl_keep isl_map *map,
1525 enum isl_dim_type type);
1527 As with C<isl_space_get_tuple_name>, the value returned points to
1528 an internal data structure.
1529 The identifiers, positions or names of individual dimensions can be
1530 read off using the following functions.
1532 __isl_give isl_set *isl_set_set_dim_id(
1533 __isl_take isl_set *set, enum isl_dim_type type,
1534 unsigned pos, __isl_take isl_id *id);
1535 int isl_set_has_dim_id(__isl_keep isl_set *set,
1536 enum isl_dim_type type, unsigned pos);
1537 __isl_give isl_id *isl_set_get_dim_id(
1538 __isl_keep isl_set *set, enum isl_dim_type type,
1540 int isl_basic_map_has_dim_id(
1541 __isl_keep isl_basic_map *bmap,
1542 enum isl_dim_type type, unsigned pos);
1543 __isl_give isl_map *isl_map_set_dim_id(
1544 __isl_take isl_map *map, enum isl_dim_type type,
1545 unsigned pos, __isl_take isl_id *id);
1546 int isl_map_has_dim_id(__isl_keep isl_map *map,
1547 enum isl_dim_type type, unsigned pos);
1548 __isl_give isl_id *isl_map_get_dim_id(
1549 __isl_keep isl_map *map, enum isl_dim_type type,
1552 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1553 enum isl_dim_type type, __isl_keep isl_id *id);
1554 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1555 enum isl_dim_type type, __isl_keep isl_id *id);
1556 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1557 enum isl_dim_type type, const char *name);
1558 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1559 enum isl_dim_type type, const char *name);
1561 const char *isl_constraint_get_dim_name(
1562 __isl_keep isl_constraint *constraint,
1563 enum isl_dim_type type, unsigned pos);
1564 const char *isl_basic_set_get_dim_name(
1565 __isl_keep isl_basic_set *bset,
1566 enum isl_dim_type type, unsigned pos);
1567 const char *isl_set_get_dim_name(
1568 __isl_keep isl_set *set,
1569 enum isl_dim_type type, unsigned pos);
1570 const char *isl_basic_map_get_dim_name(
1571 __isl_keep isl_basic_map *bmap,
1572 enum isl_dim_type type, unsigned pos);
1573 const char *isl_map_get_dim_name(
1574 __isl_keep isl_map *map,
1575 enum isl_dim_type type, unsigned pos);
1577 These functions are mostly useful to obtain the identifiers, positions
1578 or names of the parameters. Identifiers of individual dimensions are
1579 essentially only useful for printing. They are ignored by all other
1580 operations and may not be preserved across those operations.
1584 =head3 Unary Properties
1590 The following functions test whether the given set or relation
1591 contains any integer points. The ``plain'' variants do not perform
1592 any computations, but simply check if the given set or relation
1593 is already known to be empty.
1595 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1596 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1597 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1598 int isl_set_is_empty(__isl_keep isl_set *set);
1599 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1600 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1601 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1602 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1603 int isl_map_is_empty(__isl_keep isl_map *map);
1604 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1606 =item * Universality
1608 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1609 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1610 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1612 =item * Single-valuedness
1614 int isl_map_is_single_valued(__isl_keep isl_map *map);
1615 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1619 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1620 int isl_map_is_injective(__isl_keep isl_map *map);
1621 int isl_union_map_plain_is_injective(
1622 __isl_keep isl_union_map *umap);
1623 int isl_union_map_is_injective(
1624 __isl_keep isl_union_map *umap);
1628 int isl_map_is_bijective(__isl_keep isl_map *map);
1629 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1633 int isl_basic_map_plain_is_fixed(
1634 __isl_keep isl_basic_map *bmap,
1635 enum isl_dim_type type, unsigned pos,
1637 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1638 enum isl_dim_type type, unsigned pos,
1640 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1641 enum isl_dim_type type, unsigned pos,
1644 Check if the relation obviously lies on a hyperplane where the given dimension
1645 has a fixed value and if so, return that value in C<*val>.
1649 To check whether a set is a parameter domain, use this function:
1651 int isl_set_is_params(__isl_keep isl_set *set);
1652 int isl_union_set_is_params(
1653 __isl_keep isl_union_set *uset);
1657 The following functions check whether the domain of the given
1658 (basic) set is a wrapped relation.
1660 int isl_basic_set_is_wrapping(
1661 __isl_keep isl_basic_set *bset);
1662 int isl_set_is_wrapping(__isl_keep isl_set *set);
1664 =item * Internal Product
1666 int isl_basic_map_can_zip(
1667 __isl_keep isl_basic_map *bmap);
1668 int isl_map_can_zip(__isl_keep isl_map *map);
1670 Check whether the product of domain and range of the given relation
1672 i.e., whether both domain and range are nested relations.
1676 =head3 Binary Properties
1682 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1683 __isl_keep isl_set *set2);
1684 int isl_set_is_equal(__isl_keep isl_set *set1,
1685 __isl_keep isl_set *set2);
1686 int isl_union_set_is_equal(
1687 __isl_keep isl_union_set *uset1,
1688 __isl_keep isl_union_set *uset2);
1689 int isl_basic_map_is_equal(
1690 __isl_keep isl_basic_map *bmap1,
1691 __isl_keep isl_basic_map *bmap2);
1692 int isl_map_is_equal(__isl_keep isl_map *map1,
1693 __isl_keep isl_map *map2);
1694 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1695 __isl_keep isl_map *map2);
1696 int isl_union_map_is_equal(
1697 __isl_keep isl_union_map *umap1,
1698 __isl_keep isl_union_map *umap2);
1700 =item * Disjointness
1702 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1703 __isl_keep isl_set *set2);
1707 int isl_set_is_subset(__isl_keep isl_set *set1,
1708 __isl_keep isl_set *set2);
1709 int isl_set_is_strict_subset(
1710 __isl_keep isl_set *set1,
1711 __isl_keep isl_set *set2);
1712 int isl_union_set_is_subset(
1713 __isl_keep isl_union_set *uset1,
1714 __isl_keep isl_union_set *uset2);
1715 int isl_union_set_is_strict_subset(
1716 __isl_keep isl_union_set *uset1,
1717 __isl_keep isl_union_set *uset2);
1718 int isl_basic_map_is_subset(
1719 __isl_keep isl_basic_map *bmap1,
1720 __isl_keep isl_basic_map *bmap2);
1721 int isl_basic_map_is_strict_subset(
1722 __isl_keep isl_basic_map *bmap1,
1723 __isl_keep isl_basic_map *bmap2);
1724 int isl_map_is_subset(
1725 __isl_keep isl_map *map1,
1726 __isl_keep isl_map *map2);
1727 int isl_map_is_strict_subset(
1728 __isl_keep isl_map *map1,
1729 __isl_keep isl_map *map2);
1730 int isl_union_map_is_subset(
1731 __isl_keep isl_union_map *umap1,
1732 __isl_keep isl_union_map *umap2);
1733 int isl_union_map_is_strict_subset(
1734 __isl_keep isl_union_map *umap1,
1735 __isl_keep isl_union_map *umap2);
1739 =head2 Unary Operations
1745 __isl_give isl_set *isl_set_complement(
1746 __isl_take isl_set *set);
1750 __isl_give isl_basic_map *isl_basic_map_reverse(
1751 __isl_take isl_basic_map *bmap);
1752 __isl_give isl_map *isl_map_reverse(
1753 __isl_take isl_map *map);
1754 __isl_give isl_union_map *isl_union_map_reverse(
1755 __isl_take isl_union_map *umap);
1759 __isl_give isl_basic_set *isl_basic_set_project_out(
1760 __isl_take isl_basic_set *bset,
1761 enum isl_dim_type type, unsigned first, unsigned n);
1762 __isl_give isl_basic_map *isl_basic_map_project_out(
1763 __isl_take isl_basic_map *bmap,
1764 enum isl_dim_type type, unsigned first, unsigned n);
1765 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1766 enum isl_dim_type type, unsigned first, unsigned n);
1767 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1768 enum isl_dim_type type, unsigned first, unsigned n);
1769 __isl_give isl_basic_set *isl_basic_set_params(
1770 __isl_take isl_basic_set *bset);
1771 __isl_give isl_basic_set *isl_basic_map_domain(
1772 __isl_take isl_basic_map *bmap);
1773 __isl_give isl_basic_set *isl_basic_map_range(
1774 __isl_take isl_basic_map *bmap);
1775 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1776 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1777 __isl_give isl_set *isl_map_domain(
1778 __isl_take isl_map *bmap);
1779 __isl_give isl_set *isl_map_range(
1780 __isl_take isl_map *map);
1781 __isl_give isl_set *isl_union_set_params(
1782 __isl_take isl_union_set *uset);
1783 __isl_give isl_set *isl_union_map_params(
1784 __isl_take isl_union_map *umap);
1785 __isl_give isl_union_set *isl_union_map_domain(
1786 __isl_take isl_union_map *umap);
1787 __isl_give isl_union_set *isl_union_map_range(
1788 __isl_take isl_union_map *umap);
1790 __isl_give isl_basic_map *isl_basic_map_domain_map(
1791 __isl_take isl_basic_map *bmap);
1792 __isl_give isl_basic_map *isl_basic_map_range_map(
1793 __isl_take isl_basic_map *bmap);
1794 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1795 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1796 __isl_give isl_union_map *isl_union_map_domain_map(
1797 __isl_take isl_union_map *umap);
1798 __isl_give isl_union_map *isl_union_map_range_map(
1799 __isl_take isl_union_map *umap);
1801 The functions above construct a (basic, regular or union) relation
1802 that maps (a wrapped version of) the input relation to its domain or range.
1806 __isl_give isl_set *isl_set_eliminate(
1807 __isl_take isl_set *set, enum isl_dim_type type,
1808 unsigned first, unsigned n);
1809 __isl_give isl_basic_map *isl_basic_map_eliminate(
1810 __isl_take isl_basic_map *bmap,
1811 enum isl_dim_type type,
1812 unsigned first, unsigned n);
1813 __isl_give isl_map *isl_map_eliminate(
1814 __isl_take isl_map *map, enum isl_dim_type type,
1815 unsigned first, unsigned n);
1817 Eliminate the coefficients for the given dimensions from the constraints,
1818 without removing the dimensions.
1822 __isl_give isl_basic_set *isl_basic_set_fix(
1823 __isl_take isl_basic_set *bset,
1824 enum isl_dim_type type, unsigned pos,
1826 __isl_give isl_basic_set *isl_basic_set_fix_si(
1827 __isl_take isl_basic_set *bset,
1828 enum isl_dim_type type, unsigned pos, int value);
1829 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1830 enum isl_dim_type type, unsigned pos,
1832 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1833 enum isl_dim_type type, unsigned pos, int value);
1834 __isl_give isl_basic_map *isl_basic_map_fix_si(
1835 __isl_take isl_basic_map *bmap,
1836 enum isl_dim_type type, unsigned pos, int value);
1837 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1838 enum isl_dim_type type, unsigned pos, int value);
1840 Intersect the set or relation with the hyperplane where the given
1841 dimension has the fixed given value.
1843 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1844 __isl_take isl_basic_map *bmap,
1845 enum isl_dim_type type, unsigned pos, int value);
1846 __isl_give isl_set *isl_set_lower_bound_si(
1847 __isl_take isl_set *set,
1848 enum isl_dim_type type, unsigned pos, int value);
1849 __isl_give isl_map *isl_map_lower_bound_si(
1850 __isl_take isl_map *map,
1851 enum isl_dim_type type, unsigned pos, int value);
1852 __isl_give isl_set *isl_set_upper_bound_si(
1853 __isl_take isl_set *set,
1854 enum isl_dim_type type, unsigned pos, int value);
1855 __isl_give isl_map *isl_map_upper_bound_si(
1856 __isl_take isl_map *map,
1857 enum isl_dim_type type, unsigned pos, int value);
1859 Intersect the set or relation with the half-space where the given
1860 dimension has a value bounded the fixed given value.
1862 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1863 enum isl_dim_type type1, int pos1,
1864 enum isl_dim_type type2, int pos2);
1865 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1866 enum isl_dim_type type1, int pos1,
1867 enum isl_dim_type type2, int pos2);
1869 Intersect the set or relation with the hyperplane where the given
1870 dimensions are equal to each other.
1872 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1873 enum isl_dim_type type1, int pos1,
1874 enum isl_dim_type type2, int pos2);
1876 Intersect the relation with the hyperplane where the given
1877 dimensions have opposite values.
1881 __isl_give isl_map *isl_set_identity(
1882 __isl_take isl_set *set);
1883 __isl_give isl_union_map *isl_union_set_identity(
1884 __isl_take isl_union_set *uset);
1886 Construct an identity relation on the given (union) set.
1890 __isl_give isl_basic_set *isl_basic_map_deltas(
1891 __isl_take isl_basic_map *bmap);
1892 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1893 __isl_give isl_union_set *isl_union_map_deltas(
1894 __isl_take isl_union_map *umap);
1896 These functions return a (basic) set containing the differences
1897 between image elements and corresponding domain elements in the input.
1899 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1900 __isl_take isl_basic_map *bmap);
1901 __isl_give isl_map *isl_map_deltas_map(
1902 __isl_take isl_map *map);
1903 __isl_give isl_union_map *isl_union_map_deltas_map(
1904 __isl_take isl_union_map *umap);
1906 The functions above construct a (basic, regular or union) relation
1907 that maps (a wrapped version of) the input relation to its delta set.
1911 Simplify the representation of a set or relation by trying
1912 to combine pairs of basic sets or relations into a single
1913 basic set or relation.
1915 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1916 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1917 __isl_give isl_union_set *isl_union_set_coalesce(
1918 __isl_take isl_union_set *uset);
1919 __isl_give isl_union_map *isl_union_map_coalesce(
1920 __isl_take isl_union_map *umap);
1922 =item * Detecting equalities
1924 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1925 __isl_take isl_basic_set *bset);
1926 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1927 __isl_take isl_basic_map *bmap);
1928 __isl_give isl_set *isl_set_detect_equalities(
1929 __isl_take isl_set *set);
1930 __isl_give isl_map *isl_map_detect_equalities(
1931 __isl_take isl_map *map);
1932 __isl_give isl_union_set *isl_union_set_detect_equalities(
1933 __isl_take isl_union_set *uset);
1934 __isl_give isl_union_map *isl_union_map_detect_equalities(
1935 __isl_take isl_union_map *umap);
1937 Simplify the representation of a set or relation by detecting implicit
1940 =item * Removing redundant constraints
1942 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1943 __isl_take isl_basic_set *bset);
1944 __isl_give isl_set *isl_set_remove_redundancies(
1945 __isl_take isl_set *set);
1946 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1947 __isl_take isl_basic_map *bmap);
1948 __isl_give isl_map *isl_map_remove_redundancies(
1949 __isl_take isl_map *map);
1953 __isl_give isl_basic_set *isl_set_convex_hull(
1954 __isl_take isl_set *set);
1955 __isl_give isl_basic_map *isl_map_convex_hull(
1956 __isl_take isl_map *map);
1958 If the input set or relation has any existentially quantified
1959 variables, then the result of these operations is currently undefined.
1963 __isl_give isl_basic_set *isl_set_simple_hull(
1964 __isl_take isl_set *set);
1965 __isl_give isl_basic_map *isl_map_simple_hull(
1966 __isl_take isl_map *map);
1967 __isl_give isl_union_map *isl_union_map_simple_hull(
1968 __isl_take isl_union_map *umap);
1970 These functions compute a single basic set or relation
1971 that contains the whole input set or relation.
1972 In particular, the output is described by translates
1973 of the constraints describing the basic sets or relations in the input.
1977 (See \autoref{s:simple hull}.)
1983 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1984 __isl_take isl_basic_set *bset);
1985 __isl_give isl_basic_set *isl_set_affine_hull(
1986 __isl_take isl_set *set);
1987 __isl_give isl_union_set *isl_union_set_affine_hull(
1988 __isl_take isl_union_set *uset);
1989 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1990 __isl_take isl_basic_map *bmap);
1991 __isl_give isl_basic_map *isl_map_affine_hull(
1992 __isl_take isl_map *map);
1993 __isl_give isl_union_map *isl_union_map_affine_hull(
1994 __isl_take isl_union_map *umap);
1996 In case of union sets and relations, the affine hull is computed
1999 =item * Polyhedral hull
2001 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2002 __isl_take isl_set *set);
2003 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2004 __isl_take isl_map *map);
2005 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2006 __isl_take isl_union_set *uset);
2007 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2008 __isl_take isl_union_map *umap);
2010 These functions compute a single basic set or relation
2011 not involving any existentially quantified variables
2012 that contains the whole input set or relation.
2013 In case of union sets and relations, the polyhedral hull is computed
2016 =item * Optimization
2018 #include <isl/ilp.h>
2019 enum isl_lp_result isl_basic_set_max(
2020 __isl_keep isl_basic_set *bset,
2021 __isl_keep isl_aff *obj, isl_int *opt)
2022 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2023 __isl_keep isl_aff *obj, isl_int *opt);
2024 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2025 __isl_keep isl_aff *obj, isl_int *opt);
2027 Compute the minimum or maximum of the integer affine expression C<obj>
2028 over the points in C<set>, returning the result in C<opt>.
2029 The return value may be one of C<isl_lp_error>,
2030 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2032 =item * Parametric optimization
2034 __isl_give isl_pw_aff *isl_set_dim_min(
2035 __isl_take isl_set *set, int pos);
2036 __isl_give isl_pw_aff *isl_set_dim_max(
2037 __isl_take isl_set *set, int pos);
2038 __isl_give isl_pw_aff *isl_map_dim_max(
2039 __isl_take isl_map *map, int pos);
2041 Compute the minimum or maximum of the given set or output dimension
2042 as a function of the parameters (and input dimensions), but independently
2043 of the other set or output dimensions.
2044 For lexicographic optimization, see L<"Lexicographic Optimization">.
2048 The following functions compute either the set of (rational) coefficient
2049 values of valid constraints for the given set or the set of (rational)
2050 values satisfying the constraints with coefficients from the given set.
2051 Internally, these two sets of functions perform essentially the
2052 same operations, except that the set of coefficients is assumed to
2053 be a cone, while the set of values may be any polyhedron.
2054 The current implementation is based on the Farkas lemma and
2055 Fourier-Motzkin elimination, but this may change or be made optional
2056 in future. In particular, future implementations may use different
2057 dualization algorithms or skip the elimination step.
2059 __isl_give isl_basic_set *isl_basic_set_coefficients(
2060 __isl_take isl_basic_set *bset);
2061 __isl_give isl_basic_set *isl_set_coefficients(
2062 __isl_take isl_set *set);
2063 __isl_give isl_union_set *isl_union_set_coefficients(
2064 __isl_take isl_union_set *bset);
2065 __isl_give isl_basic_set *isl_basic_set_solutions(
2066 __isl_take isl_basic_set *bset);
2067 __isl_give isl_basic_set *isl_set_solutions(
2068 __isl_take isl_set *set);
2069 __isl_give isl_union_set *isl_union_set_solutions(
2070 __isl_take isl_union_set *bset);
2074 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2076 __isl_give isl_union_map *isl_union_map_power(
2077 __isl_take isl_union_map *umap, int *exact);
2079 Compute a parametric representation for all positive powers I<k> of C<map>.
2080 The result maps I<k> to a nested relation corresponding to the
2081 I<k>th power of C<map>.
2082 The result may be an overapproximation. If the result is known to be exact,
2083 then C<*exact> is set to C<1>.
2085 =item * Transitive closure
2087 __isl_give isl_map *isl_map_transitive_closure(
2088 __isl_take isl_map *map, int *exact);
2089 __isl_give isl_union_map *isl_union_map_transitive_closure(
2090 __isl_take isl_union_map *umap, int *exact);
2092 Compute the transitive closure of C<map>.
2093 The result may be an overapproximation. If the result is known to be exact,
2094 then C<*exact> is set to C<1>.
2096 =item * Reaching path lengths
2098 __isl_give isl_map *isl_map_reaching_path_lengths(
2099 __isl_take isl_map *map, int *exact);
2101 Compute a relation that maps each element in the range of C<map>
2102 to the lengths of all paths composed of edges in C<map> that
2103 end up in the given element.
2104 The result may be an overapproximation. If the result is known to be exact,
2105 then C<*exact> is set to C<1>.
2106 To compute the I<maximal> path length, the resulting relation
2107 should be postprocessed by C<isl_map_lexmax>.
2108 In particular, if the input relation is a dependence relation
2109 (mapping sources to sinks), then the maximal path length corresponds
2110 to the free schedule.
2111 Note, however, that C<isl_map_lexmax> expects the maximum to be
2112 finite, so if the path lengths are unbounded (possibly due to
2113 the overapproximation), then you will get an error message.
2117 __isl_give isl_basic_set *isl_basic_map_wrap(
2118 __isl_take isl_basic_map *bmap);
2119 __isl_give isl_set *isl_map_wrap(
2120 __isl_take isl_map *map);
2121 __isl_give isl_union_set *isl_union_map_wrap(
2122 __isl_take isl_union_map *umap);
2123 __isl_give isl_basic_map *isl_basic_set_unwrap(
2124 __isl_take isl_basic_set *bset);
2125 __isl_give isl_map *isl_set_unwrap(
2126 __isl_take isl_set *set);
2127 __isl_give isl_union_map *isl_union_set_unwrap(
2128 __isl_take isl_union_set *uset);
2132 Remove any internal structure of domain (and range) of the given
2133 set or relation. If there is any such internal structure in the input,
2134 then the name of the space is also removed.
2136 __isl_give isl_basic_set *isl_basic_set_flatten(
2137 __isl_take isl_basic_set *bset);
2138 __isl_give isl_set *isl_set_flatten(
2139 __isl_take isl_set *set);
2140 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2141 __isl_take isl_basic_map *bmap);
2142 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2143 __isl_take isl_basic_map *bmap);
2144 __isl_give isl_map *isl_map_flatten_range(
2145 __isl_take isl_map *map);
2146 __isl_give isl_map *isl_map_flatten_domain(
2147 __isl_take isl_map *map);
2148 __isl_give isl_basic_map *isl_basic_map_flatten(
2149 __isl_take isl_basic_map *bmap);
2150 __isl_give isl_map *isl_map_flatten(
2151 __isl_take isl_map *map);
2153 __isl_give isl_map *isl_set_flatten_map(
2154 __isl_take isl_set *set);
2156 The function above constructs a relation
2157 that maps the input set to a flattened version of the set.
2161 Lift the input set to a space with extra dimensions corresponding
2162 to the existentially quantified variables in the input.
2163 In particular, the result lives in a wrapped map where the domain
2164 is the original space and the range corresponds to the original
2165 existentially quantified variables.
2167 __isl_give isl_basic_set *isl_basic_set_lift(
2168 __isl_take isl_basic_set *bset);
2169 __isl_give isl_set *isl_set_lift(
2170 __isl_take isl_set *set);
2171 __isl_give isl_union_set *isl_union_set_lift(
2172 __isl_take isl_union_set *uset);
2174 Given a local space that contains the existentially quantified
2175 variables of a set, a basic relation that, when applied to
2176 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2177 can be constructed using the following function.
2179 #include <isl/local_space.h>
2180 __isl_give isl_basic_map *isl_local_space_lifting(
2181 __isl_take isl_local_space *ls);
2183 =item * Internal Product
2185 __isl_give isl_basic_map *isl_basic_map_zip(
2186 __isl_take isl_basic_map *bmap);
2187 __isl_give isl_map *isl_map_zip(
2188 __isl_take isl_map *map);
2189 __isl_give isl_union_map *isl_union_map_zip(
2190 __isl_take isl_union_map *umap);
2192 Given a relation with nested relations for domain and range,
2193 interchange the range of the domain with the domain of the range.
2195 =item * Aligning parameters
2197 __isl_give isl_set *isl_set_align_params(
2198 __isl_take isl_set *set,
2199 __isl_take isl_space *model);
2200 __isl_give isl_map *isl_map_align_params(
2201 __isl_take isl_map *map,
2202 __isl_take isl_space *model);
2204 Change the order of the parameters of the given set or relation
2205 such that the first parameters match those of C<model>.
2206 This may involve the introduction of extra parameters.
2207 All parameters need to be named.
2209 =item * Dimension manipulation
2211 __isl_give isl_set *isl_set_add_dims(
2212 __isl_take isl_set *set,
2213 enum isl_dim_type type, unsigned n);
2214 __isl_give isl_map *isl_map_add_dims(
2215 __isl_take isl_map *map,
2216 enum isl_dim_type type, unsigned n);
2217 __isl_give isl_set *isl_set_insert_dims(
2218 __isl_take isl_set *set,
2219 enum isl_dim_type type, unsigned pos, unsigned n);
2220 __isl_give isl_map *isl_map_insert_dims(
2221 __isl_take isl_map *map,
2222 enum isl_dim_type type, unsigned pos, unsigned n);
2223 __isl_give isl_basic_set *isl_basic_set_move_dims(
2224 __isl_take isl_basic_set *bset,
2225 enum isl_dim_type dst_type, unsigned dst_pos,
2226 enum isl_dim_type src_type, unsigned src_pos,
2228 __isl_give isl_basic_map *isl_basic_map_move_dims(
2229 __isl_take isl_basic_map *bmap,
2230 enum isl_dim_type dst_type, unsigned dst_pos,
2231 enum isl_dim_type src_type, unsigned src_pos,
2233 __isl_give isl_set *isl_set_move_dims(
2234 __isl_take isl_set *set,
2235 enum isl_dim_type dst_type, unsigned dst_pos,
2236 enum isl_dim_type src_type, unsigned src_pos,
2238 __isl_give isl_map *isl_map_move_dims(
2239 __isl_take isl_map *map,
2240 enum isl_dim_type dst_type, unsigned dst_pos,
2241 enum isl_dim_type src_type, unsigned src_pos,
2244 It is usually not advisable to directly change the (input or output)
2245 space of a set or a relation as this removes the name and the internal
2246 structure of the space. However, the above functions can be useful
2247 to add new parameters, assuming
2248 C<isl_set_align_params> and C<isl_map_align_params>
2253 =head2 Binary Operations
2255 The two arguments of a binary operation not only need to live
2256 in the same C<isl_ctx>, they currently also need to have
2257 the same (number of) parameters.
2259 =head3 Basic Operations
2263 =item * Intersection
2265 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2266 __isl_take isl_basic_set *bset1,
2267 __isl_take isl_basic_set *bset2);
2268 __isl_give isl_basic_set *isl_basic_set_intersect(
2269 __isl_take isl_basic_set *bset1,
2270 __isl_take isl_basic_set *bset2);
2271 __isl_give isl_set *isl_set_intersect_params(
2272 __isl_take isl_set *set,
2273 __isl_take isl_set *params);
2274 __isl_give isl_set *isl_set_intersect(
2275 __isl_take isl_set *set1,
2276 __isl_take isl_set *set2);
2277 __isl_give isl_union_set *isl_union_set_intersect_params(
2278 __isl_take isl_union_set *uset,
2279 __isl_take isl_set *set);
2280 __isl_give isl_union_map *isl_union_map_intersect_params(
2281 __isl_take isl_union_map *umap,
2282 __isl_take isl_set *set);
2283 __isl_give isl_union_set *isl_union_set_intersect(
2284 __isl_take isl_union_set *uset1,
2285 __isl_take isl_union_set *uset2);
2286 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2287 __isl_take isl_basic_map *bmap,
2288 __isl_take isl_basic_set *bset);
2289 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2290 __isl_take isl_basic_map *bmap,
2291 __isl_take isl_basic_set *bset);
2292 __isl_give isl_basic_map *isl_basic_map_intersect(
2293 __isl_take isl_basic_map *bmap1,
2294 __isl_take isl_basic_map *bmap2);
2295 __isl_give isl_map *isl_map_intersect_params(
2296 __isl_take isl_map *map,
2297 __isl_take isl_set *params);
2298 __isl_give isl_map *isl_map_intersect_domain(
2299 __isl_take isl_map *map,
2300 __isl_take isl_set *set);
2301 __isl_give isl_map *isl_map_intersect_range(
2302 __isl_take isl_map *map,
2303 __isl_take isl_set *set);
2304 __isl_give isl_map *isl_map_intersect(
2305 __isl_take isl_map *map1,
2306 __isl_take isl_map *map2);
2307 __isl_give isl_union_map *isl_union_map_intersect_domain(
2308 __isl_take isl_union_map *umap,
2309 __isl_take isl_union_set *uset);
2310 __isl_give isl_union_map *isl_union_map_intersect_range(
2311 __isl_take isl_union_map *umap,
2312 __isl_take isl_union_set *uset);
2313 __isl_give isl_union_map *isl_union_map_intersect(
2314 __isl_take isl_union_map *umap1,
2315 __isl_take isl_union_map *umap2);
2319 __isl_give isl_set *isl_basic_set_union(
2320 __isl_take isl_basic_set *bset1,
2321 __isl_take isl_basic_set *bset2);
2322 __isl_give isl_map *isl_basic_map_union(
2323 __isl_take isl_basic_map *bmap1,
2324 __isl_take isl_basic_map *bmap2);
2325 __isl_give isl_set *isl_set_union(
2326 __isl_take isl_set *set1,
2327 __isl_take isl_set *set2);
2328 __isl_give isl_map *isl_map_union(
2329 __isl_take isl_map *map1,
2330 __isl_take isl_map *map2);
2331 __isl_give isl_union_set *isl_union_set_union(
2332 __isl_take isl_union_set *uset1,
2333 __isl_take isl_union_set *uset2);
2334 __isl_give isl_union_map *isl_union_map_union(
2335 __isl_take isl_union_map *umap1,
2336 __isl_take isl_union_map *umap2);
2338 =item * Set difference
2340 __isl_give isl_set *isl_set_subtract(
2341 __isl_take isl_set *set1,
2342 __isl_take isl_set *set2);
2343 __isl_give isl_map *isl_map_subtract(
2344 __isl_take isl_map *map1,
2345 __isl_take isl_map *map2);
2346 __isl_give isl_map *isl_map_subtract_domain(
2347 __isl_take isl_map *map,
2348 __isl_take isl_set *dom);
2349 __isl_give isl_map *isl_map_subtract_range(
2350 __isl_take isl_map *map,
2351 __isl_take isl_set *dom);
2352 __isl_give isl_union_set *isl_union_set_subtract(
2353 __isl_take isl_union_set *uset1,
2354 __isl_take isl_union_set *uset2);
2355 __isl_give isl_union_map *isl_union_map_subtract(
2356 __isl_take isl_union_map *umap1,
2357 __isl_take isl_union_map *umap2);
2361 __isl_give isl_basic_set *isl_basic_set_apply(
2362 __isl_take isl_basic_set *bset,
2363 __isl_take isl_basic_map *bmap);
2364 __isl_give isl_set *isl_set_apply(
2365 __isl_take isl_set *set,
2366 __isl_take isl_map *map);
2367 __isl_give isl_union_set *isl_union_set_apply(
2368 __isl_take isl_union_set *uset,
2369 __isl_take isl_union_map *umap);
2370 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2371 __isl_take isl_basic_map *bmap1,
2372 __isl_take isl_basic_map *bmap2);
2373 __isl_give isl_basic_map *isl_basic_map_apply_range(
2374 __isl_take isl_basic_map *bmap1,
2375 __isl_take isl_basic_map *bmap2);
2376 __isl_give isl_map *isl_map_apply_domain(
2377 __isl_take isl_map *map1,
2378 __isl_take isl_map *map2);
2379 __isl_give isl_union_map *isl_union_map_apply_domain(
2380 __isl_take isl_union_map *umap1,
2381 __isl_take isl_union_map *umap2);
2382 __isl_give isl_map *isl_map_apply_range(
2383 __isl_take isl_map *map1,
2384 __isl_take isl_map *map2);
2385 __isl_give isl_union_map *isl_union_map_apply_range(
2386 __isl_take isl_union_map *umap1,
2387 __isl_take isl_union_map *umap2);
2389 =item * Cartesian Product
2391 __isl_give isl_set *isl_set_product(
2392 __isl_take isl_set *set1,
2393 __isl_take isl_set *set2);
2394 __isl_give isl_union_set *isl_union_set_product(
2395 __isl_take isl_union_set *uset1,
2396 __isl_take isl_union_set *uset2);
2397 __isl_give isl_basic_map *isl_basic_map_domain_product(
2398 __isl_take isl_basic_map *bmap1,
2399 __isl_take isl_basic_map *bmap2);
2400 __isl_give isl_basic_map *isl_basic_map_range_product(
2401 __isl_take isl_basic_map *bmap1,
2402 __isl_take isl_basic_map *bmap2);
2403 __isl_give isl_map *isl_map_domain_product(
2404 __isl_take isl_map *map1,
2405 __isl_take isl_map *map2);
2406 __isl_give isl_map *isl_map_range_product(
2407 __isl_take isl_map *map1,
2408 __isl_take isl_map *map2);
2409 __isl_give isl_union_map *isl_union_map_range_product(
2410 __isl_take isl_union_map *umap1,
2411 __isl_take isl_union_map *umap2);
2412 __isl_give isl_map *isl_map_product(
2413 __isl_take isl_map *map1,
2414 __isl_take isl_map *map2);
2415 __isl_give isl_union_map *isl_union_map_product(
2416 __isl_take isl_union_map *umap1,
2417 __isl_take isl_union_map *umap2);
2419 The above functions compute the cross product of the given
2420 sets or relations. The domains and ranges of the results
2421 are wrapped maps between domains and ranges of the inputs.
2422 To obtain a ``flat'' product, use the following functions
2425 __isl_give isl_basic_set *isl_basic_set_flat_product(
2426 __isl_take isl_basic_set *bset1,
2427 __isl_take isl_basic_set *bset2);
2428 __isl_give isl_set *isl_set_flat_product(
2429 __isl_take isl_set *set1,
2430 __isl_take isl_set *set2);
2431 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2432 __isl_take isl_basic_map *bmap1,
2433 __isl_take isl_basic_map *bmap2);
2434 __isl_give isl_map *isl_map_flat_domain_product(
2435 __isl_take isl_map *map1,
2436 __isl_take isl_map *map2);
2437 __isl_give isl_map *isl_map_flat_range_product(
2438 __isl_take isl_map *map1,
2439 __isl_take isl_map *map2);
2440 __isl_give isl_union_map *isl_union_map_flat_range_product(
2441 __isl_take isl_union_map *umap1,
2442 __isl_take isl_union_map *umap2);
2443 __isl_give isl_basic_map *isl_basic_map_flat_product(
2444 __isl_take isl_basic_map *bmap1,
2445 __isl_take isl_basic_map *bmap2);
2446 __isl_give isl_map *isl_map_flat_product(
2447 __isl_take isl_map *map1,
2448 __isl_take isl_map *map2);
2450 =item * Simplification
2452 __isl_give isl_basic_set *isl_basic_set_gist(
2453 __isl_take isl_basic_set *bset,
2454 __isl_take isl_basic_set *context);
2455 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2456 __isl_take isl_set *context);
2457 __isl_give isl_set *isl_set_gist_params(
2458 __isl_take isl_set *set,
2459 __isl_take isl_set *context);
2460 __isl_give isl_union_set *isl_union_set_gist(
2461 __isl_take isl_union_set *uset,
2462 __isl_take isl_union_set *context);
2463 __isl_give isl_union_set *isl_union_set_gist_params(
2464 __isl_take isl_union_set *uset,
2465 __isl_take isl_set *set);
2466 __isl_give isl_basic_map *isl_basic_map_gist(
2467 __isl_take isl_basic_map *bmap,
2468 __isl_take isl_basic_map *context);
2469 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2470 __isl_take isl_map *context);
2471 __isl_give isl_map *isl_map_gist_params(
2472 __isl_take isl_map *map,
2473 __isl_take isl_set *context);
2474 __isl_give isl_map *isl_map_gist_domain(
2475 __isl_take isl_map *map,
2476 __isl_take isl_set *context);
2477 __isl_give isl_map *isl_map_gist_range(
2478 __isl_take isl_map *map,
2479 __isl_take isl_set *context);
2480 __isl_give isl_union_map *isl_union_map_gist(
2481 __isl_take isl_union_map *umap,
2482 __isl_take isl_union_map *context);
2483 __isl_give isl_union_map *isl_union_map_gist_params(
2484 __isl_take isl_union_map *umap,
2485 __isl_take isl_set *set);
2486 __isl_give isl_union_map *isl_union_map_gist_domain(
2487 __isl_take isl_union_map *umap,
2488 __isl_take isl_union_set *uset);
2490 The gist operation returns a set or relation that has the
2491 same intersection with the context as the input set or relation.
2492 Any implicit equality in the intersection is made explicit in the result,
2493 while all inequalities that are redundant with respect to the intersection
2495 In case of union sets and relations, the gist operation is performed
2500 =head3 Lexicographic Optimization
2502 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2503 the following functions
2504 compute a set that contains the lexicographic minimum or maximum
2505 of the elements in C<set> (or C<bset>) for those values of the parameters
2506 that satisfy C<dom>.
2507 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2508 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2510 In other words, the union of the parameter values
2511 for which the result is non-empty and of C<*empty>
2514 __isl_give isl_set *isl_basic_set_partial_lexmin(
2515 __isl_take isl_basic_set *bset,
2516 __isl_take isl_basic_set *dom,
2517 __isl_give isl_set **empty);
2518 __isl_give isl_set *isl_basic_set_partial_lexmax(
2519 __isl_take isl_basic_set *bset,
2520 __isl_take isl_basic_set *dom,
2521 __isl_give isl_set **empty);
2522 __isl_give isl_set *isl_set_partial_lexmin(
2523 __isl_take isl_set *set, __isl_take isl_set *dom,
2524 __isl_give isl_set **empty);
2525 __isl_give isl_set *isl_set_partial_lexmax(
2526 __isl_take isl_set *set, __isl_take isl_set *dom,
2527 __isl_give isl_set **empty);
2529 Given a (basic) set C<set> (or C<bset>), the following functions simply
2530 return a set containing the lexicographic minimum or maximum
2531 of the elements in C<set> (or C<bset>).
2532 In case of union sets, the optimum is computed per space.
2534 __isl_give isl_set *isl_basic_set_lexmin(
2535 __isl_take isl_basic_set *bset);
2536 __isl_give isl_set *isl_basic_set_lexmax(
2537 __isl_take isl_basic_set *bset);
2538 __isl_give isl_set *isl_set_lexmin(
2539 __isl_take isl_set *set);
2540 __isl_give isl_set *isl_set_lexmax(
2541 __isl_take isl_set *set);
2542 __isl_give isl_union_set *isl_union_set_lexmin(
2543 __isl_take isl_union_set *uset);
2544 __isl_give isl_union_set *isl_union_set_lexmax(
2545 __isl_take isl_union_set *uset);
2547 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2548 the following functions
2549 compute a relation that maps each element of C<dom>
2550 to the single lexicographic minimum or maximum
2551 of the elements that are associated to that same
2552 element in C<map> (or C<bmap>).
2553 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2554 that contains the elements in C<dom> that do not map
2555 to any elements in C<map> (or C<bmap>).
2556 In other words, the union of the domain of the result and of C<*empty>
2559 __isl_give isl_map *isl_basic_map_partial_lexmax(
2560 __isl_take isl_basic_map *bmap,
2561 __isl_take isl_basic_set *dom,
2562 __isl_give isl_set **empty);
2563 __isl_give isl_map *isl_basic_map_partial_lexmin(
2564 __isl_take isl_basic_map *bmap,
2565 __isl_take isl_basic_set *dom,
2566 __isl_give isl_set **empty);
2567 __isl_give isl_map *isl_map_partial_lexmax(
2568 __isl_take isl_map *map, __isl_take isl_set *dom,
2569 __isl_give isl_set **empty);
2570 __isl_give isl_map *isl_map_partial_lexmin(
2571 __isl_take isl_map *map, __isl_take isl_set *dom,
2572 __isl_give isl_set **empty);
2574 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2575 return a map mapping each element in the domain of
2576 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2577 of all elements associated to that element.
2578 In case of union relations, the optimum is computed per space.
2580 __isl_give isl_map *isl_basic_map_lexmin(
2581 __isl_take isl_basic_map *bmap);
2582 __isl_give isl_map *isl_basic_map_lexmax(
2583 __isl_take isl_basic_map *bmap);
2584 __isl_give isl_map *isl_map_lexmin(
2585 __isl_take isl_map *map);
2586 __isl_give isl_map *isl_map_lexmax(
2587 __isl_take isl_map *map);
2588 __isl_give isl_union_map *isl_union_map_lexmin(
2589 __isl_take isl_union_map *umap);
2590 __isl_give isl_union_map *isl_union_map_lexmax(
2591 __isl_take isl_union_map *umap);
2593 The following functions return their result in the form of
2594 a piecewise multi-affine expression
2595 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2596 but are otherwise equivalent to the corresponding functions
2597 returning a basic set or relation.
2599 __isl_give isl_pw_multi_aff *
2600 isl_basic_map_lexmin_pw_multi_aff(
2601 __isl_take isl_basic_map *bmap);
2602 __isl_give isl_pw_multi_aff *
2603 isl_basic_set_partial_lexmin_pw_multi_aff(
2604 __isl_take isl_basic_set *bset,
2605 __isl_take isl_basic_set *dom,
2606 __isl_give isl_set **empty);
2607 __isl_give isl_pw_multi_aff *
2608 isl_basic_set_partial_lexmax_pw_multi_aff(
2609 __isl_take isl_basic_set *bset,
2610 __isl_take isl_basic_set *dom,
2611 __isl_give isl_set **empty);
2612 __isl_give isl_pw_multi_aff *
2613 isl_basic_map_partial_lexmin_pw_multi_aff(
2614 __isl_take isl_basic_map *bmap,
2615 __isl_take isl_basic_set *dom,
2616 __isl_give isl_set **empty);
2617 __isl_give isl_pw_multi_aff *
2618 isl_basic_map_partial_lexmax_pw_multi_aff(
2619 __isl_take isl_basic_map *bmap,
2620 __isl_take isl_basic_set *dom,
2621 __isl_give isl_set **empty);
2625 Lists are defined over several element types, including
2626 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2627 Here we take lists of C<isl_set>s as an example.
2628 Lists can be created, copied and freed using the following functions.
2630 #include <isl/list.h>
2631 __isl_give isl_set_list *isl_set_list_from_set(
2632 __isl_take isl_set *el);
2633 __isl_give isl_set_list *isl_set_list_alloc(
2634 isl_ctx *ctx, int n);
2635 __isl_give isl_set_list *isl_set_list_copy(
2636 __isl_keep isl_set_list *list);
2637 __isl_give isl_set_list *isl_set_list_add(
2638 __isl_take isl_set_list *list,
2639 __isl_take isl_set *el);
2640 __isl_give isl_set_list *isl_set_list_concat(
2641 __isl_take isl_set_list *list1,
2642 __isl_take isl_set_list *list2);
2643 void *isl_set_list_free(__isl_take isl_set_list *list);
2645 C<isl_set_list_alloc> creates an empty list with a capacity for
2646 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2649 Lists can be inspected using the following functions.
2651 #include <isl/list.h>
2652 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2653 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2654 __isl_give isl_set *isl_set_list_get_set(
2655 __isl_keep isl_set_list *list, int index);
2656 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2657 int (*fn)(__isl_take isl_set *el, void *user),
2660 Lists can be printed using
2662 #include <isl/list.h>
2663 __isl_give isl_printer *isl_printer_print_set_list(
2664 __isl_take isl_printer *p,
2665 __isl_keep isl_set_list *list);
2669 Matrices can be created, copied and freed using the following functions.
2671 #include <isl/mat.h>
2672 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2673 unsigned n_row, unsigned n_col);
2674 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2675 void isl_mat_free(__isl_take isl_mat *mat);
2677 Note that the elements of a newly created matrix may have arbitrary values.
2678 The elements can be changed and inspected using the following functions.
2680 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2681 int isl_mat_rows(__isl_keep isl_mat *mat);
2682 int isl_mat_cols(__isl_keep isl_mat *mat);
2683 int isl_mat_get_element(__isl_keep isl_mat *mat,
2684 int row, int col, isl_int *v);
2685 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2686 int row, int col, isl_int v);
2687 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2688 int row, int col, int v);
2690 C<isl_mat_get_element> will return a negative value if anything went wrong.
2691 In that case, the value of C<*v> is undefined.
2693 The following function can be used to compute the (right) inverse
2694 of a matrix, i.e., a matrix such that the product of the original
2695 and the inverse (in that order) is a multiple of the identity matrix.
2696 The input matrix is assumed to be of full row-rank.
2698 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2700 The following function can be used to compute the (right) kernel
2701 (or null space) of a matrix, i.e., a matrix such that the product of
2702 the original and the kernel (in that order) is the zero matrix.
2704 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2706 =head2 Piecewise Quasi Affine Expressions
2708 The zero quasi affine expression on a given domain can be created using
2710 __isl_give isl_aff *isl_aff_zero_on_domain(
2711 __isl_take isl_local_space *ls);
2713 Note that the space in which the resulting object lives is a map space
2714 with the given space as domain and a one-dimensional range.
2716 An empty piecewise quasi affine expression (one with no cells)
2717 or a piecewise quasi affine expression with a single cell can
2718 be created using the following functions.
2720 #include <isl/aff.h>
2721 __isl_give isl_pw_aff *isl_pw_aff_empty(
2722 __isl_take isl_space *space);
2723 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2724 __isl_take isl_set *set, __isl_take isl_aff *aff);
2725 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2726 __isl_take isl_aff *aff);
2728 Quasi affine expressions can be copied and freed using
2730 #include <isl/aff.h>
2731 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2732 void *isl_aff_free(__isl_take isl_aff *aff);
2734 __isl_give isl_pw_aff *isl_pw_aff_copy(
2735 __isl_keep isl_pw_aff *pwaff);
2736 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2738 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2739 using the following function. The constraint is required to have
2740 a non-zero coefficient for the specified dimension.
2742 #include <isl/constraint.h>
2743 __isl_give isl_aff *isl_constraint_get_bound(
2744 __isl_keep isl_constraint *constraint,
2745 enum isl_dim_type type, int pos);
2747 The entire affine expression of the constraint can also be extracted
2748 using the following function.
2750 #include <isl/constraint.h>
2751 __isl_give isl_aff *isl_constraint_get_aff(
2752 __isl_keep isl_constraint *constraint);
2754 Conversely, an equality constraint equating
2755 the affine expression to zero or an inequality constraint enforcing
2756 the affine expression to be non-negative, can be constructed using
2758 __isl_give isl_constraint *isl_equality_from_aff(
2759 __isl_take isl_aff *aff);
2760 __isl_give isl_constraint *isl_inequality_from_aff(
2761 __isl_take isl_aff *aff);
2763 The expression can be inspected using
2765 #include <isl/aff.h>
2766 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2767 int isl_aff_dim(__isl_keep isl_aff *aff,
2768 enum isl_dim_type type);
2769 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2770 __isl_keep isl_aff *aff);
2771 __isl_give isl_local_space *isl_aff_get_local_space(
2772 __isl_keep isl_aff *aff);
2773 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2774 enum isl_dim_type type, unsigned pos);
2775 const char *isl_pw_aff_get_dim_name(
2776 __isl_keep isl_pw_aff *pa,
2777 enum isl_dim_type type, unsigned pos);
2778 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2779 enum isl_dim_type type, unsigned pos);
2780 __isl_give isl_id *isl_pw_aff_get_dim_id(
2781 __isl_keep isl_pw_aff *pa,
2782 enum isl_dim_type type, unsigned pos);
2783 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2785 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2786 enum isl_dim_type type, int pos, isl_int *v);
2787 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2789 __isl_give isl_aff *isl_aff_get_div(
2790 __isl_keep isl_aff *aff, int pos);
2792 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2793 int (*fn)(__isl_take isl_set *set,
2794 __isl_take isl_aff *aff,
2795 void *user), void *user);
2797 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2798 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2800 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2801 enum isl_dim_type type, unsigned first, unsigned n);
2802 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2803 enum isl_dim_type type, unsigned first, unsigned n);
2805 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2806 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2807 enum isl_dim_type type);
2808 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2810 It can be modified using
2812 #include <isl/aff.h>
2813 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2814 __isl_take isl_pw_aff *pwaff,
2815 enum isl_dim_type type, __isl_take isl_id *id);
2816 __isl_give isl_aff *isl_aff_set_dim_name(
2817 __isl_take isl_aff *aff, enum isl_dim_type type,
2818 unsigned pos, const char *s);
2819 __isl_give isl_aff *isl_aff_set_dim_id(
2820 __isl_take isl_aff *aff, enum isl_dim_type type,
2821 unsigned pos, __isl_take isl_id *id);
2822 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2823 __isl_take isl_pw_aff *pma,
2824 enum isl_dim_type type, unsigned pos,
2825 __isl_take isl_id *id);
2826 __isl_give isl_aff *isl_aff_set_constant(
2827 __isl_take isl_aff *aff, isl_int v);
2828 __isl_give isl_aff *isl_aff_set_constant_si(
2829 __isl_take isl_aff *aff, int v);
2830 __isl_give isl_aff *isl_aff_set_coefficient(
2831 __isl_take isl_aff *aff,
2832 enum isl_dim_type type, int pos, isl_int v);
2833 __isl_give isl_aff *isl_aff_set_coefficient_si(
2834 __isl_take isl_aff *aff,
2835 enum isl_dim_type type, int pos, int v);
2836 __isl_give isl_aff *isl_aff_set_denominator(
2837 __isl_take isl_aff *aff, isl_int v);
2839 __isl_give isl_aff *isl_aff_add_constant(
2840 __isl_take isl_aff *aff, isl_int v);
2841 __isl_give isl_aff *isl_aff_add_constant_si(
2842 __isl_take isl_aff *aff, int v);
2843 __isl_give isl_aff *isl_aff_add_coefficient(
2844 __isl_take isl_aff *aff,
2845 enum isl_dim_type type, int pos, isl_int v);
2846 __isl_give isl_aff *isl_aff_add_coefficient_si(
2847 __isl_take isl_aff *aff,
2848 enum isl_dim_type type, int pos, int v);
2850 __isl_give isl_aff *isl_aff_insert_dims(
2851 __isl_take isl_aff *aff,
2852 enum isl_dim_type type, unsigned first, unsigned n);
2853 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2854 __isl_take isl_pw_aff *pwaff,
2855 enum isl_dim_type type, unsigned first, unsigned n);
2856 __isl_give isl_aff *isl_aff_add_dims(
2857 __isl_take isl_aff *aff,
2858 enum isl_dim_type type, unsigned n);
2859 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2860 __isl_take isl_pw_aff *pwaff,
2861 enum isl_dim_type type, unsigned n);
2862 __isl_give isl_aff *isl_aff_drop_dims(
2863 __isl_take isl_aff *aff,
2864 enum isl_dim_type type, unsigned first, unsigned n);
2865 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2866 __isl_take isl_pw_aff *pwaff,
2867 enum isl_dim_type type, unsigned first, unsigned n);
2869 Note that the C<set_constant> and C<set_coefficient> functions
2870 set the I<numerator> of the constant or coefficient, while
2871 C<add_constant> and C<add_coefficient> add an integer value to
2872 the possibly rational constant or coefficient.
2874 To check whether an affine expressions is obviously zero
2875 or obviously equal to some other affine expression, use
2877 #include <isl/aff.h>
2878 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2879 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2880 __isl_keep isl_aff *aff2);
2881 int isl_pw_aff_plain_is_equal(
2882 __isl_keep isl_pw_aff *pwaff1,
2883 __isl_keep isl_pw_aff *pwaff2);
2887 #include <isl/aff.h>
2888 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2889 __isl_take isl_aff *aff2);
2890 __isl_give isl_pw_aff *isl_pw_aff_add(
2891 __isl_take isl_pw_aff *pwaff1,
2892 __isl_take isl_pw_aff *pwaff2);
2893 __isl_give isl_pw_aff *isl_pw_aff_min(
2894 __isl_take isl_pw_aff *pwaff1,
2895 __isl_take isl_pw_aff *pwaff2);
2896 __isl_give isl_pw_aff *isl_pw_aff_max(
2897 __isl_take isl_pw_aff *pwaff1,
2898 __isl_take isl_pw_aff *pwaff2);
2899 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2900 __isl_take isl_aff *aff2);
2901 __isl_give isl_pw_aff *isl_pw_aff_sub(
2902 __isl_take isl_pw_aff *pwaff1,
2903 __isl_take isl_pw_aff *pwaff2);
2904 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2905 __isl_give isl_pw_aff *isl_pw_aff_neg(
2906 __isl_take isl_pw_aff *pwaff);
2907 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2908 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2909 __isl_take isl_pw_aff *pwaff);
2910 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2911 __isl_give isl_pw_aff *isl_pw_aff_floor(
2912 __isl_take isl_pw_aff *pwaff);
2913 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2915 __isl_give isl_pw_aff *isl_pw_aff_mod(
2916 __isl_take isl_pw_aff *pwaff, isl_int mod);
2917 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2919 __isl_give isl_pw_aff *isl_pw_aff_scale(
2920 __isl_take isl_pw_aff *pwaff, isl_int f);
2921 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2923 __isl_give isl_aff *isl_aff_scale_down_ui(
2924 __isl_take isl_aff *aff, unsigned f);
2925 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2926 __isl_take isl_pw_aff *pwaff, isl_int f);
2928 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2929 __isl_take isl_pw_aff_list *list);
2930 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2931 __isl_take isl_pw_aff_list *list);
2933 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2934 __isl_take isl_pw_aff *pwqp);
2936 __isl_give isl_aff *isl_aff_align_params(
2937 __isl_take isl_aff *aff,
2938 __isl_take isl_space *model);
2939 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2940 __isl_take isl_pw_aff *pwaff,
2941 __isl_take isl_space *model);
2943 __isl_give isl_aff *isl_aff_project_domain_on_params(
2944 __isl_take isl_aff *aff);
2946 __isl_give isl_aff *isl_aff_gist_params(
2947 __isl_take isl_aff *aff,
2948 __isl_take isl_set *context);
2949 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2950 __isl_take isl_set *context);
2951 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
2952 __isl_take isl_pw_aff *pwaff,
2953 __isl_take isl_set *context);
2954 __isl_give isl_pw_aff *isl_pw_aff_gist(
2955 __isl_take isl_pw_aff *pwaff,
2956 __isl_take isl_set *context);
2958 __isl_give isl_set *isl_pw_aff_domain(
2959 __isl_take isl_pw_aff *pwaff);
2960 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2961 __isl_take isl_pw_aff *pa,
2962 __isl_take isl_set *set);
2963 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
2964 __isl_take isl_pw_aff *pa,
2965 __isl_take isl_set *set);
2967 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2968 __isl_take isl_aff *aff2);
2969 __isl_give isl_pw_aff *isl_pw_aff_mul(
2970 __isl_take isl_pw_aff *pwaff1,
2971 __isl_take isl_pw_aff *pwaff2);
2973 When multiplying two affine expressions, at least one of the two needs
2976 #include <isl/aff.h>
2977 __isl_give isl_basic_set *isl_aff_le_basic_set(
2978 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2979 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2980 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2981 __isl_give isl_set *isl_pw_aff_eq_set(
2982 __isl_take isl_pw_aff *pwaff1,
2983 __isl_take isl_pw_aff *pwaff2);
2984 __isl_give isl_set *isl_pw_aff_ne_set(
2985 __isl_take isl_pw_aff *pwaff1,
2986 __isl_take isl_pw_aff *pwaff2);
2987 __isl_give isl_set *isl_pw_aff_le_set(
2988 __isl_take isl_pw_aff *pwaff1,
2989 __isl_take isl_pw_aff *pwaff2);
2990 __isl_give isl_set *isl_pw_aff_lt_set(
2991 __isl_take isl_pw_aff *pwaff1,
2992 __isl_take isl_pw_aff *pwaff2);
2993 __isl_give isl_set *isl_pw_aff_ge_set(
2994 __isl_take isl_pw_aff *pwaff1,
2995 __isl_take isl_pw_aff *pwaff2);
2996 __isl_give isl_set *isl_pw_aff_gt_set(
2997 __isl_take isl_pw_aff *pwaff1,
2998 __isl_take isl_pw_aff *pwaff2);
3000 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_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_le_set(
3007 __isl_take isl_pw_aff_list *list1,
3008 __isl_take isl_pw_aff_list *list2);
3009 __isl_give isl_set *isl_pw_aff_list_lt_set(
3010 __isl_take isl_pw_aff_list *list1,
3011 __isl_take isl_pw_aff_list *list2);
3012 __isl_give isl_set *isl_pw_aff_list_ge_set(
3013 __isl_take isl_pw_aff_list *list1,
3014 __isl_take isl_pw_aff_list *list2);
3015 __isl_give isl_set *isl_pw_aff_list_gt_set(
3016 __isl_take isl_pw_aff_list *list1,
3017 __isl_take isl_pw_aff_list *list2);
3019 The function C<isl_aff_ge_basic_set> returns a basic set
3020 containing those elements in the shared space
3021 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3022 The function C<isl_aff_ge_set> returns a set
3023 containing those elements in the shared domain
3024 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3025 The functions operating on C<isl_pw_aff_list> apply the corresponding
3026 C<isl_pw_aff> function to each pair of elements in the two lists.
3028 #include <isl/aff.h>
3029 __isl_give isl_set *isl_pw_aff_nonneg_set(
3030 __isl_take isl_pw_aff *pwaff);
3031 __isl_give isl_set *isl_pw_aff_zero_set(
3032 __isl_take isl_pw_aff *pwaff);
3033 __isl_give isl_set *isl_pw_aff_non_zero_set(
3034 __isl_take isl_pw_aff *pwaff);
3036 The function C<isl_pw_aff_nonneg_set> returns a set
3037 containing those elements in the domain
3038 of C<pwaff> where C<pwaff> is non-negative.
3040 #include <isl/aff.h>
3041 __isl_give isl_pw_aff *isl_pw_aff_cond(
3042 __isl_take isl_set *cond,
3043 __isl_take isl_pw_aff *pwaff_true,
3044 __isl_take isl_pw_aff *pwaff_false);
3046 The function C<isl_pw_aff_cond> performs a conditional operator
3047 and returns an expression that is equal to C<pwaff_true>
3048 for elements in C<cond> and equal to C<pwaff_false> for elements
3051 #include <isl/aff.h>
3052 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3053 __isl_take isl_pw_aff *pwaff1,
3054 __isl_take isl_pw_aff *pwaff2);
3055 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3056 __isl_take isl_pw_aff *pwaff1,
3057 __isl_take isl_pw_aff *pwaff2);
3058 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3059 __isl_take isl_pw_aff *pwaff1,
3060 __isl_take isl_pw_aff *pwaff2);
3062 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3063 expression with a domain that is the union of those of C<pwaff1> and
3064 C<pwaff2> and such that on each cell, the quasi-affine expression is
3065 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3066 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3067 associated expression is the defined one.
3069 An expression can be read from input using
3071 #include <isl/aff.h>
3072 __isl_give isl_aff *isl_aff_read_from_str(
3073 isl_ctx *ctx, const char *str);
3074 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3075 isl_ctx *ctx, const char *str);
3077 An expression can be printed using
3079 #include <isl/aff.h>
3080 __isl_give isl_printer *isl_printer_print_aff(
3081 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3083 __isl_give isl_printer *isl_printer_print_pw_aff(
3084 __isl_take isl_printer *p,
3085 __isl_keep isl_pw_aff *pwaff);
3087 =head2 Piecewise Multiple Quasi Affine Expressions
3089 An C<isl_multi_aff> object represents a sequence of
3090 zero or more affine expressions, all defined on the same domain space.
3092 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3095 #include <isl/aff.h>
3096 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3097 __isl_take isl_space *space,
3098 __isl_take isl_aff_list *list);
3100 An empty piecewise multiple quasi affine expression (one with no cells) or
3101 a piecewise multiple quasi affine expression with a single cell can
3102 be created using the following functions.
3104 #include <isl/aff.h>
3105 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3106 __isl_take isl_space *space);
3107 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3108 __isl_take isl_set *set,
3109 __isl_take isl_multi_aff *maff);
3111 A piecewise multiple quasi affine expression can also be initialized
3112 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3113 and the C<isl_map> is single-valued.
3115 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3116 __isl_take isl_set *set);
3117 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3118 __isl_take isl_map *map);
3120 Multiple quasi affine expressions can be copied and freed using
3122 #include <isl/aff.h>
3123 __isl_give isl_multi_aff *isl_multi_aff_copy(
3124 __isl_keep isl_multi_aff *maff);
3125 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3127 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3128 __isl_keep isl_pw_multi_aff *pma);
3129 void *isl_pw_multi_aff_free(
3130 __isl_take isl_pw_multi_aff *pma);
3132 The expression can be inspected using
3134 #include <isl/aff.h>
3135 isl_ctx *isl_multi_aff_get_ctx(
3136 __isl_keep isl_multi_aff *maff);
3137 isl_ctx *isl_pw_multi_aff_get_ctx(
3138 __isl_keep isl_pw_multi_aff *pma);
3139 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3140 enum isl_dim_type type);
3141 unsigned isl_pw_multi_aff_dim(
3142 __isl_keep isl_pw_multi_aff *pma,
3143 enum isl_dim_type type);
3144 __isl_give isl_aff *isl_multi_aff_get_aff(
3145 __isl_keep isl_multi_aff *multi, int pos);
3146 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3147 __isl_keep isl_pw_multi_aff *pma, int pos);
3148 const char *isl_pw_multi_aff_get_dim_name(
3149 __isl_keep isl_pw_multi_aff *pma,
3150 enum isl_dim_type type, unsigned pos);
3151 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3152 __isl_keep isl_pw_multi_aff *pma,
3153 enum isl_dim_type type, unsigned pos);
3154 const char *isl_multi_aff_get_tuple_name(
3155 __isl_keep isl_multi_aff *multi,
3156 enum isl_dim_type type);
3157 const char *isl_pw_multi_aff_get_tuple_name(
3158 __isl_keep isl_pw_multi_aff *pma,
3159 enum isl_dim_type type);
3160 int isl_pw_multi_aff_has_tuple_id(
3161 __isl_keep isl_pw_multi_aff *pma,
3162 enum isl_dim_type type);
3163 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3164 __isl_keep isl_pw_multi_aff *pma,
3165 enum isl_dim_type type);
3167 int isl_pw_multi_aff_foreach_piece(
3168 __isl_keep isl_pw_multi_aff *pma,
3169 int (*fn)(__isl_take isl_set *set,
3170 __isl_take isl_multi_aff *maff,
3171 void *user), void *user);
3173 It can be modified using
3175 #include <isl/aff.h>
3176 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3177 __isl_take isl_multi_aff *maff,
3178 enum isl_dim_type type, unsigned pos, const char *s);
3179 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3180 __isl_take isl_pw_multi_aff *pma,
3181 enum isl_dim_type type, __isl_take isl_id *id);
3183 To check whether two multiple affine expressions are
3184 obviously equal to each other, use
3186 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3187 __isl_keep isl_multi_aff *maff2);
3188 int isl_pw_multi_aff_plain_is_equal(
3189 __isl_keep isl_pw_multi_aff *pma1,
3190 __isl_keep isl_pw_multi_aff *pma2);
3194 #include <isl/aff.h>
3195 __isl_give isl_multi_aff *isl_multi_aff_add(
3196 __isl_take isl_multi_aff *maff1,
3197 __isl_take isl_multi_aff *maff2);
3198 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3199 __isl_take isl_pw_multi_aff *pma1,
3200 __isl_take isl_pw_multi_aff *pma2);
3201 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3202 __isl_take isl_pw_multi_aff *pma1,
3203 __isl_take isl_pw_multi_aff *pma2);
3204 __isl_give isl_multi_aff *isl_multi_aff_scale(
3205 __isl_take isl_multi_aff *maff,
3207 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3208 __isl_take isl_pw_multi_aff *pma,
3209 __isl_take isl_set *set);
3210 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3211 __isl_take isl_pw_multi_aff *pma,
3212 __isl_take isl_set *set);
3213 __isl_give isl_multi_aff *isl_multi_aff_lift(
3214 __isl_take isl_multi_aff *maff,
3215 __isl_give isl_local_space **ls);
3216 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3217 __isl_take isl_multi_aff *maff,
3218 __isl_take isl_set *context);
3219 __isl_give isl_multi_aff *isl_multi_aff_gist(
3220 __isl_take isl_multi_aff *maff,
3221 __isl_take isl_set *context);
3222 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3223 __isl_take isl_pw_multi_aff *pma,
3224 __isl_take isl_set *set);
3225 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3226 __isl_take isl_pw_multi_aff *pma,
3227 __isl_take isl_set *set);
3229 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3230 then it is assigned the local space that lies at the basis of
3231 the lifting applied.
3233 An expression can be read from input using
3235 #include <isl/aff.h>
3236 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3237 isl_ctx *ctx, const char *str);
3238 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3239 isl_ctx *ctx, const char *str);
3241 An expression can be printed using
3243 #include <isl/aff.h>
3244 __isl_give isl_printer *isl_printer_print_multi_aff(
3245 __isl_take isl_printer *p,
3246 __isl_keep isl_multi_aff *maff);
3247 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3248 __isl_take isl_printer *p,
3249 __isl_keep isl_pw_multi_aff *pma);
3253 Points are elements of a set. They can be used to construct
3254 simple sets (boxes) or they can be used to represent the
3255 individual elements of a set.
3256 The zero point (the origin) can be created using
3258 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3260 The coordinates of a point can be inspected, set and changed
3263 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3264 enum isl_dim_type type, int pos, isl_int *v);
3265 __isl_give isl_point *isl_point_set_coordinate(
3266 __isl_take isl_point *pnt,
3267 enum isl_dim_type type, int pos, isl_int v);
3269 __isl_give isl_point *isl_point_add_ui(
3270 __isl_take isl_point *pnt,
3271 enum isl_dim_type type, int pos, unsigned val);
3272 __isl_give isl_point *isl_point_sub_ui(
3273 __isl_take isl_point *pnt,
3274 enum isl_dim_type type, int pos, unsigned val);
3276 Other properties can be obtained using
3278 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3280 Points can be copied or freed using
3282 __isl_give isl_point *isl_point_copy(
3283 __isl_keep isl_point *pnt);
3284 void isl_point_free(__isl_take isl_point *pnt);
3286 A singleton set can be created from a point using
3288 __isl_give isl_basic_set *isl_basic_set_from_point(
3289 __isl_take isl_point *pnt);
3290 __isl_give isl_set *isl_set_from_point(
3291 __isl_take isl_point *pnt);
3293 and a box can be created from two opposite extremal points using
3295 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3296 __isl_take isl_point *pnt1,
3297 __isl_take isl_point *pnt2);
3298 __isl_give isl_set *isl_set_box_from_points(
3299 __isl_take isl_point *pnt1,
3300 __isl_take isl_point *pnt2);
3302 All elements of a B<bounded> (union) set can be enumerated using
3303 the following functions.
3305 int isl_set_foreach_point(__isl_keep isl_set *set,
3306 int (*fn)(__isl_take isl_point *pnt, void *user),
3308 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3309 int (*fn)(__isl_take isl_point *pnt, void *user),
3312 The function C<fn> is called for each integer point in
3313 C<set> with as second argument the last argument of
3314 the C<isl_set_foreach_point> call. The function C<fn>
3315 should return C<0> on success and C<-1> on failure.
3316 In the latter case, C<isl_set_foreach_point> will stop
3317 enumerating and return C<-1> as well.
3318 If the enumeration is performed successfully and to completion,
3319 then C<isl_set_foreach_point> returns C<0>.
3321 To obtain a single point of a (basic) set, use
3323 __isl_give isl_point *isl_basic_set_sample_point(
3324 __isl_take isl_basic_set *bset);
3325 __isl_give isl_point *isl_set_sample_point(
3326 __isl_take isl_set *set);
3328 If C<set> does not contain any (integer) points, then the
3329 resulting point will be ``void'', a property that can be
3332 int isl_point_is_void(__isl_keep isl_point *pnt);
3334 =head2 Piecewise Quasipolynomials
3336 A piecewise quasipolynomial is a particular kind of function that maps
3337 a parametric point to a rational value.
3338 More specifically, a quasipolynomial is a polynomial expression in greatest
3339 integer parts of affine expressions of parameters and variables.
3340 A piecewise quasipolynomial is a subdivision of a given parametric
3341 domain into disjoint cells with a quasipolynomial associated to
3342 each cell. The value of the piecewise quasipolynomial at a given
3343 point is the value of the quasipolynomial associated to the cell
3344 that contains the point. Outside of the union of cells,
3345 the value is assumed to be zero.
3346 For example, the piecewise quasipolynomial
3348 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3350 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3351 A given piecewise quasipolynomial has a fixed domain dimension.
3352 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3353 defined over different domains.
3354 Piecewise quasipolynomials are mainly used by the C<barvinok>
3355 library for representing the number of elements in a parametric set or map.
3356 For example, the piecewise quasipolynomial above represents
3357 the number of points in the map
3359 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3361 =head3 Input and Output
3363 Piecewise quasipolynomials can be read from input using
3365 __isl_give isl_union_pw_qpolynomial *
3366 isl_union_pw_qpolynomial_read_from_str(
3367 isl_ctx *ctx, const char *str);
3369 Quasipolynomials and piecewise quasipolynomials can be printed
3370 using the following functions.
3372 __isl_give isl_printer *isl_printer_print_qpolynomial(
3373 __isl_take isl_printer *p,
3374 __isl_keep isl_qpolynomial *qp);
3376 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3377 __isl_take isl_printer *p,
3378 __isl_keep isl_pw_qpolynomial *pwqp);
3380 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3381 __isl_take isl_printer *p,
3382 __isl_keep isl_union_pw_qpolynomial *upwqp);
3384 The output format of the printer
3385 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3386 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3388 In case of printing in C<ISL_FORMAT_C>, the user may want
3389 to set the names of all dimensions
3391 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3392 __isl_take isl_qpolynomial *qp,
3393 enum isl_dim_type type, unsigned pos,
3395 __isl_give isl_pw_qpolynomial *
3396 isl_pw_qpolynomial_set_dim_name(
3397 __isl_take isl_pw_qpolynomial *pwqp,
3398 enum isl_dim_type type, unsigned pos,
3401 =head3 Creating New (Piecewise) Quasipolynomials
3403 Some simple quasipolynomials can be created using the following functions.
3404 More complicated quasipolynomials can be created by applying
3405 operations such as addition and multiplication
3406 on the resulting quasipolynomials
3408 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3409 __isl_take isl_space *domain);
3410 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3411 __isl_take isl_space *domain);
3412 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3413 __isl_take isl_space *domain);
3414 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3415 __isl_take isl_space *domain);
3416 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3417 __isl_take isl_space *domain);
3418 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3419 __isl_take isl_space *domain,
3420 const isl_int n, const isl_int d);
3421 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3422 __isl_take isl_space *domain,
3423 enum isl_dim_type type, unsigned pos);
3424 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3425 __isl_take isl_aff *aff);
3427 Note that the space in which a quasipolynomial lives is a map space
3428 with a one-dimensional range. The C<domain> argument in some of
3429 the functions above corresponds to the domain of this map space.
3431 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3432 with a single cell can be created using the following functions.
3433 Multiple of these single cell piecewise quasipolynomials can
3434 be combined to create more complicated piecewise quasipolynomials.
3436 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3437 __isl_take isl_space *space);
3438 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3439 __isl_take isl_set *set,
3440 __isl_take isl_qpolynomial *qp);
3441 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3442 __isl_take isl_qpolynomial *qp);
3443 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3444 __isl_take isl_pw_aff *pwaff);
3446 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3447 __isl_take isl_space *space);
3448 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3449 __isl_take isl_pw_qpolynomial *pwqp);
3450 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3451 __isl_take isl_union_pw_qpolynomial *upwqp,
3452 __isl_take isl_pw_qpolynomial *pwqp);
3454 Quasipolynomials can be copied and freed again using the following
3457 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3458 __isl_keep isl_qpolynomial *qp);
3459 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3461 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3462 __isl_keep isl_pw_qpolynomial *pwqp);
3463 void *isl_pw_qpolynomial_free(
3464 __isl_take isl_pw_qpolynomial *pwqp);
3466 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3467 __isl_keep isl_union_pw_qpolynomial *upwqp);
3468 void isl_union_pw_qpolynomial_free(
3469 __isl_take isl_union_pw_qpolynomial *upwqp);
3471 =head3 Inspecting (Piecewise) Quasipolynomials
3473 To iterate over all piecewise quasipolynomials in a union
3474 piecewise quasipolynomial, use the following function
3476 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3477 __isl_keep isl_union_pw_qpolynomial *upwqp,
3478 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3481 To extract the piecewise quasipolynomial in a given space from a union, use
3483 __isl_give isl_pw_qpolynomial *
3484 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3485 __isl_keep isl_union_pw_qpolynomial *upwqp,
3486 __isl_take isl_space *space);
3488 To iterate over the cells in a piecewise quasipolynomial,
3489 use either of the following two functions
3491 int isl_pw_qpolynomial_foreach_piece(
3492 __isl_keep isl_pw_qpolynomial *pwqp,
3493 int (*fn)(__isl_take isl_set *set,
3494 __isl_take isl_qpolynomial *qp,
3495 void *user), void *user);
3496 int isl_pw_qpolynomial_foreach_lifted_piece(
3497 __isl_keep isl_pw_qpolynomial *pwqp,
3498 int (*fn)(__isl_take isl_set *set,
3499 __isl_take isl_qpolynomial *qp,
3500 void *user), void *user);
3502 As usual, the function C<fn> should return C<0> on success
3503 and C<-1> on failure. The difference between
3504 C<isl_pw_qpolynomial_foreach_piece> and
3505 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3506 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3507 compute unique representations for all existentially quantified
3508 variables and then turn these existentially quantified variables
3509 into extra set variables, adapting the associated quasipolynomial
3510 accordingly. This means that the C<set> passed to C<fn>
3511 will not have any existentially quantified variables, but that
3512 the dimensions of the sets may be different for different
3513 invocations of C<fn>.
3515 To iterate over all terms in a quasipolynomial,
3518 int isl_qpolynomial_foreach_term(
3519 __isl_keep isl_qpolynomial *qp,
3520 int (*fn)(__isl_take isl_term *term,
3521 void *user), void *user);
3523 The terms themselves can be inspected and freed using
3526 unsigned isl_term_dim(__isl_keep isl_term *term,
3527 enum isl_dim_type type);
3528 void isl_term_get_num(__isl_keep isl_term *term,
3530 void isl_term_get_den(__isl_keep isl_term *term,
3532 int isl_term_get_exp(__isl_keep isl_term *term,
3533 enum isl_dim_type type, unsigned pos);
3534 __isl_give isl_aff *isl_term_get_div(
3535 __isl_keep isl_term *term, unsigned pos);
3536 void isl_term_free(__isl_take isl_term *term);
3538 Each term is a product of parameters, set variables and
3539 integer divisions. The function C<isl_term_get_exp>
3540 returns the exponent of a given dimensions in the given term.
3541 The C<isl_int>s in the arguments of C<isl_term_get_num>
3542 and C<isl_term_get_den> need to have been initialized
3543 using C<isl_int_init> before calling these functions.
3545 =head3 Properties of (Piecewise) Quasipolynomials
3547 To check whether a quasipolynomial is actually a constant,
3548 use the following function.
3550 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3551 isl_int *n, isl_int *d);
3553 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3554 then the numerator and denominator of the constant
3555 are returned in C<*n> and C<*d>, respectively.
3557 To check whether two union piecewise quasipolynomials are
3558 obviously equal, use
3560 int isl_union_pw_qpolynomial_plain_is_equal(
3561 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3562 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3564 =head3 Operations on (Piecewise) Quasipolynomials
3566 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3567 __isl_take isl_qpolynomial *qp, isl_int v);
3568 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3569 __isl_take isl_qpolynomial *qp);
3570 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3571 __isl_take isl_qpolynomial *qp1,
3572 __isl_take isl_qpolynomial *qp2);
3573 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3574 __isl_take isl_qpolynomial *qp1,
3575 __isl_take isl_qpolynomial *qp2);
3576 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3577 __isl_take isl_qpolynomial *qp1,
3578 __isl_take isl_qpolynomial *qp2);
3579 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3580 __isl_take isl_qpolynomial *qp, unsigned exponent);
3582 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3583 __isl_take isl_pw_qpolynomial *pwqp1,
3584 __isl_take isl_pw_qpolynomial *pwqp2);
3585 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3586 __isl_take isl_pw_qpolynomial *pwqp1,
3587 __isl_take isl_pw_qpolynomial *pwqp2);
3588 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3589 __isl_take isl_pw_qpolynomial *pwqp1,
3590 __isl_take isl_pw_qpolynomial *pwqp2);
3591 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3592 __isl_take isl_pw_qpolynomial *pwqp);
3593 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3594 __isl_take isl_pw_qpolynomial *pwqp1,
3595 __isl_take isl_pw_qpolynomial *pwqp2);
3596 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3597 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3599 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3600 __isl_take isl_union_pw_qpolynomial *upwqp1,
3601 __isl_take isl_union_pw_qpolynomial *upwqp2);
3602 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3603 __isl_take isl_union_pw_qpolynomial *upwqp1,
3604 __isl_take isl_union_pw_qpolynomial *upwqp2);
3605 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3606 __isl_take isl_union_pw_qpolynomial *upwqp1,
3607 __isl_take isl_union_pw_qpolynomial *upwqp2);
3609 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3610 __isl_take isl_pw_qpolynomial *pwqp,
3611 __isl_take isl_point *pnt);
3613 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3614 __isl_take isl_union_pw_qpolynomial *upwqp,
3615 __isl_take isl_point *pnt);
3617 __isl_give isl_set *isl_pw_qpolynomial_domain(
3618 __isl_take isl_pw_qpolynomial *pwqp);
3619 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3620 __isl_take isl_pw_qpolynomial *pwpq,
3621 __isl_take isl_set *set);
3622 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3623 __isl_take isl_pw_qpolynomial *pwpq,
3624 __isl_take isl_set *set);
3626 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3627 __isl_take isl_union_pw_qpolynomial *upwqp);
3628 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3629 __isl_take isl_union_pw_qpolynomial *upwpq,
3630 __isl_take isl_union_set *uset);
3631 __isl_give isl_union_pw_qpolynomial *
3632 isl_union_pw_qpolynomial_intersect_params(
3633 __isl_take isl_union_pw_qpolynomial *upwpq,
3634 __isl_take isl_set *set);
3636 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3637 __isl_take isl_qpolynomial *qp,
3638 __isl_take isl_space *model);
3640 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3641 __isl_take isl_qpolynomial *qp);
3642 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3643 __isl_take isl_pw_qpolynomial *pwqp);
3645 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3646 __isl_take isl_union_pw_qpolynomial *upwqp);
3648 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3649 __isl_take isl_qpolynomial *qp,
3650 __isl_take isl_set *context);
3651 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3652 __isl_take isl_qpolynomial *qp,
3653 __isl_take isl_set *context);
3655 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3656 __isl_take isl_pw_qpolynomial *pwqp,
3657 __isl_take isl_set *context);
3658 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3659 __isl_take isl_pw_qpolynomial *pwqp,
3660 __isl_take isl_set *context);
3662 __isl_give isl_union_pw_qpolynomial *
3663 isl_union_pw_qpolynomial_gist_params(
3664 __isl_take isl_union_pw_qpolynomial *upwqp,
3665 __isl_take isl_set *context);
3666 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3667 __isl_take isl_union_pw_qpolynomial *upwqp,
3668 __isl_take isl_union_set *context);
3670 The gist operation applies the gist operation to each of
3671 the cells in the domain of the input piecewise quasipolynomial.
3672 The context is also exploited
3673 to simplify the quasipolynomials associated to each cell.
3675 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3676 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3677 __isl_give isl_union_pw_qpolynomial *
3678 isl_union_pw_qpolynomial_to_polynomial(
3679 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3681 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3682 the polynomial will be an overapproximation. If C<sign> is negative,
3683 it will be an underapproximation. If C<sign> is zero, the approximation
3684 will lie somewhere in between.
3686 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3688 A piecewise quasipolynomial reduction is a piecewise
3689 reduction (or fold) of quasipolynomials.
3690 In particular, the reduction can be maximum or a minimum.
3691 The objects are mainly used to represent the result of
3692 an upper or lower bound on a quasipolynomial over its domain,
3693 i.e., as the result of the following function.
3695 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3696 __isl_take isl_pw_qpolynomial *pwqp,
3697 enum isl_fold type, int *tight);
3699 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3700 __isl_take isl_union_pw_qpolynomial *upwqp,
3701 enum isl_fold type, int *tight);
3703 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3704 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3705 is the returned bound is known be tight, i.e., for each value
3706 of the parameters there is at least
3707 one element in the domain that reaches the bound.
3708 If the domain of C<pwqp> is not wrapping, then the bound is computed
3709 over all elements in that domain and the result has a purely parametric
3710 domain. If the domain of C<pwqp> is wrapping, then the bound is
3711 computed over the range of the wrapped relation. The domain of the
3712 wrapped relation becomes the domain of the result.
3714 A (piecewise) quasipolynomial reduction can be copied or freed using the
3715 following functions.
3717 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3718 __isl_keep isl_qpolynomial_fold *fold);
3719 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3720 __isl_keep isl_pw_qpolynomial_fold *pwf);
3721 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3722 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3723 void isl_qpolynomial_fold_free(
3724 __isl_take isl_qpolynomial_fold *fold);
3725 void *isl_pw_qpolynomial_fold_free(
3726 __isl_take isl_pw_qpolynomial_fold *pwf);
3727 void isl_union_pw_qpolynomial_fold_free(
3728 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3730 =head3 Printing Piecewise Quasipolynomial Reductions
3732 Piecewise quasipolynomial reductions can be printed
3733 using the following function.
3735 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3736 __isl_take isl_printer *p,
3737 __isl_keep isl_pw_qpolynomial_fold *pwf);
3738 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3739 __isl_take isl_printer *p,
3740 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3742 For C<isl_printer_print_pw_qpolynomial_fold>,
3743 output format of the printer
3744 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3745 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3746 output format of the printer
3747 needs to be set to C<ISL_FORMAT_ISL>.
3748 In case of printing in C<ISL_FORMAT_C>, the user may want
3749 to set the names of all dimensions
3751 __isl_give isl_pw_qpolynomial_fold *
3752 isl_pw_qpolynomial_fold_set_dim_name(
3753 __isl_take isl_pw_qpolynomial_fold *pwf,
3754 enum isl_dim_type type, unsigned pos,
3757 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3759 To iterate over all piecewise quasipolynomial reductions in a union
3760 piecewise quasipolynomial reduction, use the following function
3762 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3763 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3764 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3765 void *user), void *user);
3767 To iterate over the cells in a piecewise quasipolynomial reduction,
3768 use either of the following two functions
3770 int isl_pw_qpolynomial_fold_foreach_piece(
3771 __isl_keep isl_pw_qpolynomial_fold *pwf,
3772 int (*fn)(__isl_take isl_set *set,
3773 __isl_take isl_qpolynomial_fold *fold,
3774 void *user), void *user);
3775 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3776 __isl_keep isl_pw_qpolynomial_fold *pwf,
3777 int (*fn)(__isl_take isl_set *set,
3778 __isl_take isl_qpolynomial_fold *fold,
3779 void *user), void *user);
3781 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3782 of the difference between these two functions.
3784 To iterate over all quasipolynomials in a reduction, use
3786 int isl_qpolynomial_fold_foreach_qpolynomial(
3787 __isl_keep isl_qpolynomial_fold *fold,
3788 int (*fn)(__isl_take isl_qpolynomial *qp,
3789 void *user), void *user);
3791 =head3 Properties of Piecewise Quasipolynomial Reductions
3793 To check whether two union piecewise quasipolynomial reductions are
3794 obviously equal, use
3796 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3797 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3798 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3800 =head3 Operations on Piecewise Quasipolynomial Reductions
3802 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3803 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3805 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3806 __isl_take isl_pw_qpolynomial_fold *pwf1,
3807 __isl_take isl_pw_qpolynomial_fold *pwf2);
3809 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3810 __isl_take isl_pw_qpolynomial_fold *pwf1,
3811 __isl_take isl_pw_qpolynomial_fold *pwf2);
3813 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3814 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3815 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3817 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3818 __isl_take isl_pw_qpolynomial_fold *pwf,
3819 __isl_take isl_point *pnt);
3821 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3822 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3823 __isl_take isl_point *pnt);
3825 __isl_give isl_pw_qpolynomial_fold *
3826 sl_pw_qpolynomial_fold_intersect_params(
3827 __isl_take isl_pw_qpolynomial_fold *pwf,
3828 __isl_take isl_set *set);
3830 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3831 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3832 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3833 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3834 __isl_take isl_union_set *uset);
3835 __isl_give isl_union_pw_qpolynomial_fold *
3836 isl_union_pw_qpolynomial_fold_intersect_params(
3837 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3838 __isl_take isl_set *set);
3840 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3841 __isl_take isl_pw_qpolynomial_fold *pwf);
3843 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3844 __isl_take isl_pw_qpolynomial_fold *pwf);
3846 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3847 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3849 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
3850 __isl_take isl_qpolynomial_fold *fold,
3851 __isl_take isl_set *context);
3852 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
3853 __isl_take isl_qpolynomial_fold *fold,
3854 __isl_take isl_set *context);
3856 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3857 __isl_take isl_pw_qpolynomial_fold *pwf,
3858 __isl_take isl_set *context);
3859 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
3860 __isl_take isl_pw_qpolynomial_fold *pwf,
3861 __isl_take isl_set *context);
3863 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3864 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3865 __isl_take isl_union_set *context);
3866 __isl_give isl_union_pw_qpolynomial_fold *
3867 isl_union_pw_qpolynomial_fold_gist_params(
3868 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3869 __isl_take isl_set *context);
3871 The gist operation applies the gist operation to each of
3872 the cells in the domain of the input piecewise quasipolynomial reduction.
3873 In future, the operation will also exploit the context
3874 to simplify the quasipolynomial reductions associated to each cell.
3876 __isl_give isl_pw_qpolynomial_fold *
3877 isl_set_apply_pw_qpolynomial_fold(
3878 __isl_take isl_set *set,
3879 __isl_take isl_pw_qpolynomial_fold *pwf,
3881 __isl_give isl_pw_qpolynomial_fold *
3882 isl_map_apply_pw_qpolynomial_fold(
3883 __isl_take isl_map *map,
3884 __isl_take isl_pw_qpolynomial_fold *pwf,
3886 __isl_give isl_union_pw_qpolynomial_fold *
3887 isl_union_set_apply_union_pw_qpolynomial_fold(
3888 __isl_take isl_union_set *uset,
3889 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3891 __isl_give isl_union_pw_qpolynomial_fold *
3892 isl_union_map_apply_union_pw_qpolynomial_fold(
3893 __isl_take isl_union_map *umap,
3894 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3897 The functions taking a map
3898 compose the given map with the given piecewise quasipolynomial reduction.
3899 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3900 over all elements in the intersection of the range of the map
3901 and the domain of the piecewise quasipolynomial reduction
3902 as a function of an element in the domain of the map.
3903 The functions taking a set compute a bound over all elements in the
3904 intersection of the set and the domain of the
3905 piecewise quasipolynomial reduction.
3907 =head2 Dependence Analysis
3909 C<isl> contains specialized functionality for performing
3910 array dataflow analysis. That is, given a I<sink> access relation
3911 and a collection of possible I<source> access relations,
3912 C<isl> can compute relations that describe
3913 for each iteration of the sink access, which iteration
3914 of which of the source access relations was the last
3915 to access the same data element before the given iteration
3917 The resulting dependence relations map source iterations
3918 to the corresponding sink iterations.
3919 To compute standard flow dependences, the sink should be
3920 a read, while the sources should be writes.
3921 If any of the source accesses are marked as being I<may>
3922 accesses, then there will be a dependence from the last
3923 I<must> access B<and> from any I<may> access that follows
3924 this last I<must> access.
3925 In particular, if I<all> sources are I<may> accesses,
3926 then memory based dependence analysis is performed.
3927 If, on the other hand, all sources are I<must> accesses,
3928 then value based dependence analysis is performed.
3930 #include <isl/flow.h>
3932 typedef int (*isl_access_level_before)(void *first, void *second);
3934 __isl_give isl_access_info *isl_access_info_alloc(
3935 __isl_take isl_map *sink,
3936 void *sink_user, isl_access_level_before fn,
3938 __isl_give isl_access_info *isl_access_info_add_source(
3939 __isl_take isl_access_info *acc,
3940 __isl_take isl_map *source, int must,
3942 void isl_access_info_free(__isl_take isl_access_info *acc);
3944 __isl_give isl_flow *isl_access_info_compute_flow(
3945 __isl_take isl_access_info *acc);
3947 int isl_flow_foreach(__isl_keep isl_flow *deps,
3948 int (*fn)(__isl_take isl_map *dep, int must,
3949 void *dep_user, void *user),
3951 __isl_give isl_map *isl_flow_get_no_source(
3952 __isl_keep isl_flow *deps, int must);
3953 void isl_flow_free(__isl_take isl_flow *deps);
3955 The function C<isl_access_info_compute_flow> performs the actual
3956 dependence analysis. The other functions are used to construct
3957 the input for this function or to read off the output.
3959 The input is collected in an C<isl_access_info>, which can
3960 be created through a call to C<isl_access_info_alloc>.
3961 The arguments to this functions are the sink access relation
3962 C<sink>, a token C<sink_user> used to identify the sink
3963 access to the user, a callback function for specifying the
3964 relative order of source and sink accesses, and the number
3965 of source access relations that will be added.
3966 The callback function has type C<int (*)(void *first, void *second)>.
3967 The function is called with two user supplied tokens identifying
3968 either a source or the sink and it should return the shared nesting
3969 level and the relative order of the two accesses.
3970 In particular, let I<n> be the number of loops shared by
3971 the two accesses. If C<first> precedes C<second> textually,
3972 then the function should return I<2 * n + 1>; otherwise,
3973 it should return I<2 * n>.
3974 The sources can be added to the C<isl_access_info> by performing
3975 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3976 C<must> indicates whether the source is a I<must> access
3977 or a I<may> access. Note that a multi-valued access relation
3978 should only be marked I<must> if every iteration in the domain
3979 of the relation accesses I<all> elements in its image.
3980 The C<source_user> token is again used to identify
3981 the source access. The range of the source access relation
3982 C<source> should have the same dimension as the range
3983 of the sink access relation.
3984 The C<isl_access_info_free> function should usually not be
3985 called explicitly, because it is called implicitly by
3986 C<isl_access_info_compute_flow>.
3988 The result of the dependence analysis is collected in an
3989 C<isl_flow>. There may be elements of
3990 the sink access for which no preceding source access could be
3991 found or for which all preceding sources are I<may> accesses.
3992 The relations containing these elements can be obtained through
3993 calls to C<isl_flow_get_no_source>, the first with C<must> set
3994 and the second with C<must> unset.
3995 In the case of standard flow dependence analysis,
3996 with the sink a read and the sources I<must> writes,
3997 the first relation corresponds to the reads from uninitialized
3998 array elements and the second relation is empty.
3999 The actual flow dependences can be extracted using
4000 C<isl_flow_foreach>. This function will call the user-specified
4001 callback function C<fn> for each B<non-empty> dependence between
4002 a source and the sink. The callback function is called
4003 with four arguments, the actual flow dependence relation
4004 mapping source iterations to sink iterations, a boolean that
4005 indicates whether it is a I<must> or I<may> dependence, a token
4006 identifying the source and an additional C<void *> with value
4007 equal to the third argument of the C<isl_flow_foreach> call.
4008 A dependence is marked I<must> if it originates from a I<must>
4009 source and if it is not followed by any I<may> sources.
4011 After finishing with an C<isl_flow>, the user should call
4012 C<isl_flow_free> to free all associated memory.
4014 A higher-level interface to dependence analysis is provided
4015 by the following function.
4017 #include <isl/flow.h>
4019 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4020 __isl_take isl_union_map *must_source,
4021 __isl_take isl_union_map *may_source,
4022 __isl_take isl_union_map *schedule,
4023 __isl_give isl_union_map **must_dep,
4024 __isl_give isl_union_map **may_dep,
4025 __isl_give isl_union_map **must_no_source,
4026 __isl_give isl_union_map **may_no_source);
4028 The arrays are identified by the tuple names of the ranges
4029 of the accesses. The iteration domains by the tuple names
4030 of the domains of the accesses and of the schedule.
4031 The relative order of the iteration domains is given by the
4032 schedule. The relations returned through C<must_no_source>
4033 and C<may_no_source> are subsets of C<sink>.
4034 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4035 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4036 any of the other arguments is treated as an error.
4038 =head3 Interaction with Dependence Analysis
4040 During the dependence analysis, we frequently need to perform
4041 the following operation. Given a relation between sink iterations
4042 and potential soure iterations from a particular source domain,
4043 what is the last potential source iteration corresponding to each
4044 sink iteration. It can sometimes be convenient to adjust
4045 the set of potential source iterations before each such operation.
4046 The prototypical example is fuzzy array dataflow analysis,
4047 where we need to analyze if, based on data-dependent constraints,
4048 the sink iteration can ever be executed without one or more of
4049 the corresponding potential source iterations being executed.
4050 If so, we can introduce extra parameters and select an unknown
4051 but fixed source iteration from the potential source iterations.
4052 To be able to perform such manipulations, C<isl> provides the following
4055 #include <isl/flow.h>
4057 typedef __isl_give isl_set *(*isl_access_restrict_sources)(
4058 __isl_take isl_map *source_map,
4059 void *sink_user, void *source_user);
4060 __isl_give isl_access_info *
4061 isl_access_info_set_restrict_sources(
4062 __isl_take isl_access_info *acc,
4063 isl_access_restrict_sources fn);
4065 The function C<isl_access_info_set_restrict_sources> should be called
4066 before C<isl_access_info_compute_flow> and registers a callback function
4067 that will be called any time C<isl> is about to compute the last
4068 potential source. The first argument is the (reverse) proto-dependence,
4069 mapping sink iterations to potential source iterations.
4070 The other two arguments are the tokens corresponding to the sink
4071 and the source. The callback is expected to return a set
4072 that restricts the source iterations. The potential source iterations
4073 will be intersected with this set. If no restrictions are required
4074 for a given C<source_map>, then the callback should return
4077 isl_space_range(isl_map_get_space(source_map)));
4079 If any error occurs, the callback should return C<NULL>.
4083 B<The functionality described in this section is fairly new
4084 and may be subject to change.>
4086 The following function can be used to compute a schedule
4087 for a union of domains.
4088 By default, the algorithm used to construct the schedule is similar
4089 to that of C<Pluto>.
4090 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4092 The generated schedule respects all C<validity> dependences.
4093 That is, all dependence distances over these dependences in the
4094 scheduled space are lexicographically positive.
4095 The default algorithm tries to minimize the dependence distances over
4096 C<proximity> dependences.
4097 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4098 for groups of domains where the dependence distances have only
4099 non-negative values.
4100 When using Feautrier's algorithm, the C<proximity> dependence
4101 distances are only minimized during the extension to a
4102 full-dimensional schedule.
4104 #include <isl/schedule.h>
4105 __isl_give isl_schedule *isl_union_set_compute_schedule(
4106 __isl_take isl_union_set *domain,
4107 __isl_take isl_union_map *validity,
4108 __isl_take isl_union_map *proximity);
4109 void *isl_schedule_free(__isl_take isl_schedule *sched);
4111 A mapping from the domains to the scheduled space can be obtained
4112 from an C<isl_schedule> using the following function.
4114 __isl_give isl_union_map *isl_schedule_get_map(
4115 __isl_keep isl_schedule *sched);
4117 A representation of the schedule can be printed using
4119 __isl_give isl_printer *isl_printer_print_schedule(
4120 __isl_take isl_printer *p,
4121 __isl_keep isl_schedule *schedule);
4123 A representation of the schedule as a forest of bands can be obtained
4124 using the following function.
4126 __isl_give isl_band_list *isl_schedule_get_band_forest(
4127 __isl_keep isl_schedule *schedule);
4129 The list can be manipulated as explained in L<"Lists">.
4130 The bands inside the list can be copied and freed using the following
4133 #include <isl/band.h>
4134 __isl_give isl_band *isl_band_copy(
4135 __isl_keep isl_band *band);
4136 void *isl_band_free(__isl_take isl_band *band);
4138 Each band contains zero or more scheduling dimensions.
4139 These are referred to as the members of the band.
4140 The section of the schedule that corresponds to the band is
4141 referred to as the partial schedule of the band.
4142 For those nodes that participate in a band, the outer scheduling
4143 dimensions form the prefix schedule, while the inner scheduling
4144 dimensions form the suffix schedule.
4145 That is, if we take a cut of the band forest, then the union of
4146 the concatenations of the prefix, partial and suffix schedules of
4147 each band in the cut is equal to the entire schedule (modulo
4148 some possible padding at the end with zero scheduling dimensions).
4149 The properties of a band can be inspected using the following functions.
4151 #include <isl/band.h>
4152 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4154 int isl_band_has_children(__isl_keep isl_band *band);
4155 __isl_give isl_band_list *isl_band_get_children(
4156 __isl_keep isl_band *band);
4158 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4159 __isl_keep isl_band *band);
4160 __isl_give isl_union_map *isl_band_get_partial_schedule(
4161 __isl_keep isl_band *band);
4162 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4163 __isl_keep isl_band *band);
4165 int isl_band_n_member(__isl_keep isl_band *band);
4166 int isl_band_member_is_zero_distance(
4167 __isl_keep isl_band *band, int pos);
4169 Note that a scheduling dimension is considered to be ``zero
4170 distance'' if it does not carry any proximity dependences
4172 That is, if the dependence distances of the proximity
4173 dependences are all zero in that direction (for fixed
4174 iterations of outer bands).
4176 A representation of the band can be printed using
4178 #include <isl/band.h>
4179 __isl_give isl_printer *isl_printer_print_band(
4180 __isl_take isl_printer *p,
4181 __isl_keep isl_band *band);
4185 #include <isl/schedule.h>
4186 int isl_options_set_schedule_max_constant_term(
4187 isl_ctx *ctx, int val);
4188 int isl_options_get_schedule_max_constant_term(
4190 int isl_options_set_schedule_maximize_band_depth(
4191 isl_ctx *ctx, int val);
4192 int isl_options_get_schedule_maximize_band_depth(
4194 int isl_options_set_schedule_outer_zero_distance(
4195 isl_ctx *ctx, int val);
4196 int isl_options_get_schedule_outer_zero_distance(
4198 int isl_options_set_schedule_split_parallel(
4199 isl_ctx *ctx, int val);
4200 int isl_options_get_schedule_split_parallel(
4202 int isl_options_set_schedule_algorithm(
4203 isl_ctx *ctx, int val);
4204 int isl_options_get_schedule_algorithm(
4210 =item * schedule_max_constant_term
4212 This option enforces that the constant coefficients in the calculated schedule
4213 are not larger than the maximal constant term. This option can significantly
4214 increase the speed of the scheduling calculation and may also prevent fusing of
4215 unrelated dimensions. A value of -1 means that this option does not introduce
4216 bounds on the constant coefficients.
4218 =item * schedule_maximize_band_depth
4220 If this option is set, we do not split bands at the point
4221 where we detect splitting is necessary. Instead, we
4222 backtrack and split bands as early as possible. This
4223 reduces the number of splits and maximizes the width of
4224 the bands. Wider bands give more possibilities for tiling.
4226 =item * schedule_outer_zero_distance
4228 If this option is set, then we try to construct schedules
4229 where the outermost scheduling dimension in each band
4230 results in a zero dependence distance over the proximity
4233 =item * schedule_split_parallel
4235 If this option is set, then we try to construct schedules in which the
4236 constant term is split off from the linear part if the linear parts of
4237 the scheduling rows for all nodes in the graphs are the same.
4238 The constant term is then placed in a separate band and the linear
4241 =item * schedule_algorithm
4243 Selects the scheduling algorithm to be used.
4244 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4245 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4249 =head2 Parametric Vertex Enumeration
4251 The parametric vertex enumeration described in this section
4252 is mainly intended to be used internally and by the C<barvinok>
4255 #include <isl/vertices.h>
4256 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4257 __isl_keep isl_basic_set *bset);
4259 The function C<isl_basic_set_compute_vertices> performs the
4260 actual computation of the parametric vertices and the chamber
4261 decomposition and store the result in an C<isl_vertices> object.
4262 This information can be queried by either iterating over all
4263 the vertices or iterating over all the chambers or cells
4264 and then iterating over all vertices that are active on the chamber.
4266 int isl_vertices_foreach_vertex(
4267 __isl_keep isl_vertices *vertices,
4268 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4271 int isl_vertices_foreach_cell(
4272 __isl_keep isl_vertices *vertices,
4273 int (*fn)(__isl_take isl_cell *cell, void *user),
4275 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4276 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4279 Other operations that can be performed on an C<isl_vertices> object are
4282 isl_ctx *isl_vertices_get_ctx(
4283 __isl_keep isl_vertices *vertices);
4284 int isl_vertices_get_n_vertices(
4285 __isl_keep isl_vertices *vertices);
4286 void isl_vertices_free(__isl_take isl_vertices *vertices);
4288 Vertices can be inspected and destroyed using the following functions.
4290 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4291 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4292 __isl_give isl_basic_set *isl_vertex_get_domain(
4293 __isl_keep isl_vertex *vertex);
4294 __isl_give isl_basic_set *isl_vertex_get_expr(
4295 __isl_keep isl_vertex *vertex);
4296 void isl_vertex_free(__isl_take isl_vertex *vertex);
4298 C<isl_vertex_get_expr> returns a singleton parametric set describing
4299 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4301 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4302 B<rational> basic sets, so they should mainly be used for inspection
4303 and should not be mixed with integer sets.
4305 Chambers can be inspected and destroyed using the following functions.
4307 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4308 __isl_give isl_basic_set *isl_cell_get_domain(
4309 __isl_keep isl_cell *cell);
4310 void isl_cell_free(__isl_take isl_cell *cell);
4314 Although C<isl> is mainly meant to be used as a library,
4315 it also contains some basic applications that use some
4316 of the functionality of C<isl>.
4317 The input may be specified in either the L<isl format>
4318 or the L<PolyLib format>.
4320 =head2 C<isl_polyhedron_sample>
4322 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4323 an integer element of the polyhedron, if there is any.
4324 The first column in the output is the denominator and is always
4325 equal to 1. If the polyhedron contains no integer points,
4326 then a vector of length zero is printed.
4330 C<isl_pip> takes the same input as the C<example> program
4331 from the C<piplib> distribution, i.e., a set of constraints
4332 on the parameters, a line containing only -1 and finally a set
4333 of constraints on a parametric polyhedron.
4334 The coefficients of the parameters appear in the last columns
4335 (but before the final constant column).
4336 The output is the lexicographic minimum of the parametric polyhedron.
4337 As C<isl> currently does not have its own output format, the output
4338 is just a dump of the internal state.
4340 =head2 C<isl_polyhedron_minimize>
4342 C<isl_polyhedron_minimize> computes the minimum of some linear
4343 or affine objective function over the integer points in a polyhedron.
4344 If an affine objective function
4345 is given, then the constant should appear in the last column.
4347 =head2 C<isl_polytope_scan>
4349 Given a polytope, C<isl_polytope_scan> prints
4350 all integer points in the polytope.