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.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
167 The source of C<isl> can be obtained either as a tarball
168 or from the git repository. Both are available from
169 L<http://freshmeat.net/projects/isl/>.
170 The installation process depends on how you obtained
173 =head2 Installation from the git repository
177 =item 1 Clone or update the repository
179 The first time the source is obtained, you need to clone
182 git clone git://repo.or.cz/isl.git
184 To obtain updates, you need to pull in the latest changes
188 =item 2 Generate C<configure>
194 After performing the above steps, continue
195 with the L<Common installation instructions>.
197 =head2 Common installation instructions
201 =item 1 Obtain C<GMP>
203 Building C<isl> requires C<GMP>, including its headers files.
204 Your distribution may not provide these header files by default
205 and you may need to install a package called C<gmp-devel> or something
206 similar. Alternatively, C<GMP> can be built from
207 source, available from L<http://gmplib.org/>.
211 C<isl> uses the standard C<autoconf> C<configure> script.
216 optionally followed by some configure options.
217 A complete list of options can be obtained by running
221 Below we discuss some of the more common options.
223 C<isl> can optionally use C<piplib>, but no
224 C<piplib> functionality is currently used by default.
225 The C<--with-piplib> option can
226 be used to specify which C<piplib>
227 library to use, either an installed version (C<system>),
228 an externally built version (C<build>)
229 or no version (C<no>). The option C<build> is mostly useful
230 in C<configure> scripts of larger projects that bundle both C<isl>
237 Installation prefix for C<isl>
239 =item C<--with-gmp-prefix>
241 Installation prefix for C<GMP> (architecture-independent files).
243 =item C<--with-gmp-exec-prefix>
245 Installation prefix for C<GMP> (architecture-dependent files).
247 =item C<--with-piplib>
249 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
251 =item C<--with-piplib-prefix>
253 Installation prefix for C<system> C<piplib> (architecture-independent files).
255 =item C<--with-piplib-exec-prefix>
257 Installation prefix for C<system> C<piplib> (architecture-dependent files).
259 =item C<--with-piplib-builddir>
261 Location where C<build> C<piplib> was built.
269 =item 4 Install (optional)
277 =head2 Initialization
279 All manipulations of integer sets and relations occur within
280 the context of an C<isl_ctx>.
281 A given C<isl_ctx> can only be used within a single thread.
282 All arguments of a function are required to have been allocated
283 within the same context.
284 There are currently no functions available for moving an object
285 from one C<isl_ctx> to another C<isl_ctx>. This means that
286 there is currently no way of safely moving an object from one
287 thread to another, unless the whole C<isl_ctx> is moved.
289 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
290 freed using C<isl_ctx_free>.
291 All objects allocated within an C<isl_ctx> should be freed
292 before the C<isl_ctx> itself is freed.
294 isl_ctx *isl_ctx_alloc();
295 void isl_ctx_free(isl_ctx *ctx);
299 All operations on integers, mainly the coefficients
300 of the constraints describing the sets and relations,
301 are performed in exact integer arithmetic using C<GMP>.
302 However, to allow future versions of C<isl> to optionally
303 support fixed integer arithmetic, all calls to C<GMP>
304 are wrapped inside C<isl> specific macros.
305 The basic type is C<isl_int> and the operations below
306 are available on this type.
307 The meanings of these operations are essentially the same
308 as their C<GMP> C<mpz_> counterparts.
309 As always with C<GMP> types, C<isl_int>s need to be
310 initialized with C<isl_int_init> before they can be used
311 and they need to be released with C<isl_int_clear>
313 The user should not assume that an C<isl_int> is represented
314 as a C<mpz_t>, but should instead explicitly convert between
315 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
316 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
320 =item isl_int_init(i)
322 =item isl_int_clear(i)
324 =item isl_int_set(r,i)
326 =item isl_int_set_si(r,i)
328 =item isl_int_set_gmp(r,g)
330 =item isl_int_get_gmp(i,g)
332 =item isl_int_abs(r,i)
334 =item isl_int_neg(r,i)
336 =item isl_int_swap(i,j)
338 =item isl_int_swap_or_set(i,j)
340 =item isl_int_add_ui(r,i,j)
342 =item isl_int_sub_ui(r,i,j)
344 =item isl_int_add(r,i,j)
346 =item isl_int_sub(r,i,j)
348 =item isl_int_mul(r,i,j)
350 =item isl_int_mul_ui(r,i,j)
352 =item isl_int_addmul(r,i,j)
354 =item isl_int_submul(r,i,j)
356 =item isl_int_gcd(r,i,j)
358 =item isl_int_lcm(r,i,j)
360 =item isl_int_divexact(r,i,j)
362 =item isl_int_cdiv_q(r,i,j)
364 =item isl_int_fdiv_q(r,i,j)
366 =item isl_int_fdiv_r(r,i,j)
368 =item isl_int_fdiv_q_ui(r,i,j)
370 =item isl_int_read(r,s)
372 =item isl_int_print(out,i,width)
376 =item isl_int_cmp(i,j)
378 =item isl_int_cmp_si(i,si)
380 =item isl_int_eq(i,j)
382 =item isl_int_ne(i,j)
384 =item isl_int_lt(i,j)
386 =item isl_int_le(i,j)
388 =item isl_int_gt(i,j)
390 =item isl_int_ge(i,j)
392 =item isl_int_abs_eq(i,j)
394 =item isl_int_abs_ne(i,j)
396 =item isl_int_abs_lt(i,j)
398 =item isl_int_abs_gt(i,j)
400 =item isl_int_abs_ge(i,j)
402 =item isl_int_is_zero(i)
404 =item isl_int_is_one(i)
406 =item isl_int_is_negone(i)
408 =item isl_int_is_pos(i)
410 =item isl_int_is_neg(i)
412 =item isl_int_is_nonpos(i)
414 =item isl_int_is_nonneg(i)
416 =item isl_int_is_divisible_by(i,j)
420 =head2 Sets and Relations
422 C<isl> uses six types of objects for representing sets and relations,
423 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
424 C<isl_union_set> and C<isl_union_map>.
425 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
426 can be described as a conjunction of affine constraints, while
427 C<isl_set> and C<isl_map> represent unions of
428 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
429 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
430 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
431 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
432 where spaces are considered different if they have a different number
433 of dimensions and/or different names (see L<"Spaces">).
434 The difference between sets and relations (maps) is that sets have
435 one set of variables, while relations have two sets of variables,
436 input variables and output variables.
438 =head2 Memory Management
440 Since a high-level operation on sets and/or relations usually involves
441 several substeps and since the user is usually not interested in
442 the intermediate results, most functions that return a new object
443 will also release all the objects passed as arguments.
444 If the user still wants to use one or more of these arguments
445 after the function call, she should pass along a copy of the
446 object rather than the object itself.
447 The user is then responsible for making sure that the original
448 object gets used somewhere else or is explicitly freed.
450 The arguments and return values of all documented functions are
451 annotated to make clear which arguments are released and which
452 arguments are preserved. In particular, the following annotations
459 C<__isl_give> means that a new object is returned.
460 The user should make sure that the returned pointer is
461 used exactly once as a value for an C<__isl_take> argument.
462 In between, it can be used as a value for as many
463 C<__isl_keep> arguments as the user likes.
464 There is one exception, and that is the case where the
465 pointer returned is C<NULL>. Is this case, the user
466 is free to use it as an C<__isl_take> argument or not.
470 C<__isl_take> means that the object the argument points to
471 is taken over by the function and may no longer be used
472 by the user as an argument to any other function.
473 The pointer value must be one returned by a function
474 returning an C<__isl_give> pointer.
475 If the user passes in a C<NULL> value, then this will
476 be treated as an error in the sense that the function will
477 not perform its usual operation. However, it will still
478 make sure that all the other C<__isl_take> arguments
483 C<__isl_keep> means that the function will only use the object
484 temporarily. After the function has finished, the user
485 can still use it as an argument to other functions.
486 A C<NULL> value will be treated in the same way as
487 a C<NULL> value for an C<__isl_take> argument.
491 =head2 Error Handling
493 C<isl> supports different ways to react in case a runtime error is triggered.
494 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
495 with two maps that have incompatible spaces. There are three possible ways
496 to react on error: to warn, to continue or to abort.
498 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
499 the last error in the corresponding C<isl_ctx> and the function in which the
500 error was triggered returns C<NULL>. An error does not corrupt internal state,
501 such that isl can continue to be used. C<isl> also provides functions to
502 read the last error and to reset the memory that stores the last error. The
503 last error is only stored for information purposes. Its presence does not
504 change the behavior of C<isl>. Hence, resetting an error is not required to
505 continue to use isl, but only to observe new errors.
508 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
509 void isl_ctx_reset_error(isl_ctx *ctx);
511 Another option is to continue on error. This is similar to warn on error mode,
512 except that C<isl> does not print any warning. This allows a program to
513 implement its own error reporting.
515 The last option is to directly abort the execution of the program from within
516 the isl library. This makes it obviously impossible to recover from an error,
517 but it allows to directly spot the error location. By aborting on error,
518 debuggers break at the location the error occurred and can provide a stack
519 trace. Other tools that automatically provide stack traces on abort or that do
520 not want to continue execution after an error was triggered may also prefer to
523 The on error behavior of isl can be specified by calling
524 C<isl_options_set_on_error> or by setting the command line option
525 C<--isl-on-error>. Valid arguments for the function call are
526 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
527 choices for the command line option are C<warn>, C<continue> and C<abort>.
528 It is also possible to query the current error mode.
530 #include <isl/options.h>
531 int isl_options_set_on_error(isl_ctx *ctx, int val);
532 int isl_options_get_on_error(isl_ctx *ctx);
536 Identifiers are used to identify both individual dimensions
537 and tuples of dimensions. They consist of a name and an optional
538 pointer. Identifiers with the same name but different pointer values
539 are considered to be distinct.
540 Identifiers can be constructed, copied, freed, inspected and printed
541 using the following functions.
544 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
545 __isl_keep const char *name, void *user);
546 __isl_give isl_id *isl_id_copy(isl_id *id);
547 void *isl_id_free(__isl_take isl_id *id);
549 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
550 void *isl_id_get_user(__isl_keep isl_id *id);
551 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
553 __isl_give isl_printer *isl_printer_print_id(
554 __isl_take isl_printer *p, __isl_keep isl_id *id);
556 Note that C<isl_id_get_name> returns a pointer to some internal
557 data structure, so the result can only be used while the
558 corresponding C<isl_id> is alive.
562 Whenever a new set or relation is created from scratch,
563 the space in which it lives needs to be specified using an C<isl_space>.
565 #include <isl/space.h>
566 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
567 unsigned nparam, unsigned n_in, unsigned n_out);
568 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
570 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
571 unsigned nparam, unsigned dim);
572 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
573 void isl_space_free(__isl_take isl_space *space);
574 unsigned isl_space_dim(__isl_keep isl_space *space,
575 enum isl_dim_type type);
577 The space used for creating a parameter domain
578 needs to be created using C<isl_space_params_alloc>.
579 For other sets, the space
580 needs to be created using C<isl_space_set_alloc>, while
581 for a relation, the space
582 needs to be created using C<isl_space_alloc>.
583 C<isl_space_dim> can be used
584 to find out the number of dimensions of each type in
585 a space, where type may be
586 C<isl_dim_param>, C<isl_dim_in> (only for relations),
587 C<isl_dim_out> (only for relations), C<isl_dim_set>
588 (only for sets) or C<isl_dim_all>.
590 To check whether a given space is that of a set or a map
591 or whether it is a parameter space, use these functions:
593 #include <isl/space.h>
594 int isl_space_is_params(__isl_keep isl_space *space);
595 int isl_space_is_set(__isl_keep isl_space *space);
597 It is often useful to create objects that live in the
598 same space as some other object. This can be accomplished
599 by creating the new objects
600 (see L<Creating New Sets and Relations> or
601 L<Creating New (Piecewise) Quasipolynomials>) based on the space
602 of the original object.
605 __isl_give isl_space *isl_basic_set_get_space(
606 __isl_keep isl_basic_set *bset);
607 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
609 #include <isl/union_set.h>
610 __isl_give isl_space *isl_union_set_get_space(
611 __isl_keep isl_union_set *uset);
614 __isl_give isl_space *isl_basic_map_get_space(
615 __isl_keep isl_basic_map *bmap);
616 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
618 #include <isl/union_map.h>
619 __isl_give isl_space *isl_union_map_get_space(
620 __isl_keep isl_union_map *umap);
622 #include <isl/constraint.h>
623 __isl_give isl_space *isl_constraint_get_space(
624 __isl_keep isl_constraint *constraint);
626 #include <isl/polynomial.h>
627 __isl_give isl_space *isl_qpolynomial_get_domain_space(
628 __isl_keep isl_qpolynomial *qp);
629 __isl_give isl_space *isl_qpolynomial_get_space(
630 __isl_keep isl_qpolynomial *qp);
631 __isl_give isl_space *isl_qpolynomial_fold_get_space(
632 __isl_keep isl_qpolynomial_fold *fold);
633 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
634 __isl_keep isl_pw_qpolynomial *pwqp);
635 __isl_give isl_space *isl_pw_qpolynomial_get_space(
636 __isl_keep isl_pw_qpolynomial *pwqp);
637 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
638 __isl_keep isl_pw_qpolynomial_fold *pwf);
639 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
640 __isl_keep isl_pw_qpolynomial_fold *pwf);
641 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
642 __isl_keep isl_union_pw_qpolynomial *upwqp);
643 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
644 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
647 __isl_give isl_space *isl_aff_get_domain_space(
648 __isl_keep isl_aff *aff);
649 __isl_give isl_space *isl_aff_get_space(
650 __isl_keep isl_aff *aff);
651 __isl_give isl_space *isl_pw_aff_get_domain_space(
652 __isl_keep isl_pw_aff *pwaff);
653 __isl_give isl_space *isl_pw_aff_get_space(
654 __isl_keep isl_pw_aff *pwaff);
655 __isl_give isl_space *isl_multi_aff_get_space(
656 __isl_keep isl_multi_aff *maff);
657 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
658 __isl_keep isl_pw_multi_aff *pma);
659 __isl_give isl_space *isl_pw_multi_aff_get_space(
660 __isl_keep isl_pw_multi_aff *pma);
662 #include <isl/point.h>
663 __isl_give isl_space *isl_point_get_space(
664 __isl_keep isl_point *pnt);
666 The identifiers or names of the individual dimensions may be set or read off
667 using the following functions.
669 #include <isl/space.h>
670 __isl_give isl_space *isl_space_set_dim_id(
671 __isl_take isl_space *space,
672 enum isl_dim_type type, unsigned pos,
673 __isl_take isl_id *id);
674 int isl_space_has_dim_id(__isl_keep isl_space *space,
675 enum isl_dim_type type, unsigned pos);
676 __isl_give isl_id *isl_space_get_dim_id(
677 __isl_keep isl_space *space,
678 enum isl_dim_type type, unsigned pos);
679 __isl_give isl_space *isl_space_set_dim_name(__isl_take isl_space *space,
680 enum isl_dim_type type, unsigned pos,
681 __isl_keep const char *name);
682 __isl_keep const char *isl_space_get_dim_name(__isl_keep isl_space *space,
683 enum isl_dim_type type, unsigned pos);
685 Note that C<isl_space_get_name> returns a pointer to some internal
686 data structure, so the result can only be used while the
687 corresponding C<isl_space> is alive.
688 Also note that every function that operates on two sets or relations
689 requires that both arguments have the same parameters. This also
690 means that if one of the arguments has named parameters, then the
691 other needs to have named parameters too and the names need to match.
692 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
693 arguments may have different parameters (as long as they are named),
694 in which case the result will have as parameters the union of the parameters of
697 Given the identifier or name of a dimension (typically a parameter),
698 its position can be obtained from the following function.
700 #include <isl/space.h>
701 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
702 enum isl_dim_type type, __isl_keep isl_id *id);
703 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
704 enum isl_dim_type type, const char *name);
706 The identifiers or names of entire spaces may be set or read off
707 using the following functions.
709 #include <isl/space.h>
710 __isl_give isl_space *isl_space_set_tuple_id(
711 __isl_take isl_space *space,
712 enum isl_dim_type type, __isl_take isl_id *id);
713 __isl_give isl_space *isl_space_reset_tuple_id(
714 __isl_take isl_space *space, enum isl_dim_type type);
715 int isl_space_has_tuple_id(__isl_keep isl_space *space,
716 enum isl_dim_type type);
717 __isl_give isl_id *isl_space_get_tuple_id(
718 __isl_keep isl_space *space, enum isl_dim_type type);
719 __isl_give isl_space *isl_space_set_tuple_name(
720 __isl_take isl_space *space,
721 enum isl_dim_type type, const char *s);
722 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
723 enum isl_dim_type type);
725 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
726 or C<isl_dim_set>. As with C<isl_space_get_name>,
727 the C<isl_space_get_tuple_name> function returns a pointer to some internal
729 Binary operations require the corresponding spaces of their arguments
730 to have the same name.
732 Spaces can be nested. In particular, the domain of a set or
733 the domain or range of a relation can be a nested relation.
734 The following functions can be used to construct and deconstruct
737 #include <isl/space.h>
738 int isl_space_is_wrapping(__isl_keep isl_space *space);
739 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
740 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
742 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
743 be the space of a set, while that of
744 C<isl_space_wrap> should be the space of a relation.
745 Conversely, the output of C<isl_space_unwrap> is the space
746 of a relation, while that of C<isl_space_wrap> is the space of a set.
748 Spaces can be created from other spaces
749 using the following functions.
751 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
752 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
753 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
754 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
755 __isl_give isl_space *isl_space_params(
756 __isl_take isl_space *space);
757 __isl_give isl_space *isl_space_set_from_params(
758 __isl_take isl_space *space);
759 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
760 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
761 __isl_take isl_space *right);
762 __isl_give isl_space *isl_space_align_params(
763 __isl_take isl_space *space1, __isl_take isl_space *space2)
764 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
765 enum isl_dim_type type, unsigned pos, unsigned n);
766 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
767 enum isl_dim_type type, unsigned n);
768 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
769 enum isl_dim_type type, unsigned first, unsigned n);
770 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
771 enum isl_dim_type dst_type, unsigned dst_pos,
772 enum isl_dim_type src_type, unsigned src_pos,
774 __isl_give isl_space *isl_space_map_from_set(
775 __isl_take isl_space *space);
776 __isl_give isl_space *isl_space_map_from_domain_and_range(
777 __isl_take isl_space *domain,
778 __isl_take isl_space *range);
779 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
781 Note that if dimensions are added or removed from a space, then
782 the name and the internal structure are lost.
786 A local space is essentially a space with
787 zero or more existentially quantified variables.
788 The local space of a basic set or relation can be obtained
789 using the following functions.
792 __isl_give isl_local_space *isl_basic_set_get_local_space(
793 __isl_keep isl_basic_set *bset);
796 __isl_give isl_local_space *isl_basic_map_get_local_space(
797 __isl_keep isl_basic_map *bmap);
799 A new local space can be created from a space using
801 #include <isl/local_space.h>
802 __isl_give isl_local_space *isl_local_space_from_space(
803 __isl_take isl_space *space);
805 They can be inspected, modified, copied and freed using the following functions.
807 #include <isl/local_space.h>
808 isl_ctx *isl_local_space_get_ctx(
809 __isl_keep isl_local_space *ls);
810 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
811 int isl_local_space_dim(__isl_keep isl_local_space *ls,
812 enum isl_dim_type type);
813 const char *isl_local_space_get_dim_name(
814 __isl_keep isl_local_space *ls,
815 enum isl_dim_type type, unsigned pos);
816 __isl_give isl_local_space *isl_local_space_set_dim_name(
817 __isl_take isl_local_space *ls,
818 enum isl_dim_type type, unsigned pos, const char *s);
819 __isl_give isl_local_space *isl_local_space_set_dim_id(
820 __isl_take isl_local_space *ls,
821 enum isl_dim_type type, unsigned pos,
822 __isl_take isl_id *id);
823 __isl_give isl_space *isl_local_space_get_space(
824 __isl_keep isl_local_space *ls);
825 __isl_give isl_aff *isl_local_space_get_div(
826 __isl_keep isl_local_space *ls, int pos);
827 __isl_give isl_local_space *isl_local_space_copy(
828 __isl_keep isl_local_space *ls);
829 void *isl_local_space_free(__isl_take isl_local_space *ls);
831 Two local spaces can be compared using
833 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
834 __isl_keep isl_local_space *ls2);
836 Local spaces can be created from other local spaces
837 using the following functions.
839 __isl_give isl_local_space *isl_local_space_domain(
840 __isl_take isl_local_space *ls);
841 __isl_give isl_local_space *isl_local_space_range(
842 __isl_take isl_local_space *ls);
843 __isl_give isl_local_space *isl_local_space_from_domain(
844 __isl_take isl_local_space *ls);
845 __isl_give isl_local_space *isl_local_space_intersect(
846 __isl_take isl_local_space *ls1,
847 __isl_take isl_local_space *ls2);
848 __isl_give isl_local_space *isl_local_space_add_dims(
849 __isl_take isl_local_space *ls,
850 enum isl_dim_type type, unsigned n);
851 __isl_give isl_local_space *isl_local_space_insert_dims(
852 __isl_take isl_local_space *ls,
853 enum isl_dim_type type, unsigned first, unsigned n);
854 __isl_give isl_local_space *isl_local_space_drop_dims(
855 __isl_take isl_local_space *ls,
856 enum isl_dim_type type, unsigned first, unsigned n);
858 =head2 Input and Output
860 C<isl> supports its own input/output format, which is similar
861 to the C<Omega> format, but also supports the C<PolyLib> format
866 The C<isl> format is similar to that of C<Omega>, but has a different
867 syntax for describing the parameters and allows for the definition
868 of an existentially quantified variable as the integer division
869 of an affine expression.
870 For example, the set of integers C<i> between C<0> and C<n>
871 such that C<i % 10 <= 6> can be described as
873 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
876 A set or relation can have several disjuncts, separated
877 by the keyword C<or>. Each disjunct is either a conjunction
878 of constraints or a projection (C<exists>) of a conjunction
879 of constraints. The constraints are separated by the keyword
882 =head3 C<PolyLib> format
884 If the represented set is a union, then the first line
885 contains a single number representing the number of disjuncts.
886 Otherwise, a line containing the number C<1> is optional.
888 Each disjunct is represented by a matrix of constraints.
889 The first line contains two numbers representing
890 the number of rows and columns,
891 where the number of rows is equal to the number of constraints
892 and the number of columns is equal to two plus the number of variables.
893 The following lines contain the actual rows of the constraint matrix.
894 In each row, the first column indicates whether the constraint
895 is an equality (C<0>) or inequality (C<1>). The final column
896 corresponds to the constant term.
898 If the set is parametric, then the coefficients of the parameters
899 appear in the last columns before the constant column.
900 The coefficients of any existentially quantified variables appear
901 between those of the set variables and those of the parameters.
903 =head3 Extended C<PolyLib> format
905 The extended C<PolyLib> format is nearly identical to the
906 C<PolyLib> format. The only difference is that the line
907 containing the number of rows and columns of a constraint matrix
908 also contains four additional numbers:
909 the number of output dimensions, the number of input dimensions,
910 the number of local dimensions (i.e., the number of existentially
911 quantified variables) and the number of parameters.
912 For sets, the number of ``output'' dimensions is equal
913 to the number of set dimensions, while the number of ``input''
919 __isl_give isl_basic_set *isl_basic_set_read_from_file(
920 isl_ctx *ctx, FILE *input);
921 __isl_give isl_basic_set *isl_basic_set_read_from_str(
922 isl_ctx *ctx, const char *str);
923 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
925 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
929 __isl_give isl_basic_map *isl_basic_map_read_from_file(
930 isl_ctx *ctx, FILE *input);
931 __isl_give isl_basic_map *isl_basic_map_read_from_str(
932 isl_ctx *ctx, const char *str);
933 __isl_give isl_map *isl_map_read_from_file(
934 isl_ctx *ctx, FILE *input);
935 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
938 #include <isl/union_set.h>
939 __isl_give isl_union_set *isl_union_set_read_from_file(
940 isl_ctx *ctx, FILE *input);
941 __isl_give isl_union_set *isl_union_set_read_from_str(
942 isl_ctx *ctx, const char *str);
944 #include <isl/union_map.h>
945 __isl_give isl_union_map *isl_union_map_read_from_file(
946 isl_ctx *ctx, FILE *input);
947 __isl_give isl_union_map *isl_union_map_read_from_str(
948 isl_ctx *ctx, const char *str);
950 The input format is autodetected and may be either the C<PolyLib> format
951 or the C<isl> format.
955 Before anything can be printed, an C<isl_printer> needs to
958 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
960 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
961 void isl_printer_free(__isl_take isl_printer *printer);
962 __isl_give char *isl_printer_get_str(
963 __isl_keep isl_printer *printer);
965 The behavior of the printer can be modified in various ways
967 __isl_give isl_printer *isl_printer_set_output_format(
968 __isl_take isl_printer *p, int output_format);
969 __isl_give isl_printer *isl_printer_set_indent(
970 __isl_take isl_printer *p, int indent);
971 __isl_give isl_printer *isl_printer_indent(
972 __isl_take isl_printer *p, int indent);
973 __isl_give isl_printer *isl_printer_set_prefix(
974 __isl_take isl_printer *p, const char *prefix);
975 __isl_give isl_printer *isl_printer_set_suffix(
976 __isl_take isl_printer *p, const char *suffix);
978 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
979 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
980 and defaults to C<ISL_FORMAT_ISL>.
981 Each line in the output is indented by C<indent> (set by
982 C<isl_printer_set_indent>) spaces
983 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
984 In the C<PolyLib> format output,
985 the coefficients of the existentially quantified variables
986 appear between those of the set variables and those
988 The function C<isl_printer_indent> increases the indentation
989 by the specified amount (which may be negative).
991 To actually print something, use
994 __isl_give isl_printer *isl_printer_print_basic_set(
995 __isl_take isl_printer *printer,
996 __isl_keep isl_basic_set *bset);
997 __isl_give isl_printer *isl_printer_print_set(
998 __isl_take isl_printer *printer,
999 __isl_keep isl_set *set);
1001 #include <isl/map.h>
1002 __isl_give isl_printer *isl_printer_print_basic_map(
1003 __isl_take isl_printer *printer,
1004 __isl_keep isl_basic_map *bmap);
1005 __isl_give isl_printer *isl_printer_print_map(
1006 __isl_take isl_printer *printer,
1007 __isl_keep isl_map *map);
1009 #include <isl/union_set.h>
1010 __isl_give isl_printer *isl_printer_print_union_set(
1011 __isl_take isl_printer *p,
1012 __isl_keep isl_union_set *uset);
1014 #include <isl/union_map.h>
1015 __isl_give isl_printer *isl_printer_print_union_map(
1016 __isl_take isl_printer *p,
1017 __isl_keep isl_union_map *umap);
1019 When called on a file printer, the following function flushes
1020 the file. When called on a string printer, the buffer is cleared.
1022 __isl_give isl_printer *isl_printer_flush(
1023 __isl_take isl_printer *p);
1025 =head2 Creating New Sets and Relations
1027 C<isl> has functions for creating some standard sets and relations.
1031 =item * Empty sets and relations
1033 __isl_give isl_basic_set *isl_basic_set_empty(
1034 __isl_take isl_space *space);
1035 __isl_give isl_basic_map *isl_basic_map_empty(
1036 __isl_take isl_space *space);
1037 __isl_give isl_set *isl_set_empty(
1038 __isl_take isl_space *space);
1039 __isl_give isl_map *isl_map_empty(
1040 __isl_take isl_space *space);
1041 __isl_give isl_union_set *isl_union_set_empty(
1042 __isl_take isl_space *space);
1043 __isl_give isl_union_map *isl_union_map_empty(
1044 __isl_take isl_space *space);
1046 For C<isl_union_set>s and C<isl_union_map>s, the space
1047 is only used to specify the parameters.
1049 =item * Universe sets and relations
1051 __isl_give isl_basic_set *isl_basic_set_universe(
1052 __isl_take isl_space *space);
1053 __isl_give isl_basic_map *isl_basic_map_universe(
1054 __isl_take isl_space *space);
1055 __isl_give isl_set *isl_set_universe(
1056 __isl_take isl_space *space);
1057 __isl_give isl_map *isl_map_universe(
1058 __isl_take isl_space *space);
1059 __isl_give isl_union_set *isl_union_set_universe(
1060 __isl_take isl_union_set *uset);
1061 __isl_give isl_union_map *isl_union_map_universe(
1062 __isl_take isl_union_map *umap);
1064 The sets and relations constructed by the functions above
1065 contain all integer values, while those constructed by the
1066 functions below only contain non-negative values.
1068 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1069 __isl_take isl_space *space);
1070 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1071 __isl_take isl_space *space);
1072 __isl_give isl_set *isl_set_nat_universe(
1073 __isl_take isl_space *space);
1074 __isl_give isl_map *isl_map_nat_universe(
1075 __isl_take isl_space *space);
1077 =item * Identity relations
1079 __isl_give isl_basic_map *isl_basic_map_identity(
1080 __isl_take isl_space *space);
1081 __isl_give isl_map *isl_map_identity(
1082 __isl_take isl_space *space);
1084 The number of input and output dimensions in C<space> needs
1087 =item * Lexicographic order
1089 __isl_give isl_map *isl_map_lex_lt(
1090 __isl_take isl_space *set_space);
1091 __isl_give isl_map *isl_map_lex_le(
1092 __isl_take isl_space *set_space);
1093 __isl_give isl_map *isl_map_lex_gt(
1094 __isl_take isl_space *set_space);
1095 __isl_give isl_map *isl_map_lex_ge(
1096 __isl_take isl_space *set_space);
1097 __isl_give isl_map *isl_map_lex_lt_first(
1098 __isl_take isl_space *space, unsigned n);
1099 __isl_give isl_map *isl_map_lex_le_first(
1100 __isl_take isl_space *space, unsigned n);
1101 __isl_give isl_map *isl_map_lex_gt_first(
1102 __isl_take isl_space *space, unsigned n);
1103 __isl_give isl_map *isl_map_lex_ge_first(
1104 __isl_take isl_space *space, unsigned n);
1106 The first four functions take a space for a B<set>
1107 and return relations that express that the elements in the domain
1108 are lexicographically less
1109 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1110 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1111 than the elements in the range.
1112 The last four functions take a space for a map
1113 and return relations that express that the first C<n> dimensions
1114 in the domain are lexicographically less
1115 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1116 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1117 than the first C<n> dimensions in the range.
1121 A basic set or relation can be converted to a set or relation
1122 using the following functions.
1124 __isl_give isl_set *isl_set_from_basic_set(
1125 __isl_take isl_basic_set *bset);
1126 __isl_give isl_map *isl_map_from_basic_map(
1127 __isl_take isl_basic_map *bmap);
1129 Sets and relations can be converted to union sets and relations
1130 using the following functions.
1132 __isl_give isl_union_map *isl_union_map_from_map(
1133 __isl_take isl_map *map);
1134 __isl_give isl_union_set *isl_union_set_from_set(
1135 __isl_take isl_set *set);
1137 The inverse conversions below can only be used if the input
1138 union set or relation is known to contain elements in exactly one
1141 __isl_give isl_set *isl_set_from_union_set(
1142 __isl_take isl_union_set *uset);
1143 __isl_give isl_map *isl_map_from_union_map(
1144 __isl_take isl_union_map *umap);
1146 A zero-dimensional set can be constructed on a given parameter domain
1147 using the following function.
1149 __isl_give isl_set *isl_set_from_params(
1150 __isl_take isl_set *set);
1152 Sets and relations can be copied and freed again using the following
1155 __isl_give isl_basic_set *isl_basic_set_copy(
1156 __isl_keep isl_basic_set *bset);
1157 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1158 __isl_give isl_union_set *isl_union_set_copy(
1159 __isl_keep isl_union_set *uset);
1160 __isl_give isl_basic_map *isl_basic_map_copy(
1161 __isl_keep isl_basic_map *bmap);
1162 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1163 __isl_give isl_union_map *isl_union_map_copy(
1164 __isl_keep isl_union_map *umap);
1165 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1166 void isl_set_free(__isl_take isl_set *set);
1167 void *isl_union_set_free(__isl_take isl_union_set *uset);
1168 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1169 void isl_map_free(__isl_take isl_map *map);
1170 void *isl_union_map_free(__isl_take isl_union_map *umap);
1172 Other sets and relations can be constructed by starting
1173 from a universe set or relation, adding equality and/or
1174 inequality constraints and then projecting out the
1175 existentially quantified variables, if any.
1176 Constraints can be constructed, manipulated and
1177 added to (or removed from) (basic) sets and relations
1178 using the following functions.
1180 #include <isl/constraint.h>
1181 __isl_give isl_constraint *isl_equality_alloc(
1182 __isl_take isl_local_space *ls);
1183 __isl_give isl_constraint *isl_inequality_alloc(
1184 __isl_take isl_local_space *ls);
1185 __isl_give isl_constraint *isl_constraint_set_constant(
1186 __isl_take isl_constraint *constraint, isl_int v);
1187 __isl_give isl_constraint *isl_constraint_set_constant_si(
1188 __isl_take isl_constraint *constraint, int v);
1189 __isl_give isl_constraint *isl_constraint_set_coefficient(
1190 __isl_take isl_constraint *constraint,
1191 enum isl_dim_type type, int pos, isl_int v);
1192 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1193 __isl_take isl_constraint *constraint,
1194 enum isl_dim_type type, int pos, int v);
1195 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1196 __isl_take isl_basic_map *bmap,
1197 __isl_take isl_constraint *constraint);
1198 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1199 __isl_take isl_basic_set *bset,
1200 __isl_take isl_constraint *constraint);
1201 __isl_give isl_map *isl_map_add_constraint(
1202 __isl_take isl_map *map,
1203 __isl_take isl_constraint *constraint);
1204 __isl_give isl_set *isl_set_add_constraint(
1205 __isl_take isl_set *set,
1206 __isl_take isl_constraint *constraint);
1207 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1208 __isl_take isl_basic_set *bset,
1209 __isl_take isl_constraint *constraint);
1211 For example, to create a set containing the even integers
1212 between 10 and 42, you would use the following code.
1215 isl_local_space *ls;
1217 isl_basic_set *bset;
1219 space = isl_space_set_alloc(ctx, 0, 2);
1220 bset = isl_basic_set_universe(isl_space_copy(space));
1221 ls = isl_local_space_from_space(space);
1223 c = isl_equality_alloc(isl_local_space_copy(ls));
1224 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1225 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1226 bset = isl_basic_set_add_constraint(bset, c);
1228 c = isl_inequality_alloc(isl_local_space_copy(ls));
1229 c = isl_constraint_set_constant_si(c, -10);
1230 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1231 bset = isl_basic_set_add_constraint(bset, c);
1233 c = isl_inequality_alloc(ls);
1234 c = isl_constraint_set_constant_si(c, 42);
1235 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1236 bset = isl_basic_set_add_constraint(bset, c);
1238 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1242 isl_basic_set *bset;
1243 bset = isl_basic_set_read_from_str(ctx,
1244 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1246 A basic set or relation can also be constructed from two matrices
1247 describing the equalities and the inequalities.
1249 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1250 __isl_take isl_space *space,
1251 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1252 enum isl_dim_type c1,
1253 enum isl_dim_type c2, enum isl_dim_type c3,
1254 enum isl_dim_type c4);
1255 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1256 __isl_take isl_space *space,
1257 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1258 enum isl_dim_type c1,
1259 enum isl_dim_type c2, enum isl_dim_type c3,
1260 enum isl_dim_type c4, enum isl_dim_type c5);
1262 The C<isl_dim_type> arguments indicate the order in which
1263 different kinds of variables appear in the input matrices
1264 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1265 C<isl_dim_set> and C<isl_dim_div> for sets and
1266 of C<isl_dim_cst>, C<isl_dim_param>,
1267 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1269 A (basic) set or relation can also be constructed from a (piecewise)
1270 (multiple) affine expression
1271 or a list of affine expressions
1272 (See L<"Piecewise Quasi Affine Expressions"> and
1273 L<"Piecewise Multiple Quasi Affine Expressions">).
1275 __isl_give isl_basic_map *isl_basic_map_from_aff(
1276 __isl_take isl_aff *aff);
1277 __isl_give isl_set *isl_set_from_pw_aff(
1278 __isl_take isl_pw_aff *pwaff);
1279 __isl_give isl_map *isl_map_from_pw_aff(
1280 __isl_take isl_pw_aff *pwaff);
1281 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1282 __isl_take isl_space *domain_space,
1283 __isl_take isl_aff_list *list);
1284 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1285 __isl_take isl_multi_aff *maff)
1286 __isl_give isl_set *isl_set_from_pw_multi_aff(
1287 __isl_take isl_pw_multi_aff *pma);
1288 __isl_give isl_map *isl_map_from_pw_multi_aff(
1289 __isl_take isl_pw_multi_aff *pma);
1291 The C<domain_dim> argument describes the domain of the resulting
1292 basic relation. It is required because the C<list> may consist
1293 of zero affine expressions.
1295 =head2 Inspecting Sets and Relations
1297 Usually, the user should not have to care about the actual constraints
1298 of the sets and maps, but should instead apply the abstract operations
1299 explained in the following sections.
1300 Occasionally, however, it may be required to inspect the individual
1301 coefficients of the constraints. This section explains how to do so.
1302 In these cases, it may also be useful to have C<isl> compute
1303 an explicit representation of the existentially quantified variables.
1305 __isl_give isl_set *isl_set_compute_divs(
1306 __isl_take isl_set *set);
1307 __isl_give isl_map *isl_map_compute_divs(
1308 __isl_take isl_map *map);
1309 __isl_give isl_union_set *isl_union_set_compute_divs(
1310 __isl_take isl_union_set *uset);
1311 __isl_give isl_union_map *isl_union_map_compute_divs(
1312 __isl_take isl_union_map *umap);
1314 This explicit representation defines the existentially quantified
1315 variables as integer divisions of the other variables, possibly
1316 including earlier existentially quantified variables.
1317 An explicitly represented existentially quantified variable therefore
1318 has a unique value when the values of the other variables are known.
1319 If, furthermore, the same existentials, i.e., existentials
1320 with the same explicit representations, should appear in the
1321 same order in each of the disjuncts of a set or map, then the user should call
1322 either of the following functions.
1324 __isl_give isl_set *isl_set_align_divs(
1325 __isl_take isl_set *set);
1326 __isl_give isl_map *isl_map_align_divs(
1327 __isl_take isl_map *map);
1329 Alternatively, the existentially quantified variables can be removed
1330 using the following functions, which compute an overapproximation.
1332 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1333 __isl_take isl_basic_set *bset);
1334 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1335 __isl_take isl_basic_map *bmap);
1336 __isl_give isl_set *isl_set_remove_divs(
1337 __isl_take isl_set *set);
1338 __isl_give isl_map *isl_map_remove_divs(
1339 __isl_take isl_map *map);
1341 To iterate over all the sets or maps in a union set or map, use
1343 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1344 int (*fn)(__isl_take isl_set *set, void *user),
1346 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1347 int (*fn)(__isl_take isl_map *map, void *user),
1350 The number of sets or maps in a union set or map can be obtained
1353 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1354 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1356 To extract the set or map in a given space from a union, use
1358 __isl_give isl_set *isl_union_set_extract_set(
1359 __isl_keep isl_union_set *uset,
1360 __isl_take isl_space *space);
1361 __isl_give isl_map *isl_union_map_extract_map(
1362 __isl_keep isl_union_map *umap,
1363 __isl_take isl_space *space);
1365 To iterate over all the basic sets or maps in a set or map, use
1367 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1368 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1370 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1371 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1374 The callback function C<fn> should return 0 if successful and
1375 -1 if an error occurs. In the latter case, or if any other error
1376 occurs, the above functions will return -1.
1378 It should be noted that C<isl> does not guarantee that
1379 the basic sets or maps passed to C<fn> are disjoint.
1380 If this is required, then the user should call one of
1381 the following functions first.
1383 __isl_give isl_set *isl_set_make_disjoint(
1384 __isl_take isl_set *set);
1385 __isl_give isl_map *isl_map_make_disjoint(
1386 __isl_take isl_map *map);
1388 The number of basic sets in a set can be obtained
1391 int isl_set_n_basic_set(__isl_keep isl_set *set);
1393 To iterate over the constraints of a basic set or map, use
1395 #include <isl/constraint.h>
1397 int isl_basic_map_foreach_constraint(
1398 __isl_keep isl_basic_map *bmap,
1399 int (*fn)(__isl_take isl_constraint *c, void *user),
1401 void *isl_constraint_free(__isl_take isl_constraint *c);
1403 Again, the callback function C<fn> should return 0 if successful and
1404 -1 if an error occurs. In the latter case, or if any other error
1405 occurs, the above functions will return -1.
1406 The constraint C<c> represents either an equality or an inequality.
1407 Use the following function to find out whether a constraint
1408 represents an equality. If not, it represents an inequality.
1410 int isl_constraint_is_equality(
1411 __isl_keep isl_constraint *constraint);
1413 The coefficients of the constraints can be inspected using
1414 the following functions.
1416 void isl_constraint_get_constant(
1417 __isl_keep isl_constraint *constraint, isl_int *v);
1418 void isl_constraint_get_coefficient(
1419 __isl_keep isl_constraint *constraint,
1420 enum isl_dim_type type, int pos, isl_int *v);
1421 int isl_constraint_involves_dims(
1422 __isl_keep isl_constraint *constraint,
1423 enum isl_dim_type type, unsigned first, unsigned n);
1425 The explicit representations of the existentially quantified
1426 variables can be inspected using the following function.
1427 Note that the user is only allowed to use this function
1428 if the inspected set or map is the result of a call
1429 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1430 The existentially quantified variable is equal to the floor
1431 of the returned affine expression. The affine expression
1432 itself can be inspected using the functions in
1433 L<"Piecewise Quasi Affine Expressions">.
1435 __isl_give isl_aff *isl_constraint_get_div(
1436 __isl_keep isl_constraint *constraint, int pos);
1438 To obtain the constraints of a basic set or map in matrix
1439 form, use the following functions.
1441 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1442 __isl_keep isl_basic_set *bset,
1443 enum isl_dim_type c1, enum isl_dim_type c2,
1444 enum isl_dim_type c3, enum isl_dim_type c4);
1445 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1446 __isl_keep isl_basic_set *bset,
1447 enum isl_dim_type c1, enum isl_dim_type c2,
1448 enum isl_dim_type c3, enum isl_dim_type c4);
1449 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1450 __isl_keep isl_basic_map *bmap,
1451 enum isl_dim_type c1,
1452 enum isl_dim_type c2, enum isl_dim_type c3,
1453 enum isl_dim_type c4, enum isl_dim_type c5);
1454 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1455 __isl_keep isl_basic_map *bmap,
1456 enum isl_dim_type c1,
1457 enum isl_dim_type c2, enum isl_dim_type c3,
1458 enum isl_dim_type c4, enum isl_dim_type c5);
1460 The C<isl_dim_type> arguments dictate the order in which
1461 different kinds of variables appear in the resulting matrix
1462 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1463 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1465 The number of parameters, input, output or set dimensions can
1466 be obtained using the following functions.
1468 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1469 enum isl_dim_type type);
1470 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1471 enum isl_dim_type type);
1472 unsigned isl_set_dim(__isl_keep isl_set *set,
1473 enum isl_dim_type type);
1474 unsigned isl_map_dim(__isl_keep isl_map *map,
1475 enum isl_dim_type type);
1477 To check whether the description of a set or relation depends
1478 on one or more given dimensions, it is not necessary to iterate over all
1479 constraints. Instead the following functions can be used.
1481 int isl_basic_set_involves_dims(
1482 __isl_keep isl_basic_set *bset,
1483 enum isl_dim_type type, unsigned first, unsigned n);
1484 int isl_set_involves_dims(__isl_keep isl_set *set,
1485 enum isl_dim_type type, unsigned first, unsigned n);
1486 int isl_basic_map_involves_dims(
1487 __isl_keep isl_basic_map *bmap,
1488 enum isl_dim_type type, unsigned first, unsigned n);
1489 int isl_map_involves_dims(__isl_keep isl_map *map,
1490 enum isl_dim_type type, unsigned first, unsigned n);
1492 Similarly, the following functions can be used to check whether
1493 a given dimension is involved in any lower or upper bound.
1495 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1496 enum isl_dim_type type, unsigned pos);
1497 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1498 enum isl_dim_type type, unsigned pos);
1500 The identifiers or names of the domain and range spaces of a set
1501 or relation can be read off or set using the following functions.
1503 __isl_give isl_set *isl_set_set_tuple_id(
1504 __isl_take isl_set *set, __isl_take isl_id *id);
1505 __isl_give isl_set *isl_set_reset_tuple_id(
1506 __isl_take isl_set *set);
1507 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1508 __isl_give isl_id *isl_set_get_tuple_id(
1509 __isl_keep isl_set *set);
1510 __isl_give isl_map *isl_map_set_tuple_id(
1511 __isl_take isl_map *map, enum isl_dim_type type,
1512 __isl_take isl_id *id);
1513 __isl_give isl_map *isl_map_reset_tuple_id(
1514 __isl_take isl_map *map, enum isl_dim_type type);
1515 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1516 enum isl_dim_type type);
1517 __isl_give isl_id *isl_map_get_tuple_id(
1518 __isl_keep isl_map *map, enum isl_dim_type type);
1520 const char *isl_basic_set_get_tuple_name(
1521 __isl_keep isl_basic_set *bset);
1522 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1523 __isl_take isl_basic_set *set, const char *s);
1524 const char *isl_set_get_tuple_name(
1525 __isl_keep isl_set *set);
1526 const char *isl_basic_map_get_tuple_name(
1527 __isl_keep isl_basic_map *bmap,
1528 enum isl_dim_type type);
1529 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1530 __isl_take isl_basic_map *bmap,
1531 enum isl_dim_type type, const char *s);
1532 const char *isl_map_get_tuple_name(
1533 __isl_keep isl_map *map,
1534 enum isl_dim_type type);
1536 As with C<isl_space_get_tuple_name>, the value returned points to
1537 an internal data structure.
1538 The identifiers, positions or names of individual dimensions can be
1539 read off using the following functions.
1541 __isl_give isl_set *isl_set_set_dim_id(
1542 __isl_take isl_set *set, enum isl_dim_type type,
1543 unsigned pos, __isl_take isl_id *id);
1544 int isl_set_has_dim_id(__isl_keep isl_set *set,
1545 enum isl_dim_type type, unsigned pos);
1546 __isl_give isl_id *isl_set_get_dim_id(
1547 __isl_keep isl_set *set, enum isl_dim_type type,
1549 int isl_basic_map_has_dim_id(
1550 __isl_keep isl_basic_map *bmap,
1551 enum isl_dim_type type, unsigned pos);
1552 __isl_give isl_map *isl_map_set_dim_id(
1553 __isl_take isl_map *map, enum isl_dim_type type,
1554 unsigned pos, __isl_take isl_id *id);
1555 int isl_map_has_dim_id(__isl_keep isl_map *map,
1556 enum isl_dim_type type, unsigned pos);
1557 __isl_give isl_id *isl_map_get_dim_id(
1558 __isl_keep isl_map *map, enum isl_dim_type type,
1561 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1562 enum isl_dim_type type, __isl_keep isl_id *id);
1563 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1564 enum isl_dim_type type, __isl_keep isl_id *id);
1565 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1566 enum isl_dim_type type, const char *name);
1567 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1568 enum isl_dim_type type, const char *name);
1570 const char *isl_constraint_get_dim_name(
1571 __isl_keep isl_constraint *constraint,
1572 enum isl_dim_type type, unsigned pos);
1573 const char *isl_basic_set_get_dim_name(
1574 __isl_keep isl_basic_set *bset,
1575 enum isl_dim_type type, unsigned pos);
1576 const char *isl_set_get_dim_name(
1577 __isl_keep isl_set *set,
1578 enum isl_dim_type type, unsigned pos);
1579 const char *isl_basic_map_get_dim_name(
1580 __isl_keep isl_basic_map *bmap,
1581 enum isl_dim_type type, unsigned pos);
1582 const char *isl_map_get_dim_name(
1583 __isl_keep isl_map *map,
1584 enum isl_dim_type type, unsigned pos);
1586 These functions are mostly useful to obtain the identifiers, positions
1587 or names of the parameters. Identifiers of individual dimensions are
1588 essentially only useful for printing. They are ignored by all other
1589 operations and may not be preserved across those operations.
1593 =head3 Unary Properties
1599 The following functions test whether the given set or relation
1600 contains any integer points. The ``plain'' variants do not perform
1601 any computations, but simply check if the given set or relation
1602 is already known to be empty.
1604 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1605 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1606 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1607 int isl_set_is_empty(__isl_keep isl_set *set);
1608 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1609 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1610 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1611 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1612 int isl_map_is_empty(__isl_keep isl_map *map);
1613 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1615 =item * Universality
1617 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1618 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1619 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1621 =item * Single-valuedness
1623 int isl_map_is_single_valued(__isl_keep isl_map *map);
1624 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1628 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1629 int isl_map_is_injective(__isl_keep isl_map *map);
1630 int isl_union_map_plain_is_injective(
1631 __isl_keep isl_union_map *umap);
1632 int isl_union_map_is_injective(
1633 __isl_keep isl_union_map *umap);
1637 int isl_map_is_bijective(__isl_keep isl_map *map);
1638 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1642 int isl_basic_map_plain_is_fixed(
1643 __isl_keep isl_basic_map *bmap,
1644 enum isl_dim_type type, unsigned pos,
1646 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1647 enum isl_dim_type type, unsigned pos,
1649 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1650 enum isl_dim_type type, unsigned pos,
1653 Check if the relation obviously lies on a hyperplane where the given dimension
1654 has a fixed value and if so, return that value in C<*val>.
1658 To check whether a set is a parameter domain, use this function:
1660 int isl_set_is_params(__isl_keep isl_set *set);
1661 int isl_union_set_is_params(
1662 __isl_keep isl_union_set *uset);
1666 The following functions check whether the domain of the given
1667 (basic) set is a wrapped relation.
1669 int isl_basic_set_is_wrapping(
1670 __isl_keep isl_basic_set *bset);
1671 int isl_set_is_wrapping(__isl_keep isl_set *set);
1673 =item * Internal Product
1675 int isl_basic_map_can_zip(
1676 __isl_keep isl_basic_map *bmap);
1677 int isl_map_can_zip(__isl_keep isl_map *map);
1679 Check whether the product of domain and range of the given relation
1681 i.e., whether both domain and range are nested relations.
1685 =head3 Binary Properties
1691 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1692 __isl_keep isl_set *set2);
1693 int isl_set_is_equal(__isl_keep isl_set *set1,
1694 __isl_keep isl_set *set2);
1695 int isl_union_set_is_equal(
1696 __isl_keep isl_union_set *uset1,
1697 __isl_keep isl_union_set *uset2);
1698 int isl_basic_map_is_equal(
1699 __isl_keep isl_basic_map *bmap1,
1700 __isl_keep isl_basic_map *bmap2);
1701 int isl_map_is_equal(__isl_keep isl_map *map1,
1702 __isl_keep isl_map *map2);
1703 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1704 __isl_keep isl_map *map2);
1705 int isl_union_map_is_equal(
1706 __isl_keep isl_union_map *umap1,
1707 __isl_keep isl_union_map *umap2);
1709 =item * Disjointness
1711 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1712 __isl_keep isl_set *set2);
1716 int isl_set_is_subset(__isl_keep isl_set *set1,
1717 __isl_keep isl_set *set2);
1718 int isl_set_is_strict_subset(
1719 __isl_keep isl_set *set1,
1720 __isl_keep isl_set *set2);
1721 int isl_union_set_is_subset(
1722 __isl_keep isl_union_set *uset1,
1723 __isl_keep isl_union_set *uset2);
1724 int isl_union_set_is_strict_subset(
1725 __isl_keep isl_union_set *uset1,
1726 __isl_keep isl_union_set *uset2);
1727 int isl_basic_map_is_subset(
1728 __isl_keep isl_basic_map *bmap1,
1729 __isl_keep isl_basic_map *bmap2);
1730 int isl_basic_map_is_strict_subset(
1731 __isl_keep isl_basic_map *bmap1,
1732 __isl_keep isl_basic_map *bmap2);
1733 int isl_map_is_subset(
1734 __isl_keep isl_map *map1,
1735 __isl_keep isl_map *map2);
1736 int isl_map_is_strict_subset(
1737 __isl_keep isl_map *map1,
1738 __isl_keep isl_map *map2);
1739 int isl_union_map_is_subset(
1740 __isl_keep isl_union_map *umap1,
1741 __isl_keep isl_union_map *umap2);
1742 int isl_union_map_is_strict_subset(
1743 __isl_keep isl_union_map *umap1,
1744 __isl_keep isl_union_map *umap2);
1748 =head2 Unary Operations
1754 __isl_give isl_set *isl_set_complement(
1755 __isl_take isl_set *set);
1759 __isl_give isl_basic_map *isl_basic_map_reverse(
1760 __isl_take isl_basic_map *bmap);
1761 __isl_give isl_map *isl_map_reverse(
1762 __isl_take isl_map *map);
1763 __isl_give isl_union_map *isl_union_map_reverse(
1764 __isl_take isl_union_map *umap);
1768 __isl_give isl_basic_set *isl_basic_set_project_out(
1769 __isl_take isl_basic_set *bset,
1770 enum isl_dim_type type, unsigned first, unsigned n);
1771 __isl_give isl_basic_map *isl_basic_map_project_out(
1772 __isl_take isl_basic_map *bmap,
1773 enum isl_dim_type type, unsigned first, unsigned n);
1774 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1775 enum isl_dim_type type, unsigned first, unsigned n);
1776 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1777 enum isl_dim_type type, unsigned first, unsigned n);
1778 __isl_give isl_basic_set *isl_basic_set_params(
1779 __isl_take isl_basic_set *bset);
1780 __isl_give isl_basic_set *isl_basic_map_domain(
1781 __isl_take isl_basic_map *bmap);
1782 __isl_give isl_basic_set *isl_basic_map_range(
1783 __isl_take isl_basic_map *bmap);
1784 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1785 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1786 __isl_give isl_set *isl_map_domain(
1787 __isl_take isl_map *bmap);
1788 __isl_give isl_set *isl_map_range(
1789 __isl_take isl_map *map);
1790 __isl_give isl_set *isl_union_set_params(
1791 __isl_take isl_union_set *uset);
1792 __isl_give isl_set *isl_union_map_params(
1793 __isl_take isl_union_map *umap);
1794 __isl_give isl_union_set *isl_union_map_domain(
1795 __isl_take isl_union_map *umap);
1796 __isl_give isl_union_set *isl_union_map_range(
1797 __isl_take isl_union_map *umap);
1799 __isl_give isl_basic_map *isl_basic_map_domain_map(
1800 __isl_take isl_basic_map *bmap);
1801 __isl_give isl_basic_map *isl_basic_map_range_map(
1802 __isl_take isl_basic_map *bmap);
1803 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1804 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1805 __isl_give isl_union_map *isl_union_map_domain_map(
1806 __isl_take isl_union_map *umap);
1807 __isl_give isl_union_map *isl_union_map_range_map(
1808 __isl_take isl_union_map *umap);
1810 The functions above construct a (basic, regular or union) relation
1811 that maps (a wrapped version of) the input relation to its domain or range.
1815 __isl_give isl_set *isl_set_eliminate(
1816 __isl_take isl_set *set, enum isl_dim_type type,
1817 unsigned first, unsigned n);
1818 __isl_give isl_basic_map *isl_basic_map_eliminate(
1819 __isl_take isl_basic_map *bmap,
1820 enum isl_dim_type type,
1821 unsigned first, unsigned n);
1822 __isl_give isl_map *isl_map_eliminate(
1823 __isl_take isl_map *map, enum isl_dim_type type,
1824 unsigned first, unsigned n);
1826 Eliminate the coefficients for the given dimensions from the constraints,
1827 without removing the dimensions.
1831 __isl_give isl_basic_set *isl_basic_set_fix(
1832 __isl_take isl_basic_set *bset,
1833 enum isl_dim_type type, unsigned pos,
1835 __isl_give isl_basic_set *isl_basic_set_fix_si(
1836 __isl_take isl_basic_set *bset,
1837 enum isl_dim_type type, unsigned pos, int value);
1838 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1839 enum isl_dim_type type, unsigned pos,
1841 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1842 enum isl_dim_type type, unsigned pos, int value);
1843 __isl_give isl_basic_map *isl_basic_map_fix_si(
1844 __isl_take isl_basic_map *bmap,
1845 enum isl_dim_type type, unsigned pos, int value);
1846 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1847 enum isl_dim_type type, unsigned pos, int value);
1849 Intersect the set or relation with the hyperplane where the given
1850 dimension has the fixed given value.
1852 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1853 __isl_take isl_basic_map *bmap,
1854 enum isl_dim_type type, unsigned pos, int value);
1855 __isl_give isl_set *isl_set_lower_bound_si(
1856 __isl_take isl_set *set,
1857 enum isl_dim_type type, unsigned pos, int value);
1858 __isl_give isl_map *isl_map_lower_bound_si(
1859 __isl_take isl_map *map,
1860 enum isl_dim_type type, unsigned pos, int value);
1861 __isl_give isl_set *isl_set_upper_bound_si(
1862 __isl_take isl_set *set,
1863 enum isl_dim_type type, unsigned pos, int value);
1864 __isl_give isl_map *isl_map_upper_bound_si(
1865 __isl_take isl_map *map,
1866 enum isl_dim_type type, unsigned pos, int value);
1868 Intersect the set or relation with the half-space where the given
1869 dimension has a value bounded the fixed given value.
1871 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1872 enum isl_dim_type type1, int pos1,
1873 enum isl_dim_type type2, int pos2);
1874 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1875 enum isl_dim_type type1, int pos1,
1876 enum isl_dim_type type2, int pos2);
1878 Intersect the set or relation with the hyperplane where the given
1879 dimensions are equal to each other.
1881 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1882 enum isl_dim_type type1, int pos1,
1883 enum isl_dim_type type2, int pos2);
1885 Intersect the relation with the hyperplane where the given
1886 dimensions have opposite values.
1890 __isl_give isl_map *isl_set_identity(
1891 __isl_take isl_set *set);
1892 __isl_give isl_union_map *isl_union_set_identity(
1893 __isl_take isl_union_set *uset);
1895 Construct an identity relation on the given (union) set.
1899 __isl_give isl_basic_set *isl_basic_map_deltas(
1900 __isl_take isl_basic_map *bmap);
1901 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1902 __isl_give isl_union_set *isl_union_map_deltas(
1903 __isl_take isl_union_map *umap);
1905 These functions return a (basic) set containing the differences
1906 between image elements and corresponding domain elements in the input.
1908 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1909 __isl_take isl_basic_map *bmap);
1910 __isl_give isl_map *isl_map_deltas_map(
1911 __isl_take isl_map *map);
1912 __isl_give isl_union_map *isl_union_map_deltas_map(
1913 __isl_take isl_union_map *umap);
1915 The functions above construct a (basic, regular or union) relation
1916 that maps (a wrapped version of) the input relation to its delta set.
1920 Simplify the representation of a set or relation by trying
1921 to combine pairs of basic sets or relations into a single
1922 basic set or relation.
1924 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1925 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1926 __isl_give isl_union_set *isl_union_set_coalesce(
1927 __isl_take isl_union_set *uset);
1928 __isl_give isl_union_map *isl_union_map_coalesce(
1929 __isl_take isl_union_map *umap);
1931 =item * Detecting equalities
1933 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1934 __isl_take isl_basic_set *bset);
1935 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1936 __isl_take isl_basic_map *bmap);
1937 __isl_give isl_set *isl_set_detect_equalities(
1938 __isl_take isl_set *set);
1939 __isl_give isl_map *isl_map_detect_equalities(
1940 __isl_take isl_map *map);
1941 __isl_give isl_union_set *isl_union_set_detect_equalities(
1942 __isl_take isl_union_set *uset);
1943 __isl_give isl_union_map *isl_union_map_detect_equalities(
1944 __isl_take isl_union_map *umap);
1946 Simplify the representation of a set or relation by detecting implicit
1949 =item * Removing redundant constraints
1951 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1952 __isl_take isl_basic_set *bset);
1953 __isl_give isl_set *isl_set_remove_redundancies(
1954 __isl_take isl_set *set);
1955 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1956 __isl_take isl_basic_map *bmap);
1957 __isl_give isl_map *isl_map_remove_redundancies(
1958 __isl_take isl_map *map);
1962 __isl_give isl_basic_set *isl_set_convex_hull(
1963 __isl_take isl_set *set);
1964 __isl_give isl_basic_map *isl_map_convex_hull(
1965 __isl_take isl_map *map);
1967 If the input set or relation has any existentially quantified
1968 variables, then the result of these operations is currently undefined.
1972 __isl_give isl_basic_set *isl_set_simple_hull(
1973 __isl_take isl_set *set);
1974 __isl_give isl_basic_map *isl_map_simple_hull(
1975 __isl_take isl_map *map);
1976 __isl_give isl_union_map *isl_union_map_simple_hull(
1977 __isl_take isl_union_map *umap);
1979 These functions compute a single basic set or relation
1980 that contains the whole input set or relation.
1981 In particular, the output is described by translates
1982 of the constraints describing the basic sets or relations in the input.
1986 (See \autoref{s:simple hull}.)
1992 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1993 __isl_take isl_basic_set *bset);
1994 __isl_give isl_basic_set *isl_set_affine_hull(
1995 __isl_take isl_set *set);
1996 __isl_give isl_union_set *isl_union_set_affine_hull(
1997 __isl_take isl_union_set *uset);
1998 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1999 __isl_take isl_basic_map *bmap);
2000 __isl_give isl_basic_map *isl_map_affine_hull(
2001 __isl_take isl_map *map);
2002 __isl_give isl_union_map *isl_union_map_affine_hull(
2003 __isl_take isl_union_map *umap);
2005 In case of union sets and relations, the affine hull is computed
2008 =item * Polyhedral hull
2010 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2011 __isl_take isl_set *set);
2012 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2013 __isl_take isl_map *map);
2014 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2015 __isl_take isl_union_set *uset);
2016 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2017 __isl_take isl_union_map *umap);
2019 These functions compute a single basic set or relation
2020 not involving any existentially quantified variables
2021 that contains the whole input set or relation.
2022 In case of union sets and relations, the polyhedral hull is computed
2025 =item * Optimization
2027 #include <isl/ilp.h>
2028 enum isl_lp_result isl_basic_set_max(
2029 __isl_keep isl_basic_set *bset,
2030 __isl_keep isl_aff *obj, isl_int *opt)
2031 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2032 __isl_keep isl_aff *obj, isl_int *opt);
2033 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2034 __isl_keep isl_aff *obj, isl_int *opt);
2036 Compute the minimum or maximum of the integer affine expression C<obj>
2037 over the points in C<set>, returning the result in C<opt>.
2038 The return value may be one of C<isl_lp_error>,
2039 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2041 =item * Parametric optimization
2043 __isl_give isl_pw_aff *isl_set_dim_min(
2044 __isl_take isl_set *set, int pos);
2045 __isl_give isl_pw_aff *isl_set_dim_max(
2046 __isl_take isl_set *set, int pos);
2047 __isl_give isl_pw_aff *isl_map_dim_max(
2048 __isl_take isl_map *map, int pos);
2050 Compute the minimum or maximum of the given set or output dimension
2051 as a function of the parameters (and input dimensions), but independently
2052 of the other set or output dimensions.
2053 For lexicographic optimization, see L<"Lexicographic Optimization">.
2057 The following functions compute either the set of (rational) coefficient
2058 values of valid constraints for the given set or the set of (rational)
2059 values satisfying the constraints with coefficients from the given set.
2060 Internally, these two sets of functions perform essentially the
2061 same operations, except that the set of coefficients is assumed to
2062 be a cone, while the set of values may be any polyhedron.
2063 The current implementation is based on the Farkas lemma and
2064 Fourier-Motzkin elimination, but this may change or be made optional
2065 in future. In particular, future implementations may use different
2066 dualization algorithms or skip the elimination step.
2068 __isl_give isl_basic_set *isl_basic_set_coefficients(
2069 __isl_take isl_basic_set *bset);
2070 __isl_give isl_basic_set *isl_set_coefficients(
2071 __isl_take isl_set *set);
2072 __isl_give isl_union_set *isl_union_set_coefficients(
2073 __isl_take isl_union_set *bset);
2074 __isl_give isl_basic_set *isl_basic_set_solutions(
2075 __isl_take isl_basic_set *bset);
2076 __isl_give isl_basic_set *isl_set_solutions(
2077 __isl_take isl_set *set);
2078 __isl_give isl_union_set *isl_union_set_solutions(
2079 __isl_take isl_union_set *bset);
2083 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2085 __isl_give isl_union_map *isl_union_map_power(
2086 __isl_take isl_union_map *umap, int *exact);
2088 Compute a parametric representation for all positive powers I<k> of C<map>.
2089 The result maps I<k> to a nested relation corresponding to the
2090 I<k>th power of C<map>.
2091 The result may be an overapproximation. If the result is known to be exact,
2092 then C<*exact> is set to C<1>.
2094 =item * Transitive closure
2096 __isl_give isl_map *isl_map_transitive_closure(
2097 __isl_take isl_map *map, int *exact);
2098 __isl_give isl_union_map *isl_union_map_transitive_closure(
2099 __isl_take isl_union_map *umap, int *exact);
2101 Compute the transitive closure of C<map>.
2102 The result may be an overapproximation. If the result is known to be exact,
2103 then C<*exact> is set to C<1>.
2105 =item * Reaching path lengths
2107 __isl_give isl_map *isl_map_reaching_path_lengths(
2108 __isl_take isl_map *map, int *exact);
2110 Compute a relation that maps each element in the range of C<map>
2111 to the lengths of all paths composed of edges in C<map> that
2112 end up in the given element.
2113 The result may be an overapproximation. If the result is known to be exact,
2114 then C<*exact> is set to C<1>.
2115 To compute the I<maximal> path length, the resulting relation
2116 should be postprocessed by C<isl_map_lexmax>.
2117 In particular, if the input relation is a dependence relation
2118 (mapping sources to sinks), then the maximal path length corresponds
2119 to the free schedule.
2120 Note, however, that C<isl_map_lexmax> expects the maximum to be
2121 finite, so if the path lengths are unbounded (possibly due to
2122 the overapproximation), then you will get an error message.
2126 __isl_give isl_basic_set *isl_basic_map_wrap(
2127 __isl_take isl_basic_map *bmap);
2128 __isl_give isl_set *isl_map_wrap(
2129 __isl_take isl_map *map);
2130 __isl_give isl_union_set *isl_union_map_wrap(
2131 __isl_take isl_union_map *umap);
2132 __isl_give isl_basic_map *isl_basic_set_unwrap(
2133 __isl_take isl_basic_set *bset);
2134 __isl_give isl_map *isl_set_unwrap(
2135 __isl_take isl_set *set);
2136 __isl_give isl_union_map *isl_union_set_unwrap(
2137 __isl_take isl_union_set *uset);
2141 Remove any internal structure of domain (and range) of the given
2142 set or relation. If there is any such internal structure in the input,
2143 then the name of the space is also removed.
2145 __isl_give isl_basic_set *isl_basic_set_flatten(
2146 __isl_take isl_basic_set *bset);
2147 __isl_give isl_set *isl_set_flatten(
2148 __isl_take isl_set *set);
2149 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2150 __isl_take isl_basic_map *bmap);
2151 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2152 __isl_take isl_basic_map *bmap);
2153 __isl_give isl_map *isl_map_flatten_range(
2154 __isl_take isl_map *map);
2155 __isl_give isl_map *isl_map_flatten_domain(
2156 __isl_take isl_map *map);
2157 __isl_give isl_basic_map *isl_basic_map_flatten(
2158 __isl_take isl_basic_map *bmap);
2159 __isl_give isl_map *isl_map_flatten(
2160 __isl_take isl_map *map);
2162 __isl_give isl_map *isl_set_flatten_map(
2163 __isl_take isl_set *set);
2165 The function above constructs a relation
2166 that maps the input set to a flattened version of the set.
2170 Lift the input set to a space with extra dimensions corresponding
2171 to the existentially quantified variables in the input.
2172 In particular, the result lives in a wrapped map where the domain
2173 is the original space and the range corresponds to the original
2174 existentially quantified variables.
2176 __isl_give isl_basic_set *isl_basic_set_lift(
2177 __isl_take isl_basic_set *bset);
2178 __isl_give isl_set *isl_set_lift(
2179 __isl_take isl_set *set);
2180 __isl_give isl_union_set *isl_union_set_lift(
2181 __isl_take isl_union_set *uset);
2183 Given a local space that contains the existentially quantified
2184 variables of a set, a basic relation that, when applied to
2185 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2186 can be constructed using the following function.
2188 #include <isl/local_space.h>
2189 __isl_give isl_basic_map *isl_local_space_lifting(
2190 __isl_take isl_local_space *ls);
2192 =item * Internal Product
2194 __isl_give isl_basic_map *isl_basic_map_zip(
2195 __isl_take isl_basic_map *bmap);
2196 __isl_give isl_map *isl_map_zip(
2197 __isl_take isl_map *map);
2198 __isl_give isl_union_map *isl_union_map_zip(
2199 __isl_take isl_union_map *umap);
2201 Given a relation with nested relations for domain and range,
2202 interchange the range of the domain with the domain of the range.
2204 =item * Aligning parameters
2206 __isl_give isl_set *isl_set_align_params(
2207 __isl_take isl_set *set,
2208 __isl_take isl_space *model);
2209 __isl_give isl_map *isl_map_align_params(
2210 __isl_take isl_map *map,
2211 __isl_take isl_space *model);
2213 Change the order of the parameters of the given set or relation
2214 such that the first parameters match those of C<model>.
2215 This may involve the introduction of extra parameters.
2216 All parameters need to be named.
2218 =item * Dimension manipulation
2220 __isl_give isl_set *isl_set_add_dims(
2221 __isl_take isl_set *set,
2222 enum isl_dim_type type, unsigned n);
2223 __isl_give isl_map *isl_map_add_dims(
2224 __isl_take isl_map *map,
2225 enum isl_dim_type type, unsigned n);
2226 __isl_give isl_set *isl_set_insert_dims(
2227 __isl_take isl_set *set,
2228 enum isl_dim_type type, unsigned pos, unsigned n);
2229 __isl_give isl_map *isl_map_insert_dims(
2230 __isl_take isl_map *map,
2231 enum isl_dim_type type, unsigned pos, unsigned n);
2232 __isl_give isl_basic_set *isl_basic_set_move_dims(
2233 __isl_take isl_basic_set *bset,
2234 enum isl_dim_type dst_type, unsigned dst_pos,
2235 enum isl_dim_type src_type, unsigned src_pos,
2237 __isl_give isl_basic_map *isl_basic_map_move_dims(
2238 __isl_take isl_basic_map *bmap,
2239 enum isl_dim_type dst_type, unsigned dst_pos,
2240 enum isl_dim_type src_type, unsigned src_pos,
2242 __isl_give isl_set *isl_set_move_dims(
2243 __isl_take isl_set *set,
2244 enum isl_dim_type dst_type, unsigned dst_pos,
2245 enum isl_dim_type src_type, unsigned src_pos,
2247 __isl_give isl_map *isl_map_move_dims(
2248 __isl_take isl_map *map,
2249 enum isl_dim_type dst_type, unsigned dst_pos,
2250 enum isl_dim_type src_type, unsigned src_pos,
2253 It is usually not advisable to directly change the (input or output)
2254 space of a set or a relation as this removes the name and the internal
2255 structure of the space. However, the above functions can be useful
2256 to add new parameters, assuming
2257 C<isl_set_align_params> and C<isl_map_align_params>
2262 =head2 Binary Operations
2264 The two arguments of a binary operation not only need to live
2265 in the same C<isl_ctx>, they currently also need to have
2266 the same (number of) parameters.
2268 =head3 Basic Operations
2272 =item * Intersection
2274 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2275 __isl_take isl_basic_set *bset1,
2276 __isl_take isl_basic_set *bset2);
2277 __isl_give isl_basic_set *isl_basic_set_intersect(
2278 __isl_take isl_basic_set *bset1,
2279 __isl_take isl_basic_set *bset2);
2280 __isl_give isl_set *isl_set_intersect_params(
2281 __isl_take isl_set *set,
2282 __isl_take isl_set *params);
2283 __isl_give isl_set *isl_set_intersect(
2284 __isl_take isl_set *set1,
2285 __isl_take isl_set *set2);
2286 __isl_give isl_union_set *isl_union_set_intersect_params(
2287 __isl_take isl_union_set *uset,
2288 __isl_take isl_set *set);
2289 __isl_give isl_union_map *isl_union_map_intersect_params(
2290 __isl_take isl_union_map *umap,
2291 __isl_take isl_set *set);
2292 __isl_give isl_union_set *isl_union_set_intersect(
2293 __isl_take isl_union_set *uset1,
2294 __isl_take isl_union_set *uset2);
2295 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2296 __isl_take isl_basic_map *bmap,
2297 __isl_take isl_basic_set *bset);
2298 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2299 __isl_take isl_basic_map *bmap,
2300 __isl_take isl_basic_set *bset);
2301 __isl_give isl_basic_map *isl_basic_map_intersect(
2302 __isl_take isl_basic_map *bmap1,
2303 __isl_take isl_basic_map *bmap2);
2304 __isl_give isl_map *isl_map_intersect_params(
2305 __isl_take isl_map *map,
2306 __isl_take isl_set *params);
2307 __isl_give isl_map *isl_map_intersect_domain(
2308 __isl_take isl_map *map,
2309 __isl_take isl_set *set);
2310 __isl_give isl_map *isl_map_intersect_range(
2311 __isl_take isl_map *map,
2312 __isl_take isl_set *set);
2313 __isl_give isl_map *isl_map_intersect(
2314 __isl_take isl_map *map1,
2315 __isl_take isl_map *map2);
2316 __isl_give isl_union_map *isl_union_map_intersect_domain(
2317 __isl_take isl_union_map *umap,
2318 __isl_take isl_union_set *uset);
2319 __isl_give isl_union_map *isl_union_map_intersect_range(
2320 __isl_take isl_union_map *umap,
2321 __isl_take isl_union_set *uset);
2322 __isl_give isl_union_map *isl_union_map_intersect(
2323 __isl_take isl_union_map *umap1,
2324 __isl_take isl_union_map *umap2);
2328 __isl_give isl_set *isl_basic_set_union(
2329 __isl_take isl_basic_set *bset1,
2330 __isl_take isl_basic_set *bset2);
2331 __isl_give isl_map *isl_basic_map_union(
2332 __isl_take isl_basic_map *bmap1,
2333 __isl_take isl_basic_map *bmap2);
2334 __isl_give isl_set *isl_set_union(
2335 __isl_take isl_set *set1,
2336 __isl_take isl_set *set2);
2337 __isl_give isl_map *isl_map_union(
2338 __isl_take isl_map *map1,
2339 __isl_take isl_map *map2);
2340 __isl_give isl_union_set *isl_union_set_union(
2341 __isl_take isl_union_set *uset1,
2342 __isl_take isl_union_set *uset2);
2343 __isl_give isl_union_map *isl_union_map_union(
2344 __isl_take isl_union_map *umap1,
2345 __isl_take isl_union_map *umap2);
2347 =item * Set difference
2349 __isl_give isl_set *isl_set_subtract(
2350 __isl_take isl_set *set1,
2351 __isl_take isl_set *set2);
2352 __isl_give isl_map *isl_map_subtract(
2353 __isl_take isl_map *map1,
2354 __isl_take isl_map *map2);
2355 __isl_give isl_map *isl_map_subtract_domain(
2356 __isl_take isl_map *map,
2357 __isl_take isl_set *dom);
2358 __isl_give isl_map *isl_map_subtract_range(
2359 __isl_take isl_map *map,
2360 __isl_take isl_set *dom);
2361 __isl_give isl_union_set *isl_union_set_subtract(
2362 __isl_take isl_union_set *uset1,
2363 __isl_take isl_union_set *uset2);
2364 __isl_give isl_union_map *isl_union_map_subtract(
2365 __isl_take isl_union_map *umap1,
2366 __isl_take isl_union_map *umap2);
2370 __isl_give isl_basic_set *isl_basic_set_apply(
2371 __isl_take isl_basic_set *bset,
2372 __isl_take isl_basic_map *bmap);
2373 __isl_give isl_set *isl_set_apply(
2374 __isl_take isl_set *set,
2375 __isl_take isl_map *map);
2376 __isl_give isl_union_set *isl_union_set_apply(
2377 __isl_take isl_union_set *uset,
2378 __isl_take isl_union_map *umap);
2379 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2380 __isl_take isl_basic_map *bmap1,
2381 __isl_take isl_basic_map *bmap2);
2382 __isl_give isl_basic_map *isl_basic_map_apply_range(
2383 __isl_take isl_basic_map *bmap1,
2384 __isl_take isl_basic_map *bmap2);
2385 __isl_give isl_map *isl_map_apply_domain(
2386 __isl_take isl_map *map1,
2387 __isl_take isl_map *map2);
2388 __isl_give isl_union_map *isl_union_map_apply_domain(
2389 __isl_take isl_union_map *umap1,
2390 __isl_take isl_union_map *umap2);
2391 __isl_give isl_map *isl_map_apply_range(
2392 __isl_take isl_map *map1,
2393 __isl_take isl_map *map2);
2394 __isl_give isl_union_map *isl_union_map_apply_range(
2395 __isl_take isl_union_map *umap1,
2396 __isl_take isl_union_map *umap2);
2398 =item * Cartesian Product
2400 __isl_give isl_set *isl_set_product(
2401 __isl_take isl_set *set1,
2402 __isl_take isl_set *set2);
2403 __isl_give isl_union_set *isl_union_set_product(
2404 __isl_take isl_union_set *uset1,
2405 __isl_take isl_union_set *uset2);
2406 __isl_give isl_basic_map *isl_basic_map_domain_product(
2407 __isl_take isl_basic_map *bmap1,
2408 __isl_take isl_basic_map *bmap2);
2409 __isl_give isl_basic_map *isl_basic_map_range_product(
2410 __isl_take isl_basic_map *bmap1,
2411 __isl_take isl_basic_map *bmap2);
2412 __isl_give isl_map *isl_map_domain_product(
2413 __isl_take isl_map *map1,
2414 __isl_take isl_map *map2);
2415 __isl_give isl_map *isl_map_range_product(
2416 __isl_take isl_map *map1,
2417 __isl_take isl_map *map2);
2418 __isl_give isl_union_map *isl_union_map_range_product(
2419 __isl_take isl_union_map *umap1,
2420 __isl_take isl_union_map *umap2);
2421 __isl_give isl_map *isl_map_product(
2422 __isl_take isl_map *map1,
2423 __isl_take isl_map *map2);
2424 __isl_give isl_union_map *isl_union_map_product(
2425 __isl_take isl_union_map *umap1,
2426 __isl_take isl_union_map *umap2);
2428 The above functions compute the cross product of the given
2429 sets or relations. The domains and ranges of the results
2430 are wrapped maps between domains and ranges of the inputs.
2431 To obtain a ``flat'' product, use the following functions
2434 __isl_give isl_basic_set *isl_basic_set_flat_product(
2435 __isl_take isl_basic_set *bset1,
2436 __isl_take isl_basic_set *bset2);
2437 __isl_give isl_set *isl_set_flat_product(
2438 __isl_take isl_set *set1,
2439 __isl_take isl_set *set2);
2440 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2441 __isl_take isl_basic_map *bmap1,
2442 __isl_take isl_basic_map *bmap2);
2443 __isl_give isl_map *isl_map_flat_domain_product(
2444 __isl_take isl_map *map1,
2445 __isl_take isl_map *map2);
2446 __isl_give isl_map *isl_map_flat_range_product(
2447 __isl_take isl_map *map1,
2448 __isl_take isl_map *map2);
2449 __isl_give isl_union_map *isl_union_map_flat_range_product(
2450 __isl_take isl_union_map *umap1,
2451 __isl_take isl_union_map *umap2);
2452 __isl_give isl_basic_map *isl_basic_map_flat_product(
2453 __isl_take isl_basic_map *bmap1,
2454 __isl_take isl_basic_map *bmap2);
2455 __isl_give isl_map *isl_map_flat_product(
2456 __isl_take isl_map *map1,
2457 __isl_take isl_map *map2);
2459 =item * Simplification
2461 __isl_give isl_basic_set *isl_basic_set_gist(
2462 __isl_take isl_basic_set *bset,
2463 __isl_take isl_basic_set *context);
2464 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2465 __isl_take isl_set *context);
2466 __isl_give isl_set *isl_set_gist_params(
2467 __isl_take isl_set *set,
2468 __isl_take isl_set *context);
2469 __isl_give isl_union_set *isl_union_set_gist(
2470 __isl_take isl_union_set *uset,
2471 __isl_take isl_union_set *context);
2472 __isl_give isl_union_set *isl_union_set_gist_params(
2473 __isl_take isl_union_set *uset,
2474 __isl_take isl_set *set);
2475 __isl_give isl_basic_map *isl_basic_map_gist(
2476 __isl_take isl_basic_map *bmap,
2477 __isl_take isl_basic_map *context);
2478 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2479 __isl_take isl_map *context);
2480 __isl_give isl_map *isl_map_gist_params(
2481 __isl_take isl_map *map,
2482 __isl_take isl_set *context);
2483 __isl_give isl_map *isl_map_gist_domain(
2484 __isl_take isl_map *map,
2485 __isl_take isl_set *context);
2486 __isl_give isl_map *isl_map_gist_range(
2487 __isl_take isl_map *map,
2488 __isl_take isl_set *context);
2489 __isl_give isl_union_map *isl_union_map_gist(
2490 __isl_take isl_union_map *umap,
2491 __isl_take isl_union_map *context);
2492 __isl_give isl_union_map *isl_union_map_gist_params(
2493 __isl_take isl_union_map *umap,
2494 __isl_take isl_set *set);
2495 __isl_give isl_union_map *isl_union_map_gist_domain(
2496 __isl_take isl_union_map *umap,
2497 __isl_take isl_union_set *uset);
2498 __isl_give isl_union_map *isl_union_map_gist_range(
2499 __isl_take isl_union_map *umap,
2500 __isl_take isl_union_set *uset);
2502 The gist operation returns a set or relation that has the
2503 same intersection with the context as the input set or relation.
2504 Any implicit equality in the intersection is made explicit in the result,
2505 while all inequalities that are redundant with respect to the intersection
2507 In case of union sets and relations, the gist operation is performed
2512 =head3 Lexicographic Optimization
2514 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2515 the following functions
2516 compute a set that contains the lexicographic minimum or maximum
2517 of the elements in C<set> (or C<bset>) for those values of the parameters
2518 that satisfy C<dom>.
2519 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2520 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2522 In other words, the union of the parameter values
2523 for which the result is non-empty and of C<*empty>
2526 __isl_give isl_set *isl_basic_set_partial_lexmin(
2527 __isl_take isl_basic_set *bset,
2528 __isl_take isl_basic_set *dom,
2529 __isl_give isl_set **empty);
2530 __isl_give isl_set *isl_basic_set_partial_lexmax(
2531 __isl_take isl_basic_set *bset,
2532 __isl_take isl_basic_set *dom,
2533 __isl_give isl_set **empty);
2534 __isl_give isl_set *isl_set_partial_lexmin(
2535 __isl_take isl_set *set, __isl_take isl_set *dom,
2536 __isl_give isl_set **empty);
2537 __isl_give isl_set *isl_set_partial_lexmax(
2538 __isl_take isl_set *set, __isl_take isl_set *dom,
2539 __isl_give isl_set **empty);
2541 Given a (basic) set C<set> (or C<bset>), the following functions simply
2542 return a set containing the lexicographic minimum or maximum
2543 of the elements in C<set> (or C<bset>).
2544 In case of union sets, the optimum is computed per space.
2546 __isl_give isl_set *isl_basic_set_lexmin(
2547 __isl_take isl_basic_set *bset);
2548 __isl_give isl_set *isl_basic_set_lexmax(
2549 __isl_take isl_basic_set *bset);
2550 __isl_give isl_set *isl_set_lexmin(
2551 __isl_take isl_set *set);
2552 __isl_give isl_set *isl_set_lexmax(
2553 __isl_take isl_set *set);
2554 __isl_give isl_union_set *isl_union_set_lexmin(
2555 __isl_take isl_union_set *uset);
2556 __isl_give isl_union_set *isl_union_set_lexmax(
2557 __isl_take isl_union_set *uset);
2559 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2560 the following functions
2561 compute a relation that maps each element of C<dom>
2562 to the single lexicographic minimum or maximum
2563 of the elements that are associated to that same
2564 element in C<map> (or C<bmap>).
2565 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2566 that contains the elements in C<dom> that do not map
2567 to any elements in C<map> (or C<bmap>).
2568 In other words, the union of the domain of the result and of C<*empty>
2571 __isl_give isl_map *isl_basic_map_partial_lexmax(
2572 __isl_take isl_basic_map *bmap,
2573 __isl_take isl_basic_set *dom,
2574 __isl_give isl_set **empty);
2575 __isl_give isl_map *isl_basic_map_partial_lexmin(
2576 __isl_take isl_basic_map *bmap,
2577 __isl_take isl_basic_set *dom,
2578 __isl_give isl_set **empty);
2579 __isl_give isl_map *isl_map_partial_lexmax(
2580 __isl_take isl_map *map, __isl_take isl_set *dom,
2581 __isl_give isl_set **empty);
2582 __isl_give isl_map *isl_map_partial_lexmin(
2583 __isl_take isl_map *map, __isl_take isl_set *dom,
2584 __isl_give isl_set **empty);
2586 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2587 return a map mapping each element in the domain of
2588 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2589 of all elements associated to that element.
2590 In case of union relations, the optimum is computed per space.
2592 __isl_give isl_map *isl_basic_map_lexmin(
2593 __isl_take isl_basic_map *bmap);
2594 __isl_give isl_map *isl_basic_map_lexmax(
2595 __isl_take isl_basic_map *bmap);
2596 __isl_give isl_map *isl_map_lexmin(
2597 __isl_take isl_map *map);
2598 __isl_give isl_map *isl_map_lexmax(
2599 __isl_take isl_map *map);
2600 __isl_give isl_union_map *isl_union_map_lexmin(
2601 __isl_take isl_union_map *umap);
2602 __isl_give isl_union_map *isl_union_map_lexmax(
2603 __isl_take isl_union_map *umap);
2605 The following functions return their result in the form of
2606 a piecewise multi-affine expression
2607 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2608 but are otherwise equivalent to the corresponding functions
2609 returning a basic set or relation.
2611 __isl_give isl_pw_multi_aff *
2612 isl_basic_map_lexmin_pw_multi_aff(
2613 __isl_take isl_basic_map *bmap);
2614 __isl_give isl_pw_multi_aff *
2615 isl_basic_set_partial_lexmin_pw_multi_aff(
2616 __isl_take isl_basic_set *bset,
2617 __isl_take isl_basic_set *dom,
2618 __isl_give isl_set **empty);
2619 __isl_give isl_pw_multi_aff *
2620 isl_basic_set_partial_lexmax_pw_multi_aff(
2621 __isl_take isl_basic_set *bset,
2622 __isl_take isl_basic_set *dom,
2623 __isl_give isl_set **empty);
2624 __isl_give isl_pw_multi_aff *
2625 isl_basic_map_partial_lexmin_pw_multi_aff(
2626 __isl_take isl_basic_map *bmap,
2627 __isl_take isl_basic_set *dom,
2628 __isl_give isl_set **empty);
2629 __isl_give isl_pw_multi_aff *
2630 isl_basic_map_partial_lexmax_pw_multi_aff(
2631 __isl_take isl_basic_map *bmap,
2632 __isl_take isl_basic_set *dom,
2633 __isl_give isl_set **empty);
2637 Lists are defined over several element types, including
2638 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2639 Here we take lists of C<isl_set>s as an example.
2640 Lists can be created, copied and freed using the following functions.
2642 #include <isl/list.h>
2643 __isl_give isl_set_list *isl_set_list_from_set(
2644 __isl_take isl_set *el);
2645 __isl_give isl_set_list *isl_set_list_alloc(
2646 isl_ctx *ctx, int n);
2647 __isl_give isl_set_list *isl_set_list_copy(
2648 __isl_keep isl_set_list *list);
2649 __isl_give isl_set_list *isl_set_list_add(
2650 __isl_take isl_set_list *list,
2651 __isl_take isl_set *el);
2652 __isl_give isl_set_list *isl_set_list_concat(
2653 __isl_take isl_set_list *list1,
2654 __isl_take isl_set_list *list2);
2655 void *isl_set_list_free(__isl_take isl_set_list *list);
2657 C<isl_set_list_alloc> creates an empty list with a capacity for
2658 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2661 Lists can be inspected using the following functions.
2663 #include <isl/list.h>
2664 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2665 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2666 __isl_give isl_set *isl_set_list_get_set(
2667 __isl_keep isl_set_list *list, int index);
2668 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2669 int (*fn)(__isl_take isl_set *el, void *user),
2672 Lists can be printed using
2674 #include <isl/list.h>
2675 __isl_give isl_printer *isl_printer_print_set_list(
2676 __isl_take isl_printer *p,
2677 __isl_keep isl_set_list *list);
2681 Matrices can be created, copied and freed using the following functions.
2683 #include <isl/mat.h>
2684 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2685 unsigned n_row, unsigned n_col);
2686 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2687 void isl_mat_free(__isl_take isl_mat *mat);
2689 Note that the elements of a newly created matrix may have arbitrary values.
2690 The elements can be changed and inspected using the following functions.
2692 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2693 int isl_mat_rows(__isl_keep isl_mat *mat);
2694 int isl_mat_cols(__isl_keep isl_mat *mat);
2695 int isl_mat_get_element(__isl_keep isl_mat *mat,
2696 int row, int col, isl_int *v);
2697 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2698 int row, int col, isl_int v);
2699 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2700 int row, int col, int v);
2702 C<isl_mat_get_element> will return a negative value if anything went wrong.
2703 In that case, the value of C<*v> is undefined.
2705 The following function can be used to compute the (right) inverse
2706 of a matrix, i.e., a matrix such that the product of the original
2707 and the inverse (in that order) is a multiple of the identity matrix.
2708 The input matrix is assumed to be of full row-rank.
2710 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2712 The following function can be used to compute the (right) kernel
2713 (or null space) of a matrix, i.e., a matrix such that the product of
2714 the original and the kernel (in that order) is the zero matrix.
2716 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2718 =head2 Piecewise Quasi Affine Expressions
2720 The zero quasi affine expression on a given domain can be created using
2722 __isl_give isl_aff *isl_aff_zero_on_domain(
2723 __isl_take isl_local_space *ls);
2725 Note that the space in which the resulting object lives is a map space
2726 with the given space as domain and a one-dimensional range.
2728 An empty piecewise quasi affine expression (one with no cells)
2729 or a piecewise quasi affine expression with a single cell can
2730 be created using the following functions.
2732 #include <isl/aff.h>
2733 __isl_give isl_pw_aff *isl_pw_aff_empty(
2734 __isl_take isl_space *space);
2735 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2736 __isl_take isl_set *set, __isl_take isl_aff *aff);
2737 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2738 __isl_take isl_aff *aff);
2740 Quasi affine expressions can be copied and freed using
2742 #include <isl/aff.h>
2743 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2744 void *isl_aff_free(__isl_take isl_aff *aff);
2746 __isl_give isl_pw_aff *isl_pw_aff_copy(
2747 __isl_keep isl_pw_aff *pwaff);
2748 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2750 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2751 using the following function. The constraint is required to have
2752 a non-zero coefficient for the specified dimension.
2754 #include <isl/constraint.h>
2755 __isl_give isl_aff *isl_constraint_get_bound(
2756 __isl_keep isl_constraint *constraint,
2757 enum isl_dim_type type, int pos);
2759 The entire affine expression of the constraint can also be extracted
2760 using the following function.
2762 #include <isl/constraint.h>
2763 __isl_give isl_aff *isl_constraint_get_aff(
2764 __isl_keep isl_constraint *constraint);
2766 Conversely, an equality constraint equating
2767 the affine expression to zero or an inequality constraint enforcing
2768 the affine expression to be non-negative, can be constructed using
2770 __isl_give isl_constraint *isl_equality_from_aff(
2771 __isl_take isl_aff *aff);
2772 __isl_give isl_constraint *isl_inequality_from_aff(
2773 __isl_take isl_aff *aff);
2775 The expression can be inspected using
2777 #include <isl/aff.h>
2778 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2779 int isl_aff_dim(__isl_keep isl_aff *aff,
2780 enum isl_dim_type type);
2781 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2782 __isl_keep isl_aff *aff);
2783 __isl_give isl_local_space *isl_aff_get_local_space(
2784 __isl_keep isl_aff *aff);
2785 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2786 enum isl_dim_type type, unsigned pos);
2787 const char *isl_pw_aff_get_dim_name(
2788 __isl_keep isl_pw_aff *pa,
2789 enum isl_dim_type type, unsigned pos);
2790 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2791 enum isl_dim_type type, unsigned pos);
2792 __isl_give isl_id *isl_pw_aff_get_dim_id(
2793 __isl_keep isl_pw_aff *pa,
2794 enum isl_dim_type type, unsigned pos);
2795 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2797 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2798 enum isl_dim_type type, int pos, isl_int *v);
2799 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2801 __isl_give isl_aff *isl_aff_get_div(
2802 __isl_keep isl_aff *aff, int pos);
2804 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2805 int (*fn)(__isl_take isl_set *set,
2806 __isl_take isl_aff *aff,
2807 void *user), void *user);
2809 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2810 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2812 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2813 enum isl_dim_type type, unsigned first, unsigned n);
2814 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2815 enum isl_dim_type type, unsigned first, unsigned n);
2817 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2818 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2819 enum isl_dim_type type);
2820 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2822 It can be modified using
2824 #include <isl/aff.h>
2825 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2826 __isl_take isl_pw_aff *pwaff,
2827 enum isl_dim_type type, __isl_take isl_id *id);
2828 __isl_give isl_aff *isl_aff_set_dim_name(
2829 __isl_take isl_aff *aff, enum isl_dim_type type,
2830 unsigned pos, const char *s);
2831 __isl_give isl_aff *isl_aff_set_dim_id(
2832 __isl_take isl_aff *aff, enum isl_dim_type type,
2833 unsigned pos, __isl_take isl_id *id);
2834 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2835 __isl_take isl_pw_aff *pma,
2836 enum isl_dim_type type, unsigned pos,
2837 __isl_take isl_id *id);
2838 __isl_give isl_aff *isl_aff_set_constant(
2839 __isl_take isl_aff *aff, isl_int v);
2840 __isl_give isl_aff *isl_aff_set_constant_si(
2841 __isl_take isl_aff *aff, int v);
2842 __isl_give isl_aff *isl_aff_set_coefficient(
2843 __isl_take isl_aff *aff,
2844 enum isl_dim_type type, int pos, isl_int v);
2845 __isl_give isl_aff *isl_aff_set_coefficient_si(
2846 __isl_take isl_aff *aff,
2847 enum isl_dim_type type, int pos, int v);
2848 __isl_give isl_aff *isl_aff_set_denominator(
2849 __isl_take isl_aff *aff, isl_int v);
2851 __isl_give isl_aff *isl_aff_add_constant(
2852 __isl_take isl_aff *aff, isl_int v);
2853 __isl_give isl_aff *isl_aff_add_constant_si(
2854 __isl_take isl_aff *aff, int v);
2855 __isl_give isl_aff *isl_aff_add_coefficient(
2856 __isl_take isl_aff *aff,
2857 enum isl_dim_type type, int pos, isl_int v);
2858 __isl_give isl_aff *isl_aff_add_coefficient_si(
2859 __isl_take isl_aff *aff,
2860 enum isl_dim_type type, int pos, int v);
2862 __isl_give isl_aff *isl_aff_insert_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_insert_dims(
2866 __isl_take isl_pw_aff *pwaff,
2867 enum isl_dim_type type, unsigned first, unsigned n);
2868 __isl_give isl_aff *isl_aff_add_dims(
2869 __isl_take isl_aff *aff,
2870 enum isl_dim_type type, unsigned n);
2871 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2872 __isl_take isl_pw_aff *pwaff,
2873 enum isl_dim_type type, unsigned n);
2874 __isl_give isl_aff *isl_aff_drop_dims(
2875 __isl_take isl_aff *aff,
2876 enum isl_dim_type type, unsigned first, unsigned n);
2877 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2878 __isl_take isl_pw_aff *pwaff,
2879 enum isl_dim_type type, unsigned first, unsigned n);
2881 Note that the C<set_constant> and C<set_coefficient> functions
2882 set the I<numerator> of the constant or coefficient, while
2883 C<add_constant> and C<add_coefficient> add an integer value to
2884 the possibly rational constant or coefficient.
2886 To check whether an affine expressions is obviously zero
2887 or obviously equal to some other affine expression, use
2889 #include <isl/aff.h>
2890 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2891 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2892 __isl_keep isl_aff *aff2);
2893 int isl_pw_aff_plain_is_equal(
2894 __isl_keep isl_pw_aff *pwaff1,
2895 __isl_keep isl_pw_aff *pwaff2);
2899 #include <isl/aff.h>
2900 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2901 __isl_take isl_aff *aff2);
2902 __isl_give isl_pw_aff *isl_pw_aff_add(
2903 __isl_take isl_pw_aff *pwaff1,
2904 __isl_take isl_pw_aff *pwaff2);
2905 __isl_give isl_pw_aff *isl_pw_aff_min(
2906 __isl_take isl_pw_aff *pwaff1,
2907 __isl_take isl_pw_aff *pwaff2);
2908 __isl_give isl_pw_aff *isl_pw_aff_max(
2909 __isl_take isl_pw_aff *pwaff1,
2910 __isl_take isl_pw_aff *pwaff2);
2911 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2912 __isl_take isl_aff *aff2);
2913 __isl_give isl_pw_aff *isl_pw_aff_sub(
2914 __isl_take isl_pw_aff *pwaff1,
2915 __isl_take isl_pw_aff *pwaff2);
2916 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2917 __isl_give isl_pw_aff *isl_pw_aff_neg(
2918 __isl_take isl_pw_aff *pwaff);
2919 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2920 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2921 __isl_take isl_pw_aff *pwaff);
2922 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2923 __isl_give isl_pw_aff *isl_pw_aff_floor(
2924 __isl_take isl_pw_aff *pwaff);
2925 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2927 __isl_give isl_pw_aff *isl_pw_aff_mod(
2928 __isl_take isl_pw_aff *pwaff, isl_int mod);
2929 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
2931 __isl_give isl_pw_aff *isl_pw_aff_scale(
2932 __isl_take isl_pw_aff *pwaff, isl_int f);
2933 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
2935 __isl_give isl_aff *isl_aff_scale_down_ui(
2936 __isl_take isl_aff *aff, unsigned f);
2937 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
2938 __isl_take isl_pw_aff *pwaff, isl_int f);
2940 __isl_give isl_pw_aff *isl_pw_aff_list_min(
2941 __isl_take isl_pw_aff_list *list);
2942 __isl_give isl_pw_aff *isl_pw_aff_list_max(
2943 __isl_take isl_pw_aff_list *list);
2945 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
2946 __isl_take isl_pw_aff *pwqp);
2948 __isl_give isl_aff *isl_aff_align_params(
2949 __isl_take isl_aff *aff,
2950 __isl_take isl_space *model);
2951 __isl_give isl_pw_aff *isl_pw_aff_align_params(
2952 __isl_take isl_pw_aff *pwaff,
2953 __isl_take isl_space *model);
2955 __isl_give isl_aff *isl_aff_project_domain_on_params(
2956 __isl_take isl_aff *aff);
2958 __isl_give isl_aff *isl_aff_gist_params(
2959 __isl_take isl_aff *aff,
2960 __isl_take isl_set *context);
2961 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
2962 __isl_take isl_set *context);
2963 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
2964 __isl_take isl_pw_aff *pwaff,
2965 __isl_take isl_set *context);
2966 __isl_give isl_pw_aff *isl_pw_aff_gist(
2967 __isl_take isl_pw_aff *pwaff,
2968 __isl_take isl_set *context);
2970 __isl_give isl_set *isl_pw_aff_domain(
2971 __isl_take isl_pw_aff *pwaff);
2972 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
2973 __isl_take isl_pw_aff *pa,
2974 __isl_take isl_set *set);
2975 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
2976 __isl_take isl_pw_aff *pa,
2977 __isl_take isl_set *set);
2979 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
2980 __isl_take isl_aff *aff2);
2981 __isl_give isl_pw_aff *isl_pw_aff_mul(
2982 __isl_take isl_pw_aff *pwaff1,
2983 __isl_take isl_pw_aff *pwaff2);
2985 When multiplying two affine expressions, at least one of the two needs
2988 #include <isl/aff.h>
2989 __isl_give isl_basic_set *isl_aff_le_basic_set(
2990 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2991 __isl_give isl_basic_set *isl_aff_ge_basic_set(
2992 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
2993 __isl_give isl_set *isl_pw_aff_eq_set(
2994 __isl_take isl_pw_aff *pwaff1,
2995 __isl_take isl_pw_aff *pwaff2);
2996 __isl_give isl_set *isl_pw_aff_ne_set(
2997 __isl_take isl_pw_aff *pwaff1,
2998 __isl_take isl_pw_aff *pwaff2);
2999 __isl_give isl_set *isl_pw_aff_le_set(
3000 __isl_take isl_pw_aff *pwaff1,
3001 __isl_take isl_pw_aff *pwaff2);
3002 __isl_give isl_set *isl_pw_aff_lt_set(
3003 __isl_take isl_pw_aff *pwaff1,
3004 __isl_take isl_pw_aff *pwaff2);
3005 __isl_give isl_set *isl_pw_aff_ge_set(
3006 __isl_take isl_pw_aff *pwaff1,
3007 __isl_take isl_pw_aff *pwaff2);
3008 __isl_give isl_set *isl_pw_aff_gt_set(
3009 __isl_take isl_pw_aff *pwaff1,
3010 __isl_take isl_pw_aff *pwaff2);
3012 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_set(
3016 __isl_take isl_pw_aff_list *list1,
3017 __isl_take isl_pw_aff_list *list2);
3018 __isl_give isl_set *isl_pw_aff_list_le_set(
3019 __isl_take isl_pw_aff_list *list1,
3020 __isl_take isl_pw_aff_list *list2);
3021 __isl_give isl_set *isl_pw_aff_list_lt_set(
3022 __isl_take isl_pw_aff_list *list1,
3023 __isl_take isl_pw_aff_list *list2);
3024 __isl_give isl_set *isl_pw_aff_list_ge_set(
3025 __isl_take isl_pw_aff_list *list1,
3026 __isl_take isl_pw_aff_list *list2);
3027 __isl_give isl_set *isl_pw_aff_list_gt_set(
3028 __isl_take isl_pw_aff_list *list1,
3029 __isl_take isl_pw_aff_list *list2);
3031 The function C<isl_aff_ge_basic_set> returns a basic set
3032 containing those elements in the shared space
3033 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3034 The function C<isl_aff_ge_set> returns a set
3035 containing those elements in the shared domain
3036 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3037 The functions operating on C<isl_pw_aff_list> apply the corresponding
3038 C<isl_pw_aff> function to each pair of elements in the two lists.
3040 #include <isl/aff.h>
3041 __isl_give isl_set *isl_pw_aff_nonneg_set(
3042 __isl_take isl_pw_aff *pwaff);
3043 __isl_give isl_set *isl_pw_aff_zero_set(
3044 __isl_take isl_pw_aff *pwaff);
3045 __isl_give isl_set *isl_pw_aff_non_zero_set(
3046 __isl_take isl_pw_aff *pwaff);
3048 The function C<isl_pw_aff_nonneg_set> returns a set
3049 containing those elements in the domain
3050 of C<pwaff> where C<pwaff> is non-negative.
3052 #include <isl/aff.h>
3053 __isl_give isl_pw_aff *isl_pw_aff_cond(
3054 __isl_take isl_set *cond,
3055 __isl_take isl_pw_aff *pwaff_true,
3056 __isl_take isl_pw_aff *pwaff_false);
3058 The function C<isl_pw_aff_cond> performs a conditional operator
3059 and returns an expression that is equal to C<pwaff_true>
3060 for elements in C<cond> and equal to C<pwaff_false> for elements
3063 #include <isl/aff.h>
3064 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3065 __isl_take isl_pw_aff *pwaff1,
3066 __isl_take isl_pw_aff *pwaff2);
3067 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3068 __isl_take isl_pw_aff *pwaff1,
3069 __isl_take isl_pw_aff *pwaff2);
3070 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3071 __isl_take isl_pw_aff *pwaff1,
3072 __isl_take isl_pw_aff *pwaff2);
3074 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3075 expression with a domain that is the union of those of C<pwaff1> and
3076 C<pwaff2> and such that on each cell, the quasi-affine expression is
3077 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3078 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3079 associated expression is the defined one.
3081 An expression can be read from input using
3083 #include <isl/aff.h>
3084 __isl_give isl_aff *isl_aff_read_from_str(
3085 isl_ctx *ctx, const char *str);
3086 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3087 isl_ctx *ctx, const char *str);
3089 An expression can be printed using
3091 #include <isl/aff.h>
3092 __isl_give isl_printer *isl_printer_print_aff(
3093 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3095 __isl_give isl_printer *isl_printer_print_pw_aff(
3096 __isl_take isl_printer *p,
3097 __isl_keep isl_pw_aff *pwaff);
3099 =head2 Piecewise Multiple Quasi Affine Expressions
3101 An C<isl_multi_aff> object represents a sequence of
3102 zero or more affine expressions, all defined on the same domain space.
3104 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3107 #include <isl/aff.h>
3108 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3109 __isl_take isl_space *space,
3110 __isl_take isl_aff_list *list);
3112 An empty piecewise multiple quasi affine expression (one with no cells) or
3113 a piecewise multiple quasi affine expression with a single cell can
3114 be created using the following functions.
3116 #include <isl/aff.h>
3117 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3118 __isl_take isl_space *space);
3119 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3120 __isl_take isl_set *set,
3121 __isl_take isl_multi_aff *maff);
3123 A piecewise multiple quasi affine expression can also be initialized
3124 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3125 and the C<isl_map> is single-valued.
3127 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3128 __isl_take isl_set *set);
3129 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3130 __isl_take isl_map *map);
3132 Multiple quasi affine expressions can be copied and freed using
3134 #include <isl/aff.h>
3135 __isl_give isl_multi_aff *isl_multi_aff_copy(
3136 __isl_keep isl_multi_aff *maff);
3137 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3139 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3140 __isl_keep isl_pw_multi_aff *pma);
3141 void *isl_pw_multi_aff_free(
3142 __isl_take isl_pw_multi_aff *pma);
3144 The expression can be inspected using
3146 #include <isl/aff.h>
3147 isl_ctx *isl_multi_aff_get_ctx(
3148 __isl_keep isl_multi_aff *maff);
3149 isl_ctx *isl_pw_multi_aff_get_ctx(
3150 __isl_keep isl_pw_multi_aff *pma);
3151 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3152 enum isl_dim_type type);
3153 unsigned isl_pw_multi_aff_dim(
3154 __isl_keep isl_pw_multi_aff *pma,
3155 enum isl_dim_type type);
3156 __isl_give isl_aff *isl_multi_aff_get_aff(
3157 __isl_keep isl_multi_aff *multi, int pos);
3158 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3159 __isl_keep isl_pw_multi_aff *pma, int pos);
3160 const char *isl_pw_multi_aff_get_dim_name(
3161 __isl_keep isl_pw_multi_aff *pma,
3162 enum isl_dim_type type, unsigned pos);
3163 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3164 __isl_keep isl_pw_multi_aff *pma,
3165 enum isl_dim_type type, unsigned pos);
3166 const char *isl_multi_aff_get_tuple_name(
3167 __isl_keep isl_multi_aff *multi,
3168 enum isl_dim_type type);
3169 const char *isl_pw_multi_aff_get_tuple_name(
3170 __isl_keep isl_pw_multi_aff *pma,
3171 enum isl_dim_type type);
3172 int isl_pw_multi_aff_has_tuple_id(
3173 __isl_keep isl_pw_multi_aff *pma,
3174 enum isl_dim_type type);
3175 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3176 __isl_keep isl_pw_multi_aff *pma,
3177 enum isl_dim_type type);
3179 int isl_pw_multi_aff_foreach_piece(
3180 __isl_keep isl_pw_multi_aff *pma,
3181 int (*fn)(__isl_take isl_set *set,
3182 __isl_take isl_multi_aff *maff,
3183 void *user), void *user);
3185 It can be modified using
3187 #include <isl/aff.h>
3188 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3189 __isl_take isl_multi_aff *maff,
3190 enum isl_dim_type type, unsigned pos, const char *s);
3191 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3192 __isl_take isl_multi_aff *maff,
3193 enum isl_dim_type type, __isl_take isl_id *id);
3194 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3195 __isl_take isl_pw_multi_aff *pma,
3196 enum isl_dim_type type, __isl_take isl_id *id);
3198 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3199 __isl_take isl_multi_aff *maff,
3200 enum isl_dim_type type, unsigned first, unsigned n);
3202 To check whether two multiple affine expressions are
3203 obviously equal to each other, use
3205 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3206 __isl_keep isl_multi_aff *maff2);
3207 int isl_pw_multi_aff_plain_is_equal(
3208 __isl_keep isl_pw_multi_aff *pma1,
3209 __isl_keep isl_pw_multi_aff *pma2);
3213 #include <isl/aff.h>
3214 __isl_give isl_multi_aff *isl_multi_aff_add(
3215 __isl_take isl_multi_aff *maff1,
3216 __isl_take isl_multi_aff *maff2);
3217 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3218 __isl_take isl_pw_multi_aff *pma1,
3219 __isl_take isl_pw_multi_aff *pma2);
3220 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3221 __isl_take isl_pw_multi_aff *pma1,
3222 __isl_take isl_pw_multi_aff *pma2);
3223 __isl_give isl_multi_aff *isl_multi_aff_scale(
3224 __isl_take isl_multi_aff *maff,
3226 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3227 __isl_take isl_pw_multi_aff *pma,
3228 __isl_take isl_set *set);
3229 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3230 __isl_take isl_pw_multi_aff *pma,
3231 __isl_take isl_set *set);
3232 __isl_give isl_multi_aff *isl_multi_aff_lift(
3233 __isl_take isl_multi_aff *maff,
3234 __isl_give isl_local_space **ls);
3235 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3236 __isl_take isl_multi_aff *maff,
3237 __isl_take isl_set *context);
3238 __isl_give isl_multi_aff *isl_multi_aff_gist(
3239 __isl_take isl_multi_aff *maff,
3240 __isl_take isl_set *context);
3241 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3242 __isl_take isl_pw_multi_aff *pma,
3243 __isl_take isl_set *set);
3244 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3245 __isl_take isl_pw_multi_aff *pma,
3246 __isl_take isl_set *set);
3248 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3249 then it is assigned the local space that lies at the basis of
3250 the lifting applied.
3252 An expression can be read from input using
3254 #include <isl/aff.h>
3255 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3256 isl_ctx *ctx, const char *str);
3257 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3258 isl_ctx *ctx, const char *str);
3260 An expression can be printed using
3262 #include <isl/aff.h>
3263 __isl_give isl_printer *isl_printer_print_multi_aff(
3264 __isl_take isl_printer *p,
3265 __isl_keep isl_multi_aff *maff);
3266 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3267 __isl_take isl_printer *p,
3268 __isl_keep isl_pw_multi_aff *pma);
3272 Points are elements of a set. They can be used to construct
3273 simple sets (boxes) or they can be used to represent the
3274 individual elements of a set.
3275 The zero point (the origin) can be created using
3277 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3279 The coordinates of a point can be inspected, set and changed
3282 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3283 enum isl_dim_type type, int pos, isl_int *v);
3284 __isl_give isl_point *isl_point_set_coordinate(
3285 __isl_take isl_point *pnt,
3286 enum isl_dim_type type, int pos, isl_int v);
3288 __isl_give isl_point *isl_point_add_ui(
3289 __isl_take isl_point *pnt,
3290 enum isl_dim_type type, int pos, unsigned val);
3291 __isl_give isl_point *isl_point_sub_ui(
3292 __isl_take isl_point *pnt,
3293 enum isl_dim_type type, int pos, unsigned val);
3295 Other properties can be obtained using
3297 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3299 Points can be copied or freed using
3301 __isl_give isl_point *isl_point_copy(
3302 __isl_keep isl_point *pnt);
3303 void isl_point_free(__isl_take isl_point *pnt);
3305 A singleton set can be created from a point using
3307 __isl_give isl_basic_set *isl_basic_set_from_point(
3308 __isl_take isl_point *pnt);
3309 __isl_give isl_set *isl_set_from_point(
3310 __isl_take isl_point *pnt);
3312 and a box can be created from two opposite extremal points using
3314 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3315 __isl_take isl_point *pnt1,
3316 __isl_take isl_point *pnt2);
3317 __isl_give isl_set *isl_set_box_from_points(
3318 __isl_take isl_point *pnt1,
3319 __isl_take isl_point *pnt2);
3321 All elements of a B<bounded> (union) set can be enumerated using
3322 the following functions.
3324 int isl_set_foreach_point(__isl_keep isl_set *set,
3325 int (*fn)(__isl_take isl_point *pnt, void *user),
3327 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3328 int (*fn)(__isl_take isl_point *pnt, void *user),
3331 The function C<fn> is called for each integer point in
3332 C<set> with as second argument the last argument of
3333 the C<isl_set_foreach_point> call. The function C<fn>
3334 should return C<0> on success and C<-1> on failure.
3335 In the latter case, C<isl_set_foreach_point> will stop
3336 enumerating and return C<-1> as well.
3337 If the enumeration is performed successfully and to completion,
3338 then C<isl_set_foreach_point> returns C<0>.
3340 To obtain a single point of a (basic) set, use
3342 __isl_give isl_point *isl_basic_set_sample_point(
3343 __isl_take isl_basic_set *bset);
3344 __isl_give isl_point *isl_set_sample_point(
3345 __isl_take isl_set *set);
3347 If C<set> does not contain any (integer) points, then the
3348 resulting point will be ``void'', a property that can be
3351 int isl_point_is_void(__isl_keep isl_point *pnt);
3353 =head2 Piecewise Quasipolynomials
3355 A piecewise quasipolynomial is a particular kind of function that maps
3356 a parametric point to a rational value.
3357 More specifically, a quasipolynomial is a polynomial expression in greatest
3358 integer parts of affine expressions of parameters and variables.
3359 A piecewise quasipolynomial is a subdivision of a given parametric
3360 domain into disjoint cells with a quasipolynomial associated to
3361 each cell. The value of the piecewise quasipolynomial at a given
3362 point is the value of the quasipolynomial associated to the cell
3363 that contains the point. Outside of the union of cells,
3364 the value is assumed to be zero.
3365 For example, the piecewise quasipolynomial
3367 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3369 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3370 A given piecewise quasipolynomial has a fixed domain dimension.
3371 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3372 defined over different domains.
3373 Piecewise quasipolynomials are mainly used by the C<barvinok>
3374 library for representing the number of elements in a parametric set or map.
3375 For example, the piecewise quasipolynomial above represents
3376 the number of points in the map
3378 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3380 =head3 Input and Output
3382 Piecewise quasipolynomials can be read from input using
3384 __isl_give isl_union_pw_qpolynomial *
3385 isl_union_pw_qpolynomial_read_from_str(
3386 isl_ctx *ctx, const char *str);
3388 Quasipolynomials and piecewise quasipolynomials can be printed
3389 using the following functions.
3391 __isl_give isl_printer *isl_printer_print_qpolynomial(
3392 __isl_take isl_printer *p,
3393 __isl_keep isl_qpolynomial *qp);
3395 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3396 __isl_take isl_printer *p,
3397 __isl_keep isl_pw_qpolynomial *pwqp);
3399 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3400 __isl_take isl_printer *p,
3401 __isl_keep isl_union_pw_qpolynomial *upwqp);
3403 The output format of the printer
3404 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3405 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3407 In case of printing in C<ISL_FORMAT_C>, the user may want
3408 to set the names of all dimensions
3410 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3411 __isl_take isl_qpolynomial *qp,
3412 enum isl_dim_type type, unsigned pos,
3414 __isl_give isl_pw_qpolynomial *
3415 isl_pw_qpolynomial_set_dim_name(
3416 __isl_take isl_pw_qpolynomial *pwqp,
3417 enum isl_dim_type type, unsigned pos,
3420 =head3 Creating New (Piecewise) Quasipolynomials
3422 Some simple quasipolynomials can be created using the following functions.
3423 More complicated quasipolynomials can be created by applying
3424 operations such as addition and multiplication
3425 on the resulting quasipolynomials
3427 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3428 __isl_take isl_space *domain);
3429 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3430 __isl_take isl_space *domain);
3431 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3432 __isl_take isl_space *domain);
3433 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3434 __isl_take isl_space *domain);
3435 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3436 __isl_take isl_space *domain);
3437 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3438 __isl_take isl_space *domain,
3439 const isl_int n, const isl_int d);
3440 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3441 __isl_take isl_space *domain,
3442 enum isl_dim_type type, unsigned pos);
3443 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3444 __isl_take isl_aff *aff);
3446 Note that the space in which a quasipolynomial lives is a map space
3447 with a one-dimensional range. The C<domain> argument in some of
3448 the functions above corresponds to the domain of this map space.
3450 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3451 with a single cell can be created using the following functions.
3452 Multiple of these single cell piecewise quasipolynomials can
3453 be combined to create more complicated piecewise quasipolynomials.
3455 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3456 __isl_take isl_space *space);
3457 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3458 __isl_take isl_set *set,
3459 __isl_take isl_qpolynomial *qp);
3460 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3461 __isl_take isl_qpolynomial *qp);
3462 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3463 __isl_take isl_pw_aff *pwaff);
3465 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3466 __isl_take isl_space *space);
3467 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3468 __isl_take isl_pw_qpolynomial *pwqp);
3469 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3470 __isl_take isl_union_pw_qpolynomial *upwqp,
3471 __isl_take isl_pw_qpolynomial *pwqp);
3473 Quasipolynomials can be copied and freed again using the following
3476 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3477 __isl_keep isl_qpolynomial *qp);
3478 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3480 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3481 __isl_keep isl_pw_qpolynomial *pwqp);
3482 void *isl_pw_qpolynomial_free(
3483 __isl_take isl_pw_qpolynomial *pwqp);
3485 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3486 __isl_keep isl_union_pw_qpolynomial *upwqp);
3487 void isl_union_pw_qpolynomial_free(
3488 __isl_take isl_union_pw_qpolynomial *upwqp);
3490 =head3 Inspecting (Piecewise) Quasipolynomials
3492 To iterate over all piecewise quasipolynomials in a union
3493 piecewise quasipolynomial, use the following function
3495 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3496 __isl_keep isl_union_pw_qpolynomial *upwqp,
3497 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3500 To extract the piecewise quasipolynomial in a given space from a union, use
3502 __isl_give isl_pw_qpolynomial *
3503 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3504 __isl_keep isl_union_pw_qpolynomial *upwqp,
3505 __isl_take isl_space *space);
3507 To iterate over the cells in a piecewise quasipolynomial,
3508 use either of the following two functions
3510 int isl_pw_qpolynomial_foreach_piece(
3511 __isl_keep isl_pw_qpolynomial *pwqp,
3512 int (*fn)(__isl_take isl_set *set,
3513 __isl_take isl_qpolynomial *qp,
3514 void *user), void *user);
3515 int isl_pw_qpolynomial_foreach_lifted_piece(
3516 __isl_keep isl_pw_qpolynomial *pwqp,
3517 int (*fn)(__isl_take isl_set *set,
3518 __isl_take isl_qpolynomial *qp,
3519 void *user), void *user);
3521 As usual, the function C<fn> should return C<0> on success
3522 and C<-1> on failure. The difference between
3523 C<isl_pw_qpolynomial_foreach_piece> and
3524 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3525 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3526 compute unique representations for all existentially quantified
3527 variables and then turn these existentially quantified variables
3528 into extra set variables, adapting the associated quasipolynomial
3529 accordingly. This means that the C<set> passed to C<fn>
3530 will not have any existentially quantified variables, but that
3531 the dimensions of the sets may be different for different
3532 invocations of C<fn>.
3534 To iterate over all terms in a quasipolynomial,
3537 int isl_qpolynomial_foreach_term(
3538 __isl_keep isl_qpolynomial *qp,
3539 int (*fn)(__isl_take isl_term *term,
3540 void *user), void *user);
3542 The terms themselves can be inspected and freed using
3545 unsigned isl_term_dim(__isl_keep isl_term *term,
3546 enum isl_dim_type type);
3547 void isl_term_get_num(__isl_keep isl_term *term,
3549 void isl_term_get_den(__isl_keep isl_term *term,
3551 int isl_term_get_exp(__isl_keep isl_term *term,
3552 enum isl_dim_type type, unsigned pos);
3553 __isl_give isl_aff *isl_term_get_div(
3554 __isl_keep isl_term *term, unsigned pos);
3555 void isl_term_free(__isl_take isl_term *term);
3557 Each term is a product of parameters, set variables and
3558 integer divisions. The function C<isl_term_get_exp>
3559 returns the exponent of a given dimensions in the given term.
3560 The C<isl_int>s in the arguments of C<isl_term_get_num>
3561 and C<isl_term_get_den> need to have been initialized
3562 using C<isl_int_init> before calling these functions.
3564 =head3 Properties of (Piecewise) Quasipolynomials
3566 To check whether a quasipolynomial is actually a constant,
3567 use the following function.
3569 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3570 isl_int *n, isl_int *d);
3572 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3573 then the numerator and denominator of the constant
3574 are returned in C<*n> and C<*d>, respectively.
3576 To check whether two union piecewise quasipolynomials are
3577 obviously equal, use
3579 int isl_union_pw_qpolynomial_plain_is_equal(
3580 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3581 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3583 =head3 Operations on (Piecewise) Quasipolynomials
3585 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3586 __isl_take isl_qpolynomial *qp, isl_int v);
3587 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3588 __isl_take isl_qpolynomial *qp);
3589 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3590 __isl_take isl_qpolynomial *qp1,
3591 __isl_take isl_qpolynomial *qp2);
3592 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3593 __isl_take isl_qpolynomial *qp1,
3594 __isl_take isl_qpolynomial *qp2);
3595 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3596 __isl_take isl_qpolynomial *qp1,
3597 __isl_take isl_qpolynomial *qp2);
3598 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3599 __isl_take isl_qpolynomial *qp, unsigned exponent);
3601 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3602 __isl_take isl_pw_qpolynomial *pwqp1,
3603 __isl_take isl_pw_qpolynomial *pwqp2);
3604 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3605 __isl_take isl_pw_qpolynomial *pwqp1,
3606 __isl_take isl_pw_qpolynomial *pwqp2);
3607 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3608 __isl_take isl_pw_qpolynomial *pwqp1,
3609 __isl_take isl_pw_qpolynomial *pwqp2);
3610 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3611 __isl_take isl_pw_qpolynomial *pwqp);
3612 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3613 __isl_take isl_pw_qpolynomial *pwqp1,
3614 __isl_take isl_pw_qpolynomial *pwqp2);
3615 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3616 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3618 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3619 __isl_take isl_union_pw_qpolynomial *upwqp1,
3620 __isl_take isl_union_pw_qpolynomial *upwqp2);
3621 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3622 __isl_take isl_union_pw_qpolynomial *upwqp1,
3623 __isl_take isl_union_pw_qpolynomial *upwqp2);
3624 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3625 __isl_take isl_union_pw_qpolynomial *upwqp1,
3626 __isl_take isl_union_pw_qpolynomial *upwqp2);
3628 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3629 __isl_take isl_pw_qpolynomial *pwqp,
3630 __isl_take isl_point *pnt);
3632 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3633 __isl_take isl_union_pw_qpolynomial *upwqp,
3634 __isl_take isl_point *pnt);
3636 __isl_give isl_set *isl_pw_qpolynomial_domain(
3637 __isl_take isl_pw_qpolynomial *pwqp);
3638 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3639 __isl_take isl_pw_qpolynomial *pwpq,
3640 __isl_take isl_set *set);
3641 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3642 __isl_take isl_pw_qpolynomial *pwpq,
3643 __isl_take isl_set *set);
3645 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3646 __isl_take isl_union_pw_qpolynomial *upwqp);
3647 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3648 __isl_take isl_union_pw_qpolynomial *upwpq,
3649 __isl_take isl_union_set *uset);
3650 __isl_give isl_union_pw_qpolynomial *
3651 isl_union_pw_qpolynomial_intersect_params(
3652 __isl_take isl_union_pw_qpolynomial *upwpq,
3653 __isl_take isl_set *set);
3655 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3656 __isl_take isl_qpolynomial *qp,
3657 __isl_take isl_space *model);
3659 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3660 __isl_take isl_qpolynomial *qp);
3661 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3662 __isl_take isl_pw_qpolynomial *pwqp);
3664 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3665 __isl_take isl_union_pw_qpolynomial *upwqp);
3667 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3668 __isl_take isl_qpolynomial *qp,
3669 __isl_take isl_set *context);
3670 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3671 __isl_take isl_qpolynomial *qp,
3672 __isl_take isl_set *context);
3674 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3675 __isl_take isl_pw_qpolynomial *pwqp,
3676 __isl_take isl_set *context);
3677 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3678 __isl_take isl_pw_qpolynomial *pwqp,
3679 __isl_take isl_set *context);
3681 __isl_give isl_union_pw_qpolynomial *
3682 isl_union_pw_qpolynomial_gist_params(
3683 __isl_take isl_union_pw_qpolynomial *upwqp,
3684 __isl_take isl_set *context);
3685 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3686 __isl_take isl_union_pw_qpolynomial *upwqp,
3687 __isl_take isl_union_set *context);
3689 The gist operation applies the gist operation to each of
3690 the cells in the domain of the input piecewise quasipolynomial.
3691 The context is also exploited
3692 to simplify the quasipolynomials associated to each cell.
3694 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3695 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3696 __isl_give isl_union_pw_qpolynomial *
3697 isl_union_pw_qpolynomial_to_polynomial(
3698 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3700 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3701 the polynomial will be an overapproximation. If C<sign> is negative,
3702 it will be an underapproximation. If C<sign> is zero, the approximation
3703 will lie somewhere in between.
3705 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3707 A piecewise quasipolynomial reduction is a piecewise
3708 reduction (or fold) of quasipolynomials.
3709 In particular, the reduction can be maximum or a minimum.
3710 The objects are mainly used to represent the result of
3711 an upper or lower bound on a quasipolynomial over its domain,
3712 i.e., as the result of the following function.
3714 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3715 __isl_take isl_pw_qpolynomial *pwqp,
3716 enum isl_fold type, int *tight);
3718 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3719 __isl_take isl_union_pw_qpolynomial *upwqp,
3720 enum isl_fold type, int *tight);
3722 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3723 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3724 is the returned bound is known be tight, i.e., for each value
3725 of the parameters there is at least
3726 one element in the domain that reaches the bound.
3727 If the domain of C<pwqp> is not wrapping, then the bound is computed
3728 over all elements in that domain and the result has a purely parametric
3729 domain. If the domain of C<pwqp> is wrapping, then the bound is
3730 computed over the range of the wrapped relation. The domain of the
3731 wrapped relation becomes the domain of the result.
3733 A (piecewise) quasipolynomial reduction can be copied or freed using the
3734 following functions.
3736 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3737 __isl_keep isl_qpolynomial_fold *fold);
3738 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3739 __isl_keep isl_pw_qpolynomial_fold *pwf);
3740 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3741 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3742 void isl_qpolynomial_fold_free(
3743 __isl_take isl_qpolynomial_fold *fold);
3744 void *isl_pw_qpolynomial_fold_free(
3745 __isl_take isl_pw_qpolynomial_fold *pwf);
3746 void isl_union_pw_qpolynomial_fold_free(
3747 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3749 =head3 Printing Piecewise Quasipolynomial Reductions
3751 Piecewise quasipolynomial reductions can be printed
3752 using the following function.
3754 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3755 __isl_take isl_printer *p,
3756 __isl_keep isl_pw_qpolynomial_fold *pwf);
3757 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3758 __isl_take isl_printer *p,
3759 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3761 For C<isl_printer_print_pw_qpolynomial_fold>,
3762 output format of the printer
3763 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3764 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3765 output format of the printer
3766 needs to be set to C<ISL_FORMAT_ISL>.
3767 In case of printing in C<ISL_FORMAT_C>, the user may want
3768 to set the names of all dimensions
3770 __isl_give isl_pw_qpolynomial_fold *
3771 isl_pw_qpolynomial_fold_set_dim_name(
3772 __isl_take isl_pw_qpolynomial_fold *pwf,
3773 enum isl_dim_type type, unsigned pos,
3776 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3778 To iterate over all piecewise quasipolynomial reductions in a union
3779 piecewise quasipolynomial reduction, use the following function
3781 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3782 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3783 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3784 void *user), void *user);
3786 To iterate over the cells in a piecewise quasipolynomial reduction,
3787 use either of the following two functions
3789 int isl_pw_qpolynomial_fold_foreach_piece(
3790 __isl_keep isl_pw_qpolynomial_fold *pwf,
3791 int (*fn)(__isl_take isl_set *set,
3792 __isl_take isl_qpolynomial_fold *fold,
3793 void *user), void *user);
3794 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3795 __isl_keep isl_pw_qpolynomial_fold *pwf,
3796 int (*fn)(__isl_take isl_set *set,
3797 __isl_take isl_qpolynomial_fold *fold,
3798 void *user), void *user);
3800 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3801 of the difference between these two functions.
3803 To iterate over all quasipolynomials in a reduction, use
3805 int isl_qpolynomial_fold_foreach_qpolynomial(
3806 __isl_keep isl_qpolynomial_fold *fold,
3807 int (*fn)(__isl_take isl_qpolynomial *qp,
3808 void *user), void *user);
3810 =head3 Properties of Piecewise Quasipolynomial Reductions
3812 To check whether two union piecewise quasipolynomial reductions are
3813 obviously equal, use
3815 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3816 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3817 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3819 =head3 Operations on Piecewise Quasipolynomial Reductions
3821 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3822 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3824 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3825 __isl_take isl_pw_qpolynomial_fold *pwf1,
3826 __isl_take isl_pw_qpolynomial_fold *pwf2);
3828 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3829 __isl_take isl_pw_qpolynomial_fold *pwf1,
3830 __isl_take isl_pw_qpolynomial_fold *pwf2);
3832 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3833 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3834 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3836 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3837 __isl_take isl_pw_qpolynomial_fold *pwf,
3838 __isl_take isl_point *pnt);
3840 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3841 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3842 __isl_take isl_point *pnt);
3844 __isl_give isl_pw_qpolynomial_fold *
3845 sl_pw_qpolynomial_fold_intersect_params(
3846 __isl_take isl_pw_qpolynomial_fold *pwf,
3847 __isl_take isl_set *set);
3849 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3850 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3851 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3852 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3853 __isl_take isl_union_set *uset);
3854 __isl_give isl_union_pw_qpolynomial_fold *
3855 isl_union_pw_qpolynomial_fold_intersect_params(
3856 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3857 __isl_take isl_set *set);
3859 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3860 __isl_take isl_pw_qpolynomial_fold *pwf);
3862 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3863 __isl_take isl_pw_qpolynomial_fold *pwf);
3865 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3866 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3868 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
3869 __isl_take isl_qpolynomial_fold *fold,
3870 __isl_take isl_set *context);
3871 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
3872 __isl_take isl_qpolynomial_fold *fold,
3873 __isl_take isl_set *context);
3875 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3876 __isl_take isl_pw_qpolynomial_fold *pwf,
3877 __isl_take isl_set *context);
3878 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
3879 __isl_take isl_pw_qpolynomial_fold *pwf,
3880 __isl_take isl_set *context);
3882 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3883 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3884 __isl_take isl_union_set *context);
3885 __isl_give isl_union_pw_qpolynomial_fold *
3886 isl_union_pw_qpolynomial_fold_gist_params(
3887 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3888 __isl_take isl_set *context);
3890 The gist operation applies the gist operation to each of
3891 the cells in the domain of the input piecewise quasipolynomial reduction.
3892 In future, the operation will also exploit the context
3893 to simplify the quasipolynomial reductions associated to each cell.
3895 __isl_give isl_pw_qpolynomial_fold *
3896 isl_set_apply_pw_qpolynomial_fold(
3897 __isl_take isl_set *set,
3898 __isl_take isl_pw_qpolynomial_fold *pwf,
3900 __isl_give isl_pw_qpolynomial_fold *
3901 isl_map_apply_pw_qpolynomial_fold(
3902 __isl_take isl_map *map,
3903 __isl_take isl_pw_qpolynomial_fold *pwf,
3905 __isl_give isl_union_pw_qpolynomial_fold *
3906 isl_union_set_apply_union_pw_qpolynomial_fold(
3907 __isl_take isl_union_set *uset,
3908 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3910 __isl_give isl_union_pw_qpolynomial_fold *
3911 isl_union_map_apply_union_pw_qpolynomial_fold(
3912 __isl_take isl_union_map *umap,
3913 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3916 The functions taking a map
3917 compose the given map with the given piecewise quasipolynomial reduction.
3918 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3919 over all elements in the intersection of the range of the map
3920 and the domain of the piecewise quasipolynomial reduction
3921 as a function of an element in the domain of the map.
3922 The functions taking a set compute a bound over all elements in the
3923 intersection of the set and the domain of the
3924 piecewise quasipolynomial reduction.
3926 =head2 Dependence Analysis
3928 C<isl> contains specialized functionality for performing
3929 array dataflow analysis. That is, given a I<sink> access relation
3930 and a collection of possible I<source> access relations,
3931 C<isl> can compute relations that describe
3932 for each iteration of the sink access, which iteration
3933 of which of the source access relations was the last
3934 to access the same data element before the given iteration
3936 The resulting dependence relations map source iterations
3937 to the corresponding sink iterations.
3938 To compute standard flow dependences, the sink should be
3939 a read, while the sources should be writes.
3940 If any of the source accesses are marked as being I<may>
3941 accesses, then there will be a dependence from the last
3942 I<must> access B<and> from any I<may> access that follows
3943 this last I<must> access.
3944 In particular, if I<all> sources are I<may> accesses,
3945 then memory based dependence analysis is performed.
3946 If, on the other hand, all sources are I<must> accesses,
3947 then value based dependence analysis is performed.
3949 #include <isl/flow.h>
3951 typedef int (*isl_access_level_before)(void *first, void *second);
3953 __isl_give isl_access_info *isl_access_info_alloc(
3954 __isl_take isl_map *sink,
3955 void *sink_user, isl_access_level_before fn,
3957 __isl_give isl_access_info *isl_access_info_add_source(
3958 __isl_take isl_access_info *acc,
3959 __isl_take isl_map *source, int must,
3961 void isl_access_info_free(__isl_take isl_access_info *acc);
3963 __isl_give isl_flow *isl_access_info_compute_flow(
3964 __isl_take isl_access_info *acc);
3966 int isl_flow_foreach(__isl_keep isl_flow *deps,
3967 int (*fn)(__isl_take isl_map *dep, int must,
3968 void *dep_user, void *user),
3970 __isl_give isl_map *isl_flow_get_no_source(
3971 __isl_keep isl_flow *deps, int must);
3972 void isl_flow_free(__isl_take isl_flow *deps);
3974 The function C<isl_access_info_compute_flow> performs the actual
3975 dependence analysis. The other functions are used to construct
3976 the input for this function or to read off the output.
3978 The input is collected in an C<isl_access_info>, which can
3979 be created through a call to C<isl_access_info_alloc>.
3980 The arguments to this functions are the sink access relation
3981 C<sink>, a token C<sink_user> used to identify the sink
3982 access to the user, a callback function for specifying the
3983 relative order of source and sink accesses, and the number
3984 of source access relations that will be added.
3985 The callback function has type C<int (*)(void *first, void *second)>.
3986 The function is called with two user supplied tokens identifying
3987 either a source or the sink and it should return the shared nesting
3988 level and the relative order of the two accesses.
3989 In particular, let I<n> be the number of loops shared by
3990 the two accesses. If C<first> precedes C<second> textually,
3991 then the function should return I<2 * n + 1>; otherwise,
3992 it should return I<2 * n>.
3993 The sources can be added to the C<isl_access_info> by performing
3994 (at most) C<max_source> calls to C<isl_access_info_add_source>.
3995 C<must> indicates whether the source is a I<must> access
3996 or a I<may> access. Note that a multi-valued access relation
3997 should only be marked I<must> if every iteration in the domain
3998 of the relation accesses I<all> elements in its image.
3999 The C<source_user> token is again used to identify
4000 the source access. The range of the source access relation
4001 C<source> should have the same dimension as the range
4002 of the sink access relation.
4003 The C<isl_access_info_free> function should usually not be
4004 called explicitly, because it is called implicitly by
4005 C<isl_access_info_compute_flow>.
4007 The result of the dependence analysis is collected in an
4008 C<isl_flow>. There may be elements of
4009 the sink access for which no preceding source access could be
4010 found or for which all preceding sources are I<may> accesses.
4011 The relations containing these elements can be obtained through
4012 calls to C<isl_flow_get_no_source>, the first with C<must> set
4013 and the second with C<must> unset.
4014 In the case of standard flow dependence analysis,
4015 with the sink a read and the sources I<must> writes,
4016 the first relation corresponds to the reads from uninitialized
4017 array elements and the second relation is empty.
4018 The actual flow dependences can be extracted using
4019 C<isl_flow_foreach>. This function will call the user-specified
4020 callback function C<fn> for each B<non-empty> dependence between
4021 a source and the sink. The callback function is called
4022 with four arguments, the actual flow dependence relation
4023 mapping source iterations to sink iterations, a boolean that
4024 indicates whether it is a I<must> or I<may> dependence, a token
4025 identifying the source and an additional C<void *> with value
4026 equal to the third argument of the C<isl_flow_foreach> call.
4027 A dependence is marked I<must> if it originates from a I<must>
4028 source and if it is not followed by any I<may> sources.
4030 After finishing with an C<isl_flow>, the user should call
4031 C<isl_flow_free> to free all associated memory.
4033 A higher-level interface to dependence analysis is provided
4034 by the following function.
4036 #include <isl/flow.h>
4038 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4039 __isl_take isl_union_map *must_source,
4040 __isl_take isl_union_map *may_source,
4041 __isl_take isl_union_map *schedule,
4042 __isl_give isl_union_map **must_dep,
4043 __isl_give isl_union_map **may_dep,
4044 __isl_give isl_union_map **must_no_source,
4045 __isl_give isl_union_map **may_no_source);
4047 The arrays are identified by the tuple names of the ranges
4048 of the accesses. The iteration domains by the tuple names
4049 of the domains of the accesses and of the schedule.
4050 The relative order of the iteration domains is given by the
4051 schedule. The relations returned through C<must_no_source>
4052 and C<may_no_source> are subsets of C<sink>.
4053 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4054 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4055 any of the other arguments is treated as an error.
4057 =head3 Interaction with Dependence Analysis
4059 During the dependence analysis, we frequently need to perform
4060 the following operation. Given a relation between sink iterations
4061 and potential soure iterations from a particular source domain,
4062 what is the last potential source iteration corresponding to each
4063 sink iteration. It can sometimes be convenient to adjust
4064 the set of potential source iterations before each such operation.
4065 The prototypical example is fuzzy array dataflow analysis,
4066 where we need to analyze if, based on data-dependent constraints,
4067 the sink iteration can ever be executed without one or more of
4068 the corresponding potential source iterations being executed.
4069 If so, we can introduce extra parameters and select an unknown
4070 but fixed source iteration from the potential source iterations.
4071 To be able to perform such manipulations, C<isl> provides the following
4074 #include <isl/flow.h>
4076 typedef __isl_give isl_set *(*isl_access_restrict_sources)(
4077 __isl_take isl_map *source_map,
4078 void *sink_user, void *source_user);
4079 __isl_give isl_access_info *
4080 isl_access_info_set_restrict_sources(
4081 __isl_take isl_access_info *acc,
4082 isl_access_restrict_sources fn);
4084 The function C<isl_access_info_set_restrict_sources> should be called
4085 before C<isl_access_info_compute_flow> and registers a callback function
4086 that will be called any time C<isl> is about to compute the last
4087 potential source. The first argument is the (reverse) proto-dependence,
4088 mapping sink iterations to potential source iterations.
4089 The other two arguments are the tokens corresponding to the sink
4090 and the source. The callback is expected to return a set
4091 that restricts the source iterations. The potential source iterations
4092 will be intersected with this set. If no restrictions are required
4093 for a given C<source_map>, then the callback should return
4096 isl_space_range(isl_map_get_space(source_map)));
4098 If any error occurs, the callback should return C<NULL>.
4102 B<The functionality described in this section is fairly new
4103 and may be subject to change.>
4105 The following function can be used to compute a schedule
4106 for a union of domains.
4107 By default, the algorithm used to construct the schedule is similar
4108 to that of C<Pluto>.
4109 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4111 The generated schedule respects all C<validity> dependences.
4112 That is, all dependence distances over these dependences in the
4113 scheduled space are lexicographically positive.
4114 The default algorithm tries to minimize the dependence distances over
4115 C<proximity> dependences.
4116 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4117 for groups of domains where the dependence distances have only
4118 non-negative values.
4119 When using Feautrier's algorithm, the C<proximity> dependence
4120 distances are only minimized during the extension to a
4121 full-dimensional schedule.
4123 #include <isl/schedule.h>
4124 __isl_give isl_schedule *isl_union_set_compute_schedule(
4125 __isl_take isl_union_set *domain,
4126 __isl_take isl_union_map *validity,
4127 __isl_take isl_union_map *proximity);
4128 void *isl_schedule_free(__isl_take isl_schedule *sched);
4130 A mapping from the domains to the scheduled space can be obtained
4131 from an C<isl_schedule> using the following function.
4133 __isl_give isl_union_map *isl_schedule_get_map(
4134 __isl_keep isl_schedule *sched);
4136 A representation of the schedule can be printed using
4138 __isl_give isl_printer *isl_printer_print_schedule(
4139 __isl_take isl_printer *p,
4140 __isl_keep isl_schedule *schedule);
4142 A representation of the schedule as a forest of bands can be obtained
4143 using the following function.
4145 __isl_give isl_band_list *isl_schedule_get_band_forest(
4146 __isl_keep isl_schedule *schedule);
4148 The list can be manipulated as explained in L<"Lists">.
4149 The bands inside the list can be copied and freed using the following
4152 #include <isl/band.h>
4153 __isl_give isl_band *isl_band_copy(
4154 __isl_keep isl_band *band);
4155 void *isl_band_free(__isl_take isl_band *band);
4157 Each band contains zero or more scheduling dimensions.
4158 These are referred to as the members of the band.
4159 The section of the schedule that corresponds to the band is
4160 referred to as the partial schedule of the band.
4161 For those nodes that participate in a band, the outer scheduling
4162 dimensions form the prefix schedule, while the inner scheduling
4163 dimensions form the suffix schedule.
4164 That is, if we take a cut of the band forest, then the union of
4165 the concatenations of the prefix, partial and suffix schedules of
4166 each band in the cut is equal to the entire schedule (modulo
4167 some possible padding at the end with zero scheduling dimensions).
4168 The properties of a band can be inspected using the following functions.
4170 #include <isl/band.h>
4171 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4173 int isl_band_has_children(__isl_keep isl_band *band);
4174 __isl_give isl_band_list *isl_band_get_children(
4175 __isl_keep isl_band *band);
4177 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4178 __isl_keep isl_band *band);
4179 __isl_give isl_union_map *isl_band_get_partial_schedule(
4180 __isl_keep isl_band *band);
4181 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4182 __isl_keep isl_band *band);
4184 int isl_band_n_member(__isl_keep isl_band *band);
4185 int isl_band_member_is_zero_distance(
4186 __isl_keep isl_band *band, int pos);
4188 Note that a scheduling dimension is considered to be ``zero
4189 distance'' if it does not carry any proximity dependences
4191 That is, if the dependence distances of the proximity
4192 dependences are all zero in that direction (for fixed
4193 iterations of outer bands).
4195 A representation of the band can be printed using
4197 #include <isl/band.h>
4198 __isl_give isl_printer *isl_printer_print_band(
4199 __isl_take isl_printer *p,
4200 __isl_keep isl_band *band);
4204 #include <isl/schedule.h>
4205 int isl_options_set_schedule_max_constant_term(
4206 isl_ctx *ctx, int val);
4207 int isl_options_get_schedule_max_constant_term(
4209 int isl_options_set_schedule_maximize_band_depth(
4210 isl_ctx *ctx, int val);
4211 int isl_options_get_schedule_maximize_band_depth(
4213 int isl_options_set_schedule_outer_zero_distance(
4214 isl_ctx *ctx, int val);
4215 int isl_options_get_schedule_outer_zero_distance(
4217 int isl_options_set_schedule_split_scaled(
4218 isl_ctx *ctx, int val);
4219 int isl_options_get_schedule_split_scaled(
4221 int isl_options_set_schedule_algorithm(
4222 isl_ctx *ctx, int val);
4223 int isl_options_get_schedule_algorithm(
4229 =item * schedule_max_constant_term
4231 This option enforces that the constant coefficients in the calculated schedule
4232 are not larger than the maximal constant term. This option can significantly
4233 increase the speed of the scheduling calculation and may also prevent fusing of
4234 unrelated dimensions. A value of -1 means that this option does not introduce
4235 bounds on the constant coefficients.
4237 =item * schedule_maximize_band_depth
4239 If this option is set, we do not split bands at the point
4240 where we detect splitting is necessary. Instead, we
4241 backtrack and split bands as early as possible. This
4242 reduces the number of splits and maximizes the width of
4243 the bands. Wider bands give more possibilities for tiling.
4245 =item * schedule_outer_zero_distance
4247 If this option is set, then we try to construct schedules
4248 where the outermost scheduling dimension in each band
4249 results in a zero dependence distance over the proximity
4252 =item * schedule_split_scaled
4254 If this option is set, then we try to construct schedules in which the
4255 constant term is split off from the linear part if the linear parts of
4256 the scheduling rows for all nodes in the graphs have a common non-trivial
4258 The constant term is then placed in a separate band and the linear
4261 =item * schedule_algorithm
4263 Selects the scheduling algorithm to be used.
4264 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4265 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4269 =head2 Parametric Vertex Enumeration
4271 The parametric vertex enumeration described in this section
4272 is mainly intended to be used internally and by the C<barvinok>
4275 #include <isl/vertices.h>
4276 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4277 __isl_keep isl_basic_set *bset);
4279 The function C<isl_basic_set_compute_vertices> performs the
4280 actual computation of the parametric vertices and the chamber
4281 decomposition and store the result in an C<isl_vertices> object.
4282 This information can be queried by either iterating over all
4283 the vertices or iterating over all the chambers or cells
4284 and then iterating over all vertices that are active on the chamber.
4286 int isl_vertices_foreach_vertex(
4287 __isl_keep isl_vertices *vertices,
4288 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4291 int isl_vertices_foreach_cell(
4292 __isl_keep isl_vertices *vertices,
4293 int (*fn)(__isl_take isl_cell *cell, void *user),
4295 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4296 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4299 Other operations that can be performed on an C<isl_vertices> object are
4302 isl_ctx *isl_vertices_get_ctx(
4303 __isl_keep isl_vertices *vertices);
4304 int isl_vertices_get_n_vertices(
4305 __isl_keep isl_vertices *vertices);
4306 void isl_vertices_free(__isl_take isl_vertices *vertices);
4308 Vertices can be inspected and destroyed using the following functions.
4310 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4311 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4312 __isl_give isl_basic_set *isl_vertex_get_domain(
4313 __isl_keep isl_vertex *vertex);
4314 __isl_give isl_basic_set *isl_vertex_get_expr(
4315 __isl_keep isl_vertex *vertex);
4316 void isl_vertex_free(__isl_take isl_vertex *vertex);
4318 C<isl_vertex_get_expr> returns a singleton parametric set describing
4319 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4321 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4322 B<rational> basic sets, so they should mainly be used for inspection
4323 and should not be mixed with integer sets.
4325 Chambers can be inspected and destroyed using the following functions.
4327 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4328 __isl_give isl_basic_set *isl_cell_get_domain(
4329 __isl_keep isl_cell *cell);
4330 void isl_cell_free(__isl_take isl_cell *cell);
4334 Although C<isl> is mainly meant to be used as a library,
4335 it also contains some basic applications that use some
4336 of the functionality of C<isl>.
4337 The input may be specified in either the L<isl format>
4338 or the L<PolyLib format>.
4340 =head2 C<isl_polyhedron_sample>
4342 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4343 an integer element of the polyhedron, if there is any.
4344 The first column in the output is the denominator and is always
4345 equal to 1. If the polyhedron contains no integer points,
4346 then a vector of length zero is printed.
4350 C<isl_pip> takes the same input as the C<example> program
4351 from the C<piplib> distribution, i.e., a set of constraints
4352 on the parameters, a line containing only -1 and finally a set
4353 of constraints on a parametric polyhedron.
4354 The coefficients of the parameters appear in the last columns
4355 (but before the final constant column).
4356 The output is the lexicographic minimum of the parametric polyhedron.
4357 As C<isl> currently does not have its own output format, the output
4358 is just a dump of the internal state.
4360 =head2 C<isl_polyhedron_minimize>
4362 C<isl_polyhedron_minimize> computes the minimum of some linear
4363 or affine objective function over the integer points in a polyhedron.
4364 If an affine objective function
4365 is given, then the constant should appear in the last column.
4367 =head2 C<isl_polytope_scan>
4369 Given a polytope, C<isl_polytope_scan> prints
4370 all integer points in the polytope.