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.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
173 The source of C<isl> can be obtained either as a tarball
174 or from the git repository. Both are available from
175 L<http://freshmeat.net/projects/isl/>.
176 The installation process depends on how you obtained
179 =head2 Installation from the git repository
183 =item 1 Clone or update the repository
185 The first time the source is obtained, you need to clone
188 git clone git://repo.or.cz/isl.git
190 To obtain updates, you need to pull in the latest changes
194 =item 2 Generate C<configure>
200 After performing the above steps, continue
201 with the L<Common installation instructions>.
203 =head2 Common installation instructions
207 =item 1 Obtain C<GMP>
209 Building C<isl> requires C<GMP>, including its headers files.
210 Your distribution may not provide these header files by default
211 and you may need to install a package called C<gmp-devel> or something
212 similar. Alternatively, C<GMP> can be built from
213 source, available from L<http://gmplib.org/>.
217 C<isl> uses the standard C<autoconf> C<configure> script.
222 optionally followed by some configure options.
223 A complete list of options can be obtained by running
227 Below we discuss some of the more common options.
229 C<isl> can optionally use C<piplib>, but no
230 C<piplib> functionality is currently used by default.
231 The C<--with-piplib> option can
232 be used to specify which C<piplib>
233 library to use, either an installed version (C<system>),
234 an externally built version (C<build>)
235 or no version (C<no>). The option C<build> is mostly useful
236 in C<configure> scripts of larger projects that bundle both C<isl>
243 Installation prefix for C<isl>
245 =item C<--with-gmp-prefix>
247 Installation prefix for C<GMP> (architecture-independent files).
249 =item C<--with-gmp-exec-prefix>
251 Installation prefix for C<GMP> (architecture-dependent files).
253 =item C<--with-piplib>
255 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
257 =item C<--with-piplib-prefix>
259 Installation prefix for C<system> C<piplib> (architecture-independent files).
261 =item C<--with-piplib-exec-prefix>
263 Installation prefix for C<system> C<piplib> (architecture-dependent files).
265 =item C<--with-piplib-builddir>
267 Location where C<build> C<piplib> was built.
275 =item 4 Install (optional)
283 =head2 Initialization
285 All manipulations of integer sets and relations occur within
286 the context of an C<isl_ctx>.
287 A given C<isl_ctx> can only be used within a single thread.
288 All arguments of a function are required to have been allocated
289 within the same context.
290 There are currently no functions available for moving an object
291 from one C<isl_ctx> to another C<isl_ctx>. This means that
292 there is currently no way of safely moving an object from one
293 thread to another, unless the whole C<isl_ctx> is moved.
295 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
296 freed using C<isl_ctx_free>.
297 All objects allocated within an C<isl_ctx> should be freed
298 before the C<isl_ctx> itself is freed.
300 isl_ctx *isl_ctx_alloc();
301 void isl_ctx_free(isl_ctx *ctx);
305 All operations on integers, mainly the coefficients
306 of the constraints describing the sets and relations,
307 are performed in exact integer arithmetic using C<GMP>.
308 However, to allow future versions of C<isl> to optionally
309 support fixed integer arithmetic, all calls to C<GMP>
310 are wrapped inside C<isl> specific macros.
311 The basic type is C<isl_int> and the operations below
312 are available on this type.
313 The meanings of these operations are essentially the same
314 as their C<GMP> C<mpz_> counterparts.
315 As always with C<GMP> types, C<isl_int>s need to be
316 initialized with C<isl_int_init> before they can be used
317 and they need to be released with C<isl_int_clear>
319 The user should not assume that an C<isl_int> is represented
320 as a C<mpz_t>, but should instead explicitly convert between
321 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
322 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
326 =item isl_int_init(i)
328 =item isl_int_clear(i)
330 =item isl_int_set(r,i)
332 =item isl_int_set_si(r,i)
334 =item isl_int_set_gmp(r,g)
336 =item isl_int_get_gmp(i,g)
338 =item isl_int_abs(r,i)
340 =item isl_int_neg(r,i)
342 =item isl_int_swap(i,j)
344 =item isl_int_swap_or_set(i,j)
346 =item isl_int_add_ui(r,i,j)
348 =item isl_int_sub_ui(r,i,j)
350 =item isl_int_add(r,i,j)
352 =item isl_int_sub(r,i,j)
354 =item isl_int_mul(r,i,j)
356 =item isl_int_mul_ui(r,i,j)
358 =item isl_int_addmul(r,i,j)
360 =item isl_int_submul(r,i,j)
362 =item isl_int_gcd(r,i,j)
364 =item isl_int_lcm(r,i,j)
366 =item isl_int_divexact(r,i,j)
368 =item isl_int_cdiv_q(r,i,j)
370 =item isl_int_fdiv_q(r,i,j)
372 =item isl_int_fdiv_r(r,i,j)
374 =item isl_int_fdiv_q_ui(r,i,j)
376 =item isl_int_read(r,s)
378 =item isl_int_print(out,i,width)
382 =item isl_int_cmp(i,j)
384 =item isl_int_cmp_si(i,si)
386 =item isl_int_eq(i,j)
388 =item isl_int_ne(i,j)
390 =item isl_int_lt(i,j)
392 =item isl_int_le(i,j)
394 =item isl_int_gt(i,j)
396 =item isl_int_ge(i,j)
398 =item isl_int_abs_eq(i,j)
400 =item isl_int_abs_ne(i,j)
402 =item isl_int_abs_lt(i,j)
404 =item isl_int_abs_gt(i,j)
406 =item isl_int_abs_ge(i,j)
408 =item isl_int_is_zero(i)
410 =item isl_int_is_one(i)
412 =item isl_int_is_negone(i)
414 =item isl_int_is_pos(i)
416 =item isl_int_is_neg(i)
418 =item isl_int_is_nonpos(i)
420 =item isl_int_is_nonneg(i)
422 =item isl_int_is_divisible_by(i,j)
426 =head2 Sets and Relations
428 C<isl> uses six types of objects for representing sets and relations,
429 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
430 C<isl_union_set> and C<isl_union_map>.
431 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
432 can be described as a conjunction of affine constraints, while
433 C<isl_set> and C<isl_map> represent unions of
434 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
435 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
436 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
437 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
438 where spaces are considered different if they have a different number
439 of dimensions and/or different names (see L<"Spaces">).
440 The difference between sets and relations (maps) is that sets have
441 one set of variables, while relations have two sets of variables,
442 input variables and output variables.
444 =head2 Memory Management
446 Since a high-level operation on sets and/or relations usually involves
447 several substeps and since the user is usually not interested in
448 the intermediate results, most functions that return a new object
449 will also release all the objects passed as arguments.
450 If the user still wants to use one or more of these arguments
451 after the function call, she should pass along a copy of the
452 object rather than the object itself.
453 The user is then responsible for making sure that the original
454 object gets used somewhere else or is explicitly freed.
456 The arguments and return values of all documented functions are
457 annotated to make clear which arguments are released and which
458 arguments are preserved. In particular, the following annotations
465 C<__isl_give> means that a new object is returned.
466 The user should make sure that the returned pointer is
467 used exactly once as a value for an C<__isl_take> argument.
468 In between, it can be used as a value for as many
469 C<__isl_keep> arguments as the user likes.
470 There is one exception, and that is the case where the
471 pointer returned is C<NULL>. Is this case, the user
472 is free to use it as an C<__isl_take> argument or not.
476 C<__isl_take> means that the object the argument points to
477 is taken over by the function and may no longer be used
478 by the user as an argument to any other function.
479 The pointer value must be one returned by a function
480 returning an C<__isl_give> pointer.
481 If the user passes in a C<NULL> value, then this will
482 be treated as an error in the sense that the function will
483 not perform its usual operation. However, it will still
484 make sure that all the other C<__isl_take> arguments
489 C<__isl_keep> means that the function will only use the object
490 temporarily. After the function has finished, the user
491 can still use it as an argument to other functions.
492 A C<NULL> value will be treated in the same way as
493 a C<NULL> value for an C<__isl_take> argument.
497 =head2 Error Handling
499 C<isl> supports different ways to react in case a runtime error is triggered.
500 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
501 with two maps that have incompatible spaces. There are three possible ways
502 to react on error: to warn, to continue or to abort.
504 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
505 the last error in the corresponding C<isl_ctx> and the function in which the
506 error was triggered returns C<NULL>. An error does not corrupt internal state,
507 such that isl can continue to be used. C<isl> also provides functions to
508 read the last error and to reset the memory that stores the last error. The
509 last error is only stored for information purposes. Its presence does not
510 change the behavior of C<isl>. Hence, resetting an error is not required to
511 continue to use isl, but only to observe new errors.
514 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
515 void isl_ctx_reset_error(isl_ctx *ctx);
517 Another option is to continue on error. This is similar to warn on error mode,
518 except that C<isl> does not print any warning. This allows a program to
519 implement its own error reporting.
521 The last option is to directly abort the execution of the program from within
522 the isl library. This makes it obviously impossible to recover from an error,
523 but it allows to directly spot the error location. By aborting on error,
524 debuggers break at the location the error occurred and can provide a stack
525 trace. Other tools that automatically provide stack traces on abort or that do
526 not want to continue execution after an error was triggered may also prefer to
529 The on error behavior of isl can be specified by calling
530 C<isl_options_set_on_error> or by setting the command line option
531 C<--isl-on-error>. Valid arguments for the function call are
532 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
533 choices for the command line option are C<warn>, C<continue> and C<abort>.
534 It is also possible to query the current error mode.
536 #include <isl/options.h>
537 int isl_options_set_on_error(isl_ctx *ctx, int val);
538 int isl_options_get_on_error(isl_ctx *ctx);
542 Identifiers are used to identify both individual dimensions
543 and tuples of dimensions. They consist of a name and an optional
544 pointer. Identifiers with the same name but different pointer values
545 are considered to be distinct.
546 Identifiers can be constructed, copied, freed, inspected and printed
547 using the following functions.
550 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
551 __isl_keep const char *name, void *user);
552 __isl_give isl_id *isl_id_copy(isl_id *id);
553 void *isl_id_free(__isl_take isl_id *id);
555 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
556 void *isl_id_get_user(__isl_keep isl_id *id);
557 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
559 __isl_give isl_printer *isl_printer_print_id(
560 __isl_take isl_printer *p, __isl_keep isl_id *id);
562 Note that C<isl_id_get_name> returns a pointer to some internal
563 data structure, so the result can only be used while the
564 corresponding C<isl_id> is alive.
568 Whenever a new set or relation is created from scratch,
569 the space in which it lives needs to be specified using an C<isl_space>.
571 #include <isl/space.h>
572 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
573 unsigned nparam, unsigned n_in, unsigned n_out);
574 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
576 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
577 unsigned nparam, unsigned dim);
578 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
579 void isl_space_free(__isl_take isl_space *space);
580 unsigned isl_space_dim(__isl_keep isl_space *space,
581 enum isl_dim_type type);
583 The space used for creating a parameter domain
584 needs to be created using C<isl_space_params_alloc>.
585 For other sets, the space
586 needs to be created using C<isl_space_set_alloc>, while
587 for a relation, the space
588 needs to be created using C<isl_space_alloc>.
589 C<isl_space_dim> can be used
590 to find out the number of dimensions of each type in
591 a space, where type may be
592 C<isl_dim_param>, C<isl_dim_in> (only for relations),
593 C<isl_dim_out> (only for relations), C<isl_dim_set>
594 (only for sets) or C<isl_dim_all>.
596 To check whether a given space is that of a set or a map
597 or whether it is a parameter space, use these functions:
599 #include <isl/space.h>
600 int isl_space_is_params(__isl_keep isl_space *space);
601 int isl_space_is_set(__isl_keep isl_space *space);
603 It is often useful to create objects that live in the
604 same space as some other object. This can be accomplished
605 by creating the new objects
606 (see L<Creating New Sets and Relations> or
607 L<Creating New (Piecewise) Quasipolynomials>) based on the space
608 of the original object.
611 __isl_give isl_space *isl_basic_set_get_space(
612 __isl_keep isl_basic_set *bset);
613 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
615 #include <isl/union_set.h>
616 __isl_give isl_space *isl_union_set_get_space(
617 __isl_keep isl_union_set *uset);
620 __isl_give isl_space *isl_basic_map_get_space(
621 __isl_keep isl_basic_map *bmap);
622 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
624 #include <isl/union_map.h>
625 __isl_give isl_space *isl_union_map_get_space(
626 __isl_keep isl_union_map *umap);
628 #include <isl/constraint.h>
629 __isl_give isl_space *isl_constraint_get_space(
630 __isl_keep isl_constraint *constraint);
632 #include <isl/polynomial.h>
633 __isl_give isl_space *isl_qpolynomial_get_domain_space(
634 __isl_keep isl_qpolynomial *qp);
635 __isl_give isl_space *isl_qpolynomial_get_space(
636 __isl_keep isl_qpolynomial *qp);
637 __isl_give isl_space *isl_qpolynomial_fold_get_space(
638 __isl_keep isl_qpolynomial_fold *fold);
639 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
640 __isl_keep isl_pw_qpolynomial *pwqp);
641 __isl_give isl_space *isl_pw_qpolynomial_get_space(
642 __isl_keep isl_pw_qpolynomial *pwqp);
643 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
644 __isl_keep isl_pw_qpolynomial_fold *pwf);
645 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
646 __isl_keep isl_pw_qpolynomial_fold *pwf);
647 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
648 __isl_keep isl_union_pw_qpolynomial *upwqp);
649 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
650 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
653 __isl_give isl_space *isl_aff_get_domain_space(
654 __isl_keep isl_aff *aff);
655 __isl_give isl_space *isl_aff_get_space(
656 __isl_keep isl_aff *aff);
657 __isl_give isl_space *isl_pw_aff_get_domain_space(
658 __isl_keep isl_pw_aff *pwaff);
659 __isl_give isl_space *isl_pw_aff_get_space(
660 __isl_keep isl_pw_aff *pwaff);
661 __isl_give isl_space *isl_multi_aff_get_space(
662 __isl_keep isl_multi_aff *maff);
663 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
664 __isl_keep isl_pw_multi_aff *pma);
665 __isl_give isl_space *isl_pw_multi_aff_get_space(
666 __isl_keep isl_pw_multi_aff *pma);
667 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
668 __isl_keep isl_union_pw_multi_aff *upma);
670 #include <isl/point.h>
671 __isl_give isl_space *isl_point_get_space(
672 __isl_keep isl_point *pnt);
674 The identifiers or names of the individual dimensions may be set or read off
675 using the following functions.
677 #include <isl/space.h>
678 __isl_give isl_space *isl_space_set_dim_id(
679 __isl_take isl_space *space,
680 enum isl_dim_type type, unsigned pos,
681 __isl_take isl_id *id);
682 int isl_space_has_dim_id(__isl_keep isl_space *space,
683 enum isl_dim_type type, unsigned pos);
684 __isl_give isl_id *isl_space_get_dim_id(
685 __isl_keep isl_space *space,
686 enum isl_dim_type type, unsigned pos);
687 __isl_give isl_space *isl_space_set_dim_name(
688 __isl_take isl_space *space,
689 enum isl_dim_type type, unsigned pos,
690 __isl_keep const char *name);
691 int isl_space_has_dim_name(__isl_keep isl_space *space,
692 enum isl_dim_type type, unsigned pos);
693 __isl_keep const char *isl_space_get_dim_name(
694 __isl_keep isl_space *space,
695 enum isl_dim_type type, unsigned pos);
697 Note that C<isl_space_get_name> returns a pointer to some internal
698 data structure, so the result can only be used while the
699 corresponding C<isl_space> is alive.
700 Also note that every function that operates on two sets or relations
701 requires that both arguments have the same parameters. This also
702 means that if one of the arguments has named parameters, then the
703 other needs to have named parameters too and the names need to match.
704 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
705 arguments may have different parameters (as long as they are named),
706 in which case the result will have as parameters the union of the parameters of
709 Given the identifier or name of a dimension (typically a parameter),
710 its position can be obtained from the following function.
712 #include <isl/space.h>
713 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
714 enum isl_dim_type type, __isl_keep isl_id *id);
715 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
716 enum isl_dim_type type, const char *name);
718 The identifiers or names of entire spaces may be set or read off
719 using the following functions.
721 #include <isl/space.h>
722 __isl_give isl_space *isl_space_set_tuple_id(
723 __isl_take isl_space *space,
724 enum isl_dim_type type, __isl_take isl_id *id);
725 __isl_give isl_space *isl_space_reset_tuple_id(
726 __isl_take isl_space *space, enum isl_dim_type type);
727 int isl_space_has_tuple_id(__isl_keep isl_space *space,
728 enum isl_dim_type type);
729 __isl_give isl_id *isl_space_get_tuple_id(
730 __isl_keep isl_space *space, enum isl_dim_type type);
731 __isl_give isl_space *isl_space_set_tuple_name(
732 __isl_take isl_space *space,
733 enum isl_dim_type type, const char *s);
734 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
735 enum isl_dim_type type);
737 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
738 or C<isl_dim_set>. As with C<isl_space_get_name>,
739 the C<isl_space_get_tuple_name> function returns a pointer to some internal
741 Binary operations require the corresponding spaces of their arguments
742 to have the same name.
744 Spaces can be nested. In particular, the domain of a set or
745 the domain or range of a relation can be a nested relation.
746 The following functions can be used to construct and deconstruct
749 #include <isl/space.h>
750 int isl_space_is_wrapping(__isl_keep isl_space *space);
751 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
752 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
754 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
755 be the space of a set, while that of
756 C<isl_space_wrap> should be the space of a relation.
757 Conversely, the output of C<isl_space_unwrap> is the space
758 of a relation, while that of C<isl_space_wrap> is the space of a set.
760 Spaces can be created from other spaces
761 using the following functions.
763 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
764 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
765 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
766 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
767 __isl_give isl_space *isl_space_params(
768 __isl_take isl_space *space);
769 __isl_give isl_space *isl_space_set_from_params(
770 __isl_take isl_space *space);
771 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
772 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
773 __isl_take isl_space *right);
774 __isl_give isl_space *isl_space_align_params(
775 __isl_take isl_space *space1, __isl_take isl_space *space2)
776 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
777 enum isl_dim_type type, unsigned pos, unsigned n);
778 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
779 enum isl_dim_type type, unsigned n);
780 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
781 enum isl_dim_type type, unsigned first, unsigned n);
782 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
783 enum isl_dim_type dst_type, unsigned dst_pos,
784 enum isl_dim_type src_type, unsigned src_pos,
786 __isl_give isl_space *isl_space_map_from_set(
787 __isl_take isl_space *space);
788 __isl_give isl_space *isl_space_map_from_domain_and_range(
789 __isl_take isl_space *domain,
790 __isl_take isl_space *range);
791 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
793 Note that if dimensions are added or removed from a space, then
794 the name and the internal structure are lost.
798 A local space is essentially a space with
799 zero or more existentially quantified variables.
800 The local space of a basic set or relation can be obtained
801 using the following functions.
804 __isl_give isl_local_space *isl_basic_set_get_local_space(
805 __isl_keep isl_basic_set *bset);
808 __isl_give isl_local_space *isl_basic_map_get_local_space(
809 __isl_keep isl_basic_map *bmap);
811 A new local space can be created from a space using
813 #include <isl/local_space.h>
814 __isl_give isl_local_space *isl_local_space_from_space(
815 __isl_take isl_space *space);
817 They can be inspected, modified, copied and freed using the following functions.
819 #include <isl/local_space.h>
820 isl_ctx *isl_local_space_get_ctx(
821 __isl_keep isl_local_space *ls);
822 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
823 int isl_local_space_dim(__isl_keep isl_local_space *ls,
824 enum isl_dim_type type);
825 const char *isl_local_space_get_dim_name(
826 __isl_keep isl_local_space *ls,
827 enum isl_dim_type type, unsigned pos);
828 __isl_give isl_local_space *isl_local_space_set_dim_name(
829 __isl_take isl_local_space *ls,
830 enum isl_dim_type type, unsigned pos, const char *s);
831 __isl_give isl_local_space *isl_local_space_set_dim_id(
832 __isl_take isl_local_space *ls,
833 enum isl_dim_type type, unsigned pos,
834 __isl_take isl_id *id);
835 __isl_give isl_space *isl_local_space_get_space(
836 __isl_keep isl_local_space *ls);
837 __isl_give isl_aff *isl_local_space_get_div(
838 __isl_keep isl_local_space *ls, int pos);
839 __isl_give isl_local_space *isl_local_space_copy(
840 __isl_keep isl_local_space *ls);
841 void *isl_local_space_free(__isl_take isl_local_space *ls);
843 Two local spaces can be compared using
845 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
846 __isl_keep isl_local_space *ls2);
848 Local spaces can be created from other local spaces
849 using the following functions.
851 __isl_give isl_local_space *isl_local_space_domain(
852 __isl_take isl_local_space *ls);
853 __isl_give isl_local_space *isl_local_space_range(
854 __isl_take isl_local_space *ls);
855 __isl_give isl_local_space *isl_local_space_from_domain(
856 __isl_take isl_local_space *ls);
857 __isl_give isl_local_space *isl_local_space_intersect(
858 __isl_take isl_local_space *ls1,
859 __isl_take isl_local_space *ls2);
860 __isl_give isl_local_space *isl_local_space_add_dims(
861 __isl_take isl_local_space *ls,
862 enum isl_dim_type type, unsigned n);
863 __isl_give isl_local_space *isl_local_space_insert_dims(
864 __isl_take isl_local_space *ls,
865 enum isl_dim_type type, unsigned first, unsigned n);
866 __isl_give isl_local_space *isl_local_space_drop_dims(
867 __isl_take isl_local_space *ls,
868 enum isl_dim_type type, unsigned first, unsigned n);
870 =head2 Input and Output
872 C<isl> supports its own input/output format, which is similar
873 to the C<Omega> format, but also supports the C<PolyLib> format
878 The C<isl> format is similar to that of C<Omega>, but has a different
879 syntax for describing the parameters and allows for the definition
880 of an existentially quantified variable as the integer division
881 of an affine expression.
882 For example, the set of integers C<i> between C<0> and C<n>
883 such that C<i % 10 <= 6> can be described as
885 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
888 A set or relation can have several disjuncts, separated
889 by the keyword C<or>. Each disjunct is either a conjunction
890 of constraints or a projection (C<exists>) of a conjunction
891 of constraints. The constraints are separated by the keyword
894 =head3 C<PolyLib> format
896 If the represented set is a union, then the first line
897 contains a single number representing the number of disjuncts.
898 Otherwise, a line containing the number C<1> is optional.
900 Each disjunct is represented by a matrix of constraints.
901 The first line contains two numbers representing
902 the number of rows and columns,
903 where the number of rows is equal to the number of constraints
904 and the number of columns is equal to two plus the number of variables.
905 The following lines contain the actual rows of the constraint matrix.
906 In each row, the first column indicates whether the constraint
907 is an equality (C<0>) or inequality (C<1>). The final column
908 corresponds to the constant term.
910 If the set is parametric, then the coefficients of the parameters
911 appear in the last columns before the constant column.
912 The coefficients of any existentially quantified variables appear
913 between those of the set variables and those of the parameters.
915 =head3 Extended C<PolyLib> format
917 The extended C<PolyLib> format is nearly identical to the
918 C<PolyLib> format. The only difference is that the line
919 containing the number of rows and columns of a constraint matrix
920 also contains four additional numbers:
921 the number of output dimensions, the number of input dimensions,
922 the number of local dimensions (i.e., the number of existentially
923 quantified variables) and the number of parameters.
924 For sets, the number of ``output'' dimensions is equal
925 to the number of set dimensions, while the number of ``input''
931 __isl_give isl_basic_set *isl_basic_set_read_from_file(
932 isl_ctx *ctx, FILE *input);
933 __isl_give isl_basic_set *isl_basic_set_read_from_str(
934 isl_ctx *ctx, const char *str);
935 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
937 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
941 __isl_give isl_basic_map *isl_basic_map_read_from_file(
942 isl_ctx *ctx, FILE *input);
943 __isl_give isl_basic_map *isl_basic_map_read_from_str(
944 isl_ctx *ctx, const char *str);
945 __isl_give isl_map *isl_map_read_from_file(
946 isl_ctx *ctx, FILE *input);
947 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
950 #include <isl/union_set.h>
951 __isl_give isl_union_set *isl_union_set_read_from_file(
952 isl_ctx *ctx, FILE *input);
953 __isl_give isl_union_set *isl_union_set_read_from_str(
954 isl_ctx *ctx, const char *str);
956 #include <isl/union_map.h>
957 __isl_give isl_union_map *isl_union_map_read_from_file(
958 isl_ctx *ctx, FILE *input);
959 __isl_give isl_union_map *isl_union_map_read_from_str(
960 isl_ctx *ctx, const char *str);
962 The input format is autodetected and may be either the C<PolyLib> format
963 or the C<isl> format.
967 Before anything can be printed, an C<isl_printer> needs to
970 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
972 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
973 void isl_printer_free(__isl_take isl_printer *printer);
974 __isl_give char *isl_printer_get_str(
975 __isl_keep isl_printer *printer);
977 The behavior of the printer can be modified in various ways
979 __isl_give isl_printer *isl_printer_set_output_format(
980 __isl_take isl_printer *p, int output_format);
981 __isl_give isl_printer *isl_printer_set_indent(
982 __isl_take isl_printer *p, int indent);
983 __isl_give isl_printer *isl_printer_indent(
984 __isl_take isl_printer *p, int indent);
985 __isl_give isl_printer *isl_printer_set_prefix(
986 __isl_take isl_printer *p, const char *prefix);
987 __isl_give isl_printer *isl_printer_set_suffix(
988 __isl_take isl_printer *p, const char *suffix);
990 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
991 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
992 and defaults to C<ISL_FORMAT_ISL>.
993 Each line in the output is indented by C<indent> (set by
994 C<isl_printer_set_indent>) spaces
995 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
996 In the C<PolyLib> format output,
997 the coefficients of the existentially quantified variables
998 appear between those of the set variables and those
1000 The function C<isl_printer_indent> increases the indentation
1001 by the specified amount (which may be negative).
1003 To actually print something, use
1005 #include <isl/set.h>
1006 __isl_give isl_printer *isl_printer_print_basic_set(
1007 __isl_take isl_printer *printer,
1008 __isl_keep isl_basic_set *bset);
1009 __isl_give isl_printer *isl_printer_print_set(
1010 __isl_take isl_printer *printer,
1011 __isl_keep isl_set *set);
1013 #include <isl/map.h>
1014 __isl_give isl_printer *isl_printer_print_basic_map(
1015 __isl_take isl_printer *printer,
1016 __isl_keep isl_basic_map *bmap);
1017 __isl_give isl_printer *isl_printer_print_map(
1018 __isl_take isl_printer *printer,
1019 __isl_keep isl_map *map);
1021 #include <isl/union_set.h>
1022 __isl_give isl_printer *isl_printer_print_union_set(
1023 __isl_take isl_printer *p,
1024 __isl_keep isl_union_set *uset);
1026 #include <isl/union_map.h>
1027 __isl_give isl_printer *isl_printer_print_union_map(
1028 __isl_take isl_printer *p,
1029 __isl_keep isl_union_map *umap);
1031 When called on a file printer, the following function flushes
1032 the file. When called on a string printer, the buffer is cleared.
1034 __isl_give isl_printer *isl_printer_flush(
1035 __isl_take isl_printer *p);
1037 =head2 Creating New Sets and Relations
1039 C<isl> has functions for creating some standard sets and relations.
1043 =item * Empty sets and relations
1045 __isl_give isl_basic_set *isl_basic_set_empty(
1046 __isl_take isl_space *space);
1047 __isl_give isl_basic_map *isl_basic_map_empty(
1048 __isl_take isl_space *space);
1049 __isl_give isl_set *isl_set_empty(
1050 __isl_take isl_space *space);
1051 __isl_give isl_map *isl_map_empty(
1052 __isl_take isl_space *space);
1053 __isl_give isl_union_set *isl_union_set_empty(
1054 __isl_take isl_space *space);
1055 __isl_give isl_union_map *isl_union_map_empty(
1056 __isl_take isl_space *space);
1058 For C<isl_union_set>s and C<isl_union_map>s, the space
1059 is only used to specify the parameters.
1061 =item * Universe sets and relations
1063 __isl_give isl_basic_set *isl_basic_set_universe(
1064 __isl_take isl_space *space);
1065 __isl_give isl_basic_map *isl_basic_map_universe(
1066 __isl_take isl_space *space);
1067 __isl_give isl_set *isl_set_universe(
1068 __isl_take isl_space *space);
1069 __isl_give isl_map *isl_map_universe(
1070 __isl_take isl_space *space);
1071 __isl_give isl_union_set *isl_union_set_universe(
1072 __isl_take isl_union_set *uset);
1073 __isl_give isl_union_map *isl_union_map_universe(
1074 __isl_take isl_union_map *umap);
1076 The sets and relations constructed by the functions above
1077 contain all integer values, while those constructed by the
1078 functions below only contain non-negative values.
1080 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1081 __isl_take isl_space *space);
1082 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1083 __isl_take isl_space *space);
1084 __isl_give isl_set *isl_set_nat_universe(
1085 __isl_take isl_space *space);
1086 __isl_give isl_map *isl_map_nat_universe(
1087 __isl_take isl_space *space);
1089 =item * Identity relations
1091 __isl_give isl_basic_map *isl_basic_map_identity(
1092 __isl_take isl_space *space);
1093 __isl_give isl_map *isl_map_identity(
1094 __isl_take isl_space *space);
1096 The number of input and output dimensions in C<space> needs
1099 =item * Lexicographic order
1101 __isl_give isl_map *isl_map_lex_lt(
1102 __isl_take isl_space *set_space);
1103 __isl_give isl_map *isl_map_lex_le(
1104 __isl_take isl_space *set_space);
1105 __isl_give isl_map *isl_map_lex_gt(
1106 __isl_take isl_space *set_space);
1107 __isl_give isl_map *isl_map_lex_ge(
1108 __isl_take isl_space *set_space);
1109 __isl_give isl_map *isl_map_lex_lt_first(
1110 __isl_take isl_space *space, unsigned n);
1111 __isl_give isl_map *isl_map_lex_le_first(
1112 __isl_take isl_space *space, unsigned n);
1113 __isl_give isl_map *isl_map_lex_gt_first(
1114 __isl_take isl_space *space, unsigned n);
1115 __isl_give isl_map *isl_map_lex_ge_first(
1116 __isl_take isl_space *space, unsigned n);
1118 The first four functions take a space for a B<set>
1119 and return relations that express that the elements in the domain
1120 are lexicographically less
1121 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1122 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1123 than the elements in the range.
1124 The last four functions take a space for a map
1125 and return relations that express that the first C<n> dimensions
1126 in the domain are lexicographically less
1127 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1128 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1129 than the first C<n> dimensions in the range.
1133 A basic set or relation can be converted to a set or relation
1134 using the following functions.
1136 __isl_give isl_set *isl_set_from_basic_set(
1137 __isl_take isl_basic_set *bset);
1138 __isl_give isl_map *isl_map_from_basic_map(
1139 __isl_take isl_basic_map *bmap);
1141 Sets and relations can be converted to union sets and relations
1142 using the following functions.
1144 __isl_give isl_union_map *isl_union_map_from_map(
1145 __isl_take isl_map *map);
1146 __isl_give isl_union_set *isl_union_set_from_set(
1147 __isl_take isl_set *set);
1149 The inverse conversions below can only be used if the input
1150 union set or relation is known to contain elements in exactly one
1153 __isl_give isl_set *isl_set_from_union_set(
1154 __isl_take isl_union_set *uset);
1155 __isl_give isl_map *isl_map_from_union_map(
1156 __isl_take isl_union_map *umap);
1158 A zero-dimensional set can be constructed on a given parameter domain
1159 using the following function.
1161 __isl_give isl_set *isl_set_from_params(
1162 __isl_take isl_set *set);
1164 Sets and relations can be copied and freed again using the following
1167 __isl_give isl_basic_set *isl_basic_set_copy(
1168 __isl_keep isl_basic_set *bset);
1169 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1170 __isl_give isl_union_set *isl_union_set_copy(
1171 __isl_keep isl_union_set *uset);
1172 __isl_give isl_basic_map *isl_basic_map_copy(
1173 __isl_keep isl_basic_map *bmap);
1174 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1175 __isl_give isl_union_map *isl_union_map_copy(
1176 __isl_keep isl_union_map *umap);
1177 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1178 void isl_set_free(__isl_take isl_set *set);
1179 void *isl_union_set_free(__isl_take isl_union_set *uset);
1180 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1181 void isl_map_free(__isl_take isl_map *map);
1182 void *isl_union_map_free(__isl_take isl_union_map *umap);
1184 Other sets and relations can be constructed by starting
1185 from a universe set or relation, adding equality and/or
1186 inequality constraints and then projecting out the
1187 existentially quantified variables, if any.
1188 Constraints can be constructed, manipulated and
1189 added to (or removed from) (basic) sets and relations
1190 using the following functions.
1192 #include <isl/constraint.h>
1193 __isl_give isl_constraint *isl_equality_alloc(
1194 __isl_take isl_local_space *ls);
1195 __isl_give isl_constraint *isl_inequality_alloc(
1196 __isl_take isl_local_space *ls);
1197 __isl_give isl_constraint *isl_constraint_set_constant(
1198 __isl_take isl_constraint *constraint, isl_int v);
1199 __isl_give isl_constraint *isl_constraint_set_constant_si(
1200 __isl_take isl_constraint *constraint, int v);
1201 __isl_give isl_constraint *isl_constraint_set_coefficient(
1202 __isl_take isl_constraint *constraint,
1203 enum isl_dim_type type, int pos, isl_int v);
1204 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1205 __isl_take isl_constraint *constraint,
1206 enum isl_dim_type type, int pos, int v);
1207 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1208 __isl_take isl_basic_map *bmap,
1209 __isl_take isl_constraint *constraint);
1210 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1211 __isl_take isl_basic_set *bset,
1212 __isl_take isl_constraint *constraint);
1213 __isl_give isl_map *isl_map_add_constraint(
1214 __isl_take isl_map *map,
1215 __isl_take isl_constraint *constraint);
1216 __isl_give isl_set *isl_set_add_constraint(
1217 __isl_take isl_set *set,
1218 __isl_take isl_constraint *constraint);
1219 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1220 __isl_take isl_basic_set *bset,
1221 __isl_take isl_constraint *constraint);
1223 For example, to create a set containing the even integers
1224 between 10 and 42, you would use the following code.
1227 isl_local_space *ls;
1229 isl_basic_set *bset;
1231 space = isl_space_set_alloc(ctx, 0, 2);
1232 bset = isl_basic_set_universe(isl_space_copy(space));
1233 ls = isl_local_space_from_space(space);
1235 c = isl_equality_alloc(isl_local_space_copy(ls));
1236 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1237 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1238 bset = isl_basic_set_add_constraint(bset, c);
1240 c = isl_inequality_alloc(isl_local_space_copy(ls));
1241 c = isl_constraint_set_constant_si(c, -10);
1242 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1243 bset = isl_basic_set_add_constraint(bset, c);
1245 c = isl_inequality_alloc(ls);
1246 c = isl_constraint_set_constant_si(c, 42);
1247 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1248 bset = isl_basic_set_add_constraint(bset, c);
1250 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1254 isl_basic_set *bset;
1255 bset = isl_basic_set_read_from_str(ctx,
1256 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1258 A basic set or relation can also be constructed from two matrices
1259 describing the equalities and the inequalities.
1261 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1262 __isl_take isl_space *space,
1263 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1264 enum isl_dim_type c1,
1265 enum isl_dim_type c2, enum isl_dim_type c3,
1266 enum isl_dim_type c4);
1267 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1268 __isl_take isl_space *space,
1269 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1270 enum isl_dim_type c1,
1271 enum isl_dim_type c2, enum isl_dim_type c3,
1272 enum isl_dim_type c4, enum isl_dim_type c5);
1274 The C<isl_dim_type> arguments indicate the order in which
1275 different kinds of variables appear in the input matrices
1276 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1277 C<isl_dim_set> and C<isl_dim_div> for sets and
1278 of C<isl_dim_cst>, C<isl_dim_param>,
1279 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1281 A (basic or union) set or relation can also be constructed from a
1282 (union) (piecewise) (multiple) affine expression
1283 or a list of affine expressions
1284 (See L<"Piecewise Quasi Affine Expressions"> and
1285 L<"Piecewise Multiple Quasi Affine Expressions">).
1287 __isl_give isl_basic_map *isl_basic_map_from_aff(
1288 __isl_take isl_aff *aff);
1289 __isl_give isl_map *isl_map_from_aff(
1290 __isl_take isl_aff *aff);
1291 __isl_give isl_set *isl_set_from_pw_aff(
1292 __isl_take isl_pw_aff *pwaff);
1293 __isl_give isl_map *isl_map_from_pw_aff(
1294 __isl_take isl_pw_aff *pwaff);
1295 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1296 __isl_take isl_space *domain_space,
1297 __isl_take isl_aff_list *list);
1298 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1299 __isl_take isl_multi_aff *maff)
1300 __isl_give isl_map *isl_map_from_multi_aff(
1301 __isl_take isl_multi_aff *maff)
1302 __isl_give isl_set *isl_set_from_pw_multi_aff(
1303 __isl_take isl_pw_multi_aff *pma);
1304 __isl_give isl_map *isl_map_from_pw_multi_aff(
1305 __isl_take isl_pw_multi_aff *pma);
1306 __isl_give isl_union_map *
1307 isl_union_map_from_union_pw_multi_aff(
1308 __isl_take isl_union_pw_multi_aff *upma);
1310 The C<domain_dim> argument describes the domain of the resulting
1311 basic relation. It is required because the C<list> may consist
1312 of zero affine expressions.
1314 =head2 Inspecting Sets and Relations
1316 Usually, the user should not have to care about the actual constraints
1317 of the sets and maps, but should instead apply the abstract operations
1318 explained in the following sections.
1319 Occasionally, however, it may be required to inspect the individual
1320 coefficients of the constraints. This section explains how to do so.
1321 In these cases, it may also be useful to have C<isl> compute
1322 an explicit representation of the existentially quantified variables.
1324 __isl_give isl_set *isl_set_compute_divs(
1325 __isl_take isl_set *set);
1326 __isl_give isl_map *isl_map_compute_divs(
1327 __isl_take isl_map *map);
1328 __isl_give isl_union_set *isl_union_set_compute_divs(
1329 __isl_take isl_union_set *uset);
1330 __isl_give isl_union_map *isl_union_map_compute_divs(
1331 __isl_take isl_union_map *umap);
1333 This explicit representation defines the existentially quantified
1334 variables as integer divisions of the other variables, possibly
1335 including earlier existentially quantified variables.
1336 An explicitly represented existentially quantified variable therefore
1337 has a unique value when the values of the other variables are known.
1338 If, furthermore, the same existentials, i.e., existentials
1339 with the same explicit representations, should appear in the
1340 same order in each of the disjuncts of a set or map, then the user should call
1341 either of the following functions.
1343 __isl_give isl_set *isl_set_align_divs(
1344 __isl_take isl_set *set);
1345 __isl_give isl_map *isl_map_align_divs(
1346 __isl_take isl_map *map);
1348 Alternatively, the existentially quantified variables can be removed
1349 using the following functions, which compute an overapproximation.
1351 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1352 __isl_take isl_basic_set *bset);
1353 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1354 __isl_take isl_basic_map *bmap);
1355 __isl_give isl_set *isl_set_remove_divs(
1356 __isl_take isl_set *set);
1357 __isl_give isl_map *isl_map_remove_divs(
1358 __isl_take isl_map *map);
1360 To iterate over all the sets or maps in a union set or map, use
1362 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1363 int (*fn)(__isl_take isl_set *set, void *user),
1365 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1366 int (*fn)(__isl_take isl_map *map, void *user),
1369 The number of sets or maps in a union set or map can be obtained
1372 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1373 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1375 To extract the set or map in a given space from a union, use
1377 __isl_give isl_set *isl_union_set_extract_set(
1378 __isl_keep isl_union_set *uset,
1379 __isl_take isl_space *space);
1380 __isl_give isl_map *isl_union_map_extract_map(
1381 __isl_keep isl_union_map *umap,
1382 __isl_take isl_space *space);
1384 To iterate over all the basic sets or maps in a set or map, use
1386 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1387 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1389 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1390 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1393 The callback function C<fn> should return 0 if successful and
1394 -1 if an error occurs. In the latter case, or if any other error
1395 occurs, the above functions will return -1.
1397 It should be noted that C<isl> does not guarantee that
1398 the basic sets or maps passed to C<fn> are disjoint.
1399 If this is required, then the user should call one of
1400 the following functions first.
1402 __isl_give isl_set *isl_set_make_disjoint(
1403 __isl_take isl_set *set);
1404 __isl_give isl_map *isl_map_make_disjoint(
1405 __isl_take isl_map *map);
1407 The number of basic sets in a set can be obtained
1410 int isl_set_n_basic_set(__isl_keep isl_set *set);
1412 To iterate over the constraints of a basic set or map, use
1414 #include <isl/constraint.h>
1416 int isl_basic_map_foreach_constraint(
1417 __isl_keep isl_basic_map *bmap,
1418 int (*fn)(__isl_take isl_constraint *c, void *user),
1420 void *isl_constraint_free(__isl_take isl_constraint *c);
1422 Again, the callback function C<fn> should return 0 if successful and
1423 -1 if an error occurs. In the latter case, or if any other error
1424 occurs, the above functions will return -1.
1425 The constraint C<c> represents either an equality or an inequality.
1426 Use the following function to find out whether a constraint
1427 represents an equality. If not, it represents an inequality.
1429 int isl_constraint_is_equality(
1430 __isl_keep isl_constraint *constraint);
1432 The coefficients of the constraints can be inspected using
1433 the following functions.
1435 void isl_constraint_get_constant(
1436 __isl_keep isl_constraint *constraint, isl_int *v);
1437 void isl_constraint_get_coefficient(
1438 __isl_keep isl_constraint *constraint,
1439 enum isl_dim_type type, int pos, isl_int *v);
1440 int isl_constraint_involves_dims(
1441 __isl_keep isl_constraint *constraint,
1442 enum isl_dim_type type, unsigned first, unsigned n);
1444 The explicit representations of the existentially quantified
1445 variables can be inspected using the following function.
1446 Note that the user is only allowed to use this function
1447 if the inspected set or map is the result of a call
1448 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1449 The existentially quantified variable is equal to the floor
1450 of the returned affine expression. The affine expression
1451 itself can be inspected using the functions in
1452 L<"Piecewise Quasi Affine Expressions">.
1454 __isl_give isl_aff *isl_constraint_get_div(
1455 __isl_keep isl_constraint *constraint, int pos);
1457 To obtain the constraints of a basic set or map in matrix
1458 form, use the following functions.
1460 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1461 __isl_keep isl_basic_set *bset,
1462 enum isl_dim_type c1, enum isl_dim_type c2,
1463 enum isl_dim_type c3, enum isl_dim_type c4);
1464 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1465 __isl_keep isl_basic_set *bset,
1466 enum isl_dim_type c1, enum isl_dim_type c2,
1467 enum isl_dim_type c3, enum isl_dim_type c4);
1468 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1469 __isl_keep isl_basic_map *bmap,
1470 enum isl_dim_type c1,
1471 enum isl_dim_type c2, enum isl_dim_type c3,
1472 enum isl_dim_type c4, enum isl_dim_type c5);
1473 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1474 __isl_keep isl_basic_map *bmap,
1475 enum isl_dim_type c1,
1476 enum isl_dim_type c2, enum isl_dim_type c3,
1477 enum isl_dim_type c4, enum isl_dim_type c5);
1479 The C<isl_dim_type> arguments dictate the order in which
1480 different kinds of variables appear in the resulting matrix
1481 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1482 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1484 The number of parameters, input, output or set dimensions can
1485 be obtained using the following functions.
1487 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1488 enum isl_dim_type type);
1489 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1490 enum isl_dim_type type);
1491 unsigned isl_set_dim(__isl_keep isl_set *set,
1492 enum isl_dim_type type);
1493 unsigned isl_map_dim(__isl_keep isl_map *map,
1494 enum isl_dim_type type);
1496 To check whether the description of a set or relation depends
1497 on one or more given dimensions, it is not necessary to iterate over all
1498 constraints. Instead the following functions can be used.
1500 int isl_basic_set_involves_dims(
1501 __isl_keep isl_basic_set *bset,
1502 enum isl_dim_type type, unsigned first, unsigned n);
1503 int isl_set_involves_dims(__isl_keep isl_set *set,
1504 enum isl_dim_type type, unsigned first, unsigned n);
1505 int isl_basic_map_involves_dims(
1506 __isl_keep isl_basic_map *bmap,
1507 enum isl_dim_type type, unsigned first, unsigned n);
1508 int isl_map_involves_dims(__isl_keep isl_map *map,
1509 enum isl_dim_type type, unsigned first, unsigned n);
1511 Similarly, the following functions can be used to check whether
1512 a given dimension is involved in any lower or upper bound.
1514 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1515 enum isl_dim_type type, unsigned pos);
1516 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1517 enum isl_dim_type type, unsigned pos);
1519 The identifiers or names of the domain and range spaces of a set
1520 or relation can be read off or set using the following functions.
1522 __isl_give isl_set *isl_set_set_tuple_id(
1523 __isl_take isl_set *set, __isl_take isl_id *id);
1524 __isl_give isl_set *isl_set_reset_tuple_id(
1525 __isl_take isl_set *set);
1526 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1527 __isl_give isl_id *isl_set_get_tuple_id(
1528 __isl_keep isl_set *set);
1529 __isl_give isl_map *isl_map_set_tuple_id(
1530 __isl_take isl_map *map, enum isl_dim_type type,
1531 __isl_take isl_id *id);
1532 __isl_give isl_map *isl_map_reset_tuple_id(
1533 __isl_take isl_map *map, enum isl_dim_type type);
1534 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1535 enum isl_dim_type type);
1536 __isl_give isl_id *isl_map_get_tuple_id(
1537 __isl_keep isl_map *map, enum isl_dim_type type);
1539 const char *isl_basic_set_get_tuple_name(
1540 __isl_keep isl_basic_set *bset);
1541 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1542 __isl_take isl_basic_set *set, const char *s);
1543 const char *isl_set_get_tuple_name(
1544 __isl_keep isl_set *set);
1545 const char *isl_basic_map_get_tuple_name(
1546 __isl_keep isl_basic_map *bmap,
1547 enum isl_dim_type type);
1548 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1549 __isl_take isl_basic_map *bmap,
1550 enum isl_dim_type type, const char *s);
1551 const char *isl_map_get_tuple_name(
1552 __isl_keep isl_map *map,
1553 enum isl_dim_type type);
1555 As with C<isl_space_get_tuple_name>, the value returned points to
1556 an internal data structure.
1557 The identifiers, positions or names of individual dimensions can be
1558 read off using the following functions.
1560 __isl_give isl_set *isl_set_set_dim_id(
1561 __isl_take isl_set *set, enum isl_dim_type type,
1562 unsigned pos, __isl_take isl_id *id);
1563 int isl_set_has_dim_id(__isl_keep isl_set *set,
1564 enum isl_dim_type type, unsigned pos);
1565 __isl_give isl_id *isl_set_get_dim_id(
1566 __isl_keep isl_set *set, enum isl_dim_type type,
1568 int isl_basic_map_has_dim_id(
1569 __isl_keep isl_basic_map *bmap,
1570 enum isl_dim_type type, unsigned pos);
1571 __isl_give isl_map *isl_map_set_dim_id(
1572 __isl_take isl_map *map, enum isl_dim_type type,
1573 unsigned pos, __isl_take isl_id *id);
1574 int isl_map_has_dim_id(__isl_keep isl_map *map,
1575 enum isl_dim_type type, unsigned pos);
1576 __isl_give isl_id *isl_map_get_dim_id(
1577 __isl_keep isl_map *map, enum isl_dim_type type,
1580 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1581 enum isl_dim_type type, __isl_keep isl_id *id);
1582 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1583 enum isl_dim_type type, __isl_keep isl_id *id);
1584 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1585 enum isl_dim_type type, const char *name);
1586 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1587 enum isl_dim_type type, const char *name);
1589 const char *isl_constraint_get_dim_name(
1590 __isl_keep isl_constraint *constraint,
1591 enum isl_dim_type type, unsigned pos);
1592 const char *isl_basic_set_get_dim_name(
1593 __isl_keep isl_basic_set *bset,
1594 enum isl_dim_type type, unsigned pos);
1595 int isl_set_has_dim_name(__isl_keep isl_set *set,
1596 enum isl_dim_type type, unsigned pos);
1597 const char *isl_set_get_dim_name(
1598 __isl_keep isl_set *set,
1599 enum isl_dim_type type, unsigned pos);
1600 const char *isl_basic_map_get_dim_name(
1601 __isl_keep isl_basic_map *bmap,
1602 enum isl_dim_type type, unsigned pos);
1603 const char *isl_map_get_dim_name(
1604 __isl_keep isl_map *map,
1605 enum isl_dim_type type, unsigned pos);
1607 These functions are mostly useful to obtain the identifiers, positions
1608 or names of the parameters. Identifiers of individual dimensions are
1609 essentially only useful for printing. They are ignored by all other
1610 operations and may not be preserved across those operations.
1614 =head3 Unary Properties
1620 The following functions test whether the given set or relation
1621 contains any integer points. The ``plain'' variants do not perform
1622 any computations, but simply check if the given set or relation
1623 is already known to be empty.
1625 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1626 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1627 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1628 int isl_set_is_empty(__isl_keep isl_set *set);
1629 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1630 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1631 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1632 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1633 int isl_map_is_empty(__isl_keep isl_map *map);
1634 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1636 =item * Universality
1638 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1639 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1640 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1642 =item * Single-valuedness
1644 int isl_map_plain_is_single_valued(
1645 __isl_keep isl_map *map);
1646 int isl_map_is_single_valued(__isl_keep isl_map *map);
1647 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1651 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1652 int isl_map_is_injective(__isl_keep isl_map *map);
1653 int isl_union_map_plain_is_injective(
1654 __isl_keep isl_union_map *umap);
1655 int isl_union_map_is_injective(
1656 __isl_keep isl_union_map *umap);
1660 int isl_map_is_bijective(__isl_keep isl_map *map);
1661 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1665 int isl_basic_map_plain_is_fixed(
1666 __isl_keep isl_basic_map *bmap,
1667 enum isl_dim_type type, unsigned pos,
1669 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1670 enum isl_dim_type type, unsigned pos,
1672 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1673 enum isl_dim_type type, unsigned pos,
1676 Check if the relation obviously lies on a hyperplane where the given dimension
1677 has a fixed value and if so, return that value in C<*val>.
1681 To check whether a set is a parameter domain, use this function:
1683 int isl_set_is_params(__isl_keep isl_set *set);
1684 int isl_union_set_is_params(
1685 __isl_keep isl_union_set *uset);
1689 The following functions check whether the domain of the given
1690 (basic) set is a wrapped relation.
1692 int isl_basic_set_is_wrapping(
1693 __isl_keep isl_basic_set *bset);
1694 int isl_set_is_wrapping(__isl_keep isl_set *set);
1696 =item * Internal Product
1698 int isl_basic_map_can_zip(
1699 __isl_keep isl_basic_map *bmap);
1700 int isl_map_can_zip(__isl_keep isl_map *map);
1702 Check whether the product of domain and range of the given relation
1704 i.e., whether both domain and range are nested relations.
1708 =head3 Binary Properties
1714 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1715 __isl_keep isl_set *set2);
1716 int isl_set_is_equal(__isl_keep isl_set *set1,
1717 __isl_keep isl_set *set2);
1718 int isl_union_set_is_equal(
1719 __isl_keep isl_union_set *uset1,
1720 __isl_keep isl_union_set *uset2);
1721 int isl_basic_map_is_equal(
1722 __isl_keep isl_basic_map *bmap1,
1723 __isl_keep isl_basic_map *bmap2);
1724 int isl_map_is_equal(__isl_keep isl_map *map1,
1725 __isl_keep isl_map *map2);
1726 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1727 __isl_keep isl_map *map2);
1728 int isl_union_map_is_equal(
1729 __isl_keep isl_union_map *umap1,
1730 __isl_keep isl_union_map *umap2);
1732 =item * Disjointness
1734 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1735 __isl_keep isl_set *set2);
1739 int isl_basic_set_is_subset(
1740 __isl_keep isl_basic_set *bset1,
1741 __isl_keep isl_basic_set *bset2);
1742 int isl_set_is_subset(__isl_keep isl_set *set1,
1743 __isl_keep isl_set *set2);
1744 int isl_set_is_strict_subset(
1745 __isl_keep isl_set *set1,
1746 __isl_keep isl_set *set2);
1747 int isl_union_set_is_subset(
1748 __isl_keep isl_union_set *uset1,
1749 __isl_keep isl_union_set *uset2);
1750 int isl_union_set_is_strict_subset(
1751 __isl_keep isl_union_set *uset1,
1752 __isl_keep isl_union_set *uset2);
1753 int isl_basic_map_is_subset(
1754 __isl_keep isl_basic_map *bmap1,
1755 __isl_keep isl_basic_map *bmap2);
1756 int isl_basic_map_is_strict_subset(
1757 __isl_keep isl_basic_map *bmap1,
1758 __isl_keep isl_basic_map *bmap2);
1759 int isl_map_is_subset(
1760 __isl_keep isl_map *map1,
1761 __isl_keep isl_map *map2);
1762 int isl_map_is_strict_subset(
1763 __isl_keep isl_map *map1,
1764 __isl_keep isl_map *map2);
1765 int isl_union_map_is_subset(
1766 __isl_keep isl_union_map *umap1,
1767 __isl_keep isl_union_map *umap2);
1768 int isl_union_map_is_strict_subset(
1769 __isl_keep isl_union_map *umap1,
1770 __isl_keep isl_union_map *umap2);
1774 =head2 Unary Operations
1780 __isl_give isl_set *isl_set_complement(
1781 __isl_take isl_set *set);
1782 __isl_give isl_map *isl_map_complement(
1783 __isl_take isl_map *map);
1787 __isl_give isl_basic_map *isl_basic_map_reverse(
1788 __isl_take isl_basic_map *bmap);
1789 __isl_give isl_map *isl_map_reverse(
1790 __isl_take isl_map *map);
1791 __isl_give isl_union_map *isl_union_map_reverse(
1792 __isl_take isl_union_map *umap);
1796 __isl_give isl_basic_set *isl_basic_set_project_out(
1797 __isl_take isl_basic_set *bset,
1798 enum isl_dim_type type, unsigned first, unsigned n);
1799 __isl_give isl_basic_map *isl_basic_map_project_out(
1800 __isl_take isl_basic_map *bmap,
1801 enum isl_dim_type type, unsigned first, unsigned n);
1802 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1803 enum isl_dim_type type, unsigned first, unsigned n);
1804 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1805 enum isl_dim_type type, unsigned first, unsigned n);
1806 __isl_give isl_basic_set *isl_basic_set_params(
1807 __isl_take isl_basic_set *bset);
1808 __isl_give isl_basic_set *isl_basic_map_domain(
1809 __isl_take isl_basic_map *bmap);
1810 __isl_give isl_basic_set *isl_basic_map_range(
1811 __isl_take isl_basic_map *bmap);
1812 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1813 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1814 __isl_give isl_set *isl_map_domain(
1815 __isl_take isl_map *bmap);
1816 __isl_give isl_set *isl_map_range(
1817 __isl_take isl_map *map);
1818 __isl_give isl_set *isl_union_set_params(
1819 __isl_take isl_union_set *uset);
1820 __isl_give isl_set *isl_union_map_params(
1821 __isl_take isl_union_map *umap);
1822 __isl_give isl_union_set *isl_union_map_domain(
1823 __isl_take isl_union_map *umap);
1824 __isl_give isl_union_set *isl_union_map_range(
1825 __isl_take isl_union_map *umap);
1827 __isl_give isl_basic_map *isl_basic_map_domain_map(
1828 __isl_take isl_basic_map *bmap);
1829 __isl_give isl_basic_map *isl_basic_map_range_map(
1830 __isl_take isl_basic_map *bmap);
1831 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1832 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1833 __isl_give isl_union_map *isl_union_map_domain_map(
1834 __isl_take isl_union_map *umap);
1835 __isl_give isl_union_map *isl_union_map_range_map(
1836 __isl_take isl_union_map *umap);
1838 The functions above construct a (basic, regular or union) relation
1839 that maps (a wrapped version of) the input relation to its domain or range.
1843 __isl_give isl_set *isl_set_eliminate(
1844 __isl_take isl_set *set, enum isl_dim_type type,
1845 unsigned first, unsigned n);
1846 __isl_give isl_basic_map *isl_basic_map_eliminate(
1847 __isl_take isl_basic_map *bmap,
1848 enum isl_dim_type type,
1849 unsigned first, unsigned n);
1850 __isl_give isl_map *isl_map_eliminate(
1851 __isl_take isl_map *map, enum isl_dim_type type,
1852 unsigned first, unsigned n);
1854 Eliminate the coefficients for the given dimensions from the constraints,
1855 without removing the dimensions.
1859 __isl_give isl_basic_set *isl_basic_set_fix(
1860 __isl_take isl_basic_set *bset,
1861 enum isl_dim_type type, unsigned pos,
1863 __isl_give isl_basic_set *isl_basic_set_fix_si(
1864 __isl_take isl_basic_set *bset,
1865 enum isl_dim_type type, unsigned pos, int value);
1866 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1867 enum isl_dim_type type, unsigned pos,
1869 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1870 enum isl_dim_type type, unsigned pos, int value);
1871 __isl_give isl_basic_map *isl_basic_map_fix_si(
1872 __isl_take isl_basic_map *bmap,
1873 enum isl_dim_type type, unsigned pos, int value);
1874 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1875 enum isl_dim_type type, unsigned pos, int value);
1877 Intersect the set or relation with the hyperplane where the given
1878 dimension has the fixed given value.
1880 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1881 __isl_take isl_basic_map *bmap,
1882 enum isl_dim_type type, unsigned pos, int value);
1883 __isl_give isl_set *isl_set_lower_bound(
1884 __isl_take isl_set *set,
1885 enum isl_dim_type type, unsigned pos,
1887 __isl_give isl_set *isl_set_lower_bound_si(
1888 __isl_take isl_set *set,
1889 enum isl_dim_type type, unsigned pos, int value);
1890 __isl_give isl_map *isl_map_lower_bound_si(
1891 __isl_take isl_map *map,
1892 enum isl_dim_type type, unsigned pos, int value);
1893 __isl_give isl_set *isl_set_upper_bound(
1894 __isl_take isl_set *set,
1895 enum isl_dim_type type, unsigned pos,
1897 __isl_give isl_set *isl_set_upper_bound_si(
1898 __isl_take isl_set *set,
1899 enum isl_dim_type type, unsigned pos, int value);
1900 __isl_give isl_map *isl_map_upper_bound_si(
1901 __isl_take isl_map *map,
1902 enum isl_dim_type type, unsigned pos, int value);
1904 Intersect the set or relation with the half-space where the given
1905 dimension has a value bounded by the fixed given value.
1907 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1908 enum isl_dim_type type1, int pos1,
1909 enum isl_dim_type type2, int pos2);
1910 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1911 enum isl_dim_type type1, int pos1,
1912 enum isl_dim_type type2, int pos2);
1914 Intersect the set or relation with the hyperplane where the given
1915 dimensions are equal to each other.
1917 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1918 enum isl_dim_type type1, int pos1,
1919 enum isl_dim_type type2, int pos2);
1921 Intersect the relation with the hyperplane where the given
1922 dimensions have opposite values.
1926 __isl_give isl_map *isl_set_identity(
1927 __isl_take isl_set *set);
1928 __isl_give isl_union_map *isl_union_set_identity(
1929 __isl_take isl_union_set *uset);
1931 Construct an identity relation on the given (union) set.
1935 __isl_give isl_basic_set *isl_basic_map_deltas(
1936 __isl_take isl_basic_map *bmap);
1937 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1938 __isl_give isl_union_set *isl_union_map_deltas(
1939 __isl_take isl_union_map *umap);
1941 These functions return a (basic) set containing the differences
1942 between image elements and corresponding domain elements in the input.
1944 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1945 __isl_take isl_basic_map *bmap);
1946 __isl_give isl_map *isl_map_deltas_map(
1947 __isl_take isl_map *map);
1948 __isl_give isl_union_map *isl_union_map_deltas_map(
1949 __isl_take isl_union_map *umap);
1951 The functions above construct a (basic, regular or union) relation
1952 that maps (a wrapped version of) the input relation to its delta set.
1956 Simplify the representation of a set or relation by trying
1957 to combine pairs of basic sets or relations into a single
1958 basic set or relation.
1960 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1961 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1962 __isl_give isl_union_set *isl_union_set_coalesce(
1963 __isl_take isl_union_set *uset);
1964 __isl_give isl_union_map *isl_union_map_coalesce(
1965 __isl_take isl_union_map *umap);
1967 One of the methods for combining pairs of basic sets or relations
1968 can result in coefficients that are much larger than those that appear
1969 in the constraints of the input. By default, the coefficients are
1970 not allowed to grow larger, but this can be changed by unsetting
1971 the following option.
1973 int isl_options_set_coalesce_bounded_wrapping(
1974 isl_ctx *ctx, int val);
1975 int isl_options_get_coalesce_bounded_wrapping(
1978 =item * Detecting equalities
1980 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1981 __isl_take isl_basic_set *bset);
1982 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1983 __isl_take isl_basic_map *bmap);
1984 __isl_give isl_set *isl_set_detect_equalities(
1985 __isl_take isl_set *set);
1986 __isl_give isl_map *isl_map_detect_equalities(
1987 __isl_take isl_map *map);
1988 __isl_give isl_union_set *isl_union_set_detect_equalities(
1989 __isl_take isl_union_set *uset);
1990 __isl_give isl_union_map *isl_union_map_detect_equalities(
1991 __isl_take isl_union_map *umap);
1993 Simplify the representation of a set or relation by detecting implicit
1996 =item * Removing redundant constraints
1998 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1999 __isl_take isl_basic_set *bset);
2000 __isl_give isl_set *isl_set_remove_redundancies(
2001 __isl_take isl_set *set);
2002 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2003 __isl_take isl_basic_map *bmap);
2004 __isl_give isl_map *isl_map_remove_redundancies(
2005 __isl_take isl_map *map);
2009 __isl_give isl_basic_set *isl_set_convex_hull(
2010 __isl_take isl_set *set);
2011 __isl_give isl_basic_map *isl_map_convex_hull(
2012 __isl_take isl_map *map);
2014 If the input set or relation has any existentially quantified
2015 variables, then the result of these operations is currently undefined.
2019 __isl_give isl_basic_set *isl_set_simple_hull(
2020 __isl_take isl_set *set);
2021 __isl_give isl_basic_map *isl_map_simple_hull(
2022 __isl_take isl_map *map);
2023 __isl_give isl_union_map *isl_union_map_simple_hull(
2024 __isl_take isl_union_map *umap);
2026 These functions compute a single basic set or relation
2027 that contains the whole input set or relation.
2028 In particular, the output is described by translates
2029 of the constraints describing the basic sets or relations in the input.
2033 (See \autoref{s:simple hull}.)
2039 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2040 __isl_take isl_basic_set *bset);
2041 __isl_give isl_basic_set *isl_set_affine_hull(
2042 __isl_take isl_set *set);
2043 __isl_give isl_union_set *isl_union_set_affine_hull(
2044 __isl_take isl_union_set *uset);
2045 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2046 __isl_take isl_basic_map *bmap);
2047 __isl_give isl_basic_map *isl_map_affine_hull(
2048 __isl_take isl_map *map);
2049 __isl_give isl_union_map *isl_union_map_affine_hull(
2050 __isl_take isl_union_map *umap);
2052 In case of union sets and relations, the affine hull is computed
2055 =item * Polyhedral hull
2057 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2058 __isl_take isl_set *set);
2059 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2060 __isl_take isl_map *map);
2061 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2062 __isl_take isl_union_set *uset);
2063 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2064 __isl_take isl_union_map *umap);
2066 These functions compute a single basic set or relation
2067 not involving any existentially quantified variables
2068 that contains the whole input set or relation.
2069 In case of union sets and relations, the polyhedral hull is computed
2074 __isl_give isl_basic_set *isl_basic_set_sample(
2075 __isl_take isl_basic_set *bset);
2076 __isl_give isl_basic_set *isl_set_sample(
2077 __isl_take isl_set *set);
2078 __isl_give isl_basic_map *isl_basic_map_sample(
2079 __isl_take isl_basic_map *bmap);
2080 __isl_give isl_basic_map *isl_map_sample(
2081 __isl_take isl_map *map);
2083 If the input (basic) set or relation is non-empty, then return
2084 a singleton subset of the input. Otherwise, return an empty set.
2086 =item * Optimization
2088 #include <isl/ilp.h>
2089 enum isl_lp_result isl_basic_set_max(
2090 __isl_keep isl_basic_set *bset,
2091 __isl_keep isl_aff *obj, isl_int *opt)
2092 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2093 __isl_keep isl_aff *obj, isl_int *opt);
2094 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2095 __isl_keep isl_aff *obj, isl_int *opt);
2097 Compute the minimum or maximum of the integer affine expression C<obj>
2098 over the points in C<set>, returning the result in C<opt>.
2099 The return value may be one of C<isl_lp_error>,
2100 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2102 =item * Parametric optimization
2104 __isl_give isl_pw_aff *isl_set_dim_min(
2105 __isl_take isl_set *set, int pos);
2106 __isl_give isl_pw_aff *isl_set_dim_max(
2107 __isl_take isl_set *set, int pos);
2108 __isl_give isl_pw_aff *isl_map_dim_max(
2109 __isl_take isl_map *map, int pos);
2111 Compute the minimum or maximum of the given set or output dimension
2112 as a function of the parameters (and input dimensions), but independently
2113 of the other set or output dimensions.
2114 For lexicographic optimization, see L<"Lexicographic Optimization">.
2118 The following functions compute either the set of (rational) coefficient
2119 values of valid constraints for the given set or the set of (rational)
2120 values satisfying the constraints with coefficients from the given set.
2121 Internally, these two sets of functions perform essentially the
2122 same operations, except that the set of coefficients is assumed to
2123 be a cone, while the set of values may be any polyhedron.
2124 The current implementation is based on the Farkas lemma and
2125 Fourier-Motzkin elimination, but this may change or be made optional
2126 in future. In particular, future implementations may use different
2127 dualization algorithms or skip the elimination step.
2129 __isl_give isl_basic_set *isl_basic_set_coefficients(
2130 __isl_take isl_basic_set *bset);
2131 __isl_give isl_basic_set *isl_set_coefficients(
2132 __isl_take isl_set *set);
2133 __isl_give isl_union_set *isl_union_set_coefficients(
2134 __isl_take isl_union_set *bset);
2135 __isl_give isl_basic_set *isl_basic_set_solutions(
2136 __isl_take isl_basic_set *bset);
2137 __isl_give isl_basic_set *isl_set_solutions(
2138 __isl_take isl_set *set);
2139 __isl_give isl_union_set *isl_union_set_solutions(
2140 __isl_take isl_union_set *bset);
2144 __isl_give isl_map *isl_map_fixed_power(
2145 __isl_take isl_map *map, isl_int exp);
2146 __isl_give isl_union_map *isl_union_map_fixed_power(
2147 __isl_take isl_union_map *umap, isl_int exp);
2149 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2150 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2151 of C<map> is computed.
2153 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2155 __isl_give isl_union_map *isl_union_map_power(
2156 __isl_take isl_union_map *umap, int *exact);
2158 Compute a parametric representation for all positive powers I<k> of C<map>.
2159 The result maps I<k> to a nested relation corresponding to the
2160 I<k>th power of C<map>.
2161 The result may be an overapproximation. If the result is known to be exact,
2162 then C<*exact> is set to C<1>.
2164 =item * Transitive closure
2166 __isl_give isl_map *isl_map_transitive_closure(
2167 __isl_take isl_map *map, int *exact);
2168 __isl_give isl_union_map *isl_union_map_transitive_closure(
2169 __isl_take isl_union_map *umap, int *exact);
2171 Compute the transitive closure of C<map>.
2172 The result may be an overapproximation. If the result is known to be exact,
2173 then C<*exact> is set to C<1>.
2175 =item * Reaching path lengths
2177 __isl_give isl_map *isl_map_reaching_path_lengths(
2178 __isl_take isl_map *map, int *exact);
2180 Compute a relation that maps each element in the range of C<map>
2181 to the lengths of all paths composed of edges in C<map> that
2182 end up in the given element.
2183 The result may be an overapproximation. If the result is known to be exact,
2184 then C<*exact> is set to C<1>.
2185 To compute the I<maximal> path length, the resulting relation
2186 should be postprocessed by C<isl_map_lexmax>.
2187 In particular, if the input relation is a dependence relation
2188 (mapping sources to sinks), then the maximal path length corresponds
2189 to the free schedule.
2190 Note, however, that C<isl_map_lexmax> expects the maximum to be
2191 finite, so if the path lengths are unbounded (possibly due to
2192 the overapproximation), then you will get an error message.
2196 __isl_give isl_basic_set *isl_basic_map_wrap(
2197 __isl_take isl_basic_map *bmap);
2198 __isl_give isl_set *isl_map_wrap(
2199 __isl_take isl_map *map);
2200 __isl_give isl_union_set *isl_union_map_wrap(
2201 __isl_take isl_union_map *umap);
2202 __isl_give isl_basic_map *isl_basic_set_unwrap(
2203 __isl_take isl_basic_set *bset);
2204 __isl_give isl_map *isl_set_unwrap(
2205 __isl_take isl_set *set);
2206 __isl_give isl_union_map *isl_union_set_unwrap(
2207 __isl_take isl_union_set *uset);
2211 Remove any internal structure of domain (and range) of the given
2212 set or relation. If there is any such internal structure in the input,
2213 then the name of the space is also removed.
2215 __isl_give isl_basic_set *isl_basic_set_flatten(
2216 __isl_take isl_basic_set *bset);
2217 __isl_give isl_set *isl_set_flatten(
2218 __isl_take isl_set *set);
2219 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2220 __isl_take isl_basic_map *bmap);
2221 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2222 __isl_take isl_basic_map *bmap);
2223 __isl_give isl_map *isl_map_flatten_range(
2224 __isl_take isl_map *map);
2225 __isl_give isl_map *isl_map_flatten_domain(
2226 __isl_take isl_map *map);
2227 __isl_give isl_basic_map *isl_basic_map_flatten(
2228 __isl_take isl_basic_map *bmap);
2229 __isl_give isl_map *isl_map_flatten(
2230 __isl_take isl_map *map);
2232 __isl_give isl_map *isl_set_flatten_map(
2233 __isl_take isl_set *set);
2235 The function above constructs a relation
2236 that maps the input set to a flattened version of the set.
2240 Lift the input set to a space with extra dimensions corresponding
2241 to the existentially quantified variables in the input.
2242 In particular, the result lives in a wrapped map where the domain
2243 is the original space and the range corresponds to the original
2244 existentially quantified variables.
2246 __isl_give isl_basic_set *isl_basic_set_lift(
2247 __isl_take isl_basic_set *bset);
2248 __isl_give isl_set *isl_set_lift(
2249 __isl_take isl_set *set);
2250 __isl_give isl_union_set *isl_union_set_lift(
2251 __isl_take isl_union_set *uset);
2253 Given a local space that contains the existentially quantified
2254 variables of a set, a basic relation that, when applied to
2255 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2256 can be constructed using the following function.
2258 #include <isl/local_space.h>
2259 __isl_give isl_basic_map *isl_local_space_lifting(
2260 __isl_take isl_local_space *ls);
2262 =item * Internal Product
2264 __isl_give isl_basic_map *isl_basic_map_zip(
2265 __isl_take isl_basic_map *bmap);
2266 __isl_give isl_map *isl_map_zip(
2267 __isl_take isl_map *map);
2268 __isl_give isl_union_map *isl_union_map_zip(
2269 __isl_take isl_union_map *umap);
2271 Given a relation with nested relations for domain and range,
2272 interchange the range of the domain with the domain of the range.
2274 =item * Aligning parameters
2276 __isl_give isl_set *isl_set_align_params(
2277 __isl_take isl_set *set,
2278 __isl_take isl_space *model);
2279 __isl_give isl_map *isl_map_align_params(
2280 __isl_take isl_map *map,
2281 __isl_take isl_space *model);
2283 Change the order of the parameters of the given set or relation
2284 such that the first parameters match those of C<model>.
2285 This may involve the introduction of extra parameters.
2286 All parameters need to be named.
2288 =item * Dimension manipulation
2290 __isl_give isl_set *isl_set_add_dims(
2291 __isl_take isl_set *set,
2292 enum isl_dim_type type, unsigned n);
2293 __isl_give isl_map *isl_map_add_dims(
2294 __isl_take isl_map *map,
2295 enum isl_dim_type type, unsigned n);
2296 __isl_give isl_set *isl_set_insert_dims(
2297 __isl_take isl_set *set,
2298 enum isl_dim_type type, unsigned pos, unsigned n);
2299 __isl_give isl_map *isl_map_insert_dims(
2300 __isl_take isl_map *map,
2301 enum isl_dim_type type, unsigned pos, unsigned n);
2302 __isl_give isl_basic_set *isl_basic_set_move_dims(
2303 __isl_take isl_basic_set *bset,
2304 enum isl_dim_type dst_type, unsigned dst_pos,
2305 enum isl_dim_type src_type, unsigned src_pos,
2307 __isl_give isl_basic_map *isl_basic_map_move_dims(
2308 __isl_take isl_basic_map *bmap,
2309 enum isl_dim_type dst_type, unsigned dst_pos,
2310 enum isl_dim_type src_type, unsigned src_pos,
2312 __isl_give isl_set *isl_set_move_dims(
2313 __isl_take isl_set *set,
2314 enum isl_dim_type dst_type, unsigned dst_pos,
2315 enum isl_dim_type src_type, unsigned src_pos,
2317 __isl_give isl_map *isl_map_move_dims(
2318 __isl_take isl_map *map,
2319 enum isl_dim_type dst_type, unsigned dst_pos,
2320 enum isl_dim_type src_type, unsigned src_pos,
2323 It is usually not advisable to directly change the (input or output)
2324 space of a set or a relation as this removes the name and the internal
2325 structure of the space. However, the above functions can be useful
2326 to add new parameters, assuming
2327 C<isl_set_align_params> and C<isl_map_align_params>
2332 =head2 Binary Operations
2334 The two arguments of a binary operation not only need to live
2335 in the same C<isl_ctx>, they currently also need to have
2336 the same (number of) parameters.
2338 =head3 Basic Operations
2342 =item * Intersection
2344 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2345 __isl_take isl_basic_set *bset1,
2346 __isl_take isl_basic_set *bset2);
2347 __isl_give isl_basic_set *isl_basic_set_intersect(
2348 __isl_take isl_basic_set *bset1,
2349 __isl_take isl_basic_set *bset2);
2350 __isl_give isl_set *isl_set_intersect_params(
2351 __isl_take isl_set *set,
2352 __isl_take isl_set *params);
2353 __isl_give isl_set *isl_set_intersect(
2354 __isl_take isl_set *set1,
2355 __isl_take isl_set *set2);
2356 __isl_give isl_union_set *isl_union_set_intersect_params(
2357 __isl_take isl_union_set *uset,
2358 __isl_take isl_set *set);
2359 __isl_give isl_union_map *isl_union_map_intersect_params(
2360 __isl_take isl_union_map *umap,
2361 __isl_take isl_set *set);
2362 __isl_give isl_union_set *isl_union_set_intersect(
2363 __isl_take isl_union_set *uset1,
2364 __isl_take isl_union_set *uset2);
2365 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2366 __isl_take isl_basic_map *bmap,
2367 __isl_take isl_basic_set *bset);
2368 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2369 __isl_take isl_basic_map *bmap,
2370 __isl_take isl_basic_set *bset);
2371 __isl_give isl_basic_map *isl_basic_map_intersect(
2372 __isl_take isl_basic_map *bmap1,
2373 __isl_take isl_basic_map *bmap2);
2374 __isl_give isl_map *isl_map_intersect_params(
2375 __isl_take isl_map *map,
2376 __isl_take isl_set *params);
2377 __isl_give isl_map *isl_map_intersect_domain(
2378 __isl_take isl_map *map,
2379 __isl_take isl_set *set);
2380 __isl_give isl_map *isl_map_intersect_range(
2381 __isl_take isl_map *map,
2382 __isl_take isl_set *set);
2383 __isl_give isl_map *isl_map_intersect(
2384 __isl_take isl_map *map1,
2385 __isl_take isl_map *map2);
2386 __isl_give isl_union_map *isl_union_map_intersect_domain(
2387 __isl_take isl_union_map *umap,
2388 __isl_take isl_union_set *uset);
2389 __isl_give isl_union_map *isl_union_map_intersect_range(
2390 __isl_take isl_union_map *umap,
2391 __isl_take isl_union_set *uset);
2392 __isl_give isl_union_map *isl_union_map_intersect(
2393 __isl_take isl_union_map *umap1,
2394 __isl_take isl_union_map *umap2);
2398 __isl_give isl_set *isl_basic_set_union(
2399 __isl_take isl_basic_set *bset1,
2400 __isl_take isl_basic_set *bset2);
2401 __isl_give isl_map *isl_basic_map_union(
2402 __isl_take isl_basic_map *bmap1,
2403 __isl_take isl_basic_map *bmap2);
2404 __isl_give isl_set *isl_set_union(
2405 __isl_take isl_set *set1,
2406 __isl_take isl_set *set2);
2407 __isl_give isl_map *isl_map_union(
2408 __isl_take isl_map *map1,
2409 __isl_take isl_map *map2);
2410 __isl_give isl_union_set *isl_union_set_union(
2411 __isl_take isl_union_set *uset1,
2412 __isl_take isl_union_set *uset2);
2413 __isl_give isl_union_map *isl_union_map_union(
2414 __isl_take isl_union_map *umap1,
2415 __isl_take isl_union_map *umap2);
2417 =item * Set difference
2419 __isl_give isl_set *isl_set_subtract(
2420 __isl_take isl_set *set1,
2421 __isl_take isl_set *set2);
2422 __isl_give isl_map *isl_map_subtract(
2423 __isl_take isl_map *map1,
2424 __isl_take isl_map *map2);
2425 __isl_give isl_map *isl_map_subtract_domain(
2426 __isl_take isl_map *map,
2427 __isl_take isl_set *dom);
2428 __isl_give isl_map *isl_map_subtract_range(
2429 __isl_take isl_map *map,
2430 __isl_take isl_set *dom);
2431 __isl_give isl_union_set *isl_union_set_subtract(
2432 __isl_take isl_union_set *uset1,
2433 __isl_take isl_union_set *uset2);
2434 __isl_give isl_union_map *isl_union_map_subtract(
2435 __isl_take isl_union_map *umap1,
2436 __isl_take isl_union_map *umap2);
2440 __isl_give isl_basic_set *isl_basic_set_apply(
2441 __isl_take isl_basic_set *bset,
2442 __isl_take isl_basic_map *bmap);
2443 __isl_give isl_set *isl_set_apply(
2444 __isl_take isl_set *set,
2445 __isl_take isl_map *map);
2446 __isl_give isl_union_set *isl_union_set_apply(
2447 __isl_take isl_union_set *uset,
2448 __isl_take isl_union_map *umap);
2449 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2450 __isl_take isl_basic_map *bmap1,
2451 __isl_take isl_basic_map *bmap2);
2452 __isl_give isl_basic_map *isl_basic_map_apply_range(
2453 __isl_take isl_basic_map *bmap1,
2454 __isl_take isl_basic_map *bmap2);
2455 __isl_give isl_map *isl_map_apply_domain(
2456 __isl_take isl_map *map1,
2457 __isl_take isl_map *map2);
2458 __isl_give isl_union_map *isl_union_map_apply_domain(
2459 __isl_take isl_union_map *umap1,
2460 __isl_take isl_union_map *umap2);
2461 __isl_give isl_map *isl_map_apply_range(
2462 __isl_take isl_map *map1,
2463 __isl_take isl_map *map2);
2464 __isl_give isl_union_map *isl_union_map_apply_range(
2465 __isl_take isl_union_map *umap1,
2466 __isl_take isl_union_map *umap2);
2468 =item * Cartesian Product
2470 __isl_give isl_set *isl_set_product(
2471 __isl_take isl_set *set1,
2472 __isl_take isl_set *set2);
2473 __isl_give isl_union_set *isl_union_set_product(
2474 __isl_take isl_union_set *uset1,
2475 __isl_take isl_union_set *uset2);
2476 __isl_give isl_basic_map *isl_basic_map_domain_product(
2477 __isl_take isl_basic_map *bmap1,
2478 __isl_take isl_basic_map *bmap2);
2479 __isl_give isl_basic_map *isl_basic_map_range_product(
2480 __isl_take isl_basic_map *bmap1,
2481 __isl_take isl_basic_map *bmap2);
2482 __isl_give isl_map *isl_map_domain_product(
2483 __isl_take isl_map *map1,
2484 __isl_take isl_map *map2);
2485 __isl_give isl_map *isl_map_range_product(
2486 __isl_take isl_map *map1,
2487 __isl_take isl_map *map2);
2488 __isl_give isl_union_map *isl_union_map_range_product(
2489 __isl_take isl_union_map *umap1,
2490 __isl_take isl_union_map *umap2);
2491 __isl_give isl_map *isl_map_product(
2492 __isl_take isl_map *map1,
2493 __isl_take isl_map *map2);
2494 __isl_give isl_union_map *isl_union_map_product(
2495 __isl_take isl_union_map *umap1,
2496 __isl_take isl_union_map *umap2);
2498 The above functions compute the cross product of the given
2499 sets or relations. The domains and ranges of the results
2500 are wrapped maps between domains and ranges of the inputs.
2501 To obtain a ``flat'' product, use the following functions
2504 __isl_give isl_basic_set *isl_basic_set_flat_product(
2505 __isl_take isl_basic_set *bset1,
2506 __isl_take isl_basic_set *bset2);
2507 __isl_give isl_set *isl_set_flat_product(
2508 __isl_take isl_set *set1,
2509 __isl_take isl_set *set2);
2510 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2511 __isl_take isl_basic_map *bmap1,
2512 __isl_take isl_basic_map *bmap2);
2513 __isl_give isl_map *isl_map_flat_domain_product(
2514 __isl_take isl_map *map1,
2515 __isl_take isl_map *map2);
2516 __isl_give isl_map *isl_map_flat_range_product(
2517 __isl_take isl_map *map1,
2518 __isl_take isl_map *map2);
2519 __isl_give isl_union_map *isl_union_map_flat_range_product(
2520 __isl_take isl_union_map *umap1,
2521 __isl_take isl_union_map *umap2);
2522 __isl_give isl_basic_map *isl_basic_map_flat_product(
2523 __isl_take isl_basic_map *bmap1,
2524 __isl_take isl_basic_map *bmap2);
2525 __isl_give isl_map *isl_map_flat_product(
2526 __isl_take isl_map *map1,
2527 __isl_take isl_map *map2);
2529 =item * Simplification
2531 __isl_give isl_basic_set *isl_basic_set_gist(
2532 __isl_take isl_basic_set *bset,
2533 __isl_take isl_basic_set *context);
2534 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2535 __isl_take isl_set *context);
2536 __isl_give isl_set *isl_set_gist_params(
2537 __isl_take isl_set *set,
2538 __isl_take isl_set *context);
2539 __isl_give isl_union_set *isl_union_set_gist(
2540 __isl_take isl_union_set *uset,
2541 __isl_take isl_union_set *context);
2542 __isl_give isl_union_set *isl_union_set_gist_params(
2543 __isl_take isl_union_set *uset,
2544 __isl_take isl_set *set);
2545 __isl_give isl_basic_map *isl_basic_map_gist(
2546 __isl_take isl_basic_map *bmap,
2547 __isl_take isl_basic_map *context);
2548 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2549 __isl_take isl_map *context);
2550 __isl_give isl_map *isl_map_gist_params(
2551 __isl_take isl_map *map,
2552 __isl_take isl_set *context);
2553 __isl_give isl_map *isl_map_gist_domain(
2554 __isl_take isl_map *map,
2555 __isl_take isl_set *context);
2556 __isl_give isl_map *isl_map_gist_range(
2557 __isl_take isl_map *map,
2558 __isl_take isl_set *context);
2559 __isl_give isl_union_map *isl_union_map_gist(
2560 __isl_take isl_union_map *umap,
2561 __isl_take isl_union_map *context);
2562 __isl_give isl_union_map *isl_union_map_gist_params(
2563 __isl_take isl_union_map *umap,
2564 __isl_take isl_set *set);
2565 __isl_give isl_union_map *isl_union_map_gist_domain(
2566 __isl_take isl_union_map *umap,
2567 __isl_take isl_union_set *uset);
2568 __isl_give isl_union_map *isl_union_map_gist_range(
2569 __isl_take isl_union_map *umap,
2570 __isl_take isl_union_set *uset);
2572 The gist operation returns a set or relation that has the
2573 same intersection with the context as the input set or relation.
2574 Any implicit equality in the intersection is made explicit in the result,
2575 while all inequalities that are redundant with respect to the intersection
2577 In case of union sets and relations, the gist operation is performed
2582 =head3 Lexicographic Optimization
2584 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2585 the following functions
2586 compute a set that contains the lexicographic minimum or maximum
2587 of the elements in C<set> (or C<bset>) for those values of the parameters
2588 that satisfy C<dom>.
2589 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2590 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2592 In other words, the union of the parameter values
2593 for which the result is non-empty and of C<*empty>
2596 __isl_give isl_set *isl_basic_set_partial_lexmin(
2597 __isl_take isl_basic_set *bset,
2598 __isl_take isl_basic_set *dom,
2599 __isl_give isl_set **empty);
2600 __isl_give isl_set *isl_basic_set_partial_lexmax(
2601 __isl_take isl_basic_set *bset,
2602 __isl_take isl_basic_set *dom,
2603 __isl_give isl_set **empty);
2604 __isl_give isl_set *isl_set_partial_lexmin(
2605 __isl_take isl_set *set, __isl_take isl_set *dom,
2606 __isl_give isl_set **empty);
2607 __isl_give isl_set *isl_set_partial_lexmax(
2608 __isl_take isl_set *set, __isl_take isl_set *dom,
2609 __isl_give isl_set **empty);
2611 Given a (basic) set C<set> (or C<bset>), the following functions simply
2612 return a set containing the lexicographic minimum or maximum
2613 of the elements in C<set> (or C<bset>).
2614 In case of union sets, the optimum is computed per space.
2616 __isl_give isl_set *isl_basic_set_lexmin(
2617 __isl_take isl_basic_set *bset);
2618 __isl_give isl_set *isl_basic_set_lexmax(
2619 __isl_take isl_basic_set *bset);
2620 __isl_give isl_set *isl_set_lexmin(
2621 __isl_take isl_set *set);
2622 __isl_give isl_set *isl_set_lexmax(
2623 __isl_take isl_set *set);
2624 __isl_give isl_union_set *isl_union_set_lexmin(
2625 __isl_take isl_union_set *uset);
2626 __isl_give isl_union_set *isl_union_set_lexmax(
2627 __isl_take isl_union_set *uset);
2629 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2630 the following functions
2631 compute a relation that maps each element of C<dom>
2632 to the single lexicographic minimum or maximum
2633 of the elements that are associated to that same
2634 element in C<map> (or C<bmap>).
2635 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2636 that contains the elements in C<dom> that do not map
2637 to any elements in C<map> (or C<bmap>).
2638 In other words, the union of the domain of the result and of C<*empty>
2641 __isl_give isl_map *isl_basic_map_partial_lexmax(
2642 __isl_take isl_basic_map *bmap,
2643 __isl_take isl_basic_set *dom,
2644 __isl_give isl_set **empty);
2645 __isl_give isl_map *isl_basic_map_partial_lexmin(
2646 __isl_take isl_basic_map *bmap,
2647 __isl_take isl_basic_set *dom,
2648 __isl_give isl_set **empty);
2649 __isl_give isl_map *isl_map_partial_lexmax(
2650 __isl_take isl_map *map, __isl_take isl_set *dom,
2651 __isl_give isl_set **empty);
2652 __isl_give isl_map *isl_map_partial_lexmin(
2653 __isl_take isl_map *map, __isl_take isl_set *dom,
2654 __isl_give isl_set **empty);
2656 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2657 return a map mapping each element in the domain of
2658 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2659 of all elements associated to that element.
2660 In case of union relations, the optimum is computed per space.
2662 __isl_give isl_map *isl_basic_map_lexmin(
2663 __isl_take isl_basic_map *bmap);
2664 __isl_give isl_map *isl_basic_map_lexmax(
2665 __isl_take isl_basic_map *bmap);
2666 __isl_give isl_map *isl_map_lexmin(
2667 __isl_take isl_map *map);
2668 __isl_give isl_map *isl_map_lexmax(
2669 __isl_take isl_map *map);
2670 __isl_give isl_union_map *isl_union_map_lexmin(
2671 __isl_take isl_union_map *umap);
2672 __isl_give isl_union_map *isl_union_map_lexmax(
2673 __isl_take isl_union_map *umap);
2675 The following functions return their result in the form of
2676 a piecewise multi-affine expression
2677 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2678 but are otherwise equivalent to the corresponding functions
2679 returning a basic set or relation.
2681 __isl_give isl_pw_multi_aff *
2682 isl_basic_map_lexmin_pw_multi_aff(
2683 __isl_take isl_basic_map *bmap);
2684 __isl_give isl_pw_multi_aff *
2685 isl_basic_set_partial_lexmin_pw_multi_aff(
2686 __isl_take isl_basic_set *bset,
2687 __isl_take isl_basic_set *dom,
2688 __isl_give isl_set **empty);
2689 __isl_give isl_pw_multi_aff *
2690 isl_basic_set_partial_lexmax_pw_multi_aff(
2691 __isl_take isl_basic_set *bset,
2692 __isl_take isl_basic_set *dom,
2693 __isl_give isl_set **empty);
2694 __isl_give isl_pw_multi_aff *
2695 isl_basic_map_partial_lexmin_pw_multi_aff(
2696 __isl_take isl_basic_map *bmap,
2697 __isl_take isl_basic_set *dom,
2698 __isl_give isl_set **empty);
2699 __isl_give isl_pw_multi_aff *
2700 isl_basic_map_partial_lexmax_pw_multi_aff(
2701 __isl_take isl_basic_map *bmap,
2702 __isl_take isl_basic_set *dom,
2703 __isl_give isl_set **empty);
2707 Lists are defined over several element types, including
2708 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2709 Here we take lists of C<isl_set>s as an example.
2710 Lists can be created, copied and freed using the following functions.
2712 #include <isl/list.h>
2713 __isl_give isl_set_list *isl_set_list_from_set(
2714 __isl_take isl_set *el);
2715 __isl_give isl_set_list *isl_set_list_alloc(
2716 isl_ctx *ctx, int n);
2717 __isl_give isl_set_list *isl_set_list_copy(
2718 __isl_keep isl_set_list *list);
2719 __isl_give isl_set_list *isl_set_list_add(
2720 __isl_take isl_set_list *list,
2721 __isl_take isl_set *el);
2722 __isl_give isl_set_list *isl_set_list_concat(
2723 __isl_take isl_set_list *list1,
2724 __isl_take isl_set_list *list2);
2725 void *isl_set_list_free(__isl_take isl_set_list *list);
2727 C<isl_set_list_alloc> creates an empty list with a capacity for
2728 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2731 Lists can be inspected using the following functions.
2733 #include <isl/list.h>
2734 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2735 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2736 __isl_give isl_set *isl_set_list_get_set(
2737 __isl_keep isl_set_list *list, int index);
2738 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2739 int (*fn)(__isl_take isl_set *el, void *user),
2742 Lists can be printed using
2744 #include <isl/list.h>
2745 __isl_give isl_printer *isl_printer_print_set_list(
2746 __isl_take isl_printer *p,
2747 __isl_keep isl_set_list *list);
2751 Vectors can be created, copied and freed using the following functions.
2753 #include <isl/vec.h>
2754 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2756 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2757 void isl_vec_free(__isl_take isl_vec *vec);
2759 Note that the elements of a newly created vector may have arbitrary values.
2760 The elements can be changed and inspected using the following functions.
2762 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2763 int isl_vec_size(__isl_keep isl_vec *vec);
2764 int isl_vec_get_element(__isl_keep isl_vec *vec,
2765 int pos, isl_int *v);
2766 __isl_give isl_vec *isl_vec_set_element(
2767 __isl_take isl_vec *vec, int pos, isl_int v);
2768 __isl_give isl_vec *isl_vec_set_element_si(
2769 __isl_take isl_vec *vec, int pos, int v);
2770 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2772 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2775 C<isl_vec_get_element> will return a negative value if anything went wrong.
2776 In that case, the value of C<*v> is undefined.
2780 Matrices can be created, copied and freed using the following functions.
2782 #include <isl/mat.h>
2783 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2784 unsigned n_row, unsigned n_col);
2785 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2786 void isl_mat_free(__isl_take isl_mat *mat);
2788 Note that the elements of a newly created matrix may have arbitrary values.
2789 The elements can be changed and inspected using the following functions.
2791 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2792 int isl_mat_rows(__isl_keep isl_mat *mat);
2793 int isl_mat_cols(__isl_keep isl_mat *mat);
2794 int isl_mat_get_element(__isl_keep isl_mat *mat,
2795 int row, int col, isl_int *v);
2796 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2797 int row, int col, isl_int v);
2798 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2799 int row, int col, int v);
2801 C<isl_mat_get_element> will return a negative value if anything went wrong.
2802 In that case, the value of C<*v> is undefined.
2804 The following function can be used to compute the (right) inverse
2805 of a matrix, i.e., a matrix such that the product of the original
2806 and the inverse (in that order) is a multiple of the identity matrix.
2807 The input matrix is assumed to be of full row-rank.
2809 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2811 The following function can be used to compute the (right) kernel
2812 (or null space) of a matrix, i.e., a matrix such that the product of
2813 the original and the kernel (in that order) is the zero matrix.
2815 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2817 =head2 Piecewise Quasi Affine Expressions
2819 The zero quasi affine expression on a given domain can be created using
2821 __isl_give isl_aff *isl_aff_zero_on_domain(
2822 __isl_take isl_local_space *ls);
2824 Note that the space in which the resulting object lives is a map space
2825 with the given space as domain and a one-dimensional range.
2827 An empty piecewise quasi affine expression (one with no cells)
2828 or a piecewise quasi affine expression with a single cell can
2829 be created using the following functions.
2831 #include <isl/aff.h>
2832 __isl_give isl_pw_aff *isl_pw_aff_empty(
2833 __isl_take isl_space *space);
2834 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2835 __isl_take isl_set *set, __isl_take isl_aff *aff);
2836 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2837 __isl_take isl_aff *aff);
2839 A piecewise quasi affine expression that is equal to 1 on a set
2840 and 0 outside the set can be created using the following function.
2842 #include <isl/aff.h>
2843 __isl_give isl_pw_aff *isl_set_indicator_function(
2844 __isl_take isl_set *set);
2846 Quasi affine expressions can be copied and freed using
2848 #include <isl/aff.h>
2849 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2850 void *isl_aff_free(__isl_take isl_aff *aff);
2852 __isl_give isl_pw_aff *isl_pw_aff_copy(
2853 __isl_keep isl_pw_aff *pwaff);
2854 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2856 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2857 using the following function. The constraint is required to have
2858 a non-zero coefficient for the specified dimension.
2860 #include <isl/constraint.h>
2861 __isl_give isl_aff *isl_constraint_get_bound(
2862 __isl_keep isl_constraint *constraint,
2863 enum isl_dim_type type, int pos);
2865 The entire affine expression of the constraint can also be extracted
2866 using the following function.
2868 #include <isl/constraint.h>
2869 __isl_give isl_aff *isl_constraint_get_aff(
2870 __isl_keep isl_constraint *constraint);
2872 Conversely, an equality constraint equating
2873 the affine expression to zero or an inequality constraint enforcing
2874 the affine expression to be non-negative, can be constructed using
2876 __isl_give isl_constraint *isl_equality_from_aff(
2877 __isl_take isl_aff *aff);
2878 __isl_give isl_constraint *isl_inequality_from_aff(
2879 __isl_take isl_aff *aff);
2881 The expression can be inspected using
2883 #include <isl/aff.h>
2884 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2885 int isl_aff_dim(__isl_keep isl_aff *aff,
2886 enum isl_dim_type type);
2887 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2888 __isl_keep isl_aff *aff);
2889 __isl_give isl_local_space *isl_aff_get_local_space(
2890 __isl_keep isl_aff *aff);
2891 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2892 enum isl_dim_type type, unsigned pos);
2893 const char *isl_pw_aff_get_dim_name(
2894 __isl_keep isl_pw_aff *pa,
2895 enum isl_dim_type type, unsigned pos);
2896 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2897 enum isl_dim_type type, unsigned pos);
2898 __isl_give isl_id *isl_pw_aff_get_dim_id(
2899 __isl_keep isl_pw_aff *pa,
2900 enum isl_dim_type type, unsigned pos);
2901 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2903 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2904 enum isl_dim_type type, int pos, isl_int *v);
2905 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2907 __isl_give isl_aff *isl_aff_get_div(
2908 __isl_keep isl_aff *aff, int pos);
2910 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2911 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2912 int (*fn)(__isl_take isl_set *set,
2913 __isl_take isl_aff *aff,
2914 void *user), void *user);
2916 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2917 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2919 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2920 enum isl_dim_type type, unsigned first, unsigned n);
2921 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2922 enum isl_dim_type type, unsigned first, unsigned n);
2924 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2925 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2926 enum isl_dim_type type);
2927 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2929 It can be modified using
2931 #include <isl/aff.h>
2932 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2933 __isl_take isl_pw_aff *pwaff,
2934 enum isl_dim_type type, __isl_take isl_id *id);
2935 __isl_give isl_aff *isl_aff_set_dim_name(
2936 __isl_take isl_aff *aff, enum isl_dim_type type,
2937 unsigned pos, const char *s);
2938 __isl_give isl_aff *isl_aff_set_dim_id(
2939 __isl_take isl_aff *aff, enum isl_dim_type type,
2940 unsigned pos, __isl_take isl_id *id);
2941 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2942 __isl_take isl_pw_aff *pma,
2943 enum isl_dim_type type, unsigned pos,
2944 __isl_take isl_id *id);
2945 __isl_give isl_aff *isl_aff_set_constant(
2946 __isl_take isl_aff *aff, isl_int v);
2947 __isl_give isl_aff *isl_aff_set_constant_si(
2948 __isl_take isl_aff *aff, int v);
2949 __isl_give isl_aff *isl_aff_set_coefficient(
2950 __isl_take isl_aff *aff,
2951 enum isl_dim_type type, int pos, isl_int v);
2952 __isl_give isl_aff *isl_aff_set_coefficient_si(
2953 __isl_take isl_aff *aff,
2954 enum isl_dim_type type, int pos, int v);
2955 __isl_give isl_aff *isl_aff_set_denominator(
2956 __isl_take isl_aff *aff, isl_int v);
2958 __isl_give isl_aff *isl_aff_add_constant(
2959 __isl_take isl_aff *aff, isl_int v);
2960 __isl_give isl_aff *isl_aff_add_constant_si(
2961 __isl_take isl_aff *aff, int v);
2962 __isl_give isl_aff *isl_aff_add_coefficient(
2963 __isl_take isl_aff *aff,
2964 enum isl_dim_type type, int pos, isl_int v);
2965 __isl_give isl_aff *isl_aff_add_coefficient_si(
2966 __isl_take isl_aff *aff,
2967 enum isl_dim_type type, int pos, int v);
2969 __isl_give isl_aff *isl_aff_insert_dims(
2970 __isl_take isl_aff *aff,
2971 enum isl_dim_type type, unsigned first, unsigned n);
2972 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2973 __isl_take isl_pw_aff *pwaff,
2974 enum isl_dim_type type, unsigned first, unsigned n);
2975 __isl_give isl_aff *isl_aff_add_dims(
2976 __isl_take isl_aff *aff,
2977 enum isl_dim_type type, unsigned n);
2978 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2979 __isl_take isl_pw_aff *pwaff,
2980 enum isl_dim_type type, unsigned n);
2981 __isl_give isl_aff *isl_aff_drop_dims(
2982 __isl_take isl_aff *aff,
2983 enum isl_dim_type type, unsigned first, unsigned n);
2984 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2985 __isl_take isl_pw_aff *pwaff,
2986 enum isl_dim_type type, unsigned first, unsigned n);
2988 Note that the C<set_constant> and C<set_coefficient> functions
2989 set the I<numerator> of the constant or coefficient, while
2990 C<add_constant> and C<add_coefficient> add an integer value to
2991 the possibly rational constant or coefficient.
2993 To check whether an affine expressions is obviously zero
2994 or obviously equal to some other affine expression, use
2996 #include <isl/aff.h>
2997 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2998 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2999 __isl_keep isl_aff *aff2);
3000 int isl_pw_aff_plain_is_equal(
3001 __isl_keep isl_pw_aff *pwaff1,
3002 __isl_keep isl_pw_aff *pwaff2);
3006 #include <isl/aff.h>
3007 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3008 __isl_take isl_aff *aff2);
3009 __isl_give isl_pw_aff *isl_pw_aff_add(
3010 __isl_take isl_pw_aff *pwaff1,
3011 __isl_take isl_pw_aff *pwaff2);
3012 __isl_give isl_pw_aff *isl_pw_aff_min(
3013 __isl_take isl_pw_aff *pwaff1,
3014 __isl_take isl_pw_aff *pwaff2);
3015 __isl_give isl_pw_aff *isl_pw_aff_max(
3016 __isl_take isl_pw_aff *pwaff1,
3017 __isl_take isl_pw_aff *pwaff2);
3018 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3019 __isl_take isl_aff *aff2);
3020 __isl_give isl_pw_aff *isl_pw_aff_sub(
3021 __isl_take isl_pw_aff *pwaff1,
3022 __isl_take isl_pw_aff *pwaff2);
3023 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3024 __isl_give isl_pw_aff *isl_pw_aff_neg(
3025 __isl_take isl_pw_aff *pwaff);
3026 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3027 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3028 __isl_take isl_pw_aff *pwaff);
3029 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3030 __isl_give isl_pw_aff *isl_pw_aff_floor(
3031 __isl_take isl_pw_aff *pwaff);
3032 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3034 __isl_give isl_pw_aff *isl_pw_aff_mod(
3035 __isl_take isl_pw_aff *pwaff, isl_int mod);
3036 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3038 __isl_give isl_pw_aff *isl_pw_aff_scale(
3039 __isl_take isl_pw_aff *pwaff, isl_int f);
3040 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3042 __isl_give isl_aff *isl_aff_scale_down_ui(
3043 __isl_take isl_aff *aff, unsigned f);
3044 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3045 __isl_take isl_pw_aff *pwaff, isl_int f);
3047 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3048 __isl_take isl_pw_aff_list *list);
3049 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3050 __isl_take isl_pw_aff_list *list);
3052 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3053 __isl_take isl_pw_aff *pwqp);
3055 __isl_give isl_aff *isl_aff_align_params(
3056 __isl_take isl_aff *aff,
3057 __isl_take isl_space *model);
3058 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3059 __isl_take isl_pw_aff *pwaff,
3060 __isl_take isl_space *model);
3062 __isl_give isl_aff *isl_aff_project_domain_on_params(
3063 __isl_take isl_aff *aff);
3065 __isl_give isl_aff *isl_aff_gist_params(
3066 __isl_take isl_aff *aff,
3067 __isl_take isl_set *context);
3068 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3069 __isl_take isl_set *context);
3070 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3071 __isl_take isl_pw_aff *pwaff,
3072 __isl_take isl_set *context);
3073 __isl_give isl_pw_aff *isl_pw_aff_gist(
3074 __isl_take isl_pw_aff *pwaff,
3075 __isl_take isl_set *context);
3077 __isl_give isl_set *isl_pw_aff_domain(
3078 __isl_take isl_pw_aff *pwaff);
3079 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3080 __isl_take isl_pw_aff *pa,
3081 __isl_take isl_set *set);
3082 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3083 __isl_take isl_pw_aff *pa,
3084 __isl_take isl_set *set);
3086 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3087 __isl_take isl_aff *aff2);
3088 __isl_give isl_pw_aff *isl_pw_aff_mul(
3089 __isl_take isl_pw_aff *pwaff1,
3090 __isl_take isl_pw_aff *pwaff2);
3092 When multiplying two affine expressions, at least one of the two needs
3095 #include <isl/aff.h>
3096 __isl_give isl_basic_set *isl_aff_le_basic_set(
3097 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3098 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3099 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3100 __isl_give isl_set *isl_pw_aff_eq_set(
3101 __isl_take isl_pw_aff *pwaff1,
3102 __isl_take isl_pw_aff *pwaff2);
3103 __isl_give isl_set *isl_pw_aff_ne_set(
3104 __isl_take isl_pw_aff *pwaff1,
3105 __isl_take isl_pw_aff *pwaff2);
3106 __isl_give isl_set *isl_pw_aff_le_set(
3107 __isl_take isl_pw_aff *pwaff1,
3108 __isl_take isl_pw_aff *pwaff2);
3109 __isl_give isl_set *isl_pw_aff_lt_set(
3110 __isl_take isl_pw_aff *pwaff1,
3111 __isl_take isl_pw_aff *pwaff2);
3112 __isl_give isl_set *isl_pw_aff_ge_set(
3113 __isl_take isl_pw_aff *pwaff1,
3114 __isl_take isl_pw_aff *pwaff2);
3115 __isl_give isl_set *isl_pw_aff_gt_set(
3116 __isl_take isl_pw_aff *pwaff1,
3117 __isl_take isl_pw_aff *pwaff2);
3119 __isl_give isl_set *isl_pw_aff_list_eq_set(
3120 __isl_take isl_pw_aff_list *list1,
3121 __isl_take isl_pw_aff_list *list2);
3122 __isl_give isl_set *isl_pw_aff_list_ne_set(
3123 __isl_take isl_pw_aff_list *list1,
3124 __isl_take isl_pw_aff_list *list2);
3125 __isl_give isl_set *isl_pw_aff_list_le_set(
3126 __isl_take isl_pw_aff_list *list1,
3127 __isl_take isl_pw_aff_list *list2);
3128 __isl_give isl_set *isl_pw_aff_list_lt_set(
3129 __isl_take isl_pw_aff_list *list1,
3130 __isl_take isl_pw_aff_list *list2);
3131 __isl_give isl_set *isl_pw_aff_list_ge_set(
3132 __isl_take isl_pw_aff_list *list1,
3133 __isl_take isl_pw_aff_list *list2);
3134 __isl_give isl_set *isl_pw_aff_list_gt_set(
3135 __isl_take isl_pw_aff_list *list1,
3136 __isl_take isl_pw_aff_list *list2);
3138 The function C<isl_aff_ge_basic_set> returns a basic set
3139 containing those elements in the shared space
3140 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3141 The function C<isl_aff_ge_set> returns a set
3142 containing those elements in the shared domain
3143 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3144 The functions operating on C<isl_pw_aff_list> apply the corresponding
3145 C<isl_pw_aff> function to each pair of elements in the two lists.
3147 #include <isl/aff.h>
3148 __isl_give isl_set *isl_pw_aff_nonneg_set(
3149 __isl_take isl_pw_aff *pwaff);
3150 __isl_give isl_set *isl_pw_aff_zero_set(
3151 __isl_take isl_pw_aff *pwaff);
3152 __isl_give isl_set *isl_pw_aff_non_zero_set(
3153 __isl_take isl_pw_aff *pwaff);
3155 The function C<isl_pw_aff_nonneg_set> returns a set
3156 containing those elements in the domain
3157 of C<pwaff> where C<pwaff> is non-negative.
3159 #include <isl/aff.h>
3160 __isl_give isl_pw_aff *isl_pw_aff_cond(
3161 __isl_take isl_pw_aff *cond,
3162 __isl_take isl_pw_aff *pwaff_true,
3163 __isl_take isl_pw_aff *pwaff_false);
3165 The function C<isl_pw_aff_cond> performs a conditional operator
3166 and returns an expression that is equal to C<pwaff_true>
3167 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3168 where C<cond> is zero.
3170 #include <isl/aff.h>
3171 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3172 __isl_take isl_pw_aff *pwaff1,
3173 __isl_take isl_pw_aff *pwaff2);
3174 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3175 __isl_take isl_pw_aff *pwaff1,
3176 __isl_take isl_pw_aff *pwaff2);
3177 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3178 __isl_take isl_pw_aff *pwaff1,
3179 __isl_take isl_pw_aff *pwaff2);
3181 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3182 expression with a domain that is the union of those of C<pwaff1> and
3183 C<pwaff2> and such that on each cell, the quasi-affine expression is
3184 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3185 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3186 associated expression is the defined one.
3188 An expression can be read from input using
3190 #include <isl/aff.h>
3191 __isl_give isl_aff *isl_aff_read_from_str(
3192 isl_ctx *ctx, const char *str);
3193 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3194 isl_ctx *ctx, const char *str);
3196 An expression can be printed using
3198 #include <isl/aff.h>
3199 __isl_give isl_printer *isl_printer_print_aff(
3200 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3202 __isl_give isl_printer *isl_printer_print_pw_aff(
3203 __isl_take isl_printer *p,
3204 __isl_keep isl_pw_aff *pwaff);
3206 =head2 Piecewise Multiple Quasi Affine Expressions
3208 An C<isl_multi_aff> object represents a sequence of
3209 zero or more affine expressions, all defined on the same domain space.
3211 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3214 #include <isl/aff.h>
3215 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3216 __isl_take isl_space *space,
3217 __isl_take isl_aff_list *list);
3219 An empty piecewise multiple quasi affine expression (one with no cells),
3220 the zero piecewise multiple quasi affine expression (with value zero
3221 for each output dimension),
3222 a piecewise multiple quasi affine expression with a single cell (with
3223 either a universe or a specified domain) or
3224 a zero-dimensional piecewise multiple quasi affine expression
3226 can be created using the following functions.
3228 #include <isl/aff.h>
3229 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3230 __isl_take isl_space *space);
3231 __isl_give isl_multi_aff *isl_multi_aff_zero(
3232 __isl_take isl_space *space);
3233 __isl_give isl_pw_multi_aff *
3234 isl_pw_multi_aff_from_multi_aff(
3235 __isl_take isl_multi_aff *ma);
3236 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3237 __isl_take isl_set *set,
3238 __isl_take isl_multi_aff *maff);
3239 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3240 __isl_take isl_set *set);
3242 __isl_give isl_union_pw_multi_aff *
3243 isl_union_pw_multi_aff_empty(
3244 __isl_take isl_space *space);
3245 __isl_give isl_union_pw_multi_aff *
3246 isl_union_pw_multi_aff_add_pw_multi_aff(
3247 __isl_take isl_union_pw_multi_aff *upma,
3248 __isl_take isl_pw_multi_aff *pma);
3249 __isl_give isl_union_pw_multi_aff *
3250 isl_union_pw_multi_aff_from_domain(
3251 __isl_take isl_union_set *uset);
3253 A piecewise multiple quasi affine expression can also be initialized
3254 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3255 and the C<isl_map> is single-valued.
3257 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3258 __isl_take isl_set *set);
3259 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3260 __isl_take isl_map *map);
3262 Multiple quasi affine expressions can be copied and freed using
3264 #include <isl/aff.h>
3265 __isl_give isl_multi_aff *isl_multi_aff_copy(
3266 __isl_keep isl_multi_aff *maff);
3267 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3269 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3270 __isl_keep isl_pw_multi_aff *pma);
3271 void *isl_pw_multi_aff_free(
3272 __isl_take isl_pw_multi_aff *pma);
3274 __isl_give isl_union_pw_multi_aff *
3275 isl_union_pw_multi_aff_copy(
3276 __isl_keep isl_union_pw_multi_aff *upma);
3277 void *isl_union_pw_multi_aff_free(
3278 __isl_take isl_union_pw_multi_aff *upma);
3280 The expression can be inspected using
3282 #include <isl/aff.h>
3283 isl_ctx *isl_multi_aff_get_ctx(
3284 __isl_keep isl_multi_aff *maff);
3285 isl_ctx *isl_pw_multi_aff_get_ctx(
3286 __isl_keep isl_pw_multi_aff *pma);
3287 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3288 __isl_keep isl_union_pw_multi_aff *upma);
3289 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3290 enum isl_dim_type type);
3291 unsigned isl_pw_multi_aff_dim(
3292 __isl_keep isl_pw_multi_aff *pma,
3293 enum isl_dim_type type);
3294 __isl_give isl_aff *isl_multi_aff_get_aff(
3295 __isl_keep isl_multi_aff *multi, int pos);
3296 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3297 __isl_keep isl_pw_multi_aff *pma, int pos);
3298 const char *isl_pw_multi_aff_get_dim_name(
3299 __isl_keep isl_pw_multi_aff *pma,
3300 enum isl_dim_type type, unsigned pos);
3301 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3302 __isl_keep isl_pw_multi_aff *pma,
3303 enum isl_dim_type type, unsigned pos);
3304 const char *isl_multi_aff_get_tuple_name(
3305 __isl_keep isl_multi_aff *multi,
3306 enum isl_dim_type type);
3307 const char *isl_pw_multi_aff_get_tuple_name(
3308 __isl_keep isl_pw_multi_aff *pma,
3309 enum isl_dim_type type);
3310 int isl_pw_multi_aff_has_tuple_id(
3311 __isl_keep isl_pw_multi_aff *pma,
3312 enum isl_dim_type type);
3313 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3314 __isl_keep isl_pw_multi_aff *pma,
3315 enum isl_dim_type type);
3317 int isl_pw_multi_aff_foreach_piece(
3318 __isl_keep isl_pw_multi_aff *pma,
3319 int (*fn)(__isl_take isl_set *set,
3320 __isl_take isl_multi_aff *maff,
3321 void *user), void *user);
3323 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3324 __isl_keep isl_union_pw_multi_aff *upma,
3325 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3326 void *user), void *user);
3328 It can be modified using
3330 #include <isl/aff.h>
3331 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3332 __isl_take isl_multi_aff *multi, int pos,
3333 __isl_take isl_aff *aff);
3334 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3335 __isl_take isl_multi_aff *maff,
3336 enum isl_dim_type type, unsigned pos, const char *s);
3337 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3338 __isl_take isl_multi_aff *maff,
3339 enum isl_dim_type type, __isl_take isl_id *id);
3340 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3341 __isl_take isl_pw_multi_aff *pma,
3342 enum isl_dim_type type, __isl_take isl_id *id);
3344 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3345 __isl_take isl_multi_aff *maff,
3346 enum isl_dim_type type, unsigned first, unsigned n);
3348 To check whether two multiple affine expressions are
3349 obviously equal to each other, use
3351 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3352 __isl_keep isl_multi_aff *maff2);
3353 int isl_pw_multi_aff_plain_is_equal(
3354 __isl_keep isl_pw_multi_aff *pma1,
3355 __isl_keep isl_pw_multi_aff *pma2);
3359 #include <isl/aff.h>
3360 __isl_give isl_multi_aff *isl_multi_aff_add(
3361 __isl_take isl_multi_aff *maff1,
3362 __isl_take isl_multi_aff *maff2);
3363 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3364 __isl_take isl_pw_multi_aff *pma1,
3365 __isl_take isl_pw_multi_aff *pma2);
3366 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3367 __isl_take isl_union_pw_multi_aff *upma1,
3368 __isl_take isl_union_pw_multi_aff *upma2);
3369 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3370 __isl_take isl_pw_multi_aff *pma1,
3371 __isl_take isl_pw_multi_aff *pma2);
3372 __isl_give isl_multi_aff *isl_multi_aff_scale(
3373 __isl_take isl_multi_aff *maff,
3375 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3376 __isl_take isl_pw_multi_aff *pma,
3377 __isl_take isl_set *set);
3378 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3379 __isl_take isl_pw_multi_aff *pma,
3380 __isl_take isl_set *set);
3381 __isl_give isl_multi_aff *isl_multi_aff_lift(
3382 __isl_take isl_multi_aff *maff,
3383 __isl_give isl_local_space **ls);
3384 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3385 __isl_take isl_pw_multi_aff *pma);
3386 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3387 __isl_take isl_multi_aff *maff,
3388 __isl_take isl_set *context);
3389 __isl_give isl_multi_aff *isl_multi_aff_gist(
3390 __isl_take isl_multi_aff *maff,
3391 __isl_take isl_set *context);
3392 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3393 __isl_take isl_pw_multi_aff *pma,
3394 __isl_take isl_set *set);
3395 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3396 __isl_take isl_pw_multi_aff *pma,
3397 __isl_take isl_set *set);
3398 __isl_give isl_set *isl_pw_multi_aff_domain(
3399 __isl_take isl_pw_multi_aff *pma);
3400 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3401 __isl_take isl_union_pw_multi_aff *upma);
3402 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3403 __isl_take isl_multi_aff *ma1,
3404 __isl_take isl_multi_aff *ma2);
3405 __isl_give isl_pw_multi_aff *
3406 isl_pw_multi_aff_flat_range_product(
3407 __isl_take isl_pw_multi_aff *pma1,
3408 __isl_take isl_pw_multi_aff *pma2);
3409 __isl_give isl_union_pw_multi_aff *
3410 isl_union_pw_multi_aff_flat_range_product(
3411 __isl_take isl_union_pw_multi_aff *upma1,
3412 __isl_take isl_union_pw_multi_aff *upma2);
3414 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3415 then it is assigned the local space that lies at the basis of
3416 the lifting applied.
3418 An expression can be read from input using
3420 #include <isl/aff.h>
3421 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3422 isl_ctx *ctx, const char *str);
3423 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3424 isl_ctx *ctx, const char *str);
3426 An expression can be printed using
3428 #include <isl/aff.h>
3429 __isl_give isl_printer *isl_printer_print_multi_aff(
3430 __isl_take isl_printer *p,
3431 __isl_keep isl_multi_aff *maff);
3432 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3433 __isl_take isl_printer *p,
3434 __isl_keep isl_pw_multi_aff *pma);
3435 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3436 __isl_take isl_printer *p,
3437 __isl_keep isl_union_pw_multi_aff *upma);
3441 Points are elements of a set. They can be used to construct
3442 simple sets (boxes) or they can be used to represent the
3443 individual elements of a set.
3444 The zero point (the origin) can be created using
3446 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3448 The coordinates of a point can be inspected, set and changed
3451 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3452 enum isl_dim_type type, int pos, isl_int *v);
3453 __isl_give isl_point *isl_point_set_coordinate(
3454 __isl_take isl_point *pnt,
3455 enum isl_dim_type type, int pos, isl_int v);
3457 __isl_give isl_point *isl_point_add_ui(
3458 __isl_take isl_point *pnt,
3459 enum isl_dim_type type, int pos, unsigned val);
3460 __isl_give isl_point *isl_point_sub_ui(
3461 __isl_take isl_point *pnt,
3462 enum isl_dim_type type, int pos, unsigned val);
3464 Other properties can be obtained using
3466 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3468 Points can be copied or freed using
3470 __isl_give isl_point *isl_point_copy(
3471 __isl_keep isl_point *pnt);
3472 void isl_point_free(__isl_take isl_point *pnt);
3474 A singleton set can be created from a point using
3476 __isl_give isl_basic_set *isl_basic_set_from_point(
3477 __isl_take isl_point *pnt);
3478 __isl_give isl_set *isl_set_from_point(
3479 __isl_take isl_point *pnt);
3481 and a box can be created from two opposite extremal points using
3483 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3484 __isl_take isl_point *pnt1,
3485 __isl_take isl_point *pnt2);
3486 __isl_give isl_set *isl_set_box_from_points(
3487 __isl_take isl_point *pnt1,
3488 __isl_take isl_point *pnt2);
3490 All elements of a B<bounded> (union) set can be enumerated using
3491 the following functions.
3493 int isl_set_foreach_point(__isl_keep isl_set *set,
3494 int (*fn)(__isl_take isl_point *pnt, void *user),
3496 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3497 int (*fn)(__isl_take isl_point *pnt, void *user),
3500 The function C<fn> is called for each integer point in
3501 C<set> with as second argument the last argument of
3502 the C<isl_set_foreach_point> call. The function C<fn>
3503 should return C<0> on success and C<-1> on failure.
3504 In the latter case, C<isl_set_foreach_point> will stop
3505 enumerating and return C<-1> as well.
3506 If the enumeration is performed successfully and to completion,
3507 then C<isl_set_foreach_point> returns C<0>.
3509 To obtain a single point of a (basic) set, use
3511 __isl_give isl_point *isl_basic_set_sample_point(
3512 __isl_take isl_basic_set *bset);
3513 __isl_give isl_point *isl_set_sample_point(
3514 __isl_take isl_set *set);
3516 If C<set> does not contain any (integer) points, then the
3517 resulting point will be ``void'', a property that can be
3520 int isl_point_is_void(__isl_keep isl_point *pnt);
3522 =head2 Piecewise Quasipolynomials
3524 A piecewise quasipolynomial is a particular kind of function that maps
3525 a parametric point to a rational value.
3526 More specifically, a quasipolynomial is a polynomial expression in greatest
3527 integer parts of affine expressions of parameters and variables.
3528 A piecewise quasipolynomial is a subdivision of a given parametric
3529 domain into disjoint cells with a quasipolynomial associated to
3530 each cell. The value of the piecewise quasipolynomial at a given
3531 point is the value of the quasipolynomial associated to the cell
3532 that contains the point. Outside of the union of cells,
3533 the value is assumed to be zero.
3534 For example, the piecewise quasipolynomial
3536 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3538 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3539 A given piecewise quasipolynomial has a fixed domain dimension.
3540 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3541 defined over different domains.
3542 Piecewise quasipolynomials are mainly used by the C<barvinok>
3543 library for representing the number of elements in a parametric set or map.
3544 For example, the piecewise quasipolynomial above represents
3545 the number of points in the map
3547 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3549 =head3 Input and Output
3551 Piecewise quasipolynomials can be read from input using
3553 __isl_give isl_union_pw_qpolynomial *
3554 isl_union_pw_qpolynomial_read_from_str(
3555 isl_ctx *ctx, const char *str);
3557 Quasipolynomials and piecewise quasipolynomials can be printed
3558 using the following functions.
3560 __isl_give isl_printer *isl_printer_print_qpolynomial(
3561 __isl_take isl_printer *p,
3562 __isl_keep isl_qpolynomial *qp);
3564 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3565 __isl_take isl_printer *p,
3566 __isl_keep isl_pw_qpolynomial *pwqp);
3568 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3569 __isl_take isl_printer *p,
3570 __isl_keep isl_union_pw_qpolynomial *upwqp);
3572 The output format of the printer
3573 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3574 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3576 In case of printing in C<ISL_FORMAT_C>, the user may want
3577 to set the names of all dimensions
3579 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3580 __isl_take isl_qpolynomial *qp,
3581 enum isl_dim_type type, unsigned pos,
3583 __isl_give isl_pw_qpolynomial *
3584 isl_pw_qpolynomial_set_dim_name(
3585 __isl_take isl_pw_qpolynomial *pwqp,
3586 enum isl_dim_type type, unsigned pos,
3589 =head3 Creating New (Piecewise) Quasipolynomials
3591 Some simple quasipolynomials can be created using the following functions.
3592 More complicated quasipolynomials can be created by applying
3593 operations such as addition and multiplication
3594 on the resulting quasipolynomials
3596 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3597 __isl_take isl_space *domain);
3598 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3599 __isl_take isl_space *domain);
3600 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3601 __isl_take isl_space *domain);
3602 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3603 __isl_take isl_space *domain);
3604 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3605 __isl_take isl_space *domain);
3606 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3607 __isl_take isl_space *domain,
3608 const isl_int n, const isl_int d);
3609 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3610 __isl_take isl_space *domain,
3611 enum isl_dim_type type, unsigned pos);
3612 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3613 __isl_take isl_aff *aff);
3615 Note that the space in which a quasipolynomial lives is a map space
3616 with a one-dimensional range. The C<domain> argument in some of
3617 the functions above corresponds to the domain of this map space.
3619 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3620 with a single cell can be created using the following functions.
3621 Multiple of these single cell piecewise quasipolynomials can
3622 be combined to create more complicated piecewise quasipolynomials.
3624 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3625 __isl_take isl_space *space);
3626 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3627 __isl_take isl_set *set,
3628 __isl_take isl_qpolynomial *qp);
3629 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3630 __isl_take isl_qpolynomial *qp);
3631 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3632 __isl_take isl_pw_aff *pwaff);
3634 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3635 __isl_take isl_space *space);
3636 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3637 __isl_take isl_pw_qpolynomial *pwqp);
3638 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3639 __isl_take isl_union_pw_qpolynomial *upwqp,
3640 __isl_take isl_pw_qpolynomial *pwqp);
3642 Quasipolynomials can be copied and freed again using the following
3645 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3646 __isl_keep isl_qpolynomial *qp);
3647 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3649 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3650 __isl_keep isl_pw_qpolynomial *pwqp);
3651 void *isl_pw_qpolynomial_free(
3652 __isl_take isl_pw_qpolynomial *pwqp);
3654 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3655 __isl_keep isl_union_pw_qpolynomial *upwqp);
3656 void *isl_union_pw_qpolynomial_free(
3657 __isl_take isl_union_pw_qpolynomial *upwqp);
3659 =head3 Inspecting (Piecewise) Quasipolynomials
3661 To iterate over all piecewise quasipolynomials in a union
3662 piecewise quasipolynomial, use the following function
3664 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3665 __isl_keep isl_union_pw_qpolynomial *upwqp,
3666 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3669 To extract the piecewise quasipolynomial in a given space from a union, use
3671 __isl_give isl_pw_qpolynomial *
3672 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3673 __isl_keep isl_union_pw_qpolynomial *upwqp,
3674 __isl_take isl_space *space);
3676 To iterate over the cells in a piecewise quasipolynomial,
3677 use either of the following two functions
3679 int isl_pw_qpolynomial_foreach_piece(
3680 __isl_keep isl_pw_qpolynomial *pwqp,
3681 int (*fn)(__isl_take isl_set *set,
3682 __isl_take isl_qpolynomial *qp,
3683 void *user), void *user);
3684 int isl_pw_qpolynomial_foreach_lifted_piece(
3685 __isl_keep isl_pw_qpolynomial *pwqp,
3686 int (*fn)(__isl_take isl_set *set,
3687 __isl_take isl_qpolynomial *qp,
3688 void *user), void *user);
3690 As usual, the function C<fn> should return C<0> on success
3691 and C<-1> on failure. The difference between
3692 C<isl_pw_qpolynomial_foreach_piece> and
3693 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3694 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3695 compute unique representations for all existentially quantified
3696 variables and then turn these existentially quantified variables
3697 into extra set variables, adapting the associated quasipolynomial
3698 accordingly. This means that the C<set> passed to C<fn>
3699 will not have any existentially quantified variables, but that
3700 the dimensions of the sets may be different for different
3701 invocations of C<fn>.
3703 To iterate over all terms in a quasipolynomial,
3706 int isl_qpolynomial_foreach_term(
3707 __isl_keep isl_qpolynomial *qp,
3708 int (*fn)(__isl_take isl_term *term,
3709 void *user), void *user);
3711 The terms themselves can be inspected and freed using
3714 unsigned isl_term_dim(__isl_keep isl_term *term,
3715 enum isl_dim_type type);
3716 void isl_term_get_num(__isl_keep isl_term *term,
3718 void isl_term_get_den(__isl_keep isl_term *term,
3720 int isl_term_get_exp(__isl_keep isl_term *term,
3721 enum isl_dim_type type, unsigned pos);
3722 __isl_give isl_aff *isl_term_get_div(
3723 __isl_keep isl_term *term, unsigned pos);
3724 void isl_term_free(__isl_take isl_term *term);
3726 Each term is a product of parameters, set variables and
3727 integer divisions. The function C<isl_term_get_exp>
3728 returns the exponent of a given dimensions in the given term.
3729 The C<isl_int>s in the arguments of C<isl_term_get_num>
3730 and C<isl_term_get_den> need to have been initialized
3731 using C<isl_int_init> before calling these functions.
3733 =head3 Properties of (Piecewise) Quasipolynomials
3735 To check whether a quasipolynomial is actually a constant,
3736 use the following function.
3738 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3739 isl_int *n, isl_int *d);
3741 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3742 then the numerator and denominator of the constant
3743 are returned in C<*n> and C<*d>, respectively.
3745 To check whether two union piecewise quasipolynomials are
3746 obviously equal, use
3748 int isl_union_pw_qpolynomial_plain_is_equal(
3749 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3750 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3752 =head3 Operations on (Piecewise) Quasipolynomials
3754 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3755 __isl_take isl_qpolynomial *qp, isl_int v);
3756 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3757 __isl_take isl_qpolynomial *qp);
3758 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3759 __isl_take isl_qpolynomial *qp1,
3760 __isl_take isl_qpolynomial *qp2);
3761 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3762 __isl_take isl_qpolynomial *qp1,
3763 __isl_take isl_qpolynomial *qp2);
3764 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3765 __isl_take isl_qpolynomial *qp1,
3766 __isl_take isl_qpolynomial *qp2);
3767 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3768 __isl_take isl_qpolynomial *qp, unsigned exponent);
3770 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3771 __isl_take isl_pw_qpolynomial *pwqp1,
3772 __isl_take isl_pw_qpolynomial *pwqp2);
3773 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3774 __isl_take isl_pw_qpolynomial *pwqp1,
3775 __isl_take isl_pw_qpolynomial *pwqp2);
3776 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3777 __isl_take isl_pw_qpolynomial *pwqp1,
3778 __isl_take isl_pw_qpolynomial *pwqp2);
3779 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3780 __isl_take isl_pw_qpolynomial *pwqp);
3781 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3782 __isl_take isl_pw_qpolynomial *pwqp1,
3783 __isl_take isl_pw_qpolynomial *pwqp2);
3784 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3785 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3787 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3788 __isl_take isl_union_pw_qpolynomial *upwqp1,
3789 __isl_take isl_union_pw_qpolynomial *upwqp2);
3790 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3791 __isl_take isl_union_pw_qpolynomial *upwqp1,
3792 __isl_take isl_union_pw_qpolynomial *upwqp2);
3793 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3794 __isl_take isl_union_pw_qpolynomial *upwqp1,
3795 __isl_take isl_union_pw_qpolynomial *upwqp2);
3797 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3798 __isl_take isl_pw_qpolynomial *pwqp,
3799 __isl_take isl_point *pnt);
3801 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3802 __isl_take isl_union_pw_qpolynomial *upwqp,
3803 __isl_take isl_point *pnt);
3805 __isl_give isl_set *isl_pw_qpolynomial_domain(
3806 __isl_take isl_pw_qpolynomial *pwqp);
3807 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3808 __isl_take isl_pw_qpolynomial *pwpq,
3809 __isl_take isl_set *set);
3810 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3811 __isl_take isl_pw_qpolynomial *pwpq,
3812 __isl_take isl_set *set);
3814 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3815 __isl_take isl_union_pw_qpolynomial *upwqp);
3816 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3817 __isl_take isl_union_pw_qpolynomial *upwpq,
3818 __isl_take isl_union_set *uset);
3819 __isl_give isl_union_pw_qpolynomial *
3820 isl_union_pw_qpolynomial_intersect_params(
3821 __isl_take isl_union_pw_qpolynomial *upwpq,
3822 __isl_take isl_set *set);
3824 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3825 __isl_take isl_qpolynomial *qp,
3826 __isl_take isl_space *model);
3828 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3829 __isl_take isl_qpolynomial *qp);
3830 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3831 __isl_take isl_pw_qpolynomial *pwqp);
3833 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3834 __isl_take isl_union_pw_qpolynomial *upwqp);
3836 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3837 __isl_take isl_qpolynomial *qp,
3838 __isl_take isl_set *context);
3839 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3840 __isl_take isl_qpolynomial *qp,
3841 __isl_take isl_set *context);
3843 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3844 __isl_take isl_pw_qpolynomial *pwqp,
3845 __isl_take isl_set *context);
3846 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3847 __isl_take isl_pw_qpolynomial *pwqp,
3848 __isl_take isl_set *context);
3850 __isl_give isl_union_pw_qpolynomial *
3851 isl_union_pw_qpolynomial_gist_params(
3852 __isl_take isl_union_pw_qpolynomial *upwqp,
3853 __isl_take isl_set *context);
3854 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3855 __isl_take isl_union_pw_qpolynomial *upwqp,
3856 __isl_take isl_union_set *context);
3858 The gist operation applies the gist operation to each of
3859 the cells in the domain of the input piecewise quasipolynomial.
3860 The context is also exploited
3861 to simplify the quasipolynomials associated to each cell.
3863 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3864 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3865 __isl_give isl_union_pw_qpolynomial *
3866 isl_union_pw_qpolynomial_to_polynomial(
3867 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3869 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3870 the polynomial will be an overapproximation. If C<sign> is negative,
3871 it will be an underapproximation. If C<sign> is zero, the approximation
3872 will lie somewhere in between.
3874 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3876 A piecewise quasipolynomial reduction is a piecewise
3877 reduction (or fold) of quasipolynomials.
3878 In particular, the reduction can be maximum or a minimum.
3879 The objects are mainly used to represent the result of
3880 an upper or lower bound on a quasipolynomial over its domain,
3881 i.e., as the result of the following function.
3883 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3884 __isl_take isl_pw_qpolynomial *pwqp,
3885 enum isl_fold type, int *tight);
3887 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3888 __isl_take isl_union_pw_qpolynomial *upwqp,
3889 enum isl_fold type, int *tight);
3891 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3892 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3893 is the returned bound is known be tight, i.e., for each value
3894 of the parameters there is at least
3895 one element in the domain that reaches the bound.
3896 If the domain of C<pwqp> is not wrapping, then the bound is computed
3897 over all elements in that domain and the result has a purely parametric
3898 domain. If the domain of C<pwqp> is wrapping, then the bound is
3899 computed over the range of the wrapped relation. The domain of the
3900 wrapped relation becomes the domain of the result.
3902 A (piecewise) quasipolynomial reduction can be copied or freed using the
3903 following functions.
3905 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3906 __isl_keep isl_qpolynomial_fold *fold);
3907 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3908 __isl_keep isl_pw_qpolynomial_fold *pwf);
3909 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3910 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3911 void isl_qpolynomial_fold_free(
3912 __isl_take isl_qpolynomial_fold *fold);
3913 void *isl_pw_qpolynomial_fold_free(
3914 __isl_take isl_pw_qpolynomial_fold *pwf);
3915 void *isl_union_pw_qpolynomial_fold_free(
3916 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3918 =head3 Printing Piecewise Quasipolynomial Reductions
3920 Piecewise quasipolynomial reductions can be printed
3921 using the following function.
3923 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3924 __isl_take isl_printer *p,
3925 __isl_keep isl_pw_qpolynomial_fold *pwf);
3926 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3927 __isl_take isl_printer *p,
3928 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3930 For C<isl_printer_print_pw_qpolynomial_fold>,
3931 output format of the printer
3932 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3933 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3934 output format of the printer
3935 needs to be set to C<ISL_FORMAT_ISL>.
3936 In case of printing in C<ISL_FORMAT_C>, the user may want
3937 to set the names of all dimensions
3939 __isl_give isl_pw_qpolynomial_fold *
3940 isl_pw_qpolynomial_fold_set_dim_name(
3941 __isl_take isl_pw_qpolynomial_fold *pwf,
3942 enum isl_dim_type type, unsigned pos,
3945 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3947 To iterate over all piecewise quasipolynomial reductions in a union
3948 piecewise quasipolynomial reduction, use the following function
3950 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3951 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3952 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3953 void *user), void *user);
3955 To iterate over the cells in a piecewise quasipolynomial reduction,
3956 use either of the following two functions
3958 int isl_pw_qpolynomial_fold_foreach_piece(
3959 __isl_keep isl_pw_qpolynomial_fold *pwf,
3960 int (*fn)(__isl_take isl_set *set,
3961 __isl_take isl_qpolynomial_fold *fold,
3962 void *user), void *user);
3963 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3964 __isl_keep isl_pw_qpolynomial_fold *pwf,
3965 int (*fn)(__isl_take isl_set *set,
3966 __isl_take isl_qpolynomial_fold *fold,
3967 void *user), void *user);
3969 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3970 of the difference between these two functions.
3972 To iterate over all quasipolynomials in a reduction, use
3974 int isl_qpolynomial_fold_foreach_qpolynomial(
3975 __isl_keep isl_qpolynomial_fold *fold,
3976 int (*fn)(__isl_take isl_qpolynomial *qp,
3977 void *user), void *user);
3979 =head3 Properties of Piecewise Quasipolynomial Reductions
3981 To check whether two union piecewise quasipolynomial reductions are
3982 obviously equal, use
3984 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3985 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3986 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3988 =head3 Operations on Piecewise Quasipolynomial Reductions
3990 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3991 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3993 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3994 __isl_take isl_pw_qpolynomial_fold *pwf1,
3995 __isl_take isl_pw_qpolynomial_fold *pwf2);
3997 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3998 __isl_take isl_pw_qpolynomial_fold *pwf1,
3999 __isl_take isl_pw_qpolynomial_fold *pwf2);
4001 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4002 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4003 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4005 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4006 __isl_take isl_pw_qpolynomial_fold *pwf,
4007 __isl_take isl_point *pnt);
4009 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4010 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4011 __isl_take isl_point *pnt);
4013 __isl_give isl_pw_qpolynomial_fold *
4014 sl_pw_qpolynomial_fold_intersect_params(
4015 __isl_take isl_pw_qpolynomial_fold *pwf,
4016 __isl_take isl_set *set);
4018 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4019 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4020 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4021 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4022 __isl_take isl_union_set *uset);
4023 __isl_give isl_union_pw_qpolynomial_fold *
4024 isl_union_pw_qpolynomial_fold_intersect_params(
4025 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4026 __isl_take isl_set *set);
4028 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4029 __isl_take isl_pw_qpolynomial_fold *pwf);
4031 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4032 __isl_take isl_pw_qpolynomial_fold *pwf);
4034 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4035 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4037 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4038 __isl_take isl_qpolynomial_fold *fold,
4039 __isl_take isl_set *context);
4040 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4041 __isl_take isl_qpolynomial_fold *fold,
4042 __isl_take isl_set *context);
4044 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4045 __isl_take isl_pw_qpolynomial_fold *pwf,
4046 __isl_take isl_set *context);
4047 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4048 __isl_take isl_pw_qpolynomial_fold *pwf,
4049 __isl_take isl_set *context);
4051 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4052 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4053 __isl_take isl_union_set *context);
4054 __isl_give isl_union_pw_qpolynomial_fold *
4055 isl_union_pw_qpolynomial_fold_gist_params(
4056 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4057 __isl_take isl_set *context);
4059 The gist operation applies the gist operation to each of
4060 the cells in the domain of the input piecewise quasipolynomial reduction.
4061 In future, the operation will also exploit the context
4062 to simplify the quasipolynomial reductions associated to each cell.
4064 __isl_give isl_pw_qpolynomial_fold *
4065 isl_set_apply_pw_qpolynomial_fold(
4066 __isl_take isl_set *set,
4067 __isl_take isl_pw_qpolynomial_fold *pwf,
4069 __isl_give isl_pw_qpolynomial_fold *
4070 isl_map_apply_pw_qpolynomial_fold(
4071 __isl_take isl_map *map,
4072 __isl_take isl_pw_qpolynomial_fold *pwf,
4074 __isl_give isl_union_pw_qpolynomial_fold *
4075 isl_union_set_apply_union_pw_qpolynomial_fold(
4076 __isl_take isl_union_set *uset,
4077 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4079 __isl_give isl_union_pw_qpolynomial_fold *
4080 isl_union_map_apply_union_pw_qpolynomial_fold(
4081 __isl_take isl_union_map *umap,
4082 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4085 The functions taking a map
4086 compose the given map with the given piecewise quasipolynomial reduction.
4087 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4088 over all elements in the intersection of the range of the map
4089 and the domain of the piecewise quasipolynomial reduction
4090 as a function of an element in the domain of the map.
4091 The functions taking a set compute a bound over all elements in the
4092 intersection of the set and the domain of the
4093 piecewise quasipolynomial reduction.
4095 =head2 Dependence Analysis
4097 C<isl> contains specialized functionality for performing
4098 array dataflow analysis. That is, given a I<sink> access relation
4099 and a collection of possible I<source> access relations,
4100 C<isl> can compute relations that describe
4101 for each iteration of the sink access, which iteration
4102 of which of the source access relations was the last
4103 to access the same data element before the given iteration
4105 The resulting dependence relations map source iterations
4106 to the corresponding sink iterations.
4107 To compute standard flow dependences, the sink should be
4108 a read, while the sources should be writes.
4109 If any of the source accesses are marked as being I<may>
4110 accesses, then there will be a dependence from the last
4111 I<must> access B<and> from any I<may> access that follows
4112 this last I<must> access.
4113 In particular, if I<all> sources are I<may> accesses,
4114 then memory based dependence analysis is performed.
4115 If, on the other hand, all sources are I<must> accesses,
4116 then value based dependence analysis is performed.
4118 #include <isl/flow.h>
4120 typedef int (*isl_access_level_before)(void *first, void *second);
4122 __isl_give isl_access_info *isl_access_info_alloc(
4123 __isl_take isl_map *sink,
4124 void *sink_user, isl_access_level_before fn,
4126 __isl_give isl_access_info *isl_access_info_add_source(
4127 __isl_take isl_access_info *acc,
4128 __isl_take isl_map *source, int must,
4130 void isl_access_info_free(__isl_take isl_access_info *acc);
4132 __isl_give isl_flow *isl_access_info_compute_flow(
4133 __isl_take isl_access_info *acc);
4135 int isl_flow_foreach(__isl_keep isl_flow *deps,
4136 int (*fn)(__isl_take isl_map *dep, int must,
4137 void *dep_user, void *user),
4139 __isl_give isl_map *isl_flow_get_no_source(
4140 __isl_keep isl_flow *deps, int must);
4141 void isl_flow_free(__isl_take isl_flow *deps);
4143 The function C<isl_access_info_compute_flow> performs the actual
4144 dependence analysis. The other functions are used to construct
4145 the input for this function or to read off the output.
4147 The input is collected in an C<isl_access_info>, which can
4148 be created through a call to C<isl_access_info_alloc>.
4149 The arguments to this functions are the sink access relation
4150 C<sink>, a token C<sink_user> used to identify the sink
4151 access to the user, a callback function for specifying the
4152 relative order of source and sink accesses, and the number
4153 of source access relations that will be added.
4154 The callback function has type C<int (*)(void *first, void *second)>.
4155 The function is called with two user supplied tokens identifying
4156 either a source or the sink and it should return the shared nesting
4157 level and the relative order of the two accesses.
4158 In particular, let I<n> be the number of loops shared by
4159 the two accesses. If C<first> precedes C<second> textually,
4160 then the function should return I<2 * n + 1>; otherwise,
4161 it should return I<2 * n>.
4162 The sources can be added to the C<isl_access_info> by performing
4163 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4164 C<must> indicates whether the source is a I<must> access
4165 or a I<may> access. Note that a multi-valued access relation
4166 should only be marked I<must> if every iteration in the domain
4167 of the relation accesses I<all> elements in its image.
4168 The C<source_user> token is again used to identify
4169 the source access. The range of the source access relation
4170 C<source> should have the same dimension as the range
4171 of the sink access relation.
4172 The C<isl_access_info_free> function should usually not be
4173 called explicitly, because it is called implicitly by
4174 C<isl_access_info_compute_flow>.
4176 The result of the dependence analysis is collected in an
4177 C<isl_flow>. There may be elements of
4178 the sink access for which no preceding source access could be
4179 found or for which all preceding sources are I<may> accesses.
4180 The relations containing these elements can be obtained through
4181 calls to C<isl_flow_get_no_source>, the first with C<must> set
4182 and the second with C<must> unset.
4183 In the case of standard flow dependence analysis,
4184 with the sink a read and the sources I<must> writes,
4185 the first relation corresponds to the reads from uninitialized
4186 array elements and the second relation is empty.
4187 The actual flow dependences can be extracted using
4188 C<isl_flow_foreach>. This function will call the user-specified
4189 callback function C<fn> for each B<non-empty> dependence between
4190 a source and the sink. The callback function is called
4191 with four arguments, the actual flow dependence relation
4192 mapping source iterations to sink iterations, a boolean that
4193 indicates whether it is a I<must> or I<may> dependence, a token
4194 identifying the source and an additional C<void *> with value
4195 equal to the third argument of the C<isl_flow_foreach> call.
4196 A dependence is marked I<must> if it originates from a I<must>
4197 source and if it is not followed by any I<may> sources.
4199 After finishing with an C<isl_flow>, the user should call
4200 C<isl_flow_free> to free all associated memory.
4202 A higher-level interface to dependence analysis is provided
4203 by the following function.
4205 #include <isl/flow.h>
4207 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4208 __isl_take isl_union_map *must_source,
4209 __isl_take isl_union_map *may_source,
4210 __isl_take isl_union_map *schedule,
4211 __isl_give isl_union_map **must_dep,
4212 __isl_give isl_union_map **may_dep,
4213 __isl_give isl_union_map **must_no_source,
4214 __isl_give isl_union_map **may_no_source);
4216 The arrays are identified by the tuple names of the ranges
4217 of the accesses. The iteration domains by the tuple names
4218 of the domains of the accesses and of the schedule.
4219 The relative order of the iteration domains is given by the
4220 schedule. The relations returned through C<must_no_source>
4221 and C<may_no_source> are subsets of C<sink>.
4222 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4223 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4224 any of the other arguments is treated as an error.
4226 =head3 Interaction with Dependence Analysis
4228 During the dependence analysis, we frequently need to perform
4229 the following operation. Given a relation between sink iterations
4230 and potential soure iterations from a particular source domain,
4231 what is the last potential source iteration corresponding to each
4232 sink iteration. It can sometimes be convenient to adjust
4233 the set of potential source iterations before or after each such operation.
4234 The prototypical example is fuzzy array dataflow analysis,
4235 where we need to analyze if, based on data-dependent constraints,
4236 the sink iteration can ever be executed without one or more of
4237 the corresponding potential source iterations being executed.
4238 If so, we can introduce extra parameters and select an unknown
4239 but fixed source iteration from the potential source iterations.
4240 To be able to perform such manipulations, C<isl> provides the following
4243 #include <isl/flow.h>
4245 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4246 __isl_keep isl_map *source_map,
4247 __isl_keep isl_set *sink, void *source_user,
4249 __isl_give isl_access_info *isl_access_info_set_restrict(
4250 __isl_take isl_access_info *acc,
4251 isl_access_restrict fn, void *user);
4253 The function C<isl_access_info_set_restrict> should be called
4254 before calling C<isl_access_info_compute_flow> and registers a callback function
4255 that will be called any time C<isl> is about to compute the last
4256 potential source. The first argument is the (reverse) proto-dependence,
4257 mapping sink iterations to potential source iterations.
4258 The second argument represents the sink iterations for which
4259 we want to compute the last source iteration.
4260 The third argument is the token corresponding to the source
4261 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4262 The callback is expected to return a restriction on either the input or
4263 the output of the operation computing the last potential source.
4264 If the input needs to be restricted then restrictions are needed
4265 for both the source and the sink iterations. The sink iterations
4266 and the potential source iterations will be intersected with these sets.
4267 If the output needs to be restricted then only a restriction on the source
4268 iterations is required.
4269 If any error occurs, the callback should return C<NULL>.
4270 An C<isl_restriction> object can be created and freed using the following
4273 #include <isl/flow.h>
4275 __isl_give isl_restriction *isl_restriction_input(
4276 __isl_take isl_set *source_restr,
4277 __isl_take isl_set *sink_restr);
4278 __isl_give isl_restriction *isl_restriction_output(
4279 __isl_take isl_set *source_restr);
4280 __isl_give isl_restriction *isl_restriction_none(
4281 __isl_keep isl_map *source_map);
4282 __isl_give isl_restriction *isl_restriction_empty(
4283 __isl_keep isl_map *source_map);
4284 void *isl_restriction_free(
4285 __isl_take isl_restriction *restr);
4287 C<isl_restriction_none> and C<isl_restriction_empty> are special
4288 cases of C<isl_restriction_input>. C<isl_restriction_none>
4289 is essentially equivalent to
4291 isl_restriction_input(isl_set_universe(
4292 isl_space_range(isl_map_get_space(source_map))),
4294 isl_space_domain(isl_map_get_space(source_map))));
4296 whereas C<isl_restriction_empty> is essentially equivalent to
4298 isl_restriction_input(isl_set_empty(
4299 isl_space_range(isl_map_get_space(source_map))),
4301 isl_space_domain(isl_map_get_space(source_map))));
4305 B<The functionality described in this section is fairly new
4306 and may be subject to change.>
4308 The following function can be used to compute a schedule
4309 for a union of domains.
4310 By default, the algorithm used to construct the schedule is similar
4311 to that of C<Pluto>.
4312 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4314 The generated schedule respects all C<validity> dependences.
4315 That is, all dependence distances over these dependences in the
4316 scheduled space are lexicographically positive.
4317 The default algorithm tries to minimize the dependence distances over
4318 C<proximity> dependences.
4319 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4320 for groups of domains where the dependence distances have only
4321 non-negative values.
4322 When using Feautrier's algorithm, the C<proximity> dependence
4323 distances are only minimized during the extension to a
4324 full-dimensional schedule.
4326 #include <isl/schedule.h>
4327 __isl_give isl_schedule *isl_union_set_compute_schedule(
4328 __isl_take isl_union_set *domain,
4329 __isl_take isl_union_map *validity,
4330 __isl_take isl_union_map *proximity);
4331 void *isl_schedule_free(__isl_take isl_schedule *sched);
4333 A mapping from the domains to the scheduled space can be obtained
4334 from an C<isl_schedule> using the following function.
4336 __isl_give isl_union_map *isl_schedule_get_map(
4337 __isl_keep isl_schedule *sched);
4339 A representation of the schedule can be printed using
4341 __isl_give isl_printer *isl_printer_print_schedule(
4342 __isl_take isl_printer *p,
4343 __isl_keep isl_schedule *schedule);
4345 A representation of the schedule as a forest of bands can be obtained
4346 using the following function.
4348 __isl_give isl_band_list *isl_schedule_get_band_forest(
4349 __isl_keep isl_schedule *schedule);
4351 The list can be manipulated as explained in L<"Lists">.
4352 The bands inside the list can be copied and freed using the following
4355 #include <isl/band.h>
4356 __isl_give isl_band *isl_band_copy(
4357 __isl_keep isl_band *band);
4358 void *isl_band_free(__isl_take isl_band *band);
4360 Each band contains zero or more scheduling dimensions.
4361 These are referred to as the members of the band.
4362 The section of the schedule that corresponds to the band is
4363 referred to as the partial schedule of the band.
4364 For those nodes that participate in a band, the outer scheduling
4365 dimensions form the prefix schedule, while the inner scheduling
4366 dimensions form the suffix schedule.
4367 That is, if we take a cut of the band forest, then the union of
4368 the concatenations of the prefix, partial and suffix schedules of
4369 each band in the cut is equal to the entire schedule (modulo
4370 some possible padding at the end with zero scheduling dimensions).
4371 The properties of a band can be inspected using the following functions.
4373 #include <isl/band.h>
4374 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4376 int isl_band_has_children(__isl_keep isl_band *band);
4377 __isl_give isl_band_list *isl_band_get_children(
4378 __isl_keep isl_band *band);
4380 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4381 __isl_keep isl_band *band);
4382 __isl_give isl_union_map *isl_band_get_partial_schedule(
4383 __isl_keep isl_band *band);
4384 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4385 __isl_keep isl_band *band);
4387 int isl_band_n_member(__isl_keep isl_band *band);
4388 int isl_band_member_is_zero_distance(
4389 __isl_keep isl_band *band, int pos);
4391 Note that a scheduling dimension is considered to be ``zero
4392 distance'' if it does not carry any proximity dependences
4394 That is, if the dependence distances of the proximity
4395 dependences are all zero in that direction (for fixed
4396 iterations of outer bands).
4398 A representation of the band can be printed using
4400 #include <isl/band.h>
4401 __isl_give isl_printer *isl_printer_print_band(
4402 __isl_take isl_printer *p,
4403 __isl_keep isl_band *band);
4407 #include <isl/schedule.h>
4408 int isl_options_set_schedule_max_coefficient(
4409 isl_ctx *ctx, int val);
4410 int isl_options_get_schedule_max_coefficient(
4412 int isl_options_set_schedule_max_constant_term(
4413 isl_ctx *ctx, int val);
4414 int isl_options_get_schedule_max_constant_term(
4416 int isl_options_set_schedule_maximize_band_depth(
4417 isl_ctx *ctx, int val);
4418 int isl_options_get_schedule_maximize_band_depth(
4420 int isl_options_set_schedule_outer_zero_distance(
4421 isl_ctx *ctx, int val);
4422 int isl_options_get_schedule_outer_zero_distance(
4424 int isl_options_set_schedule_split_scaled(
4425 isl_ctx *ctx, int val);
4426 int isl_options_get_schedule_split_scaled(
4428 int isl_options_set_schedule_algorithm(
4429 isl_ctx *ctx, int val);
4430 int isl_options_get_schedule_algorithm(
4436 =item * schedule_max_coefficient
4438 This option enforces that the coefficients for variable and parameter
4439 dimensions in the calculated schedule are not larger than the specified value.
4440 This option can significantly increase the speed of the scheduling calculation
4441 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4442 this option does not introduce bounds on the variable or parameter
4445 =item * schedule_max_constant_term
4447 This option enforces that the constant coefficients in the calculated schedule
4448 are not larger than the maximal constant term. This option can significantly
4449 increase the speed of the scheduling calculation and may also prevent fusing of
4450 unrelated dimensions. A value of -1 means that this option does not introduce
4451 bounds on the constant coefficients.
4453 =item * schedule_maximize_band_depth
4455 If this option is set, we do not split bands at the point
4456 where we detect splitting is necessary. Instead, we
4457 backtrack and split bands as early as possible. This
4458 reduces the number of splits and maximizes the width of
4459 the bands. Wider bands give more possibilities for tiling.
4461 =item * schedule_outer_zero_distance
4463 If this option is set, then we try to construct schedules
4464 where the outermost scheduling dimension in each band
4465 results in a zero dependence distance over the proximity
4468 =item * schedule_split_scaled
4470 If this option is set, then we try to construct schedules in which the
4471 constant term is split off from the linear part if the linear parts of
4472 the scheduling rows for all nodes in the graphs have a common non-trivial
4474 The constant term is then placed in a separate band and the linear
4477 =item * schedule_algorithm
4479 Selects the scheduling algorithm to be used.
4480 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4481 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4485 =head2 Parametric Vertex Enumeration
4487 The parametric vertex enumeration described in this section
4488 is mainly intended to be used internally and by the C<barvinok>
4491 #include <isl/vertices.h>
4492 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4493 __isl_keep isl_basic_set *bset);
4495 The function C<isl_basic_set_compute_vertices> performs the
4496 actual computation of the parametric vertices and the chamber
4497 decomposition and store the result in an C<isl_vertices> object.
4498 This information can be queried by either iterating over all
4499 the vertices or iterating over all the chambers or cells
4500 and then iterating over all vertices that are active on the chamber.
4502 int isl_vertices_foreach_vertex(
4503 __isl_keep isl_vertices *vertices,
4504 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4507 int isl_vertices_foreach_cell(
4508 __isl_keep isl_vertices *vertices,
4509 int (*fn)(__isl_take isl_cell *cell, void *user),
4511 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4512 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4515 Other operations that can be performed on an C<isl_vertices> object are
4518 isl_ctx *isl_vertices_get_ctx(
4519 __isl_keep isl_vertices *vertices);
4520 int isl_vertices_get_n_vertices(
4521 __isl_keep isl_vertices *vertices);
4522 void isl_vertices_free(__isl_take isl_vertices *vertices);
4524 Vertices can be inspected and destroyed using the following functions.
4526 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4527 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4528 __isl_give isl_basic_set *isl_vertex_get_domain(
4529 __isl_keep isl_vertex *vertex);
4530 __isl_give isl_basic_set *isl_vertex_get_expr(
4531 __isl_keep isl_vertex *vertex);
4532 void isl_vertex_free(__isl_take isl_vertex *vertex);
4534 C<isl_vertex_get_expr> returns a singleton parametric set describing
4535 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4537 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4538 B<rational> basic sets, so they should mainly be used for inspection
4539 and should not be mixed with integer sets.
4541 Chambers can be inspected and destroyed using the following functions.
4543 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4544 __isl_give isl_basic_set *isl_cell_get_domain(
4545 __isl_keep isl_cell *cell);
4546 void isl_cell_free(__isl_take isl_cell *cell);
4550 Although C<isl> is mainly meant to be used as a library,
4551 it also contains some basic applications that use some
4552 of the functionality of C<isl>.
4553 The input may be specified in either the L<isl format>
4554 or the L<PolyLib format>.
4556 =head2 C<isl_polyhedron_sample>
4558 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4559 an integer element of the polyhedron, if there is any.
4560 The first column in the output is the denominator and is always
4561 equal to 1. If the polyhedron contains no integer points,
4562 then a vector of length zero is printed.
4566 C<isl_pip> takes the same input as the C<example> program
4567 from the C<piplib> distribution, i.e., a set of constraints
4568 on the parameters, a line containing only -1 and finally a set
4569 of constraints on a parametric polyhedron.
4570 The coefficients of the parameters appear in the last columns
4571 (but before the final constant column).
4572 The output is the lexicographic minimum of the parametric polyhedron.
4573 As C<isl> currently does not have its own output format, the output
4574 is just a dump of the internal state.
4576 =head2 C<isl_polyhedron_minimize>
4578 C<isl_polyhedron_minimize> computes the minimum of some linear
4579 or affine objective function over the integer points in a polyhedron.
4580 If an affine objective function
4581 is given, then the constant should appear in the last column.
4583 =head2 C<isl_polytope_scan>
4585 Given a polytope, C<isl_polytope_scan> prints
4586 all integer points in the polytope.