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_set *isl_set_from_pw_aff(
1290 __isl_take isl_pw_aff *pwaff);
1291 __isl_give isl_map *isl_map_from_pw_aff(
1292 __isl_take isl_pw_aff *pwaff);
1293 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1294 __isl_take isl_space *domain_space,
1295 __isl_take isl_aff_list *list);
1296 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1297 __isl_take isl_multi_aff *maff)
1298 __isl_give isl_map *isl_map_from_multi_aff(
1299 __isl_take isl_multi_aff *maff)
1300 __isl_give isl_set *isl_set_from_pw_multi_aff(
1301 __isl_take isl_pw_multi_aff *pma);
1302 __isl_give isl_map *isl_map_from_pw_multi_aff(
1303 __isl_take isl_pw_multi_aff *pma);
1304 __isl_give isl_union_map *
1305 isl_union_map_from_union_pw_multi_aff(
1306 __isl_take isl_union_pw_multi_aff *upma);
1308 The C<domain_dim> argument describes the domain of the resulting
1309 basic relation. It is required because the C<list> may consist
1310 of zero affine expressions.
1312 =head2 Inspecting Sets and Relations
1314 Usually, the user should not have to care about the actual constraints
1315 of the sets and maps, but should instead apply the abstract operations
1316 explained in the following sections.
1317 Occasionally, however, it may be required to inspect the individual
1318 coefficients of the constraints. This section explains how to do so.
1319 In these cases, it may also be useful to have C<isl> compute
1320 an explicit representation of the existentially quantified variables.
1322 __isl_give isl_set *isl_set_compute_divs(
1323 __isl_take isl_set *set);
1324 __isl_give isl_map *isl_map_compute_divs(
1325 __isl_take isl_map *map);
1326 __isl_give isl_union_set *isl_union_set_compute_divs(
1327 __isl_take isl_union_set *uset);
1328 __isl_give isl_union_map *isl_union_map_compute_divs(
1329 __isl_take isl_union_map *umap);
1331 This explicit representation defines the existentially quantified
1332 variables as integer divisions of the other variables, possibly
1333 including earlier existentially quantified variables.
1334 An explicitly represented existentially quantified variable therefore
1335 has a unique value when the values of the other variables are known.
1336 If, furthermore, the same existentials, i.e., existentials
1337 with the same explicit representations, should appear in the
1338 same order in each of the disjuncts of a set or map, then the user should call
1339 either of the following functions.
1341 __isl_give isl_set *isl_set_align_divs(
1342 __isl_take isl_set *set);
1343 __isl_give isl_map *isl_map_align_divs(
1344 __isl_take isl_map *map);
1346 Alternatively, the existentially quantified variables can be removed
1347 using the following functions, which compute an overapproximation.
1349 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1350 __isl_take isl_basic_set *bset);
1351 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1352 __isl_take isl_basic_map *bmap);
1353 __isl_give isl_set *isl_set_remove_divs(
1354 __isl_take isl_set *set);
1355 __isl_give isl_map *isl_map_remove_divs(
1356 __isl_take isl_map *map);
1358 To iterate over all the sets or maps in a union set or map, use
1360 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1361 int (*fn)(__isl_take isl_set *set, void *user),
1363 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1364 int (*fn)(__isl_take isl_map *map, void *user),
1367 The number of sets or maps in a union set or map can be obtained
1370 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1371 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1373 To extract the set or map in a given space from a union, use
1375 __isl_give isl_set *isl_union_set_extract_set(
1376 __isl_keep isl_union_set *uset,
1377 __isl_take isl_space *space);
1378 __isl_give isl_map *isl_union_map_extract_map(
1379 __isl_keep isl_union_map *umap,
1380 __isl_take isl_space *space);
1382 To iterate over all the basic sets or maps in a set or map, use
1384 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1385 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1387 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1388 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1391 The callback function C<fn> should return 0 if successful and
1392 -1 if an error occurs. In the latter case, or if any other error
1393 occurs, the above functions will return -1.
1395 It should be noted that C<isl> does not guarantee that
1396 the basic sets or maps passed to C<fn> are disjoint.
1397 If this is required, then the user should call one of
1398 the following functions first.
1400 __isl_give isl_set *isl_set_make_disjoint(
1401 __isl_take isl_set *set);
1402 __isl_give isl_map *isl_map_make_disjoint(
1403 __isl_take isl_map *map);
1405 The number of basic sets in a set can be obtained
1408 int isl_set_n_basic_set(__isl_keep isl_set *set);
1410 To iterate over the constraints of a basic set or map, use
1412 #include <isl/constraint.h>
1414 int isl_basic_map_foreach_constraint(
1415 __isl_keep isl_basic_map *bmap,
1416 int (*fn)(__isl_take isl_constraint *c, void *user),
1418 void *isl_constraint_free(__isl_take isl_constraint *c);
1420 Again, the callback function C<fn> should return 0 if successful and
1421 -1 if an error occurs. In the latter case, or if any other error
1422 occurs, the above functions will return -1.
1423 The constraint C<c> represents either an equality or an inequality.
1424 Use the following function to find out whether a constraint
1425 represents an equality. If not, it represents an inequality.
1427 int isl_constraint_is_equality(
1428 __isl_keep isl_constraint *constraint);
1430 The coefficients of the constraints can be inspected using
1431 the following functions.
1433 void isl_constraint_get_constant(
1434 __isl_keep isl_constraint *constraint, isl_int *v);
1435 void isl_constraint_get_coefficient(
1436 __isl_keep isl_constraint *constraint,
1437 enum isl_dim_type type, int pos, isl_int *v);
1438 int isl_constraint_involves_dims(
1439 __isl_keep isl_constraint *constraint,
1440 enum isl_dim_type type, unsigned first, unsigned n);
1442 The explicit representations of the existentially quantified
1443 variables can be inspected using the following function.
1444 Note that the user is only allowed to use this function
1445 if the inspected set or map is the result of a call
1446 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1447 The existentially quantified variable is equal to the floor
1448 of the returned affine expression. The affine expression
1449 itself can be inspected using the functions in
1450 L<"Piecewise Quasi Affine Expressions">.
1452 __isl_give isl_aff *isl_constraint_get_div(
1453 __isl_keep isl_constraint *constraint, int pos);
1455 To obtain the constraints of a basic set or map in matrix
1456 form, use the following functions.
1458 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1459 __isl_keep isl_basic_set *bset,
1460 enum isl_dim_type c1, enum isl_dim_type c2,
1461 enum isl_dim_type c3, enum isl_dim_type c4);
1462 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1463 __isl_keep isl_basic_set *bset,
1464 enum isl_dim_type c1, enum isl_dim_type c2,
1465 enum isl_dim_type c3, enum isl_dim_type c4);
1466 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1467 __isl_keep isl_basic_map *bmap,
1468 enum isl_dim_type c1,
1469 enum isl_dim_type c2, enum isl_dim_type c3,
1470 enum isl_dim_type c4, enum isl_dim_type c5);
1471 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1472 __isl_keep isl_basic_map *bmap,
1473 enum isl_dim_type c1,
1474 enum isl_dim_type c2, enum isl_dim_type c3,
1475 enum isl_dim_type c4, enum isl_dim_type c5);
1477 The C<isl_dim_type> arguments dictate the order in which
1478 different kinds of variables appear in the resulting matrix
1479 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1480 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1482 The number of parameters, input, output or set dimensions can
1483 be obtained using the following functions.
1485 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1486 enum isl_dim_type type);
1487 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1488 enum isl_dim_type type);
1489 unsigned isl_set_dim(__isl_keep isl_set *set,
1490 enum isl_dim_type type);
1491 unsigned isl_map_dim(__isl_keep isl_map *map,
1492 enum isl_dim_type type);
1494 To check whether the description of a set or relation depends
1495 on one or more given dimensions, it is not necessary to iterate over all
1496 constraints. Instead the following functions can be used.
1498 int isl_basic_set_involves_dims(
1499 __isl_keep isl_basic_set *bset,
1500 enum isl_dim_type type, unsigned first, unsigned n);
1501 int isl_set_involves_dims(__isl_keep isl_set *set,
1502 enum isl_dim_type type, unsigned first, unsigned n);
1503 int isl_basic_map_involves_dims(
1504 __isl_keep isl_basic_map *bmap,
1505 enum isl_dim_type type, unsigned first, unsigned n);
1506 int isl_map_involves_dims(__isl_keep isl_map *map,
1507 enum isl_dim_type type, unsigned first, unsigned n);
1509 Similarly, the following functions can be used to check whether
1510 a given dimension is involved in any lower or upper bound.
1512 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1513 enum isl_dim_type type, unsigned pos);
1514 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1515 enum isl_dim_type type, unsigned pos);
1517 The identifiers or names of the domain and range spaces of a set
1518 or relation can be read off or set using the following functions.
1520 __isl_give isl_set *isl_set_set_tuple_id(
1521 __isl_take isl_set *set, __isl_take isl_id *id);
1522 __isl_give isl_set *isl_set_reset_tuple_id(
1523 __isl_take isl_set *set);
1524 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1525 __isl_give isl_id *isl_set_get_tuple_id(
1526 __isl_keep isl_set *set);
1527 __isl_give isl_map *isl_map_set_tuple_id(
1528 __isl_take isl_map *map, enum isl_dim_type type,
1529 __isl_take isl_id *id);
1530 __isl_give isl_map *isl_map_reset_tuple_id(
1531 __isl_take isl_map *map, enum isl_dim_type type);
1532 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1533 enum isl_dim_type type);
1534 __isl_give isl_id *isl_map_get_tuple_id(
1535 __isl_keep isl_map *map, enum isl_dim_type type);
1537 const char *isl_basic_set_get_tuple_name(
1538 __isl_keep isl_basic_set *bset);
1539 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1540 __isl_take isl_basic_set *set, const char *s);
1541 const char *isl_set_get_tuple_name(
1542 __isl_keep isl_set *set);
1543 const char *isl_basic_map_get_tuple_name(
1544 __isl_keep isl_basic_map *bmap,
1545 enum isl_dim_type type);
1546 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1547 __isl_take isl_basic_map *bmap,
1548 enum isl_dim_type type, const char *s);
1549 const char *isl_map_get_tuple_name(
1550 __isl_keep isl_map *map,
1551 enum isl_dim_type type);
1553 As with C<isl_space_get_tuple_name>, the value returned points to
1554 an internal data structure.
1555 The identifiers, positions or names of individual dimensions can be
1556 read off using the following functions.
1558 __isl_give isl_set *isl_set_set_dim_id(
1559 __isl_take isl_set *set, enum isl_dim_type type,
1560 unsigned pos, __isl_take isl_id *id);
1561 int isl_set_has_dim_id(__isl_keep isl_set *set,
1562 enum isl_dim_type type, unsigned pos);
1563 __isl_give isl_id *isl_set_get_dim_id(
1564 __isl_keep isl_set *set, enum isl_dim_type type,
1566 int isl_basic_map_has_dim_id(
1567 __isl_keep isl_basic_map *bmap,
1568 enum isl_dim_type type, unsigned pos);
1569 __isl_give isl_map *isl_map_set_dim_id(
1570 __isl_take isl_map *map, enum isl_dim_type type,
1571 unsigned pos, __isl_take isl_id *id);
1572 int isl_map_has_dim_id(__isl_keep isl_map *map,
1573 enum isl_dim_type type, unsigned pos);
1574 __isl_give isl_id *isl_map_get_dim_id(
1575 __isl_keep isl_map *map, enum isl_dim_type type,
1578 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1579 enum isl_dim_type type, __isl_keep isl_id *id);
1580 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1581 enum isl_dim_type type, __isl_keep isl_id *id);
1582 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1583 enum isl_dim_type type, const char *name);
1584 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1585 enum isl_dim_type type, const char *name);
1587 const char *isl_constraint_get_dim_name(
1588 __isl_keep isl_constraint *constraint,
1589 enum isl_dim_type type, unsigned pos);
1590 const char *isl_basic_set_get_dim_name(
1591 __isl_keep isl_basic_set *bset,
1592 enum isl_dim_type type, unsigned pos);
1593 int isl_set_has_dim_name(__isl_keep isl_set *set,
1594 enum isl_dim_type type, unsigned pos);
1595 const char *isl_set_get_dim_name(
1596 __isl_keep isl_set *set,
1597 enum isl_dim_type type, unsigned pos);
1598 const char *isl_basic_map_get_dim_name(
1599 __isl_keep isl_basic_map *bmap,
1600 enum isl_dim_type type, unsigned pos);
1601 const char *isl_map_get_dim_name(
1602 __isl_keep isl_map *map,
1603 enum isl_dim_type type, unsigned pos);
1605 These functions are mostly useful to obtain the identifiers, positions
1606 or names of the parameters. Identifiers of individual dimensions are
1607 essentially only useful for printing. They are ignored by all other
1608 operations and may not be preserved across those operations.
1612 =head3 Unary Properties
1618 The following functions test whether the given set or relation
1619 contains any integer points. The ``plain'' variants do not perform
1620 any computations, but simply check if the given set or relation
1621 is already known to be empty.
1623 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1624 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1625 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1626 int isl_set_is_empty(__isl_keep isl_set *set);
1627 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1628 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1629 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1630 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1631 int isl_map_is_empty(__isl_keep isl_map *map);
1632 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1634 =item * Universality
1636 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1637 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1638 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1640 =item * Single-valuedness
1642 int isl_map_plain_is_single_valued(
1643 __isl_keep isl_map *map);
1644 int isl_map_is_single_valued(__isl_keep isl_map *map);
1645 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1649 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1650 int isl_map_is_injective(__isl_keep isl_map *map);
1651 int isl_union_map_plain_is_injective(
1652 __isl_keep isl_union_map *umap);
1653 int isl_union_map_is_injective(
1654 __isl_keep isl_union_map *umap);
1658 int isl_map_is_bijective(__isl_keep isl_map *map);
1659 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1663 int isl_basic_map_plain_is_fixed(
1664 __isl_keep isl_basic_map *bmap,
1665 enum isl_dim_type type, unsigned pos,
1667 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1668 enum isl_dim_type type, unsigned pos,
1670 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1671 enum isl_dim_type type, unsigned pos,
1674 Check if the relation obviously lies on a hyperplane where the given dimension
1675 has a fixed value and if so, return that value in C<*val>.
1679 To check whether a set is a parameter domain, use this function:
1681 int isl_set_is_params(__isl_keep isl_set *set);
1682 int isl_union_set_is_params(
1683 __isl_keep isl_union_set *uset);
1687 The following functions check whether the domain of the given
1688 (basic) set is a wrapped relation.
1690 int isl_basic_set_is_wrapping(
1691 __isl_keep isl_basic_set *bset);
1692 int isl_set_is_wrapping(__isl_keep isl_set *set);
1694 =item * Internal Product
1696 int isl_basic_map_can_zip(
1697 __isl_keep isl_basic_map *bmap);
1698 int isl_map_can_zip(__isl_keep isl_map *map);
1700 Check whether the product of domain and range of the given relation
1702 i.e., whether both domain and range are nested relations.
1706 =head3 Binary Properties
1712 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1713 __isl_keep isl_set *set2);
1714 int isl_set_is_equal(__isl_keep isl_set *set1,
1715 __isl_keep isl_set *set2);
1716 int isl_union_set_is_equal(
1717 __isl_keep isl_union_set *uset1,
1718 __isl_keep isl_union_set *uset2);
1719 int isl_basic_map_is_equal(
1720 __isl_keep isl_basic_map *bmap1,
1721 __isl_keep isl_basic_map *bmap2);
1722 int isl_map_is_equal(__isl_keep isl_map *map1,
1723 __isl_keep isl_map *map2);
1724 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1725 __isl_keep isl_map *map2);
1726 int isl_union_map_is_equal(
1727 __isl_keep isl_union_map *umap1,
1728 __isl_keep isl_union_map *umap2);
1730 =item * Disjointness
1732 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1733 __isl_keep isl_set *set2);
1737 int isl_basic_set_is_subset(
1738 __isl_keep isl_basic_set *bset1,
1739 __isl_keep isl_basic_set *bset2);
1740 int isl_set_is_subset(__isl_keep isl_set *set1,
1741 __isl_keep isl_set *set2);
1742 int isl_set_is_strict_subset(
1743 __isl_keep isl_set *set1,
1744 __isl_keep isl_set *set2);
1745 int isl_union_set_is_subset(
1746 __isl_keep isl_union_set *uset1,
1747 __isl_keep isl_union_set *uset2);
1748 int isl_union_set_is_strict_subset(
1749 __isl_keep isl_union_set *uset1,
1750 __isl_keep isl_union_set *uset2);
1751 int isl_basic_map_is_subset(
1752 __isl_keep isl_basic_map *bmap1,
1753 __isl_keep isl_basic_map *bmap2);
1754 int isl_basic_map_is_strict_subset(
1755 __isl_keep isl_basic_map *bmap1,
1756 __isl_keep isl_basic_map *bmap2);
1757 int isl_map_is_subset(
1758 __isl_keep isl_map *map1,
1759 __isl_keep isl_map *map2);
1760 int isl_map_is_strict_subset(
1761 __isl_keep isl_map *map1,
1762 __isl_keep isl_map *map2);
1763 int isl_union_map_is_subset(
1764 __isl_keep isl_union_map *umap1,
1765 __isl_keep isl_union_map *umap2);
1766 int isl_union_map_is_strict_subset(
1767 __isl_keep isl_union_map *umap1,
1768 __isl_keep isl_union_map *umap2);
1772 =head2 Unary Operations
1778 __isl_give isl_set *isl_set_complement(
1779 __isl_take isl_set *set);
1780 __isl_give isl_map *isl_map_complement(
1781 __isl_take isl_map *map);
1785 __isl_give isl_basic_map *isl_basic_map_reverse(
1786 __isl_take isl_basic_map *bmap);
1787 __isl_give isl_map *isl_map_reverse(
1788 __isl_take isl_map *map);
1789 __isl_give isl_union_map *isl_union_map_reverse(
1790 __isl_take isl_union_map *umap);
1794 __isl_give isl_basic_set *isl_basic_set_project_out(
1795 __isl_take isl_basic_set *bset,
1796 enum isl_dim_type type, unsigned first, unsigned n);
1797 __isl_give isl_basic_map *isl_basic_map_project_out(
1798 __isl_take isl_basic_map *bmap,
1799 enum isl_dim_type type, unsigned first, unsigned n);
1800 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1801 enum isl_dim_type type, unsigned first, unsigned n);
1802 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1803 enum isl_dim_type type, unsigned first, unsigned n);
1804 __isl_give isl_basic_set *isl_basic_set_params(
1805 __isl_take isl_basic_set *bset);
1806 __isl_give isl_basic_set *isl_basic_map_domain(
1807 __isl_take isl_basic_map *bmap);
1808 __isl_give isl_basic_set *isl_basic_map_range(
1809 __isl_take isl_basic_map *bmap);
1810 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1811 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1812 __isl_give isl_set *isl_map_domain(
1813 __isl_take isl_map *bmap);
1814 __isl_give isl_set *isl_map_range(
1815 __isl_take isl_map *map);
1816 __isl_give isl_set *isl_union_set_params(
1817 __isl_take isl_union_set *uset);
1818 __isl_give isl_set *isl_union_map_params(
1819 __isl_take isl_union_map *umap);
1820 __isl_give isl_union_set *isl_union_map_domain(
1821 __isl_take isl_union_map *umap);
1822 __isl_give isl_union_set *isl_union_map_range(
1823 __isl_take isl_union_map *umap);
1825 __isl_give isl_basic_map *isl_basic_map_domain_map(
1826 __isl_take isl_basic_map *bmap);
1827 __isl_give isl_basic_map *isl_basic_map_range_map(
1828 __isl_take isl_basic_map *bmap);
1829 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1830 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1831 __isl_give isl_union_map *isl_union_map_domain_map(
1832 __isl_take isl_union_map *umap);
1833 __isl_give isl_union_map *isl_union_map_range_map(
1834 __isl_take isl_union_map *umap);
1836 The functions above construct a (basic, regular or union) relation
1837 that maps (a wrapped version of) the input relation to its domain or range.
1841 __isl_give isl_set *isl_set_eliminate(
1842 __isl_take isl_set *set, enum isl_dim_type type,
1843 unsigned first, unsigned n);
1844 __isl_give isl_basic_map *isl_basic_map_eliminate(
1845 __isl_take isl_basic_map *bmap,
1846 enum isl_dim_type type,
1847 unsigned first, unsigned n);
1848 __isl_give isl_map *isl_map_eliminate(
1849 __isl_take isl_map *map, enum isl_dim_type type,
1850 unsigned first, unsigned n);
1852 Eliminate the coefficients for the given dimensions from the constraints,
1853 without removing the dimensions.
1857 __isl_give isl_basic_set *isl_basic_set_fix(
1858 __isl_take isl_basic_set *bset,
1859 enum isl_dim_type type, unsigned pos,
1861 __isl_give isl_basic_set *isl_basic_set_fix_si(
1862 __isl_take isl_basic_set *bset,
1863 enum isl_dim_type type, unsigned pos, int value);
1864 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1865 enum isl_dim_type type, unsigned pos,
1867 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1868 enum isl_dim_type type, unsigned pos, int value);
1869 __isl_give isl_basic_map *isl_basic_map_fix_si(
1870 __isl_take isl_basic_map *bmap,
1871 enum isl_dim_type type, unsigned pos, int value);
1872 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1873 enum isl_dim_type type, unsigned pos, int value);
1875 Intersect the set or relation with the hyperplane where the given
1876 dimension has the fixed given value.
1878 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1879 __isl_take isl_basic_map *bmap,
1880 enum isl_dim_type type, unsigned pos, int value);
1881 __isl_give isl_set *isl_set_lower_bound(
1882 __isl_take isl_set *set,
1883 enum isl_dim_type type, unsigned pos,
1885 __isl_give isl_set *isl_set_lower_bound_si(
1886 __isl_take isl_set *set,
1887 enum isl_dim_type type, unsigned pos, int value);
1888 __isl_give isl_map *isl_map_lower_bound_si(
1889 __isl_take isl_map *map,
1890 enum isl_dim_type type, unsigned pos, int value);
1891 __isl_give isl_set *isl_set_upper_bound(
1892 __isl_take isl_set *set,
1893 enum isl_dim_type type, unsigned pos,
1895 __isl_give isl_set *isl_set_upper_bound_si(
1896 __isl_take isl_set *set,
1897 enum isl_dim_type type, unsigned pos, int value);
1898 __isl_give isl_map *isl_map_upper_bound_si(
1899 __isl_take isl_map *map,
1900 enum isl_dim_type type, unsigned pos, int value);
1902 Intersect the set or relation with the half-space where the given
1903 dimension has a value bounded by the fixed given value.
1905 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1906 enum isl_dim_type type1, int pos1,
1907 enum isl_dim_type type2, int pos2);
1908 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1909 enum isl_dim_type type1, int pos1,
1910 enum isl_dim_type type2, int pos2);
1912 Intersect the set or relation with the hyperplane where the given
1913 dimensions are equal to each other.
1915 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1916 enum isl_dim_type type1, int pos1,
1917 enum isl_dim_type type2, int pos2);
1919 Intersect the relation with the hyperplane where the given
1920 dimensions have opposite values.
1924 __isl_give isl_map *isl_set_identity(
1925 __isl_take isl_set *set);
1926 __isl_give isl_union_map *isl_union_set_identity(
1927 __isl_take isl_union_set *uset);
1929 Construct an identity relation on the given (union) set.
1933 __isl_give isl_basic_set *isl_basic_map_deltas(
1934 __isl_take isl_basic_map *bmap);
1935 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1936 __isl_give isl_union_set *isl_union_map_deltas(
1937 __isl_take isl_union_map *umap);
1939 These functions return a (basic) set containing the differences
1940 between image elements and corresponding domain elements in the input.
1942 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1943 __isl_take isl_basic_map *bmap);
1944 __isl_give isl_map *isl_map_deltas_map(
1945 __isl_take isl_map *map);
1946 __isl_give isl_union_map *isl_union_map_deltas_map(
1947 __isl_take isl_union_map *umap);
1949 The functions above construct a (basic, regular or union) relation
1950 that maps (a wrapped version of) the input relation to its delta set.
1954 Simplify the representation of a set or relation by trying
1955 to combine pairs of basic sets or relations into a single
1956 basic set or relation.
1958 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1959 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1960 __isl_give isl_union_set *isl_union_set_coalesce(
1961 __isl_take isl_union_set *uset);
1962 __isl_give isl_union_map *isl_union_map_coalesce(
1963 __isl_take isl_union_map *umap);
1965 One of the methods for combining pairs of basic sets or relations
1966 can result in coefficients that are much larger than those that appear
1967 in the constraints of the input. By default, the coefficients are
1968 not allowed to grow larger, but this can be changed by unsetting
1969 the following option.
1971 int isl_options_set_coalesce_bounded_wrapping(
1972 isl_ctx *ctx, int val);
1973 int isl_options_get_coalesce_bounded_wrapping(
1976 =item * Detecting equalities
1978 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1979 __isl_take isl_basic_set *bset);
1980 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1981 __isl_take isl_basic_map *bmap);
1982 __isl_give isl_set *isl_set_detect_equalities(
1983 __isl_take isl_set *set);
1984 __isl_give isl_map *isl_map_detect_equalities(
1985 __isl_take isl_map *map);
1986 __isl_give isl_union_set *isl_union_set_detect_equalities(
1987 __isl_take isl_union_set *uset);
1988 __isl_give isl_union_map *isl_union_map_detect_equalities(
1989 __isl_take isl_union_map *umap);
1991 Simplify the representation of a set or relation by detecting implicit
1994 =item * Removing redundant constraints
1996 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1997 __isl_take isl_basic_set *bset);
1998 __isl_give isl_set *isl_set_remove_redundancies(
1999 __isl_take isl_set *set);
2000 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2001 __isl_take isl_basic_map *bmap);
2002 __isl_give isl_map *isl_map_remove_redundancies(
2003 __isl_take isl_map *map);
2007 __isl_give isl_basic_set *isl_set_convex_hull(
2008 __isl_take isl_set *set);
2009 __isl_give isl_basic_map *isl_map_convex_hull(
2010 __isl_take isl_map *map);
2012 If the input set or relation has any existentially quantified
2013 variables, then the result of these operations is currently undefined.
2017 __isl_give isl_basic_set *isl_set_simple_hull(
2018 __isl_take isl_set *set);
2019 __isl_give isl_basic_map *isl_map_simple_hull(
2020 __isl_take isl_map *map);
2021 __isl_give isl_union_map *isl_union_map_simple_hull(
2022 __isl_take isl_union_map *umap);
2024 These functions compute a single basic set or relation
2025 that contains the whole input set or relation.
2026 In particular, the output is described by translates
2027 of the constraints describing the basic sets or relations in the input.
2031 (See \autoref{s:simple hull}.)
2037 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2038 __isl_take isl_basic_set *bset);
2039 __isl_give isl_basic_set *isl_set_affine_hull(
2040 __isl_take isl_set *set);
2041 __isl_give isl_union_set *isl_union_set_affine_hull(
2042 __isl_take isl_union_set *uset);
2043 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2044 __isl_take isl_basic_map *bmap);
2045 __isl_give isl_basic_map *isl_map_affine_hull(
2046 __isl_take isl_map *map);
2047 __isl_give isl_union_map *isl_union_map_affine_hull(
2048 __isl_take isl_union_map *umap);
2050 In case of union sets and relations, the affine hull is computed
2053 =item * Polyhedral hull
2055 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2056 __isl_take isl_set *set);
2057 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2058 __isl_take isl_map *map);
2059 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2060 __isl_take isl_union_set *uset);
2061 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2062 __isl_take isl_union_map *umap);
2064 These functions compute a single basic set or relation
2065 not involving any existentially quantified variables
2066 that contains the whole input set or relation.
2067 In case of union sets and relations, the polyhedral hull is computed
2072 __isl_give isl_basic_set *isl_basic_set_sample(
2073 __isl_take isl_basic_set *bset);
2074 __isl_give isl_basic_set *isl_set_sample(
2075 __isl_take isl_set *set);
2076 __isl_give isl_basic_map *isl_basic_map_sample(
2077 __isl_take isl_basic_map *bmap);
2078 __isl_give isl_basic_map *isl_map_sample(
2079 __isl_take isl_map *map);
2081 If the input (basic) set or relation is non-empty, then return
2082 a singleton subset of the input. Otherwise, return an empty set.
2084 =item * Optimization
2086 #include <isl/ilp.h>
2087 enum isl_lp_result isl_basic_set_max(
2088 __isl_keep isl_basic_set *bset,
2089 __isl_keep isl_aff *obj, isl_int *opt)
2090 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2091 __isl_keep isl_aff *obj, isl_int *opt);
2092 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2093 __isl_keep isl_aff *obj, isl_int *opt);
2095 Compute the minimum or maximum of the integer affine expression C<obj>
2096 over the points in C<set>, returning the result in C<opt>.
2097 The return value may be one of C<isl_lp_error>,
2098 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2100 =item * Parametric optimization
2102 __isl_give isl_pw_aff *isl_set_dim_min(
2103 __isl_take isl_set *set, int pos);
2104 __isl_give isl_pw_aff *isl_set_dim_max(
2105 __isl_take isl_set *set, int pos);
2106 __isl_give isl_pw_aff *isl_map_dim_max(
2107 __isl_take isl_map *map, int pos);
2109 Compute the minimum or maximum of the given set or output dimension
2110 as a function of the parameters (and input dimensions), but independently
2111 of the other set or output dimensions.
2112 For lexicographic optimization, see L<"Lexicographic Optimization">.
2116 The following functions compute either the set of (rational) coefficient
2117 values of valid constraints for the given set or the set of (rational)
2118 values satisfying the constraints with coefficients from the given set.
2119 Internally, these two sets of functions perform essentially the
2120 same operations, except that the set of coefficients is assumed to
2121 be a cone, while the set of values may be any polyhedron.
2122 The current implementation is based on the Farkas lemma and
2123 Fourier-Motzkin elimination, but this may change or be made optional
2124 in future. In particular, future implementations may use different
2125 dualization algorithms or skip the elimination step.
2127 __isl_give isl_basic_set *isl_basic_set_coefficients(
2128 __isl_take isl_basic_set *bset);
2129 __isl_give isl_basic_set *isl_set_coefficients(
2130 __isl_take isl_set *set);
2131 __isl_give isl_union_set *isl_union_set_coefficients(
2132 __isl_take isl_union_set *bset);
2133 __isl_give isl_basic_set *isl_basic_set_solutions(
2134 __isl_take isl_basic_set *bset);
2135 __isl_give isl_basic_set *isl_set_solutions(
2136 __isl_take isl_set *set);
2137 __isl_give isl_union_set *isl_union_set_solutions(
2138 __isl_take isl_union_set *bset);
2142 __isl_give isl_map *isl_map_fixed_power(
2143 __isl_take isl_map *map, isl_int exp);
2144 __isl_give isl_union_map *isl_union_map_fixed_power(
2145 __isl_take isl_union_map *umap, isl_int exp);
2147 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2148 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2149 of C<map> is computed.
2151 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2153 __isl_give isl_union_map *isl_union_map_power(
2154 __isl_take isl_union_map *umap, int *exact);
2156 Compute a parametric representation for all positive powers I<k> of C<map>.
2157 The result maps I<k> to a nested relation corresponding to the
2158 I<k>th power of C<map>.
2159 The result may be an overapproximation. If the result is known to be exact,
2160 then C<*exact> is set to C<1>.
2162 =item * Transitive closure
2164 __isl_give isl_map *isl_map_transitive_closure(
2165 __isl_take isl_map *map, int *exact);
2166 __isl_give isl_union_map *isl_union_map_transitive_closure(
2167 __isl_take isl_union_map *umap, int *exact);
2169 Compute the transitive closure of C<map>.
2170 The result may be an overapproximation. If the result is known to be exact,
2171 then C<*exact> is set to C<1>.
2173 =item * Reaching path lengths
2175 __isl_give isl_map *isl_map_reaching_path_lengths(
2176 __isl_take isl_map *map, int *exact);
2178 Compute a relation that maps each element in the range of C<map>
2179 to the lengths of all paths composed of edges in C<map> that
2180 end up in the given element.
2181 The result may be an overapproximation. If the result is known to be exact,
2182 then C<*exact> is set to C<1>.
2183 To compute the I<maximal> path length, the resulting relation
2184 should be postprocessed by C<isl_map_lexmax>.
2185 In particular, if the input relation is a dependence relation
2186 (mapping sources to sinks), then the maximal path length corresponds
2187 to the free schedule.
2188 Note, however, that C<isl_map_lexmax> expects the maximum to be
2189 finite, so if the path lengths are unbounded (possibly due to
2190 the overapproximation), then you will get an error message.
2194 __isl_give isl_basic_set *isl_basic_map_wrap(
2195 __isl_take isl_basic_map *bmap);
2196 __isl_give isl_set *isl_map_wrap(
2197 __isl_take isl_map *map);
2198 __isl_give isl_union_set *isl_union_map_wrap(
2199 __isl_take isl_union_map *umap);
2200 __isl_give isl_basic_map *isl_basic_set_unwrap(
2201 __isl_take isl_basic_set *bset);
2202 __isl_give isl_map *isl_set_unwrap(
2203 __isl_take isl_set *set);
2204 __isl_give isl_union_map *isl_union_set_unwrap(
2205 __isl_take isl_union_set *uset);
2209 Remove any internal structure of domain (and range) of the given
2210 set or relation. If there is any such internal structure in the input,
2211 then the name of the space is also removed.
2213 __isl_give isl_basic_set *isl_basic_set_flatten(
2214 __isl_take isl_basic_set *bset);
2215 __isl_give isl_set *isl_set_flatten(
2216 __isl_take isl_set *set);
2217 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2218 __isl_take isl_basic_map *bmap);
2219 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2220 __isl_take isl_basic_map *bmap);
2221 __isl_give isl_map *isl_map_flatten_range(
2222 __isl_take isl_map *map);
2223 __isl_give isl_map *isl_map_flatten_domain(
2224 __isl_take isl_map *map);
2225 __isl_give isl_basic_map *isl_basic_map_flatten(
2226 __isl_take isl_basic_map *bmap);
2227 __isl_give isl_map *isl_map_flatten(
2228 __isl_take isl_map *map);
2230 __isl_give isl_map *isl_set_flatten_map(
2231 __isl_take isl_set *set);
2233 The function above constructs a relation
2234 that maps the input set to a flattened version of the set.
2238 Lift the input set to a space with extra dimensions corresponding
2239 to the existentially quantified variables in the input.
2240 In particular, the result lives in a wrapped map where the domain
2241 is the original space and the range corresponds to the original
2242 existentially quantified variables.
2244 __isl_give isl_basic_set *isl_basic_set_lift(
2245 __isl_take isl_basic_set *bset);
2246 __isl_give isl_set *isl_set_lift(
2247 __isl_take isl_set *set);
2248 __isl_give isl_union_set *isl_union_set_lift(
2249 __isl_take isl_union_set *uset);
2251 Given a local space that contains the existentially quantified
2252 variables of a set, a basic relation that, when applied to
2253 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2254 can be constructed using the following function.
2256 #include <isl/local_space.h>
2257 __isl_give isl_basic_map *isl_local_space_lifting(
2258 __isl_take isl_local_space *ls);
2260 =item * Internal Product
2262 __isl_give isl_basic_map *isl_basic_map_zip(
2263 __isl_take isl_basic_map *bmap);
2264 __isl_give isl_map *isl_map_zip(
2265 __isl_take isl_map *map);
2266 __isl_give isl_union_map *isl_union_map_zip(
2267 __isl_take isl_union_map *umap);
2269 Given a relation with nested relations for domain and range,
2270 interchange the range of the domain with the domain of the range.
2272 =item * Aligning parameters
2274 __isl_give isl_set *isl_set_align_params(
2275 __isl_take isl_set *set,
2276 __isl_take isl_space *model);
2277 __isl_give isl_map *isl_map_align_params(
2278 __isl_take isl_map *map,
2279 __isl_take isl_space *model);
2281 Change the order of the parameters of the given set or relation
2282 such that the first parameters match those of C<model>.
2283 This may involve the introduction of extra parameters.
2284 All parameters need to be named.
2286 =item * Dimension manipulation
2288 __isl_give isl_set *isl_set_add_dims(
2289 __isl_take isl_set *set,
2290 enum isl_dim_type type, unsigned n);
2291 __isl_give isl_map *isl_map_add_dims(
2292 __isl_take isl_map *map,
2293 enum isl_dim_type type, unsigned n);
2294 __isl_give isl_set *isl_set_insert_dims(
2295 __isl_take isl_set *set,
2296 enum isl_dim_type type, unsigned pos, unsigned n);
2297 __isl_give isl_map *isl_map_insert_dims(
2298 __isl_take isl_map *map,
2299 enum isl_dim_type type, unsigned pos, unsigned n);
2300 __isl_give isl_basic_set *isl_basic_set_move_dims(
2301 __isl_take isl_basic_set *bset,
2302 enum isl_dim_type dst_type, unsigned dst_pos,
2303 enum isl_dim_type src_type, unsigned src_pos,
2305 __isl_give isl_basic_map *isl_basic_map_move_dims(
2306 __isl_take isl_basic_map *bmap,
2307 enum isl_dim_type dst_type, unsigned dst_pos,
2308 enum isl_dim_type src_type, unsigned src_pos,
2310 __isl_give isl_set *isl_set_move_dims(
2311 __isl_take isl_set *set,
2312 enum isl_dim_type dst_type, unsigned dst_pos,
2313 enum isl_dim_type src_type, unsigned src_pos,
2315 __isl_give isl_map *isl_map_move_dims(
2316 __isl_take isl_map *map,
2317 enum isl_dim_type dst_type, unsigned dst_pos,
2318 enum isl_dim_type src_type, unsigned src_pos,
2321 It is usually not advisable to directly change the (input or output)
2322 space of a set or a relation as this removes the name and the internal
2323 structure of the space. However, the above functions can be useful
2324 to add new parameters, assuming
2325 C<isl_set_align_params> and C<isl_map_align_params>
2330 =head2 Binary Operations
2332 The two arguments of a binary operation not only need to live
2333 in the same C<isl_ctx>, they currently also need to have
2334 the same (number of) parameters.
2336 =head3 Basic Operations
2340 =item * Intersection
2342 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2343 __isl_take isl_basic_set *bset1,
2344 __isl_take isl_basic_set *bset2);
2345 __isl_give isl_basic_set *isl_basic_set_intersect(
2346 __isl_take isl_basic_set *bset1,
2347 __isl_take isl_basic_set *bset2);
2348 __isl_give isl_set *isl_set_intersect_params(
2349 __isl_take isl_set *set,
2350 __isl_take isl_set *params);
2351 __isl_give isl_set *isl_set_intersect(
2352 __isl_take isl_set *set1,
2353 __isl_take isl_set *set2);
2354 __isl_give isl_union_set *isl_union_set_intersect_params(
2355 __isl_take isl_union_set *uset,
2356 __isl_take isl_set *set);
2357 __isl_give isl_union_map *isl_union_map_intersect_params(
2358 __isl_take isl_union_map *umap,
2359 __isl_take isl_set *set);
2360 __isl_give isl_union_set *isl_union_set_intersect(
2361 __isl_take isl_union_set *uset1,
2362 __isl_take isl_union_set *uset2);
2363 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2364 __isl_take isl_basic_map *bmap,
2365 __isl_take isl_basic_set *bset);
2366 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2367 __isl_take isl_basic_map *bmap,
2368 __isl_take isl_basic_set *bset);
2369 __isl_give isl_basic_map *isl_basic_map_intersect(
2370 __isl_take isl_basic_map *bmap1,
2371 __isl_take isl_basic_map *bmap2);
2372 __isl_give isl_map *isl_map_intersect_params(
2373 __isl_take isl_map *map,
2374 __isl_take isl_set *params);
2375 __isl_give isl_map *isl_map_intersect_domain(
2376 __isl_take isl_map *map,
2377 __isl_take isl_set *set);
2378 __isl_give isl_map *isl_map_intersect_range(
2379 __isl_take isl_map *map,
2380 __isl_take isl_set *set);
2381 __isl_give isl_map *isl_map_intersect(
2382 __isl_take isl_map *map1,
2383 __isl_take isl_map *map2);
2384 __isl_give isl_union_map *isl_union_map_intersect_domain(
2385 __isl_take isl_union_map *umap,
2386 __isl_take isl_union_set *uset);
2387 __isl_give isl_union_map *isl_union_map_intersect_range(
2388 __isl_take isl_union_map *umap,
2389 __isl_take isl_union_set *uset);
2390 __isl_give isl_union_map *isl_union_map_intersect(
2391 __isl_take isl_union_map *umap1,
2392 __isl_take isl_union_map *umap2);
2396 __isl_give isl_set *isl_basic_set_union(
2397 __isl_take isl_basic_set *bset1,
2398 __isl_take isl_basic_set *bset2);
2399 __isl_give isl_map *isl_basic_map_union(
2400 __isl_take isl_basic_map *bmap1,
2401 __isl_take isl_basic_map *bmap2);
2402 __isl_give isl_set *isl_set_union(
2403 __isl_take isl_set *set1,
2404 __isl_take isl_set *set2);
2405 __isl_give isl_map *isl_map_union(
2406 __isl_take isl_map *map1,
2407 __isl_take isl_map *map2);
2408 __isl_give isl_union_set *isl_union_set_union(
2409 __isl_take isl_union_set *uset1,
2410 __isl_take isl_union_set *uset2);
2411 __isl_give isl_union_map *isl_union_map_union(
2412 __isl_take isl_union_map *umap1,
2413 __isl_take isl_union_map *umap2);
2415 =item * Set difference
2417 __isl_give isl_set *isl_set_subtract(
2418 __isl_take isl_set *set1,
2419 __isl_take isl_set *set2);
2420 __isl_give isl_map *isl_map_subtract(
2421 __isl_take isl_map *map1,
2422 __isl_take isl_map *map2);
2423 __isl_give isl_map *isl_map_subtract_domain(
2424 __isl_take isl_map *map,
2425 __isl_take isl_set *dom);
2426 __isl_give isl_map *isl_map_subtract_range(
2427 __isl_take isl_map *map,
2428 __isl_take isl_set *dom);
2429 __isl_give isl_union_set *isl_union_set_subtract(
2430 __isl_take isl_union_set *uset1,
2431 __isl_take isl_union_set *uset2);
2432 __isl_give isl_union_map *isl_union_map_subtract(
2433 __isl_take isl_union_map *umap1,
2434 __isl_take isl_union_map *umap2);
2438 __isl_give isl_basic_set *isl_basic_set_apply(
2439 __isl_take isl_basic_set *bset,
2440 __isl_take isl_basic_map *bmap);
2441 __isl_give isl_set *isl_set_apply(
2442 __isl_take isl_set *set,
2443 __isl_take isl_map *map);
2444 __isl_give isl_union_set *isl_union_set_apply(
2445 __isl_take isl_union_set *uset,
2446 __isl_take isl_union_map *umap);
2447 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2448 __isl_take isl_basic_map *bmap1,
2449 __isl_take isl_basic_map *bmap2);
2450 __isl_give isl_basic_map *isl_basic_map_apply_range(
2451 __isl_take isl_basic_map *bmap1,
2452 __isl_take isl_basic_map *bmap2);
2453 __isl_give isl_map *isl_map_apply_domain(
2454 __isl_take isl_map *map1,
2455 __isl_take isl_map *map2);
2456 __isl_give isl_union_map *isl_union_map_apply_domain(
2457 __isl_take isl_union_map *umap1,
2458 __isl_take isl_union_map *umap2);
2459 __isl_give isl_map *isl_map_apply_range(
2460 __isl_take isl_map *map1,
2461 __isl_take isl_map *map2);
2462 __isl_give isl_union_map *isl_union_map_apply_range(
2463 __isl_take isl_union_map *umap1,
2464 __isl_take isl_union_map *umap2);
2466 =item * Cartesian Product
2468 __isl_give isl_set *isl_set_product(
2469 __isl_take isl_set *set1,
2470 __isl_take isl_set *set2);
2471 __isl_give isl_union_set *isl_union_set_product(
2472 __isl_take isl_union_set *uset1,
2473 __isl_take isl_union_set *uset2);
2474 __isl_give isl_basic_map *isl_basic_map_domain_product(
2475 __isl_take isl_basic_map *bmap1,
2476 __isl_take isl_basic_map *bmap2);
2477 __isl_give isl_basic_map *isl_basic_map_range_product(
2478 __isl_take isl_basic_map *bmap1,
2479 __isl_take isl_basic_map *bmap2);
2480 __isl_give isl_map *isl_map_domain_product(
2481 __isl_take isl_map *map1,
2482 __isl_take isl_map *map2);
2483 __isl_give isl_map *isl_map_range_product(
2484 __isl_take isl_map *map1,
2485 __isl_take isl_map *map2);
2486 __isl_give isl_union_map *isl_union_map_range_product(
2487 __isl_take isl_union_map *umap1,
2488 __isl_take isl_union_map *umap2);
2489 __isl_give isl_map *isl_map_product(
2490 __isl_take isl_map *map1,
2491 __isl_take isl_map *map2);
2492 __isl_give isl_union_map *isl_union_map_product(
2493 __isl_take isl_union_map *umap1,
2494 __isl_take isl_union_map *umap2);
2496 The above functions compute the cross product of the given
2497 sets or relations. The domains and ranges of the results
2498 are wrapped maps between domains and ranges of the inputs.
2499 To obtain a ``flat'' product, use the following functions
2502 __isl_give isl_basic_set *isl_basic_set_flat_product(
2503 __isl_take isl_basic_set *bset1,
2504 __isl_take isl_basic_set *bset2);
2505 __isl_give isl_set *isl_set_flat_product(
2506 __isl_take isl_set *set1,
2507 __isl_take isl_set *set2);
2508 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2509 __isl_take isl_basic_map *bmap1,
2510 __isl_take isl_basic_map *bmap2);
2511 __isl_give isl_map *isl_map_flat_domain_product(
2512 __isl_take isl_map *map1,
2513 __isl_take isl_map *map2);
2514 __isl_give isl_map *isl_map_flat_range_product(
2515 __isl_take isl_map *map1,
2516 __isl_take isl_map *map2);
2517 __isl_give isl_union_map *isl_union_map_flat_range_product(
2518 __isl_take isl_union_map *umap1,
2519 __isl_take isl_union_map *umap2);
2520 __isl_give isl_basic_map *isl_basic_map_flat_product(
2521 __isl_take isl_basic_map *bmap1,
2522 __isl_take isl_basic_map *bmap2);
2523 __isl_give isl_map *isl_map_flat_product(
2524 __isl_take isl_map *map1,
2525 __isl_take isl_map *map2);
2527 =item * Simplification
2529 __isl_give isl_basic_set *isl_basic_set_gist(
2530 __isl_take isl_basic_set *bset,
2531 __isl_take isl_basic_set *context);
2532 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2533 __isl_take isl_set *context);
2534 __isl_give isl_set *isl_set_gist_params(
2535 __isl_take isl_set *set,
2536 __isl_take isl_set *context);
2537 __isl_give isl_union_set *isl_union_set_gist(
2538 __isl_take isl_union_set *uset,
2539 __isl_take isl_union_set *context);
2540 __isl_give isl_union_set *isl_union_set_gist_params(
2541 __isl_take isl_union_set *uset,
2542 __isl_take isl_set *set);
2543 __isl_give isl_basic_map *isl_basic_map_gist(
2544 __isl_take isl_basic_map *bmap,
2545 __isl_take isl_basic_map *context);
2546 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2547 __isl_take isl_map *context);
2548 __isl_give isl_map *isl_map_gist_params(
2549 __isl_take isl_map *map,
2550 __isl_take isl_set *context);
2551 __isl_give isl_map *isl_map_gist_domain(
2552 __isl_take isl_map *map,
2553 __isl_take isl_set *context);
2554 __isl_give isl_map *isl_map_gist_range(
2555 __isl_take isl_map *map,
2556 __isl_take isl_set *context);
2557 __isl_give isl_union_map *isl_union_map_gist(
2558 __isl_take isl_union_map *umap,
2559 __isl_take isl_union_map *context);
2560 __isl_give isl_union_map *isl_union_map_gist_params(
2561 __isl_take isl_union_map *umap,
2562 __isl_take isl_set *set);
2563 __isl_give isl_union_map *isl_union_map_gist_domain(
2564 __isl_take isl_union_map *umap,
2565 __isl_take isl_union_set *uset);
2566 __isl_give isl_union_map *isl_union_map_gist_range(
2567 __isl_take isl_union_map *umap,
2568 __isl_take isl_union_set *uset);
2570 The gist operation returns a set or relation that has the
2571 same intersection with the context as the input set or relation.
2572 Any implicit equality in the intersection is made explicit in the result,
2573 while all inequalities that are redundant with respect to the intersection
2575 In case of union sets and relations, the gist operation is performed
2580 =head3 Lexicographic Optimization
2582 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2583 the following functions
2584 compute a set that contains the lexicographic minimum or maximum
2585 of the elements in C<set> (or C<bset>) for those values of the parameters
2586 that satisfy C<dom>.
2587 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2588 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2590 In other words, the union of the parameter values
2591 for which the result is non-empty and of C<*empty>
2594 __isl_give isl_set *isl_basic_set_partial_lexmin(
2595 __isl_take isl_basic_set *bset,
2596 __isl_take isl_basic_set *dom,
2597 __isl_give isl_set **empty);
2598 __isl_give isl_set *isl_basic_set_partial_lexmax(
2599 __isl_take isl_basic_set *bset,
2600 __isl_take isl_basic_set *dom,
2601 __isl_give isl_set **empty);
2602 __isl_give isl_set *isl_set_partial_lexmin(
2603 __isl_take isl_set *set, __isl_take isl_set *dom,
2604 __isl_give isl_set **empty);
2605 __isl_give isl_set *isl_set_partial_lexmax(
2606 __isl_take isl_set *set, __isl_take isl_set *dom,
2607 __isl_give isl_set **empty);
2609 Given a (basic) set C<set> (or C<bset>), the following functions simply
2610 return a set containing the lexicographic minimum or maximum
2611 of the elements in C<set> (or C<bset>).
2612 In case of union sets, the optimum is computed per space.
2614 __isl_give isl_set *isl_basic_set_lexmin(
2615 __isl_take isl_basic_set *bset);
2616 __isl_give isl_set *isl_basic_set_lexmax(
2617 __isl_take isl_basic_set *bset);
2618 __isl_give isl_set *isl_set_lexmin(
2619 __isl_take isl_set *set);
2620 __isl_give isl_set *isl_set_lexmax(
2621 __isl_take isl_set *set);
2622 __isl_give isl_union_set *isl_union_set_lexmin(
2623 __isl_take isl_union_set *uset);
2624 __isl_give isl_union_set *isl_union_set_lexmax(
2625 __isl_take isl_union_set *uset);
2627 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2628 the following functions
2629 compute a relation that maps each element of C<dom>
2630 to the single lexicographic minimum or maximum
2631 of the elements that are associated to that same
2632 element in C<map> (or C<bmap>).
2633 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2634 that contains the elements in C<dom> that do not map
2635 to any elements in C<map> (or C<bmap>).
2636 In other words, the union of the domain of the result and of C<*empty>
2639 __isl_give isl_map *isl_basic_map_partial_lexmax(
2640 __isl_take isl_basic_map *bmap,
2641 __isl_take isl_basic_set *dom,
2642 __isl_give isl_set **empty);
2643 __isl_give isl_map *isl_basic_map_partial_lexmin(
2644 __isl_take isl_basic_map *bmap,
2645 __isl_take isl_basic_set *dom,
2646 __isl_give isl_set **empty);
2647 __isl_give isl_map *isl_map_partial_lexmax(
2648 __isl_take isl_map *map, __isl_take isl_set *dom,
2649 __isl_give isl_set **empty);
2650 __isl_give isl_map *isl_map_partial_lexmin(
2651 __isl_take isl_map *map, __isl_take isl_set *dom,
2652 __isl_give isl_set **empty);
2654 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2655 return a map mapping each element in the domain of
2656 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2657 of all elements associated to that element.
2658 In case of union relations, the optimum is computed per space.
2660 __isl_give isl_map *isl_basic_map_lexmin(
2661 __isl_take isl_basic_map *bmap);
2662 __isl_give isl_map *isl_basic_map_lexmax(
2663 __isl_take isl_basic_map *bmap);
2664 __isl_give isl_map *isl_map_lexmin(
2665 __isl_take isl_map *map);
2666 __isl_give isl_map *isl_map_lexmax(
2667 __isl_take isl_map *map);
2668 __isl_give isl_union_map *isl_union_map_lexmin(
2669 __isl_take isl_union_map *umap);
2670 __isl_give isl_union_map *isl_union_map_lexmax(
2671 __isl_take isl_union_map *umap);
2673 The following functions return their result in the form of
2674 a piecewise multi-affine expression
2675 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2676 but are otherwise equivalent to the corresponding functions
2677 returning a basic set or relation.
2679 __isl_give isl_pw_multi_aff *
2680 isl_basic_map_lexmin_pw_multi_aff(
2681 __isl_take isl_basic_map *bmap);
2682 __isl_give isl_pw_multi_aff *
2683 isl_basic_set_partial_lexmin_pw_multi_aff(
2684 __isl_take isl_basic_set *bset,
2685 __isl_take isl_basic_set *dom,
2686 __isl_give isl_set **empty);
2687 __isl_give isl_pw_multi_aff *
2688 isl_basic_set_partial_lexmax_pw_multi_aff(
2689 __isl_take isl_basic_set *bset,
2690 __isl_take isl_basic_set *dom,
2691 __isl_give isl_set **empty);
2692 __isl_give isl_pw_multi_aff *
2693 isl_basic_map_partial_lexmin_pw_multi_aff(
2694 __isl_take isl_basic_map *bmap,
2695 __isl_take isl_basic_set *dom,
2696 __isl_give isl_set **empty);
2697 __isl_give isl_pw_multi_aff *
2698 isl_basic_map_partial_lexmax_pw_multi_aff(
2699 __isl_take isl_basic_map *bmap,
2700 __isl_take isl_basic_set *dom,
2701 __isl_give isl_set **empty);
2705 Lists are defined over several element types, including
2706 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2707 Here we take lists of C<isl_set>s as an example.
2708 Lists can be created, copied and freed using the following functions.
2710 #include <isl/list.h>
2711 __isl_give isl_set_list *isl_set_list_from_set(
2712 __isl_take isl_set *el);
2713 __isl_give isl_set_list *isl_set_list_alloc(
2714 isl_ctx *ctx, int n);
2715 __isl_give isl_set_list *isl_set_list_copy(
2716 __isl_keep isl_set_list *list);
2717 __isl_give isl_set_list *isl_set_list_add(
2718 __isl_take isl_set_list *list,
2719 __isl_take isl_set *el);
2720 __isl_give isl_set_list *isl_set_list_concat(
2721 __isl_take isl_set_list *list1,
2722 __isl_take isl_set_list *list2);
2723 void *isl_set_list_free(__isl_take isl_set_list *list);
2725 C<isl_set_list_alloc> creates an empty list with a capacity for
2726 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2729 Lists can be inspected using the following functions.
2731 #include <isl/list.h>
2732 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2733 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2734 __isl_give isl_set *isl_set_list_get_set(
2735 __isl_keep isl_set_list *list, int index);
2736 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2737 int (*fn)(__isl_take isl_set *el, void *user),
2740 Lists can be printed using
2742 #include <isl/list.h>
2743 __isl_give isl_printer *isl_printer_print_set_list(
2744 __isl_take isl_printer *p,
2745 __isl_keep isl_set_list *list);
2749 Vectors can be created, copied and freed using the following functions.
2751 #include <isl/vec.h>
2752 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2754 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2755 void isl_vec_free(__isl_take isl_vec *vec);
2757 Note that the elements of a newly created vector may have arbitrary values.
2758 The elements can be changed and inspected using the following functions.
2760 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2761 int isl_vec_size(__isl_keep isl_vec *vec);
2762 int isl_vec_get_element(__isl_keep isl_vec *vec,
2763 int pos, isl_int *v);
2764 __isl_give isl_vec *isl_vec_set_element(
2765 __isl_take isl_vec *vec, int pos, isl_int v);
2766 __isl_give isl_vec *isl_vec_set_element_si(
2767 __isl_take isl_vec *vec, int pos, int v);
2768 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2770 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2773 C<isl_vec_get_element> will return a negative value if anything went wrong.
2774 In that case, the value of C<*v> is undefined.
2778 Matrices can be created, copied and freed using the following functions.
2780 #include <isl/mat.h>
2781 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2782 unsigned n_row, unsigned n_col);
2783 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2784 void isl_mat_free(__isl_take isl_mat *mat);
2786 Note that the elements of a newly created matrix may have arbitrary values.
2787 The elements can be changed and inspected using the following functions.
2789 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2790 int isl_mat_rows(__isl_keep isl_mat *mat);
2791 int isl_mat_cols(__isl_keep isl_mat *mat);
2792 int isl_mat_get_element(__isl_keep isl_mat *mat,
2793 int row, int col, isl_int *v);
2794 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2795 int row, int col, isl_int v);
2796 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2797 int row, int col, int v);
2799 C<isl_mat_get_element> will return a negative value if anything went wrong.
2800 In that case, the value of C<*v> is undefined.
2802 The following function can be used to compute the (right) inverse
2803 of a matrix, i.e., a matrix such that the product of the original
2804 and the inverse (in that order) is a multiple of the identity matrix.
2805 The input matrix is assumed to be of full row-rank.
2807 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2809 The following function can be used to compute the (right) kernel
2810 (or null space) of a matrix, i.e., a matrix such that the product of
2811 the original and the kernel (in that order) is the zero matrix.
2813 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2815 =head2 Piecewise Quasi Affine Expressions
2817 The zero quasi affine expression on a given domain can be created using
2819 __isl_give isl_aff *isl_aff_zero_on_domain(
2820 __isl_take isl_local_space *ls);
2822 Note that the space in which the resulting object lives is a map space
2823 with the given space as domain and a one-dimensional range.
2825 An empty piecewise quasi affine expression (one with no cells)
2826 or a piecewise quasi affine expression with a single cell can
2827 be created using the following functions.
2829 #include <isl/aff.h>
2830 __isl_give isl_pw_aff *isl_pw_aff_empty(
2831 __isl_take isl_space *space);
2832 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2833 __isl_take isl_set *set, __isl_take isl_aff *aff);
2834 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2835 __isl_take isl_aff *aff);
2837 A piecewise quasi affine expression that is equal to 1 on a set
2838 and 0 outside the set can be created using the following function.
2840 #include <isl/aff.h>
2841 __isl_give isl_pw_aff *isl_set_indicator_function(
2842 __isl_take isl_set *set);
2844 Quasi affine expressions can be copied and freed using
2846 #include <isl/aff.h>
2847 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2848 void *isl_aff_free(__isl_take isl_aff *aff);
2850 __isl_give isl_pw_aff *isl_pw_aff_copy(
2851 __isl_keep isl_pw_aff *pwaff);
2852 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2854 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2855 using the following function. The constraint is required to have
2856 a non-zero coefficient for the specified dimension.
2858 #include <isl/constraint.h>
2859 __isl_give isl_aff *isl_constraint_get_bound(
2860 __isl_keep isl_constraint *constraint,
2861 enum isl_dim_type type, int pos);
2863 The entire affine expression of the constraint can also be extracted
2864 using the following function.
2866 #include <isl/constraint.h>
2867 __isl_give isl_aff *isl_constraint_get_aff(
2868 __isl_keep isl_constraint *constraint);
2870 Conversely, an equality constraint equating
2871 the affine expression to zero or an inequality constraint enforcing
2872 the affine expression to be non-negative, can be constructed using
2874 __isl_give isl_constraint *isl_equality_from_aff(
2875 __isl_take isl_aff *aff);
2876 __isl_give isl_constraint *isl_inequality_from_aff(
2877 __isl_take isl_aff *aff);
2879 The expression can be inspected using
2881 #include <isl/aff.h>
2882 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2883 int isl_aff_dim(__isl_keep isl_aff *aff,
2884 enum isl_dim_type type);
2885 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2886 __isl_keep isl_aff *aff);
2887 __isl_give isl_local_space *isl_aff_get_local_space(
2888 __isl_keep isl_aff *aff);
2889 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2890 enum isl_dim_type type, unsigned pos);
2891 const char *isl_pw_aff_get_dim_name(
2892 __isl_keep isl_pw_aff *pa,
2893 enum isl_dim_type type, unsigned pos);
2894 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2895 enum isl_dim_type type, unsigned pos);
2896 __isl_give isl_id *isl_pw_aff_get_dim_id(
2897 __isl_keep isl_pw_aff *pa,
2898 enum isl_dim_type type, unsigned pos);
2899 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2901 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2902 enum isl_dim_type type, int pos, isl_int *v);
2903 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2905 __isl_give isl_aff *isl_aff_get_div(
2906 __isl_keep isl_aff *aff, int pos);
2908 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2909 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2910 int (*fn)(__isl_take isl_set *set,
2911 __isl_take isl_aff *aff,
2912 void *user), void *user);
2914 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2915 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2917 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2918 enum isl_dim_type type, unsigned first, unsigned n);
2919 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2920 enum isl_dim_type type, unsigned first, unsigned n);
2922 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2923 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2924 enum isl_dim_type type);
2925 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2927 It can be modified using
2929 #include <isl/aff.h>
2930 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2931 __isl_take isl_pw_aff *pwaff,
2932 enum isl_dim_type type, __isl_take isl_id *id);
2933 __isl_give isl_aff *isl_aff_set_dim_name(
2934 __isl_take isl_aff *aff, enum isl_dim_type type,
2935 unsigned pos, const char *s);
2936 __isl_give isl_aff *isl_aff_set_dim_id(
2937 __isl_take isl_aff *aff, enum isl_dim_type type,
2938 unsigned pos, __isl_take isl_id *id);
2939 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2940 __isl_take isl_pw_aff *pma,
2941 enum isl_dim_type type, unsigned pos,
2942 __isl_take isl_id *id);
2943 __isl_give isl_aff *isl_aff_set_constant(
2944 __isl_take isl_aff *aff, isl_int v);
2945 __isl_give isl_aff *isl_aff_set_constant_si(
2946 __isl_take isl_aff *aff, int v);
2947 __isl_give isl_aff *isl_aff_set_coefficient(
2948 __isl_take isl_aff *aff,
2949 enum isl_dim_type type, int pos, isl_int v);
2950 __isl_give isl_aff *isl_aff_set_coefficient_si(
2951 __isl_take isl_aff *aff,
2952 enum isl_dim_type type, int pos, int v);
2953 __isl_give isl_aff *isl_aff_set_denominator(
2954 __isl_take isl_aff *aff, isl_int v);
2956 __isl_give isl_aff *isl_aff_add_constant(
2957 __isl_take isl_aff *aff, isl_int v);
2958 __isl_give isl_aff *isl_aff_add_constant_si(
2959 __isl_take isl_aff *aff, int v);
2960 __isl_give isl_aff *isl_aff_add_coefficient(
2961 __isl_take isl_aff *aff,
2962 enum isl_dim_type type, int pos, isl_int v);
2963 __isl_give isl_aff *isl_aff_add_coefficient_si(
2964 __isl_take isl_aff *aff,
2965 enum isl_dim_type type, int pos, int v);
2967 __isl_give isl_aff *isl_aff_insert_dims(
2968 __isl_take isl_aff *aff,
2969 enum isl_dim_type type, unsigned first, unsigned n);
2970 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2971 __isl_take isl_pw_aff *pwaff,
2972 enum isl_dim_type type, unsigned first, unsigned n);
2973 __isl_give isl_aff *isl_aff_add_dims(
2974 __isl_take isl_aff *aff,
2975 enum isl_dim_type type, unsigned n);
2976 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2977 __isl_take isl_pw_aff *pwaff,
2978 enum isl_dim_type type, unsigned n);
2979 __isl_give isl_aff *isl_aff_drop_dims(
2980 __isl_take isl_aff *aff,
2981 enum isl_dim_type type, unsigned first, unsigned n);
2982 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2983 __isl_take isl_pw_aff *pwaff,
2984 enum isl_dim_type type, unsigned first, unsigned n);
2986 Note that the C<set_constant> and C<set_coefficient> functions
2987 set the I<numerator> of the constant or coefficient, while
2988 C<add_constant> and C<add_coefficient> add an integer value to
2989 the possibly rational constant or coefficient.
2991 To check whether an affine expressions is obviously zero
2992 or obviously equal to some other affine expression, use
2994 #include <isl/aff.h>
2995 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2996 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2997 __isl_keep isl_aff *aff2);
2998 int isl_pw_aff_plain_is_equal(
2999 __isl_keep isl_pw_aff *pwaff1,
3000 __isl_keep isl_pw_aff *pwaff2);
3004 #include <isl/aff.h>
3005 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3006 __isl_take isl_aff *aff2);
3007 __isl_give isl_pw_aff *isl_pw_aff_add(
3008 __isl_take isl_pw_aff *pwaff1,
3009 __isl_take isl_pw_aff *pwaff2);
3010 __isl_give isl_pw_aff *isl_pw_aff_min(
3011 __isl_take isl_pw_aff *pwaff1,
3012 __isl_take isl_pw_aff *pwaff2);
3013 __isl_give isl_pw_aff *isl_pw_aff_max(
3014 __isl_take isl_pw_aff *pwaff1,
3015 __isl_take isl_pw_aff *pwaff2);
3016 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3017 __isl_take isl_aff *aff2);
3018 __isl_give isl_pw_aff *isl_pw_aff_sub(
3019 __isl_take isl_pw_aff *pwaff1,
3020 __isl_take isl_pw_aff *pwaff2);
3021 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3022 __isl_give isl_pw_aff *isl_pw_aff_neg(
3023 __isl_take isl_pw_aff *pwaff);
3024 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3025 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3026 __isl_take isl_pw_aff *pwaff);
3027 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3028 __isl_give isl_pw_aff *isl_pw_aff_floor(
3029 __isl_take isl_pw_aff *pwaff);
3030 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3032 __isl_give isl_pw_aff *isl_pw_aff_mod(
3033 __isl_take isl_pw_aff *pwaff, isl_int mod);
3034 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3036 __isl_give isl_pw_aff *isl_pw_aff_scale(
3037 __isl_take isl_pw_aff *pwaff, isl_int f);
3038 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3040 __isl_give isl_aff *isl_aff_scale_down_ui(
3041 __isl_take isl_aff *aff, unsigned f);
3042 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3043 __isl_take isl_pw_aff *pwaff, isl_int f);
3045 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3046 __isl_take isl_pw_aff_list *list);
3047 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3048 __isl_take isl_pw_aff_list *list);
3050 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3051 __isl_take isl_pw_aff *pwqp);
3053 __isl_give isl_aff *isl_aff_align_params(
3054 __isl_take isl_aff *aff,
3055 __isl_take isl_space *model);
3056 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3057 __isl_take isl_pw_aff *pwaff,
3058 __isl_take isl_space *model);
3060 __isl_give isl_aff *isl_aff_project_domain_on_params(
3061 __isl_take isl_aff *aff);
3063 __isl_give isl_aff *isl_aff_gist_params(
3064 __isl_take isl_aff *aff,
3065 __isl_take isl_set *context);
3066 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3067 __isl_take isl_set *context);
3068 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3069 __isl_take isl_pw_aff *pwaff,
3070 __isl_take isl_set *context);
3071 __isl_give isl_pw_aff *isl_pw_aff_gist(
3072 __isl_take isl_pw_aff *pwaff,
3073 __isl_take isl_set *context);
3075 __isl_give isl_set *isl_pw_aff_domain(
3076 __isl_take isl_pw_aff *pwaff);
3077 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3078 __isl_take isl_pw_aff *pa,
3079 __isl_take isl_set *set);
3080 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3081 __isl_take isl_pw_aff *pa,
3082 __isl_take isl_set *set);
3084 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3085 __isl_take isl_aff *aff2);
3086 __isl_give isl_pw_aff *isl_pw_aff_mul(
3087 __isl_take isl_pw_aff *pwaff1,
3088 __isl_take isl_pw_aff *pwaff2);
3090 When multiplying two affine expressions, at least one of the two needs
3093 #include <isl/aff.h>
3094 __isl_give isl_basic_set *isl_aff_le_basic_set(
3095 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3096 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3097 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3098 __isl_give isl_set *isl_pw_aff_eq_set(
3099 __isl_take isl_pw_aff *pwaff1,
3100 __isl_take isl_pw_aff *pwaff2);
3101 __isl_give isl_set *isl_pw_aff_ne_set(
3102 __isl_take isl_pw_aff *pwaff1,
3103 __isl_take isl_pw_aff *pwaff2);
3104 __isl_give isl_set *isl_pw_aff_le_set(
3105 __isl_take isl_pw_aff *pwaff1,
3106 __isl_take isl_pw_aff *pwaff2);
3107 __isl_give isl_set *isl_pw_aff_lt_set(
3108 __isl_take isl_pw_aff *pwaff1,
3109 __isl_take isl_pw_aff *pwaff2);
3110 __isl_give isl_set *isl_pw_aff_ge_set(
3111 __isl_take isl_pw_aff *pwaff1,
3112 __isl_take isl_pw_aff *pwaff2);
3113 __isl_give isl_set *isl_pw_aff_gt_set(
3114 __isl_take isl_pw_aff *pwaff1,
3115 __isl_take isl_pw_aff *pwaff2);
3117 __isl_give isl_set *isl_pw_aff_list_eq_set(
3118 __isl_take isl_pw_aff_list *list1,
3119 __isl_take isl_pw_aff_list *list2);
3120 __isl_give isl_set *isl_pw_aff_list_ne_set(
3121 __isl_take isl_pw_aff_list *list1,
3122 __isl_take isl_pw_aff_list *list2);
3123 __isl_give isl_set *isl_pw_aff_list_le_set(
3124 __isl_take isl_pw_aff_list *list1,
3125 __isl_take isl_pw_aff_list *list2);
3126 __isl_give isl_set *isl_pw_aff_list_lt_set(
3127 __isl_take isl_pw_aff_list *list1,
3128 __isl_take isl_pw_aff_list *list2);
3129 __isl_give isl_set *isl_pw_aff_list_ge_set(
3130 __isl_take isl_pw_aff_list *list1,
3131 __isl_take isl_pw_aff_list *list2);
3132 __isl_give isl_set *isl_pw_aff_list_gt_set(
3133 __isl_take isl_pw_aff_list *list1,
3134 __isl_take isl_pw_aff_list *list2);
3136 The function C<isl_aff_ge_basic_set> returns a basic set
3137 containing those elements in the shared space
3138 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3139 The function C<isl_aff_ge_set> returns a set
3140 containing those elements in the shared domain
3141 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3142 The functions operating on C<isl_pw_aff_list> apply the corresponding
3143 C<isl_pw_aff> function to each pair of elements in the two lists.
3145 #include <isl/aff.h>
3146 __isl_give isl_set *isl_pw_aff_nonneg_set(
3147 __isl_take isl_pw_aff *pwaff);
3148 __isl_give isl_set *isl_pw_aff_zero_set(
3149 __isl_take isl_pw_aff *pwaff);
3150 __isl_give isl_set *isl_pw_aff_non_zero_set(
3151 __isl_take isl_pw_aff *pwaff);
3153 The function C<isl_pw_aff_nonneg_set> returns a set
3154 containing those elements in the domain
3155 of C<pwaff> where C<pwaff> is non-negative.
3157 #include <isl/aff.h>
3158 __isl_give isl_pw_aff *isl_pw_aff_cond(
3159 __isl_take isl_pw_aff *cond,
3160 __isl_take isl_pw_aff *pwaff_true,
3161 __isl_take isl_pw_aff *pwaff_false);
3163 The function C<isl_pw_aff_cond> performs a conditional operator
3164 and returns an expression that is equal to C<pwaff_true>
3165 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3166 where C<cond> is zero.
3168 #include <isl/aff.h>
3169 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3170 __isl_take isl_pw_aff *pwaff1,
3171 __isl_take isl_pw_aff *pwaff2);
3172 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3173 __isl_take isl_pw_aff *pwaff1,
3174 __isl_take isl_pw_aff *pwaff2);
3175 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3176 __isl_take isl_pw_aff *pwaff1,
3177 __isl_take isl_pw_aff *pwaff2);
3179 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3180 expression with a domain that is the union of those of C<pwaff1> and
3181 C<pwaff2> and such that on each cell, the quasi-affine expression is
3182 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3183 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3184 associated expression is the defined one.
3186 An expression can be read from input using
3188 #include <isl/aff.h>
3189 __isl_give isl_aff *isl_aff_read_from_str(
3190 isl_ctx *ctx, const char *str);
3191 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3192 isl_ctx *ctx, const char *str);
3194 An expression can be printed using
3196 #include <isl/aff.h>
3197 __isl_give isl_printer *isl_printer_print_aff(
3198 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3200 __isl_give isl_printer *isl_printer_print_pw_aff(
3201 __isl_take isl_printer *p,
3202 __isl_keep isl_pw_aff *pwaff);
3204 =head2 Piecewise Multiple Quasi Affine Expressions
3206 An C<isl_multi_aff> object represents a sequence of
3207 zero or more affine expressions, all defined on the same domain space.
3209 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3212 #include <isl/aff.h>
3213 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3214 __isl_take isl_space *space,
3215 __isl_take isl_aff_list *list);
3217 An empty piecewise multiple quasi affine expression (one with no cells),
3218 the zero piecewise multiple quasi affine expression (with value zero
3219 for each output dimension),
3220 a piecewise multiple quasi affine expression with a single cell (with
3221 either a universe or a specified domain) or
3222 a zero-dimensional piecewise multiple quasi affine expression
3224 can be created using the following functions.
3226 #include <isl/aff.h>
3227 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3228 __isl_take isl_space *space);
3229 __isl_give isl_multi_aff *isl_multi_aff_zero(
3230 __isl_take isl_space *space);
3231 __isl_give isl_pw_multi_aff *
3232 isl_pw_multi_aff_from_multi_aff(
3233 __isl_take isl_multi_aff *ma);
3234 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3235 __isl_take isl_set *set,
3236 __isl_take isl_multi_aff *maff);
3237 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3238 __isl_take isl_set *set);
3240 __isl_give isl_union_pw_multi_aff *
3241 isl_union_pw_multi_aff_empty(
3242 __isl_take isl_space *space);
3243 __isl_give isl_union_pw_multi_aff *
3244 isl_union_pw_multi_aff_add_pw_multi_aff(
3245 __isl_take isl_union_pw_multi_aff *upma,
3246 __isl_take isl_pw_multi_aff *pma);
3247 __isl_give isl_union_pw_multi_aff *
3248 isl_union_pw_multi_aff_from_domain(
3249 __isl_take isl_union_set *uset);
3251 A piecewise multiple quasi affine expression can also be initialized
3252 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3253 and the C<isl_map> is single-valued.
3255 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3256 __isl_take isl_set *set);
3257 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3258 __isl_take isl_map *map);
3260 Multiple quasi affine expressions can be copied and freed using
3262 #include <isl/aff.h>
3263 __isl_give isl_multi_aff *isl_multi_aff_copy(
3264 __isl_keep isl_multi_aff *maff);
3265 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3267 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3268 __isl_keep isl_pw_multi_aff *pma);
3269 void *isl_pw_multi_aff_free(
3270 __isl_take isl_pw_multi_aff *pma);
3272 __isl_give isl_union_pw_multi_aff *
3273 isl_union_pw_multi_aff_copy(
3274 __isl_keep isl_union_pw_multi_aff *upma);
3275 void *isl_union_pw_multi_aff_free(
3276 __isl_take isl_union_pw_multi_aff *upma);
3278 The expression can be inspected using
3280 #include <isl/aff.h>
3281 isl_ctx *isl_multi_aff_get_ctx(
3282 __isl_keep isl_multi_aff *maff);
3283 isl_ctx *isl_pw_multi_aff_get_ctx(
3284 __isl_keep isl_pw_multi_aff *pma);
3285 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3286 __isl_keep isl_union_pw_multi_aff *upma);
3287 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3288 enum isl_dim_type type);
3289 unsigned isl_pw_multi_aff_dim(
3290 __isl_keep isl_pw_multi_aff *pma,
3291 enum isl_dim_type type);
3292 __isl_give isl_aff *isl_multi_aff_get_aff(
3293 __isl_keep isl_multi_aff *multi, int pos);
3294 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3295 __isl_keep isl_pw_multi_aff *pma, int pos);
3296 const char *isl_pw_multi_aff_get_dim_name(
3297 __isl_keep isl_pw_multi_aff *pma,
3298 enum isl_dim_type type, unsigned pos);
3299 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3300 __isl_keep isl_pw_multi_aff *pma,
3301 enum isl_dim_type type, unsigned pos);
3302 const char *isl_multi_aff_get_tuple_name(
3303 __isl_keep isl_multi_aff *multi,
3304 enum isl_dim_type type);
3305 const char *isl_pw_multi_aff_get_tuple_name(
3306 __isl_keep isl_pw_multi_aff *pma,
3307 enum isl_dim_type type);
3308 int isl_pw_multi_aff_has_tuple_id(
3309 __isl_keep isl_pw_multi_aff *pma,
3310 enum isl_dim_type type);
3311 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3312 __isl_keep isl_pw_multi_aff *pma,
3313 enum isl_dim_type type);
3315 int isl_pw_multi_aff_foreach_piece(
3316 __isl_keep isl_pw_multi_aff *pma,
3317 int (*fn)(__isl_take isl_set *set,
3318 __isl_take isl_multi_aff *maff,
3319 void *user), void *user);
3321 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3322 __isl_keep isl_union_pw_multi_aff *upma,
3323 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3324 void *user), void *user);
3326 It can be modified using
3328 #include <isl/aff.h>
3329 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3330 __isl_take isl_multi_aff *multi, int pos,
3331 __isl_take isl_aff *aff);
3332 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3333 __isl_take isl_multi_aff *maff,
3334 enum isl_dim_type type, unsigned pos, const char *s);
3335 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3336 __isl_take isl_multi_aff *maff,
3337 enum isl_dim_type type, __isl_take isl_id *id);
3338 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3339 __isl_take isl_pw_multi_aff *pma,
3340 enum isl_dim_type type, __isl_take isl_id *id);
3342 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3343 __isl_take isl_multi_aff *maff,
3344 enum isl_dim_type type, unsigned first, unsigned n);
3346 To check whether two multiple affine expressions are
3347 obviously equal to each other, use
3349 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3350 __isl_keep isl_multi_aff *maff2);
3351 int isl_pw_multi_aff_plain_is_equal(
3352 __isl_keep isl_pw_multi_aff *pma1,
3353 __isl_keep isl_pw_multi_aff *pma2);
3357 #include <isl/aff.h>
3358 __isl_give isl_multi_aff *isl_multi_aff_add(
3359 __isl_take isl_multi_aff *maff1,
3360 __isl_take isl_multi_aff *maff2);
3361 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3362 __isl_take isl_pw_multi_aff *pma1,
3363 __isl_take isl_pw_multi_aff *pma2);
3364 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3365 __isl_take isl_union_pw_multi_aff *upma1,
3366 __isl_take isl_union_pw_multi_aff *upma2);
3367 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3368 __isl_take isl_pw_multi_aff *pma1,
3369 __isl_take isl_pw_multi_aff *pma2);
3370 __isl_give isl_multi_aff *isl_multi_aff_scale(
3371 __isl_take isl_multi_aff *maff,
3373 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3374 __isl_take isl_pw_multi_aff *pma,
3375 __isl_take isl_set *set);
3376 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3377 __isl_take isl_pw_multi_aff *pma,
3378 __isl_take isl_set *set);
3379 __isl_give isl_multi_aff *isl_multi_aff_lift(
3380 __isl_take isl_multi_aff *maff,
3381 __isl_give isl_local_space **ls);
3382 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3383 __isl_take isl_pw_multi_aff *pma);
3384 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3385 __isl_take isl_multi_aff *maff,
3386 __isl_take isl_set *context);
3387 __isl_give isl_multi_aff *isl_multi_aff_gist(
3388 __isl_take isl_multi_aff *maff,
3389 __isl_take isl_set *context);
3390 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3391 __isl_take isl_pw_multi_aff *pma,
3392 __isl_take isl_set *set);
3393 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3394 __isl_take isl_pw_multi_aff *pma,
3395 __isl_take isl_set *set);
3396 __isl_give isl_set *isl_pw_multi_aff_domain(
3397 __isl_take isl_pw_multi_aff *pma);
3398 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3399 __isl_take isl_union_pw_multi_aff *upma);
3400 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3401 __isl_take isl_multi_aff *ma1,
3402 __isl_take isl_multi_aff *ma2);
3403 __isl_give isl_pw_multi_aff *
3404 isl_pw_multi_aff_flat_range_product(
3405 __isl_take isl_pw_multi_aff *pma1,
3406 __isl_take isl_pw_multi_aff *pma2);
3407 __isl_give isl_union_pw_multi_aff *
3408 isl_union_pw_multi_aff_flat_range_product(
3409 __isl_take isl_union_pw_multi_aff *upma1,
3410 __isl_take isl_union_pw_multi_aff *upma2);
3412 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3413 then it is assigned the local space that lies at the basis of
3414 the lifting applied.
3416 An expression can be read from input using
3418 #include <isl/aff.h>
3419 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3420 isl_ctx *ctx, const char *str);
3421 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3422 isl_ctx *ctx, const char *str);
3424 An expression can be printed using
3426 #include <isl/aff.h>
3427 __isl_give isl_printer *isl_printer_print_multi_aff(
3428 __isl_take isl_printer *p,
3429 __isl_keep isl_multi_aff *maff);
3430 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3431 __isl_take isl_printer *p,
3432 __isl_keep isl_pw_multi_aff *pma);
3433 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3434 __isl_take isl_printer *p,
3435 __isl_keep isl_union_pw_multi_aff *upma);
3439 Points are elements of a set. They can be used to construct
3440 simple sets (boxes) or they can be used to represent the
3441 individual elements of a set.
3442 The zero point (the origin) can be created using
3444 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3446 The coordinates of a point can be inspected, set and changed
3449 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3450 enum isl_dim_type type, int pos, isl_int *v);
3451 __isl_give isl_point *isl_point_set_coordinate(
3452 __isl_take isl_point *pnt,
3453 enum isl_dim_type type, int pos, isl_int v);
3455 __isl_give isl_point *isl_point_add_ui(
3456 __isl_take isl_point *pnt,
3457 enum isl_dim_type type, int pos, unsigned val);
3458 __isl_give isl_point *isl_point_sub_ui(
3459 __isl_take isl_point *pnt,
3460 enum isl_dim_type type, int pos, unsigned val);
3462 Other properties can be obtained using
3464 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3466 Points can be copied or freed using
3468 __isl_give isl_point *isl_point_copy(
3469 __isl_keep isl_point *pnt);
3470 void isl_point_free(__isl_take isl_point *pnt);
3472 A singleton set can be created from a point using
3474 __isl_give isl_basic_set *isl_basic_set_from_point(
3475 __isl_take isl_point *pnt);
3476 __isl_give isl_set *isl_set_from_point(
3477 __isl_take isl_point *pnt);
3479 and a box can be created from two opposite extremal points using
3481 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3482 __isl_take isl_point *pnt1,
3483 __isl_take isl_point *pnt2);
3484 __isl_give isl_set *isl_set_box_from_points(
3485 __isl_take isl_point *pnt1,
3486 __isl_take isl_point *pnt2);
3488 All elements of a B<bounded> (union) set can be enumerated using
3489 the following functions.
3491 int isl_set_foreach_point(__isl_keep isl_set *set,
3492 int (*fn)(__isl_take isl_point *pnt, void *user),
3494 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3495 int (*fn)(__isl_take isl_point *pnt, void *user),
3498 The function C<fn> is called for each integer point in
3499 C<set> with as second argument the last argument of
3500 the C<isl_set_foreach_point> call. The function C<fn>
3501 should return C<0> on success and C<-1> on failure.
3502 In the latter case, C<isl_set_foreach_point> will stop
3503 enumerating and return C<-1> as well.
3504 If the enumeration is performed successfully and to completion,
3505 then C<isl_set_foreach_point> returns C<0>.
3507 To obtain a single point of a (basic) set, use
3509 __isl_give isl_point *isl_basic_set_sample_point(
3510 __isl_take isl_basic_set *bset);
3511 __isl_give isl_point *isl_set_sample_point(
3512 __isl_take isl_set *set);
3514 If C<set> does not contain any (integer) points, then the
3515 resulting point will be ``void'', a property that can be
3518 int isl_point_is_void(__isl_keep isl_point *pnt);
3520 =head2 Piecewise Quasipolynomials
3522 A piecewise quasipolynomial is a particular kind of function that maps
3523 a parametric point to a rational value.
3524 More specifically, a quasipolynomial is a polynomial expression in greatest
3525 integer parts of affine expressions of parameters and variables.
3526 A piecewise quasipolynomial is a subdivision of a given parametric
3527 domain into disjoint cells with a quasipolynomial associated to
3528 each cell. The value of the piecewise quasipolynomial at a given
3529 point is the value of the quasipolynomial associated to the cell
3530 that contains the point. Outside of the union of cells,
3531 the value is assumed to be zero.
3532 For example, the piecewise quasipolynomial
3534 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3536 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3537 A given piecewise quasipolynomial has a fixed domain dimension.
3538 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3539 defined over different domains.
3540 Piecewise quasipolynomials are mainly used by the C<barvinok>
3541 library for representing the number of elements in a parametric set or map.
3542 For example, the piecewise quasipolynomial above represents
3543 the number of points in the map
3545 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3547 =head3 Input and Output
3549 Piecewise quasipolynomials can be read from input using
3551 __isl_give isl_union_pw_qpolynomial *
3552 isl_union_pw_qpolynomial_read_from_str(
3553 isl_ctx *ctx, const char *str);
3555 Quasipolynomials and piecewise quasipolynomials can be printed
3556 using the following functions.
3558 __isl_give isl_printer *isl_printer_print_qpolynomial(
3559 __isl_take isl_printer *p,
3560 __isl_keep isl_qpolynomial *qp);
3562 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3563 __isl_take isl_printer *p,
3564 __isl_keep isl_pw_qpolynomial *pwqp);
3566 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3567 __isl_take isl_printer *p,
3568 __isl_keep isl_union_pw_qpolynomial *upwqp);
3570 The output format of the printer
3571 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3572 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3574 In case of printing in C<ISL_FORMAT_C>, the user may want
3575 to set the names of all dimensions
3577 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3578 __isl_take isl_qpolynomial *qp,
3579 enum isl_dim_type type, unsigned pos,
3581 __isl_give isl_pw_qpolynomial *
3582 isl_pw_qpolynomial_set_dim_name(
3583 __isl_take isl_pw_qpolynomial *pwqp,
3584 enum isl_dim_type type, unsigned pos,
3587 =head3 Creating New (Piecewise) Quasipolynomials
3589 Some simple quasipolynomials can be created using the following functions.
3590 More complicated quasipolynomials can be created by applying
3591 operations such as addition and multiplication
3592 on the resulting quasipolynomials
3594 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3595 __isl_take isl_space *domain);
3596 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3597 __isl_take isl_space *domain);
3598 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3599 __isl_take isl_space *domain);
3600 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3601 __isl_take isl_space *domain);
3602 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3603 __isl_take isl_space *domain);
3604 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3605 __isl_take isl_space *domain,
3606 const isl_int n, const isl_int d);
3607 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3608 __isl_take isl_space *domain,
3609 enum isl_dim_type type, unsigned pos);
3610 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3611 __isl_take isl_aff *aff);
3613 Note that the space in which a quasipolynomial lives is a map space
3614 with a one-dimensional range. The C<domain> argument in some of
3615 the functions above corresponds to the domain of this map space.
3617 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3618 with a single cell can be created using the following functions.
3619 Multiple of these single cell piecewise quasipolynomials can
3620 be combined to create more complicated piecewise quasipolynomials.
3622 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3623 __isl_take isl_space *space);
3624 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3625 __isl_take isl_set *set,
3626 __isl_take isl_qpolynomial *qp);
3627 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3628 __isl_take isl_qpolynomial *qp);
3629 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3630 __isl_take isl_pw_aff *pwaff);
3632 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3633 __isl_take isl_space *space);
3634 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3635 __isl_take isl_pw_qpolynomial *pwqp);
3636 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3637 __isl_take isl_union_pw_qpolynomial *upwqp,
3638 __isl_take isl_pw_qpolynomial *pwqp);
3640 Quasipolynomials can be copied and freed again using the following
3643 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3644 __isl_keep isl_qpolynomial *qp);
3645 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3647 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3648 __isl_keep isl_pw_qpolynomial *pwqp);
3649 void *isl_pw_qpolynomial_free(
3650 __isl_take isl_pw_qpolynomial *pwqp);
3652 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3653 __isl_keep isl_union_pw_qpolynomial *upwqp);
3654 void *isl_union_pw_qpolynomial_free(
3655 __isl_take isl_union_pw_qpolynomial *upwqp);
3657 =head3 Inspecting (Piecewise) Quasipolynomials
3659 To iterate over all piecewise quasipolynomials in a union
3660 piecewise quasipolynomial, use the following function
3662 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3663 __isl_keep isl_union_pw_qpolynomial *upwqp,
3664 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3667 To extract the piecewise quasipolynomial in a given space from a union, use
3669 __isl_give isl_pw_qpolynomial *
3670 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3671 __isl_keep isl_union_pw_qpolynomial *upwqp,
3672 __isl_take isl_space *space);
3674 To iterate over the cells in a piecewise quasipolynomial,
3675 use either of the following two functions
3677 int isl_pw_qpolynomial_foreach_piece(
3678 __isl_keep isl_pw_qpolynomial *pwqp,
3679 int (*fn)(__isl_take isl_set *set,
3680 __isl_take isl_qpolynomial *qp,
3681 void *user), void *user);
3682 int isl_pw_qpolynomial_foreach_lifted_piece(
3683 __isl_keep isl_pw_qpolynomial *pwqp,
3684 int (*fn)(__isl_take isl_set *set,
3685 __isl_take isl_qpolynomial *qp,
3686 void *user), void *user);
3688 As usual, the function C<fn> should return C<0> on success
3689 and C<-1> on failure. The difference between
3690 C<isl_pw_qpolynomial_foreach_piece> and
3691 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3692 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3693 compute unique representations for all existentially quantified
3694 variables and then turn these existentially quantified variables
3695 into extra set variables, adapting the associated quasipolynomial
3696 accordingly. This means that the C<set> passed to C<fn>
3697 will not have any existentially quantified variables, but that
3698 the dimensions of the sets may be different for different
3699 invocations of C<fn>.
3701 To iterate over all terms in a quasipolynomial,
3704 int isl_qpolynomial_foreach_term(
3705 __isl_keep isl_qpolynomial *qp,
3706 int (*fn)(__isl_take isl_term *term,
3707 void *user), void *user);
3709 The terms themselves can be inspected and freed using
3712 unsigned isl_term_dim(__isl_keep isl_term *term,
3713 enum isl_dim_type type);
3714 void isl_term_get_num(__isl_keep isl_term *term,
3716 void isl_term_get_den(__isl_keep isl_term *term,
3718 int isl_term_get_exp(__isl_keep isl_term *term,
3719 enum isl_dim_type type, unsigned pos);
3720 __isl_give isl_aff *isl_term_get_div(
3721 __isl_keep isl_term *term, unsigned pos);
3722 void isl_term_free(__isl_take isl_term *term);
3724 Each term is a product of parameters, set variables and
3725 integer divisions. The function C<isl_term_get_exp>
3726 returns the exponent of a given dimensions in the given term.
3727 The C<isl_int>s in the arguments of C<isl_term_get_num>
3728 and C<isl_term_get_den> need to have been initialized
3729 using C<isl_int_init> before calling these functions.
3731 =head3 Properties of (Piecewise) Quasipolynomials
3733 To check whether a quasipolynomial is actually a constant,
3734 use the following function.
3736 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3737 isl_int *n, isl_int *d);
3739 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3740 then the numerator and denominator of the constant
3741 are returned in C<*n> and C<*d>, respectively.
3743 To check whether two union piecewise quasipolynomials are
3744 obviously equal, use
3746 int isl_union_pw_qpolynomial_plain_is_equal(
3747 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3748 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3750 =head3 Operations on (Piecewise) Quasipolynomials
3752 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3753 __isl_take isl_qpolynomial *qp, isl_int v);
3754 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3755 __isl_take isl_qpolynomial *qp);
3756 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3757 __isl_take isl_qpolynomial *qp1,
3758 __isl_take isl_qpolynomial *qp2);
3759 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3760 __isl_take isl_qpolynomial *qp1,
3761 __isl_take isl_qpolynomial *qp2);
3762 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3763 __isl_take isl_qpolynomial *qp1,
3764 __isl_take isl_qpolynomial *qp2);
3765 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3766 __isl_take isl_qpolynomial *qp, unsigned exponent);
3768 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3769 __isl_take isl_pw_qpolynomial *pwqp1,
3770 __isl_take isl_pw_qpolynomial *pwqp2);
3771 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3772 __isl_take isl_pw_qpolynomial *pwqp1,
3773 __isl_take isl_pw_qpolynomial *pwqp2);
3774 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3775 __isl_take isl_pw_qpolynomial *pwqp1,
3776 __isl_take isl_pw_qpolynomial *pwqp2);
3777 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3778 __isl_take isl_pw_qpolynomial *pwqp);
3779 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3780 __isl_take isl_pw_qpolynomial *pwqp1,
3781 __isl_take isl_pw_qpolynomial *pwqp2);
3782 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3783 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3785 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3786 __isl_take isl_union_pw_qpolynomial *upwqp1,
3787 __isl_take isl_union_pw_qpolynomial *upwqp2);
3788 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3789 __isl_take isl_union_pw_qpolynomial *upwqp1,
3790 __isl_take isl_union_pw_qpolynomial *upwqp2);
3791 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3792 __isl_take isl_union_pw_qpolynomial *upwqp1,
3793 __isl_take isl_union_pw_qpolynomial *upwqp2);
3795 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3796 __isl_take isl_pw_qpolynomial *pwqp,
3797 __isl_take isl_point *pnt);
3799 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3800 __isl_take isl_union_pw_qpolynomial *upwqp,
3801 __isl_take isl_point *pnt);
3803 __isl_give isl_set *isl_pw_qpolynomial_domain(
3804 __isl_take isl_pw_qpolynomial *pwqp);
3805 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3806 __isl_take isl_pw_qpolynomial *pwpq,
3807 __isl_take isl_set *set);
3808 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3809 __isl_take isl_pw_qpolynomial *pwpq,
3810 __isl_take isl_set *set);
3812 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3813 __isl_take isl_union_pw_qpolynomial *upwqp);
3814 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3815 __isl_take isl_union_pw_qpolynomial *upwpq,
3816 __isl_take isl_union_set *uset);
3817 __isl_give isl_union_pw_qpolynomial *
3818 isl_union_pw_qpolynomial_intersect_params(
3819 __isl_take isl_union_pw_qpolynomial *upwpq,
3820 __isl_take isl_set *set);
3822 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3823 __isl_take isl_qpolynomial *qp,
3824 __isl_take isl_space *model);
3826 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3827 __isl_take isl_qpolynomial *qp);
3828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3829 __isl_take isl_pw_qpolynomial *pwqp);
3831 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3832 __isl_take isl_union_pw_qpolynomial *upwqp);
3834 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3835 __isl_take isl_qpolynomial *qp,
3836 __isl_take isl_set *context);
3837 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3838 __isl_take isl_qpolynomial *qp,
3839 __isl_take isl_set *context);
3841 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3842 __isl_take isl_pw_qpolynomial *pwqp,
3843 __isl_take isl_set *context);
3844 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3845 __isl_take isl_pw_qpolynomial *pwqp,
3846 __isl_take isl_set *context);
3848 __isl_give isl_union_pw_qpolynomial *
3849 isl_union_pw_qpolynomial_gist_params(
3850 __isl_take isl_union_pw_qpolynomial *upwqp,
3851 __isl_take isl_set *context);
3852 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3853 __isl_take isl_union_pw_qpolynomial *upwqp,
3854 __isl_take isl_union_set *context);
3856 The gist operation applies the gist operation to each of
3857 the cells in the domain of the input piecewise quasipolynomial.
3858 The context is also exploited
3859 to simplify the quasipolynomials associated to each cell.
3861 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3862 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3863 __isl_give isl_union_pw_qpolynomial *
3864 isl_union_pw_qpolynomial_to_polynomial(
3865 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3867 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3868 the polynomial will be an overapproximation. If C<sign> is negative,
3869 it will be an underapproximation. If C<sign> is zero, the approximation
3870 will lie somewhere in between.
3872 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3874 A piecewise quasipolynomial reduction is a piecewise
3875 reduction (or fold) of quasipolynomials.
3876 In particular, the reduction can be maximum or a minimum.
3877 The objects are mainly used to represent the result of
3878 an upper or lower bound on a quasipolynomial over its domain,
3879 i.e., as the result of the following function.
3881 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3882 __isl_take isl_pw_qpolynomial *pwqp,
3883 enum isl_fold type, int *tight);
3885 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3886 __isl_take isl_union_pw_qpolynomial *upwqp,
3887 enum isl_fold type, int *tight);
3889 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3890 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3891 is the returned bound is known be tight, i.e., for each value
3892 of the parameters there is at least
3893 one element in the domain that reaches the bound.
3894 If the domain of C<pwqp> is not wrapping, then the bound is computed
3895 over all elements in that domain and the result has a purely parametric
3896 domain. If the domain of C<pwqp> is wrapping, then the bound is
3897 computed over the range of the wrapped relation. The domain of the
3898 wrapped relation becomes the domain of the result.
3900 A (piecewise) quasipolynomial reduction can be copied or freed using the
3901 following functions.
3903 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3904 __isl_keep isl_qpolynomial_fold *fold);
3905 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3906 __isl_keep isl_pw_qpolynomial_fold *pwf);
3907 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3908 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3909 void isl_qpolynomial_fold_free(
3910 __isl_take isl_qpolynomial_fold *fold);
3911 void *isl_pw_qpolynomial_fold_free(
3912 __isl_take isl_pw_qpolynomial_fold *pwf);
3913 void *isl_union_pw_qpolynomial_fold_free(
3914 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3916 =head3 Printing Piecewise Quasipolynomial Reductions
3918 Piecewise quasipolynomial reductions can be printed
3919 using the following function.
3921 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3922 __isl_take isl_printer *p,
3923 __isl_keep isl_pw_qpolynomial_fold *pwf);
3924 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3925 __isl_take isl_printer *p,
3926 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3928 For C<isl_printer_print_pw_qpolynomial_fold>,
3929 output format of the printer
3930 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3931 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3932 output format of the printer
3933 needs to be set to C<ISL_FORMAT_ISL>.
3934 In case of printing in C<ISL_FORMAT_C>, the user may want
3935 to set the names of all dimensions
3937 __isl_give isl_pw_qpolynomial_fold *
3938 isl_pw_qpolynomial_fold_set_dim_name(
3939 __isl_take isl_pw_qpolynomial_fold *pwf,
3940 enum isl_dim_type type, unsigned pos,
3943 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3945 To iterate over all piecewise quasipolynomial reductions in a union
3946 piecewise quasipolynomial reduction, use the following function
3948 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3949 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3950 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3951 void *user), void *user);
3953 To iterate over the cells in a piecewise quasipolynomial reduction,
3954 use either of the following two functions
3956 int isl_pw_qpolynomial_fold_foreach_piece(
3957 __isl_keep isl_pw_qpolynomial_fold *pwf,
3958 int (*fn)(__isl_take isl_set *set,
3959 __isl_take isl_qpolynomial_fold *fold,
3960 void *user), void *user);
3961 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3962 __isl_keep isl_pw_qpolynomial_fold *pwf,
3963 int (*fn)(__isl_take isl_set *set,
3964 __isl_take isl_qpolynomial_fold *fold,
3965 void *user), void *user);
3967 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3968 of the difference between these two functions.
3970 To iterate over all quasipolynomials in a reduction, use
3972 int isl_qpolynomial_fold_foreach_qpolynomial(
3973 __isl_keep isl_qpolynomial_fold *fold,
3974 int (*fn)(__isl_take isl_qpolynomial *qp,
3975 void *user), void *user);
3977 =head3 Properties of Piecewise Quasipolynomial Reductions
3979 To check whether two union piecewise quasipolynomial reductions are
3980 obviously equal, use
3982 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3983 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3984 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3986 =head3 Operations on Piecewise Quasipolynomial Reductions
3988 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3989 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3991 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3992 __isl_take isl_pw_qpolynomial_fold *pwf1,
3993 __isl_take isl_pw_qpolynomial_fold *pwf2);
3995 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3996 __isl_take isl_pw_qpolynomial_fold *pwf1,
3997 __isl_take isl_pw_qpolynomial_fold *pwf2);
3999 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4000 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4001 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4003 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4004 __isl_take isl_pw_qpolynomial_fold *pwf,
4005 __isl_take isl_point *pnt);
4007 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4008 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4009 __isl_take isl_point *pnt);
4011 __isl_give isl_pw_qpolynomial_fold *
4012 sl_pw_qpolynomial_fold_intersect_params(
4013 __isl_take isl_pw_qpolynomial_fold *pwf,
4014 __isl_take isl_set *set);
4016 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4017 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4018 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4019 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4020 __isl_take isl_union_set *uset);
4021 __isl_give isl_union_pw_qpolynomial_fold *
4022 isl_union_pw_qpolynomial_fold_intersect_params(
4023 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4024 __isl_take isl_set *set);
4026 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4027 __isl_take isl_pw_qpolynomial_fold *pwf);
4029 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4030 __isl_take isl_pw_qpolynomial_fold *pwf);
4032 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4033 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4035 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4036 __isl_take isl_qpolynomial_fold *fold,
4037 __isl_take isl_set *context);
4038 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4039 __isl_take isl_qpolynomial_fold *fold,
4040 __isl_take isl_set *context);
4042 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4043 __isl_take isl_pw_qpolynomial_fold *pwf,
4044 __isl_take isl_set *context);
4045 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4046 __isl_take isl_pw_qpolynomial_fold *pwf,
4047 __isl_take isl_set *context);
4049 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4050 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4051 __isl_take isl_union_set *context);
4052 __isl_give isl_union_pw_qpolynomial_fold *
4053 isl_union_pw_qpolynomial_fold_gist_params(
4054 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4055 __isl_take isl_set *context);
4057 The gist operation applies the gist operation to each of
4058 the cells in the domain of the input piecewise quasipolynomial reduction.
4059 In future, the operation will also exploit the context
4060 to simplify the quasipolynomial reductions associated to each cell.
4062 __isl_give isl_pw_qpolynomial_fold *
4063 isl_set_apply_pw_qpolynomial_fold(
4064 __isl_take isl_set *set,
4065 __isl_take isl_pw_qpolynomial_fold *pwf,
4067 __isl_give isl_pw_qpolynomial_fold *
4068 isl_map_apply_pw_qpolynomial_fold(
4069 __isl_take isl_map *map,
4070 __isl_take isl_pw_qpolynomial_fold *pwf,
4072 __isl_give isl_union_pw_qpolynomial_fold *
4073 isl_union_set_apply_union_pw_qpolynomial_fold(
4074 __isl_take isl_union_set *uset,
4075 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4077 __isl_give isl_union_pw_qpolynomial_fold *
4078 isl_union_map_apply_union_pw_qpolynomial_fold(
4079 __isl_take isl_union_map *umap,
4080 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4083 The functions taking a map
4084 compose the given map with the given piecewise quasipolynomial reduction.
4085 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4086 over all elements in the intersection of the range of the map
4087 and the domain of the piecewise quasipolynomial reduction
4088 as a function of an element in the domain of the map.
4089 The functions taking a set compute a bound over all elements in the
4090 intersection of the set and the domain of the
4091 piecewise quasipolynomial reduction.
4093 =head2 Dependence Analysis
4095 C<isl> contains specialized functionality for performing
4096 array dataflow analysis. That is, given a I<sink> access relation
4097 and a collection of possible I<source> access relations,
4098 C<isl> can compute relations that describe
4099 for each iteration of the sink access, which iteration
4100 of which of the source access relations was the last
4101 to access the same data element before the given iteration
4103 The resulting dependence relations map source iterations
4104 to the corresponding sink iterations.
4105 To compute standard flow dependences, the sink should be
4106 a read, while the sources should be writes.
4107 If any of the source accesses are marked as being I<may>
4108 accesses, then there will be a dependence from the last
4109 I<must> access B<and> from any I<may> access that follows
4110 this last I<must> access.
4111 In particular, if I<all> sources are I<may> accesses,
4112 then memory based dependence analysis is performed.
4113 If, on the other hand, all sources are I<must> accesses,
4114 then value based dependence analysis is performed.
4116 #include <isl/flow.h>
4118 typedef int (*isl_access_level_before)(void *first, void *second);
4120 __isl_give isl_access_info *isl_access_info_alloc(
4121 __isl_take isl_map *sink,
4122 void *sink_user, isl_access_level_before fn,
4124 __isl_give isl_access_info *isl_access_info_add_source(
4125 __isl_take isl_access_info *acc,
4126 __isl_take isl_map *source, int must,
4128 void isl_access_info_free(__isl_take isl_access_info *acc);
4130 __isl_give isl_flow *isl_access_info_compute_flow(
4131 __isl_take isl_access_info *acc);
4133 int isl_flow_foreach(__isl_keep isl_flow *deps,
4134 int (*fn)(__isl_take isl_map *dep, int must,
4135 void *dep_user, void *user),
4137 __isl_give isl_map *isl_flow_get_no_source(
4138 __isl_keep isl_flow *deps, int must);
4139 void isl_flow_free(__isl_take isl_flow *deps);
4141 The function C<isl_access_info_compute_flow> performs the actual
4142 dependence analysis. The other functions are used to construct
4143 the input for this function or to read off the output.
4145 The input is collected in an C<isl_access_info>, which can
4146 be created through a call to C<isl_access_info_alloc>.
4147 The arguments to this functions are the sink access relation
4148 C<sink>, a token C<sink_user> used to identify the sink
4149 access to the user, a callback function for specifying the
4150 relative order of source and sink accesses, and the number
4151 of source access relations that will be added.
4152 The callback function has type C<int (*)(void *first, void *second)>.
4153 The function is called with two user supplied tokens identifying
4154 either a source or the sink and it should return the shared nesting
4155 level and the relative order of the two accesses.
4156 In particular, let I<n> be the number of loops shared by
4157 the two accesses. If C<first> precedes C<second> textually,
4158 then the function should return I<2 * n + 1>; otherwise,
4159 it should return I<2 * n>.
4160 The sources can be added to the C<isl_access_info> by performing
4161 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4162 C<must> indicates whether the source is a I<must> access
4163 or a I<may> access. Note that a multi-valued access relation
4164 should only be marked I<must> if every iteration in the domain
4165 of the relation accesses I<all> elements in its image.
4166 The C<source_user> token is again used to identify
4167 the source access. The range of the source access relation
4168 C<source> should have the same dimension as the range
4169 of the sink access relation.
4170 The C<isl_access_info_free> function should usually not be
4171 called explicitly, because it is called implicitly by
4172 C<isl_access_info_compute_flow>.
4174 The result of the dependence analysis is collected in an
4175 C<isl_flow>. There may be elements of
4176 the sink access for which no preceding source access could be
4177 found or for which all preceding sources are I<may> accesses.
4178 The relations containing these elements can be obtained through
4179 calls to C<isl_flow_get_no_source>, the first with C<must> set
4180 and the second with C<must> unset.
4181 In the case of standard flow dependence analysis,
4182 with the sink a read and the sources I<must> writes,
4183 the first relation corresponds to the reads from uninitialized
4184 array elements and the second relation is empty.
4185 The actual flow dependences can be extracted using
4186 C<isl_flow_foreach>. This function will call the user-specified
4187 callback function C<fn> for each B<non-empty> dependence between
4188 a source and the sink. The callback function is called
4189 with four arguments, the actual flow dependence relation
4190 mapping source iterations to sink iterations, a boolean that
4191 indicates whether it is a I<must> or I<may> dependence, a token
4192 identifying the source and an additional C<void *> with value
4193 equal to the third argument of the C<isl_flow_foreach> call.
4194 A dependence is marked I<must> if it originates from a I<must>
4195 source and if it is not followed by any I<may> sources.
4197 After finishing with an C<isl_flow>, the user should call
4198 C<isl_flow_free> to free all associated memory.
4200 A higher-level interface to dependence analysis is provided
4201 by the following function.
4203 #include <isl/flow.h>
4205 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4206 __isl_take isl_union_map *must_source,
4207 __isl_take isl_union_map *may_source,
4208 __isl_take isl_union_map *schedule,
4209 __isl_give isl_union_map **must_dep,
4210 __isl_give isl_union_map **may_dep,
4211 __isl_give isl_union_map **must_no_source,
4212 __isl_give isl_union_map **may_no_source);
4214 The arrays are identified by the tuple names of the ranges
4215 of the accesses. The iteration domains by the tuple names
4216 of the domains of the accesses and of the schedule.
4217 The relative order of the iteration domains is given by the
4218 schedule. The relations returned through C<must_no_source>
4219 and C<may_no_source> are subsets of C<sink>.
4220 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4221 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4222 any of the other arguments is treated as an error.
4224 =head3 Interaction with Dependence Analysis
4226 During the dependence analysis, we frequently need to perform
4227 the following operation. Given a relation between sink iterations
4228 and potential soure iterations from a particular source domain,
4229 what is the last potential source iteration corresponding to each
4230 sink iteration. It can sometimes be convenient to adjust
4231 the set of potential source iterations before or after each such operation.
4232 The prototypical example is fuzzy array dataflow analysis,
4233 where we need to analyze if, based on data-dependent constraints,
4234 the sink iteration can ever be executed without one or more of
4235 the corresponding potential source iterations being executed.
4236 If so, we can introduce extra parameters and select an unknown
4237 but fixed source iteration from the potential source iterations.
4238 To be able to perform such manipulations, C<isl> provides the following
4241 #include <isl/flow.h>
4243 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4244 __isl_keep isl_map *source_map,
4245 __isl_keep isl_set *sink, void *source_user,
4247 __isl_give isl_access_info *isl_access_info_set_restrict(
4248 __isl_take isl_access_info *acc,
4249 isl_access_restrict fn, void *user);
4251 The function C<isl_access_info_set_restrict> should be called
4252 before calling C<isl_access_info_compute_flow> and registers a callback function
4253 that will be called any time C<isl> is about to compute the last
4254 potential source. The first argument is the (reverse) proto-dependence,
4255 mapping sink iterations to potential source iterations.
4256 The second argument represents the sink iterations for which
4257 we want to compute the last source iteration.
4258 The third argument is the token corresponding to the source
4259 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4260 The callback is expected to return a restriction on either the input or
4261 the output of the operation computing the last potential source.
4262 If the input needs to be restricted then restrictions are needed
4263 for both the source and the sink iterations. The sink iterations
4264 and the potential source iterations will be intersected with these sets.
4265 If the output needs to be restricted then only a restriction on the source
4266 iterations is required.
4267 If any error occurs, the callback should return C<NULL>.
4268 An C<isl_restriction> object can be created and freed using the following
4271 #include <isl/flow.h>
4273 __isl_give isl_restriction *isl_restriction_input(
4274 __isl_take isl_set *source_restr,
4275 __isl_take isl_set *sink_restr);
4276 __isl_give isl_restriction *isl_restriction_output(
4277 __isl_take isl_set *source_restr);
4278 __isl_give isl_restriction *isl_restriction_none(
4279 __isl_keep isl_map *source_map);
4280 __isl_give isl_restriction *isl_restriction_empty(
4281 __isl_keep isl_map *source_map);
4282 void *isl_restriction_free(
4283 __isl_take isl_restriction *restr);
4285 C<isl_restriction_none> and C<isl_restriction_empty> are special
4286 cases of C<isl_restriction_input>. C<isl_restriction_none>
4287 is essentially equivalent to
4289 isl_restriction_input(isl_set_universe(
4290 isl_space_range(isl_map_get_space(source_map))),
4292 isl_space_domain(isl_map_get_space(source_map))));
4294 whereas C<isl_restriction_empty> is essentially equivalent to
4296 isl_restriction_input(isl_set_empty(
4297 isl_space_range(isl_map_get_space(source_map))),
4299 isl_space_domain(isl_map_get_space(source_map))));
4303 B<The functionality described in this section is fairly new
4304 and may be subject to change.>
4306 The following function can be used to compute a schedule
4307 for a union of domains.
4308 By default, the algorithm used to construct the schedule is similar
4309 to that of C<Pluto>.
4310 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4312 The generated schedule respects all C<validity> dependences.
4313 That is, all dependence distances over these dependences in the
4314 scheduled space are lexicographically positive.
4315 The default algorithm tries to minimize the dependence distances over
4316 C<proximity> dependences.
4317 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4318 for groups of domains where the dependence distances have only
4319 non-negative values.
4320 When using Feautrier's algorithm, the C<proximity> dependence
4321 distances are only minimized during the extension to a
4322 full-dimensional schedule.
4324 #include <isl/schedule.h>
4325 __isl_give isl_schedule *isl_union_set_compute_schedule(
4326 __isl_take isl_union_set *domain,
4327 __isl_take isl_union_map *validity,
4328 __isl_take isl_union_map *proximity);
4329 void *isl_schedule_free(__isl_take isl_schedule *sched);
4331 A mapping from the domains to the scheduled space can be obtained
4332 from an C<isl_schedule> using the following function.
4334 __isl_give isl_union_map *isl_schedule_get_map(
4335 __isl_keep isl_schedule *sched);
4337 A representation of the schedule can be printed using
4339 __isl_give isl_printer *isl_printer_print_schedule(
4340 __isl_take isl_printer *p,
4341 __isl_keep isl_schedule *schedule);
4343 A representation of the schedule as a forest of bands can be obtained
4344 using the following function.
4346 __isl_give isl_band_list *isl_schedule_get_band_forest(
4347 __isl_keep isl_schedule *schedule);
4349 The list can be manipulated as explained in L<"Lists">.
4350 The bands inside the list can be copied and freed using the following
4353 #include <isl/band.h>
4354 __isl_give isl_band *isl_band_copy(
4355 __isl_keep isl_band *band);
4356 void *isl_band_free(__isl_take isl_band *band);
4358 Each band contains zero or more scheduling dimensions.
4359 These are referred to as the members of the band.
4360 The section of the schedule that corresponds to the band is
4361 referred to as the partial schedule of the band.
4362 For those nodes that participate in a band, the outer scheduling
4363 dimensions form the prefix schedule, while the inner scheduling
4364 dimensions form the suffix schedule.
4365 That is, if we take a cut of the band forest, then the union of
4366 the concatenations of the prefix, partial and suffix schedules of
4367 each band in the cut is equal to the entire schedule (modulo
4368 some possible padding at the end with zero scheduling dimensions).
4369 The properties of a band can be inspected using the following functions.
4371 #include <isl/band.h>
4372 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4374 int isl_band_has_children(__isl_keep isl_band *band);
4375 __isl_give isl_band_list *isl_band_get_children(
4376 __isl_keep isl_band *band);
4378 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4379 __isl_keep isl_band *band);
4380 __isl_give isl_union_map *isl_band_get_partial_schedule(
4381 __isl_keep isl_band *band);
4382 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4383 __isl_keep isl_band *band);
4385 int isl_band_n_member(__isl_keep isl_band *band);
4386 int isl_band_member_is_zero_distance(
4387 __isl_keep isl_band *band, int pos);
4389 Note that a scheduling dimension is considered to be ``zero
4390 distance'' if it does not carry any proximity dependences
4392 That is, if the dependence distances of the proximity
4393 dependences are all zero in that direction (for fixed
4394 iterations of outer bands).
4396 A representation of the band can be printed using
4398 #include <isl/band.h>
4399 __isl_give isl_printer *isl_printer_print_band(
4400 __isl_take isl_printer *p,
4401 __isl_keep isl_band *band);
4405 #include <isl/schedule.h>
4406 int isl_options_set_schedule_max_coefficient(
4407 isl_ctx *ctx, int val);
4408 int isl_options_get_schedule_max_coefficient(
4410 int isl_options_set_schedule_max_constant_term(
4411 isl_ctx *ctx, int val);
4412 int isl_options_get_schedule_max_constant_term(
4414 int isl_options_set_schedule_maximize_band_depth(
4415 isl_ctx *ctx, int val);
4416 int isl_options_get_schedule_maximize_band_depth(
4418 int isl_options_set_schedule_outer_zero_distance(
4419 isl_ctx *ctx, int val);
4420 int isl_options_get_schedule_outer_zero_distance(
4422 int isl_options_set_schedule_split_scaled(
4423 isl_ctx *ctx, int val);
4424 int isl_options_get_schedule_split_scaled(
4426 int isl_options_set_schedule_algorithm(
4427 isl_ctx *ctx, int val);
4428 int isl_options_get_schedule_algorithm(
4434 =item * schedule_max_coefficient
4436 This option enforces that the coefficients for variable and parameter
4437 dimensions in the calculated schedule are not larger than the specified value.
4438 This option can significantly increase the speed of the scheduling calculation
4439 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4440 this option does not introduce bounds on the variable or parameter
4443 =item * schedule_max_constant_term
4445 This option enforces that the constant coefficients in the calculated schedule
4446 are not larger than the maximal constant term. This option can significantly
4447 increase the speed of the scheduling calculation and may also prevent fusing of
4448 unrelated dimensions. A value of -1 means that this option does not introduce
4449 bounds on the constant coefficients.
4451 =item * schedule_maximize_band_depth
4453 If this option is set, we do not split bands at the point
4454 where we detect splitting is necessary. Instead, we
4455 backtrack and split bands as early as possible. This
4456 reduces the number of splits and maximizes the width of
4457 the bands. Wider bands give more possibilities for tiling.
4459 =item * schedule_outer_zero_distance
4461 If this option is set, then we try to construct schedules
4462 where the outermost scheduling dimension in each band
4463 results in a zero dependence distance over the proximity
4466 =item * schedule_split_scaled
4468 If this option is set, then we try to construct schedules in which the
4469 constant term is split off from the linear part if the linear parts of
4470 the scheduling rows for all nodes in the graphs have a common non-trivial
4472 The constant term is then placed in a separate band and the linear
4475 =item * schedule_algorithm
4477 Selects the scheduling algorithm to be used.
4478 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4479 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4483 =head2 Parametric Vertex Enumeration
4485 The parametric vertex enumeration described in this section
4486 is mainly intended to be used internally and by the C<barvinok>
4489 #include <isl/vertices.h>
4490 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4491 __isl_keep isl_basic_set *bset);
4493 The function C<isl_basic_set_compute_vertices> performs the
4494 actual computation of the parametric vertices and the chamber
4495 decomposition and store the result in an C<isl_vertices> object.
4496 This information can be queried by either iterating over all
4497 the vertices or iterating over all the chambers or cells
4498 and then iterating over all vertices that are active on the chamber.
4500 int isl_vertices_foreach_vertex(
4501 __isl_keep isl_vertices *vertices,
4502 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4505 int isl_vertices_foreach_cell(
4506 __isl_keep isl_vertices *vertices,
4507 int (*fn)(__isl_take isl_cell *cell, void *user),
4509 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4510 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4513 Other operations that can be performed on an C<isl_vertices> object are
4516 isl_ctx *isl_vertices_get_ctx(
4517 __isl_keep isl_vertices *vertices);
4518 int isl_vertices_get_n_vertices(
4519 __isl_keep isl_vertices *vertices);
4520 void isl_vertices_free(__isl_take isl_vertices *vertices);
4522 Vertices can be inspected and destroyed using the following functions.
4524 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4525 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4526 __isl_give isl_basic_set *isl_vertex_get_domain(
4527 __isl_keep isl_vertex *vertex);
4528 __isl_give isl_basic_set *isl_vertex_get_expr(
4529 __isl_keep isl_vertex *vertex);
4530 void isl_vertex_free(__isl_take isl_vertex *vertex);
4532 C<isl_vertex_get_expr> returns a singleton parametric set describing
4533 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4535 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4536 B<rational> basic sets, so they should mainly be used for inspection
4537 and should not be mixed with integer sets.
4539 Chambers can be inspected and destroyed using the following functions.
4541 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4542 __isl_give isl_basic_set *isl_cell_get_domain(
4543 __isl_keep isl_cell *cell);
4544 void isl_cell_free(__isl_take isl_cell *cell);
4548 Although C<isl> is mainly meant to be used as a library,
4549 it also contains some basic applications that use some
4550 of the functionality of C<isl>.
4551 The input may be specified in either the L<isl format>
4552 or the L<PolyLib format>.
4554 =head2 C<isl_polyhedron_sample>
4556 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4557 an integer element of the polyhedron, if there is any.
4558 The first column in the output is the denominator and is always
4559 equal to 1. If the polyhedron contains no integer points,
4560 then a vector of length zero is printed.
4564 C<isl_pip> takes the same input as the C<example> program
4565 from the C<piplib> distribution, i.e., a set of constraints
4566 on the parameters, a line containing only -1 and finally a set
4567 of constraints on a parametric polyhedron.
4568 The coefficients of the parameters appear in the last columns
4569 (but before the final constant column).
4570 The output is the lexicographic minimum of the parametric polyhedron.
4571 As C<isl> currently does not have its own output format, the output
4572 is just a dump of the internal state.
4574 =head2 C<isl_polyhedron_minimize>
4576 C<isl_polyhedron_minimize> computes the minimum of some linear
4577 or affine objective function over the integer points in a polyhedron.
4578 If an affine objective function
4579 is given, then the constant should appear in the last column.
4581 =head2 C<isl_polytope_scan>
4583 Given a polytope, C<isl_polytope_scan> prints
4584 all integer points in the polytope.