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);
668 #include <isl/point.h>
669 __isl_give isl_space *isl_point_get_space(
670 __isl_keep isl_point *pnt);
672 The identifiers or names of the individual dimensions may be set or read off
673 using the following functions.
675 #include <isl/space.h>
676 __isl_give isl_space *isl_space_set_dim_id(
677 __isl_take isl_space *space,
678 enum isl_dim_type type, unsigned pos,
679 __isl_take isl_id *id);
680 int isl_space_has_dim_id(__isl_keep isl_space *space,
681 enum isl_dim_type type, unsigned pos);
682 __isl_give isl_id *isl_space_get_dim_id(
683 __isl_keep isl_space *space,
684 enum isl_dim_type type, unsigned pos);
685 __isl_give isl_space *isl_space_set_dim_name(
686 __isl_take isl_space *space,
687 enum isl_dim_type type, unsigned pos,
688 __isl_keep const char *name);
689 int isl_space_has_dim_name(__isl_keep isl_space *space,
690 enum isl_dim_type type, unsigned pos);
691 __isl_keep const char *isl_space_get_dim_name(
692 __isl_keep isl_space *space,
693 enum isl_dim_type type, unsigned pos);
695 Note that C<isl_space_get_name> returns a pointer to some internal
696 data structure, so the result can only be used while the
697 corresponding C<isl_space> is alive.
698 Also note that every function that operates on two sets or relations
699 requires that both arguments have the same parameters. This also
700 means that if one of the arguments has named parameters, then the
701 other needs to have named parameters too and the names need to match.
702 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
703 arguments may have different parameters (as long as they are named),
704 in which case the result will have as parameters the union of the parameters of
707 Given the identifier or name of a dimension (typically a parameter),
708 its position can be obtained from the following function.
710 #include <isl/space.h>
711 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
712 enum isl_dim_type type, __isl_keep isl_id *id);
713 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
714 enum isl_dim_type type, const char *name);
716 The identifiers or names of entire spaces may be set or read off
717 using the following functions.
719 #include <isl/space.h>
720 __isl_give isl_space *isl_space_set_tuple_id(
721 __isl_take isl_space *space,
722 enum isl_dim_type type, __isl_take isl_id *id);
723 __isl_give isl_space *isl_space_reset_tuple_id(
724 __isl_take isl_space *space, enum isl_dim_type type);
725 int isl_space_has_tuple_id(__isl_keep isl_space *space,
726 enum isl_dim_type type);
727 __isl_give isl_id *isl_space_get_tuple_id(
728 __isl_keep isl_space *space, enum isl_dim_type type);
729 __isl_give isl_space *isl_space_set_tuple_name(
730 __isl_take isl_space *space,
731 enum isl_dim_type type, const char *s);
732 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
733 enum isl_dim_type type);
735 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
736 or C<isl_dim_set>. As with C<isl_space_get_name>,
737 the C<isl_space_get_tuple_name> function returns a pointer to some internal
739 Binary operations require the corresponding spaces of their arguments
740 to have the same name.
742 Spaces can be nested. In particular, the domain of a set or
743 the domain or range of a relation can be a nested relation.
744 The following functions can be used to construct and deconstruct
747 #include <isl/space.h>
748 int isl_space_is_wrapping(__isl_keep isl_space *space);
749 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
750 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
752 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
753 be the space of a set, while that of
754 C<isl_space_wrap> should be the space of a relation.
755 Conversely, the output of C<isl_space_unwrap> is the space
756 of a relation, while that of C<isl_space_wrap> is the space of a set.
758 Spaces can be created from other spaces
759 using the following functions.
761 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
762 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
763 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
764 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
765 __isl_give isl_space *isl_space_params(
766 __isl_take isl_space *space);
767 __isl_give isl_space *isl_space_set_from_params(
768 __isl_take isl_space *space);
769 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
770 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
771 __isl_take isl_space *right);
772 __isl_give isl_space *isl_space_align_params(
773 __isl_take isl_space *space1, __isl_take isl_space *space2)
774 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
775 enum isl_dim_type type, unsigned pos, unsigned n);
776 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
777 enum isl_dim_type type, unsigned n);
778 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
779 enum isl_dim_type type, unsigned first, unsigned n);
780 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
781 enum isl_dim_type dst_type, unsigned dst_pos,
782 enum isl_dim_type src_type, unsigned src_pos,
784 __isl_give isl_space *isl_space_map_from_set(
785 __isl_take isl_space *space);
786 __isl_give isl_space *isl_space_map_from_domain_and_range(
787 __isl_take isl_space *domain,
788 __isl_take isl_space *range);
789 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
791 Note that if dimensions are added or removed from a space, then
792 the name and the internal structure are lost.
796 A local space is essentially a space with
797 zero or more existentially quantified variables.
798 The local space of a basic set or relation can be obtained
799 using the following functions.
802 __isl_give isl_local_space *isl_basic_set_get_local_space(
803 __isl_keep isl_basic_set *bset);
806 __isl_give isl_local_space *isl_basic_map_get_local_space(
807 __isl_keep isl_basic_map *bmap);
809 A new local space can be created from a space using
811 #include <isl/local_space.h>
812 __isl_give isl_local_space *isl_local_space_from_space(
813 __isl_take isl_space *space);
815 They can be inspected, modified, copied and freed using the following functions.
817 #include <isl/local_space.h>
818 isl_ctx *isl_local_space_get_ctx(
819 __isl_keep isl_local_space *ls);
820 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
821 int isl_local_space_dim(__isl_keep isl_local_space *ls,
822 enum isl_dim_type type);
823 const char *isl_local_space_get_dim_name(
824 __isl_keep isl_local_space *ls,
825 enum isl_dim_type type, unsigned pos);
826 __isl_give isl_local_space *isl_local_space_set_dim_name(
827 __isl_take isl_local_space *ls,
828 enum isl_dim_type type, unsigned pos, const char *s);
829 __isl_give isl_local_space *isl_local_space_set_dim_id(
830 __isl_take isl_local_space *ls,
831 enum isl_dim_type type, unsigned pos,
832 __isl_take isl_id *id);
833 __isl_give isl_space *isl_local_space_get_space(
834 __isl_keep isl_local_space *ls);
835 __isl_give isl_aff *isl_local_space_get_div(
836 __isl_keep isl_local_space *ls, int pos);
837 __isl_give isl_local_space *isl_local_space_copy(
838 __isl_keep isl_local_space *ls);
839 void *isl_local_space_free(__isl_take isl_local_space *ls);
841 Two local spaces can be compared using
843 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
844 __isl_keep isl_local_space *ls2);
846 Local spaces can be created from other local spaces
847 using the following functions.
849 __isl_give isl_local_space *isl_local_space_domain(
850 __isl_take isl_local_space *ls);
851 __isl_give isl_local_space *isl_local_space_range(
852 __isl_take isl_local_space *ls);
853 __isl_give isl_local_space *isl_local_space_from_domain(
854 __isl_take isl_local_space *ls);
855 __isl_give isl_local_space *isl_local_space_intersect(
856 __isl_take isl_local_space *ls1,
857 __isl_take isl_local_space *ls2);
858 __isl_give isl_local_space *isl_local_space_add_dims(
859 __isl_take isl_local_space *ls,
860 enum isl_dim_type type, unsigned n);
861 __isl_give isl_local_space *isl_local_space_insert_dims(
862 __isl_take isl_local_space *ls,
863 enum isl_dim_type type, unsigned first, unsigned n);
864 __isl_give isl_local_space *isl_local_space_drop_dims(
865 __isl_take isl_local_space *ls,
866 enum isl_dim_type type, unsigned first, unsigned n);
868 =head2 Input and Output
870 C<isl> supports its own input/output format, which is similar
871 to the C<Omega> format, but also supports the C<PolyLib> format
876 The C<isl> format is similar to that of C<Omega>, but has a different
877 syntax for describing the parameters and allows for the definition
878 of an existentially quantified variable as the integer division
879 of an affine expression.
880 For example, the set of integers C<i> between C<0> and C<n>
881 such that C<i % 10 <= 6> can be described as
883 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
886 A set or relation can have several disjuncts, separated
887 by the keyword C<or>. Each disjunct is either a conjunction
888 of constraints or a projection (C<exists>) of a conjunction
889 of constraints. The constraints are separated by the keyword
892 =head3 C<PolyLib> format
894 If the represented set is a union, then the first line
895 contains a single number representing the number of disjuncts.
896 Otherwise, a line containing the number C<1> is optional.
898 Each disjunct is represented by a matrix of constraints.
899 The first line contains two numbers representing
900 the number of rows and columns,
901 where the number of rows is equal to the number of constraints
902 and the number of columns is equal to two plus the number of variables.
903 The following lines contain the actual rows of the constraint matrix.
904 In each row, the first column indicates whether the constraint
905 is an equality (C<0>) or inequality (C<1>). The final column
906 corresponds to the constant term.
908 If the set is parametric, then the coefficients of the parameters
909 appear in the last columns before the constant column.
910 The coefficients of any existentially quantified variables appear
911 between those of the set variables and those of the parameters.
913 =head3 Extended C<PolyLib> format
915 The extended C<PolyLib> format is nearly identical to the
916 C<PolyLib> format. The only difference is that the line
917 containing the number of rows and columns of a constraint matrix
918 also contains four additional numbers:
919 the number of output dimensions, the number of input dimensions,
920 the number of local dimensions (i.e., the number of existentially
921 quantified variables) and the number of parameters.
922 For sets, the number of ``output'' dimensions is equal
923 to the number of set dimensions, while the number of ``input''
929 __isl_give isl_basic_set *isl_basic_set_read_from_file(
930 isl_ctx *ctx, FILE *input);
931 __isl_give isl_basic_set *isl_basic_set_read_from_str(
932 isl_ctx *ctx, const char *str);
933 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
935 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
939 __isl_give isl_basic_map *isl_basic_map_read_from_file(
940 isl_ctx *ctx, FILE *input);
941 __isl_give isl_basic_map *isl_basic_map_read_from_str(
942 isl_ctx *ctx, const char *str);
943 __isl_give isl_map *isl_map_read_from_file(
944 isl_ctx *ctx, FILE *input);
945 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
948 #include <isl/union_set.h>
949 __isl_give isl_union_set *isl_union_set_read_from_file(
950 isl_ctx *ctx, FILE *input);
951 __isl_give isl_union_set *isl_union_set_read_from_str(
952 isl_ctx *ctx, const char *str);
954 #include <isl/union_map.h>
955 __isl_give isl_union_map *isl_union_map_read_from_file(
956 isl_ctx *ctx, FILE *input);
957 __isl_give isl_union_map *isl_union_map_read_from_str(
958 isl_ctx *ctx, const char *str);
960 The input format is autodetected and may be either the C<PolyLib> format
961 or the C<isl> format.
965 Before anything can be printed, an C<isl_printer> needs to
968 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
970 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
971 void isl_printer_free(__isl_take isl_printer *printer);
972 __isl_give char *isl_printer_get_str(
973 __isl_keep isl_printer *printer);
975 The behavior of the printer can be modified in various ways
977 __isl_give isl_printer *isl_printer_set_output_format(
978 __isl_take isl_printer *p, int output_format);
979 __isl_give isl_printer *isl_printer_set_indent(
980 __isl_take isl_printer *p, int indent);
981 __isl_give isl_printer *isl_printer_indent(
982 __isl_take isl_printer *p, int indent);
983 __isl_give isl_printer *isl_printer_set_prefix(
984 __isl_take isl_printer *p, const char *prefix);
985 __isl_give isl_printer *isl_printer_set_suffix(
986 __isl_take isl_printer *p, const char *suffix);
988 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
989 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
990 and defaults to C<ISL_FORMAT_ISL>.
991 Each line in the output is indented by C<indent> (set by
992 C<isl_printer_set_indent>) spaces
993 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
994 In the C<PolyLib> format output,
995 the coefficients of the existentially quantified variables
996 appear between those of the set variables and those
998 The function C<isl_printer_indent> increases the indentation
999 by the specified amount (which may be negative).
1001 To actually print something, use
1003 #include <isl/set.h>
1004 __isl_give isl_printer *isl_printer_print_basic_set(
1005 __isl_take isl_printer *printer,
1006 __isl_keep isl_basic_set *bset);
1007 __isl_give isl_printer *isl_printer_print_set(
1008 __isl_take isl_printer *printer,
1009 __isl_keep isl_set *set);
1011 #include <isl/map.h>
1012 __isl_give isl_printer *isl_printer_print_basic_map(
1013 __isl_take isl_printer *printer,
1014 __isl_keep isl_basic_map *bmap);
1015 __isl_give isl_printer *isl_printer_print_map(
1016 __isl_take isl_printer *printer,
1017 __isl_keep isl_map *map);
1019 #include <isl/union_set.h>
1020 __isl_give isl_printer *isl_printer_print_union_set(
1021 __isl_take isl_printer *p,
1022 __isl_keep isl_union_set *uset);
1024 #include <isl/union_map.h>
1025 __isl_give isl_printer *isl_printer_print_union_map(
1026 __isl_take isl_printer *p,
1027 __isl_keep isl_union_map *umap);
1029 When called on a file printer, the following function flushes
1030 the file. When called on a string printer, the buffer is cleared.
1032 __isl_give isl_printer *isl_printer_flush(
1033 __isl_take isl_printer *p);
1035 =head2 Creating New Sets and Relations
1037 C<isl> has functions for creating some standard sets and relations.
1041 =item * Empty sets and relations
1043 __isl_give isl_basic_set *isl_basic_set_empty(
1044 __isl_take isl_space *space);
1045 __isl_give isl_basic_map *isl_basic_map_empty(
1046 __isl_take isl_space *space);
1047 __isl_give isl_set *isl_set_empty(
1048 __isl_take isl_space *space);
1049 __isl_give isl_map *isl_map_empty(
1050 __isl_take isl_space *space);
1051 __isl_give isl_union_set *isl_union_set_empty(
1052 __isl_take isl_space *space);
1053 __isl_give isl_union_map *isl_union_map_empty(
1054 __isl_take isl_space *space);
1056 For C<isl_union_set>s and C<isl_union_map>s, the space
1057 is only used to specify the parameters.
1059 =item * Universe sets and relations
1061 __isl_give isl_basic_set *isl_basic_set_universe(
1062 __isl_take isl_space *space);
1063 __isl_give isl_basic_map *isl_basic_map_universe(
1064 __isl_take isl_space *space);
1065 __isl_give isl_set *isl_set_universe(
1066 __isl_take isl_space *space);
1067 __isl_give isl_map *isl_map_universe(
1068 __isl_take isl_space *space);
1069 __isl_give isl_union_set *isl_union_set_universe(
1070 __isl_take isl_union_set *uset);
1071 __isl_give isl_union_map *isl_union_map_universe(
1072 __isl_take isl_union_map *umap);
1074 The sets and relations constructed by the functions above
1075 contain all integer values, while those constructed by the
1076 functions below only contain non-negative values.
1078 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1079 __isl_take isl_space *space);
1080 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1081 __isl_take isl_space *space);
1082 __isl_give isl_set *isl_set_nat_universe(
1083 __isl_take isl_space *space);
1084 __isl_give isl_map *isl_map_nat_universe(
1085 __isl_take isl_space *space);
1087 =item * Identity relations
1089 __isl_give isl_basic_map *isl_basic_map_identity(
1090 __isl_take isl_space *space);
1091 __isl_give isl_map *isl_map_identity(
1092 __isl_take isl_space *space);
1094 The number of input and output dimensions in C<space> needs
1097 =item * Lexicographic order
1099 __isl_give isl_map *isl_map_lex_lt(
1100 __isl_take isl_space *set_space);
1101 __isl_give isl_map *isl_map_lex_le(
1102 __isl_take isl_space *set_space);
1103 __isl_give isl_map *isl_map_lex_gt(
1104 __isl_take isl_space *set_space);
1105 __isl_give isl_map *isl_map_lex_ge(
1106 __isl_take isl_space *set_space);
1107 __isl_give isl_map *isl_map_lex_lt_first(
1108 __isl_take isl_space *space, unsigned n);
1109 __isl_give isl_map *isl_map_lex_le_first(
1110 __isl_take isl_space *space, unsigned n);
1111 __isl_give isl_map *isl_map_lex_gt_first(
1112 __isl_take isl_space *space, unsigned n);
1113 __isl_give isl_map *isl_map_lex_ge_first(
1114 __isl_take isl_space *space, unsigned n);
1116 The first four functions take a space for a B<set>
1117 and return relations that express that the elements in the domain
1118 are lexicographically less
1119 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1120 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1121 than the elements in the range.
1122 The last four functions take a space for a map
1123 and return relations that express that the first C<n> dimensions
1124 in the domain are lexicographically less
1125 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1126 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1127 than the first C<n> dimensions in the range.
1131 A basic set or relation can be converted to a set or relation
1132 using the following functions.
1134 __isl_give isl_set *isl_set_from_basic_set(
1135 __isl_take isl_basic_set *bset);
1136 __isl_give isl_map *isl_map_from_basic_map(
1137 __isl_take isl_basic_map *bmap);
1139 Sets and relations can be converted to union sets and relations
1140 using the following functions.
1142 __isl_give isl_union_map *isl_union_map_from_map(
1143 __isl_take isl_map *map);
1144 __isl_give isl_union_set *isl_union_set_from_set(
1145 __isl_take isl_set *set);
1147 The inverse conversions below can only be used if the input
1148 union set or relation is known to contain elements in exactly one
1151 __isl_give isl_set *isl_set_from_union_set(
1152 __isl_take isl_union_set *uset);
1153 __isl_give isl_map *isl_map_from_union_map(
1154 __isl_take isl_union_map *umap);
1156 A zero-dimensional set can be constructed on a given parameter domain
1157 using the following function.
1159 __isl_give isl_set *isl_set_from_params(
1160 __isl_take isl_set *set);
1162 Sets and relations can be copied and freed again using the following
1165 __isl_give isl_basic_set *isl_basic_set_copy(
1166 __isl_keep isl_basic_set *bset);
1167 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1168 __isl_give isl_union_set *isl_union_set_copy(
1169 __isl_keep isl_union_set *uset);
1170 __isl_give isl_basic_map *isl_basic_map_copy(
1171 __isl_keep isl_basic_map *bmap);
1172 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1173 __isl_give isl_union_map *isl_union_map_copy(
1174 __isl_keep isl_union_map *umap);
1175 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1176 void isl_set_free(__isl_take isl_set *set);
1177 void *isl_union_set_free(__isl_take isl_union_set *uset);
1178 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1179 void isl_map_free(__isl_take isl_map *map);
1180 void *isl_union_map_free(__isl_take isl_union_map *umap);
1182 Other sets and relations can be constructed by starting
1183 from a universe set or relation, adding equality and/or
1184 inequality constraints and then projecting out the
1185 existentially quantified variables, if any.
1186 Constraints can be constructed, manipulated and
1187 added to (or removed from) (basic) sets and relations
1188 using the following functions.
1190 #include <isl/constraint.h>
1191 __isl_give isl_constraint *isl_equality_alloc(
1192 __isl_take isl_local_space *ls);
1193 __isl_give isl_constraint *isl_inequality_alloc(
1194 __isl_take isl_local_space *ls);
1195 __isl_give isl_constraint *isl_constraint_set_constant(
1196 __isl_take isl_constraint *constraint, isl_int v);
1197 __isl_give isl_constraint *isl_constraint_set_constant_si(
1198 __isl_take isl_constraint *constraint, int v);
1199 __isl_give isl_constraint *isl_constraint_set_coefficient(
1200 __isl_take isl_constraint *constraint,
1201 enum isl_dim_type type, int pos, isl_int v);
1202 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1203 __isl_take isl_constraint *constraint,
1204 enum isl_dim_type type, int pos, int v);
1205 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1206 __isl_take isl_basic_map *bmap,
1207 __isl_take isl_constraint *constraint);
1208 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1209 __isl_take isl_basic_set *bset,
1210 __isl_take isl_constraint *constraint);
1211 __isl_give isl_map *isl_map_add_constraint(
1212 __isl_take isl_map *map,
1213 __isl_take isl_constraint *constraint);
1214 __isl_give isl_set *isl_set_add_constraint(
1215 __isl_take isl_set *set,
1216 __isl_take isl_constraint *constraint);
1217 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1218 __isl_take isl_basic_set *bset,
1219 __isl_take isl_constraint *constraint);
1221 For example, to create a set containing the even integers
1222 between 10 and 42, you would use the following code.
1225 isl_local_space *ls;
1227 isl_basic_set *bset;
1229 space = isl_space_set_alloc(ctx, 0, 2);
1230 bset = isl_basic_set_universe(isl_space_copy(space));
1231 ls = isl_local_space_from_space(space);
1233 c = isl_equality_alloc(isl_local_space_copy(ls));
1234 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1235 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1236 bset = isl_basic_set_add_constraint(bset, c);
1238 c = isl_inequality_alloc(isl_local_space_copy(ls));
1239 c = isl_constraint_set_constant_si(c, -10);
1240 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1241 bset = isl_basic_set_add_constraint(bset, c);
1243 c = isl_inequality_alloc(ls);
1244 c = isl_constraint_set_constant_si(c, 42);
1245 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1246 bset = isl_basic_set_add_constraint(bset, c);
1248 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1252 isl_basic_set *bset;
1253 bset = isl_basic_set_read_from_str(ctx,
1254 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1256 A basic set or relation can also be constructed from two matrices
1257 describing the equalities and the inequalities.
1259 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1260 __isl_take isl_space *space,
1261 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1262 enum isl_dim_type c1,
1263 enum isl_dim_type c2, enum isl_dim_type c3,
1264 enum isl_dim_type c4);
1265 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1266 __isl_take isl_space *space,
1267 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1268 enum isl_dim_type c1,
1269 enum isl_dim_type c2, enum isl_dim_type c3,
1270 enum isl_dim_type c4, enum isl_dim_type c5);
1272 The C<isl_dim_type> arguments indicate the order in which
1273 different kinds of variables appear in the input matrices
1274 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1275 C<isl_dim_set> and C<isl_dim_div> for sets and
1276 of C<isl_dim_cst>, C<isl_dim_param>,
1277 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1279 A (basic) set or relation can also be constructed from a (piecewise)
1280 (multiple) affine expression
1281 or a list of affine expressions
1282 (See L<"Piecewise Quasi Affine Expressions"> and
1283 L<"Piecewise Multiple Quasi Affine Expressions">).
1285 __isl_give isl_basic_map *isl_basic_map_from_aff(
1286 __isl_take isl_aff *aff);
1287 __isl_give isl_set *isl_set_from_pw_aff(
1288 __isl_take isl_pw_aff *pwaff);
1289 __isl_give isl_map *isl_map_from_pw_aff(
1290 __isl_take isl_pw_aff *pwaff);
1291 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1292 __isl_take isl_space *domain_space,
1293 __isl_take isl_aff_list *list);
1294 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1295 __isl_take isl_multi_aff *maff)
1296 __isl_give isl_set *isl_set_from_pw_multi_aff(
1297 __isl_take isl_pw_multi_aff *pma);
1298 __isl_give isl_map *isl_map_from_pw_multi_aff(
1299 __isl_take isl_pw_multi_aff *pma);
1301 The C<domain_dim> argument describes the domain of the resulting
1302 basic relation. It is required because the C<list> may consist
1303 of zero affine expressions.
1305 =head2 Inspecting Sets and Relations
1307 Usually, the user should not have to care about the actual constraints
1308 of the sets and maps, but should instead apply the abstract operations
1309 explained in the following sections.
1310 Occasionally, however, it may be required to inspect the individual
1311 coefficients of the constraints. This section explains how to do so.
1312 In these cases, it may also be useful to have C<isl> compute
1313 an explicit representation of the existentially quantified variables.
1315 __isl_give isl_set *isl_set_compute_divs(
1316 __isl_take isl_set *set);
1317 __isl_give isl_map *isl_map_compute_divs(
1318 __isl_take isl_map *map);
1319 __isl_give isl_union_set *isl_union_set_compute_divs(
1320 __isl_take isl_union_set *uset);
1321 __isl_give isl_union_map *isl_union_map_compute_divs(
1322 __isl_take isl_union_map *umap);
1324 This explicit representation defines the existentially quantified
1325 variables as integer divisions of the other variables, possibly
1326 including earlier existentially quantified variables.
1327 An explicitly represented existentially quantified variable therefore
1328 has a unique value when the values of the other variables are known.
1329 If, furthermore, the same existentials, i.e., existentials
1330 with the same explicit representations, should appear in the
1331 same order in each of the disjuncts of a set or map, then the user should call
1332 either of the following functions.
1334 __isl_give isl_set *isl_set_align_divs(
1335 __isl_take isl_set *set);
1336 __isl_give isl_map *isl_map_align_divs(
1337 __isl_take isl_map *map);
1339 Alternatively, the existentially quantified variables can be removed
1340 using the following functions, which compute an overapproximation.
1342 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1343 __isl_take isl_basic_set *bset);
1344 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1345 __isl_take isl_basic_map *bmap);
1346 __isl_give isl_set *isl_set_remove_divs(
1347 __isl_take isl_set *set);
1348 __isl_give isl_map *isl_map_remove_divs(
1349 __isl_take isl_map *map);
1351 To iterate over all the sets or maps in a union set or map, use
1353 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1354 int (*fn)(__isl_take isl_set *set, void *user),
1356 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1357 int (*fn)(__isl_take isl_map *map, void *user),
1360 The number of sets or maps in a union set or map can be obtained
1363 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1364 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1366 To extract the set or map in a given space from a union, use
1368 __isl_give isl_set *isl_union_set_extract_set(
1369 __isl_keep isl_union_set *uset,
1370 __isl_take isl_space *space);
1371 __isl_give isl_map *isl_union_map_extract_map(
1372 __isl_keep isl_union_map *umap,
1373 __isl_take isl_space *space);
1375 To iterate over all the basic sets or maps in a set or map, use
1377 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1378 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1380 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1381 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1384 The callback function C<fn> should return 0 if successful and
1385 -1 if an error occurs. In the latter case, or if any other error
1386 occurs, the above functions will return -1.
1388 It should be noted that C<isl> does not guarantee that
1389 the basic sets or maps passed to C<fn> are disjoint.
1390 If this is required, then the user should call one of
1391 the following functions first.
1393 __isl_give isl_set *isl_set_make_disjoint(
1394 __isl_take isl_set *set);
1395 __isl_give isl_map *isl_map_make_disjoint(
1396 __isl_take isl_map *map);
1398 The number of basic sets in a set can be obtained
1401 int isl_set_n_basic_set(__isl_keep isl_set *set);
1403 To iterate over the constraints of a basic set or map, use
1405 #include <isl/constraint.h>
1407 int isl_basic_map_foreach_constraint(
1408 __isl_keep isl_basic_map *bmap,
1409 int (*fn)(__isl_take isl_constraint *c, void *user),
1411 void *isl_constraint_free(__isl_take isl_constraint *c);
1413 Again, the callback function C<fn> should return 0 if successful and
1414 -1 if an error occurs. In the latter case, or if any other error
1415 occurs, the above functions will return -1.
1416 The constraint C<c> represents either an equality or an inequality.
1417 Use the following function to find out whether a constraint
1418 represents an equality. If not, it represents an inequality.
1420 int isl_constraint_is_equality(
1421 __isl_keep isl_constraint *constraint);
1423 The coefficients of the constraints can be inspected using
1424 the following functions.
1426 void isl_constraint_get_constant(
1427 __isl_keep isl_constraint *constraint, isl_int *v);
1428 void isl_constraint_get_coefficient(
1429 __isl_keep isl_constraint *constraint,
1430 enum isl_dim_type type, int pos, isl_int *v);
1431 int isl_constraint_involves_dims(
1432 __isl_keep isl_constraint *constraint,
1433 enum isl_dim_type type, unsigned first, unsigned n);
1435 The explicit representations of the existentially quantified
1436 variables can be inspected using the following function.
1437 Note that the user is only allowed to use this function
1438 if the inspected set or map is the result of a call
1439 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1440 The existentially quantified variable is equal to the floor
1441 of the returned affine expression. The affine expression
1442 itself can be inspected using the functions in
1443 L<"Piecewise Quasi Affine Expressions">.
1445 __isl_give isl_aff *isl_constraint_get_div(
1446 __isl_keep isl_constraint *constraint, int pos);
1448 To obtain the constraints of a basic set or map in matrix
1449 form, use the following functions.
1451 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1452 __isl_keep isl_basic_set *bset,
1453 enum isl_dim_type c1, enum isl_dim_type c2,
1454 enum isl_dim_type c3, enum isl_dim_type c4);
1455 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1456 __isl_keep isl_basic_set *bset,
1457 enum isl_dim_type c1, enum isl_dim_type c2,
1458 enum isl_dim_type c3, enum isl_dim_type c4);
1459 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1460 __isl_keep isl_basic_map *bmap,
1461 enum isl_dim_type c1,
1462 enum isl_dim_type c2, enum isl_dim_type c3,
1463 enum isl_dim_type c4, enum isl_dim_type c5);
1464 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1465 __isl_keep isl_basic_map *bmap,
1466 enum isl_dim_type c1,
1467 enum isl_dim_type c2, enum isl_dim_type c3,
1468 enum isl_dim_type c4, enum isl_dim_type c5);
1470 The C<isl_dim_type> arguments dictate the order in which
1471 different kinds of variables appear in the resulting matrix
1472 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1473 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1475 The number of parameters, input, output or set dimensions can
1476 be obtained using the following functions.
1478 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1479 enum isl_dim_type type);
1480 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1481 enum isl_dim_type type);
1482 unsigned isl_set_dim(__isl_keep isl_set *set,
1483 enum isl_dim_type type);
1484 unsigned isl_map_dim(__isl_keep isl_map *map,
1485 enum isl_dim_type type);
1487 To check whether the description of a set or relation depends
1488 on one or more given dimensions, it is not necessary to iterate over all
1489 constraints. Instead the following functions can be used.
1491 int isl_basic_set_involves_dims(
1492 __isl_keep isl_basic_set *bset,
1493 enum isl_dim_type type, unsigned first, unsigned n);
1494 int isl_set_involves_dims(__isl_keep isl_set *set,
1495 enum isl_dim_type type, unsigned first, unsigned n);
1496 int isl_basic_map_involves_dims(
1497 __isl_keep isl_basic_map *bmap,
1498 enum isl_dim_type type, unsigned first, unsigned n);
1499 int isl_map_involves_dims(__isl_keep isl_map *map,
1500 enum isl_dim_type type, unsigned first, unsigned n);
1502 Similarly, the following functions can be used to check whether
1503 a given dimension is involved in any lower or upper bound.
1505 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1506 enum isl_dim_type type, unsigned pos);
1507 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1508 enum isl_dim_type type, unsigned pos);
1510 The identifiers or names of the domain and range spaces of a set
1511 or relation can be read off or set using the following functions.
1513 __isl_give isl_set *isl_set_set_tuple_id(
1514 __isl_take isl_set *set, __isl_take isl_id *id);
1515 __isl_give isl_set *isl_set_reset_tuple_id(
1516 __isl_take isl_set *set);
1517 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1518 __isl_give isl_id *isl_set_get_tuple_id(
1519 __isl_keep isl_set *set);
1520 __isl_give isl_map *isl_map_set_tuple_id(
1521 __isl_take isl_map *map, enum isl_dim_type type,
1522 __isl_take isl_id *id);
1523 __isl_give isl_map *isl_map_reset_tuple_id(
1524 __isl_take isl_map *map, enum isl_dim_type type);
1525 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1526 enum isl_dim_type type);
1527 __isl_give isl_id *isl_map_get_tuple_id(
1528 __isl_keep isl_map *map, enum isl_dim_type type);
1530 const char *isl_basic_set_get_tuple_name(
1531 __isl_keep isl_basic_set *bset);
1532 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1533 __isl_take isl_basic_set *set, const char *s);
1534 const char *isl_set_get_tuple_name(
1535 __isl_keep isl_set *set);
1536 const char *isl_basic_map_get_tuple_name(
1537 __isl_keep isl_basic_map *bmap,
1538 enum isl_dim_type type);
1539 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1540 __isl_take isl_basic_map *bmap,
1541 enum isl_dim_type type, const char *s);
1542 const char *isl_map_get_tuple_name(
1543 __isl_keep isl_map *map,
1544 enum isl_dim_type type);
1546 As with C<isl_space_get_tuple_name>, the value returned points to
1547 an internal data structure.
1548 The identifiers, positions or names of individual dimensions can be
1549 read off using the following functions.
1551 __isl_give isl_set *isl_set_set_dim_id(
1552 __isl_take isl_set *set, enum isl_dim_type type,
1553 unsigned pos, __isl_take isl_id *id);
1554 int isl_set_has_dim_id(__isl_keep isl_set *set,
1555 enum isl_dim_type type, unsigned pos);
1556 __isl_give isl_id *isl_set_get_dim_id(
1557 __isl_keep isl_set *set, enum isl_dim_type type,
1559 int isl_basic_map_has_dim_id(
1560 __isl_keep isl_basic_map *bmap,
1561 enum isl_dim_type type, unsigned pos);
1562 __isl_give isl_map *isl_map_set_dim_id(
1563 __isl_take isl_map *map, enum isl_dim_type type,
1564 unsigned pos, __isl_take isl_id *id);
1565 int isl_map_has_dim_id(__isl_keep isl_map *map,
1566 enum isl_dim_type type, unsigned pos);
1567 __isl_give isl_id *isl_map_get_dim_id(
1568 __isl_keep isl_map *map, enum isl_dim_type type,
1571 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1572 enum isl_dim_type type, __isl_keep isl_id *id);
1573 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1574 enum isl_dim_type type, __isl_keep isl_id *id);
1575 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1576 enum isl_dim_type type, const char *name);
1577 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1578 enum isl_dim_type type, const char *name);
1580 const char *isl_constraint_get_dim_name(
1581 __isl_keep isl_constraint *constraint,
1582 enum isl_dim_type type, unsigned pos);
1583 const char *isl_basic_set_get_dim_name(
1584 __isl_keep isl_basic_set *bset,
1585 enum isl_dim_type type, unsigned pos);
1586 int isl_set_has_dim_name(__isl_keep isl_set *set,
1587 enum isl_dim_type type, unsigned pos);
1588 const char *isl_set_get_dim_name(
1589 __isl_keep isl_set *set,
1590 enum isl_dim_type type, unsigned pos);
1591 const char *isl_basic_map_get_dim_name(
1592 __isl_keep isl_basic_map *bmap,
1593 enum isl_dim_type type, unsigned pos);
1594 const char *isl_map_get_dim_name(
1595 __isl_keep isl_map *map,
1596 enum isl_dim_type type, unsigned pos);
1598 These functions are mostly useful to obtain the identifiers, positions
1599 or names of the parameters. Identifiers of individual dimensions are
1600 essentially only useful for printing. They are ignored by all other
1601 operations and may not be preserved across those operations.
1605 =head3 Unary Properties
1611 The following functions test whether the given set or relation
1612 contains any integer points. The ``plain'' variants do not perform
1613 any computations, but simply check if the given set or relation
1614 is already known to be empty.
1616 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1617 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1618 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1619 int isl_set_is_empty(__isl_keep isl_set *set);
1620 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1621 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1622 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1623 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1624 int isl_map_is_empty(__isl_keep isl_map *map);
1625 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1627 =item * Universality
1629 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1630 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1631 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1633 =item * Single-valuedness
1635 int isl_map_plain_is_single_valued(
1636 __isl_keep isl_map *map);
1637 int isl_map_is_single_valued(__isl_keep isl_map *map);
1638 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1642 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1643 int isl_map_is_injective(__isl_keep isl_map *map);
1644 int isl_union_map_plain_is_injective(
1645 __isl_keep isl_union_map *umap);
1646 int isl_union_map_is_injective(
1647 __isl_keep isl_union_map *umap);
1651 int isl_map_is_bijective(__isl_keep isl_map *map);
1652 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1656 int isl_basic_map_plain_is_fixed(
1657 __isl_keep isl_basic_map *bmap,
1658 enum isl_dim_type type, unsigned pos,
1660 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1661 enum isl_dim_type type, unsigned pos,
1663 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1664 enum isl_dim_type type, unsigned pos,
1667 Check if the relation obviously lies on a hyperplane where the given dimension
1668 has a fixed value and if so, return that value in C<*val>.
1672 To check whether a set is a parameter domain, use this function:
1674 int isl_set_is_params(__isl_keep isl_set *set);
1675 int isl_union_set_is_params(
1676 __isl_keep isl_union_set *uset);
1680 The following functions check whether the domain of the given
1681 (basic) set is a wrapped relation.
1683 int isl_basic_set_is_wrapping(
1684 __isl_keep isl_basic_set *bset);
1685 int isl_set_is_wrapping(__isl_keep isl_set *set);
1687 =item * Internal Product
1689 int isl_basic_map_can_zip(
1690 __isl_keep isl_basic_map *bmap);
1691 int isl_map_can_zip(__isl_keep isl_map *map);
1693 Check whether the product of domain and range of the given relation
1695 i.e., whether both domain and range are nested relations.
1699 =head3 Binary Properties
1705 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1706 __isl_keep isl_set *set2);
1707 int isl_set_is_equal(__isl_keep isl_set *set1,
1708 __isl_keep isl_set *set2);
1709 int isl_union_set_is_equal(
1710 __isl_keep isl_union_set *uset1,
1711 __isl_keep isl_union_set *uset2);
1712 int isl_basic_map_is_equal(
1713 __isl_keep isl_basic_map *bmap1,
1714 __isl_keep isl_basic_map *bmap2);
1715 int isl_map_is_equal(__isl_keep isl_map *map1,
1716 __isl_keep isl_map *map2);
1717 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1718 __isl_keep isl_map *map2);
1719 int isl_union_map_is_equal(
1720 __isl_keep isl_union_map *umap1,
1721 __isl_keep isl_union_map *umap2);
1723 =item * Disjointness
1725 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1726 __isl_keep isl_set *set2);
1730 int isl_basic_set_is_subset(
1731 __isl_keep isl_basic_set *bset1,
1732 __isl_keep isl_basic_set *bset2);
1733 int isl_set_is_subset(__isl_keep isl_set *set1,
1734 __isl_keep isl_set *set2);
1735 int isl_set_is_strict_subset(
1736 __isl_keep isl_set *set1,
1737 __isl_keep isl_set *set2);
1738 int isl_union_set_is_subset(
1739 __isl_keep isl_union_set *uset1,
1740 __isl_keep isl_union_set *uset2);
1741 int isl_union_set_is_strict_subset(
1742 __isl_keep isl_union_set *uset1,
1743 __isl_keep isl_union_set *uset2);
1744 int isl_basic_map_is_subset(
1745 __isl_keep isl_basic_map *bmap1,
1746 __isl_keep isl_basic_map *bmap2);
1747 int isl_basic_map_is_strict_subset(
1748 __isl_keep isl_basic_map *bmap1,
1749 __isl_keep isl_basic_map *bmap2);
1750 int isl_map_is_subset(
1751 __isl_keep isl_map *map1,
1752 __isl_keep isl_map *map2);
1753 int isl_map_is_strict_subset(
1754 __isl_keep isl_map *map1,
1755 __isl_keep isl_map *map2);
1756 int isl_union_map_is_subset(
1757 __isl_keep isl_union_map *umap1,
1758 __isl_keep isl_union_map *umap2);
1759 int isl_union_map_is_strict_subset(
1760 __isl_keep isl_union_map *umap1,
1761 __isl_keep isl_union_map *umap2);
1765 =head2 Unary Operations
1771 __isl_give isl_set *isl_set_complement(
1772 __isl_take isl_set *set);
1773 __isl_give isl_map *isl_map_complement(
1774 __isl_take isl_map *map);
1778 __isl_give isl_basic_map *isl_basic_map_reverse(
1779 __isl_take isl_basic_map *bmap);
1780 __isl_give isl_map *isl_map_reverse(
1781 __isl_take isl_map *map);
1782 __isl_give isl_union_map *isl_union_map_reverse(
1783 __isl_take isl_union_map *umap);
1787 __isl_give isl_basic_set *isl_basic_set_project_out(
1788 __isl_take isl_basic_set *bset,
1789 enum isl_dim_type type, unsigned first, unsigned n);
1790 __isl_give isl_basic_map *isl_basic_map_project_out(
1791 __isl_take isl_basic_map *bmap,
1792 enum isl_dim_type type, unsigned first, unsigned n);
1793 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1794 enum isl_dim_type type, unsigned first, unsigned n);
1795 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1796 enum isl_dim_type type, unsigned first, unsigned n);
1797 __isl_give isl_basic_set *isl_basic_set_params(
1798 __isl_take isl_basic_set *bset);
1799 __isl_give isl_basic_set *isl_basic_map_domain(
1800 __isl_take isl_basic_map *bmap);
1801 __isl_give isl_basic_set *isl_basic_map_range(
1802 __isl_take isl_basic_map *bmap);
1803 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1804 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1805 __isl_give isl_set *isl_map_domain(
1806 __isl_take isl_map *bmap);
1807 __isl_give isl_set *isl_map_range(
1808 __isl_take isl_map *map);
1809 __isl_give isl_set *isl_union_set_params(
1810 __isl_take isl_union_set *uset);
1811 __isl_give isl_set *isl_union_map_params(
1812 __isl_take isl_union_map *umap);
1813 __isl_give isl_union_set *isl_union_map_domain(
1814 __isl_take isl_union_map *umap);
1815 __isl_give isl_union_set *isl_union_map_range(
1816 __isl_take isl_union_map *umap);
1818 __isl_give isl_basic_map *isl_basic_map_domain_map(
1819 __isl_take isl_basic_map *bmap);
1820 __isl_give isl_basic_map *isl_basic_map_range_map(
1821 __isl_take isl_basic_map *bmap);
1822 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1823 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1824 __isl_give isl_union_map *isl_union_map_domain_map(
1825 __isl_take isl_union_map *umap);
1826 __isl_give isl_union_map *isl_union_map_range_map(
1827 __isl_take isl_union_map *umap);
1829 The functions above construct a (basic, regular or union) relation
1830 that maps (a wrapped version of) the input relation to its domain or range.
1834 __isl_give isl_set *isl_set_eliminate(
1835 __isl_take isl_set *set, enum isl_dim_type type,
1836 unsigned first, unsigned n);
1837 __isl_give isl_basic_map *isl_basic_map_eliminate(
1838 __isl_take isl_basic_map *bmap,
1839 enum isl_dim_type type,
1840 unsigned first, unsigned n);
1841 __isl_give isl_map *isl_map_eliminate(
1842 __isl_take isl_map *map, enum isl_dim_type type,
1843 unsigned first, unsigned n);
1845 Eliminate the coefficients for the given dimensions from the constraints,
1846 without removing the dimensions.
1850 __isl_give isl_basic_set *isl_basic_set_fix(
1851 __isl_take isl_basic_set *bset,
1852 enum isl_dim_type type, unsigned pos,
1854 __isl_give isl_basic_set *isl_basic_set_fix_si(
1855 __isl_take isl_basic_set *bset,
1856 enum isl_dim_type type, unsigned pos, int value);
1857 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1858 enum isl_dim_type type, unsigned pos,
1860 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1861 enum isl_dim_type type, unsigned pos, int value);
1862 __isl_give isl_basic_map *isl_basic_map_fix_si(
1863 __isl_take isl_basic_map *bmap,
1864 enum isl_dim_type type, unsigned pos, int value);
1865 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1866 enum isl_dim_type type, unsigned pos, int value);
1868 Intersect the set or relation with the hyperplane where the given
1869 dimension has the fixed given value.
1871 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1872 __isl_take isl_basic_map *bmap,
1873 enum isl_dim_type type, unsigned pos, int value);
1874 __isl_give isl_set *isl_set_lower_bound(
1875 __isl_take isl_set *set,
1876 enum isl_dim_type type, unsigned pos,
1878 __isl_give isl_set *isl_set_lower_bound_si(
1879 __isl_take isl_set *set,
1880 enum isl_dim_type type, unsigned pos, int value);
1881 __isl_give isl_map *isl_map_lower_bound_si(
1882 __isl_take isl_map *map,
1883 enum isl_dim_type type, unsigned pos, int value);
1884 __isl_give isl_set *isl_set_upper_bound(
1885 __isl_take isl_set *set,
1886 enum isl_dim_type type, unsigned pos,
1888 __isl_give isl_set *isl_set_upper_bound_si(
1889 __isl_take isl_set *set,
1890 enum isl_dim_type type, unsigned pos, int value);
1891 __isl_give isl_map *isl_map_upper_bound_si(
1892 __isl_take isl_map *map,
1893 enum isl_dim_type type, unsigned pos, int value);
1895 Intersect the set or relation with the half-space where the given
1896 dimension has a value bounded by the fixed given value.
1898 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1899 enum isl_dim_type type1, int pos1,
1900 enum isl_dim_type type2, int pos2);
1901 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1902 enum isl_dim_type type1, int pos1,
1903 enum isl_dim_type type2, int pos2);
1905 Intersect the set or relation with the hyperplane where the given
1906 dimensions are equal to each other.
1908 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1909 enum isl_dim_type type1, int pos1,
1910 enum isl_dim_type type2, int pos2);
1912 Intersect the relation with the hyperplane where the given
1913 dimensions have opposite values.
1917 __isl_give isl_map *isl_set_identity(
1918 __isl_take isl_set *set);
1919 __isl_give isl_union_map *isl_union_set_identity(
1920 __isl_take isl_union_set *uset);
1922 Construct an identity relation on the given (union) set.
1926 __isl_give isl_basic_set *isl_basic_map_deltas(
1927 __isl_take isl_basic_map *bmap);
1928 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1929 __isl_give isl_union_set *isl_union_map_deltas(
1930 __isl_take isl_union_map *umap);
1932 These functions return a (basic) set containing the differences
1933 between image elements and corresponding domain elements in the input.
1935 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1936 __isl_take isl_basic_map *bmap);
1937 __isl_give isl_map *isl_map_deltas_map(
1938 __isl_take isl_map *map);
1939 __isl_give isl_union_map *isl_union_map_deltas_map(
1940 __isl_take isl_union_map *umap);
1942 The functions above construct a (basic, regular or union) relation
1943 that maps (a wrapped version of) the input relation to its delta set.
1947 Simplify the representation of a set or relation by trying
1948 to combine pairs of basic sets or relations into a single
1949 basic set or relation.
1951 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1952 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1953 __isl_give isl_union_set *isl_union_set_coalesce(
1954 __isl_take isl_union_set *uset);
1955 __isl_give isl_union_map *isl_union_map_coalesce(
1956 __isl_take isl_union_map *umap);
1958 One of the methods for combining pairs of basic sets or relations
1959 can result in coefficients that are much larger than those that appear
1960 in the constraints of the input. By default, the coefficients are
1961 not allowed to grow larger, but this can be changed by unsetting
1962 the following option.
1964 int isl_options_set_coalesce_bounded_wrapping(
1965 isl_ctx *ctx, int val);
1966 int isl_options_get_coalesce_bounded_wrapping(
1969 =item * Detecting equalities
1971 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1972 __isl_take isl_basic_set *bset);
1973 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1974 __isl_take isl_basic_map *bmap);
1975 __isl_give isl_set *isl_set_detect_equalities(
1976 __isl_take isl_set *set);
1977 __isl_give isl_map *isl_map_detect_equalities(
1978 __isl_take isl_map *map);
1979 __isl_give isl_union_set *isl_union_set_detect_equalities(
1980 __isl_take isl_union_set *uset);
1981 __isl_give isl_union_map *isl_union_map_detect_equalities(
1982 __isl_take isl_union_map *umap);
1984 Simplify the representation of a set or relation by detecting implicit
1987 =item * Removing redundant constraints
1989 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1990 __isl_take isl_basic_set *bset);
1991 __isl_give isl_set *isl_set_remove_redundancies(
1992 __isl_take isl_set *set);
1993 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1994 __isl_take isl_basic_map *bmap);
1995 __isl_give isl_map *isl_map_remove_redundancies(
1996 __isl_take isl_map *map);
2000 __isl_give isl_basic_set *isl_set_convex_hull(
2001 __isl_take isl_set *set);
2002 __isl_give isl_basic_map *isl_map_convex_hull(
2003 __isl_take isl_map *map);
2005 If the input set or relation has any existentially quantified
2006 variables, then the result of these operations is currently undefined.
2010 __isl_give isl_basic_set *isl_set_simple_hull(
2011 __isl_take isl_set *set);
2012 __isl_give isl_basic_map *isl_map_simple_hull(
2013 __isl_take isl_map *map);
2014 __isl_give isl_union_map *isl_union_map_simple_hull(
2015 __isl_take isl_union_map *umap);
2017 These functions compute a single basic set or relation
2018 that contains the whole input set or relation.
2019 In particular, the output is described by translates
2020 of the constraints describing the basic sets or relations in the input.
2024 (See \autoref{s:simple hull}.)
2030 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2031 __isl_take isl_basic_set *bset);
2032 __isl_give isl_basic_set *isl_set_affine_hull(
2033 __isl_take isl_set *set);
2034 __isl_give isl_union_set *isl_union_set_affine_hull(
2035 __isl_take isl_union_set *uset);
2036 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2037 __isl_take isl_basic_map *bmap);
2038 __isl_give isl_basic_map *isl_map_affine_hull(
2039 __isl_take isl_map *map);
2040 __isl_give isl_union_map *isl_union_map_affine_hull(
2041 __isl_take isl_union_map *umap);
2043 In case of union sets and relations, the affine hull is computed
2046 =item * Polyhedral hull
2048 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2049 __isl_take isl_set *set);
2050 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2051 __isl_take isl_map *map);
2052 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2053 __isl_take isl_union_set *uset);
2054 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2055 __isl_take isl_union_map *umap);
2057 These functions compute a single basic set or relation
2058 not involving any existentially quantified variables
2059 that contains the whole input set or relation.
2060 In case of union sets and relations, the polyhedral hull is computed
2065 __isl_give isl_basic_set *isl_basic_set_sample(
2066 __isl_take isl_basic_set *bset);
2067 __isl_give isl_basic_set *isl_set_sample(
2068 __isl_take isl_set *set);
2069 __isl_give isl_basic_map *isl_basic_map_sample(
2070 __isl_take isl_basic_map *bmap);
2071 __isl_give isl_basic_map *isl_map_sample(
2072 __isl_take isl_map *map);
2074 If the input (basic) set or relation is non-empty, then return
2075 a singleton subset of the input. Otherwise, return an empty set.
2077 =item * Optimization
2079 #include <isl/ilp.h>
2080 enum isl_lp_result isl_basic_set_max(
2081 __isl_keep isl_basic_set *bset,
2082 __isl_keep isl_aff *obj, isl_int *opt)
2083 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2084 __isl_keep isl_aff *obj, isl_int *opt);
2085 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2086 __isl_keep isl_aff *obj, isl_int *opt);
2088 Compute the minimum or maximum of the integer affine expression C<obj>
2089 over the points in C<set>, returning the result in C<opt>.
2090 The return value may be one of C<isl_lp_error>,
2091 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2093 =item * Parametric optimization
2095 __isl_give isl_pw_aff *isl_set_dim_min(
2096 __isl_take isl_set *set, int pos);
2097 __isl_give isl_pw_aff *isl_set_dim_max(
2098 __isl_take isl_set *set, int pos);
2099 __isl_give isl_pw_aff *isl_map_dim_max(
2100 __isl_take isl_map *map, int pos);
2102 Compute the minimum or maximum of the given set or output dimension
2103 as a function of the parameters (and input dimensions), but independently
2104 of the other set or output dimensions.
2105 For lexicographic optimization, see L<"Lexicographic Optimization">.
2109 The following functions compute either the set of (rational) coefficient
2110 values of valid constraints for the given set or the set of (rational)
2111 values satisfying the constraints with coefficients from the given set.
2112 Internally, these two sets of functions perform essentially the
2113 same operations, except that the set of coefficients is assumed to
2114 be a cone, while the set of values may be any polyhedron.
2115 The current implementation is based on the Farkas lemma and
2116 Fourier-Motzkin elimination, but this may change or be made optional
2117 in future. In particular, future implementations may use different
2118 dualization algorithms or skip the elimination step.
2120 __isl_give isl_basic_set *isl_basic_set_coefficients(
2121 __isl_take isl_basic_set *bset);
2122 __isl_give isl_basic_set *isl_set_coefficients(
2123 __isl_take isl_set *set);
2124 __isl_give isl_union_set *isl_union_set_coefficients(
2125 __isl_take isl_union_set *bset);
2126 __isl_give isl_basic_set *isl_basic_set_solutions(
2127 __isl_take isl_basic_set *bset);
2128 __isl_give isl_basic_set *isl_set_solutions(
2129 __isl_take isl_set *set);
2130 __isl_give isl_union_set *isl_union_set_solutions(
2131 __isl_take isl_union_set *bset);
2135 __isl_give isl_map *isl_map_fixed_power(
2136 __isl_take isl_map *map, isl_int exp);
2137 __isl_give isl_union_map *isl_union_map_fixed_power(
2138 __isl_take isl_union_map *umap, isl_int exp);
2140 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2141 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2142 of C<map> is computed.
2144 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2146 __isl_give isl_union_map *isl_union_map_power(
2147 __isl_take isl_union_map *umap, int *exact);
2149 Compute a parametric representation for all positive powers I<k> of C<map>.
2150 The result maps I<k> to a nested relation corresponding to the
2151 I<k>th power of C<map>.
2152 The result may be an overapproximation. If the result is known to be exact,
2153 then C<*exact> is set to C<1>.
2155 =item * Transitive closure
2157 __isl_give isl_map *isl_map_transitive_closure(
2158 __isl_take isl_map *map, int *exact);
2159 __isl_give isl_union_map *isl_union_map_transitive_closure(
2160 __isl_take isl_union_map *umap, int *exact);
2162 Compute the transitive closure of C<map>.
2163 The result may be an overapproximation. If the result is known to be exact,
2164 then C<*exact> is set to C<1>.
2166 =item * Reaching path lengths
2168 __isl_give isl_map *isl_map_reaching_path_lengths(
2169 __isl_take isl_map *map, int *exact);
2171 Compute a relation that maps each element in the range of C<map>
2172 to the lengths of all paths composed of edges in C<map> that
2173 end up in the given element.
2174 The result may be an overapproximation. If the result is known to be exact,
2175 then C<*exact> is set to C<1>.
2176 To compute the I<maximal> path length, the resulting relation
2177 should be postprocessed by C<isl_map_lexmax>.
2178 In particular, if the input relation is a dependence relation
2179 (mapping sources to sinks), then the maximal path length corresponds
2180 to the free schedule.
2181 Note, however, that C<isl_map_lexmax> expects the maximum to be
2182 finite, so if the path lengths are unbounded (possibly due to
2183 the overapproximation), then you will get an error message.
2187 __isl_give isl_basic_set *isl_basic_map_wrap(
2188 __isl_take isl_basic_map *bmap);
2189 __isl_give isl_set *isl_map_wrap(
2190 __isl_take isl_map *map);
2191 __isl_give isl_union_set *isl_union_map_wrap(
2192 __isl_take isl_union_map *umap);
2193 __isl_give isl_basic_map *isl_basic_set_unwrap(
2194 __isl_take isl_basic_set *bset);
2195 __isl_give isl_map *isl_set_unwrap(
2196 __isl_take isl_set *set);
2197 __isl_give isl_union_map *isl_union_set_unwrap(
2198 __isl_take isl_union_set *uset);
2202 Remove any internal structure of domain (and range) of the given
2203 set or relation. If there is any such internal structure in the input,
2204 then the name of the space is also removed.
2206 __isl_give isl_basic_set *isl_basic_set_flatten(
2207 __isl_take isl_basic_set *bset);
2208 __isl_give isl_set *isl_set_flatten(
2209 __isl_take isl_set *set);
2210 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2211 __isl_take isl_basic_map *bmap);
2212 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2213 __isl_take isl_basic_map *bmap);
2214 __isl_give isl_map *isl_map_flatten_range(
2215 __isl_take isl_map *map);
2216 __isl_give isl_map *isl_map_flatten_domain(
2217 __isl_take isl_map *map);
2218 __isl_give isl_basic_map *isl_basic_map_flatten(
2219 __isl_take isl_basic_map *bmap);
2220 __isl_give isl_map *isl_map_flatten(
2221 __isl_take isl_map *map);
2223 __isl_give isl_map *isl_set_flatten_map(
2224 __isl_take isl_set *set);
2226 The function above constructs a relation
2227 that maps the input set to a flattened version of the set.
2231 Lift the input set to a space with extra dimensions corresponding
2232 to the existentially quantified variables in the input.
2233 In particular, the result lives in a wrapped map where the domain
2234 is the original space and the range corresponds to the original
2235 existentially quantified variables.
2237 __isl_give isl_basic_set *isl_basic_set_lift(
2238 __isl_take isl_basic_set *bset);
2239 __isl_give isl_set *isl_set_lift(
2240 __isl_take isl_set *set);
2241 __isl_give isl_union_set *isl_union_set_lift(
2242 __isl_take isl_union_set *uset);
2244 Given a local space that contains the existentially quantified
2245 variables of a set, a basic relation that, when applied to
2246 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2247 can be constructed using the following function.
2249 #include <isl/local_space.h>
2250 __isl_give isl_basic_map *isl_local_space_lifting(
2251 __isl_take isl_local_space *ls);
2253 =item * Internal Product
2255 __isl_give isl_basic_map *isl_basic_map_zip(
2256 __isl_take isl_basic_map *bmap);
2257 __isl_give isl_map *isl_map_zip(
2258 __isl_take isl_map *map);
2259 __isl_give isl_union_map *isl_union_map_zip(
2260 __isl_take isl_union_map *umap);
2262 Given a relation with nested relations for domain and range,
2263 interchange the range of the domain with the domain of the range.
2265 =item * Aligning parameters
2267 __isl_give isl_set *isl_set_align_params(
2268 __isl_take isl_set *set,
2269 __isl_take isl_space *model);
2270 __isl_give isl_map *isl_map_align_params(
2271 __isl_take isl_map *map,
2272 __isl_take isl_space *model);
2274 Change the order of the parameters of the given set or relation
2275 such that the first parameters match those of C<model>.
2276 This may involve the introduction of extra parameters.
2277 All parameters need to be named.
2279 =item * Dimension manipulation
2281 __isl_give isl_set *isl_set_add_dims(
2282 __isl_take isl_set *set,
2283 enum isl_dim_type type, unsigned n);
2284 __isl_give isl_map *isl_map_add_dims(
2285 __isl_take isl_map *map,
2286 enum isl_dim_type type, unsigned n);
2287 __isl_give isl_set *isl_set_insert_dims(
2288 __isl_take isl_set *set,
2289 enum isl_dim_type type, unsigned pos, unsigned n);
2290 __isl_give isl_map *isl_map_insert_dims(
2291 __isl_take isl_map *map,
2292 enum isl_dim_type type, unsigned pos, unsigned n);
2293 __isl_give isl_basic_set *isl_basic_set_move_dims(
2294 __isl_take isl_basic_set *bset,
2295 enum isl_dim_type dst_type, unsigned dst_pos,
2296 enum isl_dim_type src_type, unsigned src_pos,
2298 __isl_give isl_basic_map *isl_basic_map_move_dims(
2299 __isl_take isl_basic_map *bmap,
2300 enum isl_dim_type dst_type, unsigned dst_pos,
2301 enum isl_dim_type src_type, unsigned src_pos,
2303 __isl_give isl_set *isl_set_move_dims(
2304 __isl_take isl_set *set,
2305 enum isl_dim_type dst_type, unsigned dst_pos,
2306 enum isl_dim_type src_type, unsigned src_pos,
2308 __isl_give isl_map *isl_map_move_dims(
2309 __isl_take isl_map *map,
2310 enum isl_dim_type dst_type, unsigned dst_pos,
2311 enum isl_dim_type src_type, unsigned src_pos,
2314 It is usually not advisable to directly change the (input or output)
2315 space of a set or a relation as this removes the name and the internal
2316 structure of the space. However, the above functions can be useful
2317 to add new parameters, assuming
2318 C<isl_set_align_params> and C<isl_map_align_params>
2323 =head2 Binary Operations
2325 The two arguments of a binary operation not only need to live
2326 in the same C<isl_ctx>, they currently also need to have
2327 the same (number of) parameters.
2329 =head3 Basic Operations
2333 =item * Intersection
2335 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2336 __isl_take isl_basic_set *bset1,
2337 __isl_take isl_basic_set *bset2);
2338 __isl_give isl_basic_set *isl_basic_set_intersect(
2339 __isl_take isl_basic_set *bset1,
2340 __isl_take isl_basic_set *bset2);
2341 __isl_give isl_set *isl_set_intersect_params(
2342 __isl_take isl_set *set,
2343 __isl_take isl_set *params);
2344 __isl_give isl_set *isl_set_intersect(
2345 __isl_take isl_set *set1,
2346 __isl_take isl_set *set2);
2347 __isl_give isl_union_set *isl_union_set_intersect_params(
2348 __isl_take isl_union_set *uset,
2349 __isl_take isl_set *set);
2350 __isl_give isl_union_map *isl_union_map_intersect_params(
2351 __isl_take isl_union_map *umap,
2352 __isl_take isl_set *set);
2353 __isl_give isl_union_set *isl_union_set_intersect(
2354 __isl_take isl_union_set *uset1,
2355 __isl_take isl_union_set *uset2);
2356 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2357 __isl_take isl_basic_map *bmap,
2358 __isl_take isl_basic_set *bset);
2359 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2360 __isl_take isl_basic_map *bmap,
2361 __isl_take isl_basic_set *bset);
2362 __isl_give isl_basic_map *isl_basic_map_intersect(
2363 __isl_take isl_basic_map *bmap1,
2364 __isl_take isl_basic_map *bmap2);
2365 __isl_give isl_map *isl_map_intersect_params(
2366 __isl_take isl_map *map,
2367 __isl_take isl_set *params);
2368 __isl_give isl_map *isl_map_intersect_domain(
2369 __isl_take isl_map *map,
2370 __isl_take isl_set *set);
2371 __isl_give isl_map *isl_map_intersect_range(
2372 __isl_take isl_map *map,
2373 __isl_take isl_set *set);
2374 __isl_give isl_map *isl_map_intersect(
2375 __isl_take isl_map *map1,
2376 __isl_take isl_map *map2);
2377 __isl_give isl_union_map *isl_union_map_intersect_domain(
2378 __isl_take isl_union_map *umap,
2379 __isl_take isl_union_set *uset);
2380 __isl_give isl_union_map *isl_union_map_intersect_range(
2381 __isl_take isl_union_map *umap,
2382 __isl_take isl_union_set *uset);
2383 __isl_give isl_union_map *isl_union_map_intersect(
2384 __isl_take isl_union_map *umap1,
2385 __isl_take isl_union_map *umap2);
2389 __isl_give isl_set *isl_basic_set_union(
2390 __isl_take isl_basic_set *bset1,
2391 __isl_take isl_basic_set *bset2);
2392 __isl_give isl_map *isl_basic_map_union(
2393 __isl_take isl_basic_map *bmap1,
2394 __isl_take isl_basic_map *bmap2);
2395 __isl_give isl_set *isl_set_union(
2396 __isl_take isl_set *set1,
2397 __isl_take isl_set *set2);
2398 __isl_give isl_map *isl_map_union(
2399 __isl_take isl_map *map1,
2400 __isl_take isl_map *map2);
2401 __isl_give isl_union_set *isl_union_set_union(
2402 __isl_take isl_union_set *uset1,
2403 __isl_take isl_union_set *uset2);
2404 __isl_give isl_union_map *isl_union_map_union(
2405 __isl_take isl_union_map *umap1,
2406 __isl_take isl_union_map *umap2);
2408 =item * Set difference
2410 __isl_give isl_set *isl_set_subtract(
2411 __isl_take isl_set *set1,
2412 __isl_take isl_set *set2);
2413 __isl_give isl_map *isl_map_subtract(
2414 __isl_take isl_map *map1,
2415 __isl_take isl_map *map2);
2416 __isl_give isl_map *isl_map_subtract_domain(
2417 __isl_take isl_map *map,
2418 __isl_take isl_set *dom);
2419 __isl_give isl_map *isl_map_subtract_range(
2420 __isl_take isl_map *map,
2421 __isl_take isl_set *dom);
2422 __isl_give isl_union_set *isl_union_set_subtract(
2423 __isl_take isl_union_set *uset1,
2424 __isl_take isl_union_set *uset2);
2425 __isl_give isl_union_map *isl_union_map_subtract(
2426 __isl_take isl_union_map *umap1,
2427 __isl_take isl_union_map *umap2);
2431 __isl_give isl_basic_set *isl_basic_set_apply(
2432 __isl_take isl_basic_set *bset,
2433 __isl_take isl_basic_map *bmap);
2434 __isl_give isl_set *isl_set_apply(
2435 __isl_take isl_set *set,
2436 __isl_take isl_map *map);
2437 __isl_give isl_union_set *isl_union_set_apply(
2438 __isl_take isl_union_set *uset,
2439 __isl_take isl_union_map *umap);
2440 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2441 __isl_take isl_basic_map *bmap1,
2442 __isl_take isl_basic_map *bmap2);
2443 __isl_give isl_basic_map *isl_basic_map_apply_range(
2444 __isl_take isl_basic_map *bmap1,
2445 __isl_take isl_basic_map *bmap2);
2446 __isl_give isl_map *isl_map_apply_domain(
2447 __isl_take isl_map *map1,
2448 __isl_take isl_map *map2);
2449 __isl_give isl_union_map *isl_union_map_apply_domain(
2450 __isl_take isl_union_map *umap1,
2451 __isl_take isl_union_map *umap2);
2452 __isl_give isl_map *isl_map_apply_range(
2453 __isl_take isl_map *map1,
2454 __isl_take isl_map *map2);
2455 __isl_give isl_union_map *isl_union_map_apply_range(
2456 __isl_take isl_union_map *umap1,
2457 __isl_take isl_union_map *umap2);
2459 =item * Cartesian Product
2461 __isl_give isl_set *isl_set_product(
2462 __isl_take isl_set *set1,
2463 __isl_take isl_set *set2);
2464 __isl_give isl_union_set *isl_union_set_product(
2465 __isl_take isl_union_set *uset1,
2466 __isl_take isl_union_set *uset2);
2467 __isl_give isl_basic_map *isl_basic_map_domain_product(
2468 __isl_take isl_basic_map *bmap1,
2469 __isl_take isl_basic_map *bmap2);
2470 __isl_give isl_basic_map *isl_basic_map_range_product(
2471 __isl_take isl_basic_map *bmap1,
2472 __isl_take isl_basic_map *bmap2);
2473 __isl_give isl_map *isl_map_domain_product(
2474 __isl_take isl_map *map1,
2475 __isl_take isl_map *map2);
2476 __isl_give isl_map *isl_map_range_product(
2477 __isl_take isl_map *map1,
2478 __isl_take isl_map *map2);
2479 __isl_give isl_union_map *isl_union_map_range_product(
2480 __isl_take isl_union_map *umap1,
2481 __isl_take isl_union_map *umap2);
2482 __isl_give isl_map *isl_map_product(
2483 __isl_take isl_map *map1,
2484 __isl_take isl_map *map2);
2485 __isl_give isl_union_map *isl_union_map_product(
2486 __isl_take isl_union_map *umap1,
2487 __isl_take isl_union_map *umap2);
2489 The above functions compute the cross product of the given
2490 sets or relations. The domains and ranges of the results
2491 are wrapped maps between domains and ranges of the inputs.
2492 To obtain a ``flat'' product, use the following functions
2495 __isl_give isl_basic_set *isl_basic_set_flat_product(
2496 __isl_take isl_basic_set *bset1,
2497 __isl_take isl_basic_set *bset2);
2498 __isl_give isl_set *isl_set_flat_product(
2499 __isl_take isl_set *set1,
2500 __isl_take isl_set *set2);
2501 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2502 __isl_take isl_basic_map *bmap1,
2503 __isl_take isl_basic_map *bmap2);
2504 __isl_give isl_map *isl_map_flat_domain_product(
2505 __isl_take isl_map *map1,
2506 __isl_take isl_map *map2);
2507 __isl_give isl_map *isl_map_flat_range_product(
2508 __isl_take isl_map *map1,
2509 __isl_take isl_map *map2);
2510 __isl_give isl_union_map *isl_union_map_flat_range_product(
2511 __isl_take isl_union_map *umap1,
2512 __isl_take isl_union_map *umap2);
2513 __isl_give isl_basic_map *isl_basic_map_flat_product(
2514 __isl_take isl_basic_map *bmap1,
2515 __isl_take isl_basic_map *bmap2);
2516 __isl_give isl_map *isl_map_flat_product(
2517 __isl_take isl_map *map1,
2518 __isl_take isl_map *map2);
2520 =item * Simplification
2522 __isl_give isl_basic_set *isl_basic_set_gist(
2523 __isl_take isl_basic_set *bset,
2524 __isl_take isl_basic_set *context);
2525 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2526 __isl_take isl_set *context);
2527 __isl_give isl_set *isl_set_gist_params(
2528 __isl_take isl_set *set,
2529 __isl_take isl_set *context);
2530 __isl_give isl_union_set *isl_union_set_gist(
2531 __isl_take isl_union_set *uset,
2532 __isl_take isl_union_set *context);
2533 __isl_give isl_union_set *isl_union_set_gist_params(
2534 __isl_take isl_union_set *uset,
2535 __isl_take isl_set *set);
2536 __isl_give isl_basic_map *isl_basic_map_gist(
2537 __isl_take isl_basic_map *bmap,
2538 __isl_take isl_basic_map *context);
2539 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2540 __isl_take isl_map *context);
2541 __isl_give isl_map *isl_map_gist_params(
2542 __isl_take isl_map *map,
2543 __isl_take isl_set *context);
2544 __isl_give isl_map *isl_map_gist_domain(
2545 __isl_take isl_map *map,
2546 __isl_take isl_set *context);
2547 __isl_give isl_map *isl_map_gist_range(
2548 __isl_take isl_map *map,
2549 __isl_take isl_set *context);
2550 __isl_give isl_union_map *isl_union_map_gist(
2551 __isl_take isl_union_map *umap,
2552 __isl_take isl_union_map *context);
2553 __isl_give isl_union_map *isl_union_map_gist_params(
2554 __isl_take isl_union_map *umap,
2555 __isl_take isl_set *set);
2556 __isl_give isl_union_map *isl_union_map_gist_domain(
2557 __isl_take isl_union_map *umap,
2558 __isl_take isl_union_set *uset);
2559 __isl_give isl_union_map *isl_union_map_gist_range(
2560 __isl_take isl_union_map *umap,
2561 __isl_take isl_union_set *uset);
2563 The gist operation returns a set or relation that has the
2564 same intersection with the context as the input set or relation.
2565 Any implicit equality in the intersection is made explicit in the result,
2566 while all inequalities that are redundant with respect to the intersection
2568 In case of union sets and relations, the gist operation is performed
2573 =head3 Lexicographic Optimization
2575 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2576 the following functions
2577 compute a set that contains the lexicographic minimum or maximum
2578 of the elements in C<set> (or C<bset>) for those values of the parameters
2579 that satisfy C<dom>.
2580 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2581 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2583 In other words, the union of the parameter values
2584 for which the result is non-empty and of C<*empty>
2587 __isl_give isl_set *isl_basic_set_partial_lexmin(
2588 __isl_take isl_basic_set *bset,
2589 __isl_take isl_basic_set *dom,
2590 __isl_give isl_set **empty);
2591 __isl_give isl_set *isl_basic_set_partial_lexmax(
2592 __isl_take isl_basic_set *bset,
2593 __isl_take isl_basic_set *dom,
2594 __isl_give isl_set **empty);
2595 __isl_give isl_set *isl_set_partial_lexmin(
2596 __isl_take isl_set *set, __isl_take isl_set *dom,
2597 __isl_give isl_set **empty);
2598 __isl_give isl_set *isl_set_partial_lexmax(
2599 __isl_take isl_set *set, __isl_take isl_set *dom,
2600 __isl_give isl_set **empty);
2602 Given a (basic) set C<set> (or C<bset>), the following functions simply
2603 return a set containing the lexicographic minimum or maximum
2604 of the elements in C<set> (or C<bset>).
2605 In case of union sets, the optimum is computed per space.
2607 __isl_give isl_set *isl_basic_set_lexmin(
2608 __isl_take isl_basic_set *bset);
2609 __isl_give isl_set *isl_basic_set_lexmax(
2610 __isl_take isl_basic_set *bset);
2611 __isl_give isl_set *isl_set_lexmin(
2612 __isl_take isl_set *set);
2613 __isl_give isl_set *isl_set_lexmax(
2614 __isl_take isl_set *set);
2615 __isl_give isl_union_set *isl_union_set_lexmin(
2616 __isl_take isl_union_set *uset);
2617 __isl_give isl_union_set *isl_union_set_lexmax(
2618 __isl_take isl_union_set *uset);
2620 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2621 the following functions
2622 compute a relation that maps each element of C<dom>
2623 to the single lexicographic minimum or maximum
2624 of the elements that are associated to that same
2625 element in C<map> (or C<bmap>).
2626 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2627 that contains the elements in C<dom> that do not map
2628 to any elements in C<map> (or C<bmap>).
2629 In other words, the union of the domain of the result and of C<*empty>
2632 __isl_give isl_map *isl_basic_map_partial_lexmax(
2633 __isl_take isl_basic_map *bmap,
2634 __isl_take isl_basic_set *dom,
2635 __isl_give isl_set **empty);
2636 __isl_give isl_map *isl_basic_map_partial_lexmin(
2637 __isl_take isl_basic_map *bmap,
2638 __isl_take isl_basic_set *dom,
2639 __isl_give isl_set **empty);
2640 __isl_give isl_map *isl_map_partial_lexmax(
2641 __isl_take isl_map *map, __isl_take isl_set *dom,
2642 __isl_give isl_set **empty);
2643 __isl_give isl_map *isl_map_partial_lexmin(
2644 __isl_take isl_map *map, __isl_take isl_set *dom,
2645 __isl_give isl_set **empty);
2647 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2648 return a map mapping each element in the domain of
2649 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2650 of all elements associated to that element.
2651 In case of union relations, the optimum is computed per space.
2653 __isl_give isl_map *isl_basic_map_lexmin(
2654 __isl_take isl_basic_map *bmap);
2655 __isl_give isl_map *isl_basic_map_lexmax(
2656 __isl_take isl_basic_map *bmap);
2657 __isl_give isl_map *isl_map_lexmin(
2658 __isl_take isl_map *map);
2659 __isl_give isl_map *isl_map_lexmax(
2660 __isl_take isl_map *map);
2661 __isl_give isl_union_map *isl_union_map_lexmin(
2662 __isl_take isl_union_map *umap);
2663 __isl_give isl_union_map *isl_union_map_lexmax(
2664 __isl_take isl_union_map *umap);
2666 The following functions return their result in the form of
2667 a piecewise multi-affine expression
2668 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2669 but are otherwise equivalent to the corresponding functions
2670 returning a basic set or relation.
2672 __isl_give isl_pw_multi_aff *
2673 isl_basic_map_lexmin_pw_multi_aff(
2674 __isl_take isl_basic_map *bmap);
2675 __isl_give isl_pw_multi_aff *
2676 isl_basic_set_partial_lexmin_pw_multi_aff(
2677 __isl_take isl_basic_set *bset,
2678 __isl_take isl_basic_set *dom,
2679 __isl_give isl_set **empty);
2680 __isl_give isl_pw_multi_aff *
2681 isl_basic_set_partial_lexmax_pw_multi_aff(
2682 __isl_take isl_basic_set *bset,
2683 __isl_take isl_basic_set *dom,
2684 __isl_give isl_set **empty);
2685 __isl_give isl_pw_multi_aff *
2686 isl_basic_map_partial_lexmin_pw_multi_aff(
2687 __isl_take isl_basic_map *bmap,
2688 __isl_take isl_basic_set *dom,
2689 __isl_give isl_set **empty);
2690 __isl_give isl_pw_multi_aff *
2691 isl_basic_map_partial_lexmax_pw_multi_aff(
2692 __isl_take isl_basic_map *bmap,
2693 __isl_take isl_basic_set *dom,
2694 __isl_give isl_set **empty);
2698 Lists are defined over several element types, including
2699 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2700 Here we take lists of C<isl_set>s as an example.
2701 Lists can be created, copied and freed using the following functions.
2703 #include <isl/list.h>
2704 __isl_give isl_set_list *isl_set_list_from_set(
2705 __isl_take isl_set *el);
2706 __isl_give isl_set_list *isl_set_list_alloc(
2707 isl_ctx *ctx, int n);
2708 __isl_give isl_set_list *isl_set_list_copy(
2709 __isl_keep isl_set_list *list);
2710 __isl_give isl_set_list *isl_set_list_add(
2711 __isl_take isl_set_list *list,
2712 __isl_take isl_set *el);
2713 __isl_give isl_set_list *isl_set_list_concat(
2714 __isl_take isl_set_list *list1,
2715 __isl_take isl_set_list *list2);
2716 void *isl_set_list_free(__isl_take isl_set_list *list);
2718 C<isl_set_list_alloc> creates an empty list with a capacity for
2719 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2722 Lists can be inspected using the following functions.
2724 #include <isl/list.h>
2725 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2726 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2727 __isl_give isl_set *isl_set_list_get_set(
2728 __isl_keep isl_set_list *list, int index);
2729 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2730 int (*fn)(__isl_take isl_set *el, void *user),
2733 Lists can be printed using
2735 #include <isl/list.h>
2736 __isl_give isl_printer *isl_printer_print_set_list(
2737 __isl_take isl_printer *p,
2738 __isl_keep isl_set_list *list);
2742 Matrices can be created, copied and freed using the following functions.
2744 #include <isl/mat.h>
2745 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2746 unsigned n_row, unsigned n_col);
2747 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2748 void isl_mat_free(__isl_take isl_mat *mat);
2750 Note that the elements of a newly created matrix may have arbitrary values.
2751 The elements can be changed and inspected using the following functions.
2753 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2754 int isl_mat_rows(__isl_keep isl_mat *mat);
2755 int isl_mat_cols(__isl_keep isl_mat *mat);
2756 int isl_mat_get_element(__isl_keep isl_mat *mat,
2757 int row, int col, isl_int *v);
2758 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2759 int row, int col, isl_int v);
2760 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2761 int row, int col, int v);
2763 C<isl_mat_get_element> will return a negative value if anything went wrong.
2764 In that case, the value of C<*v> is undefined.
2766 The following function can be used to compute the (right) inverse
2767 of a matrix, i.e., a matrix such that the product of the original
2768 and the inverse (in that order) is a multiple of the identity matrix.
2769 The input matrix is assumed to be of full row-rank.
2771 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2773 The following function can be used to compute the (right) kernel
2774 (or null space) of a matrix, i.e., a matrix such that the product of
2775 the original and the kernel (in that order) is the zero matrix.
2777 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2779 =head2 Piecewise Quasi Affine Expressions
2781 The zero quasi affine expression on a given domain can be created using
2783 __isl_give isl_aff *isl_aff_zero_on_domain(
2784 __isl_take isl_local_space *ls);
2786 Note that the space in which the resulting object lives is a map space
2787 with the given space as domain and a one-dimensional range.
2789 An empty piecewise quasi affine expression (one with no cells)
2790 or a piecewise quasi affine expression with a single cell can
2791 be created using the following functions.
2793 #include <isl/aff.h>
2794 __isl_give isl_pw_aff *isl_pw_aff_empty(
2795 __isl_take isl_space *space);
2796 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2797 __isl_take isl_set *set, __isl_take isl_aff *aff);
2798 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2799 __isl_take isl_aff *aff);
2801 A piecewise quasi affine expression that is equal to 1 on a set
2802 and 0 outside the set can be created using the following function.
2804 #include <isl/aff.h>
2805 __isl_give isl_pw_aff *isl_set_indicator_function(
2806 __isl_take isl_set *set);
2808 Quasi affine expressions can be copied and freed using
2810 #include <isl/aff.h>
2811 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2812 void *isl_aff_free(__isl_take isl_aff *aff);
2814 __isl_give isl_pw_aff *isl_pw_aff_copy(
2815 __isl_keep isl_pw_aff *pwaff);
2816 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2818 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2819 using the following function. The constraint is required to have
2820 a non-zero coefficient for the specified dimension.
2822 #include <isl/constraint.h>
2823 __isl_give isl_aff *isl_constraint_get_bound(
2824 __isl_keep isl_constraint *constraint,
2825 enum isl_dim_type type, int pos);
2827 The entire affine expression of the constraint can also be extracted
2828 using the following function.
2830 #include <isl/constraint.h>
2831 __isl_give isl_aff *isl_constraint_get_aff(
2832 __isl_keep isl_constraint *constraint);
2834 Conversely, an equality constraint equating
2835 the affine expression to zero or an inequality constraint enforcing
2836 the affine expression to be non-negative, can be constructed using
2838 __isl_give isl_constraint *isl_equality_from_aff(
2839 __isl_take isl_aff *aff);
2840 __isl_give isl_constraint *isl_inequality_from_aff(
2841 __isl_take isl_aff *aff);
2843 The expression can be inspected using
2845 #include <isl/aff.h>
2846 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2847 int isl_aff_dim(__isl_keep isl_aff *aff,
2848 enum isl_dim_type type);
2849 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2850 __isl_keep isl_aff *aff);
2851 __isl_give isl_local_space *isl_aff_get_local_space(
2852 __isl_keep isl_aff *aff);
2853 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2854 enum isl_dim_type type, unsigned pos);
2855 const char *isl_pw_aff_get_dim_name(
2856 __isl_keep isl_pw_aff *pa,
2857 enum isl_dim_type type, unsigned pos);
2858 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2859 enum isl_dim_type type, unsigned pos);
2860 __isl_give isl_id *isl_pw_aff_get_dim_id(
2861 __isl_keep isl_pw_aff *pa,
2862 enum isl_dim_type type, unsigned pos);
2863 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2865 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2866 enum isl_dim_type type, int pos, isl_int *v);
2867 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2869 __isl_give isl_aff *isl_aff_get_div(
2870 __isl_keep isl_aff *aff, int pos);
2872 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2873 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2874 int (*fn)(__isl_take isl_set *set,
2875 __isl_take isl_aff *aff,
2876 void *user), void *user);
2878 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2879 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2881 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2882 enum isl_dim_type type, unsigned first, unsigned n);
2883 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2884 enum isl_dim_type type, unsigned first, unsigned n);
2886 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2887 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2888 enum isl_dim_type type);
2889 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2891 It can be modified using
2893 #include <isl/aff.h>
2894 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2895 __isl_take isl_pw_aff *pwaff,
2896 enum isl_dim_type type, __isl_take isl_id *id);
2897 __isl_give isl_aff *isl_aff_set_dim_name(
2898 __isl_take isl_aff *aff, enum isl_dim_type type,
2899 unsigned pos, const char *s);
2900 __isl_give isl_aff *isl_aff_set_dim_id(
2901 __isl_take isl_aff *aff, enum isl_dim_type type,
2902 unsigned pos, __isl_take isl_id *id);
2903 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2904 __isl_take isl_pw_aff *pma,
2905 enum isl_dim_type type, unsigned pos,
2906 __isl_take isl_id *id);
2907 __isl_give isl_aff *isl_aff_set_constant(
2908 __isl_take isl_aff *aff, isl_int v);
2909 __isl_give isl_aff *isl_aff_set_constant_si(
2910 __isl_take isl_aff *aff, int v);
2911 __isl_give isl_aff *isl_aff_set_coefficient(
2912 __isl_take isl_aff *aff,
2913 enum isl_dim_type type, int pos, isl_int v);
2914 __isl_give isl_aff *isl_aff_set_coefficient_si(
2915 __isl_take isl_aff *aff,
2916 enum isl_dim_type type, int pos, int v);
2917 __isl_give isl_aff *isl_aff_set_denominator(
2918 __isl_take isl_aff *aff, isl_int v);
2920 __isl_give isl_aff *isl_aff_add_constant(
2921 __isl_take isl_aff *aff, isl_int v);
2922 __isl_give isl_aff *isl_aff_add_constant_si(
2923 __isl_take isl_aff *aff, int v);
2924 __isl_give isl_aff *isl_aff_add_coefficient(
2925 __isl_take isl_aff *aff,
2926 enum isl_dim_type type, int pos, isl_int v);
2927 __isl_give isl_aff *isl_aff_add_coefficient_si(
2928 __isl_take isl_aff *aff,
2929 enum isl_dim_type type, int pos, int v);
2931 __isl_give isl_aff *isl_aff_insert_dims(
2932 __isl_take isl_aff *aff,
2933 enum isl_dim_type type, unsigned first, unsigned n);
2934 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
2935 __isl_take isl_pw_aff *pwaff,
2936 enum isl_dim_type type, unsigned first, unsigned n);
2937 __isl_give isl_aff *isl_aff_add_dims(
2938 __isl_take isl_aff *aff,
2939 enum isl_dim_type type, unsigned n);
2940 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
2941 __isl_take isl_pw_aff *pwaff,
2942 enum isl_dim_type type, unsigned n);
2943 __isl_give isl_aff *isl_aff_drop_dims(
2944 __isl_take isl_aff *aff,
2945 enum isl_dim_type type, unsigned first, unsigned n);
2946 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
2947 __isl_take isl_pw_aff *pwaff,
2948 enum isl_dim_type type, unsigned first, unsigned n);
2950 Note that the C<set_constant> and C<set_coefficient> functions
2951 set the I<numerator> of the constant or coefficient, while
2952 C<add_constant> and C<add_coefficient> add an integer value to
2953 the possibly rational constant or coefficient.
2955 To check whether an affine expressions is obviously zero
2956 or obviously equal to some other affine expression, use
2958 #include <isl/aff.h>
2959 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
2960 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
2961 __isl_keep isl_aff *aff2);
2962 int isl_pw_aff_plain_is_equal(
2963 __isl_keep isl_pw_aff *pwaff1,
2964 __isl_keep isl_pw_aff *pwaff2);
2968 #include <isl/aff.h>
2969 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
2970 __isl_take isl_aff *aff2);
2971 __isl_give isl_pw_aff *isl_pw_aff_add(
2972 __isl_take isl_pw_aff *pwaff1,
2973 __isl_take isl_pw_aff *pwaff2);
2974 __isl_give isl_pw_aff *isl_pw_aff_min(
2975 __isl_take isl_pw_aff *pwaff1,
2976 __isl_take isl_pw_aff *pwaff2);
2977 __isl_give isl_pw_aff *isl_pw_aff_max(
2978 __isl_take isl_pw_aff *pwaff1,
2979 __isl_take isl_pw_aff *pwaff2);
2980 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
2981 __isl_take isl_aff *aff2);
2982 __isl_give isl_pw_aff *isl_pw_aff_sub(
2983 __isl_take isl_pw_aff *pwaff1,
2984 __isl_take isl_pw_aff *pwaff2);
2985 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
2986 __isl_give isl_pw_aff *isl_pw_aff_neg(
2987 __isl_take isl_pw_aff *pwaff);
2988 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
2989 __isl_give isl_pw_aff *isl_pw_aff_ceil(
2990 __isl_take isl_pw_aff *pwaff);
2991 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
2992 __isl_give isl_pw_aff *isl_pw_aff_floor(
2993 __isl_take isl_pw_aff *pwaff);
2994 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
2996 __isl_give isl_pw_aff *isl_pw_aff_mod(
2997 __isl_take isl_pw_aff *pwaff, isl_int mod);
2998 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3000 __isl_give isl_pw_aff *isl_pw_aff_scale(
3001 __isl_take isl_pw_aff *pwaff, isl_int f);
3002 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3004 __isl_give isl_aff *isl_aff_scale_down_ui(
3005 __isl_take isl_aff *aff, unsigned f);
3006 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3007 __isl_take isl_pw_aff *pwaff, isl_int f);
3009 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3010 __isl_take isl_pw_aff_list *list);
3011 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3012 __isl_take isl_pw_aff_list *list);
3014 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3015 __isl_take isl_pw_aff *pwqp);
3017 __isl_give isl_aff *isl_aff_align_params(
3018 __isl_take isl_aff *aff,
3019 __isl_take isl_space *model);
3020 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3021 __isl_take isl_pw_aff *pwaff,
3022 __isl_take isl_space *model);
3024 __isl_give isl_aff *isl_aff_project_domain_on_params(
3025 __isl_take isl_aff *aff);
3027 __isl_give isl_aff *isl_aff_gist_params(
3028 __isl_take isl_aff *aff,
3029 __isl_take isl_set *context);
3030 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3031 __isl_take isl_set *context);
3032 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3033 __isl_take isl_pw_aff *pwaff,
3034 __isl_take isl_set *context);
3035 __isl_give isl_pw_aff *isl_pw_aff_gist(
3036 __isl_take isl_pw_aff *pwaff,
3037 __isl_take isl_set *context);
3039 __isl_give isl_set *isl_pw_aff_domain(
3040 __isl_take isl_pw_aff *pwaff);
3041 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3042 __isl_take isl_pw_aff *pa,
3043 __isl_take isl_set *set);
3044 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3045 __isl_take isl_pw_aff *pa,
3046 __isl_take isl_set *set);
3048 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3049 __isl_take isl_aff *aff2);
3050 __isl_give isl_pw_aff *isl_pw_aff_mul(
3051 __isl_take isl_pw_aff *pwaff1,
3052 __isl_take isl_pw_aff *pwaff2);
3054 When multiplying two affine expressions, at least one of the two needs
3057 #include <isl/aff.h>
3058 __isl_give isl_basic_set *isl_aff_le_basic_set(
3059 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3060 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3061 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3062 __isl_give isl_set *isl_pw_aff_eq_set(
3063 __isl_take isl_pw_aff *pwaff1,
3064 __isl_take isl_pw_aff *pwaff2);
3065 __isl_give isl_set *isl_pw_aff_ne_set(
3066 __isl_take isl_pw_aff *pwaff1,
3067 __isl_take isl_pw_aff *pwaff2);
3068 __isl_give isl_set *isl_pw_aff_le_set(
3069 __isl_take isl_pw_aff *pwaff1,
3070 __isl_take isl_pw_aff *pwaff2);
3071 __isl_give isl_set *isl_pw_aff_lt_set(
3072 __isl_take isl_pw_aff *pwaff1,
3073 __isl_take isl_pw_aff *pwaff2);
3074 __isl_give isl_set *isl_pw_aff_ge_set(
3075 __isl_take isl_pw_aff *pwaff1,
3076 __isl_take isl_pw_aff *pwaff2);
3077 __isl_give isl_set *isl_pw_aff_gt_set(
3078 __isl_take isl_pw_aff *pwaff1,
3079 __isl_take isl_pw_aff *pwaff2);
3081 __isl_give isl_set *isl_pw_aff_list_eq_set(
3082 __isl_take isl_pw_aff_list *list1,
3083 __isl_take isl_pw_aff_list *list2);
3084 __isl_give isl_set *isl_pw_aff_list_ne_set(
3085 __isl_take isl_pw_aff_list *list1,
3086 __isl_take isl_pw_aff_list *list2);
3087 __isl_give isl_set *isl_pw_aff_list_le_set(
3088 __isl_take isl_pw_aff_list *list1,
3089 __isl_take isl_pw_aff_list *list2);
3090 __isl_give isl_set *isl_pw_aff_list_lt_set(
3091 __isl_take isl_pw_aff_list *list1,
3092 __isl_take isl_pw_aff_list *list2);
3093 __isl_give isl_set *isl_pw_aff_list_ge_set(
3094 __isl_take isl_pw_aff_list *list1,
3095 __isl_take isl_pw_aff_list *list2);
3096 __isl_give isl_set *isl_pw_aff_list_gt_set(
3097 __isl_take isl_pw_aff_list *list1,
3098 __isl_take isl_pw_aff_list *list2);
3100 The function C<isl_aff_ge_basic_set> returns a basic set
3101 containing those elements in the shared space
3102 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3103 The function C<isl_aff_ge_set> returns a set
3104 containing those elements in the shared domain
3105 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3106 The functions operating on C<isl_pw_aff_list> apply the corresponding
3107 C<isl_pw_aff> function to each pair of elements in the two lists.
3109 #include <isl/aff.h>
3110 __isl_give isl_set *isl_pw_aff_nonneg_set(
3111 __isl_take isl_pw_aff *pwaff);
3112 __isl_give isl_set *isl_pw_aff_zero_set(
3113 __isl_take isl_pw_aff *pwaff);
3114 __isl_give isl_set *isl_pw_aff_non_zero_set(
3115 __isl_take isl_pw_aff *pwaff);
3117 The function C<isl_pw_aff_nonneg_set> returns a set
3118 containing those elements in the domain
3119 of C<pwaff> where C<pwaff> is non-negative.
3121 #include <isl/aff.h>
3122 __isl_give isl_pw_aff *isl_pw_aff_cond(
3123 __isl_take isl_pw_aff *cond,
3124 __isl_take isl_pw_aff *pwaff_true,
3125 __isl_take isl_pw_aff *pwaff_false);
3127 The function C<isl_pw_aff_cond> performs a conditional operator
3128 and returns an expression that is equal to C<pwaff_true>
3129 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3130 where C<cond> is zero.
3132 #include <isl/aff.h>
3133 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3134 __isl_take isl_pw_aff *pwaff1,
3135 __isl_take isl_pw_aff *pwaff2);
3136 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3137 __isl_take isl_pw_aff *pwaff1,
3138 __isl_take isl_pw_aff *pwaff2);
3139 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3140 __isl_take isl_pw_aff *pwaff1,
3141 __isl_take isl_pw_aff *pwaff2);
3143 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3144 expression with a domain that is the union of those of C<pwaff1> and
3145 C<pwaff2> and such that on each cell, the quasi-affine expression is
3146 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3147 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3148 associated expression is the defined one.
3150 An expression can be read from input using
3152 #include <isl/aff.h>
3153 __isl_give isl_aff *isl_aff_read_from_str(
3154 isl_ctx *ctx, const char *str);
3155 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3156 isl_ctx *ctx, const char *str);
3158 An expression can be printed using
3160 #include <isl/aff.h>
3161 __isl_give isl_printer *isl_printer_print_aff(
3162 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3164 __isl_give isl_printer *isl_printer_print_pw_aff(
3165 __isl_take isl_printer *p,
3166 __isl_keep isl_pw_aff *pwaff);
3168 =head2 Piecewise Multiple Quasi Affine Expressions
3170 An C<isl_multi_aff> object represents a sequence of
3171 zero or more affine expressions, all defined on the same domain space.
3173 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3176 #include <isl/aff.h>
3177 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3178 __isl_take isl_space *space,
3179 __isl_take isl_aff_list *list);
3181 An empty piecewise multiple quasi affine expression (one with no cells) or
3182 a piecewise multiple quasi affine expression with a single cell can
3183 be created using the following functions.
3185 #include <isl/aff.h>
3186 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3187 __isl_take isl_space *space);
3188 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3189 __isl_take isl_set *set,
3190 __isl_take isl_multi_aff *maff);
3192 A piecewise multiple quasi affine expression can also be initialized
3193 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3194 and the C<isl_map> is single-valued.
3196 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3197 __isl_take isl_set *set);
3198 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3199 __isl_take isl_map *map);
3201 Multiple quasi affine expressions can be copied and freed using
3203 #include <isl/aff.h>
3204 __isl_give isl_multi_aff *isl_multi_aff_copy(
3205 __isl_keep isl_multi_aff *maff);
3206 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3208 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3209 __isl_keep isl_pw_multi_aff *pma);
3210 void *isl_pw_multi_aff_free(
3211 __isl_take isl_pw_multi_aff *pma);
3213 The expression can be inspected using
3215 #include <isl/aff.h>
3216 isl_ctx *isl_multi_aff_get_ctx(
3217 __isl_keep isl_multi_aff *maff);
3218 isl_ctx *isl_pw_multi_aff_get_ctx(
3219 __isl_keep isl_pw_multi_aff *pma);
3220 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3221 enum isl_dim_type type);
3222 unsigned isl_pw_multi_aff_dim(
3223 __isl_keep isl_pw_multi_aff *pma,
3224 enum isl_dim_type type);
3225 __isl_give isl_aff *isl_multi_aff_get_aff(
3226 __isl_keep isl_multi_aff *multi, int pos);
3227 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3228 __isl_keep isl_pw_multi_aff *pma, int pos);
3229 const char *isl_pw_multi_aff_get_dim_name(
3230 __isl_keep isl_pw_multi_aff *pma,
3231 enum isl_dim_type type, unsigned pos);
3232 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3233 __isl_keep isl_pw_multi_aff *pma,
3234 enum isl_dim_type type, unsigned pos);
3235 const char *isl_multi_aff_get_tuple_name(
3236 __isl_keep isl_multi_aff *multi,
3237 enum isl_dim_type type);
3238 const char *isl_pw_multi_aff_get_tuple_name(
3239 __isl_keep isl_pw_multi_aff *pma,
3240 enum isl_dim_type type);
3241 int isl_pw_multi_aff_has_tuple_id(
3242 __isl_keep isl_pw_multi_aff *pma,
3243 enum isl_dim_type type);
3244 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3245 __isl_keep isl_pw_multi_aff *pma,
3246 enum isl_dim_type type);
3248 int isl_pw_multi_aff_foreach_piece(
3249 __isl_keep isl_pw_multi_aff *pma,
3250 int (*fn)(__isl_take isl_set *set,
3251 __isl_take isl_multi_aff *maff,
3252 void *user), void *user);
3254 It can be modified using
3256 #include <isl/aff.h>
3257 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3258 __isl_take isl_multi_aff *maff,
3259 enum isl_dim_type type, unsigned pos, const char *s);
3260 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3261 __isl_take isl_multi_aff *maff,
3262 enum isl_dim_type type, __isl_take isl_id *id);
3263 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3264 __isl_take isl_pw_multi_aff *pma,
3265 enum isl_dim_type type, __isl_take isl_id *id);
3267 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3268 __isl_take isl_multi_aff *maff,
3269 enum isl_dim_type type, unsigned first, unsigned n);
3271 To check whether two multiple affine expressions are
3272 obviously equal to each other, use
3274 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3275 __isl_keep isl_multi_aff *maff2);
3276 int isl_pw_multi_aff_plain_is_equal(
3277 __isl_keep isl_pw_multi_aff *pma1,
3278 __isl_keep isl_pw_multi_aff *pma2);
3282 #include <isl/aff.h>
3283 __isl_give isl_multi_aff *isl_multi_aff_add(
3284 __isl_take isl_multi_aff *maff1,
3285 __isl_take isl_multi_aff *maff2);
3286 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3287 __isl_take isl_pw_multi_aff *pma1,
3288 __isl_take isl_pw_multi_aff *pma2);
3289 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3290 __isl_take isl_pw_multi_aff *pma1,
3291 __isl_take isl_pw_multi_aff *pma2);
3292 __isl_give isl_multi_aff *isl_multi_aff_scale(
3293 __isl_take isl_multi_aff *maff,
3295 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3296 __isl_take isl_pw_multi_aff *pma,
3297 __isl_take isl_set *set);
3298 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3299 __isl_take isl_pw_multi_aff *pma,
3300 __isl_take isl_set *set);
3301 __isl_give isl_multi_aff *isl_multi_aff_lift(
3302 __isl_take isl_multi_aff *maff,
3303 __isl_give isl_local_space **ls);
3304 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3305 __isl_take isl_pw_multi_aff *pma);
3306 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3307 __isl_take isl_multi_aff *maff,
3308 __isl_take isl_set *context);
3309 __isl_give isl_multi_aff *isl_multi_aff_gist(
3310 __isl_take isl_multi_aff *maff,
3311 __isl_take isl_set *context);
3312 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3313 __isl_take isl_pw_multi_aff *pma,
3314 __isl_take isl_set *set);
3315 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3316 __isl_take isl_pw_multi_aff *pma,
3317 __isl_take isl_set *set);
3318 __isl_give isl_set *isl_pw_multi_aff_domain(
3319 __isl_take isl_pw_multi_aff *pma);
3321 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3322 then it is assigned the local space that lies at the basis of
3323 the lifting applied.
3325 An expression can be read from input using
3327 #include <isl/aff.h>
3328 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3329 isl_ctx *ctx, const char *str);
3330 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3331 isl_ctx *ctx, const char *str);
3333 An expression can be printed using
3335 #include <isl/aff.h>
3336 __isl_give isl_printer *isl_printer_print_multi_aff(
3337 __isl_take isl_printer *p,
3338 __isl_keep isl_multi_aff *maff);
3339 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3340 __isl_take isl_printer *p,
3341 __isl_keep isl_pw_multi_aff *pma);
3345 Points are elements of a set. They can be used to construct
3346 simple sets (boxes) or they can be used to represent the
3347 individual elements of a set.
3348 The zero point (the origin) can be created using
3350 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3352 The coordinates of a point can be inspected, set and changed
3355 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3356 enum isl_dim_type type, int pos, isl_int *v);
3357 __isl_give isl_point *isl_point_set_coordinate(
3358 __isl_take isl_point *pnt,
3359 enum isl_dim_type type, int pos, isl_int v);
3361 __isl_give isl_point *isl_point_add_ui(
3362 __isl_take isl_point *pnt,
3363 enum isl_dim_type type, int pos, unsigned val);
3364 __isl_give isl_point *isl_point_sub_ui(
3365 __isl_take isl_point *pnt,
3366 enum isl_dim_type type, int pos, unsigned val);
3368 Other properties can be obtained using
3370 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3372 Points can be copied or freed using
3374 __isl_give isl_point *isl_point_copy(
3375 __isl_keep isl_point *pnt);
3376 void isl_point_free(__isl_take isl_point *pnt);
3378 A singleton set can be created from a point using
3380 __isl_give isl_basic_set *isl_basic_set_from_point(
3381 __isl_take isl_point *pnt);
3382 __isl_give isl_set *isl_set_from_point(
3383 __isl_take isl_point *pnt);
3385 and a box can be created from two opposite extremal points using
3387 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3388 __isl_take isl_point *pnt1,
3389 __isl_take isl_point *pnt2);
3390 __isl_give isl_set *isl_set_box_from_points(
3391 __isl_take isl_point *pnt1,
3392 __isl_take isl_point *pnt2);
3394 All elements of a B<bounded> (union) set can be enumerated using
3395 the following functions.
3397 int isl_set_foreach_point(__isl_keep isl_set *set,
3398 int (*fn)(__isl_take isl_point *pnt, void *user),
3400 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3401 int (*fn)(__isl_take isl_point *pnt, void *user),
3404 The function C<fn> is called for each integer point in
3405 C<set> with as second argument the last argument of
3406 the C<isl_set_foreach_point> call. The function C<fn>
3407 should return C<0> on success and C<-1> on failure.
3408 In the latter case, C<isl_set_foreach_point> will stop
3409 enumerating and return C<-1> as well.
3410 If the enumeration is performed successfully and to completion,
3411 then C<isl_set_foreach_point> returns C<0>.
3413 To obtain a single point of a (basic) set, use
3415 __isl_give isl_point *isl_basic_set_sample_point(
3416 __isl_take isl_basic_set *bset);
3417 __isl_give isl_point *isl_set_sample_point(
3418 __isl_take isl_set *set);
3420 If C<set> does not contain any (integer) points, then the
3421 resulting point will be ``void'', a property that can be
3424 int isl_point_is_void(__isl_keep isl_point *pnt);
3426 =head2 Piecewise Quasipolynomials
3428 A piecewise quasipolynomial is a particular kind of function that maps
3429 a parametric point to a rational value.
3430 More specifically, a quasipolynomial is a polynomial expression in greatest
3431 integer parts of affine expressions of parameters and variables.
3432 A piecewise quasipolynomial is a subdivision of a given parametric
3433 domain into disjoint cells with a quasipolynomial associated to
3434 each cell. The value of the piecewise quasipolynomial at a given
3435 point is the value of the quasipolynomial associated to the cell
3436 that contains the point. Outside of the union of cells,
3437 the value is assumed to be zero.
3438 For example, the piecewise quasipolynomial
3440 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3442 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3443 A given piecewise quasipolynomial has a fixed domain dimension.
3444 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3445 defined over different domains.
3446 Piecewise quasipolynomials are mainly used by the C<barvinok>
3447 library for representing the number of elements in a parametric set or map.
3448 For example, the piecewise quasipolynomial above represents
3449 the number of points in the map
3451 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3453 =head3 Input and Output
3455 Piecewise quasipolynomials can be read from input using
3457 __isl_give isl_union_pw_qpolynomial *
3458 isl_union_pw_qpolynomial_read_from_str(
3459 isl_ctx *ctx, const char *str);
3461 Quasipolynomials and piecewise quasipolynomials can be printed
3462 using the following functions.
3464 __isl_give isl_printer *isl_printer_print_qpolynomial(
3465 __isl_take isl_printer *p,
3466 __isl_keep isl_qpolynomial *qp);
3468 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3469 __isl_take isl_printer *p,
3470 __isl_keep isl_pw_qpolynomial *pwqp);
3472 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3473 __isl_take isl_printer *p,
3474 __isl_keep isl_union_pw_qpolynomial *upwqp);
3476 The output format of the printer
3477 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3478 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3480 In case of printing in C<ISL_FORMAT_C>, the user may want
3481 to set the names of all dimensions
3483 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3484 __isl_take isl_qpolynomial *qp,
3485 enum isl_dim_type type, unsigned pos,
3487 __isl_give isl_pw_qpolynomial *
3488 isl_pw_qpolynomial_set_dim_name(
3489 __isl_take isl_pw_qpolynomial *pwqp,
3490 enum isl_dim_type type, unsigned pos,
3493 =head3 Creating New (Piecewise) Quasipolynomials
3495 Some simple quasipolynomials can be created using the following functions.
3496 More complicated quasipolynomials can be created by applying
3497 operations such as addition and multiplication
3498 on the resulting quasipolynomials
3500 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3501 __isl_take isl_space *domain);
3502 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3503 __isl_take isl_space *domain);
3504 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3505 __isl_take isl_space *domain);
3506 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3507 __isl_take isl_space *domain);
3508 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3509 __isl_take isl_space *domain);
3510 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3511 __isl_take isl_space *domain,
3512 const isl_int n, const isl_int d);
3513 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3514 __isl_take isl_space *domain,
3515 enum isl_dim_type type, unsigned pos);
3516 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3517 __isl_take isl_aff *aff);
3519 Note that the space in which a quasipolynomial lives is a map space
3520 with a one-dimensional range. The C<domain> argument in some of
3521 the functions above corresponds to the domain of this map space.
3523 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3524 with a single cell can be created using the following functions.
3525 Multiple of these single cell piecewise quasipolynomials can
3526 be combined to create more complicated piecewise quasipolynomials.
3528 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3529 __isl_take isl_space *space);
3530 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3531 __isl_take isl_set *set,
3532 __isl_take isl_qpolynomial *qp);
3533 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3534 __isl_take isl_qpolynomial *qp);
3535 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3536 __isl_take isl_pw_aff *pwaff);
3538 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3539 __isl_take isl_space *space);
3540 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3541 __isl_take isl_pw_qpolynomial *pwqp);
3542 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3543 __isl_take isl_union_pw_qpolynomial *upwqp,
3544 __isl_take isl_pw_qpolynomial *pwqp);
3546 Quasipolynomials can be copied and freed again using the following
3549 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3550 __isl_keep isl_qpolynomial *qp);
3551 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3553 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3554 __isl_keep isl_pw_qpolynomial *pwqp);
3555 void *isl_pw_qpolynomial_free(
3556 __isl_take isl_pw_qpolynomial *pwqp);
3558 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3559 __isl_keep isl_union_pw_qpolynomial *upwqp);
3560 void isl_union_pw_qpolynomial_free(
3561 __isl_take isl_union_pw_qpolynomial *upwqp);
3563 =head3 Inspecting (Piecewise) Quasipolynomials
3565 To iterate over all piecewise quasipolynomials in a union
3566 piecewise quasipolynomial, use the following function
3568 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3569 __isl_keep isl_union_pw_qpolynomial *upwqp,
3570 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3573 To extract the piecewise quasipolynomial in a given space from a union, use
3575 __isl_give isl_pw_qpolynomial *
3576 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3577 __isl_keep isl_union_pw_qpolynomial *upwqp,
3578 __isl_take isl_space *space);
3580 To iterate over the cells in a piecewise quasipolynomial,
3581 use either of the following two functions
3583 int isl_pw_qpolynomial_foreach_piece(
3584 __isl_keep isl_pw_qpolynomial *pwqp,
3585 int (*fn)(__isl_take isl_set *set,
3586 __isl_take isl_qpolynomial *qp,
3587 void *user), void *user);
3588 int isl_pw_qpolynomial_foreach_lifted_piece(
3589 __isl_keep isl_pw_qpolynomial *pwqp,
3590 int (*fn)(__isl_take isl_set *set,
3591 __isl_take isl_qpolynomial *qp,
3592 void *user), void *user);
3594 As usual, the function C<fn> should return C<0> on success
3595 and C<-1> on failure. The difference between
3596 C<isl_pw_qpolynomial_foreach_piece> and
3597 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3598 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3599 compute unique representations for all existentially quantified
3600 variables and then turn these existentially quantified variables
3601 into extra set variables, adapting the associated quasipolynomial
3602 accordingly. This means that the C<set> passed to C<fn>
3603 will not have any existentially quantified variables, but that
3604 the dimensions of the sets may be different for different
3605 invocations of C<fn>.
3607 To iterate over all terms in a quasipolynomial,
3610 int isl_qpolynomial_foreach_term(
3611 __isl_keep isl_qpolynomial *qp,
3612 int (*fn)(__isl_take isl_term *term,
3613 void *user), void *user);
3615 The terms themselves can be inspected and freed using
3618 unsigned isl_term_dim(__isl_keep isl_term *term,
3619 enum isl_dim_type type);
3620 void isl_term_get_num(__isl_keep isl_term *term,
3622 void isl_term_get_den(__isl_keep isl_term *term,
3624 int isl_term_get_exp(__isl_keep isl_term *term,
3625 enum isl_dim_type type, unsigned pos);
3626 __isl_give isl_aff *isl_term_get_div(
3627 __isl_keep isl_term *term, unsigned pos);
3628 void isl_term_free(__isl_take isl_term *term);
3630 Each term is a product of parameters, set variables and
3631 integer divisions. The function C<isl_term_get_exp>
3632 returns the exponent of a given dimensions in the given term.
3633 The C<isl_int>s in the arguments of C<isl_term_get_num>
3634 and C<isl_term_get_den> need to have been initialized
3635 using C<isl_int_init> before calling these functions.
3637 =head3 Properties of (Piecewise) Quasipolynomials
3639 To check whether a quasipolynomial is actually a constant,
3640 use the following function.
3642 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3643 isl_int *n, isl_int *d);
3645 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3646 then the numerator and denominator of the constant
3647 are returned in C<*n> and C<*d>, respectively.
3649 To check whether two union piecewise quasipolynomials are
3650 obviously equal, use
3652 int isl_union_pw_qpolynomial_plain_is_equal(
3653 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3654 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3656 =head3 Operations on (Piecewise) Quasipolynomials
3658 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3659 __isl_take isl_qpolynomial *qp, isl_int v);
3660 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3661 __isl_take isl_qpolynomial *qp);
3662 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3663 __isl_take isl_qpolynomial *qp1,
3664 __isl_take isl_qpolynomial *qp2);
3665 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3666 __isl_take isl_qpolynomial *qp1,
3667 __isl_take isl_qpolynomial *qp2);
3668 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3669 __isl_take isl_qpolynomial *qp1,
3670 __isl_take isl_qpolynomial *qp2);
3671 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3672 __isl_take isl_qpolynomial *qp, unsigned exponent);
3674 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3675 __isl_take isl_pw_qpolynomial *pwqp1,
3676 __isl_take isl_pw_qpolynomial *pwqp2);
3677 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3678 __isl_take isl_pw_qpolynomial *pwqp1,
3679 __isl_take isl_pw_qpolynomial *pwqp2);
3680 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3681 __isl_take isl_pw_qpolynomial *pwqp1,
3682 __isl_take isl_pw_qpolynomial *pwqp2);
3683 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3684 __isl_take isl_pw_qpolynomial *pwqp);
3685 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3686 __isl_take isl_pw_qpolynomial *pwqp1,
3687 __isl_take isl_pw_qpolynomial *pwqp2);
3688 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3689 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3691 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3692 __isl_take isl_union_pw_qpolynomial *upwqp1,
3693 __isl_take isl_union_pw_qpolynomial *upwqp2);
3694 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3695 __isl_take isl_union_pw_qpolynomial *upwqp1,
3696 __isl_take isl_union_pw_qpolynomial *upwqp2);
3697 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3698 __isl_take isl_union_pw_qpolynomial *upwqp1,
3699 __isl_take isl_union_pw_qpolynomial *upwqp2);
3701 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3702 __isl_take isl_pw_qpolynomial *pwqp,
3703 __isl_take isl_point *pnt);
3705 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3706 __isl_take isl_union_pw_qpolynomial *upwqp,
3707 __isl_take isl_point *pnt);
3709 __isl_give isl_set *isl_pw_qpolynomial_domain(
3710 __isl_take isl_pw_qpolynomial *pwqp);
3711 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3712 __isl_take isl_pw_qpolynomial *pwpq,
3713 __isl_take isl_set *set);
3714 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3715 __isl_take isl_pw_qpolynomial *pwpq,
3716 __isl_take isl_set *set);
3718 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3719 __isl_take isl_union_pw_qpolynomial *upwqp);
3720 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3721 __isl_take isl_union_pw_qpolynomial *upwpq,
3722 __isl_take isl_union_set *uset);
3723 __isl_give isl_union_pw_qpolynomial *
3724 isl_union_pw_qpolynomial_intersect_params(
3725 __isl_take isl_union_pw_qpolynomial *upwpq,
3726 __isl_take isl_set *set);
3728 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3729 __isl_take isl_qpolynomial *qp,
3730 __isl_take isl_space *model);
3732 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3733 __isl_take isl_qpolynomial *qp);
3734 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3735 __isl_take isl_pw_qpolynomial *pwqp);
3737 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3738 __isl_take isl_union_pw_qpolynomial *upwqp);
3740 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3741 __isl_take isl_qpolynomial *qp,
3742 __isl_take isl_set *context);
3743 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3744 __isl_take isl_qpolynomial *qp,
3745 __isl_take isl_set *context);
3747 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3748 __isl_take isl_pw_qpolynomial *pwqp,
3749 __isl_take isl_set *context);
3750 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3751 __isl_take isl_pw_qpolynomial *pwqp,
3752 __isl_take isl_set *context);
3754 __isl_give isl_union_pw_qpolynomial *
3755 isl_union_pw_qpolynomial_gist_params(
3756 __isl_take isl_union_pw_qpolynomial *upwqp,
3757 __isl_take isl_set *context);
3758 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3759 __isl_take isl_union_pw_qpolynomial *upwqp,
3760 __isl_take isl_union_set *context);
3762 The gist operation applies the gist operation to each of
3763 the cells in the domain of the input piecewise quasipolynomial.
3764 The context is also exploited
3765 to simplify the quasipolynomials associated to each cell.
3767 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3768 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3769 __isl_give isl_union_pw_qpolynomial *
3770 isl_union_pw_qpolynomial_to_polynomial(
3771 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3773 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3774 the polynomial will be an overapproximation. If C<sign> is negative,
3775 it will be an underapproximation. If C<sign> is zero, the approximation
3776 will lie somewhere in between.
3778 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3780 A piecewise quasipolynomial reduction is a piecewise
3781 reduction (or fold) of quasipolynomials.
3782 In particular, the reduction can be maximum or a minimum.
3783 The objects are mainly used to represent the result of
3784 an upper or lower bound on a quasipolynomial over its domain,
3785 i.e., as the result of the following function.
3787 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3788 __isl_take isl_pw_qpolynomial *pwqp,
3789 enum isl_fold type, int *tight);
3791 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3792 __isl_take isl_union_pw_qpolynomial *upwqp,
3793 enum isl_fold type, int *tight);
3795 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3796 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3797 is the returned bound is known be tight, i.e., for each value
3798 of the parameters there is at least
3799 one element in the domain that reaches the bound.
3800 If the domain of C<pwqp> is not wrapping, then the bound is computed
3801 over all elements in that domain and the result has a purely parametric
3802 domain. If the domain of C<pwqp> is wrapping, then the bound is
3803 computed over the range of the wrapped relation. The domain of the
3804 wrapped relation becomes the domain of the result.
3806 A (piecewise) quasipolynomial reduction can be copied or freed using the
3807 following functions.
3809 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3810 __isl_keep isl_qpolynomial_fold *fold);
3811 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3812 __isl_keep isl_pw_qpolynomial_fold *pwf);
3813 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3814 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3815 void isl_qpolynomial_fold_free(
3816 __isl_take isl_qpolynomial_fold *fold);
3817 void *isl_pw_qpolynomial_fold_free(
3818 __isl_take isl_pw_qpolynomial_fold *pwf);
3819 void isl_union_pw_qpolynomial_fold_free(
3820 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3822 =head3 Printing Piecewise Quasipolynomial Reductions
3824 Piecewise quasipolynomial reductions can be printed
3825 using the following function.
3827 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3828 __isl_take isl_printer *p,
3829 __isl_keep isl_pw_qpolynomial_fold *pwf);
3830 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3831 __isl_take isl_printer *p,
3832 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3834 For C<isl_printer_print_pw_qpolynomial_fold>,
3835 output format of the printer
3836 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3837 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3838 output format of the printer
3839 needs to be set to C<ISL_FORMAT_ISL>.
3840 In case of printing in C<ISL_FORMAT_C>, the user may want
3841 to set the names of all dimensions
3843 __isl_give isl_pw_qpolynomial_fold *
3844 isl_pw_qpolynomial_fold_set_dim_name(
3845 __isl_take isl_pw_qpolynomial_fold *pwf,
3846 enum isl_dim_type type, unsigned pos,
3849 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
3851 To iterate over all piecewise quasipolynomial reductions in a union
3852 piecewise quasipolynomial reduction, use the following function
3854 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3855 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3856 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3857 void *user), void *user);
3859 To iterate over the cells in a piecewise quasipolynomial reduction,
3860 use either of the following two functions
3862 int isl_pw_qpolynomial_fold_foreach_piece(
3863 __isl_keep isl_pw_qpolynomial_fold *pwf,
3864 int (*fn)(__isl_take isl_set *set,
3865 __isl_take isl_qpolynomial_fold *fold,
3866 void *user), void *user);
3867 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3868 __isl_keep isl_pw_qpolynomial_fold *pwf,
3869 int (*fn)(__isl_take isl_set *set,
3870 __isl_take isl_qpolynomial_fold *fold,
3871 void *user), void *user);
3873 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
3874 of the difference between these two functions.
3876 To iterate over all quasipolynomials in a reduction, use
3878 int isl_qpolynomial_fold_foreach_qpolynomial(
3879 __isl_keep isl_qpolynomial_fold *fold,
3880 int (*fn)(__isl_take isl_qpolynomial *qp,
3881 void *user), void *user);
3883 =head3 Properties of Piecewise Quasipolynomial Reductions
3885 To check whether two union piecewise quasipolynomial reductions are
3886 obviously equal, use
3888 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3889 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3890 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3892 =head3 Operations on Piecewise Quasipolynomial Reductions
3894 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
3895 __isl_take isl_qpolynomial_fold *fold, isl_int v);
3897 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
3898 __isl_take isl_pw_qpolynomial_fold *pwf1,
3899 __isl_take isl_pw_qpolynomial_fold *pwf2);
3901 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
3902 __isl_take isl_pw_qpolynomial_fold *pwf1,
3903 __isl_take isl_pw_qpolynomial_fold *pwf2);
3905 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
3906 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
3907 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
3909 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
3910 __isl_take isl_pw_qpolynomial_fold *pwf,
3911 __isl_take isl_point *pnt);
3913 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
3914 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3915 __isl_take isl_point *pnt);
3917 __isl_give isl_pw_qpolynomial_fold *
3918 sl_pw_qpolynomial_fold_intersect_params(
3919 __isl_take isl_pw_qpolynomial_fold *pwf,
3920 __isl_take isl_set *set);
3922 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3923 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3924 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
3925 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3926 __isl_take isl_union_set *uset);
3927 __isl_give isl_union_pw_qpolynomial_fold *
3928 isl_union_pw_qpolynomial_fold_intersect_params(
3929 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3930 __isl_take isl_set *set);
3932 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
3933 __isl_take isl_pw_qpolynomial_fold *pwf);
3935 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
3936 __isl_take isl_pw_qpolynomial_fold *pwf);
3938 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
3939 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3941 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
3942 __isl_take isl_qpolynomial_fold *fold,
3943 __isl_take isl_set *context);
3944 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
3945 __isl_take isl_qpolynomial_fold *fold,
3946 __isl_take isl_set *context);
3948 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
3949 __isl_take isl_pw_qpolynomial_fold *pwf,
3950 __isl_take isl_set *context);
3951 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
3952 __isl_take isl_pw_qpolynomial_fold *pwf,
3953 __isl_take isl_set *context);
3955 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
3956 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3957 __isl_take isl_union_set *context);
3958 __isl_give isl_union_pw_qpolynomial_fold *
3959 isl_union_pw_qpolynomial_fold_gist_params(
3960 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3961 __isl_take isl_set *context);
3963 The gist operation applies the gist operation to each of
3964 the cells in the domain of the input piecewise quasipolynomial reduction.
3965 In future, the operation will also exploit the context
3966 to simplify the quasipolynomial reductions associated to each cell.
3968 __isl_give isl_pw_qpolynomial_fold *
3969 isl_set_apply_pw_qpolynomial_fold(
3970 __isl_take isl_set *set,
3971 __isl_take isl_pw_qpolynomial_fold *pwf,
3973 __isl_give isl_pw_qpolynomial_fold *
3974 isl_map_apply_pw_qpolynomial_fold(
3975 __isl_take isl_map *map,
3976 __isl_take isl_pw_qpolynomial_fold *pwf,
3978 __isl_give isl_union_pw_qpolynomial_fold *
3979 isl_union_set_apply_union_pw_qpolynomial_fold(
3980 __isl_take isl_union_set *uset,
3981 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3983 __isl_give isl_union_pw_qpolynomial_fold *
3984 isl_union_map_apply_union_pw_qpolynomial_fold(
3985 __isl_take isl_union_map *umap,
3986 __isl_take isl_union_pw_qpolynomial_fold *upwf,
3989 The functions taking a map
3990 compose the given map with the given piecewise quasipolynomial reduction.
3991 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
3992 over all elements in the intersection of the range of the map
3993 and the domain of the piecewise quasipolynomial reduction
3994 as a function of an element in the domain of the map.
3995 The functions taking a set compute a bound over all elements in the
3996 intersection of the set and the domain of the
3997 piecewise quasipolynomial reduction.
3999 =head2 Dependence Analysis
4001 C<isl> contains specialized functionality for performing
4002 array dataflow analysis. That is, given a I<sink> access relation
4003 and a collection of possible I<source> access relations,
4004 C<isl> can compute relations that describe
4005 for each iteration of the sink access, which iteration
4006 of which of the source access relations was the last
4007 to access the same data element before the given iteration
4009 The resulting dependence relations map source iterations
4010 to the corresponding sink iterations.
4011 To compute standard flow dependences, the sink should be
4012 a read, while the sources should be writes.
4013 If any of the source accesses are marked as being I<may>
4014 accesses, then there will be a dependence from the last
4015 I<must> access B<and> from any I<may> access that follows
4016 this last I<must> access.
4017 In particular, if I<all> sources are I<may> accesses,
4018 then memory based dependence analysis is performed.
4019 If, on the other hand, all sources are I<must> accesses,
4020 then value based dependence analysis is performed.
4022 #include <isl/flow.h>
4024 typedef int (*isl_access_level_before)(void *first, void *second);
4026 __isl_give isl_access_info *isl_access_info_alloc(
4027 __isl_take isl_map *sink,
4028 void *sink_user, isl_access_level_before fn,
4030 __isl_give isl_access_info *isl_access_info_add_source(
4031 __isl_take isl_access_info *acc,
4032 __isl_take isl_map *source, int must,
4034 void isl_access_info_free(__isl_take isl_access_info *acc);
4036 __isl_give isl_flow *isl_access_info_compute_flow(
4037 __isl_take isl_access_info *acc);
4039 int isl_flow_foreach(__isl_keep isl_flow *deps,
4040 int (*fn)(__isl_take isl_map *dep, int must,
4041 void *dep_user, void *user),
4043 __isl_give isl_map *isl_flow_get_no_source(
4044 __isl_keep isl_flow *deps, int must);
4045 void isl_flow_free(__isl_take isl_flow *deps);
4047 The function C<isl_access_info_compute_flow> performs the actual
4048 dependence analysis. The other functions are used to construct
4049 the input for this function or to read off the output.
4051 The input is collected in an C<isl_access_info>, which can
4052 be created through a call to C<isl_access_info_alloc>.
4053 The arguments to this functions are the sink access relation
4054 C<sink>, a token C<sink_user> used to identify the sink
4055 access to the user, a callback function for specifying the
4056 relative order of source and sink accesses, and the number
4057 of source access relations that will be added.
4058 The callback function has type C<int (*)(void *first, void *second)>.
4059 The function is called with two user supplied tokens identifying
4060 either a source or the sink and it should return the shared nesting
4061 level and the relative order of the two accesses.
4062 In particular, let I<n> be the number of loops shared by
4063 the two accesses. If C<first> precedes C<second> textually,
4064 then the function should return I<2 * n + 1>; otherwise,
4065 it should return I<2 * n>.
4066 The sources can be added to the C<isl_access_info> by performing
4067 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4068 C<must> indicates whether the source is a I<must> access
4069 or a I<may> access. Note that a multi-valued access relation
4070 should only be marked I<must> if every iteration in the domain
4071 of the relation accesses I<all> elements in its image.
4072 The C<source_user> token is again used to identify
4073 the source access. The range of the source access relation
4074 C<source> should have the same dimension as the range
4075 of the sink access relation.
4076 The C<isl_access_info_free> function should usually not be
4077 called explicitly, because it is called implicitly by
4078 C<isl_access_info_compute_flow>.
4080 The result of the dependence analysis is collected in an
4081 C<isl_flow>. There may be elements of
4082 the sink access for which no preceding source access could be
4083 found or for which all preceding sources are I<may> accesses.
4084 The relations containing these elements can be obtained through
4085 calls to C<isl_flow_get_no_source>, the first with C<must> set
4086 and the second with C<must> unset.
4087 In the case of standard flow dependence analysis,
4088 with the sink a read and the sources I<must> writes,
4089 the first relation corresponds to the reads from uninitialized
4090 array elements and the second relation is empty.
4091 The actual flow dependences can be extracted using
4092 C<isl_flow_foreach>. This function will call the user-specified
4093 callback function C<fn> for each B<non-empty> dependence between
4094 a source and the sink. The callback function is called
4095 with four arguments, the actual flow dependence relation
4096 mapping source iterations to sink iterations, a boolean that
4097 indicates whether it is a I<must> or I<may> dependence, a token
4098 identifying the source and an additional C<void *> with value
4099 equal to the third argument of the C<isl_flow_foreach> call.
4100 A dependence is marked I<must> if it originates from a I<must>
4101 source and if it is not followed by any I<may> sources.
4103 After finishing with an C<isl_flow>, the user should call
4104 C<isl_flow_free> to free all associated memory.
4106 A higher-level interface to dependence analysis is provided
4107 by the following function.
4109 #include <isl/flow.h>
4111 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4112 __isl_take isl_union_map *must_source,
4113 __isl_take isl_union_map *may_source,
4114 __isl_take isl_union_map *schedule,
4115 __isl_give isl_union_map **must_dep,
4116 __isl_give isl_union_map **may_dep,
4117 __isl_give isl_union_map **must_no_source,
4118 __isl_give isl_union_map **may_no_source);
4120 The arrays are identified by the tuple names of the ranges
4121 of the accesses. The iteration domains by the tuple names
4122 of the domains of the accesses and of the schedule.
4123 The relative order of the iteration domains is given by the
4124 schedule. The relations returned through C<must_no_source>
4125 and C<may_no_source> are subsets of C<sink>.
4126 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4127 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4128 any of the other arguments is treated as an error.
4130 =head3 Interaction with Dependence Analysis
4132 During the dependence analysis, we frequently need to perform
4133 the following operation. Given a relation between sink iterations
4134 and potential soure iterations from a particular source domain,
4135 what is the last potential source iteration corresponding to each
4136 sink iteration. It can sometimes be convenient to adjust
4137 the set of potential source iterations before or after each such operation.
4138 The prototypical example is fuzzy array dataflow analysis,
4139 where we need to analyze if, based on data-dependent constraints,
4140 the sink iteration can ever be executed without one or more of
4141 the corresponding potential source iterations being executed.
4142 If so, we can introduce extra parameters and select an unknown
4143 but fixed source iteration from the potential source iterations.
4144 To be able to perform such manipulations, C<isl> provides the following
4147 #include <isl/flow.h>
4149 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4150 __isl_keep isl_map *source_map,
4151 __isl_keep isl_set *sink, void *source_user,
4153 __isl_give isl_access_info *isl_access_info_set_restrict(
4154 __isl_take isl_access_info *acc,
4155 isl_access_restrict fn, void *user);
4157 The function C<isl_access_info_set_restrict> should be called
4158 before calling C<isl_access_info_compute_flow> and registers a callback function
4159 that will be called any time C<isl> is about to compute the last
4160 potential source. The first argument is the (reverse) proto-dependence,
4161 mapping sink iterations to potential source iterations.
4162 The second argument represents the sink iterations for which
4163 we want to compute the last source iteration.
4164 The third argument is the token corresponding to the source
4165 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4166 The callback is expected to return a restriction on either the input or
4167 the output of the operation computing the last potential source.
4168 If the input needs to be restricted then restrictions are needed
4169 for both the source and the sink iterations. The sink iterations
4170 and the potential source iterations will be intersected with these sets.
4171 If the output needs to be restricted then only a restriction on the source
4172 iterations is required.
4173 If any error occurs, the callback should return C<NULL>.
4174 An C<isl_restriction> object can be created and freed using the following
4177 #include <isl/flow.h>
4179 __isl_give isl_restriction *isl_restriction_input(
4180 __isl_take isl_set *source_restr,
4181 __isl_take isl_set *sink_restr);
4182 __isl_give isl_restriction *isl_restriction_output(
4183 __isl_take isl_set *source_restr);
4184 __isl_give isl_restriction *isl_restriction_none(
4185 __isl_keep isl_map *source_map);
4186 __isl_give isl_restriction *isl_restriction_empty(
4187 __isl_keep isl_map *source_map);
4188 void *isl_restriction_free(
4189 __isl_take isl_restriction *restr);
4191 C<isl_restriction_none> and C<isl_restriction_empty> are special
4192 cases of C<isl_restriction_input>. C<isl_restriction_none>
4193 is essentially equivalent to
4195 isl_restriction_input(isl_set_universe(
4196 isl_space_range(isl_map_get_space(source_map))),
4198 isl_space_domain(isl_map_get_space(source_map))));
4200 whereas C<isl_restriction_empty> is essentially equivalent to
4202 isl_restriction_input(isl_set_empty(
4203 isl_space_range(isl_map_get_space(source_map))),
4205 isl_space_domain(isl_map_get_space(source_map))));
4209 B<The functionality described in this section is fairly new
4210 and may be subject to change.>
4212 The following function can be used to compute a schedule
4213 for a union of domains.
4214 By default, the algorithm used to construct the schedule is similar
4215 to that of C<Pluto>.
4216 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4218 The generated schedule respects all C<validity> dependences.
4219 That is, all dependence distances over these dependences in the
4220 scheduled space are lexicographically positive.
4221 The default algorithm tries to minimize the dependence distances over
4222 C<proximity> dependences.
4223 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4224 for groups of domains where the dependence distances have only
4225 non-negative values.
4226 When using Feautrier's algorithm, the C<proximity> dependence
4227 distances are only minimized during the extension to a
4228 full-dimensional schedule.
4230 #include <isl/schedule.h>
4231 __isl_give isl_schedule *isl_union_set_compute_schedule(
4232 __isl_take isl_union_set *domain,
4233 __isl_take isl_union_map *validity,
4234 __isl_take isl_union_map *proximity);
4235 void *isl_schedule_free(__isl_take isl_schedule *sched);
4237 A mapping from the domains to the scheduled space can be obtained
4238 from an C<isl_schedule> using the following function.
4240 __isl_give isl_union_map *isl_schedule_get_map(
4241 __isl_keep isl_schedule *sched);
4243 A representation of the schedule can be printed using
4245 __isl_give isl_printer *isl_printer_print_schedule(
4246 __isl_take isl_printer *p,
4247 __isl_keep isl_schedule *schedule);
4249 A representation of the schedule as a forest of bands can be obtained
4250 using the following function.
4252 __isl_give isl_band_list *isl_schedule_get_band_forest(
4253 __isl_keep isl_schedule *schedule);
4255 The list can be manipulated as explained in L<"Lists">.
4256 The bands inside the list can be copied and freed using the following
4259 #include <isl/band.h>
4260 __isl_give isl_band *isl_band_copy(
4261 __isl_keep isl_band *band);
4262 void *isl_band_free(__isl_take isl_band *band);
4264 Each band contains zero or more scheduling dimensions.
4265 These are referred to as the members of the band.
4266 The section of the schedule that corresponds to the band is
4267 referred to as the partial schedule of the band.
4268 For those nodes that participate in a band, the outer scheduling
4269 dimensions form the prefix schedule, while the inner scheduling
4270 dimensions form the suffix schedule.
4271 That is, if we take a cut of the band forest, then the union of
4272 the concatenations of the prefix, partial and suffix schedules of
4273 each band in the cut is equal to the entire schedule (modulo
4274 some possible padding at the end with zero scheduling dimensions).
4275 The properties of a band can be inspected using the following functions.
4277 #include <isl/band.h>
4278 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4280 int isl_band_has_children(__isl_keep isl_band *band);
4281 __isl_give isl_band_list *isl_band_get_children(
4282 __isl_keep isl_band *band);
4284 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4285 __isl_keep isl_band *band);
4286 __isl_give isl_union_map *isl_band_get_partial_schedule(
4287 __isl_keep isl_band *band);
4288 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4289 __isl_keep isl_band *band);
4291 int isl_band_n_member(__isl_keep isl_band *band);
4292 int isl_band_member_is_zero_distance(
4293 __isl_keep isl_band *band, int pos);
4295 Note that a scheduling dimension is considered to be ``zero
4296 distance'' if it does not carry any proximity dependences
4298 That is, if the dependence distances of the proximity
4299 dependences are all zero in that direction (for fixed
4300 iterations of outer bands).
4302 A representation of the band can be printed using
4304 #include <isl/band.h>
4305 __isl_give isl_printer *isl_printer_print_band(
4306 __isl_take isl_printer *p,
4307 __isl_keep isl_band *band);
4311 #include <isl/schedule.h>
4312 int isl_options_set_schedule_max_coefficient(
4313 isl_ctx *ctx, int val);
4314 int isl_options_get_schedule_max_coefficient(
4316 int isl_options_set_schedule_max_constant_term(
4317 isl_ctx *ctx, int val);
4318 int isl_options_get_schedule_max_constant_term(
4320 int isl_options_set_schedule_maximize_band_depth(
4321 isl_ctx *ctx, int val);
4322 int isl_options_get_schedule_maximize_band_depth(
4324 int isl_options_set_schedule_outer_zero_distance(
4325 isl_ctx *ctx, int val);
4326 int isl_options_get_schedule_outer_zero_distance(
4328 int isl_options_set_schedule_split_scaled(
4329 isl_ctx *ctx, int val);
4330 int isl_options_get_schedule_split_scaled(
4332 int isl_options_set_schedule_algorithm(
4333 isl_ctx *ctx, int val);
4334 int isl_options_get_schedule_algorithm(
4340 =item * schedule_max_coefficient
4342 This option enforces that the coefficients for variable and parameter
4343 dimensions in the calculated schedule are not larger than the specified value.
4344 This option can significantly increase the speed of the scheduling calculation
4345 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4346 this option does not introduce bounds on the variable or parameter
4349 =item * schedule_max_constant_term
4351 This option enforces that the constant coefficients in the calculated schedule
4352 are not larger than the maximal constant term. This option can significantly
4353 increase the speed of the scheduling calculation and may also prevent fusing of
4354 unrelated dimensions. A value of -1 means that this option does not introduce
4355 bounds on the constant coefficients.
4357 =item * schedule_maximize_band_depth
4359 If this option is set, we do not split bands at the point
4360 where we detect splitting is necessary. Instead, we
4361 backtrack and split bands as early as possible. This
4362 reduces the number of splits and maximizes the width of
4363 the bands. Wider bands give more possibilities for tiling.
4365 =item * schedule_outer_zero_distance
4367 If this option is set, then we try to construct schedules
4368 where the outermost scheduling dimension in each band
4369 results in a zero dependence distance over the proximity
4372 =item * schedule_split_scaled
4374 If this option is set, then we try to construct schedules in which the
4375 constant term is split off from the linear part if the linear parts of
4376 the scheduling rows for all nodes in the graphs have a common non-trivial
4378 The constant term is then placed in a separate band and the linear
4381 =item * schedule_algorithm
4383 Selects the scheduling algorithm to be used.
4384 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4385 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4389 =head2 Parametric Vertex Enumeration
4391 The parametric vertex enumeration described in this section
4392 is mainly intended to be used internally and by the C<barvinok>
4395 #include <isl/vertices.h>
4396 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4397 __isl_keep isl_basic_set *bset);
4399 The function C<isl_basic_set_compute_vertices> performs the
4400 actual computation of the parametric vertices and the chamber
4401 decomposition and store the result in an C<isl_vertices> object.
4402 This information can be queried by either iterating over all
4403 the vertices or iterating over all the chambers or cells
4404 and then iterating over all vertices that are active on the chamber.
4406 int isl_vertices_foreach_vertex(
4407 __isl_keep isl_vertices *vertices,
4408 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4411 int isl_vertices_foreach_cell(
4412 __isl_keep isl_vertices *vertices,
4413 int (*fn)(__isl_take isl_cell *cell, void *user),
4415 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4416 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4419 Other operations that can be performed on an C<isl_vertices> object are
4422 isl_ctx *isl_vertices_get_ctx(
4423 __isl_keep isl_vertices *vertices);
4424 int isl_vertices_get_n_vertices(
4425 __isl_keep isl_vertices *vertices);
4426 void isl_vertices_free(__isl_take isl_vertices *vertices);
4428 Vertices can be inspected and destroyed using the following functions.
4430 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4431 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4432 __isl_give isl_basic_set *isl_vertex_get_domain(
4433 __isl_keep isl_vertex *vertex);
4434 __isl_give isl_basic_set *isl_vertex_get_expr(
4435 __isl_keep isl_vertex *vertex);
4436 void isl_vertex_free(__isl_take isl_vertex *vertex);
4438 C<isl_vertex_get_expr> returns a singleton parametric set describing
4439 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4441 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4442 B<rational> basic sets, so they should mainly be used for inspection
4443 and should not be mixed with integer sets.
4445 Chambers can be inspected and destroyed using the following functions.
4447 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4448 __isl_give isl_basic_set *isl_cell_get_domain(
4449 __isl_keep isl_cell *cell);
4450 void isl_cell_free(__isl_take isl_cell *cell);
4454 Although C<isl> is mainly meant to be used as a library,
4455 it also contains some basic applications that use some
4456 of the functionality of C<isl>.
4457 The input may be specified in either the L<isl format>
4458 or the L<PolyLib format>.
4460 =head2 C<isl_polyhedron_sample>
4462 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4463 an integer element of the polyhedron, if there is any.
4464 The first column in the output is the denominator and is always
4465 equal to 1. If the polyhedron contains no integer points,
4466 then a vector of length zero is printed.
4470 C<isl_pip> takes the same input as the C<example> program
4471 from the C<piplib> distribution, i.e., a set of constraints
4472 on the parameters, a line containing only -1 and finally a set
4473 of constraints on a parametric polyhedron.
4474 The coefficients of the parameters appear in the last columns
4475 (but before the final constant column).
4476 The output is the lexicographic minimum of the parametric polyhedron.
4477 As C<isl> currently does not have its own output format, the output
4478 is just a dump of the internal state.
4480 =head2 C<isl_polyhedron_minimize>
4482 C<isl_polyhedron_minimize> computes the minimum of some linear
4483 or affine objective function over the integer points in a polyhedron.
4484 If an affine objective function
4485 is given, then the constant should appear in the last column.
4487 =head2 C<isl_polytope_scan>
4489 Given a polytope, C<isl_polytope_scan> prints
4490 all integer points in the polytope.